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Admission control and burst scheduling in multiservice cellular CDMA systems

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Admission control and burst scheduling in multiservice cellular CDMA systems

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Content ADMISSION CONTROL AND BURST SCHEDULING IN MULTI-SERVICE CELLULAR CDMA SYSTEMS by Lei Zhuge A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) May 2002 Copyright 2002 Lei Zhuge R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UMI Number: 3093424 UMI UMI Microform 3093424 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UNIVERSITY OF SOUTHERN CALIFORNIA The Graduate School University Park LOS ANGELES, CALIFORNIA 90089-1695 This dissertation, w ritten b y X i f <j£ Under the direction o f h. Dissertation C om m ittee, and approved b y a ll its m em bers, has been p resen ted to an d accepted b y The Graduate School, in p a rtia l fu lfillm en t o f requirem ents fo r th e degree o f DOCTOR OF PHILOSOPHY w o f Graduate Studies A ugus.t6, 2QQ2 .............. DISSER TA TION COMMITTEE i a -m a y v - R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. D edication To my parents Zhen Zhuge and Hong Lu And my mentor Professor Shangjie Gu R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Acknowledgem ents Pursuing Ph.D. is not just a routine procedure of learning courses and publishing papers, but to me it is more importantly a phase of role change from a passive learner to an active researcher. From these years of valuable research under the guidance of my advisor, Prof. Victor Li, I have gained much on many research-related issues such as choosing a topic, finding the problem, setting up models, analyzing results, and so on, as well as the attitude towards research and colleagues. Therefore, I would like to express my deepest gratitude to Prof. Li for his continuous support, encouragement and advising in all these years. I wish to express my sincere appreciation to Dr. Vincent Lau for his priceless help on my research. His great knowledge and experience on CDMA have shortened my paths to solutions. My appreciation is also extended to Prof. Jiangzhou Wang, Dr. Wing Lau, Prof. Lawrence Yang, and Prof. Ricky Kwok, for their informative discussions with me on wireless communications and networking. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. I would also like to thank Prof. Daniel C. Lee, Prof. P. Vijay Kumar, Prof. John Heidemann, Prof. Zhen Zhang, and Prof. Doug Ierardi, for being in my qualifying and dissertation committees, and providing valuable comments during the exams. I am especially grateful for the help from the staff members at the USC and HKU, specifically from Ms. Danita Lee of HKU/EEE, Ms. Milly Montenegro, Ms. Mayumi Thrasher, and Ms. Diane Demetras of USC/EE, Dr. Dixon Johnson and Ms. Laurie Cox of USC/OIS. Without the warm-heartedness of these people it would be impossible for me to complete my Ph.D. degree across the two cities of Los Angeles and Hong Kong which are thousands of miles apart. My life as a Ph.D. student has been greatly enriched from the last three years’ stay in Hong Kong, where I finished most part of my Ph.D. research and enjoyed peaceful and healthy life. I wish to thank all of my group-mates at HKU and USC for bringing me friendship, encouragement, a lot of happy time, and a wide range of information about their research topics including video transmission, packet schedul ing, multicast, border gateway routing, self-similar traffic, effective bandwidth, satel lite communications, and optical networks. My thanks especially go to Dr. Senthil Sengodan, Prof. Wanjiun Liao, Dr. Tat-Keung Chan, Dr. Spiridon Bakiras, Dr. Ka- Cheong Leung, Mr. Yaxin Cao, Mr. Zaichen Zhang, Mr. Xiaochun Yuan, Mr. Fung Lam, and Ms. Yurong Hu. I also wish to express my thanks to my other friends at USC. They are Dr. Xiaopeng Chen, Dr. Guangcai Zhou, Mr. Min Wei, Mr. Jun Xu, R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Ms. Yubei Song, Ms. Dan Peng, Ms. Huiwen Li, Mr. Jun Yang, Mr. Yuankai Wang and Mr. Robert Weaver. Finally, I would like to thank those friends from the Paowang Club, a virtual club in the Internet. Their humor, smartness, sincerity, and enthusiasm shared with me have been one of the most colorful and indivisible parts of my life in these years of my Ph.D. course. The major netnames1 I wish to thank are Luren, Shazi, Daoke, Nbke, Dajale, and Nana. xForgive me for creating this word. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Contents D edication ii Acknowledgem ents iii List of Tables x List of Figures xi A bstract xiii 1 Introduction 1 1.1 3G Wireless A c tiv itie s ................................................................................. 2 1.2 Wideband CDMA featu res.......................................................................... 5 1.3 Overview of This D issertatio n .................................................................... 6 2 Adm ission Control in M ulti-service C DM A System s 9 2.1 C a p a city R ela ted B asic I s s u e s .................................................................................... 11 2.1.1 Cell layout.......................................................................................... 12 vi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.1.2 User location distribution.................................................................. 13 2.1.3 Channel m o d e l.................................................................................. 13 2.1.4 Handoff model ................................................................................. 15 2.1.5 QoS p a ra m e te r.................................................................................. 17 2.1.6 Power c o n tro l..................................................................................... 18 2.1.7 Interference limit in reverse li n k ...................................................... 19 2.1.8 Power limit in forward link ............................................................ 19 2.2 Existing W o rk ................................................................................................. 20 2.2.1 Voice-only system ........................................................................... 21 2.2.2 Voice/data integrated s y s t e m ........................................................ 23 2.2.3 Multi-service systems .................................................................... 25 2.2.4 Forward link analysis .................................................................... 26 2.3 Reverse Link Analysis ................................................................................. 27 2.3.1 Virtual bandwidth u tiliz a tio n ....................................................... 27 2.3.2 Lognormal approximation and the capacity fo rm u la................. 31 2.3.3 Handoff considerations.................................................................... 36 2.4 Forward Link A n aly sis................................................................................. 45 2.4.1 The capacity constraint ................................................................. 45 2.4.2 Handoff considerations.................................................................... 50 2.5 Other Considerations ................................................................................. 60 2.5.1 Variable data r a t e s .......................................................................... 60 vii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.5.2 Effective virtual bandwidth ........................................................... 63 2.6 Numerical E x a m p le s.................................................................................... 64 2.6.1 Reverse link re su lts........................................................................... 66 2.6.2 Forward link results........................................................................... 68 3 Capacity of M ultiband Overlaid C DM A System s 71 3.1 System Layout and Definitions ................................................................. 73 3.2 General Overlay Pattern A nalysis............................................................. 75 3.2.1 Reverse link capacity co n strain t..................................................... 75 3.2.2 The decomposition method ........................................................... 83 3.2.3 Maximum bandwidth utilization .................................................. 89 3.2.4 Considering the interference l i m i t .................................................. 92 3.2.5 Considering imperfect power control ........................................... 97 3.2.6 Numerical re s u lts .................................................................................100 3.3 Multiband System with Interference Differentials...................................... 107 3.3.1 Reverse link a n a ly sis ...........................................................................108 3.3.2 Forward link analysis ....................................................................... 115 3.3.3 Numerical results ..............................................................................122 4 Burst Scheduling in W ideband C DM A System s 127 4.1 Existing Burst Admission Algorithm in Cdma2000 ................................ 129 4.2 Load Estimation and Prediction for Burst A d m ission.............................131 4.2.1 Load estim ation....................................................................................131 viii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4.2.2 Load prediction.................................................................................133 4.3 New Burst Scheduling A lgorithm s.................................................................134 4.3.1 Information exchange............................................................................135 4.3.2 Admission d ecisio n ............................................................................. 136 4.4 Numerical E xam ple.........................................................................................138 Reference List 142 ix R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Tables 2.1 Three cell types in interference evaluation .............................................. 40 2.2 Moments of vc under different shadowing (reverse l i n k ) ................... 44 2.3 Moments of v with different handoff margin (reverse link) ......................44 2.4 Comparison of v between circular and hexagonal cells (reverse link) . 45 2.5 Moments of vc in different handoff scenarios (forward l i n k ) ............. 59 2.6 System and traffic parameters in an example multi-service system . . 66 2.7 Capacity solutions in the reverse l i n k ................................................... 67 3.1 Simulation parameters for multiband sy ste m ........................................101 3.2 Outage probabilities of example multiband system .................................102 3.3 Example multiband system with subband power differentials...........122 3.4 Capacity comparison in the reverse link of the multiband system . . 125 3.5 Capacity comparison in the forward l i n k .............................................. 125 4.1 Simulation parameters for burst scheduling (reverse l i n k ) ................. 139 x R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Figures 1.1 Major proposals for IMT-2000 ..................................................................... 4 2.1 Cell lay o u t........................................................................................................ 12 2.2 Interference in the reverse lin k ..................................................................... 28 2.3 Equivalence between the interference from local and neighbor sectors 38 2.4 Interference in the forward link ................................................................. 46 2.5 Moments of the path loss ratio v (< re = 6 dB, forward link) .............. 61 2.6 Two-state Markov source m o d e l................................................................. 62 2.7 Simulated outage probabilities for the reverse l i n k ................................. 67 2.8 Simulation results under different handoff schemes in the forward link 69 3.1 An example of multiband spectrum overlaid s y s te m .............................. 74 3.2 Two basic overlay patterns ........................................................................ 83 3.3 Merging of basic overlay patterns in a multiband s y s t e m .................... 84 3.4 Partially overlaid c a s e s ................................................................................. 88 3.5 Uniform power distribution test under imperfect power control .... 103 3.5 Uniform power distribution test under imperfect power control (cont’ d)104 xi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.6 Full bandwidth coverage test under imperfect power control ................ 105 3.6 Full bandwidth coverage test under imperfect power control (cont’ d) . 106 3.7 Multiband spectrum overlaid systems with full bandwidth coverage . 108 3.8 Multiband simulated outage probabilities of the reverse link ................ 124 3.9 Multiband simulated outage probabilities of the forward l i n k .........126 4.1 Illustration of burst scheduling with load p red ictio n ......................... 137 4.2 Performance comparison of different burst scheduling algorithms . . 141 4.3 Performance of burst scheduling with random burst deadlines .... 143 xii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A bstract This dissertation is about a few capacity and admission issues in the future wideband CDMA systems. The objective of this work is to provide on these issues a relatively complete framework which leads to solutions with better applicability and accu racy than the existing methods. Firstly, we derive an analytical model for capacity evaluation in wideband CDMA systems supporting multiple services with QoS guar antees. This model has included many capacity-related issues such as soft handoff, other cell interference, imperfect power control, and variable data rates. The impor tant concepts developed in this model, namely, the virtual bandwidth and lognormal approximation, are applied throughout the work included in this dissertation. In the second part of this work we analyze the capacity of multiband overlaid CDMA systems where the system spectrum is shared by possibly overlapping sub bands with different bandwidths. This kind of systems may be an important format of future wideband CDMA. Finally, we study the burst scheduling problem and pro pose load prediction-based algorithms to achieve lower burst blocking probability and higher system resource utilization. xiii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 1 Introduction Mobile cellular systems started in the early 1980s. The introduction of the cellular concept and frequency reuse techniques greatly improved the capacity in wireless systems, and thus was a turning point in the application of wireless communica tions. The first generation of analog mobile systems include Advanced Mobile Phone Service (AMPS) by AT&T, Nordic Mobile Telephone (NMT) by Ericsson, Nippon Telephone and Telegraph (NTT) in Japan, and so on. These systems are based on frequency division multiple access (FDMA) [32, 33, 39, 49], The deployment of Global System for Mobile Communications (GSM) in 1992 ushered in the digital era for mobile communications. Time division multiple access (TDMA) was chosen in GSM. In North America, second generation digital cellular systems were developed with backward compatibility with AMPS, resulting in two standards - IS-54/IS-136 TDMA cellular system, and IS-95 based on code division multiple access (CDMA). The second generation cellular system in Japan is called Personal Digital Cellular (PDC). 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The digital cellular systems have much higher capacity than the analog systems, while the service cost is much lower. Therefore, the demand for wireless mobile ser vices has grown enormously in the 1990s. To fulfil this fast-expanding demand, and also stimulated by the tremendous success of the second generation cellular systems, the development and standardization of next generation mobile communication sys tems are now rapidly progressing all over the world. In this section first the major standards proposed for third generation (3G) mo bile communication systems are introduced. Then we briefly describe the wideband CDMA standards on which the work in this dissertation is based. Finally an overview of the dissertation is given. 1.1 3G W ireless A ctivities The International Telecommunication Union (ITU) considered developing the 3G mobile communication system as early as 1985, when digital cellular systems were still in their infancy. The new system was previously termed Future Public Land Mobile Telephone System (FPLMTS). Later the name was changed to International Mobile Telecommunications-2000 (IMT-2000). The main objectives of IMT-2000 air interface can be summarized as [39]: • Full coverage and mobility for 144 Kbps, preferably 384 Kbps; • Limited coverage and mobility for 2 Mbps; 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. • High spectrum efficiency compared to existing systems; • High flexibility to introduce new services. While many standardization groups in several countries have been involved in the work for IMT-2000, the fast development in recent years is largely due to the Association for Radio Industry and Business (ARIB) of Japan. In 1997 ARIB pro posed a Wideband-CDMA (W-CDMA) scheme. It is a direct sequence (DS) CDMA system where channels of bandwidth 1.25, 5, 10, 20 MHz are defined [1]. Since then began the competition for IMT-2000 among the standardization bodies. The ARIB W-CDMA scheme was then selected by European Telecommunications Stan dards Institute (ETSI) as the Universal Mobile Communication System (UMTS) air interface specification. In North America the cdma2000 standard has recently been published [51] as a candidate of IMT-2000. Cdma2000 shares many similarities with W-CDMA of ARIB/ETSI, including data modulation schemes, coherent detection of signals, vari able spreading factors, fast closed loop power control, and so on [38], However, in cdma2000 a multi-carrier option is defined for forward link transmission, where the modulated symbols after coding and interleaving are demultiplexed onto N carri ers of 1.25 MHz each (N = 3,6,9,12). This property makes cdma2000 backward compatible with the current narrow-band CDMA system (IS-95). More details of wideband CDMA are discussed in Section I.2.1 1From now on we use the term “wideband CDMA” to generally refer to CDMA systems of next generations (including both W-CDMA and cdma2000), not just the W-CDMA system. 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. TDMA FD/TDMA CDMA TD/CDMA TD-SCDMA UTRATDD UWC-136 EDGE DECT W-CDMA cdma2000 IMT-2000 RTT Family Figure 1.1: Major proposals for IMT-2000 The Enhanced Data Services for GSM Evolution (EDGE) is a high speed TDMA system with channel bandwidth of 200 kHz, first proposed to ETSI in 1997 and now under standardization [15]. A nice feature of EDGE is that it adopts an adaptive channel coding scheme where the rate of the error correction code is adapted to the channel status and interference level [37], The EDGE concept is also included in the Universal Wireless Communications-136 (UWC-136), a U.S. proposal for IMT-2000.2 China joined the IMT-2000 family in 1997 with the TD-SCDMA proposal. This is a hybrid TDM A/CDMA scheme where up to 64 combined TDMA and synchronous CDMA (SCDMA) channels can be aggregated to provide up to 2 Mbps data services [58]. Figure 1.1 shows the major proposals approved in the ITU meeting (November 1999) on IMT-2000 [22], 2EDGE and UWC-136 are regarded as evolutions of both GSM and IS-136. UWC-136 also defines a 1.6 MHz wideband TDMA mode for indoor services. 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1.2 W ideband CDM A features The concepts of spread spectrum and CDMA can be traced back to the work of John Pierce, Claude Shannon, and Robert Pierce in 1949 [39], However, it had not been applied to personal wireless communications until Qualcomm investigated DS-CDMA techniques in the 1980s, which finally led to the narrowband CDMA IS-95 standard in 1993. DS-CDMA has the following major features which make it suitable for third generation mobile communication: • Full multiplexing of traffic: All the users in the DS-CDMA systems transmit over the entire channel bandwidth using different codes. This takes full ad vantage of the activity factor in each traffic stream and avoids the complexity in designing smart slot allocation algorithms in TDMA systems. • Capability of combating multipath fading: From the wideband signal the Rake receiver exploits frequency diversity therefore can significantly reduce multi- path fading. • Resistance to narrowband interference: In the DS-CDMA receiver the narrow band interference is spread over a wide spectrum by the pseudorandom code, and thus degenerates to the background noise. Compared with IS-95, today’ s wideband CDMA employs more advanced tech niques to meet the requirements of high data rates (up to 2 Mbps) and multimedia services (video, audio, and packet data services). These techniques include [27, 38]: 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. • Multiple code or variable spreading code to support a wide range of data rates; • Fast power control in both forward and reverse links (800/1500 Hz); • Coherent detection in both forward and reverse links; • Multiuser detection in the reverse link; • Inter-frequency handover. Besides these physical layer features, wideband CDMA systems also define a set of link layer protocols to provide a wide range of upper layer services. Specifically, Cdma2000 MAC protocol supports short high speed data burst by assigning multiple codes to a user [11, 51]. The traffic channels in cdma2000 have two types. An active mobile user is assigned a fundamental channel for data transmission within the basic rate (9.6 Kbps for rate set 1, 14.4 Kbps for rate set 2.). In case there is a need for high speed data transmission, the user asks for supplemental channels by sending a burst request message to the base station. The base station can accept (with possible modifications in data rate and burst duration) or reject this request based on the burst admission algorithm [21, 30]. The burst admission algorithm in cdma2000 is the topic discussed in Chapter 4. 1.3 Overview of This D issertation We propose to work on several unresolved system level issues of cellular wideband CDMA systems with the focus on capacity and admission problems. Some parts 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. of this work are based on cdma2000, but the principles can be applied to a general wideband CDMA system. In Chapter 2 we discuss the problem of admission control in multi-service CDMA systems from the capacity analysis aspect. This problem has not been satisfactorily handled in spite of all the existing work on CDMA capacity and admissions. In this chapter we will setup a complete framework on CDMA capacity analysis considering multiple service classes, soft handoff, variable data rates, and imperfect power con trol. During the analysis we also introduce a new lognormal approximation method which has higher accuracy than the conventional Gaussian approximation in this context. Spectrum overlay is a feature of DS-CDMA. It can provide flexible solutions of sharing the limited spectrum among multiple systems. It will probably be one of the major options of the future wideband CDMA systems if we think about the possible existence of multiple services and multiple versions of CDMA standards at that time. However, the capacity of multiband spectrum overlaid CDMA systems has not been properly analyzed except for very special cases. In Chapter 3 we present a general method for the capacity solution and compare the capacity between the multiband and single band systems. As mentioned above, the cdma2000 MAC protocol allows high speed burst data transmission with a burst admission algorithm. However, it does not specify how to determine the start time and duration of an approved burst transmission. In 7 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 4 we discuss the joint burst admission and scheduling problem. We will design new burst admission/scheduling algorithms with better performance than the existing one. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 2 A dm ission Control in M ulti-service C D M A System s The capacity and admission control in CDMA systems have been studied extensively since 1990s (e. g. [14, 18, 23, 54]). Based on the analytical and experimental results on the signal propagation and channel model, and the performance of the Rake receiver, error recovery and power control, the capacity and admission criterion of a CDMA system can be derived. The major difficulty in the capacity analysis lies in the existence of various random factors including user location, shadowing, imperfect power control, and the randomness in the received signal power caused by soft handoff. All the existing results, however, consider only a part of these random factors. The major objective of this chapter is thus a capacity formula which includes the effects of all these random factors while it is still in a simple format. In addition, when there is a need to approximate the sum of random variables, most of the existing work uses Gaussian approximation by applying the central limit 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. theorem. In CDMA the system interference is the contribution of many signal powers having lognormal variations caused by shadowing and imperfect power control. The system performance expressed in “outage probability” is therefore the tail probability of a sum of lognormal random variables. The problem of Gaussian approximation is that it tends to underestimate the tail probability of the sum of lognormal random variables with large “shape parameter” such as the shadowing variable, and thereby overestimate the system capacity in the analysis. In this chapter we propose a new lognormal approximation and show that it has higher accuracy than the Gaussian approximation for the interference and capacity evaluation in CDMA. The problem of capacity and admission control becomes more complicated when we consider the future wideband CDMA system where there exist multiple kinds of services. The implication of the multi-service system is the guarantee of multi ple quality-of-service (QoS) requirements. The majority of existing work on multi service CDMA admission control discusses the integration of data and voice services [34, 40, 45, 56, 57], considering such issues as different source models, service pri orities, and joint number-of-user distributions, etc. Our method is to focus on the total interference from all the traffic in the system and its relations to the signal power and the QoS parameter. By this means the capacity analysis is almost a linear extension of that in the single service system, and can thus be applied to a system with arbitrary number of service classes. Because of the simplicity of our model, the random system factors (shadowing, imperfect power control, etc.) can 10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. be fully integrated, while the source model and priority considerations can still be incorporated because they are actually orthogonal to the capacity and interference analysis. Our idea is similar to some recently-published papers [13, 25, 48], but our method is more general as including all the random factors and allowing different traffic distributions among the neighbor cells, as will be seen in this chapter. Among all the discussions on the CDMA capacity issues, the forward link has been paid much less attention than the reverse link. Among the few sources on the forward link performance [39, 52, 55], most of the results are obtained by simulations, and there is almost no analysis on the effect of soft handoff on the forward link capacity. Unlike the reverse link where the user’s signal is received by the neighboring base stations whether or not it is in soft handoff, additional transmissions from the neighboring base stations are required for forward-link soft handoff, and thus more power is consumed and more interference is produced in the neighboring cells. Therefore, whether soft handoff can really increase the forward link capacity or not is arguable [52], Completing this part of capacity analysis is also one of our objectives in this chapter. 2.1 Capacity R elated Basic Issues In this section we define the basic terms and models we will use throughout the ca p a city an alysis in th is d issertation . T h ese b asic d efin ition s h ave b een w id ely u sed in CDMA performance evaluation. 11 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 2.1: Cell layout 2.1.1 C ell layout We use circular cells with 60-degree overlap as shown in Figure 2.1. This is the circular cell layout with the smallest overlapping area while ensuring full coverage. The base station of a cell is located at the center of the circle. Compared with the conventional hexagonal cells, the advantage of using circular cells is the much simplicity in calculation and simulation. In fact the shape of the cells does not affect interference analysis so long as handoff is made according to the strength of the received signal power, not the physical location of the mobile. It does, however, affect the user location distribution (see the next section) since the circular cells have overlapping area. We will roughly show the difference in the other cell interference obtained in the hexagonal cell layout and the overlapping circular cell layout by numerical data in section 2.3.3. 12 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. For the convenience of our discussion we use two tiers of totally 18 neighbor cells in all numerical examples, although the analytical results can be applied to a more general cell layout. 2.1.2 U ser location distribu tion We assume that the users are uniformly distributed among the cells. This means the user locations follow the uniform distribution in a circle with the density function In order to approximate the uniform distribution in hexagonal cell layout, we set so that a circular cell has the same area as a hexagonal cell. Note that we do not have to care about the unit of the cell radius R. is proportional to the m-th power of the distance, where m = 2-4 [32, 49]. In this d isserta tio n w e u se m = 4 in all th e calcu lation s an d sim u lation s for th e n on-line- of-sight cases. (2 .1) (2 .2) 2.1.3 C hannel m odel It is well known that the path loss (power degradation) in a wireless channel follows 13 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Shadowing or slow fading caused by the reflection and diffraction of terrain con tour or large objects is modelled by a lognormal random variable e with parameter (0, of), which means the decibel value 101og10 e has a normal distribution A/"(0, of). The shadowing variable e has density function and moments where h = In 1 0 / 1 0 is a constant. af is called the “shape parameter” of the lognormal variable e. It is in the range of 5-10 dB in the wideband environment [39]. According to experiments the shadowing variable can be factorized into two components: the shadowing near the user and the shadowing near the base station [35, 53], In [53] Viterbi expresses it as where £a and are independent jV(0, of) variables, and a2 + b2 = 1 . Furthermore, (2.4) (2.5) he claims that it is reasonable to assume a2 — b2 — Since the values of a and b do not affect any analysis, for simplicity we also use a2 = b2 = without loss of generality. 14 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. As a result of the path loss and shadowing, the signal attenuation a as a function of the distance r is proportional to a(r) = rme (2 .6 ) For our convenience a is just called the path loss variable in this dissertation. As in [53] we do not consider the fast Raleigh fading because it is largely com pensated by the Rake receiver and close loop power control. The remaining power variation is taken by the imperfect power control variable (section 2 .1 .6 ). 2.1.4 H andoff m odel In CDMA handoff decisions are made according to the pilot strengths of neighboring base stations reported from the mobile user. Geographic location-based handoff is never used in CDMA. Although in reality the thresholds of the pilot strengths are generally fixed for adding/dropping a base station to/from the active soft handoff set, these thresholds are actually adjustable as declared in cdma2 0 0 0 specifications [51]. Hence, we use in our analysis the hysteresis handoff model [33, 43] where the difference in the neighboring pilot strengths determines handoff times. In the hysteresis model hard handoff does not occur until the pilot from the neighbor cell (say, cell 1) is stronger than the local cell (cell 0 ) by a margin A dB- This margin is used to prevent the so-called “ping-pong effect” where the mobile user continuously switches between two base stations when it is in the boundary region of 15 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. both cells, and thereby cause excessive signaling overhead. On the other hand, the soft handoff is triggered as early as the strength of the neighbor pilot is A^b less than the local pilot, and the local pilot remains in the active set until the neighbor pilot is AdB stronger than the local pilot (and then the neighbor pilot becomes the current local pilot of the mobile). If assuming same amount of pilot power transmitted from the two base stations, from the last section we know that the received pilot strength is inversely proportional to the path loss (including shadowing). As a result the condition for being in the soft handoff region can be expressed as where the subscript 0 , 1 denotes the corresponding base stations or cells, respectively, and i denotes the mobile user. In this work we only consider two-way soft handoff, for simplicity, and the results can readily be extended to multiple-station soft handoff. Note that the soft handoff is handled differently between the forward link and the reverse link. In the reverse link all the base stations in soft handoff receive data frames from the mobile. These frames are demodulated independently and then sent to a entity called “frame selector” [16, 39] and the best frame (in terms of error rate, for example) is selected as the received data. (The frame selector may reside in the base station controller or mobile switching center according to the system architecture.) This is approximately equivalent to the case that the mobile only communicates with one base station which has the strongest pilot. On the 16 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. other hand, in the forward link all the base stations in soft handoff transmit to the mobile at the same time, and the mobile is thus possible to combine the signals from multiple sources and make full use of the power in the multipath signals. Soft handoff will be discussed in more detail in our capacity analysis that follows. 2.1.5 QoS param eter QoS is characterized by the bit energy to interference density ratio (BIR) at the receiver side (the base station in the reverse link or the mobile user in the forward link). Let S be the received signal power, I the received interference plus noise power, R the data rate, W the channel bandwidth, then the bit energy in the received signal is equal to e^ = S /R , and the interference density is z 0 = I /W , and thus BIR is calculated as or the product of the signal to interference ratio (SIR) and the spreading gain. W ith given channel model, modulation and coding schemes, the BIR corresponds to the bit error rate (BER) in the received data. For example, a BER of 10- 3 is achieved by 7 « 5 dB in a wideband CDMA channel [39]. Hence, the QoS requirement is that the BIR must be greater a threshold value 7 *. 17 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.1.6 Pow er control In wideband CDMA power control is achieved in a close loop (with explicit feed back) in both forward and reverse links. In the ideal condition of perfect power control, the received BIR is assumed to be controlled at just the threshold value, or 7 = 7 *. In this way the received signal power is controlled at the lowest acceptable level. Since in CDMA system the signal from a user is actually the interference to other users, the interference in the system is thus controlled at the lowest level under perfect power control. In addition, the “near-far problem” is eliminated by perfect power control since signals from all users of the same service class in the cell are received at the same power level. In real systems the performance of the power control loop can not be perfect due to the fast varying channel. Analytical and experimental results [39, 52] show that the error in the power control loop causes a lognormal deviation of the BIR 7 from its target value 7 *, which can be expressed as 7 = 7T 7 * (2-9) where n is a lognormal variable with parameter (0, cA). <77 is 1.5-2.5 dB in the reverse link of the IS-95 system [52], In the forward link since the channel is designed to be orthogonal and synchronous, power control is close to perfect so the deviation 0 7 is very small. 18 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.1.7 Interference lim it in reverse link In the CDMA reverse link the capacity is limited by the interference level in the system. New traffic can be admitted so long as the interference in the system does in the system can be guaranteed. This reverse link interference limit is defined as ratio to the noise density noise to interference ratio (NIR) in the system. 2.1.8 Pow er lim it in forward link In the forward link the QoS is still determined by the system interference level. The capacity bottleneck, however, lies in the total power that can be provided by the station. Through the power control procedure, the base station can always increase the signal power if the received BIR is too low at the user side, until it reaches the power limit. Among the maximum base station power Pm ax a fraction fi is used for common control purposes such as pilot, paging, and synchronization. The rest of the power is assigned to user signals. Let fa be the fraction of Pmax used by the signal to user not exceed the acceptable level and the QoS (or BIR in our context) of all the users n0W (2.10) I V where n0 is the thermal noise density (assumed to be a constant), rj is called the 19 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. i in the system, the power limit for the traffic is thus the total signal transmission power (in terms of a fraction of Pmax) does not exceed (1 — /?), or N $ = 1-/3 (2.11) 4 = 1 where N is the total number of users in the system. 2.2 E xisting Work CDMA capacity analysis using BIR as the QoS parameter is first tackled by Viterbi et al. for a voice-only homogeneous system. Our analysis is extended from Viterbi’s results to general multi-service systems. In this section we review Viterbi’s results and other related work on capacity and admission control of CDMA systems with two or more service classes. Some formulations are reformatted to show their relationship to our analysis which will be introduced in the following sections. Existing work on the reverse link analysis are summarized in sections 2.2.1, 2.2.2, and 2.2.3. Only section 2.2.4 is about the forward link analysis since there are not many references yet on forward link. Besides these results, there are numerous publications on CDMA performance analysis using the bit error rate (BER) or frame error rate as the QoS parameter. Since they are not directly related to our work, these references are not included here for the purpose of conciseness. 20 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.2.1 V oice-only system The capacity analysis on the voice-only CDMA system is summarized from [14, 18, 23, 25, 52, 53, 54], First consider the reverse link of an isolated system with perfect power control, where all the user signals are received with the same power. Let e & be the received bit energy, R be the data rate, then the received power is e^R. The total received interference at the base station is approximately the total received power (if no signal power from any single user is prominent compared with the total power), and is equal to where pi is the voice activity variable of user i, n0 is the thermal noise density, i0 is the interference density, W is the channel bandwidth, and N is the number of users in the system, respectively. The reverse link interference limit n0W /I ^ rj thus translates into N (2 .12) i= 1 (2.13) where 7 — eb/i0. 21 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In the evaluation of N for a real system, Viterbi considers imperfect power control deviation 7q (for user i) and average other cell interference factor V, and defines the outage probability ( N (i+ v) (2.14) { N ( 1+17) ^ 2 Pi^i > No to be the probability of system load exceeding the acceptable level. N ( l+V) A Gaussian random variable is used to approximate piir,; so that the number 2 = 1 of users N can be solved for any given outage probability requirement. Actually Viterbi gives the expression for Erlang capacity X/p where A is the call arrival rate and p is the average call duration, respectively, assuming Poisson arrival process. By treating N in (2.14) as a random variable determined by A and p, the Erlang capacity can be solved from the outage probability requirement (under Gaussian approximation) Q / JVo-(A/rift+17)m,mA ^ g ^ \ v(A //z)(l + ^)m 2i ( 9m2 ) 7 r J where m x and m 2) X denote the first and second moments of variable x , respectively, 8 is the upper bound for the outage probability. Since the processing of Poisson arrival calls is a quite standard method, and the Erlang capacity is directly related to the maximum number of users in the system, in our analysis throughout this thesis we just use the maximum number of users as the capacity measure. 22 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The other cell interference factor V is related to handoff schemes. Suppose a user is in two-way soft handoff between base station 1 and 2 , the average interference it causes at the local base station 0 is calculated as E r{ ei r{ ei r™e o’ r^e 2 + E ^ > 1 rfj'eo r*2 €2 (2.16) where 7j and €j are the distance and the shadowing variable of the path from the user to base station j, respectively. V is then calculated as (2.16) plus the case when the local base station 0 is in soft handoff with the user. However, when evaluating (2.16) Viterbi mistakenly thinks that the two terms in (2.16) are equal by exchanging the positions of base station 1 and 2. In the next section we will show why this observation is wrong, and give the correct expression for the moments of other cell interference factor v. In [14] and [23] a distribution function for v is derived assuming circular cells. However, their result can not be easily extended to soft handoff context due to its complexity. 2.2.2 V o ic e/d a ta integrated system For CDMA systems with voice and data services [ 8 , 31, 34, 45, 56, 57], it is easily shown that the interference limit in the reverse link is equivalent to 23 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. NvRvr )v + N dRd'Yd ^ W ( l - 7 ] ) (2.17) where the subscript v is for voice service, and d for data service. The change of Nv and N r i can be characterized by two Markov chains if we set higher priority to voice service in admission, or by a joint two-dimension Markov chain. Based on voice and data traffic models (e. g. on-off model, Poisson arrival, etc.), the blocking probability for voice and data users can be calculated according to the constraint (2.17). This method, however, can not be extended to systems with multiple (more than two) services. If the priorities of all the service classes are strictly ordered, the system has to always satisfy the users with higher priority, then this case is just trivial with one Markov chain for each service class. Otherwise we need to solve a multiple- dimension Markov chain which is generally very difficult. In addition, we think that a more important problem is to find out the general relationship among the number of users in each service class. The priority and blocking probability issues can be “overlaid” on top of that general relationship. Therefore, in our analysis we consider the system variables such as imperfect power control, shadowing, handoff margins, etc., and try to include them in the capacity formulas regarding the number of users in each service class to reflect the “soft” outage probability constraint. 24 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.2.3 M ulti-service system s Not many results on general multi-service systems have been published yet. The only papers we find on capacity of multi-service CDMA systems are [13] and [48], In [48] other cell interference is considered as a quantity that can be measured on site. Since measurement-based capacity analysis is not our purpose, here we only introduce the method used in [13]. For user i in the local cell 0, let S 0i be its signal power received at the base station, Roi be its data rate, then its BIR is equal to S 0i ^ 0i M N c 53 53 ^ c i V ci c= 0 j = 1 where S C j is the received power at a neighbor base station c from a user j in cell c (c= 0 for local cell), v C j is the ratio of the path loss from user j to base station c to the path loss from user j to base station 0 (V 0j = 1 for a user in the local cell). Sc jVc j is therefore the signal/interference power received at base station 0 from user j in cell c. N c is the total number of users in cell c, and M is the number of neighbor cells in consideration. Thermal noise is not considered here. In [13] the authors assume that the received power S0 i is proportional to 7 0;, then the QoS requirements yC J ^ 7 * . (for every user j in every cell c) extends into M N c (2.19) c= 0 j = 1 25 W_ (2.18) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The author evaluates vC j using the distribution in [14], where soft handoff is not considered. While (2.19) is a nice constraint on the number of users N c, the proportionality of S0 i and 7 0; does not clearly hold in a general CDMA system. In this chapter we will derive a similar constraint in a more rigorous way, trying to include issues such as imperfect power control, soft handoff, thermal noise and the interference limit. 2.2.4 Forward link analysis The forward link is designed to be orthogonal and synchronous. Therefore, at the mobile user only a fraction of the received power from the local base station acts as interference due to loss of orthogonality in signals coming from multiple paths. This fraction is characterized by a orthogonality factor f D , then the BIR for user 1 in the local cell 0 assuming equal base station transmission power with single service is where < / > 0 i is the fraction of base station transmission power for user Vs signal, v q ; is the ratio of the path loss from a neighbor base station c to user i to the path loss from the local base station to user i. 7o i = fo i w _ J L R 0 i (2 .20) C= 1 26 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Hence, according to the forward link power constraint X lti fioi ^ 1 — ft is equiv alent to N 0 / M \ l - / o + X ; ^ K W ( l - / i ) (2.21) i = 1 \ c = 1 / (2.21) is the only analytical result we find in the publications [19, 39, 55], In these references all the capacity results are obtained by experiments or simulations even with (2 .2 1 ) due to the difficulty in evaluating ^ c = i and no handoff issues are discussed. In Section 2.4 we will derive the forward link capacity formula for multi service systems. We will show that can be calculated analytically for systems with hard handoff. For soft handoff uci has to be evaluated by simulation, while the system capacity can still be determined by our capacity formula. 2.3 Reverse Link Analysis 2.3.1 V irtu al bandw idth u tilization We begin our discussion of the multi-service CDMA capacity with the reverse link analysis. As mentioned in the previous sections, in the CDMA reverse link the system capacity is limited by the interference received at the base station. The total received interference power at the base station consists of three parts: the intra-cell interference, the other cell interference, and the thermal noise. In th e C D M A sy stem every tra n sm itter is a in terference sou rce to oth er users. The received signal power from one user contributes approximately the same amount 27 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 2.2: Interference in the reverse link of interference for receiving signals from other users [41, 52], If the signal power from any single user is small compared with the total interference power, the intra-cell interference can be approximated by the total received signal power i> where the subscript 0 denotes the local cell under analysis, S 0i is the received signal power from user i, and N 0 is the total number of users in the local cell. In order to evaluate the other cell interference, let S C j be the received signal power from user j by the base station in a neighbor cell c, the interference in the base station of cell 0 from user j in cell c is then equal to (see Figure 2.2) (2 .22) where a cj and a 0j are the path loss variable (including shadowing) from user j in cell c to th e b ase sta tio n o f cell c and cell 0, resp ectively. O L r c o w . O Q j c ? a oj 28 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The total interference at the local base station is therefore N 0 M N c O Lr Scj- ^ + n 0W (2.23) i=1 c=l j=1 ^ where N c is the total number of users in cell c (c = 0,..., M ), M is the number of neighbor cells in consideration (M — 18 in the layout of Figure 2.1), n 0 is the thermal noise density, and W is the cell bandwidth. Assume that the channel bandwidth W is the same in all the cells. The definition of BIR gives SA W Sci R d C jc i / c\ c\ a\ ^ = 0 1 T r^ r ( 2 ' 2 4 ) On the other hand, the interference limit defines the noise to interference ratio (2.25) j 0 Therefore, the signal and noise symbols in (2.23) can be cancelled by dividing the both sides of (2.23) by / 0 and bringing in (2.24) and (2.25) N q t - j M M c 7- ) j < * * > i—1 c— 1 j —1 ^ In order to cancel the term Ic/ h in (2.26), we assume Ic « Io, which means an approximately uniform interference density among all the cells. Note that the uniform interference does not necessarily mean homogeneous traffic where the service 29 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. classes and number of users in each service class are the same in all the cells. It is possible that two cells have different number of users using different services while the total interference in each cell is about the same. Under the uniform interference density assumption, and define No D M N c D - = (227) i = 1 c = l j = l where uc j = a c j/aoj is the path loss ratio variable, the constraint (2.26) becomes l o ^ 1 — t) (2.28) (2.28) is a nice constraint on the traffic in the local cell and neighbor cells with the QoS ("fai) taken into consideration. The constraint guarantees that the interference in the local cell does not exceed the limit defined by (2.25). u > is thus a good index on the system load including the signals from the users within the local cell and from neighbor cells for a given set of number of users {N c} in the system. In addition, (2.28) is equivalent to u jW ^ (1 — rj)W, so l o can be thought as the fraction of cell bandwidth “virtually utilized” by local and neighbor users (although signals from all users are actually spread over the full bandwidth), and (2.28) means that at least a fraction 7 7 of the bandwidth has to be left for the thermal noise to “consume” it. We therefore name u > the virtual bandwidth utilization of the cell. 30 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Note that if Ic is set to 0, (2.26) becomes (2.29) which gives the constraint on the case of no other cell interference, or equivalently, the single-cell system. It is interesting to see that we can also get (2.29) from (2.28) by setting all {N c} in u > (2.27) to 0, where {N c} = 0 also means no other cell interference. Hence, (2.28) is a valid constraint for both cases of uniform interference (/c « / 0) and no other cell interference (Ic = 0). It is therefore reasonable to infer that (2.28) may be used to constrain heterogeneous interference systems where Ic ranges from 0 to / 0, without causing too much error. We are, however, currently unable to prove this conjecture, and thus have to leave it as our future work. 2.3.2 Lognorm al approxim ation and th e capacity form ula In (2.28) the path loss ratio uc j is a random variable related to shadowing and the user location. There is another random variable when considering imperfect power control, since 7ci = (c = 0,..., M, i = 1,..., JV C ) (2.30) according to (2.9). 31 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. With these random variables the deterministic constraint (2.28) is not accurate enough to operate on the probabilistic behavior of the system load. We need to reformat (2.28) into a statistical version as Pr {cj > 1 — rj} ^ 8 (2.31) From the discussion of the last section, we know that (2.31) is equivalent to and thus 8 is the probability of the interference in the system exceeding the ac ceptable level. 8 is therefore defined as the outage probability of the system, and is specified as a system parameter in admission control. (2.31) is actually a constraint on the tail probability of the random variable to. It may be translated into a deterministic constraint in term of the moments of u if we know the distribution of u > . Unfortunately the distribution of l o is not analytically obtainable, and we have to use approximation to estimate it. 2.3.2.1 Gaussian approximation Since ui is the sum of many random variables, it can usually be approximated by a Gaussian variable with the same mean and variance as u > [14, 52]. The capacity (2.32) 32 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. analysis by Gaussian approximation are reported as fairly close to simulation results. Here the Gaussian approximation for u is ui k, + X\Ag (Gaussian approx.) (2.33) where x is a standard 7V(0 . 1 ) Gaussian variable, and N° U M N c d * E ^ O i l o i . \ ^ \ ^ 7 1 c j l c j 2 = 1 C— 1 j — 1 ( Roiloi\ 2 , w ) V 7 r + Z ^ Z ^ ( w J V { ' V c " " ) 2 = 1 ' ' C = 1 j = l X 7 (2.34) where mx and vx stand for mean and variance of x , respectively. Note that the mean and variance of the path loss ratio variable vc i are independent of user i. The product (yc • 7r) produces a new random variable, whose mean and variance can be calculated according to the following formula m{x-y) = m xm y, v^x.y) — vxvy + m 2vy + m 2vx (2.35) The path loss ratio v will be discussed in detail in the next section about handoff. It is well known that the tail probability of a A /"(/U , a2) Gaussian variable greater than x is equal to Q((a; — /r)/cr), where 1 f°° 2 Q (x) = , — / e ~ dt (2.36) V 27T Jx 33 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Since Q(x) is a monotonically decreasing function, the condition for achieving (2.31) under Gaussian approximation is found to be mu + tx^/vZ ^ 1 — 7/ (Gaussian approx.) (2.37) where t x = Q \5 ) or Q (tx) = 8 (2.38) Note that (2.37) is an explicit constraint on the number of users. To see this, let Lc be the number of service classes in cell c, then the general terms in m u and vu respectively, where the subscript c is for cell, k for service class, and j for user, and the same Rck and -y * k. 2.3.2.2 Lognormal approximation Although it is simple, we find (and also found in other reports e. g. [25]) that the Gaussian approximation tends to underestimate the tail probability of the sum of many lognormal variables with different shape parameters, and thus (2.37) overes timates the system capacity. (In [14, 52] only voice service is considered.) This is (2.34) are (2.39) we have N c = Ylk=l ^cfe- Here we assume all users in service class k of cell c have 34 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. clearly seen in our simulations, especially when the shape parameters of the lognor mal variables are large as the shadowing variable. The major reason, we think, is that the lognormal distribution has a “longer” tail than the Gaussian distribution, and the tail is not much reduced even after the multiplexing of many lognormal variables. In fact, there exists an observation that the sum of lognormal variables is still approximately a lognormal variable [5, 7, 49]. However, the existing lognormal ap proximation methods are generally too complex in format to be used in our problem here. Our aim is to find an explicit constraint on the number of users from (2.31), and the constraint should be easy to solve for the number of users. Our method is to approximate u > by the linear conversion (scaling and shifting) of a lognormal variable with fixed shape parameter (i. e. the shape parameter is independent to traffic parameters). From (2.27) we see that in ui the “lognormal component” with the largest shape parameter (thus the longest tail) is (u ■ 7r) (u in cludes the shadowing parameter), so we define a lognormal variable ( with parameter (0, ( 7^) to approximate this component. Specifically, let M M C = 1 c = 1 M M (2.40) V (V * ) = Y l V (Vc-*) = ' 5 2 ( V VcV * + m l c V * + m W ) c = 1 c = 1 35 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. then according to (2.4) we set (241) Note that the variable ( defined in this way actually has a non-zero first parameter, but this can be taken care of by scaling ( in the approximation of to. o j is then approximated by the linear conversion of ( while keeping and vu unchanged uj « mu + (C ~ m c ) ^ - (lognorm. approx.) (2.42) Using the relationship between lognormal and Gaussian distributions, the capac ity constraint satisfying (2.31) under the lognormal approximation (2.42) is proved to be m L + (Tf — ^ 1 — V (lognorm. approx.) (2.43) where r c = e ° < h Q ~ \s ) ^2>44j 2.3.3 H andoff considerations The path loss ratio variable vc j = aC j / a 0 j (Section 2.3.1) is used to characterize the attenuation of the signal power from the user j in cell c, which is received by the local base station as interference. When considering handoff, however, vc j is not just the ratio of the path loss a c j and a 0j , because there is a probability that user j is 36 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. power controlled by a base station in the neighbor of cell c. It is also possible that a user in the neighbor of cell c is power controlled by base station c, and we need to consider these kinds of users when calculating the moments of vC J so that they can be included in the sum ^w*'’ U c i (2-27). Nc is thus the number of users power controlled by the base station in cell c, not just the number of users in the cell. From the introduction of the hysteresis model in Section 2.1.4, we can write the expressions for vC ] under different handoff situations, then calculate its moments for capacity analysis. The calculation is similar to what Yiterbi did in [52] for the basic CDMA system with a single service class and homogeneous traffic distribution. In fact, the moments of uc j should not depend on the service class of the user, but it is related to the position of cell c so it is different for different cells, and we need to consider this difference because the traffic distribution may not be the same among the cells although we assume that the total interference in each cell is about the same. In addition, Viterbi made a mistake in that he treated the interference from a user power controlled by either of the two neighbor stations as symmetric cases, so he just calculated the portion of interference when the user is power controlled by a certain neighbor station and then doubled the amount to account for both neighbor stations. By this means he made the interference calculation for the whole area at a time. In the following we will see that this is not a symmetric case, and we have to evaluate the interference for each 60-degree sector of all the cells for the two-way 37 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) numbering the cells (b) correspondence between sectors and cells in (a) F igu re 2.3: E q uivalen ce b etw een th e interference from local an d n eigh b or sectors 38 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. handoff consideration. The 60-degree sector is used because each of such sectors determines a neighbor base station in the two-way handoff. Note that the path loss ratio actually reflects the normalized other cell interference, so here we use the two terms in a interchangeable way. This interference or path loss ratio evaluation can be simplified a little bit by taking advantage of the symmetry in the cell layout. First, we only need to inspect one-sixth of the entire layout, i. e. the area between the two dashed line in Fig ure 2.3(a). Second and more interestingly, we find that the interference received at the local base station from a sector of a neighbor cell is equal to the interference received at a neighbor base station from the local sector (the shaded sector in Fig ure 2.3(a), called the “base sector”), and the correspondence between a interfering neighbor sector (interfering the local base station) and a interfered neighbor base station (interfered by the base sector) is a one-to-one mapping for equivalence. This can be easily seen from the geometry of the cell layout in Figure 2.3, where each sector in Figure 2.3(b) corresponds to a base station with the same number in Fig ure 2.3(a). For example, the interference to the local base station from sector 7 in Figure 2.3(b) is equal to the interference to base station 7 in Figure 2.3(a) from the base sector. Consequently, the total normalized interference from a neighbor cell is equal to the sum of the interference from the base sector to all the neighbor stations which correspond to the sectors in that neighbor cell. On the other hand, we can divide 39 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2.1: Three cell types in interference evaluation Cell type Cell number Associated sectors I 1, 2, 3, 4, 5, 6 S l> S2, S3, S4, S 5 , s6 Ha 7, 9, 11, 13, 15, 17 Sj, Sg, S11, S13, S15, S17 Hb 8 , 10, 12, 14, 16, 18 $8 , SlO , - ^ 12, Sl4) 516, Sl8 the 18 neighbor cells into three categories according to their relative positions to the local cell: type I for the first tier cells, type IIa for the second tier cells 2^/2>R away from the local cell (2\/3R is the distance between the two cell centers, R = cell radius), and type Hb for the second tier cells 3R away from the local cell. Table 2.1 lists the cell numbers of each type and the sectors in Figure 2.3(b) included in each type of cells. Our work is then to calculate the normalized interference from each sector to the local base station, or equivalently from the base sector to each neighbor station, and average over the appropriate group of sectors for the path loss ratio from each cell.1 Specifically, let us consider hard handoff between cell 0 and cell 1 with hysteresis margin AdB in the base sector. As specified in Section 2.1.4, in the reverse link the soft handoff scenario is approximately equivalent to the case that at any time the user only communicates with the base station having the strongest pilot. Hence, the soft handoff can be regarded as a special case of hard handoff with A dB = 0 or A = 1. A ctually due to symmetry we only need to calculate 12 cells. These 12 cells include the local cell and cells 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13. 40 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Let v'j be the path loss ratio from the base sector to a neighbor station j in Figure 2.3(a), and aj = r™ej be the path loss variable to the base station in cell j. As introduced in Section 2.1.4, when ® > A or > A the user will be power controlled by station 1. Therefore, 4 = < r fe i o rpe o rTei r j± i rT €i r j e o when 0 0 > A r?e i otherwise when ^ > A rfe i otherwise V > 1 ) (2.45) The moments of z/ are calculated to be m v[ m 2y E r™ ei _ r p o Lr0 me0 ’ r f £l > A + E r'^e0 rg'eo ei r'{'€\ t In S: + Ads Q a £/i + + = E Q ( er£/i + ■ ■ In a - A,dB r o 6r dr dd rTe i rj^eo rpe0 l > A + E rpe 0 \ ro e0 r" e i A = e 2 cr? fi2 /:r 2m ^ r Q ( w > + flnS+AjB 2m ^ l n ^ _ A dB - , Q 2aeh + -A !2- n 7 V cr, 6r d r dO (2.46) 41 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. and m 2y. F, r ' • ; r° £° . > A + E /y^TTl £ ro eo r.m ,- r » £o < A [ r f e j r™ex J i 1 j 1-rei J £ rR n r Q ( ^ + f ‘" S ± ^ + ( - ) Q < y , + dB < ? e 6 r ^R 2 dr dO = E r£ei ' j F r o £0 rj^e! > A + E ry cp V . r^ e 0 rr ej / ’ r r ei a : 3 2m 2m Q ( < r £ /i + + I - ) Q f cre/i + - ln ri A' c Z B + Ad B ft ro a °€ 6 r oe 7rR2 drdO U > 1 ) (2.47) where the distance { r j } are functions of r and 9. In Viterbi’s calculation the two cases of z/ in (2.45) are regarded as symmetric (when A = 1 or A dB = 0) by exchanging r x and ro, so only one term in the integral of m vi in (2.47) is evaluated (without the A dB term). The problem is that changing r x and ro means moving the user to a new location which is symmetric to its original location with respect to the two base stations, and thus may change r,- or the distance from the user to the station j, unless station 0 and 1 have the same distance to station j. 42 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The path loss ratio vc used in the mean and variance of to (2.34) is then deter mined by = $ = \ Vv'i= I S (m2> ^ ~ m -'j) (2-48) jesc j£Sc jesc where S c is the set of associated sectors of cell c (Table 2.1). Note that when these values of v are applied to the capacity formula, the users in soft handoff should be counted only once in N c. The base stations should be able to know this from their message exchange when setting up the soft handoff. Now let us see some numerical values of the moments of v obtained by numerical integration of (2.46) and (2.47). Table 2.2 shows the moments of vc under different shadowing deviations cre, without considering the handoff margin (this is equivalent to the soft handoff case). The values are multiplied by six so they reflect the con tributions of all six cells of the same type. It is clear to see that the tier-one cells contribute the vast majority of the total interference and variation. Type IIb cells have more influence than type IIa cells since they are closer to the local cell. When the shadowing is so serious as ae = 10 dB, the large variation of vc shows that the two-way soft handoff is not adequate to absorb the interference variation under this condition. Table 2.3 illustrates the effects of handoff margin on v. For conciseness here we show the total sums of m V o and vV c over all neighbor cells. The values tell us that the mean and variance of v increases with the handoff margin A dg, which complies 43 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2.2: Moments of uc under different shadowing (reverse link) (A<ib = 0) Shadowing Type I cell Type IIa cell Type IIb cell dev. < y e mean 6 rn„c var. 6 v„c mean 6 m V c var. 6 ryc mean 6 m„c var. QvV c 2 dB 0.369 0.088 0 .0 1 2 0 .0 0 0 0.023 0 . 0 0 0 4 dB 0.375 0.093 0.013 0 .0 0 0 0.024 0 . 0 0 0 6 dB 0.395 0.118 0.015 0 .0 0 0 0.029 0 .0 0 1 8 dB 0.473 0.397 0.023 0 .0 0 1 0.043 0.004 10 dB 0.975 34.24 0.066 0.109 0.126 0.442 Table 2.3: Moments of v with different handoff margin (reverse link) (ae = 6 dB) Handoff margin A dB Mean m„ Var. vu 0 dB 0.438 0.119 2 dB 0.465 0.157 4 dB 0.519 0.249 6 dB 0.566 0.369 8 dB 0.603 0.502 with our intuition. What can not be shown here is the decrease of signaling overhead with larger A dB, due to less ping-pong effect. Finally, since v is the only parameter related to the cell layout in our analysis, we compare the moments of v between our circular cell layout and the conventional hexagonal cell layout in Table 2.4. It is seen that the other cell interference as shown by v is smaller in our circular cells (both mean and variance are smaller). This is because we use a cell radius R & 0.9094 (Section 2.1.2) to achieve the same area of a hexagonal cell, and thus rule out those high-interference locations 44 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2.4: Comparison of v between circular and hexagonal cells (reverse link) (A^b = 0) Shadowing Circular cell Hexagonal cell dev. ae mean m v var. vu mean m v var. vu 2 dB 0.404 0.088 0.423 0.099 4 dB 0.413 0.093 0.431 0.107 6 dB 0.438 0.119 0.459 0.145 8 dB 0.537 0.404 0.567 0.546 10 dB 1.163 34.80 1.240 47.67 which are close to the hexagonal vertices. However, our analysis is almost not affected by the cell shape. Hexagonal cells can be easily incorporated by changing the coordinates and integrating area in (2.46) and (2.47) for the moments of v, as we just did to produce the data in Table 2.4. The problem is that hexagonal area brings troubles to simulations since it is difficult to generate uniform location distribution and determine the cell boundaries in the hexagonal cell layout. Circular cells also facilitate analytical calculation. For these reasons we use circular cells throughout this work, which does not affect the generality of our results. 2.4 Forward Link Analysis 2.4.1 T he capacity constraint As introduced in Section 2.1.8, in the forward link the total transmission power for user signals (normalized by the maximum base station power Pmax) is limited by 45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. user j user i cell c user i cell 0 Figure 2.4: Interference in the forward link (1 — (3) where f3 is the fraction of the base station power reserved for common control commands. At the same time, the user’s BIR requirements must be satisfied. Consider a user i in the local cell 0. It receives a power S0i from the local base station, and Sci from the base station in a neighbor cell c (see Figure 2.4). Owing to the synchronous and orthogonal properties of the forward link, only a fraction of the received intra-cell power (1 — f 0)Soi from the local base station acts as interference, where f Q is the orthogonality factor [39] (a given system parameter), and the intra cell interference is due to partial loss of orthogonality in the received signals. The total interference received by user i is therefore M I0 i = (l-fo )S o i + J 2 S ™ (2-49) c = 1 Here we have ignored the thermal noise since it is small compared with the total received power. 46 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Let (p a ,, be the fraction of Prnax for transmitting user i’s signal. When the local cell is fully loaded (a necessary condition for calculating the capacity), the local base uses up the maximum transmission power Pmox> so the total received power by user i from the local base station is S0 i ~ P-max/°0i where is the path loss variable from the local base station to user i. The BIR of user i is 4> 0iS 0 i W < f > 0i w 7 0 < » - f — p - = ---------------- M---------R- (2-50) lQ i ttoi J-L 1 * 0 i o - f o ) + J 2 s * / s ' 0 i c= 1 Hence, M (2.51) where So and Sc are the total transmission power in cell 0 and cell c, respectively (So ~ Pmax)- O L C i is the path loss variable from base station c to user i. We estimate the ratio Sc/S 0 by considering only the user signal part and disre garding the other cell interference in each cell. This approximation is valid when the intra-cell interference plays a major role or it takes a similar fraction of the total interference in each cell, and the total user signals consume a similar fraction of the total base station transmission power in each cell. The error in this estimate is 47 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. reduced further when the path loss ratio aoi/ac i is small. From (2.50) we can get the BIR for a user j in cell c ignoring the other cell interference as b P W u c j 1 m a x * r (1 - f 0)Sc R, (2.52) ■ C j Hence, the normalized base station transmission power estimated in the way described above is N c N c '52< i> cj = ( i - f o ) 5 2 P c j ' l c j w (2.53) 1=1 j=i where N c is the total number of users in cell c (c = 0 for the local cell). Bringing (2.53) into (2.51) and adding up 0oi for all users in the local cell N o N 0 2 = 1 2 = 1 P q ib fO i w I M N c \ 1 - fo + C_1 v N o 5 2 -^0*'70i' i ' = 1 (2.54) The outage probability in the forward link is defined as the probability of the fraction of the total transmission power for user signals exceeding the limit (1 — f3), and the constraint on the outage probability is then Pr { < f > > 1 — /?} ^ 8 (2.55) As in the reverse link we use Gaussian and lognormal approximations to get the capacity constraint on the number of users. The constraint is expressed in terms of 48 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the mean and variance of < f > . Note that by averaging $ regarding ^ in (2.54) (so that the dependence of the path loss ratio on i is erased) the denominator R w lw in the parentheses is cancelled with the term 1 -^oiToi outside the parentheses. Define the path loss ratio vci = ^2i. We get E > M N c r> *^ = £ " W ^ 1 _ f 0)771w £ “^ m (— ) 4 = 1 C = 1 j = l N) / n * \ 2 M N c / r> ,ry* \ 2 t = l v 7 c = l j ' = l v 7 (2.56) where 7r is the imperfect power control variable as in the reverse link. In forward link the power control is almost perfect so ov is very small. (2.56) is very similar to (2.34) for u in the reverse link. In fact, we can also define the virtual bandwidth utilization for the forward link as N o 7-) M N c tj - - « + £ E R c Qc j vc (forward link) (2.57) 4=1 C = 1 j = 1 with the first term for the intra-cell interference and second term for the other cell interference. Note that aj has the same mean and variance as $. Using the Gaussian and lognormal approximations, the capacity formulas for the forward link are, respectively, + Tx - S f v ^ < 1 - / 3 (G au ssian ap prox.) (2.58) 49 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. where rx = Q 1 (< 5 ), and I v < $ m$ + (r^ — m^). — ^ 1 — f3 (lognorm. approx.) (2.59) V v ( where = e a< hQ ^ and is defined in (2.41). 2.4.2 H andoff considerations The handoff scenarios in the forward link differ from the reverse link, especially in soft handoff, in that the received data frames are demodulated independently in each base station in the reverse link soft handoff, while in the forward link the signals from different base stations can be combined at the user device and thus decoded with a higher power. However, soft handoff in the forward link requires active transmissions from all the base stations participating in the soft handoff, and thereby consumes more system resource and generates more interference compared with hard handoff. A study of the performance of forward link handoff is therefore important to make clear these mixed effects on the system capacity. In this section we compute and compare the moments of the path loss ratio vc under different handoff schemes. The results can be used in the formulas derived in the last section to completely determine the forward link capacity. 50 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.4.2.1 Hard handoff First let us compare the two path loss ratios defined in the reverse and forward link context. W ith the help of Figure 2.2 and Figure 2.4, we find that the path loss ratio uC j = aC j/aoj for the reverse link and uct = a^ijaci for the forward link have almost the same physical meaning, both are ratios of the path loss between a user and the base station which the user “belongs to” and the path loss between the user and another base station. If the reverse link and the forward link have the same statistical properties, the two path loss ratios should follow the same distribution. Note that the path loss ratio in the forward link also has the meaning of normalized other cell interference as the reverse link (2.3.3). The correspondence between a neighbor cell and its associated sectors (Figure 2.3 and Table 2.1) discussed in the reverse link also exists in the forward link. For example, in Figure 2.3 the interference from base station 7 to the “base sector” in the local cell 0 is equal to the interference from the base station 0 to sector 7. Therefore, the evaluation of the path loss ratio vci in the forward link hard handoff 51 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. under the hysteresis model is completely analogous to the reverse link. Namely, if v '- is the path loss ratio from base station 0 to sector j , then vi = r j e i r0 me o r™e o rT* i r ? e i rfe j r p €0 rme ■ 1 j when > A otherwise when > A otherwise and the path loss ratio vc for cell c is determined by U > !) (2.60) m U c jesc 1 6 (2.61) (2.60) and (2.61) are exactly the same as (2.45) and (2.48). Consequently, the moments of vc are calculated from (2.46), (2.47), and (2.61). Note that the handoff margin A dB — 0 may refer to the soft handoff in the reverse link, but in the forward link this condition only describes the case where the mobile user communicates with the single base station having the strongest pilot. This hard handoff without hysteresis margin is rarely implemented in reality due to the ping-pong effect. We will use this case for comparison purpose only. 52 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.4.2.2 Soft handoff: Equal power assignment In forward link soft handoff under the hysteresis model, when the relative pilot strengths from the two neighbor stations fall into the handoff range, or equivalently, the path loss ratio falls into the range the mobile user begins to receive signal from both base stations (in a two-way soft handoff). Usually when the user is in the soft handoff region it is located near the border of the two cells, or it has about the same distance to the two base stations. Then each station transmits to the user with about the same power as the result of power control, if the channel conditions from both stations are similar. Hence, we assume equal transmission power from the two base stations to the user for modelling this situation. Let ( f > 0 i and (pn be the fractions of the maximum base station power transmitted to user i in the base sector from cell 0 and cell 1, respectively. The total received signal power for user i is then m a x (2.63) 53 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The BIR expression (2.50) needs to be rewritten as To i = + 4 > li r0 £0 i rl eU W (1 - f o ) roi€oi r™e u r'.f c = 2 ™ 01 (2.64) Under the equal transmission power assumption < p o i = 4> u, so we have (note S0 ^ Pmax)i Poi'JO i w r^eoi S 1 rTitu So M + E c = 2 r™ i€ o i Sc So when 1 < ^ < A A rlieli 1 + r0ie0i r fc u -l (2.65) where the first term in the square bracket contains the path loss ratios from cell 0 and cell 1, and the second term is for other cells. The base station transmission powers S0, Si, and Sc can be handled by (2.53). Note that the user consumes totally ^(pOiPmax power from the two base stations. 54 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. When the user is not in the soft handoff, the path loss ratio is defined as in hard handoff. Therefore, we have the following path loss ratio definitions 2 ( 1 - fo) r^e o r™ e i 1 + 1 - f o rpep r?e i when -j- < A otherwise when rpeo r™ e i < A r j e o < 1 rre i A r'oe0 1 + rT fi rj"e0 rpe 0 y*iti _ 'j O 0 eo -m , '.7 fc J e0 p h ---- r o €o rfe i when when ! < ! £ 2 < a A r f d rpep r?e i 1 + r™€i m q r . V • 'j when when when !AA£ < _L rfe i ^ A »0 *0 1 -r < A ^ 0 rre i (2.66) < A (j > 1) where we have omitted the subscript i. 55 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The capacity formulas (2.58) and (2.59) are still valid in this soft handoff scenario, but the mean and variance of $ should be updated to where m V c and vV c are determined by (2.61) for c ^ 1 , and u0 = v'0. Unfortunately, the moments of z/ defined by (2.66) can not be calculated an alytically as in the reverse link (2.47), but have to be evaluated by Monte Carlo 2.4.2.3 Soft handoff: M aximum ratio power assignm ent Since maximum ratio combining is performed in the CDMA receiver, it is reasonable to have a similar power assignment scheme in soft handoff, namely, assigning more power to the better channel, so that the system resource is used most efficiently.2 This power assignment can be achieved by the base station controller [16, 39]. Under this power assignment model, the transmission power to a user from a base station is inversely proportional to the path loss between the base station and the user, i. e. c=0 j =1 (2.67) simulation. Some numerical values will be shown in Section 2.4.2.4. (2.68) 2 This observation is owing to Dr. Vincent Lau who was in the faculty of the University of Hong Kong and now works for Bell Labs, Lucent Technologies. 56 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. As in the last section, we can get the expression for ( f > 0 i from BIR RpiJOi w rTi^u So M r ^ o i Sc c=2 r ri£ci So 1 + r'6^oi rTitu - i w he„ I < ^ A r%eu < A (2.69) Since the total amount of power the user consumes is (4>0i + 4>1 i ) P m a x — < t> 0iP m ax (2.70) 57 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the path loss ratios for the maximum ratio power assignment soft handoff are defined to be r0 ep 1 1 + 1 - f o r™ e0 rT d rpeo r?e 1 1 *o*e0 . when — < -------< A A rfe j otherwise (1 - fo) 1 + r0 r™ e0 r™ei / r^ei 1 + 7q g Q rfe i 0 ' j when when when r j e 0 < j. r^ex " A r'oto 1 - 7 - < A r'{‘e x < A rpeo r?e 1 1 + /ytTTL £■ \ iy>TTl/ f- r o €o \ r0 e0 1 + rTfi rfe,- r o 6o r^ex r-ej -^2— when when when roleQ rV1 6x I < S 5 » < a O' > l) A rfe 1 w ' 7 "o e0 rfe 1 (2.71) The moments of these path loss ratios can only be evaluated by Monte Carlo simulation. The expressions for mean and variance of $ are the same as the equal power assignment (2.67). 58 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2.5: Moments of vc in different handoff scenarios (forward link) (A dB = 6 dB) Shadowing Hard handoff Equal power Maximum ratio dev. ae mean m u var. vv mean niv var. vv mean m v var. vv 2 dB 0.742 0.148 0.654 0.028 0.598 0.026 4 dB 0.785 0 .2 2 0 0 .6 6 6 0.038 0.609 0.033 6 dB 0 .8 6 6 0.369 0.702 0.080 0.639 0.060 8 dB 1.042 0.980 0.827 0.480 0.747 0.341 2.4.2.4 Num erical values for v Table 2.5 shows the values of the mean and variance of v with the handoff margin A = 6 dB. The values are the sums of uc from all neighbor cells. Except the hard handoff scenario (where the moments of v are the same as in the reverse link), the values for the soft handoff are obtained by simulations as the following. 1 0 0 ,0 0 0 samples are generated for uniformly distributed user locations (in polar coordinates) and lognormally distributed shadowing variables. The path loss ratio v is then produced by the corresponding formulas (2.66) or (2.71) and its mean and variance are evaluated from the 100,000 samples. The data shown in Table 2.5 are the average value of 100 such experiments. These data tell us that the soft handoff can considerably reduce the path loss ratio and thus the other cell interference. This translates to higher system capacity, as we will see in the numerical results in Section 2.6. N ow let u s fix th e sh adow in g d ev ia tio n cr£ = 6 d B , an d see th e effect o f ch an ging the hysteresis margin A. From Figure 2.5 we see that soft handoff produces both 59 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. smaller mean and variance of v than even the hard handoff with no hysteresis margin (i. e. the user is always communicating with the base station with the strongest pilot). The mean m v in the equal power soft handoff displays an interesting track that it first decreases with the increase of A, then increases when A is greater than 4 dB. This is because when A is too large, the requirement of equal transmission power from the two base stations may result in excessive power demand from the base station with a relatively weak pilot signal. The maximum ratio soft handoff, on the other hand, can always benefit from the increase of A, showing that this is an appropriate method for forward link soft handoff, if arranging the power assignment (by the base station controller, for example) does not cause too much signaling overhead in the system. 2.5 Other Considerations 2.5.1 Variable d ata rates Since in the capacity formulas we only care about the first two moments of the variables, the data rate variations can be taken care of by just plugging their means and variances into the suitable places of the formulas. The new formulas will contain the moments of the product variables (R ■ 7r) and (R ■ n ■ v). The validity of this method of adding new variables depends on the its effect on the tail of the product variables. 60 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. — t - hard handoff ■ -*• • equal pow er -© - maximum ratio E o A € a o c 0.7 0 4 6 8 2 Handoff hysteresis m argin A (dB) (a) mean of v - + - hard handoff -*• • equal pow er - © - m aximum ratio 0.5 1 04 A V) o I 0.3 CL ■S 0 .2 •c A > Handoff h y steresis m argin A (dB) (b) variance of v Figure 2.5: Moments of the path loss ratio v (ae = 6 dB, forward link) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. X R. a Figure 2.6: Two-state Markov source model For example, the simple two-state Markov source model (Figure 2.6) are widely used for voice, bursty data, or even as a simple model for video source. In this model the source has two states, a and b, and in each state it generates traffic with a fixed data rate, R a or Rj,, respectively. The holding time at each state is exponential. Under this model the data rate of the generated traffic at any given time is a random variable taking two values R = Ra with prob. p Rh with prob. 1 — p (2.72) where p = is usually called the activity factor of the source if R& = 0 . R has mean m,R and variance vr given by m R = pRa + (1 - p)Rb , vR = p{ 1 - p)(Ra - R b f (2.73) 62 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. There exists a similar model called Markov-modulated Poisson process (MMPP), where the traffic generated from the two states are both Poisson processes. The MMPP model is regarded as a better model for video source than the two-state Markov model [47]. If the average data rates of the two Poisson traffic are equal to Ra and Rb, respectively, the moments of the overall data rate can also be calculated by (2.73). Since in these Markov models the distribution of the data rate variable does not have a long tail, it should be able to be directly incorporated into our capacity formulas. 2.5.2 E ffective virtual bandw idth When we compare the performance of two multi-service systems, say two systems with the same kinds of traffic but different handoff schemes, what metric should we use in order to say that one scheme can achieve higher capacity than the other? Usually people use the total data rate that can be supported in the system as the measure of system capacity or bandwidth efficiency. This metric, however, is not accurate enough in the multi-service environment, since it does not take the QoS into account. For example, 10 kbps voice signal and 10 kbps FTP stream should not consume the same amount of system bandwidth, because the voice traffic can tolerate more errors than the FTP traffic. In other words, given the same system bandwidth, more voice users can be accommodated in the system than FTP users with the same (average) data rate. 63 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. From the capacity analysis in the last sections, we find that the aggregate product of data rate and BIR may be a good choice for the system performance measure (in terms of capacity or bandwidth efficiency). As mentioned in (2.28), the virtual bandwidth utilization l o can be thought as an index of the system load, and it consists of the user traffic within the cell R°w'h an<^ ^he interference from other cells R < w'J I attenuated by the path loss ratio vc. Therefore, we define No C = J ^R o a o i (2-74) i =1 or the “effective” part of the virtual bandwidth (consumed by the traffic in the local cell) as the system resource utilization index. C is called the effective virtual bandwidth of the system. It is easily seen that the maximum value for C in the reverse link is (1 — rj)W when there is no other cell interference, while in the forward link this maximum value is 2— @-W. • L - Jo 2.6 Num erical Exam ples We consider a system with three diverse traffic types (service classes) as listed in Table 2.6 (together with system parameters). Classes 1 and 2 are high-speed bursty traffic, while class 3 is voice-like traffic. For simplicity we assume homogeneous traffic distribution, i. e. the services and number of users in each service are exactly the same 64 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. in each cell. Although our capacity formulas can be applied to heterogeneous traffic environment (with similar total amount of interference in each cell), simulations for this case require the inclusion of the power control procedure so that the signal and interference power can be determined. We perform experiments as the following. First we solve the capacity formulas ((2.37) or (2.43) for the reverse link and (2.58) or (2.59) for the forward fink) with given system parameters. In order to let the solved number of users fall into a good range, we choose N\ to be half of its maximum possible value, then choose jV 2 to be one less its maximum possible value with the given Ni, and finally calculate N 3 using the determined Ni and JV 2. Based on the solved {iVf c } we then run simulations on the 19 (two tiers) overlap ping circular cell layout to “measure” the outage probabilities and compare them with the target values, so that the errors of the Gaussian and lognormal approxima tions can be examined. In each simulation, 100,000 random samples are generated for each user’s location, data rate, shadowing, and imperfect power control factor, respectively, according to their stochastic models. The instant system load (virtual bandwidth) is then evaluated from (2.27) or (2.57), and the number of its samples exceeding the limit ((1 — rj) in the reverse link or (1 — 3) in the forward link) is counted and divided by 1 0 0 ,0 0 0 to produce the simulated outage probability. 65 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2.6: System and traffic parameters in an example multi-service system System bandwidth W = = 15 MHz Path loss exponent m == 4 Reverse link parameters Noise to interference ratio limit 7 = 0 .1 Imperfect power control dev. *br,r = 2.5 dB Forward link parameters Orthogonality factor fo = = 0.7 Common control power fraction (3 = 0 .1 Imperfect power control dev. = 1 dB Service class Data rates Act. factor BIR k (f^fe,fli Rk,b) Pk 71 1 (1 Mbps, 100 kbps) 0.08 6 dB 2 (384 kbps, 0) 0.15 5 dB 3 (9.6 kbps, 0) 0.35 4 dB 2.6.1 R everse link results The solutions {Nk} for the reverse link with hard handoff (hysteresis margin A = 4 dB) and soft handoff are shown in Table 2.7, and the simulated outage probability in Figure 2.7. Note that the outage probabilities are plotted on a log-log scale. Table 2.7 shows that the system in soft handoff has more capacity (in terms of effective virtual bandwidth C) than hard handoff, but the capacity gain is not so large as compared with the results in the voice only system [53]. This implies that the data rate variations may have considerable effect on the system capacity in CDMA. 66 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 2.7: Capacity solutions in the reverse link (Lognormal approximation) Outage IV i Soft handoff Hard handoff (A=4 dB) prob n 2 n 3 Virt b.w. (MHz) n 2 IV 3 Virt b.w. (MHz) 0.005 1 5 1 0 2 2.456 3 116 2 . 2 1 0 0.007 1 7 80 2.635 5 89 2.347 0 .0 1 1 9 77 2.974 7 84 2.669 0 .0 2 2 1 0 43 3.554 8 47 3.223 0.03 2 13 50 4.159 1 1 58 3.863 0.05 3 14 29 4.849 1 2 39 4.569 0.07 3 17 37 5.463 15 49 5.200 0 .1 4 17 28 6.072 15 40 5.809 0.2 0.1 0.05, 0.02 0 .01< ^ — target value - o - soft handoff, lognorm ■ hard handoff, A=4dB, lognorm - d - soft handoff, G aussian -+• - hard handoff, A=4dB, G aussian 0.005 0.002 0.005 0.007 0.01 0.02 0.03 T arget outage probability 0.07 0.05 Figure 2.7: Simulated outage probabilities for the reverse link R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. It can be seen from Figure 2.7 that the simulated outage probabilities under our lognormal approximation can generally follow the slope of the target outage probability. There is a gap between our results and the target values, but the gap is much smaller than the Gaussian approximation results in the usual operating range of 5 = 0.01-0.05 in most CDMA systems. This is the reason why we only consider lognormal approximation when comparing the effective virtual bandwidth between the soft handoff and hard handoff Table 2.7. 2.6.2 Forward link results Figure 8 (a) and Figure 8 (b) illustrate the simulated outage probabilities and effec tive virtual bandwidths, respectively, of forward link simulations. Two soft handoff schemes (equal power assignment and maximum ratio power assignment) and the “ideal” hard handoff (with hysteresis margin A = 0) are simulated and compared in these figures. It can be clearly seen that the two soft handoff schemes outperform the hard handoff even no hysteresis margin is considered, and the maximum ratio soft handoff has the highest bandwidth utilization (in terms of virtual bandwidth) among the handoff schemes in consideration. The outage probability results Fig ure 8 (a) shows more accurate data of both lognormal and Gaussian approximations in the forward link than the reverse link (Figure 2.7), which reflects the effect of larger imperfect power control deviation in the reverse link. 68 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. & 0.05 target value maximum ratio, A=6dB, lognorm #- equal power, A=6dB, lognorm • hard handoff, A=0dB, lognorm maximum ratio, A=6dB, G aussian equal power, A=6dB, G aussian • hard handoff. A=0dB. G aussian 3 0.01 0.005 0.05 0.07 0.02 0.03 Target outage probability (a) simulated outage probability - e - m axim um ratio, A=6dB, lognorm -H - equal pow er, A=6dB, lognorm hard handoff, A=0dB, lognorm 513 5 12 S 1 1 0.005 0.007 0.01 0.02 0.03 0.05 0.07 0.1 T arg et o u ta g e probability 8 (b) simulated effective virtual bandwidth Figure 2.8: Simulation results under different handoff schemes in the forward link 69 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. It should be noted that the capacity of reverse link can be dramatically increased (more than doubled) by applying multiuser detection and antenna array at the base station [39], which are not considered in our analysis. At the same time, these techniques do not provide a large capacity gain on the forward link. The overall reverse link capacity with these new features may even overrun the forward link. Therefore, the results shown in this dissertation do not provide an accurate estimate on the reverse link and forward link capacity in systems with multiuser detection and antenna array. However, we have provided a general framework on the CDMA capacity analysis, and hopefully the capacity gain provided by multiuser detection and antenna array can be easily added into our analytical model. 70 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 3 Capacity of M ultiband Overlaid C D M A System s CDMA inherently supports spectrum overlay, where systems with different services and bandwidths share the same spectrum [4, 42]. Although this kind of systems have not been brought into reality yet, we believe they will appear in the future, because of the needs of accommodating various services with different resource requirements, deploying multiple wireless networks within the same spectrum, and ensuring com patibility among systems with different protocol versions in the future multi-service wideband CDMA systems. Among the various services (voice, video, packet data, etc.) that will be provided in the 3G/4G CDMA systems, not all of them require the large bandwidth (above 10 MHz) provided by the next generation wireless systems. For example, the 1.25 MHz channel bandwidth in existing IS-95 systems is quite adequate for voice-oriented handsets, which may still be preferred by people who are not interested in watching videos on the move. Spreading the signal over excessive bandwidth will increase hardware cost in the handset. On the other hand, in the proposed wideband CDMA 71 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. standards channels of different bandwidths are supported, so that a service provider has the flexibility to choose one or more kinds of channels, or any combination of them, to accommodate multiple traffic types. In fact, the pre-defined channel band widths in the Europe/Japan-proposed WCDMA and the North American standard cdma2000 are 1.25/5/10/20 MHz and K x 1.25 MHz (K = 1, 3, 6 , 9, 12), respec tively, and data rates ranging from 2.4 kbps to 2 Mbps are to be supported in these systems [38]. In addition, when a wideband CDMA system is deployed in the same service area as the narrowband IS-95 system, spectrum overlay may occur if the two systems occupy the same spectrum band. In cdma2000 there is a multi-carrier option sup porting this kind of spectrum overlay [28]. In fact, wideband CDMA systems allow arbitrary spectrum overlay as shown in [4], Since bandwidth resource is very lim ited, it may be very hard to allocate multiple continuous wideband spectra (e. g. 2 0 MHz) for CDMA systems in a place. Hence, in a geographic area with large pop ulation (e. g. a city) several wideband CDMA service providers may have to share the same spectrum, unless there are only one or two “CDMA monopolies.” The gradual development of wideband CDMA systems may also result in several phases of implementation with different system bandwidths, and spectrum overlay provides seamless compatibility among different versions of CDMA standards. 72 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In the existing proposed systems, the multi-carrier CDMA [28] can be thought as a special case of the multiband system without. A similar approach for uplink communications is also proposed in [3]. The performance analysis of overlaid multiband CDMA systems is more difficult than the single-band system, since the amount of interference in overlaid subbands is dependent on the “overlay pattern” . The analysis of bandwidth utilization and system capacity is essential to many system-level issues such as cell planning, ad mission control, and resource allocation. In [24] and [26] the authors have made the reverse and forward link capacity analysis for the simplest CDMA overlay system which is single-cell (isolated), perfectly power controlled, and consisting of subbands with at most three different bandwidths with special relationship among the band widths. To prepare for all possibilities, we need a more general method that can solve a arbitrary overlay pattern and can consider imperfect power control, other cell interference, and different power constraints among the subbands. This is the objective of this chapter. 3.1 System Layout and Definitions Figure 3.1 illustrates an example of multiband spectrum overlaid CDMA systems, where we use rectangles to represent subbands. The width of a rectangle shows the relative bandwidth of a subband. The height of a rectangle has no meaning since we only care about the bandwidth relationship of the subbands. As a convention we 73 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 3.1: An example of multiband spectrum overlaid system always put a smaller subband (in terms of bandwidth) on top of a larger subband if they have overlapping spectra, and we say the larger subband is overlaid with the smaller subband. For the convenience of our discussion, we define some terms regarding the over laid spectrum layout. A subband is called a top subband if there are no other subbands overlaying it. All subbands overlaying a common subband, together with the common subband, form a overlay group, and the common subband being over laid is called the base subband of the group. For example, in Figure 3.1 subbands W3, W4, and W 5 are top subbands, and there are two overlay groups in this layout: {W2, 11'4 , W5} with base subband W2, and {W 4, W2, H 3 , W4, W5} with base subband W\. In this chapter Wk denotes both the bandwidth of subband k and subband k itself, when causing no confusion. Wi is always the largest subband spanning the entire system bandwidth. Note that any subband, if it is not a top subband, is always a base subband of a overlay group. Assume that in each subband there is only one kind of service, since a subband with two or more services can be just split into multiple subbands with the same 74 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. spectrum band. The quality of service (QoS) can be characterized, as in the single band system, by the bit energy to interference density ratio (BIR) in the receiver, denoted as j ki for user i in subband k , which is calculated from the received signal power S^, data rate of the service Rk, total interference power from other users Iki, and bandwidth Wk, as [18, 52] Iki = -J 5 “ (3-1) J-ki Kk and the target BIR for the service class in subband k is denoted as 7 ] * . For conciseness we use constant bit rates {Rk} in the multiband system. Variable bit rates can be accommodated in the same way as in the single band system (Section 2.5). 3.2 General Overlay Pattern A nalysis Most part of this chapter deals with the reverse link capacity analysis for multiband systems. The forward link analysis is similar to the reverse link and it is only discussed in Section 3.3.2 for simplicity. 3.2.1 R everse link capacity constraint For our convenience of discussion we first consider a single cell system with a general spectrum overlay pattern under perfect power control. Later we will extend the results to include the imperfect power control scenario. Other cell interference will be discussed in Section 3.3. 75 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. When power control is perfect, signals for all users in subband k are received at the same power level in the base station because these users are in the same service class. The received BIR 7 7 is also controlled at its target value for all users, and calculated as *k -ftfc The interference power Ik (including noise) in subband k consists of four parts: the total received signal power from all subbands overlaying it, the total interference power from other users within the subband k, a portion of received signal power from all subbands it overlays, and the thermal noise power. Since in a subband the signal power is uniformly spread over the spectrum covered by the subband, if subband j is overlaid with subband k (and thus has a spectrum broader than subband k), the interference received by subband k from subband j is a fraction W k/ W j of the total signal power in subband j. Define Bk the set of all base subbands overlaid by subband k, and Qk the set of all subbands in the group with base subband k (including subband k itself), then the total interference in subband k is equal to (3.3) where n 0 is thermal noise density (assumed to be the same in all subbands), N t is the number of users in the subband i, and L is the number of subbands in the system. 76 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (3.2) and (3.3) can be combined into (Kk- N k) S k - Y J NiS ^ - Y J N iS i= n Q Wk (k = l ,. .. ,L ) (3.4) *eef e * ieg'k where Kk = „ k is actually the maximum number of class k users in Wk for a single Rkik band system with Wk [18, 52], and Q 'k contains all the subbands in Qk except the subband k. (3.4) is a set of linear equations for {S tjjtli. Let M = [ ] be its coefficient matrix where rriij = K i-N i i = j - Nj ^ when j e Bt - N j j e g ; 0 otherwise (3.5) and vectors s = [S1, S 2, - - . , S l } t n = [n0Wu n0W2, ■■■,n0WL \1 then the matrix form of (3.4) is M s = n (3.6) 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. If we temporarily do not consider the interference-limit constraint, it can be proved that (3.6) has positive solution for s if and only if det(M r) > 0 (r — \ ,...,L ) (3.7) where M r is the principal submatrix containing the first r rows and columns of M. Since det(M r)(r = 1 ,L) are explicit expressions for the number of users {Ar f c }, (3.7) is just the capacity formula for a general overlaid multiband CDMA system. Actually, among the L inequalities of (3.7), only the one with r = L, i. e. det(M) > 0 contains all {iVk}£=1. The other (L — 1) inequalities serve as nec essary conditions to rule out unrealistically large solutions of Nk- Such solutions result in some negative £*,, and thus have no physical meaning. 3.2.1.1 P ro o f of G eneral C apacity C o n strain t As derived earlier in this section, the general capacity constraint assuming perfect power control is determined by the positivity requirement on the solutions of M s = n (3.6), where M is the coefficient matrix of the linear equation set (3.4), s is the vector of received signal powers in each subband, and n is the vector of noise powers in each subband. Note that the constraint on M exists only for our multiband capacity problem, not for a general equation in the format of (3.6). For th e con ven ien ce of proving th e con strain t, w e d ivid e b o th sid es o f (3.4) b y Wk, but still write the matrix form of the new equation set as M s = n. Now s is 78 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. still the vector of received signal powers, n becomes a vector with all elements equal to n 0 (noise density), and the elements of M = [my] change into Kj — Nj Wi when j € B{ i = j rriij = w, El 'Wi ( ■ i,j = 1,... ,L) 0 3 G G [ otherwise where L is the number of subbands in the system. As an example, the matrix M for the system shown in Figure 3.1 is M = ki- N i W t N % _ Wi N 3 Wi - E l W i JV 5 Wi JV i Wi k2- N 2 W 2 0 - E l w 2 n 5 w 2 El W i 0 kx— Nz w 3 0 0 ^ E l W i Ni W 2 0 K4—N4 W 4 0 E l W i n 2 w 2 0 0 — Nr, w5 For conciseness we use the following notations: 79 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. M; coefficient matrix of system with subbands 1 through I; M 2 ); coefficient matrix of system with subbands 2 through Z ; (a) same as M; except that all elements in k-th column are replaced by a; Di D2J . D\k\a ) determinants of corresponding matrices M;, M 2 ];, and M \k\a) si s2,1 vectors of received signal powers in corresponding systems; S; > 0 all elements of S ; are positive. W ith these notations, the proposition that the system with L subbands is within its capacity limit if and only if det(M r) > 0 for all r = 1,..., L is, equivalently, s i > 0 if and only if Dr > 0 for all r = 1,..., L (3.8) In the following we prove this proposition by mathematical induction. When L = 2, (3.8) is easily proved by directly solving the equation set (3.4). Suppose (3.8) holds for L = I, i. e. any system with I subbands is within its capacity limit (s; > 0) if and only if its Dr > 0 for all r = 1 . When L = I + 1, for either the “if” or “only if” part of (3.8), we have s; > 0 or Dr > 0 for all r = 1,... ,Z because of the following: (1) This is obviously true if Dr > 0 for all r = 1,...,Z + 1 (the “if” part). (2) If s;+i > 0 (the “only if” p art), w hich m ean s th is sy stem w ith I + 1 su b b an d s is w ith in its ca p a city lim it, w e 80 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. take away subband I + 1 and keep other subbands unchanged, the new system with subbands 1 through I must also be within its capacity limit, and thus s; > 0 . Now we add the (I + l)-th subband back, but not with the original iV ;+ 1 users. Instead, we increase the number of users from 0 to Ni+i (here we take the number of users as a real number instead of an integer, for the purpose of our proof). At the beginning the system must be within its capacity limit, i. e. S/+i > 0. We consider another system with all subbands (and the users within the subbands) except subband 1 of the given system. At this time it must also be within the capacity limit, i. e. s2,/+i > 0. Since there are I subbands (subbands 2 through I +1) in this system, we have D2 > i+i > 0 according to the last step of the induction, and thus D $ +1(no) > 0 for all k = 1,..., I by Cramer’ s rule. Taking advantage of the special structure of the coefficient matrix Mj+i, it is straightforward to prove the following identities k = 1,..., I + 1. (Note that D ^ ^ a ) and .0 ^ (1 ) have the same sign if a > 0.) We then increase the number of users in subband I + 1 to the given W+i- If the original system can accommodate N/+- \ users in subband I + 1, i. e. s ;+1 > 0, from (3.9) i = 1 a (5m = ( k = 2, . . . , i + 1) Therefore, if s2i;+i > 0 and thus jD^z+i^o) > 0 , we have D ^^rio) > 0 for all 81 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the above discussion we know s2 i;+i > 0 so (n0) > 0 for all k = 1,..., I + 1 , and thus Di+ 1 > 0 by Cramer’ s rule. On the other hand, if S ;+1 > 0 does not hold for the given Ni+ 1 users in subband I + 1, we show that D;+1 must be negative. Consider the point when the number of users in subband I + 1 just exceeds the capacity limit. At this time s2,;+i > 0 still holds because the system without subband 1 can accommodate more users in subband I + 1 (recall that subband 1 is assumed to overlap with all other subbands). Hence, D^^rio) > 0 for all k = 1,..., I + 1. We claim that Di+i < 0 at this point because if it is not true then s;+ 1 > 0 by Cramer’ s rule x. Furthermore, since only the last column of M ;+ 1 contains Ar i+i, the derivative ( \ ^!+ ~ is independent of 7 V (+i- dNi+ 1 Hence, A + i should be monotonically decreasing with W+i- Consequently, Di+\ < 0 at the given A ^ ;+i. Since the system with subbands 2 through I + 1 may not have a subband overlap ping with all other subbands, we should also consider this kind of disjoint pattern. However, in this case we can simply perform the same analysis on the sub-system containing subband l + l (i. e. disregard the rest of the system which has no influence on subband l + l). We have proved S/+i > 0 if and only if A + i > 0; given Dr > 0 for all r = 1,..., /, and thus completed the last step in the induction. xWe do not consider the unstable case D i+\ = 0. 82 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) vertical (b) ver- (c) horizontal pattern pattern tical pattern after the first merging Figure 3.2: Two basic overlay patterns 3.2.2 T h e decom p osition m eth od A major problem with the capacity formula derived in the last section (3.7) is that it needs to calculate the determinants of high-order matrices, which are long ex pressions with high-degree terms (e. g. the product N 1N 2 ■ ■ ■ N&) when expanded. In this section we introduce a way to decompose a general overlay pattern into two basic overlay patterns, so that the general capacity formula (3.7) degrades to a set of low-order expressions. The decomposition method also plays a major role in the following sections in discussing the maximum bandwidth utilization conditions, systems with power constraint, and imperfect power control. 3.2.2.1 Basic Overlay Patterns The two basic overlay patterns are named vertical pattern and horizontal pattern. In the vertical pattern (Figure 3.2(a)) all subbands overlap each other, while in the 83 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. w w w W, w W, w w w, w W, (a) example system (b) merging of W 4 and We into W (c) merging of W4 and W 5 into W 'l w2 w 2 w2 w W, I W, (d) merging of W 4 and W 2 into W ! ± Figure 3.3: Merging of basic overlay patterns in a multiband system horizontal pattern (Figure 3.2(c)) all subbands except the largest one are mutually exclusive with each other. A general overlaid multiband system, no matter how complicated, can be seen as combinations of these two basic overlay patterns. For example, in Figure 3.3(a) the subbands W4 and W6 form a vertical pattern. If W4 and W6 can be “merged” into an equivalent subband W4 without affecting the capacity of other subbands, the three subbands W2,W^ and W5 will form a horizontal pattern (Figure 3.3(b)). We can continue this merging process until the system contains only a horizontal pattern (Figure 3.3(d)). From another angle, this procedure can be seen as decomposing the system into basic overlay patterns. The benefit of this merging/decomposition is the reduction of the problem scale, which results in low-degree capacity formulas. (In Figure 3.3(a) W5 and W6 are examples 84 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. of subbands combined from two identical subbands with the same bandwidth and service class.) V ertical p a tte rn — Consider a vertical pattern with L subbands (Figure 3.2(a)). Without loss of generality, assume that W\ ^ W2 ^ W3 - A WL, then the total interference in subband Wk is equal to the total signal power from subbands Wk to Wl plus partial signal power from subbands W\ to Wk-\- Hence, we have, by (3.4), (Kf c - Nk) S k - J 2 - J ] NiSi = n0Wk (k = l ,.. ., L ) . (3.10) capacity of other parts in the system. Due to the special structure of (3.10), we find that this merging can be performed in the “top-down” order. First Wl and Wl- i is merged into W[_x (Figure 3.2(b)), then W^_1 and Wl- 2 is merged into W'L_2, and so on, until only W '^ and W\ are left in the vertical pattern. At each step of this merging, say W'k and Wk_1, the resultant W'k_l has the same bandwidth as Wk_lt and it contains N'k_1 users of service class k — 1. A r( ._ 1 can be found as where N'L = N l, so that the two subbands W'k and Wk-i together have the same interference on the rest of the system as the merged subband Wk_k, i. e. N'k_lSk_] = k - 1 L 1 We need to find a general procedure of merging subbands without affecting the (3.11) 85 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Nk-iSk-i + N'kSk- We name Wk_l the class-(fc — 1) equivalent subband of W'k and Wk-i, and Nk_x the class-(k — 1 ) equivalent capacity of Wk and Wk-i- Finally, for the last two subbands W'2 and W\ we apply the general capacity formula (3.7) and expand it as (L = 2 in the vertical pattern) with an additional requirement N\ < K\. By this means, we can “decompose” the capacity formula of the vertical pattern into (3.12) and (L — 2 ) equations for equivalent capacities (3.11), with a degree of two in each of these expressions. H orizontal p a tte rn — We repeat the above analysis for horizontal pattern, where all subbands W2 to WL are disjoint, and each overlays Wi (Figure 3.2(c)). Again we can set up L linear equations for {£'fc} £ _ 1 The expansion of the capacity formula (3.7) for horizontal pattern has a short, though still high-degree, format as (3.12) (3.13) (3.14) 86 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Note that (3.14) includes all the L inequalities in (3.7). To decompose the capacity formula, we can merge any two subbands W) and Wj (2 ^ i. j ^ L ) into an equivalent class-* subband W [ with bandwidth W t + W j , and the equivalent capacity N ' is determined by W - N - W - N ■ W - N - ’ ’ - ‘ ( 2 < i J < L ) (3.15) K • - N [ Ki — N i Kj ~ N j where W - = W t + W j , k [ = n 1 . This equation has a degree of three. A A W ! ' i± or/ I ir/ » By using (3.15) repeatedly until all subbands W 2 through W l are merged into one subband W'2, the remaining system is a vertical pattern with two subbands and Wi, and (3.12) is applied with K 2 replaced by k'2. C om bining th e basic p a tte rn s — Since any general overlay pattern can be decomposed into combinations of the two basic overlay patterns, we can always apply the merging process to the “top” two subbands in either the vertical or the horizontal pattern, until the system turns into a basic overlay pattern. Figure 3.3 shows an example of this procedure. Following these steps, the decomposed system capacity formula is obtained as a set of expressions in the format of (3.11), (3.12), and (3.15). One way to determine {Nk}k-i from the decomposed capacity formula is as follows: choose an appropriate N i from (0 , k,j); find N'2 from (3.12) with given N x] choose an appropriate iV 2 from (0, N 2)\ find N'3 from the equation for N 2 ((3-11) or (3.15)), and so on. Complete solutions can be easily calculated in this way. 87 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (a) (b) (c) (d) w w w2 w w w, (e) Figure 3.4: Partially overlaid cases 3.2.2.2 P a rtia lly O verlaid Cases Apart from the two basic overlay patterns, we may also encounter partially overlaid cases where one or more subbands are partially included in other subbands, such as subbands W2,W 3 and W4 in Figure 3.4(a). Such cases should generally be avoided in system planning, because they may greatly impact bandwidth allocation, power control, call admission, etc. due to complicated power interaction among the overlaid subbands. Under the assumption of perfect power control, however, they can be split easily into the basic overlay patterns. Hence we discuss such cases here for completeness. To obtain the capacity formula for a partially overlaid system, simply split a subband along the border of the subbands it overlays, so that the system turns 88 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. into a combination of the basic vertical and horizontal patterns. For example, in Figure 3.4(a) we split W4 into W4a and W4h, the partially overlaid W2,W 3 and W4 it can be easily shown that the two systems in Figure 3.4(a) and Figure 3.4(b) are equivalent so long as — llpL — i. e. the number of users in the subband W ia W 4b W 4 after splitting is proportional to the bandwidth left in this subband. This result is valid for all partially overlaid cases, such as those in Figure 3.4(c),(d),(e). 3.2.3 M axim um ban dw id th utilization Each capacity formula of a given overlaid multiband system has multiple boundary solutions {N k}£=1. Therefore, it would be interesting if we can find “optimal” over lay patterns or “optimal” solutions with a given overlay pattern. Here we borrow the effective virtual bandwidth defined in the single-band system as the metric of optimization, and rewrite it for the multiband environment as where Ck = NkRklk is the effective virtual bandwidth of the service class in subband k. In the following, we derive the general conditions to achieve maximum effective virtual bandwidth C using the two basic overlay patterns. are resolved into two vertical patterns (Figure 3.4(b)). From interference analysis (3.16) A 89 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. V ertical p a tte rn — From equation (3.11) of the merging process we have (recall that Wk- i ^ Wk) where C 'k = N'kRk^k- Equality holds in (3.17) only when Wk = Wk_i (if C 'k ^ 0). Therefore, this merging process can preserve virtual bandwidth only when all bandwidths {lF1 }(t= 2 are equal. Furthermore, it follows from (3.12) that the boundary for C \ + C 2 = N i R ^ f i + N^R-i'n reaches its maximum value Wi when Wi = W2. Together with the merging process, we have proved that the condition to achieve maximum virtual bandwidth in the vertical pattern is (3.17) ^ Ck-i + C 'k Wi = w 2 = ■ ■ ■ = WL (3.18) and the capacity formula under this condition is reduced to L (3.19) k = 1 90 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. H orizontal p a tte rn — By applying the Lagrange multipliers on the capacity formula (3.14) of the horizontal pattern, it can be easily proved that the maximum We can show further that (3.20) results in equal interference density in all sub bands W2 through WL. Another nice feature of (3.20) is that it complies with the user fairness principle (in terms of virtual bandwidth). If W2 the capacity formula of the horizontal pattern is also (3.19). In summary, the conditions to achieve the maximum system virtual bandwidth for a general overlay pattern are given by (3.18) in each of its vertical patterns, and (3.20) in each of its horizontal patterns (including the basic patterns formed in the merging process). These conditions can be abstracted as the following principles: • Full bandwidth coverage — Every subband expands as “widely” as possible provided that the spectrum overlay pattern does not change. • Uniform power distribution — The total signal or interference power is dis tributed uniformly over the entire system bandwidth. The second principle actually implies the first one because if there is a bandwidth “gap” between two adjacent subbands in either the vertical or horizontal pattern, the interference density can not be the same over the whole system bandwidth. value of J2k= 2 is reached (for fixed Cf) when cL = c% WL W'2 (3.20) 91 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A system with uniform power distribution is in fact equivalent to the single-band multi-service case where all users transmit over the whole system bandwidth, thus taking full advantage of the interference-limited property of CDMA. For an overlaid multiband system if both of the above optimality conditions are satisfied, the capacity formula is always (3.19). 3.2.4 C onsidering th e interference lim it The above discussion has not considered the received power constraint. In (3.6) when det(M ) approaches zero, very large {S'fc } £ _ 1 are required to guarantee {7 k}k=v Considering the interference constraint, the condition limiting the capacity becomes the interference density not exceeding n0/r) in every subband, instead of just having positive signal power. Still assuming perfect power control, from (3.2) we have Sk = j~ -R k^k- Hence, yVk the general interference expressions with {Sfc}fc=i (3-3) can be rewritten as linear equations of interference densities 'k where Ik Q where Ik0 = 777- , ck = —k k^k _ —k an(j C f c js effective virtual bandwidth Wk Wk Kk utilization of subband k. 92 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. V ertical p a tte rn — Applying (3.21) to the vertical pattern (Figure 3.2(a)), we have fc-i Wi ho — C fc/jto + Cilio + Cilio^y - + no i= i i=k+ 1 (3.22) (k = l ,...,L ) (3.22) implies that the top subband Wl has the highest interference density, because I lo = ciho, while ho in any other subband (1 ^ k < L) has at least one term Cj/^VFi/fVfc) ^ Ciho- This observation also agrees with our intuition. Therefore, we only need to guarantee ho ^ no/rl- and the power constraint is then satisfied in all subbands. The coefficient matrix of (3.22) M v = [m,a] has a very special format as mij - —c W i 'JW, i < j 1 — C j when i = j (h j — T • • • > h) i > j Using Cramer’s rule, it is straightforward to solve (3.22) for ho (3.23) I T ,0 = n0 det(M-\ (3.24) Therefore, the capacity under the power constraint ho ^ no/v (k = 1 is determined by det(M v) > t ) (3.25) 93 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. And, to ensure meaningful solutions, the determinant of all the principal matrices with the first r (r = 1,..., L) rows and columns of M y should be greater than rj. Horizontal pattern — The interference density expressions of the horizontal pattern (Figure 3.2(c)) are Wi ho — c < ^i0 jy- n° i=1 (3.26) ho — ciho + C fc /fc o + U q (k — 2 , L) The solutions of (3.26) are, by Cramer’s rule, n 0 <10 det(M H' ci n 1 - Ci no Cl ho — n 0 det(M n ■ 11(1 - c.) (k = 2 ,...,L ) (3.27) i=2 i^k where M h is the coefficient matrix of (3.26). From (3.27) we see that the interference densities in subbands W 2 through W l can reach the limit no/77 at the same time, when their effective virtual bandwidth utilizations are equal, i. e. c2 = c3 = • • • = cL (3.28) Note that (3.28) is just the condition for maximum bandwidth utilization in the horizontal pattern (3.20). Since a general capacity constraint is hard to find, here we assume (3.28) to derive the constraint for maximum system capacity. 94 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. W ith the condition (3.28), the solutions (3.27) reduce to (3.29) where D < L f c = 2 Therefore, the capacity limit is obtained from the expression of ho (k ^ 2) as Note that D 2 is the determinant of a vertical pattern with subbands W 4 and W ' 2 (see (3.12)). Since C 2 in (3.30) can be replaced with any of {cfc}^=2, (3.30) suggests that each subband of W 2 through WL can take part in the capacity calculation individually as a subband with bandwidth W'2. Hence, in a general overlaid system we can separate the subbands in the “upper layer” of any horizontal pattern so that the system is decomposed into several vertical patterns, then calculate the capacity using (3.25). For example, the system in Figure 3.3 can be decomposed calculating capacity in the decomposed vertical patterns W 2 and W 3 should both have bandwidth W2 + W3 in the ratio W2/W 4 and W3/W 1, and W4 and W 5 both have b a n d w id th W 4 + W 5 in th eir b a n d w id th ratios over W 4 an d IV2 . N o te th a t w h en (3.30) into three vertical patterns {Wi, W2, W4, W6}, {W4, W2, W5}, and {W4, W^}. When 95 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. using this method the common subbands in multiple decomposed vertical patterns (e. g. W{) must be assigned the same capacity. This method, however, may give us only an approximation of the system ca pacity. When we apply (3.25) to the decomposed vertical patterns, the capacity is determined such that the top subbands of the vertical patterns (W3, W5 , and We in Figure 3.3) all have the maximum interference density no/77. Hence the subbands in the “upper layer” of a horizontal pattern (e. g. W'A and W 5 in Figure 3.3(b)) may not have the same interference density, and thus (3.28) may not hold. Fortunately, the error of this approximation is very small (a few percent) as shown by our sim ulations. Therefore, this simple method can give a good estimate of the maximum system capacity. Note also that we can not decompose the vertical formula (3.25) using the equiv alent capacity as in the last section, because the determinant of M y may change in the merging process. Fortunately, the orders of the decomposed vertical pattern determinants are not as high as the original pattern (it is approximately the number of “layers” of the original pattern), and it is possible to write a general expression for the determinant due to the special format of M y . For systems satisfying both maximum bandwidth utilization conditions defined in Section 3.2.3, the capacity formula with interference constraint can be derived as L (3.31) f c = 1 96 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.2.5 C onsidering im perfect pow er control Under imperfect power control, since the received signal powers from users of the same service class are different, we have to rewrite the interference expression (3.3) as the following iV fc N[ - j , Ni + E E « | + E E Su + n 0Wk (fc = l,...,L) (3.32) i=i i e B k i=i 1 l e g 1 *=l where subscript i denotes the user, and subscript k denotes the subband (or service class) as before. SkiWk Since 7 ki — -j— - 5 - , if we define h R k N f c t j N f z 7 ") * 1 A -ttk'Y k i /o oo\ = = (3-33) 1 = 1 i=\ i=l as the effective virtual bandwidth utilization in subband k (see (3.21)), the interfer ence density in each subband has exactly the same expression as (3.21), except that now C f c and I k0 are random numbers (note that the 7 ^ in (3.21) means 7 ^). This observation simplifies the capacity analysis because many previous expressions for perfect power control can also be applied here. As in the single band system, we have the outage probability constraint as the following Pr{/M > ^ } o (fc = 1,..., L) (3.34) 97 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. V ertical p a tte rn — Since the top subband Wl always has the highest interfer ence density, we only need to control the tail probability of IL0. Hence, the capacity constraint for the vertical pattern with imperfect power control is, by (3.25), P r{ d et(M v) < rj} ^ 8 (3.35) We derive the capacity formula for {Nk}%= i in three steps. First we expand det(M y) as, approximately, d e t ( M v ) « 1 - C i + C i C i f 1 “ ^ ) ( 3 -3 6 ) i= 1 i = 1 j = i + 1 ' ? The approximation here follows the fact that q < 1 {i = 1,..., L), or more strictly, the probability of q (i = 1,..., L) greater than or equal to 1 is very small. We simply discard those terms with the product of more than two q {i — 1,..., L) and arrive at (3.36). Next, we define * = £ « - £ £ « < * ( i - f O (M 7) 2=1 i = 1 j = i + 1 ^ and find its mean and variance as v-* Ni V NiNj / W1 \ m e « V — "V - V V - 1 - rn2 > x ^ K j f - ' f r i Ki Kj \ Wi ’ 2 = 1 2 = 1 J = 2 + l ./ \ / Ni n ^ Nt Ni ( 1 IN / W7 - x (3.38) 98 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. where we have again discarded small terms according to Nk/t^k < 1 - Then the capacity constraint (3.35) changes into P r{ F > 1 -r ] } < < 5 (3.39) Finally, since the lognormal shape parameter of the imperfect power control variable is not very large (1.5-2.5 dB), we can use the Gaussian approximation, i. e. approximating c by a Gaussian random variable with the same mean and variance C — Tfl~ of c, i. e. — — - ~ J\f (0, 1), it can be shown that the capacity constraint to satisfy (3.39) is fnz + t sjvz ^ 1 — rj (3.40) where r = Q-1(< 5 ). H orizontal p a tte rn — Since subband W\ has the lowest interference density, and {Iko}k= 2 can reach the outage probability 5 at the same time, we assume {Iko}k= 2 are approximately the same to achieve the maximum system capacity. Hence, all {°k}k= 2 are approximately equal. Although the maximum bandwidth utilization conditions are derived under perfect power control, they should be valid in general. To see this, consider a system with non-uniform power distribution. In such a system if we are allowed to move some signal power from the higher interference density subband to other subbands with lower interference density, the interference level in the former subband will be reduced, and thus we can add new power there 99 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. and increase the system capacity. Therefore, systems with maximum capacity must have power density distribution as uniformly as possible over the available spectrum band. We can then decompose the system into several vertical patterns containing dif ferent subbands in the “upper layer” of horizontal patterns, as in perfect power control, and apply (3.40) for capacity analysis. Again this method gives approxima tion of the system capacity, but the approximation error is small. For systems satisfying both maximum bandwidth utilization conditions defined in Section 3.2.3, the capacity formula is (3.40) with 3.2.6 N um erical results We consider the system shown in Figure 3.1 as it contains typical combinations of basic overlay patterns for our experiments. Simulation parameters are listed in Table 3.1, where, without loss of generality, we have chosen 7 k as 6 dB for all service classes. Assume imperfect power control with maximum received interference limit. Us ing the method discussed in sections 3.2.4 and 3.2.5, we decompose the system into three vertical patterns, {Wi, W2, W4}, {IFj, W2, W5}, and {W i,W 3}, then ap ply (3.40) to calculate {Nk}5 k=i from the “bottom” subband to the “top” subband. (3.41) 100 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 3.1: Simulation parameters for multiband system Subband k Bandwidth Wk Data rate Rk BIR ratio 7 ^ 1 15 MHz 1 0 0 kbps 6 dB 2 9 MHz 50 kbps 6 dB 3 5 MHz 2 0 kbps 6 dB 4 4 MHz 1 0 kbps 6 dB 5 4 MHz 5 kbps 6 dB Other n°/^° ratio 77 = 0 ,1 parameters outa§e Probability = 10~ 3 to K T 1 imperfect power-ctrl deviation < t„ = 2.5 dB Here we choose N x = 8 as 1/3 of its maximum value when < 5 = 10— 3, and 1 V 2 = 10 as 1 / 2 of its maximum value when 8 = 1 0 - 3 and N\ = 8 . To verify the accuracy of the solutions, we simulate the system outage prob ability with each set of solutions {Nk}k=1 and compare it with the target outage probability. The simulation is done as follows. First {cfc} / = 1 are calculated as in (3.33) with the given {A /}/=] and computer-generated lognormal random numbers T T f e * {i = 1, • • •, N k , k = 1,..., 5, 100,000 samples for each 7rfei in our simulation). Then the linear equation set (3.21) is solved with each sample of {ck}\=i for the in terference densities {Iko}l=i- Finally, the simulated outage probability in a subband k is calculated as the total proportion of Ik0 > no/77 and Ik0 < 0 . As shown in Table 3.2, the “top” subbands W4 and W5 have the largest (and almost the same) interference densities as expected. The difference between the simulated outage probability in subband W4 or W5 and the target value shows that our method slightly underestimates the system capacity when the target outage 101 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 3.2: Outage probabilities of example multiband system Target value Simulated value subband 1 subband 2 subband 3 subband 4 subband 5 0.005 0.0025 0.0036 0.0032 0.0046 0.0044 0.007 0.0030 0.0047 0.0035 0.0057 0.0059 0 .0 1 0 0.0056 0.0073 0.0072 0.0090 0.0089 0 .0 2 0 0.0106 0.0132 0.0143 0.0165 0.0160 0.030 0.0148 0.0193 0.0181 0.0235 0.0233 0.050 0.0266 0.0327 0.0347 0.0396 0.0394 0.070 0.0356 0.0456 0.0420 0.0555 0.0557 0 .1 0 0 0.0605 0.0731 0.0746 0.0876 0.0876 probability is relatively high. The error is small, however, since adding one or two users in W4 or W3 will cause the outage probability to exceed the target value. We have performed simulations with other overlay patterns and system parameters, and obtained similar results. In the following we check the effectiveness of the maximum bandwidth utilization conditions under imperfect power control. We fix the outage probability 5 = 0.01, and choose N\ = 8 and 1 V 2 = 11. From our capacity formula the number of users in other subbands are calculated as (N3, N4, N5) = (32,28,58). To check the uniform power distribution condition, we keep N i,N 2, and N3 un changed, but change N4 from 20 to 35, then find N5 by simulation so that the simulated outage probability does not exceed 0.01 (in this case 1 V 5 can not be ob tained from our capacity formula because the interference densities in W4 and W5 are different). The results are shown in Figure 3.5, where it is clearly seen that 102 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. X o o I N um ber of u se rs N . (a) system virtual bandwidth I ® o ■ § 0 s ( D s 1 < / ) • 4 - s u b -b a n d 4 N um ber of u se rs N . (b) simulated outage probabilities Figure 3.5: Uniform power distribution test under imperfect power control (5 = 0.01) 103 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. N um ber of u s e rs N4 (c) normalized interference densities Figure 3.5: Uniform power distribution test under imperfect power control (5 = 0.01, cont’d) the maximum system virtual bandwidth is reached when N 4 = 28, which is just the solution of our capacity formula. On the other hand, N 4 = 28 is also the point where the interference densities (obtained by simulation) in W 4 and W 5 are closest to each other (for integers N 4 and N5). Hence, the uniform power distribution condition is still valid for maximum bandwidth utilization under imperfect power control, and our capacity formula gives the solution under this condition. Next we check the full coverage condition by changing W 4 from 0.5 MHz to 5 MHz, and solving the capacity formula for N 4 and N$ with fixed N\ and N2. The results are shown in Figure 3.6, where the system virtual bandwidth increases mono- tonically with W4, and the interference are more and more uniformly distributed 104 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. X 8 o g I 3 ? B andwidth W4 (x 100 kHz) (a) system virtual bandwidth su b -b a n d 1 su b -b a n d 2 su b -b a n d 3 su b -b a n d 4 su b -b a n d 5 B andwidth W4 (x 100 kHz) (b) simulated outage probabilities Figure 3.6: Full bandwidth coverage test under imperfect power control (6 = 0.01) 105 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5 < e_ Bandw idth W4 {x 100 kHz) (c) normalized interference densities Figure 3.6: Full bandwidth coverage test under imperfect power control (5 = 0.01, cont’ d) 106 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. among the subbands as W4 increases. In particular, when IV4 — 5 MHz, the three subbands W 2,W 4 , and W 5 have almost the same interference density, which corre sponds to the fact that the subbands W2, W4, and W 5 form a sub-system satisfying the maximum bandwidth utilization conditions. Therefore, the full coverage condi tion is also valid for maximum bandwidth utilization under imperfect power control. This experiment also shows the effectiveness of our capacity formula. 3.3 M ultiband System w ith Interference Differentials In the above analysis of multiband overlaid systems, we assume that the interference limit (characterized by the r/ parameter) is the same in all subbands. This may not be true in reality when we think about the various user devices that will coexist in the future CDMA systems. For example, Today’ s mobile phone will probably still be used for voice and basic data (e.g. e-mail, small file transfer) transmission. At the same time there will be devices similar to today’ s PDA and laptop providing high speed services such as audio, video, web browsing, etc. Possible services also include high-quality video conference in a moving vehicle, for example, taking advantage of power from the car battery. 107 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. w 4 W5 W2 W3 w, W 2 W3 w, (a) (b) Figure 3.7: Multiband spectrum overlaid systems with full bandwidth coverage Different kinds of user devices have different interference constraints. Devices with smaller power supply can usually tolerate lower interference level in the sys tem. The capacity of a single band CDMA system is determined by the maximum interference level acceptable to all users, and therefore is limited by the devices with the smallest power. In a multiband CDMA system, however, since different services can be assigned into different subbands, some of them may not directly interfere with each other if their spectra do not overlap. It is therefore interesting to see how the overlay and separation of subbands with interference limit differentials will affect the entire system capacity. 3.3.1 R everse link analysis We assume that the full bandwidth coverage generally holds for the system we are considering, since otherwise the system capacity will surely be reduced. Let 7} be 108 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the set of all top subbands overlaying a base subband j (e. g. T\ = {W3, W4, W 5} in Figure 3.7(a)), the full bandwidth coverage condition means that J 2 w i = w J M leTj In addition, since a base subband always has a larger bandwidth than the top subbands overlaying it, we assume it includes a service with a higher data rate and a stronger power, and thus a smaller r/, i. e. Therefore, the total interference power in a base subband j, which is equal to the sum of the interference power in all top subbands in Tj, should satisfy ^ - E ^ E ^ E 5^ - 5^ i&Tj ze % ' i< = T j '3 '3 if the interference limit is satisfied in all the top subbands in Tj. This means that we only need to consider the interference limit n 0Wk ^ _ ,o r ^ T jk (3.45) for all the top subbands in the system. 109 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. From the general analysis in the last section we have the interference Ik in a top subband k equal to where Pk is the total signal power in subband k, and C k is the effective virtual bandwidth utilization of subband k Here we have plugged in the definition of 7 (3.1). iV f c is the number of users in subband k. T is, the set of all top subbands in the system. When the capacity is reached in all the top subbands, equality holds in (3.45), and thus for any two top subbands k and I we have Hence, the interferences of a base subband j and a top subband k overlaying it have the relationship h (3.46) k h rjk Wl m w k (3.48) 110 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. W ith (3.45) and (3.48) we obtain a set of capacity constraints by dividing both sides of (3.46) by Ik ' 7 (3.49) = j e B k VVJ \ i e T j 1 1 1 j In the following we discuss the effects of imperfect power control and other cell interference on the capacity constraints (3.49), then compare the performance of single-band and multiband systems with the same traffic conditions. 3.3.1.1 Considering Im perfect Power Control As in the single band system (Section 2.3.1), we define = < 3-50> j £ B k 1 \ l e T i as the load index in subband k. Then the outage probability constraint is Pr{o;fc > 1 — rjk] ^ 8 , k € T (3.51) 111 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Using the Gaussian approximation, we can get the capacity constraint on the number of users as + r \Ah^ ^ 1 -V k, k £ T (3.52) where r = Q (5), 1 W j € B k 3 \ l t T j V l j € B k " 3 \ l e T j are the mean and variance of ojk) m , and are the mean and variance of 7r, and cl = Ni Rkii , * ¥ ( RkikX l u ' d“ = Nt ( l u ) (3.53) 3.3.1.2 Considering Other Cell Interference Analysis of a multicell multiband spectrum overlaid system is generally very difficult, since the spectrum allocation and traffic distribution can be different from one cell to the other. Here we consider a simple case where the spectrum overlay pattern and planned traffic load in each subband are the same for all cells. Although simple, this case is still realistic when a certain area (e. g. a city) is covered with the same kinds of services. Since we assume the number of users in a subband k is equal to Nk for all cells, we can treat the other cell interference in a subband in the same way as in the 112 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. homogeneous single-band single-service system, where the only one kind of traffic load is uniformly distributed among the cells. Specifically, we may just use the analysis in section 3.3.1.1 with an updated expression for c * , to include the traffic load from other cells (see (2.27) for reference) where 7 r 'ki is the imperfect power control variable for the neighbor cells, v is the sum of the path loss ratios from all the neighbor base stations. As mentioned in Section 2.3.2 when considering shadow fading which is a log normal variable with a large shape parameter (5 - 10 dB), we need to use lognormal approximation, and the capacity formula is obtained as 3.3.1.3 Comparing w ith Single-band System For a single-band system where each user transmits with the entire system band- (3.54) (3.55) where ^ width, the capacity is limited by the service class with the largest r] (or the weakest 113 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. interference tolerability). The capacity constraint in this case can be easily found to be L Y cf e ^ 1 - 77f e . (3.56) k= 1 where L is the number of service classes in the system, and k* is the “sequence number” of the subband with the largest rj. When considering imperfect power control and other cell interference, this capacity constraint should be developed further into the format of (3.55) with ck defined in (3.54). As defined in Section 3.2.3, we use the metric effective virtual bandwidth L L c = Y c * W k = E N k R ^* (3-57) f c = 1 k= 1 to compare the capacity of the single-band and multiband systems. For systems under perfect power control, it can be shown that the multiband system has higher effective virtual bandwidth than the single-band system with the same service classes under the following condition X"' _2_ jeis 3 < E (3.58) where B is the set of all base subbands in the system, and r)k* is the largest among {Vk}- (3.58) shows an upper bound for the base subband traffic because it is the difference of interference limit in the top subbands that contributes to the higher capacity of the multiband system. The larger this difference is, the looser the bound 114 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. (3.58). On the other hand, if all r /jt have the same value, the multiband system will have the same capacity (in terms of C) as its single-band counterpart. For systems with all the random variables considered, we can also find the con dition to achieve higher effective virtual bandwidth in the multiband system, but the condition does not have a neat format like (3.58) so we skip it here. In addition, when considering the random factors the capacity increase in the multiband system over the single-band system is slightly smaller than in perfect power control. This is because the standard deviation of the traffic becomes larger in the sum when the traffic is split into different subbands, and thus the overall capacity is decreased (see (3.55)). 3.3.2 Forward link analysis When analyzing the forward link in multiband overlay, we need to consider two possible kinds of systems in terms of number of base stations in the system. In one case the overlaid subbands belong to independent systems so each subband is controlled by a different base station, while in the other case all the subbands in the system are covered by a common base station with multiple antennas. The multi carrier CDMA system [28], one of the options proposed in cdma2000, can be thought as a special case of the second category with exclusive subband spectra. The two cases must be distinguished in forward link analysis because they are governed by different base station power constraints. They do not make difference in the reverse 115 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. link, however, since the reverse link capacity is limited by the total interference in the subband, so long as our assumption on the rjk of different subbands (3.43) is maintained. 3.3.2.1 Single Base Station Case For simplicity, we set the base station power limit to 1, and thus use normalized signal and interference power in the forward link analysis for the one base station case. Let (3 be the fraction of the base station power used for common control purposes such as pilot, paging and synchronization. In the multiband system, different power (3k may be reserved for common control signals in different subbands, with (3 = Pk- Assume {(3k] are fixed. Let < j> k i be the (normalized) transmission power for user i in subband k, pk = 4 > k i be the total user signal transmission power for all users in subband k, and S f c be the total power transmitted over subband k including the transmission power for users in other overlapping subbands and for control signals, then we have all subbands in the group with base subband k (including subband k itself). Here we have ign ored th e th erm al n oise sin ce it is sm all com p ared w ith th e to ta l tran sm ission power from the base station. (3.59) where Bk is the set of all base subbands overlaid by subband k, and Qk is the set of 116 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. On the other hand, the power constraint limiting the capacity is L L N k E ^ E E ^ 1 - - 0 (3-60) fc=1 fc=1 i= 1 or ( L N k 'l Pr E E ^ ^ 1- ^ 5 l/c=l i=l J (3.61) in its statistical format when we consider power variations in the real system. At the user side, let aki be the path loss variable from the base station to user i in subband k, and assume the total transmission power sk over subband k is the same among all the cells, then the received signal and interference power are Sf c i = — , = + 4 - (3-62) ^ki ^ki ^ki respectively, where is equal to the sum of the inverse of path loss variables from a ki all the neighbor base stations to the user. The user’ s BIR is thus 'Pki Rfe /q (?n\ 7fci = 1 ■ \ p (3 ‘6 3 ) ( 1 J o “ I ” V ) S k where v — aki/oi'ki is the path loss ratio variable. Similar to the single-band case, the v here may be different from the path loss ratio in the reverse link because different soft handoff schemes may be used in the forward and reverse links. 117 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Therefore, Pk = ' l ^ ( Pki = 2_^ ~ f° + V)Sk = °kSk (3'64) „ -_ 1 1 ^ i= l i— 1 where (3.65) Bring (3.64) into (3.59) (3.66) We can solve (3.66) for {s*,}, and then get the capacity constraint using (3.60) or Note that (3.66) is similar in format to the interference expression (3.3) in the reverse link of a general multiband overlaid system , and (3.60), which is equivalent the reverse link (without considering interference differentials). Therefore, similar to the reverse link analysis in Section 3.2.4, we can show that in the forward link the top subbands have the largest power density (in terms of Sk/Wk) in the system. Consequently, the constraint si ^ 1 will be satisfied if Sj for each top subband j satisfies sj ^ W j/W\. This problem is thus completely analogous to the reverse link capacity analysis, and we can apply the decomposition methods to get the capacity formulas. (3.61). to C f c - S f c ^ 1 — (3, or Si ^ 1, corresponds to the constraint I\ ^ n0W i/rj in 118 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. However, if assuming full bandwidth coverage and uniform power distribution, we can get the optimal solution achieving maximum capacity (in terms of virtual bandwidth) in a simple and explicit format. To see this, we begin with the uniform power assumption w r w s k e T (3-67) For a top subband k, we have Since sk = SiWk/W i ^ Wk/Wi, we can reformat (3.68) into the capacity con straints or (3.68) (3.69) If we define (3.70) th e sta tistic a l ca p a city con strain ts (con sid ering real sy stem ran d om factors) are ju st the same expressions as the reverse link (3.55). 119 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.3.2.2 M ultiple Base Station Case The capacity analysis is easier if there is a base station (and thus a transmission power limit) in each subband. Let SI be the power limit of the base station in subband k, then the total power transmitted over subband k is upper-bounded by ^ « £ s i w +£ <3-71> je B k 3 iegk On the other hand, similar to (3.63), the received BIR of user i in subband k is /V = fikiSl W k 7 fel (1 - f 0 + v)Ik Rk ( ‘ } Hence, N k N k T> T T = E ( 1 _ /o + ^ | . ct| \3eBh bk Wj ieGkbk/ (3.73) where C k has the same definition as (3.65). The power constraint Pki 1 — Pk thus directly translates to the capacity constraint ( „ S* W, „ < 7 .* \ (3.74) W * ' le e ,* / The statistical version can be obtained accordingly. Note that for a given k , c * , can be d irectly ca lcu la ted from (3.74). 120 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.3.2.3 Comparing w ith Single-band System It would be unfair to compare the capacity of the multi-station multiband system with the single-band system, since the multiple base stations usually provide a larger total amount of power than the single base station. Hence, we only make the com parison for the single-station multiband system. For the single-band system, the capacity constraint in the forward link is L (3.75) k= 1 It is easily shown that, when assuming perfect power control and fixed path loss ratio v, the single-station multiband system (3.69) has exactly the same virtual bandwidth as the single-band system (3.75). When considering statistical variations (shadowing, imperfect power control, etc.), however, the capacity of the multiband system is proved to be less than the single-band system, due to the increase of the to tal standard deviation of the power variation in the multiband system. Fortunately, the capacity reduction due to the power variation is small. This observation is sim ilar to the reverse link case, where the capacity increase in the multiband system is slightly reduced when power randomness is considered. 121 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 3.3: Example multiband system with subband power differentials Path loss exponent m = 4 Shadowing shape parameter = 6 dB Orthogonality factor (fwd link) fo = 0.7 Imperfect power ctrl (rev link) £br,r = 2.5 dB Imperfect power ctrl (fwd link) = 1 dB Subband Bandwidth Data rate BIR NIR Common ctrl k w k Rk Ik rjk 0 k 1 10 MHz 144 kbps 6 dB 0 .1 0 .1 2 7.5 MHz 28.8 kbps 5 dB 0.15 0.05 3 2.5 MHz 9.6 kbps 4 dB 0.25 0.05 3.3.3 N um erical results For conciseness we use a simple three-subband system (Figure 3.7(b)) for our nu merical experiments. We consider the following system conditions: (a) single base station, (b) complete real-system random variables, (c) two-way soft handoff in both reverse link and forward link, and (d) other cell interference from two layers of neigh bor cells (totally 18 neighbor cells). The last two conditions are used to calculate the path loss ratio variable v and the lognormal approximation variable (. The system and traffic parameters are listed in Table 3.3, where the NIR rjk is for the reverse link, normalized common control power 0 k is for the forward link, other parameters are for both links (unless specified). 122 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.3.3.1 Reverse Link R esults First we check the accuracy of the lognormal approximation. Let the shadowing shape parameter at = 6 dB, and the target outage probability range from 0.005 to 0.1. We solve the capacity constraints (3.55) for the number of users {Nk} (k = 1, 2, 3) in the reverse link. (In order to calculate N 2 and IV 3 , N \ is chosen to be half of its maximum value.) Based on these solutions we perform simulation to “measure” the outage probabilities and compare them with the target values. In the simulation we generate for each user 1 0 0 ,0 0 0 log-normal random samples for the BIR deviation tx caused by imperfect power control, then solve the interference expressions (3.46) and get the NIR n 0W k/Ik in the top subbands W 2 and W 3. The number of the samples of n 0Wk/Ik {k = 2, 3) below rjk is counted and divided by the total number of samples (1 0 0 ,0 0 0 ) to produce the simulated outage probability. Such simulation is repeated 10 times for each set of {Nk}, and the average simulated outage probabilities are calculated and shown in Figure 3.8. For comparison we have also included the simulation results for Gaussian approximation. From Figure 3.8 We can see that the Gaussian approximation tends to overestimate the capacity so the simulated outage probability is always larger than the target value, while our lognormal approximation can roughly follow the change of the target outage probability. The “zigzag” of the simulated lines is caused by the discrete changes of Nk, especially Ni for high-speed users. 123 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 0.2 0.05 •o 0.01 target value ■ € > • • Lognorm su b b an d 2 Lognorm su b b an d 3 •a- ■ G aussian subband 2 — i- G a u ssia n su b b an d 3 t/3 0.005 0.002 r. 0.05 0.07 ).005 0.007 0.01 0.02 0.03 T arget o utage probability Figure 3.8: Multiband simulated outage probabilities of the reverse link In order to compare the capacity between the multiband system and single-band system, we solve the statistical version of (3.56) for { ./V fc} in the single-band system, using the same Ni as in the multiband system, then calculate the virtual bandwidth for both systems. The results are shown in Table 3.4, where the virtual bandwidth of the multiband system is 6-7.5% higher than the single-band system in the range of the outage probability being considered. More simulations show that the capacity gain for the multiband system is higher with larger difference between r ]2 and 773, and with more bandwidth assigned to W2. 3.3.3.2 Forward Link R esults In the forward link {iV fc} are solved from the statistical version of (3.69), and the outage probability is determined by (3.61). The simulated outage probabilities with 124 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 3.4: Capacity comparison in the reverse link of the multiband system Outage JV i Multiband Single-band prob n 2 n 3 Virt bw (MHz) n 2 n 3 Virt Bw (MHz) 0.005 2 2 0 5 3.089 18 5 2.906 0.007 2 2 2 8 3.343 19 1 0 3.118 0 .0 1 2 23 1 0 3.482 2 1 1 0 3.300 0.03 2 28 18 4.131 27 1 0 3.847 0.05 3 25 1 1 4.262 2 2 1 0 3.965 0.07 3 26 13 4.401 24 9 4.123 0 .1 3 27 15 4.541 26 8 4.280 Table 3.5: Capacity comparison in the forward link Outage IV i Multiband Single-band prob n 2 N 3 Virt bw (MHz) n 2 n 3 Virt Bw (MHz) 0.005 4 37 31 6.410 37 39 6.603 0.007 4 40 35 6.780 41 39 6.968 0 .0 1 5 37 31 6.984 37 37 7.128 0.03 6 41 35 8.018 41 40 8.138 0.05 6 45 40 8.503 46 43 8 . 6 6 6 0.07 7 43 37 8.821 43 41 8.918 0 .1 7 46 41 9.191 46 44 9.263 the solved {N k} are illustrated in Figure 3.9, which shows again the better perfor mance of lognormal approximation over Gaussian approximation. Table 3.5 com pares the forward link capacity between the multiband system and the single-band system, where we can see that the virtual bandwidth of the multiband system is 1-3% smaller than the single-band system. As explained in Section 3.3.2.3, this capacity reduction is due to the slightly larger total standard deviation of the traffic variations in the multiband system. 125 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 0.2 0 " ' " 0.05 S. 0.02 0.01 {/) 0.005 — target value -#• • Lognorm approx - -o • G aussian approx 0.002 J.005 0.007 0.01 0.02 0.03 T arget outage probability 0.05 0.07 0.1 Figure 3.9: Multiband simulated outage probabilities of the forward link To avoid misleading of the numerical results in this section, please note that Table 3.4 and 3.5 are intended for capacity comparison between the multiband and single-band systems, not for that between the reverse and forward links. In the wideband CDMA standards proposed in the recent years, several advanced tech niques such as multiuser detection, coherent demodulation in the reverse link, and new pseudorandom codes are adopted. These new features, which are not included in our analysis, will offer more capacity benefits in the reverse link than the for ward link [39]. The numerical results presented here therefore do not provide a fair comparison between the reverse link and the forward link capacity. 126 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Chapter 4 Burst Scheduling in W ideband C D M A System s Voice is the single major kind of traffic in the traditional cellular communication networks, although there exists a very small part of low-rate data applications such as those in the Cellular Digital Packet Data (CDPD) systems. In recent years, however, there is an increasing need of wireless data services, and new systems and protocols are designed for this purpose, such as the Japanese i-mode system and the Wireless Application Protocol (WAP) [2, 29, 36]. Some people even suggest all- packet-data wireless systems where all services are based on packet transmissions, like the current Internet [6, 59]. In IS-95-B and cdma2000 standards a burst data transmission mode is defined to support high speed packet data [21, 28, 30]. Using this option, the user sends to the base station a Burst-request message whenever it has a data backlog which requires a data rate higher than that provided by the fundamental channel. The base station estimates the interference level in the local cell and the neighbor cells from the pilot strength reports from the user, check if admitting the burst will cause the interference 127 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. to exceed the acceptable level, and then make the admission decision. The decision is sent back to the user in the Burst-assignment message. In the forward link, the base station may request the user to report pilot strength measurements, and inform the details of the next burst transmission in the Burst-assignment message. The burst admission algorithm used in the above protocol is an instant admis sion algorithm in the sense that it uses only the current interference condition to determine burst acceptance. It is possible that a burst request rejected in this way can actually be scheduled to start at a later time when the system load is lighter. This scheduling, however, requires the prediction of system load into a future time. In fact the burst start time has been defined as a parameter in the Burst-assignment message, but it can not be assigned by the instant admission algorithm. On the other hand, the capacity estimation methods discussed in Chapter 2 provides a pos sible way to predict the system load in the future if the current burst schedules of the local and neighbor cells are known. In this chapter we will present new burst scheduling algorithms based on this load prediction, and compare their performance with the existing instant admission algorithm. Before discussing the new burst scheduling algorithms, in the next section we first give a brief review of the burst admission algorithm in cdma2 0 0 0 . 128 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4.1 E xisting Burst Adm ission Algorithm in Cdma2000 A group of researchers in the Bell Labs, Lucent Technologies have proposed a burst admission algorithm named Load and Interference Based Demand Assignment (LIDA) [21, 30] for cdma2000. The following is a brief description of this algorithm. In a CDMA system define in each cell the nominal number of voice users Nnom. This is the maximum number of voice users that can be supported in the cell if there are no users of other services. The total nominal interference at each base station is then I = pNnom(l + u) (4.1) where p is the speech activity factor, u is the average other cell interference factor or our average path loss ratio defined in Chapter 2. A high speed data user transmitting at m times the voice data rate (the basic rate) is considered as m /p equivalent voice users. Suppose in a local cell (cell 0) there are N / equivalent voice users, and there is a burst transmission with a rate of M times the basic rate. Let A T * be the number of equivalent voice users in a neighbor cell i. The total interference in base station i is then composed of three parts: the interference from the N l v equivalent voice users, from the average number 129 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. of equivalent voice users per cell in the neighborhood N v, and from the high speed burst transmission M Ii = p(Ni + N vV) + Mvi (4.2) where i or the path loss ratio from the user to base station i is estimated by the pilot strength reports from the user. Note that i — 0 for the local cell, and = 1 - The high speed burst can be admitted only when the interference at all the local and neighbor base stations is lower than the nominal interference, namely, (4.3) is satisfied for all i. This decision can be made in the local base station so long as it has the JV * of all the neighbor cells. The base station may alternatively determine the largest m satisfying p(Nl + N vv) + mi'i < / (m < M ) (4.4) and admit the burst with rate m times the basic rate. This algorithm does not consider the rate variation of the high speed data user, but this is reasonable because it deals with just one data burst. The algorithm requires the mobile report pilot strength measurements in the burst request, and base stations periodically exchange information of their current load. 130 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4.2 Load Estim ation and Prediction for Burst A dm ission Besides the unavailability of burst scheduling, the major problem of the LIDA al gorithm is that it uses the average interference level for the burst admission. In Chapter 2 we have seen that the power variations due to shadowing, imperfect power control, etc. can considerably reduce the system capacity. In fact our capacity formulas ((2.43) for the reverse link and (2.59) for the forward link) are readily applied to this burst admission problem. Here we use the reverse link to describe our burst admission schemes. The burst admission in the forward link is very similar to the reverse link since their capacity formulas are in the similar format. 4.2.1 Load estim ation For convenience we define a new quantity for the system load index (4.5) 131 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. where all the variables are defined in Section 2.3. Here we copy the moments of u > as the following N ° R /V* M N o TJ * E ttO iloi , “ c jT c j Z = 1 c= 1 j = 1 -No / t- j # \ 2 A / iVe / D \ 2 * - E ^ * + E E ( ^ ) < w > t=l v 7 c=l j= l v ' (4.6) The reverse link capacity constraint is then (see (2.43)) uw ^ 1 - t] (4.7) Suppose the local base station has the knowledge of the number of users in each service class in all the neighbor cells. Let Rj, and be the data rate and BIR requirement of the data burst waiting for admission. The base station can then « easily calculate the mu and vu in (4.5) after admitting the burst to be m l = m w + v 'u = v u + v* (4.8) The new load index u'u is calculated thereafter by (4.5). In addition, if the neighboring base stations also exchange information of their load index uU iC (subscript c is the base station identifier) in the format of (mU tC , 132 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. vu,c), the local base station can also estimate the load update for its neighbor cells by calculating where uc is the path loss ratio defined in Section 2.3. Note that the information contained in m u > c and vu > c includes not only the traffic load from the users in cell c, but also the other cell interference into cell c. Therefore, both the number of users {N c} and (mU iC , vU tC ) need to be transferred between the neighbor cells for calculating the local uw and updating the neighbor uU iC . With all this information, the local station can check if the capacity constraint (4.7) is still satisfied in the local cell and all the neighbor cells after admitting the burst, and then make the decision on whether to admit or reject the burst request. 4.2.2 Load prediction We can extend the burst admission scheme described in the last section into a load prediction-based method. As mentioned in the introduction part of this chapter, it is possible that a burst request not accepted currently due to system interference limit may be admissible at a later time when the system load is lighter. If the base station can predict this interference change, it may admit the burst request by sending the Burst-assignment message containing the assigned start time of the burst. The advantage of a prediction-based burst admission algorithm is that it (4.9) 133 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. may reduce the burst blocking probability and thus increase the system resource utilization. In order to predict the interference level, we assume that the non-bursty traffic can be well characterized by its given model. Since we only care about the first two moments of the data rate variables, the traffic models is required to be able to provide reasonable accurate value of the mean and variance of the data rates. The other possible way is to simply use the average data rate in the estimation, assuming that the variance of non-bursty traffic is not large. For high-speed data bursts, since they must be admitted at each base station, their start times and durations are fixed and can be acknowledged by exchanging burst scheduling information between the neighbor base stations. Together with the parameters about the non-bursty traffic, the local base station can then predict the interference level in the near future and preform the prediction-based burst admission. This is discussed in more detail in the next section. 4.3 N ew Burst Scheduling Algorithm s The prediction-based burst admission consists of two complementary procedures, namely, the information exchange procedure, and the admission decision procedure. 134 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4.3.1 Inform ation exchange In order to estimate and predict the interference level in the local and neighbor cells, the base stations in the neighboring cells need to exchange the following information: (a) For non-bursty traffic, the currentiy-admitted number of users in each traffic type and the characteristic parameters of all traffic types (data rate, activity factor, BIR, etc.) in the focal cell. The means and variances of the data rates of these traffic types are used in the calculation of the load index uu. (b) The burst scheduling table containing the information of the bursty data transmissions that have been scheduled in the local cell, including the burst start time, burst length, data rate, BIR, etc. (c) The load estimate (mu, vu) until a certain time point in the future. This load estimate can be calculated based on the currently-admitted bursty and non-bursty traffics in the local cell and the neighbor cells (items (a) and (b)). In realtime communication the data burst usually has a lifetime (deadline) before which the burst must be transmitted. Hence, the load prediction described here should be long enough to accommodate the admission deadlines of all burst types (assume these deadlines are known to all the base stations). Although the load estimate is continuous in time, the exchanged values have to be on discrete time points (with fixed interval, for example), and the time points or sequence number need to be transmitted together with the load estimate. 135 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The above load and scheduling information needs to be retransferred whenever there is a change on the current load or schedule in the local cell, e. g. admission of a burst or non-bursty traffic, termination of a non-bursty traffic, or any load change in the neighbor cells which affects the load prediction in the local cell. The load and scheduling information can also be exchanged as periodic updates. Each information exchange packet should be associated with a sequence number. 4.3.2 A dm ission decision The admission decision steps are the following. Step 1 — Upon receiving the burst request, the local base station calculate the load estimate (4.5) for the local cell and the first-tier (six) neighbor cells to check if the outage probability limit in these cells is still guaranteed after admitting the burst. (We assume the burst admission does not affect other-tier cells because they are far away.) The calculation should be performed for every time point (also called check points here) with fixed interval from the current time until the burst completes. The calculation is a simple update as (4.8) for the local cell and (4.9) for the neighbor cells. When considering soft handoff, the load estimate for the neighbor cells in soft handoff with the user should be based on (4.8) instead of (4.9). Soft handoff infor mation is obtained from the handoff message exchange among the base stations and the user [17, 39]. If some neighbor base stations in the soft handoff can not support 136 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Interference Level Estim ate |First Fit deadline Lowest Fit threshold Time now Figure 4.1: Illustration of burst scheduling with load prediction the burst request but can tolerate the indirect other-cell interference caused by the burst, the burst can still be admitted with less direct communication links. Under this consideration both (4.8) and (4.9) may need to be evaluated for a base station in soft handoff. Step 2 — If the admission check in the first step fails, in the instant admission algorithm the burst request is rejected. Here we design two prediction-based burst algorithms as the following. First fit adm ission — If the admission check at any time points fails, restart the check from the next time point. This step is repeated until a check is successful, or the checking time point reaches the delay deadline of the burst. Lowest fit adm ission — Find all the “time slots” over which the burst can be transmitted from the current time point until the deadline of the burst. Assign the time slot (start time and duration) with the lowest average interference level in terms of the load estimate uu. 137 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 4.1 illustrates the basic ideas of first fit and lowest fit algorithms. In the next section we give some numerical results on the performance of these burst admission algorithms. Step 3 — If in Step 1 or Step 2 a time slot for the burst can be scheduled, respond to the user with the burst assignment message including the burst start time. Otherwise send a burst assignment message with reject information (e.g. burst start time or allocated code is equal to zero). This step is the same as the existing instant burst admission algorithm. The forward link burst scheduling is almost the same as the reverse link. How ever, in the forward link the burst start time should be assigned as ensuring the transmission orthogonality with the Walsh codes, and the queueing limit in the base station may need to be considered. 4.4 Num erical Exam ple For illustration purpose we consider a simple reverse-link example where there are a fixed number of 100 voice users in every cell of the 19-cell layout, and burst requests of the same type are generated only in the central cell. We perform burst scheduling in the central cell using the algorithms described in the last section, except that here only the admission check for the local cell is needed. T h e sim u la tio n p aram eters are listed in T ab le 4.1. V oice traffic is m o d elled as a on-off source with exponentially distributed talk and silent spurts. The average 138 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 4.1: Simulation parameters for burst scheduling (reverse link) Item Symbol Value System bandwidth W 10 MHz Path loss exponent m 4 Soft handoff margin A 6 dB Noise to interference ratio 0 .1 Outage probability 5r 0 .0 1 Shadowing deviation 6 dB Imperfect power control deviation 0 2 dB Simulation length T 1 0 0 0 s Checking interval Ay 1 0 ms Voice rate Rv 9.6 kbps Voice activity factor Pv 0.35 Voice BIR 4 dB Average talk spurt Tv 0.7 s Number of voice users N v 1 0 0 Burst rate Rb 144 kbps Burst BIR 71 6 dB Average burst length Tb 2 0 0 ms Maximum burst length r Rb,m ax 2 s Burst delay deadline Db 1 0 0 ms Burst arrival rate (per 10 ms) ^ 6 0 .1 - 2 data rate of Rvpv is used in the load estimation for voice. The data burst arrivals follow a Poisson process with rate The length of data bursts is also exponentially distributed. Two-way soft handoff with a hysteresis margin of 6 dB is assumed for estimating the path loss ratio v. Fig. 4.2 show the comparison of the instant admission algorithm and our burst scheduling algorithms with load prediction, where the average burst load is calcu la ted as th e b urst arrival rate over th e average b urst co m p letio n ra te ( \ b / p b = XbTb). 139 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. It can be seen that both the first fit and the lowest fit algorithms have lower block ing probability (unless the cell is heavily loaded, where no algorithm can possibly reduce the blocking probability), and higher system load (which means higher system resource utilization). It is interesting to see that the performance of the more complicated lowest fit algorithm is worse than the simple first fit algorithm. This is somehow against our intuition because in the lowest fit algorithm we try to put the burst in the place that would result in the least overall interference, which we thought to be the optimal solution. However, it looks that the burst deadlines play the major role in the performance. When a long burst starts at a later time than it could, it may affect the forthcoming burst requests and get them delayed further, and finally some bursts will be blocked because all the time slots before their deadlines are taken. On the other hand, the resource saved from this late burst assignment may not be used by other bursts because everyone is assigned an as-late-as-possible time slot. In the next experiment we set the burst deadline as uniformly varied in the range [0, 2Dj,}. The purpose is to simulate the situation where the data bursts have different deadlines. The performances of the burst admission algorithms in this experiment are shown in Figure 4.3, where we can see that the performance gain of the algorithms with load prediction over the instant algorithm gets smaller than the fixed deadline case. Actually the instant algorithm is not affected by the variation of the burst deadline, but the prediction-based algorithms performs worse just because 140 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Instant adm ission First fit -© - Low est fit________ 1 0 - 4 I -------------------1 -------------- 1 ---------------- 1 ---------------- 1 ---------------- 1 ---------------- 1 ---------------- 1 ---------------- 1 -----------------1 6 8 10 12 14 16 18 20 22 24 A verage burst load ^ b/(*b (a) blocking probability 1 -H s E V) d ) O ) 2 1 Instant adm ission First fit - e - Low est fit________ 0.5 0.4 A verage burst load (b) average system load Figure 4.2: Performance comparison of different burst scheduling algorithms R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. there are now many bursts with shorter deadlines (and the previous burst deadline Db = 1 0 0 ms is large enough for the prediction-based algorithms to work well). 142 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A 2 Q . O ) C 8 £3 to | 10' -**- Instant adm ission - a - First fit - e - Low est fit________ 20 22 A verage burst load Xb/p,b (a) blocking probability 1-ri Is 0.8 o e 0 ) £ 0.7 < J > Q ) 2 I Instant adm ission First fit - © - Lowest fit 0.5 0.4 22 A verage burst loadX b/|if a (b) average system load Figure 4.3: Performance of burst scheduling with random burst deadlines 143 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Reference List [1 ] Adachi F., Sawahashi M., and Suda H., “Wideband DS-CDMA for next- generation mobile communications systems,” IEEE Commun. Mag., pp. 56-69, Sep. 1998. 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Creator Zhuge, Lei (author)

Core Title Admission control and burst scheduling in multiservice cellular CDMA systems

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Doctor of Philosophy

Degree Program Electrical Engineering

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

Tag engineering, electronics and electrical,OAI-PMH Harvest

Language English

Advisor Li, Victor (committee chair), Heidemann, John (committee member), Kumar, P.Vijay (committee member), Lee, Daniel C. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-241672

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Legacy Identifier 3093424.pdf

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