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Achieving efficient MU-MIMO and indoor localization via switched-beam antennas

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Achieving efficient MU-MIMO and indoor localization via switched-beam antennas

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Content ACHIEVING EFFICIENT MU-MIMO AND INDOOR LOCALIZATION VIA
SWITCHED-BEAM ANTENNAS
by
Yonglong Zhang
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
December 2018
Copyright 2018 Yonglong Zhang
Dedication
To my wife Jiani, my daughter Aria and my parents for their unconditional love and support.
ii
Acknowledgments
First of all, I would like to thank my advisor Prof. Konstantinos Psounis for his consistent guidance
and help throughout my PhD study. Prof. Psounis has always provided me with freedom to work
on problems that I found interesting while oering his encouragements and unique insights that
guided me to the completion of this dissertation. I will always be grateful to Prof. Psounis and
see him as my role model.
Also, I want to express my sincere gratitude to professors Leana Golubchik, Bhaskar Krishna-
machari, Keith Chugg and Peter Beerel for serving on my qualication and defense committees.
I do appreciate their constructive feedback based on which I was able to improve my work.
What is more, the work presented in Chapter 2 of this dissertation is the result of collaborations
between myself and Antonios Michaloliakos, Ryan Rogalin, Prof. Giuseppe Caire and Weng Chon
Ao. All work was guided by my advisor Prof. Psounis as well. I am truly thankful for them as I
have learned a lot from these collaborations.
Next, I would like to thank my internship mentors Dr. Beliz Gokkaya and Dr. Rong Pan
for giving me such precious opportunities. I gained valuable experience and skills from their
extraordinary mentoring, and their kindness made those summers so enjoyable.
Lastly, I want to thank my friends and colleagues in the USC, Tianyu, Rong, Shangxing,
Mengjiong, Hang, Kaidong, Po-Han, Kwame-Lante, Jason, Ranjan, Pedro, Martin and all my lab
mates who have been inspiring me with their brilliance all the time. Without them, my life at
the USC would be much less exciting.
iii
Table of Contents
Dedication ii
Acknowledgments iii
List Of Tables vii
List Of Figures viii
Abstract x
Chapter 1: Introduction 1
Chapter 2: Evaluating the Performance of Next-generation, Densely-deployed,
Coordinated Wireless Networks via Simulations and Experiments 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 The ACME Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.1 Main architectural decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1.1 Multi-time scale feature . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.1.2 Asynchronous coordination feature . . . . . . . . . . . . . . . . . . 12
2.4.1.3 Intra-cluster coordination using smart antennas . . . . . . . . . . 13
2.4.1.4 Local MIMO-based precoding . . . . . . . . . . . . . . . . . . . . 13
2.4.1.5 Collection and integration of slow varying statistics . . . . . . . . 14
2.4.2 The Joint User-Beam Scheduling Problem . . . . . . . . . . . . . . . . . . . 14
2.5 Equation-based Performance Analysis for the Simulation Framework . . . . . . . . 19
2.5.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Testbed Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 3: Consistently High MIMO Rates via Switched-beam Antennas 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Prior Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Omni-mode can be bad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Condition number matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.3 Finding a good user group is expensive . . . . . . . . . . . . . . . . . . . . 38
3.3.4 Directionality to the rescue . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4.1 The long-term CSI matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
iv
3.4.2 Formulating the problem of nding the best antenna conguration . . . . . 43
3.4.3 Greedy algorithms for the best antenna conguration problem . . . . . . . 44
3.4.4 Long-term gains versus instantaneous CSI . . . . . . . . . . . . . . . . . . . 46
3.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.1 Experiments with SDRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.1.1 Typical topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5.1.2 Randomly generated topologies . . . . . . . . . . . . . . . . . . . . 49
3.5.1.3 Multiplexing downgrading . . . . . . . . . . . . . . . . . . . . . . 52
3.5.1.4 8x8 MIMO experiments . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.1.5 Channel pre-conditioning versus power gain . . . . . . . . . . . . . 55
3.5.2 Experiments with commercial devices . . . . . . . . . . . . . . . . . . . . . 55
3.6 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6.1 Joint selection of antenna modes and users . . . . . . . . . . . . . . . . . . 56
3.6.2 Support for OFDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.7 Protocol Support for 802.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7.1 Active feedback protocol extension . . . . . . . . . . . . . . . . . . . . . . . 62
3.7.2 Passive feedback protocol extension . . . . . . . . . . . . . . . . . . . . . . 64
3.7.3 User mobility and long-run performance . . . . . . . . . . . . . . . . . . . . 65
3.8 Implementation Overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.9 Conclusion/Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Chapter 4: Ecient Indoor Localization via Switched-beam Antennas 69
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Prior Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.1 One AP is not enough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.2 Higher diversity via multiple APs . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.3 Higher diversity via SBAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4.1 System description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.2 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.3 Machine learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.4 DoA via MUSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.5 User mobility and Hidden Markov Model . . . . . . . . . . . . . . . . . . . 83
4.4.5.1 Multiple Measurements . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4.5.2 Hidden Markov Model . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5.1 Baseline results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5.2 Results using all directions of all antennas . . . . . . . . . . . . . . . . . . . 87
4.5.3 Results using MUSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.4 Results using user mobility and Hidden Markov Model . . . . . . . . . . . . 88
4.5.5 Results varying other parameters . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.5.1 Experiments in a corridor . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.5.2 Using CSI instead of RSSI . . . . . . . . . . . . . . . . . . . . . . 91
4.5.5.3 Dierent grid sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.5.5.4 Number of antenna and number of directions . . . . . . . . . . . . 93
4.6 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6.1 Collecting RSSI measurements in a standard compatible manner . . . . . . 95
4.6.1.1 RSSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6.1.2 CSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6.2 Collecting RSSI measurements for all directions/modes . . . . . . . . . . . 96
v
4.6.3 Airtime overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.6.4 Integrating with other techniques . . . . . . . . . . . . . . . . . . . . . . . . 97
4.7 ToA Localization and Switched-beam Antennas . . . . . . . . . . . . . . . . . . . . 97
4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Chapter 5: Conclusion 101
Reference List 102
vi
List Of Tables
2.1 Notation Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Avg. spectral eciency in bps/Hz for various topology dimensions. For all scenarios
the number of APs is 20 and the number of users 200. Numbers in parenthesis show
improvement over 802.11ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Avg. spectral eciency in bps/Hz for various topology dimensions. For all scenarios
the number of APs is 8 and the number of users 200. Numbers in parenthesis show
improvement over 802.11ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Statistics of CROSS simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Antenna directions at each beacon/transmission . . . . . . . . . . . . . . . . . . . . 62
vii
List Of Figures
2.1 ACME Architecture Example Deployment. Five clusters with 3 stations each are
shown, cluster heads are outlined with a solid line and all stations are connected
to a server. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Greedy user/beam selection in an example 40x40m conference hall. . . . . . . . . . 18
2.3 Conference Hall Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 WiFi 200 users, 20 APs, user/AP ratio 10 scenarios. . . . . . . . . . . . . . . . . . 23
2.5 WiFi 200 users, 8 APs, user/AP ratio 25 scenarios. . . . . . . . . . . . . . . . . . . 24
2.6 The testbed used in the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 Radiation patterns of the antennas and the experiment setup. . . . . . . . . . . . . 26
2.8 Experimental setup topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 MIMO capacity heavily depends on channel matrix H. . . . . . . . . . . . . . . . . 33
3.2 Changing antenna direction yields higher capacity. . . . . . . . . . . . . . . . . . . 39
3.3 Properties of long-term CSI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Results of 10 typical topologies and 100 random topologies. . . . . . . . . . . . . . 48
3.5 Averaged results of random topologies. . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Condition number of varying number of antennas. . . . . . . . . . . . . . . . . . . 51
3.7 Results of experiments with and without downgrading. . . . . . . . . . . . . . . . . 52
3.8 Condition number determines the outcome of 8x8 transmission. . . . . . . . . . . . 54
3.9 Experiment performed with commercial hardware. . . . . . . . . . . . . . . . . . . 55
3.10 Example of cross selection: combining user grouping and antenna mode selection. . 57
viii
3.11 Condition number achieved by dierent approaches. . . . . . . . . . . . . . . . . . 59
3.12 Simulation of antenna mode selection for 802.11ax. . . . . . . . . . . . . . . . . . . 61
3.13 Experiments with mobile users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1 Experiment using either one AP with 8 antennas or 8 separate APs. . . . . . . . . 74
4.2 Accuracy with omni and directional antennas. . . . . . . . . . . . . . . . . . . . . . 76
4.3 RSSI yields dierent patterns in dierent directional modes. . . . . . . . . . . . . . 77
4.4 Error versus number of APs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5 Average correlation coecients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6 DNN structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.7 The transition probability to one location depends on its distance to the current
location (the center) where darker color represents higher probability (assuming
the system estimates the client's location every second). . . . . . . . . . . . . . . . 84
4.8 Experiments in the oce room. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.9 DoA and squares can further narrow down RP candidates. . . . . . . . . . . . . . . 87
4.10 Experiment on the HMM performance. . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.11 A Viterbi path could change drastically when new observation is made (see the blue
path and red path), while the instantaneous path is found by tracking the states
with the highest V
t;k
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.12 Experiments in the corridor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.13 Localization accuracy using RSSI vs CSI for 33cm and 16cm grids. . . . . . . . . . 91
4.14 Localization and DoA accuracy depends on the number of directional modes. . . . 94
4.15 Using more APs to cover non-LOS areas. . . . . . . . . . . . . . . . . . . . . . . . 94
4.16 Example of TDoA combined with DoA estimation via SBAs. . . . . . . . . . . . . 98
4.17 SBAs can also improve the performance of TDoA localization methods. . . . . . . 98
ix
Abstract
Recent advancement in wireless technologies have changed everyone's life forever: latest WiFi
standard allows people to surf, play or even stream high-denition videos wirelessly without any
latency, while location-based services like Google Maps have already become part of our everyday
life. Still, important yet unsolved problems lie ahead when we want to take one step further: on
one hand, in order to achieve even higher throughput we must reuse the limited radio spectrum via
either smaller cells and denser AP deployment, or more advanced PHY techniques, most notably
multi-user (MU) MIMO. However, the former approach suers from inter-cell interference because
of too closely located APs, while the latter could hardly deliver its theoretical performance in
practice due to typically not-so-well-conditioned MIMO channel matrices. On the other hand,
localization in indoor scenarios still remains an open question: despite the enormous potential of
WiFi-based indoor localization techniques, existing methods often require major and expensive
changes to current wireless devices or protocols. As a result, no scheme has been widely accepted
and implemented to this day.
The goal of my work has been to address those challenges with the help of switched-beam
antennas (SBAs): in Chapter 2, we rst develop a simulation framework and a software-dened
radio (SDR) testbed to evaluate the performance and provide deployment guidance for next-
generation networks. Both simulation and experiment show that properly congured SBAs can
eectively reduce inter-cell interference in those scenarios through spatial multiplexing, and thus
yield the 10x gains of the theoretically optimal approach with much less hassle. Then, in Chapter
3 we use SBAs to pre-condition the MIMO channel and obtain well-conditioned channel matrices,
x
achieving an average of 3.5x-5x throughput improvement in our experiment. Finally, in Chapter 4,
we take advantage of the SBAs to increase the diversity of RSSI measurements used for ngerprint-
based localization, allowing a single commodity AP to deliver half-meter localization accuracy in
any indoor environment with zero airtime overhead and zero client support, as shown by our
testbed experiment.
xi
Chapter 1
Introduction
One major challenge in small-cell networks today is the inter-cell interference. In Chapter 2, my
colleagues have proposed a new coordination architecture for APs in an enterprise WiFi network
that allows us to achieve high performance gains without the high overhead and deployment cost
that usually come with coordination. To verify the idea, we developed a simulation framework
based on an accurate and practical analytical model to evaluate the performance and compare
it to other advanced techniques such as MU-MIMO and coordinated MU-MIMO. We then built
a software-dened radio (SDR) testbed that combines analog and digital beamforming using
switched-beam antennas to further validate such architecture. The performance results of both
simulations and testbed experiments show that such approach can achieve huge gains without the
need to tightly coordinate the remote transmitters.
Inspired by the above work, we realized that apart from reducing inter-cell interference,
switched-beam antennas can also help to enhance intra-cell MIMO performance: as shown in
Chapter 3, by carefully selecting the antenna mode for each Tx antenna, we can achieve a well-
conditioned channel matrix such that the performance of MIMO transmission can be optimized.
Today's MU-MIMO-enabled APs are mostly equipped with omni-directional antennas that are
usually tightly placed in a small area due to size limitation. Such architecture leads to a high
spatial correlation [30] among the Tx antennas. As a result, the condition number of the eventual
1
channel matrix H will be increased as well (we have shown with both analysis and experiment
that condition number is indeed an important measure of MIMO capacity), which severely aects
the resulting MIMO throughput. Therefore, based on slow varying channel statistics, we can
nd a Tx antenna conguration that achieves a small channel condition number, and thus greatly
improve the MIMO performance. To nd the optimal antenna conguration which is NP-hard, we
have also developed a greedy algorithm that performs closely to the optimal. As a result, we have
achieved a 3.5x capacity gain in the experiments using software-dened radio testbed, followed by
proposing a protocol to implement such mode-selection algorithm in practice, with zero overhead
and full compatibility to the current 802.11 standard. Motivated by the such results, we proposed
a new scheme that combines both antenna mode selection and user grouping [169, 46, 170] to
obtain an even better-conditioned channel matrix. Since the two problems are both NP-hard,
we have designed a greedy algorithm that performs user grouping and antenna mode selection
simultaneously in linear time. Simulation results show that this new scheme further reduces the
average condition number by 50%.
After observing that switched-beam antennas do eectively reduce spatial correlation among
Tx/Rx in the previous work, we propose to take advantage of such ability in the eld of WiFi-
based indoor localization. Today's existing ngerprint-based indoor localization schemes require
uncorrelated measurements from multiple APs to achieve a reasonable localization accuracy. How-
ever, since the main reason of having a WLAN is for data transmission, there is no incentive to
cover locations with multiple APs. What is more, multiple overlapping APs may cause inter-cell
interference harming data rates. Therefore we propose to use switched-beam antennas to increase
the diversity of measurements used for ngerprint-based localization. We show using experiments
that a single AP equipped with n SBAs may infer equally rich localization information as n APs
equipped with n omnidirectional antennas each, as long as the SBAs are properly congured.
We then establish via extensive experiments that a single packet reception from a commodity
client at a single AP equipped with a handful of switched-beam antennas leads to highly accurate
2
localization with or without line-of-sight. To further improve the accuracy, we apply a Hidden
Markov Model to smooth the sequential location predictions using Viterbi algorithm. At last we
also show the possibility of using switched-beam antennas to improve the performance of another
type of indoor localization scheme | the Time-of-Arrival (ToA) methods.
3
Chapter 2
Evaluating the Performance of Next-generation,
Densely-deployed, Coordinated Wireless Networks via
Simulations and Experiments
In this chapter I will present a simulation framework and a software-dened radio testbed for
evaluating the performance of next-generation wireless networks. The simulation framework and
testbed are then used to validate the eectiveness of ACME | a coordination algorithm for
densely deployed access points | and shows that switched-beam antennas can eectively reduce
inter-cell interference while greatly improving MU-MIMO throughput in small-cell networks.
2.1 Introduction
In this chapter, I will present our work of developing a simulation framework and building a
software-dened radio (SDR) testbed for evaluating the performance of next generation wireless
networks, including small-cell, densely-deployed networks implemented with advanced PHY tech-
niques such as MU-MIMO. Despite the vast body of academic work in analyzing physical layer
techniques in the context of large-scale wireless networks, these models tend to be quite hard
to use and ignore important, real-world aspects of the problem, e.g. MAC layer considerations,
topology characteristics, and protocol overhead. On the other hand, the industry is relying on
4
onsite surveys and simulation tools which do not scale, cannot eciently optimize the design of
such a network, and do not explain why one design choice is better than another. In this Chapter
I will use a simple yet accurate analytical model to build a simulation framework which combines
the realism and practicality of industrial simulation tools with the ability to scale, analyze the
eect of various design parameters, and optimize the performance of real-world deployments. The
framework takes into account all central system parameters, including channelization, power al-
location, user scheduling, load balancing, MAC, advanced PHY techniques (single and multi user
MIMO as well as cooperative transmission from multiple access points), topological characteristics
and protocol overhead. This simulation framework can be used to study a wide range of real world
scenarios, providing design guidelines on the eect of various design parameters on performance.
Furthermore, I built a testbed using software-dened radio platform WARPv3. Equipped with
switched-beam antennas and controlled by a desktop PC, the testbed is capable of performing a
large variety of experiments covering multiple layers of wireless communication.
2.2 Related Work
There is a large body of academic work on modelling and analyzing the performance of wireless
network, based on which we can build the simulation framework. Those literatures cover a large
variety of wireless network settings including large-scale networks, small-cell networks, dense AP
deployments etc, while studying the performance of dierent PHY techniques from the very basic
SISO to the very advanced coordinated MU-MIMO in those scenarios. Furthermore, people also
deign and build many testbeds to verify the real-world performance of those advanced PHY
techniques.
Researchers have been developing wireless network models from dierent angles. On the one
hand, the communication community analyzes the performance of wireless networks in two ma-
jor approaches. The rst makes use of techniques based on random matrix theory to extract
5
performance measures (such as achievable rates, SINRs etc.) combined with combinatorial and
convex optimization methods to solve problems that appear in multi-cell wireless networks. Such
problems include but are not limited to: nding the optimal achievable rates under power con-
trol [75, 94], massive MIMO system asymptotics [135, 72], base station cooperation towards a
distributed MU-MIMO solution [74, 53, 173, 43]. The second approach is based on stochastic
geometry results and focus on eects of random placement of APs and users according to some
stochastic point process. The developed techniques have been extensively applied in heterogeneous
cellular networks on problems such as load balancing [11], user-AP association [44] and K-tier base
station modeling [45]. However most of these works do not consider MIMO and advanced interfer-
ence management schemes at the PHY layer since they introduce statistical dependence between
the nodes, and this would break the independence on which most of these results are based (re-
cent advances in incorporating more advanced PHY schemes in the stochastic geometry approach
are reported in [60]). A common theme of the aforementioned information theoretic literature is
that the eects of the MAC scheduling algorithms, that all wireless networks make use of, are
neglected. Instead, we propose a simple analytic approach that incorporates recent PHY layer
advances in a single PHY/MAC layer model.
On the other hand, the networking community looked at the problem of wireless network
performance analysis from a dierent angle. For example, focusing on CSMA/CA infrastructure
wireless networks, early work of Bianchi [28] on 802.11 MAC layer proposed an analytical model
to analyze CSMA/CA overhead and performance. Meanwhile in [180] the authors investigated the
performance of the exponential backo mechanism in terms of throughput and delay. In [99, 77,
155] similar models of CSMA/CA are developed and employed to develop algorithms optimizing
various performance metrics. These works are mostly based on pure upper layer modeling and
do not take the advances of the PHY layer into account, which is the main contribution of our
simulation framework.
6
Furthermore, there are a number of tools that the industry currently uses for wireless network
deployment guidance. For example, Fluke Networks has developed a solution called AirMagnet
[8] which allows the administrator to create a model of the wireless environment which can be
used to simulate and predict performance. Such tools, now industry standards, mostly resort to
real time on-site surveys and simulations to predict the user rates. Such an approach does not
scale for the extreme situations our model handles, does not incorporate state-of-the-art advances
in PHY layer techniques and gives minimal intuition to network architects.
In addition to theoretical analysis, there exists experimental/simulation literatures on evalu-
ating the performance of next-generation networks as well. In recent years, researchers have built
dierent testbeds to examine the performance of advanced PHY techniques. In [15], the authors
present the design and implementation of the rst MU-MIMO system using Zero-forcing Beam-
forming (ZFBF), and evaluate the impact of many practical factors on its performance. Following
this, the rst coordinated MU-MIMO system using a common clock source is built by researchers
in [141]. In [18] however, the authors propose and implement a scheme that provides the tight
timing and phase synchronization without the need of a shared clock, which greatly improves the
scalability of distributed MU-MIMO systems.
Alternatively, some researchers seek to suppress the inter-cell interference via a combination
of analog and digital beamforming using smart antennas. In [90], the authors apply the theory of
JSDM presented in [6] on switched-beam antenna front-ends and show via simulations multiplexing
gains in a toy indoor deployment of two APs which do not coordinate with each other, further
motivating our work. In [165], a testbed implementation of a multi-cell beamforming system
is presented where the main contribution of the paper is a neat algorithm to infer the Angles of
Arrival needed for analog beamforming. However, the system assumes a global clock for scheduling
purposes which is incompatible with WiFi, allows only a single user per beam which is suboptimal,
and its performance is not studied in large scale scenarios of relevance.
7
2.3 Motivation
Modern wireless devices such as tablets and smartphones are pushing the demand for higher and
higher wireless data rates while causing signicant stress to existing wireless networks. While
successive generations of wireless standards achieve continuous improvement, it is the general
understanding of both academic research and industry that a signicant increase in wireless traf-
c demand can be met only by a dramatically denser spectrum reuse, i.e., by deploying more
base stations/access points per square kilometer, coupled with advanced physical (PHY) layer
techniques to reduce inter-cell interference.
Enterprise WiFi networks have been deployed following this paradigm for years. As a matter
of fact, the density of access points (APs) has increased to a point where inter-cell interference
is canceling any additional gains from even denser deployments. At the same time, advanced
physical layer techniques have been incorporated into the standards, most notably single-user
MIMO in 802.11n and multi-user MIMO in 802.11ac. Cellular networks, unable to satisfy the
bandwidth demand of data plans, resort to WiFi ooading, i.e. they deploy WiFi networks to
ooad the cellular network. Future cellular network architectures will most likely follow a similar
pattern, that is, they will consist of many small cells densely deployed and use advanced physical
layer techniques, e.g. massive MIMO.
It is evident that a wireless network consisting of a large number of small, overlapping cells
cannot be left to operate in a completely decentralized manner. The industry has responded
to the need to eciently manage such networks with tools which are mostly based on on-site
measurements, simulations, and simplistic analytical models. Based on the available public infor-
mation about such tools in the enterprise WiFi market [40, 13], these tools perform three main
operations: (i) user load balancing among APs, (ii) interference management between APs by
channel allocation and power control, and (iii) optimization of the Clear Channel Assessment
8
(CCA) CSMA threshold in order to allow for concurrent transmissions which can tolerate inter-
ference from nearby APs. While such network management tools have increased the performance
of enterprise WiFi networks, they do not scale well, cannot be used to eciently optimize the
system, and do not incorporate the eects of advanced physical layer techniques.
Motivated by such challenges, we have created a simulation framework based on an accurate
and practical analytical model which takes into consideration all the important parameters aect-
ing the performance of today's and tomorrow's wireless networks. Specically, we model and inves-
tigate the performance impact of physical layer features such as channelization, power allocation,
topological characteristics (e.g. user density and AP distribution in various buildings/structures)
and physical layer techniques like single-user (SU), multi-user (MU), and distributed MU-MIMO
[18, 130] (where a number of remote APs coordinate and transmit concurrently and jointly to mul-
tiple users). Additionally, we model the performance impact of MAC and higher layer features
such as user-AP association, MAC parametrization and adaptive coding/modulation.
Furthermore, in order to validate the analytical model and obtain practical results from ex-
periments, we have built a software-dened radio (SDR) testbed using WARPv3 platforms. Such
testbed allows us to conduct a large variety of experiments on SISO, SU-MIMO, MU-MIMO and
other new techniques of dierent layers of wireless communication.
2.4 The ACME Architecture
For completeness purposes, I would like to brie
y present an architecture designed by my col-
leagues in the USC for dense cell deployment: ACME [110]. ACME stands for Asynchronously
Coordinated Multi-timescale beamforming architecture. We validated its performance by both
the simulation framework and the testbed.
It is well-known that one of the challenges for small-cell wireless networks is that as the APs are
located closely to each other, the inter-cell interference becomes stronger on the user's side which
9
greatly aect the throughput. One way to suppress such interference is to use the distributed MU-
MIMO, sometimes referred as coordinated MU-MIMO, where nearby APs form a virtual single
transmitter and jointly MU-MIMO towards a large number of users thus eliminating inter-cell
interference and achieving, in theory, the best possible performance [20, 21, 131, 172]. The cellular
industry has also been investigating various coordination approaches under the umbrella term of
coordinated multipoint (CoMP). However, it has become apparent that coordination comes with
high overhead and deployment cost, often requiring tight time and frequency synchronization
among remote transmitters which is impractical. Thus, the real challenge is how to do \CoMP"
in a way that achieves the high gains without the need for unrealistic synchronization requirements
and unreasonably high overhead in todays commodity WiFi networks.
In contrast, the ACME architecture does not require such tight coordination that causes
too much overhead. Unlike coordinated MU-MIMO, ACME consists of a network of loosely
coordinated APs. While such architecture is applicable to both cellular and WiFi networks, the
motivation to avoid tight time and frequency synchronization and to use inexpensive and thus
constrained analog front-ends is very strong in the case of WiFi. Thus, any protocol-specic
discussion will be limited to WiFi.
Every station in the system is equipped with multiple RF chains attached to smart antenna
front-ends, which provide the ability to specify to some extent the direction of power radiation.
Considering the cost and capabilities trade-o, we envision such an architecture to employ the use
of switched-beam smart antennas, which can select from a predetermined set of relatively narrow
and overlapping beams that cover the whole surrounding area (more details on this selection can
be found in Section 2.4.1.3). Thus, every station has the ability to perform directional and MIMO
transmissions or a combination of the two, depending on the specic choice of the beams for each
front-end and the users to be served.
For scalability, stations are grouped into coordination clusters, such that, by means of fre-
quency reuse, inter-cluster interference is low. Stations that belong to the same coordination
10
Figure 2.1: ACME Architecture Example Deployment. Five clusters with 3 stations each are
shown, cluster heads are outlined with a solid line and all stations are connected to a server.
cluster are scheduled to transmit at the same time during a coordinated downlink slot. A cluster
head is responsible to orchestrate these coordinated downlink transmissions, to be referred to as
cluster transmissions henceforth. The cluster head is also the representative of the cluster when
it comes to accessing the channel via random access, competing against uplink trac and, in case
of non-negligible inter-cluster interferences, other downlink cluster tranmissions. For each cluster
transmission, the cluster head will jointly select the users that each station will serve and cong-
ure the RF front-ends of all participating stations, based on long term statistics collected slowly
over time. At the same time, each individual station will locally perform digital beamforming
operations within the space available to it from the front-end conguration, using instantaneous
channel state information that will be collected per the existing standards, e.g. 802.11ac.
In Figure 2.1 we give a schematic example of the proposed architecture.
2.4.1 Main architectural decisions
We will proceed with the presentation of the key architectural decisions that were made for the
proposed system.
11
2.4.1.1 Multi-time scale feature
The ACME architecture operates in two dierent time-scales in parallel. Coordination and in-
terference suppression between stations within a cluster rely on long-term statistics of channel
characteristics such as the average amplitude of the received power and the average Direction of
Arrival (DOA) of incoming transmissions. These channel properties change slowly with time in
the nomadic moving WiFi environments that we examine [115]. Interference suppression based
on these metrics is implemented in the analog domain by appropriately forming beams at the
antenna front-ends. At the same time, scheduled users are served from their assigned stations
utilizing advanced PHY layer schemes such as conjugate beamforming and MU-MIMO. These
digital precoding schemes require instantaneous CSI at the transmitter which is collected through
the regular procedures dened in the WiFi standards (that is, either through explicit or implicit
feedback when channel reciprocity allows). It is important to note that the two decisions (beam-
forming in the analog and the digital domain) are not orthogonal to each other rather they are
made jointly taking into account both the slow varying channel statics and the multiplexing gains
from digital precoding schemes as will be seen in Section 2.4.2.
2.4.1.2 Asynchronous coordination feature
As stated already, ACME's inter-station coordination depends only on slow varying channel char-
acteristics and no tight synchronization of stations is required. It is important to note that
contrary to what happens in a fully coordinated MU-MIMO system where a user receives useful
signal from multiple stations, in ACME each station serves solely its own users. Therefore, ACME
can operate in a very loosely synchronized fashion while still unlocking a big portion of the inter-
ference suppression and multiplexing gains of tightly synchronized fully-coordinated MU-MIMO
technologies.
12
2.4.1.3 Intra-cluster coordination using smart antennas
In order to enable intra-cluster interference suppression in the analog domain we employ the use
of smart antenna front-ends. Using analog beamforming and exploiting the slow varying DOA
channel statistics, we manage to minimize the interference caused from stations to users currently
being served by other stations in the same cluster. In Figure 2.2 we have an exposition of such
a behavior of our proposed system. Each station is assigned users and beams appropriately such
that no transmission will cause signicant interference to users served by neighboring stations.
In general, smart antennas are antennas with multiple elements, where signals can be combined
by an adaptive algorithm in an \intelligent" way to exploit the directional properties of the channel
[115]. Smart antennas can be of two types: i) adaptive arrays and ii) switched-beam antennas.
The rst category provides full
exibility in the linear combinations of the signals of the dierent
antenna elements and thus the biggest capacity gains, however it comes with a signicant cost since
it requires baseband processing and thus downconversion chains. Thus, for a commodity network
the practical and viable choice is that of switched-beam antennas that provide a more restricted
choice of selectable transmission/reception directions, but can be realized with inexpensive phase-
shifters in the Radio Frequency (RF) domain.
1
2.4.1.4 Local MIMO-based precoding
The ACME system does not rely solely on the inter-station interference suppression described in
the previous subsection for capacity increase. It combines it with local digital precoding schemes
to extract the multiplexing and/or power gains of the MU-MIMO channel. Thus, after the joint
selection of station beams and users to be served based on the available statistics, every station
serves potentially multiple users, in a Point-to-Point/MU MIMO fashion. The decision of the
1
In particular, antenna manufacturers oer switched beam antennas for a few dollars, whereas adaptive arrays
cost thousands of dollars.
13
local digital precoding scheme is taken in parallel with the beam scheduling through the algorithm
described in Section 2.4.2.
2.4.1.5 Collection and integration of slow varying statistics
The ACME architecture collects, stores and monitors the average received power for every user/beam
pair. In order to track this statistic without having to sample every single beam in each station
we may rely on the DOA of the signal components to infer the corresponding beam that is ac-
tive. Since DOA and average receive power are channel characteristics that vary slowly over time
and frequency, channel reciprocity can be exploited to sample the uplink (UL) transmissions and
populate a table similar to the one in Figure 2.2c for the downlink (DL) channel.
2.4.2 The Joint User-Beam Scheduling Problem
Consider a cluster of N stations. Without loss of generality, consider K single-antenna users
associated with these stations forming the setS. Each station is equipped with M RF chains
that allow it to transmit up to M independent streams simultaneously using MIMO techniques.
Finally, every RF front-end is attached to a switched-beam antenna with B beams. We focus on
the downlink scheduling problem which consists of jointly selecting the users to be served by each
AP of the cluster under study, and, the beams to be used by each RF chain of each AP of the
cluster, such that a function of the users' rates is maximized.
We formulate the scheduling decision as a network utility maximization (NUM) problem tar-
geting proportionally fair rate allocation and propose a novel greedy algorithm to solve the com-
putationally hard problem that arises. Following a similar approach like the one used for the
traditional user selection problem in the context of MU-MIMO [47], we start with the objective
to maximize some component-wise concave utility function g() of the users' average rate vector
R = [R
1
;R
2
;:::;R
K
], that is:
14
Symbol Denition
N , number of APs in cluster
M , number of antennas per AP
B , number of beams per switched-beam
antenna
K , number of users in cluster
R
k
, rate of user k
S , set of compatible user-beam tuples
I , family of independent sets
SINR
k
(I
i
) , Signal to Interference plus Noise Ratio
at user k from independent set I
i
I
C
k
(I
i
) , instantaneous rate of user k for a given
independent set I
i
I
Q
k
(t) , virtual queue weight for user k at time
t
P
i
, transmit power of AP i
R
ik
, rate of user k from AP i
g
ik
, pathloss from AP i to user k
S
i
, number of downlink streams from
AP/cluster i
K
i
, number of users associated with AP i
N
i
, number of APs in cluster i
Table 2.1: Notation Summary.
max g(R) (2.1)
s.t. R2R;
whereR is the achievable rate region.
We dene the partition matroidM = (S;I) [156] with ground set the set of user-beam tuples
S that are compatible (that is, the user is within the area covered by the beam and is assigned
to the station the beam belongs to) andI the set of the so called independent sets such that
I =fI :IS; jI\S
i
jM8 i = 1; 2;:::;Ng, whereS
1
;S
2
;:::;S
N
is a partition of the user-
beam tuple setS in N non-overlapping subsets associated with stations 1; 2;:::;N respectively,
15
by some user-station association algorithm. The instantaneous rate for user k for a given active
independent set of user-beam tuples I
i
I, is given by
C
k
(I
i
) =
8
>
>
<
>
>
:
0 for k = 2u(I
i
)
log (1 +SINR
k
(I
i
)) for k2u(I
i
);
(2.2)
where u(I
i
) extracts all users from the tuples in I
i
and SINR
k
(I
i
) is the Signal to Noise and
Interference Ratio under some local beamforming scheme, e.g. MU-MIMO.
Following the stochastic network optimization theory [142] and assuming a proportional fair-
ness objective we can formulate Problem (2.1) as a time evolving weighted sum-rate maximization
problem, where the weightsQ
k
(t), k = 1;:::;K are derived from an appropriately updated vir-
tual queue for every user k at time t. LettingK denote the set of all users, K =jKj, Problem
(2.1) becomes:
max
K
X
k=1
Q
k
(t)R
k
(t) (2.3)
s.t. R
k
(t)2R 8k2K;
where the virtual queues evolve according to: Q
k
(t + 1) = maxf0;Q
k
(t) R
k
(t)g + a
k
(t)g
where a
k
(t) maximizes Vg(a(t))
P
K
k=1
a
k
(t)Q
k
(t), with a(t) : 0 a
k
(t) A
max
, a(t) =
(a
1
(t);:::;a
K
(t)), and A
max
, V are appropriately chosen constants.
Taking into account the partition matroid and the instantaneous rates from Equation (2.2)
and focusing on a particular timeslot t we can rewrite the problem as:
max
Ii2I
X
k2Ii
Q
k
(t)C
k
(I
i
) 8k2K: (2.4)
16
Problem (2.4) is a maximization of a set function that is neither sub-modular
2
nor super-
modular under a partition matroid constraint. The independent sets we would have to compute in
order to optimally solve the above problem are exponential in the number of stations in the network
and thus such an approach is impractical. Instead, we apply a greedy approach (Algorithm 1)
where we schedule users based on the weighted sum-rate they produce, adding the user that gives
the higher marginal gains every time till we reach the maximum number of users per station or
the weighted sum-rate decreases by adding additional users.
Algorithm 1 Greedy Algorithm for Problem (2.4)
Initialization:
J =;; C(J) = 0
whileJ2I do
k

= argmax
k= 2J;(J[fkg)2I
P
K
k=1
Q
k
(t)C
k
(J[fkg)
if
P
K
k=1
Q
k
(t)C
k
(J[fk

g)
P
K
k=1
Q
k
(t)C
k
(J) or k

=; then break;
else
J J[fk

g
end if
end while
Figure 2.2 shows a simplied example of how the greedy scheme would operate. The example
topology is a conference hall with 4 APs with 4 beams each and 10 users. The system collects
the average received power statistics for every user-beam pair and greedily selects a viable set of
user-beam tuples starting from the user that has the highest receive power from AP 1 (say user 1
via beam 1), excluding all beams that cause interference to the selected user (e.g. beam 1 of AP
2) and all users that see interference from the scheduled tuple (e.g. user 5, unless MU-MIMO is
used to transmit to both users 1 and 5 from beam 1 of AP 1) and continuing in this fashion till
no more users can be added. Notice that, although beam 2 of AP 2 is causing some interference
to user 3, due to the large distance this interference is probably low and the scheduler may select
user 3 as well to be served by beam 3 of AP 3.
2
A set function f : 2
S
!R is sub-modular when for every X;Y S with XY and every x2SnY we have
f(X[fxg)f(X)f(Y[fxg)f(Y ). Whenf is sub-modular f is called super-modular.
17
AP 1
AP 3
AP 2
AP 4
1
5
7
8
4
6 2
9
10
3
3
1
2
4
1
4
3
2
(a) Available transmition beams
AP 1
AP 3
AP 2
AP 4
(b) Greedy beam selection
AP
1 AP
2 AP
3 AP
4
Beam

User
1 2 3 4 1 2 3 4 1 2 3 4 1
2 3 4
1 19 -‐∞ -‐∞ -‐∞ 12 -‐∞ -‐∞ -‐∞ 13 -‐∞ -‐∞ -‐∞ 10 -‐∞ -‐∞ -‐∞
2 -‐∞ -‐∞ 13 -‐∞ -‐∞ 19 -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ 12 18 -‐∞ -‐∞ -‐∞
3 -‐∞ 10 -‐∞
-‐∞
-‐∞ 9 -‐∞ -‐∞ -‐∞ 18 -‐∞ -‐∞ -‐∞ 10 -‐∞ -‐∞
4 -‐∞ -‐∞ 12 -‐∞ -‐∞ -‐∞ 18 -‐∞ -‐∞ -‐∞ -‐∞ 13 -‐∞ -‐∞ -‐∞ 18
5 17 -‐∞ -‐∞ -‐∞ 12 -‐∞ -‐∞ -‐∞ 12 -‐∞ -‐∞ -‐∞ 10 -‐∞ -‐∞ -‐∞
6 -‐∞ -‐∞ 14 -‐∞ -‐∞ 17 -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ 14 18 -‐∞ -‐∞ -‐∞
7 -‐∞ -‐∞ -‐∞ 18 15 -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ 11 11 -‐∞ -‐∞ -‐∞
8 -‐∞ -‐∞ -‐∞ 17 16 -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ 12 11 -‐∞ -‐∞ -‐∞
9 -‐∞ -‐∞ 13 -‐∞ -‐∞ 14 -‐∞ -‐∞ -‐∞ -‐∞ -‐∞ 16 18 -‐∞ -‐∞ -‐∞
10 -‐∞ -‐∞ 10 -‐∞ -‐∞ -‐∞ 12 -‐∞ -‐∞ -‐∞ 13 -‐∞ -‐∞ -‐∞ 17 -‐∞
(c) Avg. Received Power for every beam/user pair
Figure 2.2: Greedy user/beam selection in an example 40x40m conference hall.
18
2.5 Equation-based Performance Analysis for the Simulation
Framework
Now I would like to present an equation-based analytical model based on which the simulation
framework is developed. The model is designed by the creators of ACME and we develop the
simulation framework because we wish to study the performance of ACME under realistic large
scale scenarios, e.g. typical Enterprise WiFi scenarios with hundreds or even thousands of APs
densely deployed in crowded areas, while our experimental testbed cannot reach anywhere near
those scales. Motivated by this, a well-established analytical approach was built (see [113, 75, 10,
100] and references therein) which allows us to compute user rates accurately and eciently, as
well as study the system performance as we vary key system parameters.
Assume a system with clusters of stations with setN
i
denoting the stations of cluster i. In
an architecture that employs proportional fairness to serve users in the DL, the average rate that
user k gets from the station or cluster i it is assigned to is given by
R
ik
=
S
i
K
i
log (1 +SINR
ik
); (2.5)
where S
i
is the number of downlink streams, K
i
the number of associated users, and SINR
ik
is
the SINR at user k, all in relation to station/cluster i.
The goal of the framework is to study the performance of ACME and the state-of-the-art and
forthcoming technologies. Specically the SU-MISO (most common form of transmission in LTE
and 802.11n/ac), local MU-MIMO (available in the second generation of 802.11ac chipsets), and
a fully coordinated MU-MIMO system where stations form a single \virtual" transmitter and
MU-MIMO towards a large number of users. Next I will brie
y discuss how to arrive to useful
approximations for these approaches.
19
Local SU-MISO: In the SU-MISO case only a single user, useri, can be served at a time (S
i
= 1).
In the regime where M is large enough such that the eect of small-scale fading disappears [71],
one may show that the achieved SINR is given by:
SINR
ik
=
g
ik
MP
i
1 +
P
j:j6=i
g
jk
P
j
; (2.6)
where g
ik
is the channel gain from station i to user k and P
i
is the transmit power of station i.
Local MU-MIMO: In MU-MIMO, under the regime where both M and S
i
become large while
keeping the ratio S
i
=M 1 xed, one may use the so called diversity gain result [158] as well
as the random matrix theory trace lemma [41] to obtain a deterministic approximation for the
SINR. Specically, it can be shown that the SINR achieved by user k when served from station i
converges to [112, 10]:
SINR
ik
=
(MS
i
+ 1)g
ik
P
i
=S
i
1 +
P
j:j6=i
g
jk
P
j
: (2.7)
Note that for simplicity this analysis assumes equal power allocation per user/stream, which is
typical in real world implementations of the MU-MIMO mode in 802.11ac chipsets.
Coordinated MU-MIMO: Assuming the same regime as in MU-MIMO and special symmetric
conditions in the pathloss coecients such that an underlying system of xed point equations
can be uncoupled [75], the SINR achieved by user k when served from the coordinated cluster of
stations in the setN
i
is approximated by [75]:
SINR
ik
=
(MjN
i
jS
i
+ 1)
P
l2N
i
g
lk
jNij
P
l2N
i
P
l
Si
1 +
P
j:j= 2Ni
g
jk
P
j
: (2.8)
Note that despite the somewhat restrictive nature of the symmetric conditions required to get
this expression, its accuracy is quite good, see [112, 10] for validation.
ACME: Finally, following the assumptions of largeM andS
i
and xedS
i
=M 1 for the ACME
system as well, a good asymptotic approximation of SINR
k
(I
i
) (extending the local MU-MIMO
20
(a) Example topology
0 10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Rates (in Mbits/sec)
CDF

SU−MISO Simulation
MU−MIMO Simulation
ACME Simulation
Coor. MU−MIMO Simulation
SU−MISO Analytic
MU−MIMO Analytic
ACME Analytic
Coor. MU−MIMO Analytic
(b) Validation of analytic formulas
Figure 2.3: Conference Hall Example
results to take into account beams serving users), where I
i
is the independent set of user/beam
tuples scheduled, is given by:
SINR
k
(I
i
) =
(MS
a(k)
+ 1)g
b(k)k
P
a(k)
=S
a(k)
1 +
P
j2u(Ii)nk
g
b(j)k
P
a(j)
=S
a(j)
; (2.9)
with S
n
and P
n
representing the number of users served with MU-MIMO and the power for
stationn respectively, and functionsa(k) andb(k) returning the station and the beam for user k.
Finally, g
bk
denotes the pathloss between beam b and user k, with b taking values 1; 2;:::;BN
for a given ordering of the beams.
The above formulas are validated by comparing the analytic results with a Monte Carlo sim-
ulation. Random channels based on Rayleigh fading are generated for the small-scale fading of
the channel between the stations' antennas and the users' antennas[115], compute channel gains
based on the widely accepted WINNER-II model [92] which captures the distance between a given
station and a user and other \large-scale" eects, such as blocking objects, walls and trees, and
implement MU-MIMO using ZFBF [115]. Figure 2.3a depicts a 30x30m conference hall with 200
21
users and 20 stations grouped in 4 clusters operating at non-overlapping 20 MHz channels, which
is used for the comparison. In Figure 2.3b it can be seen that results of the simulations and notice
that the analytic CDF closely tracks the simulated one for every PHY technology with an error
around 5-10%.
2.5.1 Simulation Results
Topology 802.11n 802.11ac ACME 1x ACME 2x ACME 8x Coor. MU-MIMO
20x20 0.23 0.24 (1x) 1.69 (7x) 1.92 (8x) 2.36 (10x) 1.98 (8.5x)
30x30 0.28 0.32 (1x) 1.68 (5x) 1.90 (6x) 2.35 (7.5x) 1.85 (6x)
40x40 0.31 0.36 (1x) 1.63 (4.5x) 1.85 (5x) 2.30 (6.5x) 1.75 (5x)
Table 2.2: Avg. spectral eciency in bps/Hz for various topology dimensions. For all scenarios
the number of APs is 20 and the number of users 200. Numbers in parenthesis show improvement
over 802.11ac.
Topology 802.11n 802.11ac ACME 1x ACME 2x ACME 8x Coor. MU-MIMO
20x20 0.17 0.23 (1x) 0.77 (3.5x) 0.89 (4x) 1.11 (5x) 0.71 (3x)
30x30 0.18 0.25 (1x) 0.71 (3x) 0.83 (3.5x) 1.06 (4x) 0.66 (2.5x)
40x40 0.19 0.25 (1x) 0.66 (2.5x) 0.78 (3x) 1 (4x) 0.61 (2.5x)
Table 2.3: Avg. spectral eciency in bps/Hz for various topology dimensions. For all scenarios
the number of APs is 8 and the number of users 200. Numbers in parenthesis show improvement
over 802.11ac.
In this section we present the results of the evaluation of the ACME architecture compared to
the technologies presented in Section 2.5 using the equation-based simulation framework.
We assume an enterprise WiFi setting where multiple APs with 3 RF chains each are placed
in conference halls of various dimensions and user densities (see Figure 2.3a for an example
topology). For this set of experiments we assume an 80MHz-wide band divided into 4 non-
overlapping channels as is the case in the 802.11 2:4 GHz band and a transmit power of 90dB
above the noise
oor. The channel gain, g
ik
, is a function of the distance, d
ik
, between AP i and
user k, the carrier frequency, f
c
, and other \large-scale" eects, such as blocking objects, walls
and trees. It is modeled using the B3 (indoor hotspot) scenario of the WINNER-II model [92].
According to this model the pathloss, g
ik
, is given in dB from the formula below:
22
0 10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Rates (in Mbits/sec)
CDF

SU−MIMO (802.11n)
MU−MIMO (802.11ac)
ACME 1x Power
ACME 2x Power
ACME 8x Power
Coor. MU−MIMO
(a) 20x20 meters scenario
0 10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Rates (in Mbits/sec)
CDF

SU−MIMO (802.11n)
MU−MIMO (802.11ac)
ACME 1x Power
ACME 2x Power
ACME 8x Power
Coor. MU−MIMO
(b) 30x30 meters scenario
0 10 20 30 40 50
0
0.2
0.4
0.6
0.8
1
Rates (in Mbits/sec)
CDF

SU−MIMO (802.11n)
MU−MIMO (802.11ac)
ACME 1x Power
ACME 2x Power
ACME 8x Power
Coor. MU−MIMO
(c) 40x40 meters scenario
Figure 2.4: WiFi 200 users, 20 APs, user/AP ratio 10 scenarios.
g
ik
[dB] =A log
10
(d
ik
[m]) +B +C log
10
(f
c
[GHz]=5) +X;
where A, B, C and X are scenario-dependent parameters which in our case take the values:
A = 13:9, B = 64:4, C = 20, and X = 0.
For the coordinated MU-MIMO and ACME schemes, we group APs in four clusters, each
operating at one of the four channels. For the ACME results, we assume that each RF chain is
connected to a switched-beam antenna which is able to select from a xed number of directional
beams. Unless otherwise stated, we assume there are 16 45-degree beams available with a 22.5
degree step. We provide 3 alternatives for the directionality gain, 0 dB, 3 dB and 9 dB, which
translate to 1x, 2x and 8x transmit power respectively. The 1x case corresponds to transmitting
at the same power per degree as in the omnidirectional case. The 2x case follows FCC rules
which allow to double the power per degree when using directional transmissions. The 8x case
corresponds to transmitting the same total power as in the omnidirectional case.
Upcoming dense deployments: In Table 2.2 we compare the avg. spectral eciency of various
schemes and their full CDFs can be seen in Figure 2.4. For these scenarios, a xed number of
APs and users (20 APs and 200 users) was used in dierent sized topologies, thus changing the
density of APs and users. For example, in the 40x40m topology each AP covers an area of 80 sq.m
whereas in the more dense 20x20m topology each AP covers an area of 20 sq.m. Also, assuming
23
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Rates (in Mbits/sec)
CDF

SU−MIMO (802.11n)
MU−MIMO (802.11ac)
ACME 1x Power
ACME 2x Power
ACME 8x Power
Coor. MU−MIMO
(a) 20x20 meters scenario
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Rates (in Mbits/sec)
CDF

SU−MIMO (802.11n)
MU−MIMO (802.11ac)
ACME 1x Power
ACME 2x Power
ACME 8x Power
Coor. MU−MIMO
(b) 40x40 meters scenario
Figure 2.5: WiFi 200 users, 8 APs, user/AP ratio 25 sce-
narios.
a typical seat setup in a conference hall, a 20x20m hall would t around 500 people so the 200
users that we consider imply about 40% of the people are actively using the internet, whereas
in the 40x40m hall only 10% of the people would be active. As expected, the fully coordinated
MU-MIMO transmissions benet from a denser populated area since distances of APs and active
users decrease without an interference increase. On the other hand, \local" 802.11n/ac take a
performance hit from the increased interference.
Interestingly, the ACME system exhibits the same gains and average behavior as the in-
terference free fully coordinated system. For example, in the 20x20m case it yields up to 10x
improvement as compared to local 802.11ac (local MU-MIMO), with the coordinated MU-MIMO
system trailing with an 8:5x gain, and its spectral eciency increases in denser AP deployments.
Even without any power gains (1x case) ACME can still deliver a 7x improvement (see Figure
2.4a) which is very close to that of the fully coordinated system. This is explained by ACME's
ability to serve many users concurrently almost interference free thanks to the smart combination
of analog and digital beamforming.
Today's typical deployments: In Figure 2.5 and Table 2.3, the number of APs was lowered
increasing the user/AP ratio from 10 to 25 and decreasing the density of APs and thus the
interference seen by local 802.11n/ac schemes. As a result, in this less dense scenario the gains
of ACME and the coordinated MU-MIMO scheme over the local schemes are still sizable yet
24
smaller than before, ranging from 2:5x to 5x. Also, in this lower interference regime, the ACME's
approach to take advantage of MU-MIMO locally yields consistently higher gains than going for
a fully coordinated MU-MIMO approach, see black (ACME) versus red (coordinated mu-MIMO)
lines in Figure 2.5.
2.6 Testbed Experiments
To further verify the underlying concepts of ACME, we built a testbed using WARPv3 software-
dened radio platforms. The photo of the testbed can be found in Figure 2.6a. As illustrated
in Figure 2.6b, each WARP board has four RF front-ends, equipped with directional or omni-
directional antennas provided by Adant [76]. As a result, each WARP board can either serve as
an access point with up to four antennas, or serve as four independent users with one antenna
each using WARP's ability to separately process each RF chain and by positioning the antennas
corresponding to each user at dierent locations using long cables. Furthermore, in the case of
coordinated MU-MIMO, we can connect the clocks of multiple WARP boards such that they will
have tight synchronization required by distributed MU-MIMO. All the boards are connected to
the computer via a gigabit switch so that we can control the transmission with Matlab.
We then developed multiple applications that conduct SU-MIMO, MU-MIMO, coordinated
MU-MIMO and ACME experiments using WARPLab, a framework for physical layer prototyping
on WARPv3 [105]. Following the latest 802.11 protocol, for the MU-MIMO and coordinated MU-
MIMO transmission, we implement the so-called \explicit feedback" mechanism which involves
the AP transmitting channel sounding symbols to the users, followed by each user sending one
by one its channel estimation back to the AP. After the AP received the channel matrix, it
would perform the Zero-forcing Beamforming (ZFBF) by precoding the transmitted data with
the pseudo-inverse of the channel matrix. As a result, each user will only receive its own data
while interference (data for other users) is cancelled.
25
(a) WARPv3 testbed (b) Testbed abstraction
Figure 2.6: The testbed used in the experiment
Omni Dir. ACME Coor.
0
1
2
3
4
5
6
7
8
System
Avg. Spectral efficiency [bps/Hz]

Non−overlapping Beams
Overlapping Beams
Omni−directional Antennas
(a) Avg. spectral eciency (b) Directional mode (c) Omni mode
Figure 2.7: Radiation patterns of the antennas and the experiment setup.
Now with both hardware and software ready, the following experiments (see Figure 2.8 for
experimental setup schematics) were administered and the results can be found in Figure 2.7a
where the average spectral eciency in bps/Hz is depicted. The experiments were repeated 10
times for each setup and the average spectral eciencies of the users were computed. Moreover,
errors of 1 standard deviation are incorporated in the plot.
Omnidirectional with MU-MIMO (Omni): The two APs with two omni-directional anten-
nas each serve two users each in an MU-MIMO fashion (without any coordination between the
APs). This is representing today's uncoordinated 802.11ac setups. As expected, interference from
26
Non-overlap dir (no MU-MIMO)
Overlap dir (no MU-MIMO)
Non-overlap ACME
Overlap ACME
Omni
Coor
Figure 2.8: Experimental setup topologies.
the omni-directional antennas results in very low SINRs and a corresponding spectral eciency
smaller than 2 bps/Hz. Note that in this experimental scenario only one AP is interfering to a
user. We have seen in the simulation results in Section 2.5.1 that, as the APs density increases
and the number of interfering APs grows, the SINR and spectral eciencies reduce even more.
Non-overlapping directional without MU-MIMO (Non-overlap dir): The two APs,
equipped with two directional antennas each, serve two users each which are carefully placed such
that the interference to a user from the side and back lobes of antennas serving other users is low.
For comparison purposes, the users are placed in the same locations as in the omnidirectional
experiment (see Figure 2.8). The expectation that the directionality of the antennas mitigates a
big part of the interference and thus leads to SINR gains compared to the Omni setup is met and
SINRs greater than 15dB were achieved for all 4 users leading to an average spectral eciency of
5:3bps/Hz.
Overlapping directional without MU-MIMO (Overlap dir): We alter the previous setup
by placing users assigned to the same AP closer to each other. As a result, those users cannot
be targeted with two directional antennas without sizable interference to each other, unless MU-
MIMO precoding is used. Indeed, the interference to a user from the main lobe serving the other
user assigned to the same AP yields a very low SINR and an average spectral eciency lower
than 2bps/Hz.
27
Non-overlapping directional with MU-MIMO (Non-ovelap ACME): Here we have the
same setup and user placement as in the Non-overlap dir experiment but now MU-MIMO pre-
coding abilities of the APs are used to mitigate any residual interference to one user assigned
to an AP from the same AP's antenna serving the other user. Since the residual interference
from side and back lobes was small, the gains from using MU-MIMO are, as expected, negligible.
Specically, the average spectral eciency is close to 5:3bps/Hz like in the Non-overlap dir setup.
It is interesting to note that the standard deviation here is larger, which is due to the dependence
of MU-MIMO in instantaneous channel state information, which increases the variability among
repetitions of the experiment.
Overlapping directional with MU-MIMO (Overlap ACME): We alter the previous setup
by placing users assigned to the same AP closer to each other such that the beams serving them
are overlapping. In the Overlap dir experiment, without the use of MU-MIMO, we found that
users get 4dB, however, using MU-MIMO to mitigate interference leads to an SINR of 22dB
for all users leading to an average spectral eciency of 7:3bps/Hz. It's interesting to note here
that the average SINR achieved is greater than the case where the beams are not overlapping.
This is a by-product of the fact that the directional antenna modules used have a very small back
lobe but bigger side lobes apart from the main lobe (see radiation pattern in Figure 2.7b). Thus,
as can be seen in Figure 2.8 the interference from the neighboring AP is smaller in this case since
the users are only in the back-lobe of the non-serving AP. Compare this to the non-overlap user
placement scenario where users are aected also from the side lobes of the non-serving AP.
Coordinated MU-MIMO (Coor): The two APs are connected with a clock line and simul-
taneously serve the 4 users in an MU-MIMO fashion. This represents a coordinated MU-MIMO
system with tight phase/frequency synchronization. As expected, due to the complete absence of
interference this scenario will give high SINR for all users. Indeed, it achieves an SINR of 18dB
and an average spectral eciency of 6:3bps/Hz, which is a bit higher than in the Non-ovelap
ACME scenario. If the users are placed closer to each other, then the performance of Coor lowers
28
a bit because the corresponding channel matrix has a worse condition number (less channel diver-
sity). Interestingly, notice that the Coor setup SINR even with favorable user placement is lower
compared to the Overlap ACME setup. In addition to the directional power gain, the WARP v3
boards implement MU-MIMO using equal power allocation instead of waterlling (which is also
what all commercially available 802.11ac wave 2 chipsets do as well), providing an explanation
for the superiority of ACME over the coordinated MU-MIMO system, in line with the simulation
results presented in Section 2.5.1.
Finally, before concluding this section we draw some comparisons between the simulation and
experimental results. The results in Table 2.3 are appropriate for such a comparison since a system
with 8 APs divided in 4 non-overlapping channels consists of 2 APs per cluster competing for the
same channel. Figure 2.7b implies that the power gain between the directional and omnidirectional
modes of the used antennas is about 3-4dB thus we will be focusing on the 2x directional power
gain cases in the table. We see from the results comparison, that, although the absolute values of
spectral eciencies are dierent (due to dierences in transmission powers, distances between APs
and users, and number of antennas per AP) the relative results are comparable. For instance, in
simulations, the ACME system with a 2x directionality gain gives a 4x relative spectral eciency
gain over its 802.11ac counterpart, and, in experiments, the Non-ovelap ACME and Overlap
ACME cases give about a 3-4x relatively gain over the Omni case. And, the coordinated MU-
MIMO case also gives similar relative gains which are around 3-3.5x in both simulations and
experiments.
2.7 Conclusion
We have developed a simulation framework and an experiment testbed that can be used to eval-
uated the performance and provide deployment guidance for next-generation wireless networks.
Specically, we use them to compare the performance of ACME against other advanced techniques
29
such as MU-MIMO and coordinated MU-MIMO, and thus validate the idea of the proposed ar-
chitecture.
30
Chapter 3
Consistently High MIMO Rates via Switched-beam
Antennas
Following the work of Chapter 2, in this chapter use switched-beam antennas to further improve
MU-MIMO performance | instead of reducing inter-cell interference as discussed in the previous
chapter, this time we focus on eliminating intra-cell interference by selecting antenna modes that
achieve a good channel matrix. Testbed experiments show that our algorithm leads to a 3.5x
average throughput improvement in MU-MIMO transmission.
3.1 Introduction
The rapid increase in the quantity and capability of consumer mobile wireless devices has ac-
celerated the growth in demand for wireless bandwidth tremendously. The US government has
responded to this wireless bandwidth crunch with an eort to release new spectrum for wireless
communications and promote spectrum sharing technologies. The industry has responded with
including in the latest standards novel, highly promising PHY techniques. Most notably, MU-
MIMO was included in the latest WiFi and LTE standards, 802.11ac and LTE-Advanced, and
implemented in the 2nd wave of 802.11ac chipsets.
31
In theory, MU-MIMO oers signicant spatial multiplexing gains: a transmitter with n an-
tennas may concurrently transmit to n users, yielding an n times performance gain. In practice
however, this requires the collection of instantaneous channel state information (CSI) from the n
users and a corresponding channel matrix which is well-conditioned [49, 7]. Since it is rarely the
case that a randomly selected set ofn users will yield a well-conditioned channel matrix, more than
n users need to be probed [169, 170]. But, unfortunately, the overhead to collect instantaneous
CSI is so large that the industry has settled with probing n users only, and, in the likely event
that the resulting channel matrix is not well-conditioned, go for a smaller than n multiplexing
gain.
In this chapter we propose to use inexpensive switched-beam antennas in place of typical omni-
directional antennas at transmitters to pre-condition the channel and ensure that the channel
matrix of any random selection of users is well conditioned. Pre-conditioning the channel with
analog front ends is not a new idea [5, 164]. However, we do so using inexpensive antennas that
can nd their way in commercial WiFi access points (APs), and, more importantly, not only
conduct extensive experiments using software dened radios (SDRs) and commercial chipsets
showcasing under real world conditions that we can achieve surprisingly large gains thanks to
this pre-conditioning (3.5x-5x on average in indoors environments depending on the number of
antennas) but also present (i) protocol extensions which are compatible with the 802.11ac standard
to collect long-term channel statistics with zero overhead, and (ii) ecient algorithms which use
those long-term channel statistics to appropriately congure the switched-beam antennas such
that gains are materialized in practice.
The rest of the chapter is organized as follows. Section 4.2 discusses prior work, Section 3.3
motivates this work by showing how large the gap can be when using omnidirectional versus
directional antennas for indoors MU-MIMO, Section 3.4 discusses how to eciently select the
antenna congurations to achieve the 3.5x-5x gains, Section 3.5 presents extensive experiments
with SDRs and commercial devices, and Section 3.7 discusses how to collect long-term channel
32
0 5 10 15 20 25
Sum Capacity, [bit/s/Hz]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
(a) Omni capacity for dierent locations
0 50 100 150 200 250
Average Condition Number
0
5
10
15
20
25
Sum Capacity, [bit/s/Hz]
Sum Capacity vs. Condition Number
Fitting Curve
(b) Omni capacity vs channel condition
number
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Correlation Coefficient Among Users
5
5.5
6
6.5
7
7.5
8
8.5
Number of Users to be Sampled
(c) Finding a good user group
Figure 3.1: MIMO capacity heavily depends on channel matrix H.
statistics, used by the antenna conguration algorithms, in an 802.11ac backward compatible
manner and with zero overhead, and what is the eect of mobility on performance.
3.2 Prior Work
There is a large body of work on switched-beam antennas, ranging from traditional Butler matrix
antennas [121, 97] to more compact ones [34, 93] with varying directionality properties and price.
Researchers rst focused on the use of switched-beam antennas in cellular networks [104, 70]
to improve the signal to noise ratio (SNR) of SISO transmissions. Recently, researchers have
used the directionality of switched-beam antennas to allow concurrent nearby transmissions, e.g.
[110] uses switched-beam antennas to minimize inter-cell interference in a multi-cell setup via
coordination. Also, switched-beam antennas have found their way to commercial WiFi products
[134]. In all these prior instances, switched-beam antennas are used to improve the SNR thanks
to their directionality. In contrast, in our work we use switched-beam antennas to improve the
channel matrix in the context of MU-MIMO transmissions, and, as a matter of fact, the line-of-
sight directions are not the ones that yield the best improvement.
MU-MIMO can increase wireless capacity sizably thanks to its multiplexing gain [146] and
a large body of experimental work has showcased MIMO benets in various real world setups
[19, 84, 86, 166, 55, 27, 127]. To achieve the large multiplexing gain in practice, the MU-MIMO
33
channel matrix needs to have a small condition number [49, 7, 107, 175]. Motivated by this, in
recent years researchers have proposed various approaches to achieve a channel matrix with a
small condition number. The most classic approach is to choose the best subset from a large
group of users in each round of MU-MIMO transmission such that the resulting channel matrix
is well conditioned and the sum data rate of users is maximized, see, for example, [169, 46, 170].
However, not only is it NP-hard to select the best user group, but also the overhead from collecting
instantaneous CSI from all these users is prohibitively large. Thus, while greedy approaches have
been proposed to select a good enough user group [46, 111], the fact of the matter is commercial
chipsets collect CSI from the minimum possible number of users and it is very unlikely that a
large number of users will ever be sampled for CSI purposes in practice, due to the signicant
overhead.
Another approach to get a good channel matrix may be to pre-condition the channel using
directional antennas. For example, the authors in [84] have observed that directional antennas
may yield higher MIMO performance not thanks to higher signal strength, but rather thanks
to a better ensuing channel. However, they didn't proceed to design a scheme that would col-
lect CSI information and then select the best directions using this information. Other recent
work on directional antennas has considered the use of recongurable phased-array antennas in
conjunction with MIMO to either reduce the number of RF chains [5] or to reduce inter-cell inter-
ference in the context of a multi-cell environment [4, 164] with [164] also making the observation
that directionality helps to decorrelate users within a cell and thus achieve a better channel ma-
trix. However, recongurable phased-array antennas are too expensive and large, especially for
commercial WiFi systems which is the focus of our work, and, we consider instead inexpensive
switched-beam antennas which leads to a fundamentally dierent antenna conguration problem
which does not require any signal processing due to the small number of predetermined modes
that switched-beam antennas oer. Finally, in [152] the researchers work with a theoretical model
for a \switched-beam based" antenna array which assumes very sharp beams and no inter-beam
34
interference. In practice this requires an antenna array with a very large number of antenna
elements and it is completely dierent from real world switched-beam antennas of the type that
we consider. Other major dierences from this work is that it focuses on millimeter wave massive
MIMO systems (whereas our algorithm is designed for 802.11 devices which have less tightly fo-
cused beam pattern and much less number of Tx antennas), and it does not consider the condition
number as a factor.
Last, even though no prior work has attempted to build a 802.11-compatible system to con-
gure and use switched-beam antennas for MIMO channel pre-conditioning, there are works that
have discussed metrics to select \good" directions of directional antennas or \good" user groups.
We do consider such metrics, e.g. the signal-to-leakage ratio and the user orthogonality, and
establish that they lead to suboptimal selection of directions in our setup, further motivating our
work.
3.3 Motivation
In this section, we present experimental results where a single AP transmits to a number of users
using MU-MIMO over OFDM. We highlight scenarios where omni-directional antennas yield bad
performance whereas switched-beam antennas can signicantly increase the throughput thanks
to channel pre-conditioning.
Recall that in theory and under appropriate conditions an AP withn antennas can transmit to
up to n users' antennas concurrently on the same frequency band by precoding the transmitting
signal based on CSI. Each user antenna receives its own signal while interference (from signals for
other user antennas) is cancelled, yielding a spatial diversity multiplexing gain of n.
35
3.3.1 Omni-mode can be bad
Today's MU-MIMO-enabled APs are mostly equipped with omni-directional antennas. Due to
size limitations of commercial APs, those omni-directional antennas are tightly placed in a small
area and end up with high spatial correlation [30]. As a result, the correlation of the eventual
channel matrix H will be signicantly increased (see, for example, the widely used Kronecker
model), especially when users are located close to each other, severely aecting the capacity of
the MIMO channel.
To see this experimentally, we conduct 4x4 MU-MIMO communication between one AP with
4 omni-directional antennas and 4 users (we use software radio platform WARP v3 to act as both
AP and user) in a typical oce environment, each equipped with one omni-directional antenna.
(For more details on experiment topology and settings see Section 3.5.) We measure the channel
capacity based on the receivers' eective SNRs
1
and constantly change their locations while
maintaining the same distance towards the AP in such a way that all users maintain LOS and
constant received signal strength (RSS) from the AP. As shown in Figure 3.1a, the system capacity
has a huge variation when users are on dierent locations even though they are under the same
RSS level. For example, when users are located closely in the room, we measured a sum capacity
of only 1:7 bits/s/Hz, which is nearly one fth of the average capacity over all tested topologies.
3.3.2 Condition number matters
The condition number of an n-by-n channel matrix H is dened as the ratio of the largest to the
smallest singular value [146]. For a channel matrix H, its condition number is directly determined
by the channel correlation coecient [108], and it is a good indication of the multipath richness
of the channel [49].
1
In the context of a MIMO transmission, the eective SNR of a specic user is dened as the user's \useful"
signal strength over noise which consists of 1) the signal for other users that has not been entirely canceled though
MIMO due to real world imperfections and 2) the usual background noise. The former would be much larger than
the latter and will greatly aect the transmission when the channel is ill-conditioned as will be illustrated later in
Sec. 3.3.2.
36
A channel matrix that has a low condition number (often referred as \well-conditioned")
benets MIMO transmissions in two ways: (i) it implies a higher eective channel gain for each
user [146, 169], and (ii) it reduces the eect of the error caused by using a noisy estimate of the
channel to perform precoding, as illustrated in the next paragraph. (Note that this is directly
related to the notion of condition number in the context of numerical analysis, which is used to
measure how sensitive a system is to the imprecision in the input and how much imprecision in
the output results from it [25]). As a result of these two reasons, the lower the condition number,
the higher the capacity that the channel can support [7, 107].
2
To better illustrate the eect of the condition number on error propagation, we consider two
matrices:
A =
2
6
6
4
1 4
2:1 2
3
7
7
5
B =
2
6
6
4
1 2
2:1 4
3
7
7
5
;
which stand for two ground-truth 2-by-2 MIMO channel matrices (for simplicity we use real rather
than imaginary numbers). Note that both matrices have the same power gain, while matrix A
has a lower condition number than B. Now, we add the same amount of noise to both matrices
and obtain:
A
noise
=
2
6
6
4
1:1 4:1
2:2 2:1
3
7
7
5
B
noise
=
2
6
6
4
1:1 2:1
2:2 4:1
3
7
7
5
;
which represent the measured, noisy channel matrices. Recall that in Zero-forcing Beamforming
(ZFBF, the most popular MU-MIMO precoding scheme), we compute the pseudo-inverse of the
measured channel matrix and use it to precode the transmission signal, hoping to obtain an
2
To accommodate non-square matrices, the condition number ofW =HH
y
is sometimes used wherey denotes
the conjugate-transpose operation. When H is a square matrix the condition number of W equals the square of
that of H, and, minimizing the non-negative condition number of W is equivalent to minimizing that of H.
37
identity matrix after the signal propagates through the actual channel. We compute the result of
this operation for both matrices and get:
AA
1
noise
=
2
6
6
4
0:999 0:044
0:001 0:955
3
7
7
5
BB
1
noise
=
2
6
6
4
2:727 0:909
1:727 0:091
3
7
7
5
:
Observe that while AA
1
noise
is very close to the identity matrix and both users may achieve a
good eective SNR. (From the denition of the eective SNR in the rst footnote
1
and assuming
no background noise, we get 10 log
10
0:999
2
(0:044)
2
= 27dB and 10 log
10
0:955
2
(0:001)
2
= 56dB respectively.)
BB
1
noise
is very far from the identity matrix and the MIMO transmission would fail due to
too much cross interference (e.g. the achieved SNRs of the two users are only 9dB and -26dB
respectively). It is evident that the eect of the same level of noise in the case of the matrix with
larger condition number is disproportionally larger.
We next perform a total of 500 MU-MIMO communication measurements to show the rela-
tionship between the condition number of H and the channel capacity. We take the average of all
the 64 OFDM sub-carriers' condition numbers
3
and plot them in Figure 3.1b where we use an
exponential function to t the individual measurements. It is evident that the condition number
has a drastic eect on the channel capacity.
3.3.3 Finding a good user group is expensive
To get a good condition number an AP needs to collect CSI from a number of users and select
a good user group. Consider an AP with n omni-directional antennas. The AP may randomly
pickn users and examine their CSI to form the n-by-n channel matrix H. If H is ill-conditioned,
the AP may pick another user, examine its CSI and try all the

n+1
n

combinations to see if it is
3
Unless otherwise specied, in this work we assume MU-MIMO transmissions on a typical 20MHz channel under
802.11ac standard. Like in 802.11a/g/n, each 20MHz channel in 802.11ac contains 64 OFDM subcarriers.
38
(a) Dierent antennas cong
Omni Directional
0
5
10
15
Sum Capacity, [bit/s/Hz]
(b) Throughput comparison
Figure 3.2: Changing antenna direction yields higher capacity.
possible to get a well-conditioned channel matrix with this new user and n 1 of the old users.
If not, the AP may pick yet another user and so on and so forth.
Finding the best user group among many users is NP-hard and a number of greedy approaches
have been suggested. But the main issue is not the computational cost, it is the overhead of
collecting the CSI for all those users. As a concrete example, today's WiFi chipsets implement
the so-called \explicit feedback" mechanism which involves the AP transmitting channel sounding
symbols to the users, followed by each user sending one by one its channel estimation back to the
AP under the lowest data rate. This is so expensive that 4x4 MU-MIMO WiFi chipsets randomly
select 4 users and settle with a user group of cardinality 3 or less if the resulting channel matrix is
not full rank. This means the AP would rather not take advantage of the maximum multiplexing
gain than engage in collecting additional CSI from more users.
4
We use a modied simulator based on [31], where we employ the Kronecker model to generate
channel matrices using the formula H = R
1
2
R
e
HR
1
2
T
(R
R
and R
T
are correlation matrices deter-
mined by the spatial correlations among transmitter antennas and receiver antennas, respectively,
while
e
H hasCN (0; 1) entries, see [31] for more details), to compute the expected number of users
4
Instead of explicit feedback, in theory one may use the so called implicit feedback mechanism which has less
overhead. But, because in this case the system needs to be calibrated [133], the WiFi industry has rejected its use
for practical reasons.
39
to be examined before a well-conditioned subset can be found in the context of 4x4 MU-MIMO. We
use measured data from [30] to set the correlation coecient of R
T
to a xed value and vary the
correlation coecient of R
R
, eectively simulating a wide range of real world conditions. Figure
3.1c plots the number of users to be sampled to achieve a condition number of 25 or less (which,
based on Figure 3.1b yields good rates), as a function of the correlation coecient among users.
It is evident that even with low user correlation the AP has to examine a handful of additional
users before it can nd a good subset, which increases the overhead sizably.
Last, note that there are cases where improving the condition number by sampling more users
is not even an option as there might not be any more users to transmit to. With the trend to
design wireless networks with smaller and smaller cells, this case will become even more likely.
Concluding, attempting to correct a channel matrix by sampling additional users is very expensive,
and sometimes it may not even be an option.
3.3.4 Directionality to the rescue
Consider the scenario illustrated in Figure 3.2. We replace the 4 antennas with compact switched-
beam antennas with 9 modes (8 directional modes, and an omin-directional one, which, as a matter
of fact, is the mode we used for the omni-directional experiments above) in the same experimental
setting as the one used in Section 3.3.1 and select the directional modes illustrated in the lower
Figure 3.2a. Figure 3.2b shows that we get 6x the performance of the omni mode by using a
carefully selected antenna direction conguration while maintaining the same level of RSS for all
users.
While the rest of the chapter discusses important issues such as how and at what cost one
may select the right directional modes, it is interesting to note that the best modes are not
necessarily the ones corresponding to a line-of-sight. Also, the channel pre-conditioning achieved
by the antennas is apparently enough to yield the maximum multiplexing gain even in the most
correlated scenarios. Further, as we will establish later, any random set of 4 users with appropriate
40
directional modes can achieve near-optimal rates, the results hold even in the case of 8x8 MIMO
channels (which are of interest given that the maximum number of antennas in the 802.11ac
standard is 8), and, nomadic user mobility is not a problem either as the timescale of indoors
mobility is much slower than the timescale of updating the long term CSI information of a user
that moves to a new location. Last, note that due to the nature of MU-MIMO, the beam patterns
do not need to be super directional or \sharp", as the purpose of changing antenna direction is to
get a better channel when the channel is ill-conditioned, thus not only we have some room when
selecting the right modes (a sizable number of sets of modes would do the trick) but also there
is no performance benet from using more directional and thus much more expensive antennas,
such as phased-array antennas.
3.4 System Design
Consider an MU-MIMO enabled AP with n switched-beam antennas, each having d modes (di-
rections). Without loss of generality, we assume that there are a total of m users in the network
(mn), and each user is equipped with one omni-directional antenna. At each transmission the
AP may serve n users concurrently.
Withn antennas each havingd modes, the AP has a total ofd
n
possible antenna congurations
to choose from. This gives us d
n
possible channel realizations for every n users being served. To
improve channel capacity, our goal is to nd the antenna conguration that results in the lowest
channel condition number for a given group of n users with as little overhead as possible.
3.4.1 The long-term CSI matrix
We use long term channel statistics, that is, MIMO channel statistics that are relatively steady
over a long period of time, to determine the best antenna conguration. (See later in this section
for the precise long-term statistics that we use.) This way we keep the overhead low while ensuring
41
0 20 40 60 80 100 120 140 160 180
Time in Seconds
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Average Amplitude
Antenna 1
Antenna 2
Antenna 3
Antenna 4
drastic change
when the
user moves
mild change
when other
objects move
(a) Change of long-term CSI
0 5 10 15 20 25 30
CN of Long-term Channel Matrix
0
5
10
15
20
25
30
CN of Channel Matrix with Phases
(b) Condition number (CN)
Figure 3.3: Properties of long-term CSI.
a high mode selection accuracy. Denote by G them by (dn) matrix where theith row contains
the long-term statistics of user i towards every transmit antenna for every direction:
G =
2
6
6
4
Antenna 1
z }| {
g
1
1;1
g
2
1;1
::: g
d
1;1
Antenna 2
z }| {
g
1
1;2
::: g
d
1;2
:::
Antenna n
z }| {
g
1
1;n
::: g
d
1;n
g
1
2;1
g
2
2;1
::: g
d
2;1
g
1
2;2
::: g
d
2;2
::: g
1
2;n
::: g
d
2;n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
g
1
m;1
g
2
m;1
::: g
d
m;1
g
1
m;2
::: g
d
m;2
::: g
1
m;n
::: g
d
m;n
3
7
7
5
(3.1)
whereg
k
i;j
represents the long-term channel gain between useri and antennaj, given that antenna
is set to direction k.
We dene and compute the long-term channel gain as follows: leth
k;c
i;j
=ja
k;c
i;j
je
j!
represent the
instantaneous channel gain between useri and antennaj on subcarrierc, given that the transmit
antenna is set to directionk. This contains both amplitude and phase information of the channel.
We ignore the phase! since it changes very fast and focus on the amplitudeja
k;c
i;j
j which remains
relatively steady as long as neither of the antennas change their physical location. Thus, we take
the average amplitude of all OFDM subcarriers (as dened 802.11ac standard) between useri and
antennaj on directionk, and save it asg
k
i;j
. Without loss of generality consider 20MHz channels
where 52 of the total 64 are data subcarriers and we have g
k
i;j
=
P
52
c=1
jh
k;c
i;j
j
52
.
42
To verify the time-invariant nature of the long-term gain, we perform an experiment where we
constantly measure the elements of G for 3 minutes in a typical oce room. In the rst minute
and a half the environment is relatively steady: about 6 people work on their desks. In the middle
of the experiment we change the location of the user by about 1 meter. In the second half of
the experiment, the 6 people begin to walk around in the oce, opening and closing doors. As
shown in Figure 3.3a, the long-term channel gains are quite steady during the rst half of the
experiment. In the second half, the long-term gains vary a little bit due to moving objects, but
within a small magnitude (less than 10%). Last, as expected, there is a sizable change when the
user/antenna moves. Concluding, we conrm that in a typical oce environment the entries in
G stay valid for a relatively long time since the location of laptops, tablets, etc. changes in the
order of minutes [17, 145, 22].
3.4.2 Formulating the problem of nding the best antenna conguration
We address how to populate and keep on updating the G matrix in Section 3.7. Here we assume
that the AP has access to the G matrix and solve the following problem. Let G
u;d
denote ann byn
submatrix of G formed by the rows whose indices are dictated by vector u and the columns whose
indices are dictated by vector d. For a given subset of users with user indices u = (u
1
;u
2
;:::;u
n
),
nd a vector of column indices d = (d
1
;d
2
;:::;d
n
) where d
i
2 [(i 1)n + 1;in] for all i2 [1;n],
such that the condition number of G
u;d
is minimized. That is,
d

= argmin
(d
1
;:::;dn):d
i
2[(i1)n+1;in];8i
(G
(u
1
;u
2
;:::;un);(d
1
;d
2
;:::;dn)
) (3.2)
where() denotes the 2-norm condition number of a matrix. Note that the \feasibility" constraint
d
i
2 [(i 1)n + 1;in] ensures that we assign exactly one direction to each antenna and we will
refer to vectors d that satisfy this as \feasible".
Such column selection problems are NP-hard even without the feasibility constraint [33]. In our
setting, an AP with 4 antennas and 9 modes per antenna yields a modest 6561 possible antenna
43
congurations, but, raising the antennas to 8 (max number of antennas on 802.11ac) raises the
number of possible congurations to 43 million. Thus, using brute-force search algorithm to nd
d

is not appealing.
3.4.3 Greedy algorithms for the best antenna conguration problem
As already discussed, there is a large body of work on greedy approaches to improve channel
matrices. For example, multiple researchers including [169] proposed dierent greedy user selection
algorithms to maximize users' orthogonality, while some other authors proposed to maximize the
system's signal-to-leakage ratio (SLR). We apply these approaches to our problem and show (in
Section 3.5) that they fail to select very good modes. Motivated by this, we propose a novel
algorithm based on singular value and orthogonal-triangular decomposition. We will refer to this
algorithm as the Condition Number SVD (CN-SVD) algorithm.
Before we describe the CN-SVD algorithm, we brie
y describe how to apply to our problem
the two prior-work approaches mentioned above. First, the orthogonality of two vectors h andg is
determined by the ratio
jhg

j
khkkgk
. (The smaller the ratio, the more orthogonal the two vectors are.)
Using this approach, the goal is to nd the feasible direction vector d such that for the given set
of users u, the columns of indices in d are as orthogonal to each other as possible. This approach,
applied to the user grouping problem under a very large number of choices has been shown to
work well, but when applied to our directional antenna mode selection problem which has much
more limited number of feasible choices it does not perform well, see Section 3.5. Second, the
algorithm based on SLR maps each transmit antenna i to a unique user j. As a result, for user
j, only the signal sent from its designated antenna i is considered useful while signals sent from
other antennas are considered leakage, and the SLR of user j is dened as SLR
i;j
=
Pi;j
P
k6=i
P
k;j
,
where P
i;j
is the received power from antenna i to user j. Then, the direction vector d that
yields the maximum system-wide SLR is selected. Section 3.5 shows that this approach does not
44
perform well in our setting either. We conjecture this is because in indoor environments MU-
MIMO benets more from a well-conditioned channel than from stronger signal strength, as we
will show later in Section 3.5.
The CN-SVD algorithm
The CN-SVD algorithm uses a subroutine, which is based on singular value and orthogonal-
triangular decomposition, for selecting the \best" k columns from a large matrix in polynomial
time. The subroutine starts by performing a singular value decomposition of a scaled (see below
for more details) version of G = UV

and lets W be the submatrix of V's rst k columns.
Then, an orthogonal-triangular (QR) decomposition of W
|
is performed such that W
|
E = QR,
where Q is unitary, R is upper triangular and E is a permutation matrix designed to make the
absolute value of diagonal elements of R decreasing. Finally, it outputs a vector consisting of
the column indices of non-zero elements of E's rst n rows. We denote the above subroutine by
ALG(A;k) where A is the input matrix and k is the number of columns we want to select from
A.
Algorithm 2 below presents the subroutine using pseudo-code, whereSCALE(A) divides each
entry of a matrix A by its column's root-sum-of-squares (i.e. by
pP
i
ja
ij
j
2
for each column
j), SVD(A) stands for the singular-value decomposition of A, and QR(A;k) represents the QR
decomposition described above on the rst k rows of A. At last, the algorithm shall return a
vector of the selected column indices (c
1
;c
2
;:::;c
k
). More details of how and why this subroutine
works can be found in [56, 83].
Algorithm 2 The ALG Algorithm
procedure ALG(G;k)
A SCALE(G)
(U;S;V) SVD(A)
(Q;R;E) QR(V
|
;k)
for i = 1:::k do
c
i
arg max
j
E
i;j
endfor
return (c
1
;c
2
;:::;c
k
)
endprocedure
45
The output vector from the subroutine above may contain multiple columns (modes) corre-
sponding to a single antenna and no columns corresponding to some of the antennas. For this
reason, the CN-SVD algorithm uses a combination of a recursive application of the ALG subrou-
tine to select at least one mode for each antenna, and a greedy step to select one of the multiple
modes of those antennas which have multiple modes selected.
Look at the pseudo-code of Algorithm 3 below. Let a denote the set of all Tx antennas and
u denote the set of users to which the AP is transmitting. Denote by d
f
the set of Tx antennas'
nalized directions/modes, which the algorithm populates as it settles on which mode to use
for each antenna in a. getColumns(a) extracts the set of indices of columns (of matrix G)
belonging to the antennas in set a. CNSVD(a;u; G;d
f
) starts with calling subroutine ALG
on the submatrix of G corresponding to the users u and the directions/columns of the antennas
in a. The subroutine selects columns and yields three sets of antennas, a
us
, a
ms
, and a
ns
,
corresponding to the set of antennas with a unique selected mode, with multiple selected modes,
and with no selected mode. (We use getUniqueSelectAnt(d) and getMultiSelectAnt(d)
to extract the sets a
us
, a
ms
from d.) For antennas in a
us
, their modes can thus be xed and
stored in d
f
, and if a
ns
is not emptyCNSVD is recursively called till every Tx antenna has been
assigned to a mode. Last, getting back from the recursions, for each antenna in a
ms
that have
multiple selected modes, we greedily select the one which minimizes the condition number of the
submatrix which consists of the already nalized modes in d
f
and this mode.
3.4.4 Long-term gains versus instantaneous CSI
We use long-term channel gains to select antenna modes which yield a low condition number,
whereas it is the instantaneous CSI that determines the actual condition number. Thus, it is
interesting to investigate the dierence among the condition number of the actual channel matrix
H (with phase information) versus that of the G
u;d
matrix. To do so we start with a measured
long-term gain matrix G
u;d
and add a random phase [116] and some amplitude turbulence to
46
Algorithm 3 The CN-SVD Algorithm
procedure CNSVD(a;u;G;d
f
)
c getColumns(a)
d ALG(Gu;c;jaj)
aus getUniqueSelectAnt(d)
ams getMultiSelectAnt(d)
ans an (aus[ams)
d
f
d
f
[ (d\getColumns(aus))
if ans6=;then
d
f
CNSVD(ans;u;G;d
f
)
else
return d
f
endif
for all a2ams do
d

arg min
d2 d\getColumns(fag)
(G
u;fdg[d
f
)
d
f
d
f
[fd

g
endfor
return d
f
endprocedure
create a corresponding channel matrix H. We do this for all the OFDM sub-carriers and compute
the resulting average condition number. Figure 3.3b plots the condition number of G
u;d
and
H for 1000 dierent long-term gain matrices. As conjectured, it is evident from the plot that
well-conditioned G
u;d
matrices are strongly correlated with well-conditioned H matrices, see the
green circle on the plot.
3.5 Experimental Results
3.5.1 Experiments with SDRs
We rst conduct experiments with 2 WARPv3 boards, each with 4 RF ports. We use one WARP as
a transmitter with 4 switched-beam antennas (Adant Star 160 [3]), while the other WARP acts as 4
independent users by using WARP's ability to separately process each RF chain and by positioning
the antennas corresponding to each user at dierent locations using long cables. Each user is
equipped with an omni-directional antenna. We conduct MU-MIMO downlink communication
between the AP and the 4 users using ZFBF with explicit feedback (as in 802.11ac).
47
(a) The oce room plan
1 2 3 4 5 6 7 8 9 10
Topology
0
5
10
15
20
25
Sum Capacity, [bit/s/Hz]
Omni
CN-BF
CN-SVD
SLR
Orthogonal
(b) Capacity in 10 typical topologies
0 5 10 15 20 25
Sum Capacity, [bit/s/Hz]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Omni
CN-BF
CN-SVD
SLR
Orthogonal
(c) Capacity in 100 random topologies
0 1 2 3 4 5 6 7 8 9 10
Capacity Gain
0
0.2
0.4
0.6
0.8
1
CDF
CN-BF
CN-SVD
(d) Performance gain over omni
Figure 3.4: Results of 10 typical topologies and 100 random topologies.
The experiments are done in a typical oce room as shown in Figure 3.4a. We place users
in dierent locations and measure their SNR and the resulting sum capacity under: (i)the omni-
directional mode for all AP antennas (Omni), (ii) directional modes selected by minimizing the
condition number using brute-force search (CN-BF), (iii) directions selected by the CN-SVD algo-
rithm (CN-SVD), (iv) directions selected by maximizing the SLR using brute-force search (SLR)
and (v) directions selected by maximizing the orthogonality using brute-force search (Orthogonal).
48
3.5.1.1 Typical topologies
We choose 10 typical topologies of varying spatial user correlation. These topologies range from
cases where users are well-separated to cases where all four users are close to each other. Figure
3.4a shows one typical topology where three users are close to each other. For each topology, we
get 10 measurements and report the average. Figure 3.4b plots the results, where topologies are
numbered in decreasing level of spatial user correlation. It is evident that the algorithms which
minimize the condition number (CN-BF and CN-SVD) outperform the others, especially when
users are highly correlated. Note that the SLR and Orthogonal approaches do not have a steady
performance. We discuss the reasons for this in the next subsection.
3.5.1.2 Randomly generated topologies
We compare the performance of the algorithms under 100 random topologies. For each topology we
decide the location of each user by uniformly generating two values and using them as coordinates.
Like before, for each topology we measure the channel capacity 10 times and compute the average.
Figure 3.4c plots the empirical CDF of those averages, where, like before, the algorithms based on
the condition number outperform the others, and, Figure 3.4d plots the CDF of the relative gain
of CN-BF and CN-SVD over Omni. Note that we zoom in the interesting part and don't show the
CDF when the gain is more than 10x, since in such scenarios Omni has such a poorly-conditioned
matrix that in practice it makes sense to nd a well-conditioned submatrix than insisting on
transmitting to 4 users concurrently. Last, Figure 3.5a plots the relative performance of all 4
schemes over Omni, averaged over all 100 topologies. CN-BF and CN-SVD outperform Omni by
about 3.5x, while SLR and Orthogonal outperform it by 1.7x and 2.4x respectively.
To better understand the results, we order the topologies in increasing Omni performance
and group them in three cases: (i) bottom third w.r.t Omni performance due to relatively high
correlation of users, (ii) middle third due to mild correlation and (iii) top third due to almost no
user correlation. Figure 3.5b plots the sum capacity in the rst case. Omni yields a bad condition
49
Omni CN-BF CN-SVD SLR Orthogonal
Direction Selecting Algorithm
0
1
2
3
4
Relative Capacity over Omni
(a) Relative performance over omni
Omni CN-BF CN-SVD SLR Orthogonal
Direction Selecting Algorithm
0
5
10
15
Sum Capacity, [bit/s/Hz]
(b) Highly correlated users
Omni CN-BF CN-SVD SLR Orthogonal
Direction Selecting Algorithm
0
5
10
15
20
Sum Capacity, [bit/s/Hz]
(c) Mildly correlated users
Omni CN-BF CN-SVD SLR Orthogonal
Direction Selecting Algorithm
0
5
10
15
20
25
Sum Capacity, [bit/s/Hz]
(d) Low user correlation
Figure 3.5: Averaged results of random topologies.
number but the CN-BF and CN-SVD algorithms search for antenna directions which minimize
the channel condition number and achieve 5x the Omni's performance. Figure 3.5c shows the
results when users have mild correlation. In this case Omni performs much better than before,
CN-BF and CN-SVD achieve about 1.5x the performance of Omni, and SLR and Orthogonal
perform similar to Omni. Figure 3.5d shows the results when users have almost no correlation.
All algorithms perform well since the channel is well-conditioned.
5
5
Note that the reported gains in Fig. 3.5a represent the average over all topologies of the throughput ratio of a
scheme over Omni, as we aim to give equal weight to all topologies. That said, since Omni does particularly bad
in some topologies, if one were to rst compute the average throughput over all topologies for each scheme and
then compute the ratio, the gains are still signicant but lower.
50
5 10 15 20 25 30 35 40
Case Index
0
50
100
150
200
250
300
350
400
450
500
Condition Number
Omni, mean=90.367
CN-BF, mean=12.5968
CN-SVD, mean=20.4507
SLR, mean=6838.7929
Orthogonal, mean=147.8915
(a) 4x4 MU-MIMO
5 10 15 20 25 30 35 40
Case Index
0
5
10
15
20
25
30
35
40
45
50
Condition Number
Omni, mean=28.6372
CN-BF, mean=4.816
CN-SVD, mean=5.9633
SLR, mean=7.8048
Orthogonal, mean=6.0295
(b) 2x2 MU-MIMO
0 20 40 60 80 100 120 140 160 180 200
Condition Number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
CDF
Omni
CN-BF
CN-SVD
SLR
Orthogonal
(c) 4x4 MU-MIMO CDF
0 5 10 15 20 25 30 35 40 45 50
Condition Number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Omni
CN-BF
CN-SVD
SLR
Orthogonal
(d) 2x2 MU-MIMO CDF
Figure 3.6: Condition number of varying number of antennas.
To explain the large
uctuations on the performance of SLR and Orthogonal as well as their
lower-than-Omni performance when users are not spatially correlated, we compare the condition
number of the G
u;d
matrix resulting from selecting directions using the 4 selection algorithms.
Figure 3.6a plots the results for 40 topologies under the 4x4 MU-MIMO setup, and reports their
average condition numbers, which is referred to as mean in the legend, for each algorithm. The
spikes on the condition number for SLR and Orthogonal cause the performance
uctuations
noticed in Figure 3.4b and the lower-than-Omni performance observed in Figure 3.5d. Figure
3.6b plots the results for the same 40 topologies under a 2x2 MU-MIMO setup. In this smaller
scale problem, SLR and Orthogonal make better directional mode selections and are expected to
51
Omni-rand Omni CN-BF CN-SVD Orthogonal
Direction Selecting Algorithm
0
0.5
1
1.5
Relative Capacity over Omni
(a) 4x4 with downgrading
0 1000 2000 3000 4000 5000 6000 7000
Antenna Configuration Index
0
5
10
15
20
25
30
Sum Capacity, [bit/s/Hz]
4x4
4x2
4x3
4x3 Omni
4x4 Omni
4x2 Omni
(b) 4x4, 4x3 and 4x2
Omni CN-SVD Orthogonal
Direction Selecting Algorithm
0
1
2
3
4
5
Relative Capacity over Omni
(c) 8x8
Omni-rand Omni CN-SVD Orthogonal
Direction Selecting Algorithm
0
0.5
1
1.5
2
Relative Capacity over Omni-rand
(d) 8x8 with downgrading
Figure 3.7: Results of experiments with and without downgrading.
perform similar to the CN-BF and CN-SVD schemes, which is consistent with the 2x2 MU-MIMO
results reported in [164] for SLR.
3.5.1.3 Multiplexing downgrading
An AP may choose to serve less than the maximum number users when the channel matrix is ill-
conditioned, such that the extra transmit antennas can be used to increase the diversity gain and
thus obtain a better-conditioned channel matrix (of lower dimension). For example, downgrading
from a multiplexing gain of 4 to 3 causes a 25% multiplexing loss but if the 4x3 sub-matrix is
well-conditioned while the original 4x4 is not we may end up with a better throughput overall.
52
To investigate this idea we proceed as follows: If the condition number of the original 4x4 channel
matrix is less than a threshold (equal to 30) then we transmit to the 4 users like before. If not, we
select the best 3 users to transmit to, by computing the condition number of the ensuing four 4x3
sub-matrices and selecting the one with the smallest condition number, unless no 4x3 sub-matrix
has a condition number smaller than the threshold, in which case we select the best 2 users to
transmit to by computing the condition number of the ensuing six 4x2 sub-matrices. (We never
had to downgrade to a single user only.)
We apply the above procedure to Omni, CN-BF, CN-SVD, and Orthogonal. Also, motivated
by real-world chipsets which, in the interest of simplicity, may randomly choose 3 (or 2) out of
the 4 users to serve when the original 4x4 channel matrix is ill conditioned, we also consider
Omni with such random user selection for downgrading purposes and denote this as Omni-rand.
Figure 3.7a shows the average capacity for all the ve schemes over both typical and random
topologies as before. We can see that both CN-BF and CN-SVD achieve a sizable improvement
over Omni, thought the gains are smaller than when we enforce to serve 4 users utilizing the
maximum multiplexing gain.
To better understand the tradeo between the multiplexing gain and the ensuing condition
number, we measure and sort the capacity of 4x4, 4x3 and 4x2 transmissions over all 9
4
=
6561 antenna congurations for one specic topology in Figure 3.7b. As expected, 4x2 and 4x3
transmissions are more robust than 4x4 due to the diversity gain from the extra transmit antennas.
However a 4x4 transmission may still achieve higher performance when the correct conguration
is used thanks to the combination of a low condition number with the highest multiplexing gain.
The plot also indicates the performance of Omni for each of the three multiplexing gain cases for
comparison purposes.
53
5 10 15 20 25
Case Index
0
100
200
300
400
500
600
700
800
900
1000
Condition Number
CN-BF, mean=40.711
CN-SVD, mean=82.4421
SLR, mean=6630.7841
Orthogonal, mean=272.9055
(a) 8x8 MU-MIMO
0 200 400 600 800 1000 1200 1400 1600 1800
Condition Number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
CN-BF
CN-SVD
SLR
Orthogonal
(b) 8x8 MU-MIMO CDF
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Experiment Index
0
5
10
15
20
25
Effective Capacity, [bits/s/Hz]
1.16
1.18
1.2
1.22
1.24
1.26
1.28
Power Gain
×10
5
Capacity 1
Capacity 2
Gain 1
Gain 2
(c) Capacity vs. power gain
Figure 3.8: Condition number determines the outcome of 8x8 transmission.
3.5.1.4 8x8 MIMO experiments
We conduct the same set of experiments under an 8x8 MIMO setup, since 802.11ac allows up
to 8 antennas at the transmit side. Note that CN-BF can no longer be computed easily so we
do not report results for it. Figure 3.7c reports the throughput averaged over the same typical
and random topologies used before. CN-SVD achieves a nearly 5x gain over Omni, higher than
the 3.5x average gain in the 4x4 case. Note however that the absolute throughput of the CN-
SVD algorithm in the 8x8 case does not increase signicantly comparing to the 4x4 case. This
is because the larger the multiplexing gain the harder it is to get a channel matrix with a low
condition number [126]. The signicant spikes in Figure 3.8a, which shows the condition numbers
achieved by dierent direction-selecting algorithms under the 8x8 setup, is further evidence of
the diculty to get the maximum multiplexing gain in an 8x8 channel. Motivated by this we
conjecture that if 8x8 chipsets become available in the future, some of the additional antennas
will mostly be used for diversity than for multiplexing gains.
Like in the 4x4 case, we also consider multiplexing downgrading, and, in particular, 8x8, 8x7
and 8x6 MIMO transmissions according to a condition number threshold. As shown in Figure
3.7d, we observe that the CN-SVD algorithm has a sizable capacity gain over Omni, which,
nevertheless, is smaller than when we enforce to serve the maximum possible number of users (8
in this case).
54
(a) Floor Plan
1 2 3 4
Topology
0
50
100
150
200
250
300
350
400
Sum Rate, [MB/s]
Omni
Direction
Different
Direction
(b) Sum rate for each topology
0 5 10 15 20 25 30 35 40
Antenna Configuration
200
220
240
260
280
300
320
340
360
380
Average Throughput, [MB/s]
Omni-direction
Line of Sight Direction
(c) Throughput under dierent congs
Figure 3.9: Experiment performed with commercial hardware.
3.5.1.5 Channel pre-conditioning versus power gain
Last, to illustrate the fact that the capacity gains of CV-SVD are mainly caused by the pre-
conditioning of the channel matrix and not by a higher Received Signal Strength (RSS), we conduct
an 8x8 experiment with two dierent antenna congurations, one which achieves a low condition
number and one which achieves a higher condition number. We perform 5 transmissions with both
congurations and record (i) their total capacity and, (ii) their total power gain of the channel
(computed by Tr[HH

] =
P
i;j
jh
ij
j
2
). As shown in Figure 3.8c, although the second conguration
has a slightly higher total power gain it achieves a much lower total MIMO throughput because
of the higher condition number.
3.5.2 Experiments with commercial devices
To further validate our proposed approach, we conduct experiments using commercial 802.11ac
wave 2 devices: a Netgear Nighthawk AP with a Quacomm chipset equipped with 4 Adant Star
160 switched-beam antennas and 3 Xiaomi Mi4i smartphones acting as users. (This chipset is
congured to transmit to up to 3 users.) The experiments are performed in a typical oce

oor shown in Figure 3.9a. We present results from four typical topologies where users are
sometimes located in dierent and sometimes at the same room. A number of typical antenna
congurations are chosen including congurations where antennas point to the same direction,
55
and congurations where they point to dierent directions. We let the AP perform backlogged
MU-MIMO transmissions towards the users for 12 hours in each antenna conguration, and record
the achieved throughput of each user. All transmissions are conducted under the generic 802.11ac
wave2 standard that is built-in in the chipsets of the commercial devices that we are using.
In Figure 3.9b we compare the sum rate of the 3 users averaged over time using the omni
mode against the highest throughput achieved by one of the preset directional congurations.
Due to commercial hardware limitations, we only consider 36 out of the 8
4
= 4096 total antenna
congurations. Thus, it is unlikely that one of them is the one that maximizes the throughput.
What is more, transmitting to 3 rather than 4 users protects the omni mode from very poorly-
conditioned matrices since it operates on a 4x3 submatrix of the channel matrix (but, of course,
also reduces the multiplexing gain from 4 to 3). Still, the system's throughput increases on average
by 50%. Last, Figure 3.9c plots the performance of all 36 antenna congurations including the
omni-mode and the conguration which uses the \line-of-sight" directions (main lobes pointing to
users), for the topology in Figure 3.9a. Interestingly the line-of-sight conguration that has the
highest antenna gain is not the one that maximizes the throughput. This observation is consistent
with the one we made earlier in Figure 3.8c and is something that occurs frequently in indoor
environments.
3.6 Extensions
3.6.1 Joint selection of antenna modes and users
Although we have shown that with the CN-SVD algorithm we can achieve a low condition number
with almost any given group of users, it is worth investigating how to select antenna modes and
users, which we refer as \cross selection" because essentially we are selecting a subset of columns
and a subset of rows from the G matrix at the same time, such that the resulting submatrix has
a low condition number (see Figure 3.10).
56
2
6
6
6
6
6
6
6
6
4
g
1
1;1
g
2
1;1
g
3
1;1
g
1
1;2
g
2
1;2
g
3
1;2
g
1
1;3
g
2
1;3
g
3
1;3
g
1
2;1
g
2
2;1
g
3
2;1
g
1
2;2
g
2
2;2
g
3
2;2
g
1
2;3
g
2
2;3
g
3
2;3
g
1
3;1
g
2
3;1
g
3
3;1
g
1
3;2
g
2
3;2
g
3
3;2
g
1
3;3
g
2
3;3
g
3
3;3
g
1
4;1
g
2
4;1
g
3
4;1
g
1
4;2
g
2
4;2
g
3
4;2
g
1
4;3
g
2
4;3
g
3
4;3
g
1
5;1
g
2
5;1
g
3
5;1
g
1
5;2
g
2
5;2
g
3
5;2
g
1
5;3
g
2
5;3
g
3
5;3
g
1
6;1
g
2
6;1
g
3
6;1
g
1
6;2
g
2
6;2
g
3
6;2
g
1
6;3
g
2
6;3
g
3
6;3
::: ::: ::: ::: ::: ::: ::: ::: :::
3
7
7
7
7
7
7
7
7
5
+
2
4
g
3
2;1
g
1
2;2
g
2
2;3
g
3
4;1
g
1
4;2
g
2
4;3
g
3
6;1
g
1
6;2
g
2
6;3
3
5
Figure 3.10: Example of cross selection: combining user grouping and antenna mode selection.
Algorithm 4 The Cross Selection Algorithm
procedure CROSS(a;G)
u ALG(G
|
;jaj)
d
f
CNSVD(a;u;Gu;;)
return u;d
f
endprocedure
As shown below, our proposed \cross selection" algorithm works as follows: given a set of m
users and their long-term channel gain matrix G, we rst use the ALG algorithm on G
|
to nd
the most independent k out of m users (assuming the AP transmits to k users concurrently).
Then, we run the CN-SVD algorithm on those k users, and thus obtain the best antenna modes
to minimize the condition number of those k users. For fairness purposes already selected users
won't be selected again until all them users are served once (else we would be always picking the
best set of users).
We investigate the performance of theCROSS algorithm with simulations using actual channel
data collected in the previous experiments assuming a total of 40 to 100 users and a 4x4 MU-
MIMO setup. We compare the condition numbers achieved by 6 dierent approaches: 1) CN-SVD
with ALG user-selection, where we perform both user grouping and antenna selection as proposed
in Algorithm 4, 2) CN-SVD without user-selection, which means we randomly select a group of
57
4 users at each round, and transmit to them under the antenna modes found by the CN-SVD
algorithm, 3) Omni without user-selection, where the AP randomly selects 4 users each time and
then transmits to them in omni mode, 4) Omni with ALG user selection, in which case we rst
select the best 4 users from the not-yet-served users as described in the rst step of the cross
selection algorithm, and then transmit to them using omni mode, 5) CN-SVD with SUS user-
selection, where we rst do user grouping using the orthogonality method proposed in [169] and
then select antenna modes with the CN-SVD algorithm, and 6) Omni with SUS user grouping,
where we rst select users based on their orthogonality and then transmit to them using omni
antenna mode. For each simulation run, we generate a G matrix containing 40 or 100 users's data
randomly from more than 300 real channel measurements. We then simulate the 6 approaches
mentioned above and record the condition numbers achieved by each one, at each transmission
(for example, for a total of 40 users there would be 10 transmissions in each experiment to serve
all of them 4 at a time, similarly with 100 users there would be 25 transmissions).
We repeat the experiment 1000 times for each case, and report the mean and median condition
number over all transmissions in Table 3.1. We also plot the average condition number in each
transmission and their corresponding CDFs in Fig. 3.11. As we can see, the cross selection
algorithm can further reduce the mean condition number by almost half on top of the plain
antenna-mode selection method (CN-SVD without user grouping), while keeping the condition
numbers low even for the last transmissions. In contrast, if we only select the users but not
the antenna modes (as shown by Omni with ALG grouping and Omni with SUS grouping), the
condition numbers are highly unstable, especially when there are fewer users left to select. Last,
it is worth noting that the ALG user grouping method yields a lower condition number than SUS
irrespectively of whether we perform antenna mode selection afterwards or not. This is expected
since the ALG algorithm is specically designed to reduce the condition number of the channel
matrix.
58
1 2 3 4 5 6 7 8 9 10
Transmission Index
0
50
100
150
200
250
300
350
400
450
500
Condition Number
1. CN-SVD w/ ALG grouping
2. CN-SVD w/o user grouping
3. Omni w/o user grouping
4. Omni w/ ALG grouping
5. CN-SVD w/ SUS grouping
6. Omni w/ SUS grouping
(a) 40 users
5 10 15 20 25
Transmission Index
0
50
100
150
200
250
300
350
400
450
500
Condition Number
1. CN-SVD w/ ALG grouping
2. CN-SVD w/o user grouping
3. Omni w/o user grouping
4. Omni w/ ALG grouping
5. CN-SVD w/ SUS grouping
6. Omni w/ SUS grouping
(b) 100 users
0 50 100 150 200 250 300 350 400
Condition Number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
1. CN-SVD w/ALG grouping
2. CN-SVD w/o user grouping
3. Omni w/o user grouping
4. Omni w/ ALG grouping
5. CN-SVD w/ SUS grouping
6. Omni w/ SUS grouping
(c) 40 users CDF
0 50 100 150 200 250 300 350 400
Condition Number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
1. CN-SVD w/ALG grouping
2. CN-SVD w/o user grouping
3. Omni w/o user grouping
4. Omni w/ ALG grouping
5. CN-SVD w/ SUS grouping
6. Omni w/ SUS grouping
(d) 100 users CDF
Figure 3.11: Condition number achieved by dierent approaches.
Mean CN Median CN
Scheme 40 100 40 100
1 17.77 10.08 14.22 8.82
2 29.52 18.10 28.09 18.84
3 257.2 43.91 186.6 47.16
4 108.7 22.38 61.14 16.42
5 23.44 19.99 29.81 22.75
6 696.4 183.4 376.0 142.1
Table 3.1: Statistics of CROSS simulation
59
3.6.2 Support for OFDMA
The latest 802.11 standard, 802.11ax, allows to use OFDMA, that is, the spectrum can be split
in time-frequency resource units (RUs) and the AP can assign subsets of subcarriers to dierent
users, achieving more
exible multiple access. This new feature complicates the antenna mode
selection problem for the following reason: suppose the OFDM subcarriers are divided into two
RU groups, each group having 4 users, and the AP transmits to all these 8 users concurrently using
802.11ax MU-MIMO. Now, it is likely that each group of users has a distinct optimal antenna
conguration. However, the AP can only transmit under one specic antenna conguration, which
means we need to nd good antenna modes that work well for both RU groups.
To do so we start with a simple approach based on the CN-SVD algorithm: given multiple
RUs u
1
;u
2
;:::;u
n
and their corresponding long-term channel gains G, we rst nd the best
antenna conguration d for each RU separately using the CN-SVD algorithm, then from those
congurations we select the one that works best for all the RUs (for instance, the one that
minimizes the maximum condition number of all RUs), as shown in Algorithm 5.
To investigate the performance of this approach we perform the following simulation: given 2,
4 or 8 RUs each containing 4 users, we compare the average condition number over 100 experi-
ments (referred to as mean in plot legends) achieved 1) by our algorithm, 2) by omni-directional
antennas and 3) by the optimal solution (found by brute-force search). Again we use actual chan-
nel measurements collected in the previous experiments to generate the channel matrices of the
dierent RUs. As illustrated in Figure 3.12, our greedy algorithm performs signicantly better
than the Omni, and also closely to the optimal solution in all the cases of dierent number of RUs.
Also, it is interesting to note that as the number of RU grows, the achieved average condition
number (both the optimal one and the one of our algorithm) increases slightly. We conjecture
this is because the more the groups the harder to \satisfy" all of them at the same time with a
single antenna conguration.
60
Algorithm 5 The CN-SVD for 802.11ax Algorithm
procedure CN-SVDax(a;u
1
;u
2
;:::;un;G)
for i = 1:::n do
d
i
CNSVD(a;u
i
;G;;)
endfor

minmax
1
for i = 1:::n do

i
= 0
for j = 1:::n do

i
max

i
;

G
u
j
;d
i

endfor
if
i
<
minmax
then

minmax

i
d
f
d
i
endif
endfor
return d
f
endprocedure
0 10 20 30 40 50 60 70 80 90 100
Experiment Index
0
50
100
150
200
250
300
350
400
450
500
Average Condition Number of All RUs
Optimal, mean=16.0569
CN-SVDax, mean=30.3942
Omni
(a) 2 RUs, 8 users total
0 10 20 30 40 50 60 70 80 90 100
Experiment Index
0
50
100
150
200
250
300
350
400
450
500
Average Condition Number of All RUs
Optimal, mean=21.3468
CN-SVDax, mean=37.9632
Omni
(b) 4 RUs, 16 users total
0 10 20 30 40 50 60 70 80 90 100
Experiment Index
0
50
100
150
200
250
300
350
400
450
500
Average Condition Number of All RUs
Optimal, mean=26.1715
CN-SVDax, mean=40.7144
Omni
(c) 8 RUs, 32 users total
Figure 3.12: Simulation of antenna mode selection for 802.11ax.
It is worth noting that the above approach is obviously not optimal. In the context of 802.11ax,
one may envision to jointly optimize the antenna conguration problem with the problem of user
selection, or even with the problem of jointly dividing the channel into multiple RUs and assigning
users to them so that the total throughput can be maximized, see [154] for a treatment of RU
scheduling. However, the complexity of this problem increases sizably rendering any solution
impractical in the context of real world APs.
3.7 Protocol Support for 802.11
We propose two protocol extensions by which a commercial 802.11 system can benet from our
direction selecting algorithm. The main purpose of these protocol extensions is to update the G
61
matrix at minimum overhead. Unless otherwise stated, we consider a 4x4 MU-MIMO system,
where the AP is equipped with switched-beam antennas with 8 directional modes. In this case,
each user has a total of 8 4 = 32 long-term gain entries in G.
3.7.1 Active feedback protocol extension
The rst protocol extension, which we refer to as Active Feedback, allows the system to actively
update the G matrix with almost zero overhead but requires minor support from end clients. The
key idea is to inject training symbols into beacon frames. Beacon frames are used to announce the
presence of a wireless network, and are typically broadcasted to the users every 100ms. We insert
4 training symbols into the beacon frame, one for each antenna. Then, beacons are sent while
setting the antennas in dierent directions using a round robin fashion to cover all directions as
fast as possible as illustrated in Table 3.2. Upon reception of the training symbols, users compute
their instantaneous CSI per subcarrier, and compute the average channel gain values as discussed
in Section 3.4.1. Thus, each beacon frame informs 4 values and after 8 beacons (about 800ms) all
32 entries of the user are known. Once the user has obtained all its channel gain information, it
injects the information into an ACK frame and sends it to the AP. Upon reception of the channel
gain entries, the AP updates the row of G corresponding to this user.
Table 3.2: Antenna directions at each beacon/transmission
Direction beacon/Tx 1 beacon/Tx 2 beacon/Tx 3 ...
ANT 1 " % ! ...
ANT 2 ! & # ...
ANT 3 # . ...
ANT 4 - " ...
One may worry that beacons may not be overheard by users if they are sent with directional
modes, and/or that new users or mobile users that just changed their location won't be able to
62
successfully receive packets during the warm up period of updating their row in the G matrix.
Intuitively though, the main lobe of the inexpensive switched-beam antenna modes we consider is
often more than 90 degrees, the main to side/back lobe gain ratio is often less than 6dB [3], and
these two together with indoors multipathing imply we should not worry: the wireless coverage
would be as good as before. To remove any doubt that this is not a real concern, we conduct
the following experiment with the WARP boards. We measure the SNR received by users when
using the 8 training congurations of Table 3.2 and when using the omni mode under 20 randomly
generated topologies. We compute the average sum capacity (over the dierent topologies) for
both approaches, where the sum capacity of the training congurations are also averaged over
the 8 dierent congurations. Figure 3.13a shows that, somewhat surprisingly, the 8 training
congurations yield on average 1.2x higher rates than the omni mode, varying from 0.6x to 1.9x
depending on the conguration and the topology.
Airtime overhead
We introduce overhead by increasing the size of the beacon frame and of some ACKs. We rst
compute the beacon overhead. A beacon frame is typically 50-100 bytes long and is modulated in
BPSK. A training symbol is merely an OFDM symbol and thus equivalent to 8 bytes (for 20MHz
channels). Therefore, we add 4 8 = 32 bytes to each beacon frame for all 4 antennas. The
data rate for beacon frames is normally set to the lowest PHY rate which is 6.5 Mbps (for 20MHz
channels), thus we introduce approximately 40s of additional airtime per beacon. Since beacons
are sent every 100ms, the overhead is only 40s/100ms = 0.04%.
We now compute the overhead in the ACK frame. For each channel gain value, 2 bytes
precision is more than enough. Therefore, to feedback all the long-term CSI of a given user we
add 32 2 = 64 bytes into the ACK, which corresponds to about 80s of additional airtime since
the ACK is also modulated in the lowest PHY rate in order to be robust. Since channel gain
updates occur every 800ms, and assuming say a network with 40 active users, on average every
63
Omni Training Round Robin
Transmit Antennas Configuration
0
5
10
15
20
25
Sum Capacity, [bits/s/Hz]
(a) Round-robin capacity VS Omni ca-
pacity
0 5 10 15 20 25 30 35 40 45 50
Transmission Index
5
10
15
20
25
30
Effective Capacity, [bits/s/Hz]
Omni
CN-SVD
(b) Remeasuring process
6.4 3.2 1.6 0.8 0.4 0.2 0.1 0.05
User Moving Rate (seconds for each move)
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Directional Rate over Omni Rate
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Portion of Time with Full CSI
(c) Gain VS user mobility
Figure 3.13: Experiments with mobile users.
800
40
= 20ms one user will need to update its long-term CSI to the AP, which results in a small
overhead of 80s/20ms = 0.4%. The total overhead is less than 0.5% of airtime, and even in an
8x8 MU-MIMO system it would be less than 1%.
3.7.2 Passive feedback protocol extension
The Passive Feedback protocol extension requires no support from end clients and relies on the
channel sounding stage of a standard MU-MIMO transmission to update the G matrix. Similar
to the active feedback extension, the AP sets its antennas to dierent directions in a round
robin fashion so that all antenna modes can be eventually trained. The dierence is that instead
of changing directions when transmitting beacon frames, it changes directions during normal
transmissions.
Clearly this protocol extension is fully compatible with the 802.11 standard and it introduces
no airtime overhead whatsoever. However, every time a new user joins the AP or an already
associated user moves by a sizable amount, the AP has to use 8 data transmissions towards a user
group that includes this user to update the row of the G matrix corresponding to this user. To
do so, the 8 antenna congurations shown in Table 3.2 have to be used. As already discussed, the
average performance of these 8 congurations is still 1.2x that of the omni mode, but clearly they
perform far from the 3.5x gains achieved by the best congurations. The performance hit from
64
this depends on the portion of time that transmissions take place using these 8 congurations
versus using a conguration found by the CN-SVD algorithm. This, in turn, depends on user
dynamics, e.g. how often new users join, and, more important, how mobile the users are, forcing
the system to update elements of the G matrix. We investigate the eect of mobility and estimate
the long-run performance gain in the presence of period G matrix updates below.
3.7.3 User mobility and long-run performance
When a user changes its location, the G matrix may need to be updated either with the active
or the passive feedback protocol, and, there is a temporary performance hit. To see this, we
perform MU-MIMO transmissions in a dynamic oce environment and report the performance of
Omni versus CN-SVD with passive feedback. Specically, we conduct 20 transmissions with static
users, change the location of some users at transmission 21, and conduct further transmissions
after that. Figure 3.13b shows the higher throughput achieved by the CN-SVD algorithm during
the rst 20 transmissions, the throughput drop at transmission 21 at the levels of Omni, and the
quick rebound after the update of the G matrix during the 8 transmissions following transmission
21. Note that at transmission 21 the system automatically detects the drastic change in some
users' long-term CSI as shown in Figure 3.3a and triggers the use of the 8 antenna congurations
shown in Table 3.2 to update G matrix.
How often does the system has to update the G matrix? Not too often, since wireless devices
connected to a WiFi network change their location in minute time-scales [17, 145, 22], whereas
the process of updating the row of a device/user in the G matrix takes much less. To make
this precise and compute the long-run performance gain we resort to both back of the envelope
calculations and to simulations.
In 802.11ac, the maximum transmission length is about 5ms when packet aggregation is used.
A feedback report, which contains the instantaneous CSI of the users, is typically 16 12 52 =
9984 bits long in a 4x4 scenario and takes up to 1:5ms to transmit [14]. Including the airtime
65
for sounding and the ACK transmissions from the 4 users (each ACK frame takes 48s to be
transmitted [147]), it takes up to 7ms to complete an MU-MIMO transmission. An AP needs 8
transmissions to learn the long-term gain information of 4 users, or, equivalently, at most 56ms.
(Clearly, it makes no sense to use packet aggregation when transmitting with the 8 training
antenna congurations, but we choose to be conservative in our calculations.) Let's assume that
a user changes location every say 10 seconds. Assuming there are 40 active users associated with
the AP and the AP serves them equally, the user under consideration will be part of 10% of the
user groups. Thus, during the 10 seconds that the user stays put, it is receiving data for 1 second
(assuming saturation regime). Based on the previous analysis, for 56ms the user's gain is 1.2x
and for the rest of time it is 3.5x, resulting in a 1:2 56=1000 + 3:5 944=1000 3:4x average
performance gain.
Last, we use simulations to determine the eect of varying mobility to erfomrance. An AP
serves a total of 40 mobile users through 8x8 MU-MIMO transmissions. Users' inter-move times
are exponentially distributed with an average of less than 10 seconds (see x-axis in Figure 3.13c
for used values). Whenever a user moves, its long-term CSI changes and has to be remeasured.
We run the simulation for 100 seconds and compare the average capacity obtained by Omni versus
CN-SVD with passive feedback. We also record the proportion of time that the passive feedback
mechanism spends on remeasuring the long-term CSI. As shown in Figure 3.13c, even if the users
move as frequently as every 3 seconds we still achieve a signicant gain over Omni.
3.8 Implementation Overhead
In this section we are going to discuss the implementation overhead of our proposed algorithm in
practice. Three types of overhead will be introduced to the WiFi system: 1) the airtime overhead
for measuring the long-term channel gains, 2) the computation overhead for nding the best
antenna congurations and 3) the additional power consumption from the use of switched-beam
66
antennas. As we have already discussed the airtime overhead in Section 3.7, we will be focusing
on the additional computation and power consumption here.
Assume the AP is equipped with n switched-beam antennas to serve n users concurrently,
while each antenna has a total of d directional modes. In this case, we would have a G matrix
of size n-by-nd. Recall that we use Algorithm 3 to recursively search for the best mode for each
of the n antennas. The number of total recursions could vary from 1 to n: in the worst case, we
will need to run the ALG algorithm (see Algorithm 2) n times and compute (G
u;fdg[d
f
) for
1 + 2 + +n =O(n
2
) times. Now, both ALG and operations are dominated by a singular-
value decomposition (SVD), which costsO(min(mn
2
;m
2
n)) for an m-by-n matrix. Thus, the
total worst-case time complexity of the CN-SVD algorithm would beO(n
4
d
2
+n
5
). Since the
latest standard (802.11ax) only allows the AP to serve up to 8 users concurrently via MU-MIMO
transmission, it is reasonable to assume thatd>n and thus the overall time complexity becomes
O(n
4
d
2
), which is much smaller than the time complexity of brute-force search,O(n
3
d
n
).
Similarly, the worst-case time complexity of the extended algorithms can be found as follows:
assuming a total of m users and other things remain unchanged, the Cross Selection algorithm
(CROSS, see Algorithm 4) rst selectsn out of them users and then performs CN-SVD on them.
The rst operation costsO(min(m
2
nd;n
2
d
2
m)) and will only be executed once. Therefore, the
total worst-case time is upper-bounded by eitherO(n
4
d
2
) orO(min(m
2
nd;n
2
d
2
m)) depending
on the value of m, as opposed toO(n
3
m
n
d
n
) by brute-force search. On the other hand, the time
complexity of CN-SVD for 802.11ax (CN-SVDax, see Algorithm 5) is upper-bounded byO(kn
4
d
2
)
withk being the number of RU groups, where the brute-force search still has an exponential time
complexityO(n
3
d
n
).
In practice, the CN-SVD algorithm takes a couple of millisecond to nish in a standard CPU
in Matlab, and will take much shorter time if programmed in C. As a result, such time would be
shorter than the total time of a typical MU-MIMO transmission, which allows the AP to nd the
67
best antenna conguration to be used in the next transmission in advance while performing the
current transmission.
Finally, our proposed algorithm poses little additional power consumption to the system.
Under the Active Feedback mechanism described in Section 3.7.1, the AP injects training symbols
to its beacons, while the user sends back its long-term channel gain information by also injecting it
into the ACK frame. As a result, we have not introduced any new transmission into the system,
but rather slightly extended some existing ones (beacon and ACK). Clearly, the extra power
consumption is negligible in this case. Similarly, for the Passive Feedback mechanism (Section
3.7.2), all additional information is collected through ordinary data transmissions, thus no extra
power consumption to the system is incurred.
3.9 Conclusion/Acknowledgements
In this chapter we use SDRs and commercial hardware to show that switched-beam antennas
conjunction with MU-MIMO can achieve a 3.5x-5x performance gain over omni-mode MU-MIMO,
with negligible overhead and while being fully compatible with the 802.11ac standard.
We would like to thank Adant Technologies, Inc. for their assistance in conguring the switched
beam antennas as well as with the experiments involving commercial devices.
68
Chapter 4
Ecient Indoor Localization via Switched-beam Antennas
In this chapter we will discuss another application of switched-beam antennas, which is WiFi-based
indoor localization. By taking advantage of switched-beam antennas to increase the diversity of
measurements used for ngerprint-based localization schemes, we can achieve a good localization
accuracy in the order of half-meter in any indoor environment with zero airtime overhead and
zero client support.
4.1 Introduction
Despite its huge market potential, indoor localization still remains an open problem today: in
environments like airports, shopping malls or oce buildings, people will often nd themselves
in need of navigation to get to their destinations. This has to be done without using the Global
Positioning System (GPS) since the GPS signal is greatly attenuated by roofs. Motivated by this,
in recent years researchers in both academia and industry have come up with numerous approaches
to locate nodes, for example using WiFi RF signals [153, 58, 148, 16, 171, 138, 87, 159], sensor
network RF signals [119, 103, 151, 174, 177, 168, 144, 51, 95, 160, 96, 42, 114, 26, 124, 162, 98, 67,
122, 12], acoustic signals [125, 37, 73, 88], visible light [179, 23], the relative position information
between nodes [117, 101, 80, 48, 91, 68], and more. Among those works, positioning techniques
based on WiFi signals have attracted a lot of attention for indoor scenarios in the academia and
69
industry thanks to the enormous popularity of WLAN system in the past decades. A WiFi-based
indoor positioning system can take advantage of the already-existing wireless infrastructure in
the site, and thus posing little additional cost. Similarly, the users of the system can receive
the service via their WiFi-enabled device such as smartphones and tablets, at no additional cost
either.
WiFi-based positioning mechanisms have certain shortcomings. For example, time-of-arrival
(ToA) [148, 138, 36, 57, 9] and direction-of-arrival (DoA) [118, 87, 29] methods require line-of-
sight (LOS) between the access point (AP) and the user, which is often not the case in indoor
environments that contain a lot of obstacles and partitions. Fingerprint-based schemes [16, 171,
159, 157, 63, 143, 52] don't require LOS, but require measurements from many dierent APs to
get accurate results. Since the main reason of having a WLAN is for data transmission, there is
no incentive to cover locations with multiple APs. What is more, multiple overlapping APs may
cause inter-cell interference harming data rates. Last, many indoor positioning proposals require
the AP and/or user to perform operations that are not dened in the current 802.11 standard,
thus requiring hardware and/or software modications on the user's side. As a result, no WiFi-
based indoor positioning system has yet been widely accepted and implemented. Instead, the
industry has mostly settled for Bluetooth iBeacons to make rough proximity estimates.
In this chapter, we propose a practical, ecient and powerful ngerprint-based method for
WiFi indoor positioning using switched-beam antennas (SBAs). SBAs are inexpensive
1
, compact
antennas that can switch between some predened directional modes. By switching the SBA to
dierent directional modes, we can get multiple independent, uncorrelated measurements from a
given user using only one AP rather than multiple APs located in dierent places. Furthermore,
SBAs can be used to estimate the DoA of the signal using the well known MUSIC algorithm
[136, 123]. While the resulting estimate is rough, it directs ngerprinting to certain areas and
1
SBAs cost only a couple of dollars more than standard omni antennas and allow ngerprint-based localization
improvements as discussed in this work, as well as better MIMO rates [176] and low overhead AP coordination
capabilities [109].
70
further improves the localization accuracy. As a result, our method signicantly improves a
ngerprint-based positioning system's localization accuracy, achieving half-meter level of accuracy
with a single AP, with the reception of single packet from a commodity client, e.g. an ACK,
without requiring line-of-sight, and while being fully compatible to the current 802.11 standard.
Note that this accuracy can be sizably improved by using on top of our core system any of
the ngerprinting \add-on" ideas found in the literature, see the related work section for more
details. Our contribution consists of signicantly improving the accuracy of the core ngerprinting
approach with almost no overhead and with an easy path to industry adoption.
Fingerprinting-based localization requires the oine creation of ngerprint maps. It is beyond
the scope of this work to investigate how to do this eciently, see [102, 79, 59, 178] for recent
ideas.
In addition to using SBAs to improve ngerprinting-based localization, we also show how the
increased diversity from SBAs and the DoA information that they provide can benet not only
ngerprinting-based localization schemes but also other localization approaches such that ToA
ones.
This chapter is organized as follows: Section 3.2 discusses prior work and Section 4.3 moti-
vates the work by showing the gain we get from SBAs comparing to ordinary omni-directional
antennas. Section 4.4 describes how our method works in detail and Section 4.5 presents extensive
experimental results. Last, Section 4.6 discusses how the method can be implemented in a 802.11
compatible manner with zero or very little overhead, and Section 4.7 uses SBAs in the context of
ToA localization.
71
4.2 Prior Work
There is a large body of work on indoor localization, mostly relying on Time-of-Arrival (ToA),
Direction-of-Arrival (DoA), and ngerprint-based approaches. In this section we mostly focus on
papers in the context of WLANs.
Under ToA, see, for example, [61, 148, 138, 106], an AP measures the \time-of-
ight" of the
wireless signal between a user and itself to estimate their distance. If at least 3 APs measure
their distance to the user, we can predict the user's location through triangulation. Under DoA,
see, for example, [87], an AP measures the angle of the arriving signal sent by the user, in order
to estimate the direction of the user's location. As a result, the user's location can be projected
if we obtain angles from two or more APs. Despite often yielding good accuracy in theory and
testbeds, those two approaches have signicant practical/deployment drawbacks.
Under ToA, an inaccuracy as small as 3 nano seconds would cause an estimation error of 1
meter due to the speed of light. To get accurate timing measurements, researchers have proposed
to tightly synchronize the clock between the AP and the user. However, those synchronization
schemes are costly and often require hardware changes not only on the AP but also on the client
side, which means they won't be deployed anytime soon. Although systems based on DoA do
not require such tight synchronization, they require precise DoA measurements which can only
be obtained by expensive antennas which are also too big for commercial APs, e.g. phased-
array antennas. Besides those issues, both ToA and DoA methods need line-of-sight (LOS),
as a dominant multipath component may render ToA and DoA measurements very inaccurate
leading to unusable localization predictions. Since most indoor environments with real world
WiFi deployments have a plethora of non-LOS locations, these methods cannot be used in most
practical settings as is.
Motivated by this, the third major indoor positioning scheme called \ngerprinting", see,
for example, [16, 171, 159, 157, 63, 143, 52] has attracted a lot of attention. Fingerprint-based
72
localization systems involve two phases: during the oine phase vectors of received signal strength
indicator (RSSI) from APs are collected at many reference points whose locations are known, and,
during the online phase, RSSI vectors from a user in an unknown location are compared with the
RSSI vectors of the known locations to estimate the most likely user location. The main issue
with ngerprinting is that RSSI, and, more general, RF signal measurements are noisy and a large
number of uncorrelated measurements are required for high accuracy. The omni antennas of an
AP yield highly correlated measurements, thus the need for many APs to collectively receive and
process measurements to achieve good accuracy, which is also impractical.
To improve ngerprinting many \add-on" techniques have been proposed [66, 85, 140, 150, 65,
78, 117, 101, 80, 132, 69, 163, 137]. For example, in [85, 140], the authors take advantage of the
sequence of RSSI data collected along the user's walking trajectory, and use the patterns found in
such temporal sequences to assist the underlying localization process. In [150, 65, 78], the authors
notice that the WiFi signal shows unique patterns in certain locations, and use such \landmarks"
to determine the user's location. Another idea is to use information on the relative positions
between multiple users, taking advantage of WiFi end devices discovering other nearby devices, to
improve the accuracy of the traditional ngerprint process [117, 101, 80]. Last, the motion sensors
in today's smartphones provide us with additional information like user's walking direction and
speed, allowing researchers to further increase the ngerprinting accuracy [132, 69, 163, 137]. Our
work signicantly improves the core ngerprinting mechanism and could be then used with any
such ideas to further increase accuracy.
Last, researchers have been taking advantage of directionality in ngerprinting systems by
equipping APs with directional antennas [82, 62], which reduces the ngerprints' correlation level
and increases their dissimilarity, making it easier for the system to distinguish between dierent
locations. What is more, researchers have also implemented ngerprinting systems equipped with
one antenna array that localizes the client via signal subspace analysis [89]. Those ndings further
motivate our work, as we have made consistent observations in our experiments which we will
73
Metal Obstacle
2m
2m
Test Point
Reference Points
AP with 8 antennas
8 APs with 1 antenna each
Figure 4.1: Experiment using either one AP with 8 antennas or 8 separate APs.
discuss in the next section. Note however that unlike directional antennas which only have a xed
directional mode, or antenna arrays which cost a lot more than ordinary antennas, SBAs bring
a new degree of freedom and thus a sizable improvement in localization performance with little
extra cost.
4.3 Motivation
4.3.1 One AP is not enough
Despite all the add-on ideas for ngerprint-based localization, the underlying mechanism stays
the same and requires a large number of independent, uncorrelated RSSI measurements to achieve
good accuracy. This, in turn, requires a dense deployment of APs such that uncorrelated mea-
surements are collected by dierent APs within range of each client. It should be clear to the
reader than no business model would support the extra cost fo deploying 2-3x more dense APs
74
solely for the purpose of localization. What is more, considering the number of non-overlapping
WiFi channels available, a dense deployment may reduce the overall throughput due to inter-cell
interference.
Motivated by the shortcomings of existing approaches, our goal is to design and implement
a practical WiFi-based indoor localization mechanism that carries the following properties: (i)
it yields accurate localization even with a single AP, (ii) it is fully compatible with the current
802.11 standard, (iii) it has little or no impact on the performance of data transmissions, (iv) no
hardware or software changes on the client's side are required, and (v) any changes on the AP
side are inexpensive and straightforward.
Previous ngerprinting methods involve collecting RSSI measurements from multiple APs
located at dierent locations. Typically, the more APs there are, the higher accuracy the system
can achieve. However, as discussed, larger number of APs has its drawbacks. Our rst experiment
uses a single AP equipped with up to 8 omni-directional antennas (one at each RF chain). As
shown in the Fig. 4.1, we x 27 reference points on the
oor with 33cm distance between two
adjacent points and place the AP close to these reference points, resulting in two thirds of the area
having line-of-sight towards the AP. We pick test points randomly within the area surrounded by
4 reference points. We then measure the RSSI vector (ngerprint) between the user's antenna
and the AP's antennas at each reference point, and store those ngerprints in a database. This
phase is often referred as the oine phase, or the survey phase. Now that we have collected the
RSSI vectors of all the reference points, we move to the so-called online phase or query phase
where we perform pattern matching between the RSSI vector collected on the test points against
the known ngerprints to nd out the closest reference point towards the user. In this work, this
pattern matching is done using a deep neural network that we describe later.
We start with the case where the AP has only one antenna, in which case the ngerprint is
merely a scalar (the user has only one antenna). We plot the localization errors in dotted red line
in Fig. 4.2, where we dene the error as the distance between the test point and the projected
75
0 1 2 3 4
Error in Meters
0
0.2
0.4
0.6
0.8
1
F(x)
1 AP - 8 directional antennas
8 AP - 1 omni ant. each, 8 different locations
1 AP - 1 omni antenna
1 AP - 8 omni antennas
Figure 4.2: Accuracy with omni and directional antennas.
reference point. As expected, the localization error is quite large and the accuracy is not far from
pure \guessing".
Now, instead of only 1 antenna, we use all the 8 antennas on the AP, making the RSSI
measurement an 1 8 vector. Unfortunately, as shown by the dotted blue line in Fig. 4.2, there
is no signicant performance improvement when we increase the number of antennas from 1 to 8.
This is due to the high correlation among the antennas on the AP since they are closely located
to each other. We conclude that the extra antennas do not provide much new information to
predict the user's location.
4.3.2 Higher diversity via multiple APs
To obtain more diversity in the RSSI vector, this time we place the 8 antennas in dierent locations
surrounding the reference points, as shown by the 8 antenna symbols in Fig. 4.1 so that we could
get 8 uncorrelated RSSI measurements for each ngerprint. (Note that we setup the testbed such
that each RF chain operates independently as if we have 8 separate APs with 1 omni antenna
each.) The solid purple line in Fig. 4.2 shows that the localization accuracy has been greatly
improved thanks to the spatial diversity among the APs, as has been reported extensively in prior
ngerprinting works.
76
Omni
2 4 6 8 10 12
2
4
6
8
10
12
Direction 1
2 4 6 8 10 12
2
4
6
8
10
12
Direction 2
2 4 6 8 10 12
2
4
6
8
10
12
Direction 3
2 4 6 8 10 12
2
4
6
8
10
12
Direction 4
2 4 6 8 10 12
2
4
6
8
10
12
Direction 5
2 4 6 8 10 12
2
4
6
8
10
12
Direction 6
2 4 6 8 10 12
2
4
6
8
10
12
Direction 7
2 4 6 8 10 12
2
4
6
8
10
12
Direction 8
2 4 6 8 10 12
2
4
6
8
10
12
Figure 4.3: RSSI yields dierent patterns in dierent directional modes.
4.3.3 Higher diversity via SBAs
However, as we have argued earlier, it is not practical to assume that every location is covered by
multiple APs. To increase measurement diversity within a single AP we swap the omni antennas
with 8 directional switched-beam antennas, where each antenna is set to one distinct direction.
(For more information about the specic hardware used in our experiments see the next section.)
To judge how much diversity one may obtain from dierent directions, we rst collect RSSI
measurements on a total of 144 dierent locations across a whole oce room, and compare the
RSSI heatmaps for the dierent directions/modes available by the inexpensive SBAs that we use.
As can be seen in Fig. 4.3, the RSSI measurements have drastically dierent patterns for each
mode (yellow stands for high RSSI and blue for low). This implies that a single SBA withn modes
may yieldn relatively uncorrelated RSSI measurements, or, equivalently, an AP withn SBAs each
77
8 SBA 8AP 7AP 6AP 5AP 4AP 3AP 2AP 1AP
0
0.5
1
1.5
2
Average Error in Meters
Figure 4.4: Error versus num-
ber of APs.
8 APs 1 AP 8 SBA ANT 1 AP 8 Omni ANT
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Average Correlation Coefficient
Figure 4.5: Average correlation
coecients.
P1
P2
Pn
RSSI
Input Layer
Hidden Layers
Output Layer
Figure 4.6: DNN structure.
one congured in a dierent mode, may yield n relatively uncorrelated RSSI measurements from
a single packet reception. Motivated by this, we perform the same experiment as in Fig. 4.1, this
time using one AP with 8 SBAs each congured in a dierent mode. As shown by the solid blue
line in Fig. 4.2, the localization accuracy increases signicantly compared to the case of 8 omni
antennas. Remarkably, in Fig. 4.4 we plot the average error achieved by a variable number of
APs and compare it against the error achieved by a single AP equipped with 8 SBAs, and we can
see that the latter setup is as good as having 8 separate APs.
To investigate this further, we compare the correlation matrix of RSSI measurements collected
by (i) 8 separate APs, (ii) a single AP with 8 directional antennas (SBAs) and, (iii) a single AP
with 8 omni-directional antennas. Since the RSSI values collected by dierent antennas tend
to follow the same distribution with similar mean and variance, we simply compute the average
correlation coecients from the correlation matrices and plot the results in Fig. 4.5. As we can
see, by using directional antennas we manage to reduce the average correlation coecient from
0.7 to 0.26, which is at the same level as that from the 8 separate APs setup.
4.4 System Design
This section describes in detail the proposed ngerprint-based localization system, which takes
advantage of SBAs.
78
4.4.1 System description
We use a single AP with 4 to 8 SBAs, each with 9 predened directional modes to choose from
including the omni-direction. (Note that current WiFi standards provision for up to 8 RF chains
per chipset.) We assume users are equipped with one omni-directional antenna like many handhold
devices today (more antennas on the user side won't change the performance or design of the
system sizably). We restrict both the AP and users to operate within the 802.11 standard, i.e.
they can only perform operations that are dened by 802.11, including: user connecting to the
AP, AP sounding the channel, up- and down-link transmission between the AP and users etc.
No non-802.11-compatible operations are allowed because they would require hardware/software
modications on the devices. No multiple-AP-coordination or a central localization server is
needed either.
Like previous ngerprint methods, the system works in two phases: the oine and the online
phase. In the oine phase, RSSI readings in multiple directional modes, either from a single
antenna or from multiple antennas, are collected for all the reference points across the site under
study. These data will be processed, labeled (each reference point will be considered as one
distinct class) and then used to train a deep neural network classier built using TensorFlow [1].
In the online phase, the AP measures the RSSI values from a user, and then feeds this vector to
the classier. The user's location will thus be estimated to be the reference point/class with the
highest probability.
4.4.2 Hardware
We use 3 WARPv3 software dened radio boards [2] in our experiment. Two act as one single
AP with 8 Adant Star 160 [76] switched-beam antennas (SBAs), while the other board serves
as the user equipped with one omni-directional antenna. To test the localization performance,
we use WARPLab, a non-real-time system which makes real-time use of the channel but all
79
the transmitter and receiver processing is done oine in MATLAB, which allows us to collect
the RSSI (or CSI) measurements and feed them to the machine learning estimator located in a
desktop computer.
4.4.3 Machine learning
We are using a typical Deep Neural Network (DNN) classier with 2 hidden layers to predict the
user's location. The structure of the DNN can be seen in Fig. 4.6.
Brie
y speaking, we train the neural network using as input the RSSI vectors of the reference
points whose correct class is known, while the output is a vector of zeros and ones indicating the
correct class for the input. For example, if there are a total of 5 reference points, the correct
output for the second reference point would be [0; 1; 0; 0; 0]. We use the ReLU (Rectied Linear
Unit) function as the activation function for each node and initialize their weights randomly. At
last we perform forward propagation and back propagation on the training data to update the
parameters of the network using gradient descent. We have also applied common techniques such
as cross-validation and dropout to avoid overtting and improve the accuracy [64].
In the online phase where we make predictions of a user's location, we feed the input to the
model and obtain the output, which in the online phase is a vector of probabilities equal to the
chance that each reference point is the estimated location. We thus can assert that the location
of the input vector is closest to the reference point that has the highest probability in the output.
If there are multiple RSSI vectors corresponding to each test point, we rst make predictions for
each vector independently and then decide the user's location via majority voting.
4.4.4 DoA via MUSIC
As we have seen in Fig. 4.2, while the use of directional antennas does bring the average error
in the half a meter range, it is still possible to get multiple meters error (see the tail of the
distribution in Fig. 4.2). This is because due to the complex environment which is common for
80
indoor scenarios, two locations that are far way from each other might still have similar RSSI
readings.
Previous researchers overcome this challenge by either increasing the number of APs to cover
each location, or by acquiring additional information from other sensors or devices. For example,
the authors in [132, 69, 163] use the step count of a user to predict the user's movement, and the
authors in [117, 101, 80] use the relative location between two users obtained by collaborating client
devices to assist the decision-making of the not-so-accurate underlying ngerprinting scheme. Such
ideas can be used on top of any basic ngerprinting approach to further improve the accuracy.
In this work we are interested to improve the performance of basic ngerprinting. We have
already shown how SBAs can do so thanks to the increased diversity of the measurements collected
by SBAs congured in dierent modes, even when they are located at the same point in space.
But there is one more direct benet from using SBAs which comes for free: using the MUSIC
algorithm [136] modied to work with RSSI measurements [123], one may acquire rough DoA
estimates without any additional overhead. While such DoA estimates may not be accurate
enough to be used for DoA-based localization, they may guide the machine learning estimation
process by weeding out some erroneous potential locations that are in the wrong direction, so
that we can narrow down the choices for the correct location (see the green triangle in Fig. 4.9
for example). This has the potential to improve the localization accuracy sizable without any
extra eort, rather than running MUSIC on existing data and feeding the DoA estimates to the
machine learning estimator.
Specically, the MUSIC algorithm is a widely-used tool for estimating the arrival angle of an
RF signal based on the received signal amplitudes/phases at each element of an antenna array, of
which the covariance matrix is analyzed by eigenvalue decomposition. Due to space limitations,
please refer to [136] for more details on the algorithm. The conventional MUSIC algorithm requires
an antenna array, plus both amplitude and phase information of the received signal, which are
not always available in commercial 802.11 products: antenna arrays are often too expensive and
81
too big for indoor WiFi APs, while phase information may not be accessible on certain WiFi
chipsets as they don't provide any APIs to get this information. Motivated by this, the authors in
[123] have proposed an adapted MUSIC algorithm which achieves good DoA estimation accuracy
even though it only requires RSSI readings, which are available in every 802.11 compatible device.
Specically, the adapted MUSIC algorithm uses the so called MUSIC pseudospectrum function,
PS(), to obtain an estimate for the direction of arrival. The pseudospectrum function is dened
as follows:
PS () =
v
u
u
u
u
t
1 +
P
L
i=2

gi()
g1()

2
P
L
i=2

gi()
g1()

RSSIi
RSSI1

2
; (4.1)
whereRSSI
i
is the RSSI reading obtained when setting the antenna to directional modei,RSSI
1
is the RSSI reading obtained when setting the antenna to directional mode 1 which is used for
calibration purposes, g
i
() is this antenna's power gain towards direction in directional mode
i, and g
1
() is this antenna's power gain towards direction in directional mode 1. Note that
the power gain of an antenna towards a given direction can be found from the antenna pattern
provided by the antenna manufacturer and we have used the data-sheets of the SBAs that we use
to obtain those values. Also note that we use the Omni mode for calibration purposes.
With the above in mind, given a vector of RSSI measurements collected at one or more
antennas while setting them to one or more directional modes, the estimated DoA
^
would be the
direction that maximizes the MUSIC pseudospectrum dened in (4.1), that is:
^
= arg max
2[0;2)
PS (): (4.2)
The DoA can be easily computed using brute-force. For more details about the RSSI-based
MUSIC algorithm please refer to [123].
82
4.4.5 User mobility and Hidden Markov Model
The core of our proposal is the use of SBAs for higher measurement diversity and DoA esti-
mation as described above. With the core system at hand, one may add a number of potential
enhancements along the lines of prior work [66, 85, 140, 150, 65, 78, 117, 101, 80, 132, 69, 163, 137].
To illustrate the potential improvement from such enhancements, we introduce a simple ap-
proach that takes advantage of user's mobility to reduce the chances that a far away reference
point is selected. We do so in two steps: 1) rst we collect multiple measurements from a user in
a short period to obtain multiple independent measurements from the neighborhood around the
user to estimate the neighborhood using all measurements and rene the localization decision; 2)
then we implement a Hidden Markov Model (HMM) to further improve the localization accuracy
by exploiting the dependency between consecutive location estimations of the user. Details of
both steps will be discussed below.
4.4.5.1 Multiple Measurements
One may compose \squares" which consist of, say 9 reference points such that each square is
about 1 square meter (see orange grid at the top left of Fig. 4.9), take say 10 consecutive RSSI
measurements within a short time period (say 0.1 seconds, such that it is likely that the user has
not moved longer than 1m during this period), predict the location from each measurement (see
shaded reference points in Fig. 4.9), and nally use these 10 predictions together to determine
the probability of the user being in each square. This step allows us to signicantly reduce the
noise of the estimation by averaging the results from multiple measurements.
4.4.5.2 Hidden Markov Model
A Hidden Markov Model is a Markov Model with unobserved, or \hidden" states [81, 24]. In our
case, we consider the client's locations (or to be more specic, the square in which the client is
83
9 5 0 5 9
Distance to Current Location (Meters)
9
5
0
5
9
Distance to Current Location (Meters)
Figure 4.7: The transition probability to one location depends on its distance to the current loca-
tion (the center) where darker color represents higher probability (assuming the system estimates
the client's location every second).
inside) as the discrete hidden states, and treat the location predictions obtained from the previous
step as observable states.
We then apply the Viterbi Algorithm [149, 50, 128] to the HMM to nd the most likely path
of the client. Specically, given a state space S with n hidden states, transition probabilities a
i;j
from state i to state j, observations at each time slot y
1
;y
2
;:::;y
T
, and emission probabilities
P (y
i
jk) where k represents a hidden state, we want to nd the most likely sequence of hidden
states x
1
;x
2
;:::;x
T
which represents the path that the client has taken between time 1 and T .
According to the Viterbi Algorithm, we deneV
t;k
as the probability of the most likely sequence
ending in state k at time t, based on the rst t observations. The following recurrence relations
can be shown to hold:
V
t;k
=P (y
t
jk) max
x2S
(a
x;k
V
t1;x
): (4.3)
We proceed as follows: we rst determine the transition probabilities between any pair of hidden
states based on their distance: as shown in Fig. 4.7, the closer one location is to the current
location, the higher their transition probability would be. For example, if the system localizes a
client every one second, the probability that the client is 2 meters away from the current location
84
at the next second (in which case he/she is walking at normal speed) is much larger than the
probability that the client has moved by 10 meters in one second (in which case the client is
sprinting). Then, we determine the emission probabilities: note that the observed state y
t
is
merely the probability distribution of the client being in each state/location at time slot t (for
instance, one possible observed state could be \the client has 20% chance in square 1 and 80%
chance in square 4"). In other words, y
t
= (p
t
1
;p
t
2
;:::;p
t
n
), where
P
n
i=1
p
t
i
= 1. Clearly, p
t
i
can
thus be seen as the probability of the client being in hidden state i, given observation y
t
. Or,
more formally, p
t
k
=P (kjy
t
), and, using Bayes' Formula we obtain:
P (y
t
jk) =
P (kjy
t
)P (y
t
)
P (k)
=p
t
k

P (y
t
)
P (k)
: (4.4)
As a result, Eq. 4.3 becomes:
V
t;k
=p
t
k
max
x2S
(a
x;k
V
t1;x
)
P (y
t
)
P (k)
: (4.5)
To simplify the analysis, it is reasonable to assume thatP (k) =
1
n
;8k, i.e., the client is equally
likely to be at any location. This, in turn, implies that P (y
t
) can also be assumed to be the
same for all possible y
t
vectors, since each location corresponds to a specic observed state and
the observed states have the same structure by symmetry. Note that although we do not know
the exact value for the term
P(yt)
P(k)
, it can be ignored since it is a constant factor that would be
multiplied to all V
t;k
where t2 [1;T ] and k2 [1;n], and thus poses no change to the decision of
x that maximizes V
t;k
.
Starting from V
1;k
, we can now compute V
t;k
recursively for all t between 2 and T . The
Viterbi algorithm initializes V
1;k
as follows: V
1;k
= P (1;k)P (y
1
jk), where P (1;k) denotes the
85
initial probabilities. By assuming P (1;k) is uniformly distributed and using Bayes' Formula for
P (y
1
jk) we obtain:
V
1;k
=
p
1
k
n

P (y
1
)
P (k)
: (4.6)
Besides the value of V
t;k
, we also need to record which state x was used to maximize it in
order to retrieve the full Viterbi path. By letting Ptr(k;t) be the function that returns the state
x that maximizes V
t;k
, we can nd the client's most likely path (x
1
;x
2
;:::;x
T
) by backtracking
from the end:
x
T
= arg max
x2S
(V
T;x
); (4.7)
x
t1
= Ptr (x
t
;t);t =T;:::; 2: (4.8)
4.5 Experimental Results
In this section we present extensive experimental results that we perform under a variety of
indoor environments. To make our results/ndings realistic, we deliberately conduct the online
localization phase in a dynamic environment where people are moving around, doors are being
opened and closed, etc.
We will start with experiments conducted inside a large oce room of 7 by 10 meters size, see
Fig. 4.8a. This is a typical oce environment that has desks, chairs, and other furniture including
some metal shelves in the middle, blocking and re
ecting any RF signals. We install the AP in
the center of the room as shown in the gure. A total of 144 reference points are distributed
evenly in the green area, with 33cm distance between each other. For each reference point, we
collect 1000 measurements in about 10 seconds in the training phase to eliminate the in
uence of
AWGN noise. A total of 160 test points are randomly picked across the room, and we dene the
error as the distance between the actual location of the test point and the reference point that it
is classied to.
86
(a) Oce room topology.
0 2 4 6 8
Error in Meters
0
0.2
0.4
0.6
0.8
1
F(x)
8-RSSI
8-RSSI + MUSIC
8-RSSI + MUSIC + HMM
72-RSSI
72-RSSI + MUSIC
72-RSSI + MUSIC + HMM
8 APs
(b) Localization accuracy.
Figure 4.8: Experiments in the oce room.
Reference Points
“S qu ar e” Candidate RPs filtered by DoA
Intrinsic
Error
Figure 4.9: DoA and squares
can further narrow down RP
candidates.
4.5.1 Baseline results
In the previous experiments shown in Fig. 4.2 the size of the test area was relatively small.
Here we consider a more challenging setup where a single AP needs to localize users in a 7x10
meter room without line-of-sight towards all possible locations and under a dynamic environment
involving human and object mobility. As we have seen in the small-scale experiment, the RSSI
vectors collected by omni antennas are highly correlated and are totally unusable with an average
error in this environment of more than 5 meters. Therefore, we set the 8 antennas to dierent
directions in order to obtain uncorrelated RSSI readings and improve the classication accuracy.
The results are shown in the solid blue line in Fig. 4.8b: some test points are classied correctly
to their nearby reference points, but some are being classied to wrong reference points that
are relatively away from their actual location. Overall, the average error achieved by using 8
RSSIs collected by 8 dierent directional modes is in the order of 2m in this more challenging
environment.
4.5.2 Results using all directions of all antennas
Now we would like to examine whether we could get better performance than the baseline by using
more features for the machine learning model: instead of one direction per antenna, we switch
the antenna modes in a round-robin manner and obtain a total of 89=72 RSSI measurements,
87
9 measurements from each of the 8 antennas. By doing so, we observe some performance gain as
shown in the dotted blue line in Fig. 4.8b which is nevertheless small. This is consistent with
our prior observation that antennas on the same AP have a high correlation when congured
to the same mode, which holds irrespectively of whether this is an omni mode or a directional
mode. In summary, although we have 8 times more features than before, we do not get a sizable
performance improvement and it is thus more ecient to collect up to 9 measurements, one for
each mode, from either one of the antennas.
4.5.3 Results using MUSIC
Now we are going to add the DoA estimation into the features. For each RSSI vector, we compute
its estimated DoA using the MUSIC algorithm as described before, and feed it to the machine
learning model along with the original RSSIs. The additional information of DoA allows the
model to lter out most of the wrong candidate reference points (RPs) during the classication
process as illustrated by the green triangle in Fig. 4.9. The new results are plotted in the red
solid line in Fig. 4.8b. As we can see the localization accuracy has been greatly improved thanks
to the DoA information, with an average error of 1.1 meters. Note that the DoA information
can be obtained directly from the RSSI vector thanks to the directionality of SBA. Similarly, we
do the same for the 72 RSSI case (the dotted red line), where we can again observe some minor
performance gain thanks to the additional RSSI and DoA information.
4.5.4 Results using user mobility and Hidden Markov Model
We investigate the performance improvement from the HMM approach in the same oce room
setup, where a client walks around the oce room, and compare the localization results between
1) plain ngerprinting, as described in Section 4.5.3; 2) instantaneous path, where the client's
locationx at timet is considered as the location with the largestV
t;k
, given observations till time
t (y
1
;y
2
;:::;y
t
); 3) nal Viterbi path, in which case we rst nd the last location x
T
based on
88
(a) The ground truth. (b) Raw localization results.
(c) Instantaneous path. (d) Final Viterbi path.
Figure 4.10: Experiment on the HMM performance.
all the observations, and then obtain the client's path by backtracking, see Eq. 4.8. As shown
in Fig. 4.10, clearly the nal Viterbi path would be more accurate than the other two since it
takes advantage of all the observations, but it can only be computed at the end. On the other
hand, instantaneous path can be computed on the
y since each estimation only requires the
observations till that moment. Also, the accuracy of instantaneous path grows with the number
of observations, and will eventually converge to the Viterbi path, as illustrated by Fig. 4.10c
and Fig. 4.10d. In other words, the longer the client stays in the system, the higher localization
accuracy he/she would get.
Fig. 4.11 shows the dierence between the Viterbi and Instantaneous paths for a HMM with
n hidden states after 3 observations. At each step, the state with the highest V
t;k
is coloured in
grey. The instantaneous path follows the grey circles at each step, while the Viterbi path only
89
State 1
State 2
State n
Observation 1
Observation 2 Observation 3
Start
Viterbi path based on all observations
Viterbi path based on observations 1 and 2
Instantaneous path
Figure 4.11: A Viterbi path could change drastically when new observation is made (see the blue
path and red path), while the instantaneous path is found by tracking the states with the highest
V
t;k
.
has to end at a grey circle. Also, when a new observation is made, the Viterbi path could change
drastically with a whole new sequence of states, as shown by the red path and the blue path.
Finally, we plot the localization error distribution achieved by our system when the HMM
approach is used in yellow curves in Fig. 4.8b (like before, solid line for the 8-RSSI measure-
ments case, dotted line for the 72-RSSI case). The average error is now reduced to sub-meter
levels, to 0.87 in the 8-RSSI vector case, and to 0.81 in the 72-RSSI vector case. Note that our
heuristic is only oered as an example. Prior work focusing on augmenting the core ngerprinting
methodology with mobility (or other) information will likely improve the accuracy of our core
system even further. For instance, using the smartphone's magnetic compass and accelerometer,
one can measure a client's moving direction and speed, and thus obtain more accurate transition
probabilities that would further improve the performance of the HMM.
90
(a) Corridor topology.
0 1 2 3 4 5 6
Error in Meters
0
0.2
0.4
0.6
0.8
1
F(x)
8-RSSI
8-RSSI + MUSIC
8-RSSI + MUSIC + HMM
72-RSSI
72-RSSI + MUSIC
72-RSSI + MUSIC + HMM
8 APs
(b) Localization accuracy.
Figure 4.12: Experiments in the corridor.
0 0.5 1 1.5 2
Error in Meters
0
0.2
0.4
0.6
0.8
1
F(x)
RSSI - 16cm grid
CSI - 33cm grid
RSSI - 33cm grid
Figure 4.13: Localization accu-
racy using RSSI vs CSI for 33cm
and 16cm grids.
4.5.5 Results varying other parameters
We study the impact of various other factors on the localization accuracy.
4.5.5.1 Experiments in a corridor
We conduct another set of experiments in a corridor instead of the oce room, to study the
performance of our system in dierent environments. The topology of the corridor can be seen
in Fig. 4.12a, which is about the same size as the oce room, but with less obstacles and most
of the area has a line-of-sight towards the AP. We x 130 reference points evenly in the green
area, in which 140 test points are randomly selected. The localization results are shown in Fig.
4.12b, where the accuracy using RSSI only is better than that in the oce room because of
a less complex environment with fewer obstacles and plenty of LOS. Also, we notice that the
improvement brought by the DoA is modest in this case since all the reference and test points are
located on the same side of the AP, which gives them similar DoA estimations. However, we can
still improve the performance via multiple measurements and mobility, resulting in an average
error of 0.85 and 0.77 for 8-RSSI and 72-RSSI measurements respectively.
4.5.5.2 Using CSI instead of RSSI
Besides RSSI, researchers have leveraged the Channel State Information (CSI) measurements to
perform ngerprinting [161]. Fig. 4.13 shows a comparison of localization errors when using either
91
RSSI measurements or CSI amplitude measurements. Note that we use the amplitude only rather
than the full CSI because a channel's phase changes fast and is often considered random [116].
We conduct the experiments in the setting of Fig. 4.1 using vectors of RSSI and CSI amplitudes
as the input for the neural network classier. As can be seen from Fig. 4.13, there is no signicant
dierence in terms of localization performance when we switch between RSSI (the blue line) and
CSI (the red line). However, since CSI measurements are much harder to obtain (they can only
be collected via the MIMO channel sounding process), we recommend the use of RSSI.
4.5.5.3 Dierent grid sizes
We study the impact of dierent grid sizes on the localization accuracy in the setting of Fig. 4.1.
Since the user can only be localized to one of the reference points which are discrete in space,
the \intrinsic error" of the system depends on the grid size, as illustrated in Fig. 4.9. More
specically, assuming that the distance between two adjacent reference points is d and that the
user is uniformly randomly positioned in a 2-D space, we use basic probability and some algebra
to compute the intrinsic error, i.e., the expected error when the user is accurately located to the
nearest reference point, and obtain:
Z d
2
0
Z d
2
0
4
d
2
p
x
2
+y
2
dydx =
d
6

p
2 + sinh
1
(1)

: (4.9)
As an example, with d = 33cm, the localization accuracy is limited by a system's intrinsic error
of 13cm.
We reduce the grid size by half from 33cm to 16cm, so that there are roughly 4x reference
points in the same area and the intrinsic error becomes 6cm. The results are plotted in the green
line in Fig. 4.13, which shows that, as expected, a smaller grid size can indeed improve the
accuracy, especially for test points which are correctly classied to one of the nearby reference
points. That said, the smaller the grid size the larger the number of reference points, which, in
92
turn, increases the cost of the oine phase. While the oine phase may take place with robots
and other automated means in large industrial facilities today, there is clearly a limit to how small
the grid size may be for the approach to stay practical.
4.5.5.4 Number of antenna and number of directions
Next, we examine the impact of the number of antennas/RF chains of the AP, and the impact of
the number of dierent directional modes on each SBA. We perform the experiments in the oce
room (Fig. 4.8a) using both the RSSI vector and DoA estimation to predict the user's location.
First, we x the number of directional modes to 8 and reduce the number of antennas on the
AP. For the cases with less than 8 antennas, we switch the directional modes to cover all the 8
directions. As shown by the dotted blue line in Fig. 4.14, reducing the number of antennas only
has a minor in
uence on the localization performance. This is mainly because of the high spatial
correlation among the antennas on the same AP, which means that the RSSI measurements of
dierent antennas on the same directional mode are likely to be similar and thus higher number
of antennas could not give us much more useful information, as already discussed. However, as
we elaborate on later in the implementation section, reducing the number of antennas increases
the number of packets that an AP has to receive from a user to get enough RSSI readings.
For instance, to get a measurement for 8 directions/modes, we would need either an AP with 8
antennas set in dierent directions/modes to receive a single packet from a user, or an AP with
1 antenna to switch between the 8 dierent directions/modes and receive one packet under each
mode for a total of 8 packets.
While the number of antennas does not aect the results by much as long as all available
modes are used, the solid blue curve on that plot shows that the number of directional modes
does have a huge impact on the localization decision. To get this curve we x the number of
antennas to be 8 but reduce the number of directional modes used for both RSSI measurements
and DoA estimation. As the number of directional modes decreases the inaccuracy of the system
93
2 4 6 8
Number of Modes/Antennas
1
1.5
2
2.5
3
Average Error in Meters
10
20
30
40
50
60
Average Error in Degrees
Loc. error by different number of directional modes
Loc. error by different number of antennas
DoA error by different number of directional modes
Figure 4.14: Localization and DoA accuracy de-
pends on the number of directional modes.
0 0.5 1 1.5 2
Error in Meters
0
0.2
0.4
0.6
0.8
1
F(x)
1 AP - 8 antennas
2 AP - 4 antennas each
Figure 4.15: Using more APs to cover non-LOS
areas.
increases drastically, because we lose diversity in the RSSI measurements and we lose accuracy in
the DoA estimation, the latter because the accuracy of the MUSIC algorithm is strongly related
to the number of independent measurement using distinct directional modes [123]. For example,
as shown by the red line in Fig. 4.14, the average error of the DoA estimation increases from 15
degrees to over 50 degrees as the number of modes goes down from 8 to 2.
Finally, although the purpose of this work is to provide a way to get good ngerprint accuracy
using only one AP, we would also like to examine whether we can get any performance gain when
we have more than one AP. With this in mind, we use 2 APs each equipped with 4 SBAs to cover
the area of Fig. 4.1 and compare the localization accuracy from this setup against 1 AP with 8
antennas. As shown in Fig. 4.15, we get a mild performance gain with two APs. The improvement
is due to a combination of two factors brought by the second AP: the reduced non-LOS area and
a slightly higher diversity in the RSSI readings.
In the comparison above we kept the total number of uncorrelated measurements the same.
More general, in an enterprise WiFi scenario where it is common to have a couple of APs within
range of a user, the localization accuracy would improve when using say two AP, as in this case
the total number of uncorrelated measurements fed into the machine learning and DoA estimation
modules would obviously double.
94
4.6 Implementation
In this section we discuss how to implement our ngerprint scheme under the current 802.11
protocol and show that it introduces little or no overhead to the wireless network.
4.6.1 Collecting RSSI measurements in a standard compatible manner
As we have mentioned before, two types of RF signal measurements can be used for indoor
localization purposes: RSSI or CSI. Although we have not observed any signicant dierence
in terms of localization performance between the two, we describe how to get both types of
measurements for completeness.
4.6.1.1 RSSI
RSSI can be easily collected during multiple phases. For example, during the pairing process
or any type of data transmission (SISO, SU-MIMO, MU-MIMO) where there exist packet ex-
change between the AP and the user. Note that the RSSI is easily accessible in all commodity
hardware/WiFi chipsets via predened APIs.
When no data transmission is going on, the AP can actively probe a user and obtain the RSSI
vector by receiving an ACK message. With a tiny or zero payload, the total transmission time
to send such a probe and receive an ACK would be about 100s, assuming say a 54 Mbps SISO
transmission under 802.11g (and it would be even less under 802.11n/ac).
4.6.1.2 CSI
CSI information can be obtained through the channel sounding process in the beginning of any
SU-MIMO or MU-MIMO downlink transmission under 802.11n/ac. During this process the AP
sends a short, predened channel sounding sequence to the user. After receiving the sounding
sequence, the user estimates the downlink channel and sends the estimated CSI back to the AP so
that the AP can use it to perform MIMO transmission afterwards. Note that the CSI information
95
can be retrieved from the AP hardware in many commodity chipsets today, though not all chipset
manufacturers open up the corresponding API to WiFi system integrators.
4.6.2 Collecting RSSI measurements for all directions/modes
As we have shown by our experiments, the accuracy of localization heavily depends on the number
of uncorrelated RSSI measurements. With 8 directional modes per SBA, our goal is to obtain
at least 8 RSSI readings, one from each of the 8 distinct modes. For example, if the AP has 8
antennas, we can set each antenna to one distinct direction and get 8 readings with a single packet
reception. If the AP has less than 8 antennas, say only 1 antenna, we would set the antenna to one
mode at a time and receive one packet per mode or 8 packets in total. If the AP has 8 antennas
but we want to collect RSSI measurements at each antenna for each mode, that is, 8 8 = 64
RSSI readings in total, then again 8 packets in total are enough since each packet reception will
yield one measurement per antenna for the mode the antenna is currently congured at.
4.6.3 Airtime overhead
We consider a realistic scenario and perform back-of-the envelope calculations to nd any airtime
overhead due to our localization scheme. Assume say 40 users are paired with an AP equipped
with 8 SBAs. Say users wish to have localization estimates every one second for navigation
purposes.
If the users are actively transmitting data, then there would be at least one packet exchange
per user during a one second period, and thus the airtime overhead is zero. If the users are idle,
then the AP does need to probe the users (which would take at most 100s per user as discussed
earlier) every one second, and thus the overall overhead would be
40100s
1000ms
= 0:4%. However,
since the users are not transmitting data packets anyway, this overhead can still be considered as
zero since the channel is idle.
96
Now suppose we wish to collect say 10 independent measurements per user every one second,
to take advantage of user mobility as discussed before, and assume users are not transmitting
data packets and ACKs thus all those measurements need to be collected through probing. 10
measurements take less than 1ms to complete, and thus less than 40ms for all the 40 users.
Therefore, the overall airtime overhead caused by localization would be
40ms
1000ms
= 4%. But again,
this is when the channel is idle as users don't transmit any data packets. If they do, then probing
is not required as regular ACKs will provide the required measurements.
4.6.4 Integrating with other techniques
The goal of this work is to provide a way to improve the core of the ngerprinting methodology.
Our proposal applies to most of today's cutting-edge ngerprint-based localization techniques,
such as those discussed in Section 3.2, thus it is complementary to those prior works. Besides
prior works on improving localization accuracy, many researchers have proposed solutions to
reduce the workload of the oine phase [102, 120, 39, 79, 167] and algorithms to adapt to the
changes of the ngerprints [171, 35, 38]. Our proposal again applies to these techniques and it is
complementary to them.
4.7 ToA Localization and Switched-beam Antennas
Other than ngerprinting, SBAs can also be used in other indoor localization techniques such
as Time-of-Arrival (ToA) methods, where APs measure the total travel time t of the RF signal
between the client and itself, and then infer their distance by multiplying t by the speed of light.
The client's location can be thus xed by triangulation. However, the clock of the AP and the
clock of the client need to be tightly synchronized in order to obtain a precise distance estimation,
which is very hard in practice. Therefore, a more practical method called Time-Dierence-of-
Arrival (TDoA) has been invented: instead of measuring the absolute time between the client
97
Estimated Location
Figure 4.16: Example of TDoA combined with
DoA estimation via SBAs.
0 5 10 15 20 25 30
Error in Meters
0
0.2
0.4
0.6
0.8
1
F(x)
Plain TDoA
TDoA + DoA
Figure 4.17: SBAs can also improve the perfor-
mance of TDoA localization methods.
and each AP, the APs would simply measure the dierences of arrival times from the same signal
broadcast by the client. At last, the client's location can be determined by the intersection of two
hyperbolas. In this case, only the APs' clocks need to be synchronized, which is much easier to
achieve.
To improve the performance of these techniques, researchers have proposed several \hybrid"
methods that combine ToA and DoA estimation to localize the client, often using antenna arrays
[54, 139]. Inspired by those works, we have studied the possibility of using SBAs to improve the
accuracy of TDoA methods thanks to their ability of DoA estimation. As mentioned above, a
TDoA localization system rst measures two time dierences from two pairs of APs (for example,
the signal arrival time dierence between AP-1 and AP-2t
1;2
, and the signal arrival time dierence
between AP-1 and AP-3 t
1;3
), convert the time dierences into distance dierences d
1;2
andd
1;3
,
and then predict the client's location to be the intersection of two hyperbolas generated by the
distance dierences. If the hyperbolas do not intersect or intersect twice, the system could select
another two pairs of APs to get two new hyperbolas until one unique intersection is found. Now
with the additional DoA information provided by the SBAs, the system can further rene the
area for the client's potential location and thus improve the overall accuracy. Fig. 4.16 illustrates
such mechanism.
98
To see how much improvement we can get from SBAs, we perform a simulation using results
from real world testbeds of ours (see previous sections) and others [54, 139, 129, 32], as follows:
in a round topology having a radius of 40 meters, three APs are located near the center, with 15
meters distance between each other. The client is uniformly randomly located inside the topology,
and is broadcasting to the APs. Upon receiving the signal from the user, the APs would measure
the TDoA between themselves and try to locate the client based on the time dierences. On the
basis of existing techniques, we conservatively set the inaccuracy of distance dierence estimation
(inferred from the time dierence) to be normally distributed with a mean of absolute value of 3
meters, see [129, 32] for details, while the inaccuracy of DoA estimation is set to be 30 degrees
based on our previous results in Section 4.5. We then compare the error between 1) plain TDoA,
where the system would x the client's location as long as there is one and only one intersection of
the two hyperbolas, and 2) TDoA + DoA, where the system would rst try to nd an intersection
as in plain TDoA method, and then take an additional step to verify if such intersection is within
the DoA estimation range of the APs. For both methods, the system would traverse through all
the possible combinations of AP pairs until the client's location can be xed, or it will perform
the measurement again if none can be found. The results are shown in Fig. 4.17, from which it
is clear that the extra DoA estimation signicantly lowers the upper bound of error, achieving an
average error of nearly half as before.
4.8 Conclusions
In this chapter we show with SDR experiments that SBAs can help ngerprint-based indoor
positioning mechanisms achieve signicantly better accuracy with a single AP, a single packet
reception, no changes to clients, negligible to zero airtime overhead, and in full compatibility to
the 802.11 standard. The only required change is to swap omni antennas with SBAs. Such SBAs
cost a couple of dollars more than omni antennas, and are already integrated with WiFi chipsets
99
from all major chipset manufacturers. Thus, at the cost of a handful of dollars per AP, highly
accurate indoor localization is possible via WiFi ngerprinting.
100
Chapter 5
Conclusion
In this dissertation, I discuss some important challenges brought by the two features of next-
generation wireless networks: denser deployment and more advanced PHY techniques. First, we
have developed an analytical simulation framework that allows us to study the performance and to
evaluate the design of advanced techniques for the next-generation wireless networks, followed by
building an SDR testbed equipped with switched-beam antennas to conduct experiments. We then
validated the idea of ACME by both simulation and experiment, and compared its performance
with other advanced techniques including MU-MIMO and coordinated MU-MIMO. Furthermore,
despite the theoretical promise of large multiplexing gain, in practice the performance of MU-
MIMO can be heavily aected by not-so-well-conditioned channel matrices. Thus, we developed
a scheme to x this issue using switched-beam antennas: by carefully selecting the mode for
each Tx antenna, we can obtain a better-conditioned channel matrix and thus achieve a higher
throughput. We have also proposed a backward compatible protocol extension to implement
our scheme in commercial devices with almost zero overhead. Lastly, Despite the plethora of
existing WiFi-based indoor localization approaches, no method can achieve high accuracy without
major, expensive changes to existing systems. We take advantage of switched-beam antennas to
increase the diversity of measurements used for ngerprint-based localization, and achieve half-
meter localization accuracy using a single AP, with zero airtime overhead and zero client support.
101
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Abstract (if available)

Abstract Recent advancement in wireless technologies have changed everyone's life forever: latest WiFi standard allows people to surf, play or even stream high-definition videos wirelessly without any latency, while location-based services like Google Maps have already become part of our everyday life. Still, important yet unsolved problems lie ahead when we want to take one step further: on one hand, in order to achieve even higher throughput we must reuse the limited radio spectrum via either smaller cells and denser AP deployment, or more advanced PHY techniques, most notably multi-user (MU) MIMO. However, the former approach suffers from inter-cell interference because of too closely located APs, while the latter could hardly deliver its theoretical performance in practice due to typically not-so-well-conditioned MIMO channel matrices. On the other hand, localization in indoor scenarios still remains an open question: despite the enormous potential of WiFi-based indoor localization techniques, existing methods often require major and expensive changes to current wireless devices or protocols. As a result, no scheme has been widely accepted and implemented to this day. ❧ The goal of my work has been to address those challenges with the help of switched-beam antennas (SBAs): in Chapter 2, we first develop a simulation framework and a software-defined radio (SDR) testbed to evaluate the performance and provide deployment guidance for next-generation networks. Both simulation and experiment show that properly configured SBAs can effectively reduce inter-cell interference in those scenarios through spatial multiplexing, and thus yield the 10x gains of the theoretically optimal approach with much less hassle. Then, in Chapter 3 we use SBAs to pre-condition the MIMO channel and obtain well-conditioned channel matrices, achieving an average of 3.5x-5x throughput improvement in our experiment. Finally, in Chapter 4, we take advantage of the SBAs to increase the diversity of RSSI measurements used for fingerprint-based localization, allowing a single commodity AP to deliver half-meter localization accuracy in any indoor environment with zero airtime overhead and zero client support, as shown by our testbed experiment.

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Creator Zhang, Yonglong (author)

Core Title Achieving efficient MU-MIMO and indoor localization via switched-beam antennas

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 10/17/2018

Defense Date 09/04/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fingerprinting,indoor localization,MU-MIMO,OAI-PMH Harvest,switched-beam antennas,wireless

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Psounis, Konstantinos (committee chair), Golubchik, Leana (committee member), Krishnamachari, Bhaskar (committee member)

Creator Email antonyzyl@gmail.com,yonglonz@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-81177

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