RADIO RESOURCE SCHEDULING AND SMART ANTENNAS IN CELLULAR CDMA COMMUNICATION SYSTEMS

Transcription

1 Helsnk Unversty of Technology Control Engneerng Laboratory Espoo 004 Report 4 RADIO RESOURCE SCHEDULING AND SMART ANTENNAS IN CELLULAR CDMA COMMUNICATION SYSTEMS Mohammed S. Elmusrat TEKNILLINEN KORKEAKOULU TEKNISKA HÖGSKOLAN HELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D HELSINKI

2 Helsnk Unversty of Technology Control Engneerng Laboratory Espoo August 004 Report 4 RADIO RESOURCE SCHEDULING AND SMART ANTENNAS IN CELLULAR CDMA COMMUNICATION SYSTEMS Mohammed S. Elmusrat Dssertaton for the degree of Doctor of Scence n Technology to be presented wth due permsson of the Department of Automaton and Systems Technology, for publc examnaton and debate n Audtorum AS at Helsnk Unversty of Technology (Espoo, Fnland) on the 30th of August, 004, at noon. Helsnk Unversty of Technology Department of Automaton and Systems Technology Control Engneerng Laboratory

3 Dstrbuton: Helsnk Unversty of Technology Control Engneerng Laboratory P.O. Box 5500 FIN-005 HUT, Fnland Tel Fax E-mal: ISBN (prnted) ISBN (pdf) ISSN Pcaset Oy Helsnk 004 Avalable on net at

4 HELSINKI UNIVERSITY OF TECHNOLOGY P.O. BOX 000, FIN-005 HUT ABSTRACT OF DOCTORAL DISSERTATION Author Name of the dssertaton Date of manuscrpt Monograph Department Laboratory Feld of research Opponent(s) Supervsor (Instructor) Abstract Date of the dssertaton Artcle dssertaton (summary + orgnal artcles) Keywords UDC ISBN (prnted) ISBN (others) Publsher Prnt dstrbuton The dssertaton can be read at Number of pages ISBN (pdf) ISSN

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6 Ths work s dedcated to the nearest persons to my heart my father Salem Elmusrat and n lovng memory of my mother, Zaka Mohamed ( )

7 Preface I joned Helsnk Unversty of Technology, Control Engneerng Laboratory n August 999 as a postgraduate student. I started wth postgraduate courses. In January 00 I started the research work for Lcentate degree. I obtaned the Lcentate degree n August 00. In September 00 I contnued the research work presented n ths thess. Frst of all I would lke to thank my lord Allah who has helped me to complete ths work. O my Lord! Gude me to the successful way that allows me to succeed n ths lfe and n the hereafter. I could not have completed my dssertaton wthout the support and help from several people. Frst, my sncere apprecaton goes to my advsor, Professor Hekk Kovo who has provded an nvaluable support and encouragement over the past years. I would lke to thank all my Lbyan frends here n Helsnk as well as n Lbya and Canada for ther care and encouragement. My warm thanks for the revewers of ths thess, Dr. Hassan El-Sallab and Professor Tapan Rstanem for ther constructve comments. I wsh to express my grattude to all my frends and colleagues n the Control Engneerng Laboratory, for creatng a frendly and stmulatng atmosphere. My especal thanks for Professor Rku Jäntt, Lc.Tec. Naser Tarhun, Lc.Tec. Abdalla Abouda, Lc.Tec. Vesa Hasu and Lc.Tec. Matt Rntämäk for the frutful scentfc dscussons about topcs related to ths thess. My deep apprecatons are for all my famly and relatves especally my brother Dr. Ahmed Elmusrat, for ther support and encouragement. Ths work would not have been acheved wthout the ultmate support, the great generosty, and the bg lovngness of my wfe Nagat and my daughters Aa and Zaka. I would lke to say that no words can express my cordalty feelng towards them. Ths thess has been supported by a grant from Garyouns Unversty Benghaz- Lbya and partally from Exste project. The author has receved grants that are gratefully acknowledged, from NOKIA FOUNDATION and ELLA JA GEORG EHRNROOTIN Foundaton.

8 ABBREVIATIONS 3G B-BPC BS CDF CDMA CIR CN CPC CMTTP CSN CSOPC DBA DCPC DPC DS-CDMA EN ESPC FDMA FDPC FMA FSPC GSM IP ISDN QoS LMS LS-DRMTA Thrd Generaton Bang-Bang Power Control Algorthm Base Staton Cumulatve Dstrbuton Functon Code Dvson Multple Access Carrer to Interference Rato Core Network Centralzed Power Control Centralzed Mnmum Total Transmtted Power Algorthm Crcut Swtched Network Constraned Second Order Power Control Algorthm Dstrbuted Balancng Algorthm Dstrbuted Constraned Power Control Algorthm Dstrbuted Power Control Algorthm Drect Sequence CDMA External Network Estmated Step Power Control Frequency Dvson Multple Access Fully Dstrbuted Power Control Algorthm Foschn's and Mljanc's Algorthm Fxed Step Power Control Global System for Moble Communcaton Internet Protocol Integrated Servces Dgtal Network Qualty of Servce Least Mean Square Least Square De-spread Re-spread Mult-target Array v

9 LRPC MC-CDMA MIMO MMSE MS MO MODPC MOTDPC MODPRC MOTDPRC MTMPC MTPC MVDR GMVDR Pdf PSN PSTN RNC RLS RRM RRS SINR SPC TDMA VSL-CDMA UMTS UTRAN UE WCDMA Lagrangan Multpler Power Control Mult-Code-CDMA Multple Input Multple Output Mnmum Mean Square Error Moble Staton Mult-Objectve Mult-Objectve Dstrbuted Power Control Algorthm Mult-Objectve Totally Dstrbuted Power Control Algorthm Mult-Objectve Dstrbuted Power and rate Control Algorthm Mult-Objectve Totally Dstrbuted Power and rate Control Algorthm Maxmum Throughput and Mnmum Power Control Maxmum Throughput Power Control Mnmum Varance Dstortonless Response General Mnmum Varance Dstortonless Response Probablty densty functon Packet Swtched Network Publc Swtched Telephone Network Rado Network Controller Recursve Least Square Algorthm Rado Resource Management (or Manager) Rado Resource Scheduler Sgnal to Interference and Nose Rato Selectve power control algorthm Tme Dvson Multple Access Varable-spreadng length-cdma Unversal Moble Telecommuncaton System UMTS Terrestral Rado Access Network User Equpment Wdeband Code Dvson Multple Access v

10 CONTENTS ABSTRACT PREFACE... ABBREVIATIONS...v CHAPTER ONE: INTRODUCTION..... Network Archtecture of 3G moble communcaton system..... Rado Resource Management (RRM) Wdeband Code Dvson Multple Access Channel characterstcs of moble rado systems Contrbutons Outlne of the thess... CHAPTER TWO: POWER CONTROL ALGORITHMS.... Introducton.... Centralzed power control Two-User power control Dstrbuted Power Control Algorthms Dstrbuted Balancng Algorthm (DBA) The Dstrbuted Power Control (DPC) Dstrbuted Constraned Power Control (DCPC) Fully Dstrbuted Power Control (FDPC) Algorthm Foschn s and Mljanc s Algorthm (FMA) Constraned Second Order Power Control (CSOPC) Estmated Step Power Control Algorthm (ESPC)...6

11 .4.7. Smulaton Example Mult-Objectve Dstrbuted Power Control Algorthm (MODPC) Mult-Objectve Totally Dstrbuted Power Control algorthm Soft Droppng Power Control Kalman Dstrbuted Power Control Convergence Speed Comparson of Power Control Algorthms Smulaton Results...49 CHAPTER THREE: COMBINING POWER AND RATE CONTROL IN WIRELESS COMMUNICATION SYSTEMS Introducton Optmal Centralzed Power and Rate Control Maxmum Throughput Power Control (MTPC) Algorthm Centralzed Mnmum Total Transmtted Power (CMTTP) Algorthm Statstcal Dstrbuted Mult-rate Power Control (SDMPC) Algorthm Lagrangan Multpler Power Control (LRPC) Algorthm Selectve Power Control (SPC) Algorthm Mathematcal formulaton of the RRM problem n MO framework Mult-Objectve Dstrbuted Power and Rate Control (MODPRC) Mult-Objectve Totally Dstrbuted Power and Rate Control Algorthm Centralzed Algorthm for the Tradeoff between Total Throughput Maxmzaton and Total Power Mnmzaton (MTMPC) Algorthm Mult-rate Dstrbuted Power Control usng Kalman Flter Mnmum Varance Dstrbuted Power and Rate Control Smulaton Results...9 CHAPTER FOUR: SMART ANTENNA SYSTEMS Introducton The smart antenna and adaptaton Conventonal Beamformer Null-Steerng Beamformer Mnmum Varance Dstortonless Response (MVDR) beamformer...6

12 4..4 Mnmum Mean Square Error (MMSE) beamformer Recursve Least Square (RLS) Algorthm Subspace Methods for Beamformng Adaptve Beamformng usng Kalman Flter Least Square Despread Respread Multtarget Array (LS-DRMTA) Spatal-Temporal Processng General MVDR (GMVDR) algorthm for frequency selectve channels Informaton-theoretc analyss of uplnk beamformng Some nformaton theory concepts Capacty of a channel wth sngle user and mult-recevers Capacty of a channel wth mult users and mult-recevers Capacty of a channel wth mult users, mult-recevers, and mult-path Smulaton results...35 CHAPTER FIVE: JOINING RADIO RESOURCE MANAGEMENT AND SMART ANTENNAS Introducton Influence of MIMO beamformng on communcaton system performance Jonng Algorthms for Smart Antenna and RRS Jonng Smart Antenna and RRS usng Kalman Flters Influence of Smart Antenna Systems on the Performance of Rado Resource Schedulng n CDMA Cellular Systems...5 CHAPTER SIX: CONCLUSIONS...58 APPENDIX ) INTRODUCTION TO MULTI-OBJECTIVE OPTIMIZATION TECHNIQUES...6 ) SPECTRAL RADIUS COMPARISONS.. 67 BIBLIOGRAPHY...69

13 Chapter One Introducton CHAPTER ONE INTRODUCTION Less than ffteen years ago, the man challenges n moble communcatons were how to connect people wherever they were and provdng cheap servces as well as cheap and small handsets. Snce ambton s one of human characterstcs, these challenges have gradually been met and surpassed. The current challenges are how to provde multmeda communcaton, explorng the unlmted nformaton of the Internet, watchng TV channels, and many other servces on small and handy moble phones. The servces to the customers should be cheap and of hgh qualty. To reach these novel servces, the frst step s to use a multple access method that can support hgh data rate transmsson over wreless and moble channels. Wdeband Code Dvson Multple Access (WCDMA) has been chosen to be the multple access technque for the 3G moble communcaton system. The reasons of selectng WCDMA wll be dscussed n secton.3. To acheve cheap servces, the moble communcaton systems should be able to support a large number of users smultaneously. The users n WCDMA systems are usually sendng messages at the same tme and wth the same bandwdth but wth dfferent codes. The man nose source of each user s the nterference sgnals from other users due to the mperfect orthogonalzaton of the spreadng codes and the channel dsperson characterstcs such as mult-path and Doppler shft. Ths nterference lmts the capacty of the moble communcaton system. To ncrease the capacty and to enhance the system performance one should optmze the usage of the avalable rado resources. The system performance can further be enhanced by explotng the spatal dstrbuton of users to reduce the nterference usng smart antennas. In CDMA cellular systems, the base statons (BS) represent the access ponts of the moble statons (MS). The communcaton from the BS to the MS s called downlnk (DL) and from MS to BS s uplnk (UL). Wthout loss of generalty only the uplnk communcaton s consdered n ths thess. The rado resource management s very mportant n mult-user communcaton systems. It regulates the sharng of the rado resource between users. There are two man controllable rado resources: the transmtted

14 Chapter One Introducton power and data rate. The transmtted power should be adjusted to the mnmum power requred to acheve the target Qualty of Servce (QoS). The target QoS s a lst of condtons whch should be fulflled to obtan successful communcaton. The transmtted data rate, maxmum packet delay, and the packet loss probablty are examples of the QoS lst. The adjustng process of power s called power control. Power control s not an easy task due to the tme-varyng fluctuatons n the channel gan as well as the lag n nformaton about the total channel stuaton. If the data rate can be adjusted as well, we should use a combned power and rate control algorthm. Spatal flterng s an mportant nterference management tem whch can consderably enhance the communcaton system performance. The transmtted sgnals from moble statons arrve to the base staton antenna n mult-path fashon and n dfferent drectons of arrvals (DoA). The DoA of each multpath component of each MS depends on ts locaton as well as the mult-path characterstcs. Usng spatal flterng, one can enhance the recepton of the recevng antenna from certan DoAs and attenuate the others. Ths means, f the DoA of the requred user can be estmated, we can enhance the Sgnal to Interference Rato (SIR) by reducng the nterference sgnals whch have dfferent DoAs. Spatal flterng s possble by usng mult-antenna arrays wth adaptve weghts (smart antennas). Mult-user detecton methods are utlzed as well to further enhance the system performance. The code structures of the users are employed to reduce the co-channel nterference. It should be notced that for a large number of users the optmum mult-user detecton method s computatonally very ntensve. In ths thess, we wll focus on the rado resource management and smart antennas. Although the topcs are treated n a general way, more attenton s gven to the UMTS standards.. Network Archtecture of 3G moble communcaton system A smplfed network archtecture of the Unversal Moble Telecommuncaton System (UMTS) s shown n Fgure. [64]. As seen n Fgure. the UMTS Terrestral Rado Access Network (UTRAN) has two nterfaces. The frst nterface s wth User Equpment (UE) usng WCDMA. The second nterface s wth the Core Network (CN). The UTRAN conssts of Base Statons (BS) and Rado Network Controllers (RNC). The core network s the nterface between UTRAN and the External Network (EN). It conssts of two

15 Chapter One Introducton 3 networks, the Crcut Swtched Network (CSN), whch s the same as the old GSM swtchng network and the packet swtched network (PSN), whch s based on Internet Protocol (IP) address. The CSN s connected to the conventonal swtchng systems, such as Publc Swtched Telephone Network (PSTN) and Integrated Servces Dgtal Network (ISDN). PSTN, ISDN,.. EN INTERNET Crcut Swtched Network CN Packet Swtched Network RNC UTRAN RNC BS BS DL UL User Equpment Fgure. UMTS network archtecture

16 Chapter One Introducton 4 The PSN, on the other hand, s connected to the Internet network [64]. The transmtted power controls n uplnk and downlnk are very mportant ssues n CDMA systems. Two man types of power control are used wth UMTS networks. The closed (fast) loop power control regulates the transmtted power of all UE to mnmze the nterference between them. The control command s updated at the rate of 500 Hz. The outer (slow) loop power control updates the target Sgnal to Interference and Nose Rato (SINR), whch s determned by Rado Network Controller (RNC). Detaled descrpton of the power control concept and algorthms wll be ntroduced n Chapter. The data rate can be updated as well as explaned n Chapter 3.. Rado Resource Management (RRM) In the UMTS archtecture, each BS has a rado resource management module that attempts to preserve the traffc s QoS requrements across the rado access network (RAN) [8]. The QoS attrbutes are usually specfed n terms of bt error rate (BER), data rate, delay, and so on. The man role of the RRM s to assgn resources to users accordng to ther QoS requrements. As shown n Fgure., the RRM msson starts by performng connecton admsson control (CAC). Snce the decson s based on resource avalablty, CAC consults the Rado Resource Scheduler (RRS) before acceptng or rejectng the requested call [8]. Upon call acceptance, the traffc classfer (TC), another RRM component, categorzes the ncomng traffc accordng to ts QoS specfcaton, whch s typcally ncluded n each packet header. Data flows are then drected to a correspondng queue accordng to ts QoS feld. Each QoS class (QoSc) s represented by at least one queue. Fnally, the traffc dspatcher (TD) drans the multple queues accordng to some prorty logc after gettng the assgned rado resources from the RRS, whch reles on the channel condtons and the requested QoS n ts response. Based on the above, t s evdent that RRS bears a great responsblty n havng a successful RRM [8]. In a CDMA network the RRM has two mportant rado resources to control: MS transmttng power and data rate. Combnng the transmtted power control and data rate control n an optmum way s a very mportant ssue as wll be shown n Chapter 3. One of the mportant goals of the multple access systems, such as n the UMTS, s to maxmze the number of smultaneous users. If each MS s assgned the mnmum resources necessary for meetng or exceedng ts QoS requrements, the capacty of the

17 Chapter One Introducton 5 system wll be maxmzed [8]. Another mportant goal for non-voce users s to maxmze ther data rates. All these ssues wll be dscussed n more detals n Chapters and 3. QoSc CAC TC QoSc TD QoSc3 QoSc4 RRS Fgure.. Block dagram of the Rado Resource Manager [8]..3 Wdeband Code Dvson Multple Access In mult-user envronment, t s very mportant to separate the users, so that they are not nterferng wth one another. For example, users of Frequency Dvson Multple Access (FDMA) are separated by allocatng certan frequency bands for each user. In Tme Dvson Multple Access (TDMA), each user has a repeated tme slot. In CDMA all users share smultaneously the same bandwdth, but wth dfferent codes, as s llustrated n Fgure.3. CDMA has many advantages over TDMA or FDMA technologes. CDMA technques are wdeband n the sense that the entre transmsson bandwdth s shared between all users at all tmes. Ths s accomplshed by spreadng the baseband sgnals onto a bandwdth much larger than ts actual bandwdth. Ths spreadng s acheved by usng spreadng codes. The spreadng leads to smpler statstcal multplexng wthout the explct schedulng of tme or frequency slots, unversal frequency reuse between cells, and graceful degradaton of qualty near congeston. It explots the frequency selectvty of the channel (whch uses a rake recever that resolves ndvdual mult-path components

18 Chapter One Introducton 6 and then coherently combnes them) to avod the harmful effects of deep fades that afflct narrowband systems, and the explotaton of slence perods n voce conversatons. Fgure.3. Prncple tme and frequency dvson n FDMA, TDMA and CDMA. It s then possble n the CDMA envronment to provde unque benefts for cellular applcatons [6], [63]. There s no sngle, unversally accepted, defnton of Wdeband CDMA [4]. In fact, one may fnd two commonly accepted defntons. One s based on system parameters such as chp rate, or bandwdth expressed as a fracton of the center frequency; and the other s based on the characterstcs of the channel. If the bandwdth of the sgnal exceeds the coherence bandwdth of the channel, the term Wdeband CDMA s used. Yet there s no dstnct bandwdth threshold that separates the narrowband CDMA from the Wdeband CDMA [4]. Currently the term WCDMA s used for the UMTS standard..4 Channel characterstcs of moble rado systems The modulaton type, the carrer frequency and the codng/decodng methods depend on the characterstcs of the channel. The channel s the meda between the transmtter and the recever. We need to know, or at least to estmate, ts behavour to desgn successful communcaton system. Unfortunately, most of rado channels have characterstcs that vary over tme,.e. they are tme-varyng channels. Ths complcates channel parameter estmaton. The problem s much more acute n moble channels due to the nature of the

19 Chapter One Introducton 7 moblty of the moble termnals. Fgure.4 shows an overvew of fadng channel manfestatons [65]. From Fgure.4, the large-scale fadng manfestaton s shown n blocks,, and 3. Ths phenomenon s affected by promnent terran contours (hlls, forests, bllboards, buldngs, etc.) between the transmtter and the recever. The recever s often represented as beng shadowed by such obstacles. Ths phenomenon can be modelled as a mean-power loss usng a path loss exponent n, and a random varable wth log-normal dstrbuton. The small-scale fadng refers to a rapd fluctuaton n the receved sgnal due to very small movement of the moble. The reason s that the receved sgnal s usually comng through dfferent paths. Every path causes a tme delay, whch changes the phase. The receved sgnal s the complex sum of the sgnals from all paths. Then f the path sgnals are n-phase, the receved sgnal power wll acheve ts hghest value. If the path sgnals are out of phase, the receved sgnal power wll be at the lowest value. The receved sgnal power may vary as much as 40 db, when the moble moves only a fracton of a wavelength []. A more detaled descrpton of Fgure.4 s presented n [65]. Fgure.4. Overvew of fadng channel.

20 Chapter One Introducton 8.5 Contrbutons In ths thess we focus on power control algorthms, combned power and rate control, smart antennas and jonng rado resource scheduler and smart antenna. The contrbutons can be classfed from the methodology pont of vew under three man categores as follows: A. The Mult-Objectve Optmzaton I. Mult-objectve dstrbuted power control (MODPC) algorthm. Power control problem s frst formulated n a new way, as a mult-objectve (MO) optmzaton problem. In the formulaton, dynamcal behavour of the moble communcaton channel s also taken nto consderaton. The problem s then transformed nto a sngle-objectve optmzaton problem and solved. Certan propertes of the convergence are proved. Smulaton studes show the superorty of the proposed power control algorthm over several other wellknown power control algorthms. These topcs are presented n Secton.4.8 II. Mathematcal formulaton of the RRM problem n Mult-Objectve framework. New mathematcal formulaton of the RRM problem s proposed. In the lterature the RRM problem s treated as a sngle optmzaton problem wth constrants. We propose to use mult-objectve optmzaton to solve the RRM. More flexble and sophstcated solutons can be obtaned. These topcs are covered n Secton 3.8. III. Mult-Objectve dstrbuted power and rate control (MODPRC) algorthm. Ths topc s an applcaton of the MO optmzaton n RRM. The (MODPRC) algorthm s a dstrbuted algorthm and the smulatons show that ts performance outperforms many other combned power and rate control algorthms. The algorthm s based on mnmzng a mult-objectve defnton of an error functon. Three objectves are defned. The objectves are ) mnmzng the transmtted power, ) achevng at least the target CIR whch s defned at the mnmum data rate, and 3) achevng the maxmum CIR whch s defned at the maxmum data rate. The topc s covered n Secton 3.8..

21 Chapter One Introducton 9 IV. Centralzed algorthm for the tradeoff between total throughput maxmzaton and total power mnmzaton (MTMPC) algorthm. Ths algorthm s another applcaton of the MO optmzaton n RRM feld. Power control algorthm for total throughput maxmzaton s proposed n [74]. In the proposed algorthm, we use the same throughput maxmzaton objectve, but an added objectve for power mnmzaton s used. The Mult-objectve optmzaton problem s solved usng the weghtng method. A centralzed power control algorthm s obtaned. Ths topc s treated n Secton V. Mult-Objectve Totally Dstrbuted Power Control (MOTDPC) algorthm. In realty, only a quantzed verson of the estmated CIR s avalable at the moble staton. Therefore, MODPC s modfed to take nto consderaton the quantzed CIR. Ths algorthm uses the concept of ESPC algorthm to estmate the CIR. The topc s presented n Secton.4.8. VI. Mult-objectve totally dstrbuted power and rate control (MOTDPRC) algorthm. Ths algorthm s the same as MODPRC algorthm but wth estmated CIR. We use the same concept as n ESPC to estmate the CIR from the ON-OFF commands of power control. The performance of the system s nvestgated by smulatons. The topc s covered n Secton 3.8. VII. Soft droppng power control. If the CIR target cannot be acheved for every user, then power control becomes nfeasble. In ths case some connectons should be dropped from the current lnk. The MODPC s modfed to be used for connecton droppng. The topc s presented n Secton.4.8. VIII. Jonng algorthms for smart antenna and RRS. The man concept of jonng smart antenna and RRS usng MO optmzaton s summarzed n Secton 5.3. B. Kalman Flters IX. Kalman dstrbuted power control. Kalman flter s proposed to be used n power control of CDMA moble communcaton systems. The motvaton to use Kalman flter s the known fact that Kalman flter s the optmum lnear trackng devce on the bass of second order statstcs [0]. The topc s presented n Secton.4.9.

22 Chapter One Introducton 0 X. Mult-rate dstrbuted power control usng Kalman flters. We propose a new mult-rate dstrbuted power control algorthm based on Kalman flter. The algorthm s a drect extenson of the Kalman power control algorthm. Ths topc s treated n Secton 3.9 XI. Mnmum varance dstrbuted power and rate control. Ths algorthm s a dfferent formulaton to solve the RRM problem usng Kalman flters. The topc s dscussed n Secton XII. Jonng smart antenna and RRS usng Kalman flters. Smple method to jon smart antenna and power control usng Kalman flter s proposed n Secton C. Others XIII. Estmated step power control (ESPC) algorthm. We propose a new method to estmate the uplnk Carrer to Interference Rato (CIR) usng the power control ON-OFF commands at the MS. The estmated CIR s used to adjust the transmtted power from the moble termnal usng the Dstrbuted Constraned Power Control (DCPC) algorthm. The man advantage of the proposed algorthm s that t can mprove the performance of power control wthout any ncrease n power control sgnallng. Ths method has been used wth other algorthms throughout ths thess. The algorthm s explaned n Secton.4.7 XIV. General MVDR algorthm for frequency selectve channels. The mnmum varance dstortonless response (MVDR) s a very well known algorthm to obtan the optmum weght vector whch maxmzes the output sgnal to nterference and nose rato (SINR) of multple antennas. In ths part we generalze the algorthm to be used n mult-path and frequency selectve channels to capture the dfferent path sgnal components. The topc s covered n Secton Also the nfluence of usng GMVDR algorthm on the upper channel capacty s treated n Secton XV. Convergence speed comparson of power control algorthms. The convergence speed s an mportant factor n the selecton of the optmum power control algorthm for a wreless communcaton system. In ths part we ntroduce

23 Chapter One Introducton a smple method to compare the convergence speed of power control algorthms. So far most of the studes on power control have used spectral radus of the correspondng teraton matrx as a convergence speed measure. However, ths method s only applcable to lnear algorthms. In addton, although always possble, fndng the spectral radus can sometmes be tedous. We show n Secton.5 that a smple dfferentaton of the power control algorthm can be used to compare the convergence speed of algorthms. XVI. Influence of smart antenna systems on the performance of rado resource schedulng n CDMA cellular systems. In ths part the jonng procedure between the RRS and the adaptve antenna s explaned. A pseudo-code algorthm to jon the smart antenna wth RRS s ntroduced. Chp level smulatons are performed to evaluate the nfluence of a smart antenna on CDMA cellular systems. More detals are gven n Secton Outlne of the thess The concepts of power control theory n cellular communcaton systems are explaned n Chapter. Dfferent algorthms from lterature as well as the new proposed algorthms and ntensve smulatons are presented also n Chapter. Combned algorthms of power and rate control are presented n Chapter 3. The smart antenna concept and dfferent adaptaton algorthms are ntroduced n Chapter 4. The jonng procedures of rado resource scheduler algorthms and smart antennas are dscussed n Chapter 5. Fnally, our conclusons and remarks are gven n Chapter 6. Appendx summarzes bascs of multobjectve optmzaton. Some extra proofs for the spectral radus comparsons are presented n Appendx.

24 Chapter Two Power Control Algorthms CHAPTER TWO POWER CONTROL ALGORITHMS. Introducton Power control s essental n moble communcaton systems, because t can mtgate the near-far problem, ncrease the system capacty, mprove the qualty of servce, ncrease the battery lfe of the moble termnal, and decrease the bologcal effects of electromagnetc radaton. The objectve of the power control algorthm s to keep the transmtted power (for the moble staton n the uplnk power control and for base-staton n downlnk power control) at the mnmum power requred to acheve the target Qualty of Servce (QoS) n the system. The QoS of a communcaton system s a lst of requrements to be fulflled by the operator. Some of these terms are the bt error rate (BER), the data rate, the packet delay, the outage probablty, etc. In ths Chapter we wll consder only the BER as an ndcaton of the QoS. The BER s drectly mapped (depends on modulaton type) to the CIR. The mappng of fxed CIR to BER s well known and can be found n classcal dgtal communcaton books such as [4] and [50]. For more real stuaton when the CIR s random varable, one should average the BER over the probablty densty functon (pdf) of the CIR. The resultant mappng s usually rather dffcult [07]. There are dfferent approxmatons for CDMA channels [07],[]. To generalze as well as to smplfy the analyss we wll use CIR as an ndcaton of the QoS. Mult-rate power control wll be covered n the next Chapter. Before gvng a precse mathematcal formulaton for the optmum power control problem, some notatons and defntons are gven. Let the transmtted power control vector be a Q-dmensonal column vector P = [ P, P,.., P Q ], where P s the transmtted power of user. CIR of user s denoted by Γ. Mathematcally the power control problem s formulated as follows: Fnd the power control vector P that mnmzes the cost functon

25 Chapter Two Power Control Algorthms 3 J subject to ( ) Q P P P (.) = = j= j = PG k Γ k = Γ mn, =,..., Q, k =,..., M, Q PG + N j kj (.) and P,,,, mn P Pmax = Q (.3) where = [,, ], Q = Number of moble statons. M = Number of base statons. G kj = Channel gan between moble staton j and base-staton k, as shown n Fgure.. N = The average power of the addtve nose at recever. Because t results from many sources, t s convenent to represent t as Gaussan whte nose wth zero mean. P max = Maxmum power, whch can be handled by the transmtter. P mn = Mnmum power, whch can be handled by the transmtter. Γ mn = Mnmum predefned CIR. For smplcty, we wll refer to user wthout usng the subscrpt of ts assgned base staton. For example, we wll use Γ nstead of Γ k. If the CIR of user, Γ <Γ mn, and the transmtted power P = P max, then user (or some other users) has to be dropped from T ths lnk. Another mportant factor s the target CIR ( Γ ). It should be noted that the superscrpt (T) means (Target). The dash ( ) s used to ndcate transpose operaton. The dfference between the target CIR and the mnmum predefned CIR s called CIR margn. The target CIR value s determned by the outer-loop power control to acheve certan QoS n the cell. The target CIR could be dfferent from user to user because t depends on the type of servce requested by the user. The mult-servces power control wll be covered n the next chapter.

26 Chapter Two Power Control Algorthms 4 The optmzaton problem of (.)-(.3) seems to be a smple lnear programmng problem, but ths s not totally true due to the fact that the channel gan G kj and the addtve nose N are not accurately known. The parameters, such as the channel gan, the nose and the number of users are tme varyng, and they change n a random manner. Snce the power control algorthm should be able to regulate the transmtted power n real tme, t should be fast convergent and robust. Power control subject s classfed n the lterature nto open-loop and closed-loop power control, sgnal-strength based and CIRbased power control, centralzed and dstrbuted power control, determnstc and stochastc power control, and so on. A bref revew of the most well-known power control algorthms s gven next. BS b BS a G b G aj G bj G a MS j MS Fgure.. Lnk geometry and lnk gan model. Centralzed power control If the nformaton of the lnk gans and the nose levels are avalable for all users, then the centralzed power control algorthm can be appled to solve the power control problem gven n (.)-(.3) perfectly [56]. For noseless case, N = 0, (.) becomes

27 Chapter Two Power Control Algorthms 5 PG k Γ = Γ mn, Q =,..., Q, k =,..., M. PG j= j j kj (.4) Equaton (.4) can be wrtten n a matrx form as P Γ mn HP (.5) where H s a nonnegatve matrx wth the followng elements 0 = j H = G j kj (.6) > 0 j Gk ( ) The problem s how to fnd the power vector P>0 such that (.5) s satsfed. Equaton (.5) can be wrtten as Γ mn I H P = 0 (.7) The nequalty s dropped n (.7), snce equalty sgn holds for the mnmum power vector. It s known from lnear algebra that a nontrval soluton of (.7) exsts f and only f Γ mn I H s a sngular matrx. It s seen from (.7) that ths happens, f Γ mn s an egenvalue of H, and the optmum power vector P s the correspondng egenvector. The power vector P should be postve. Perron-Frobenus theorem [5] says that for a nonnegatve and rreducble QxQ matrx H there exsts a postve vector P assocated wth the maxmum egenvalue * λ ρ λ = ( H ) = max, =,..., Q, (.8) where λ s the th egenvalue of the matrx H, and ρ(h) s the spectral radus of matrx H. Based on ths the maxmum achevable CIR can be expressed as * γ = = * λ ρ( H) (.9) Now by consderng the addtve whte nose at the recevers, (.) can be wrtten n a matrx form as T [ I Γ H] P u (.0) where u s a vector wth postve elements u specfed by

28 Chapter Two Power Control Algorthms 6 u Γ N G T =, =,,Q, k =,, M. (.) k It can be shown [5] that f postve. In ths case, the power vector P* T Γ < ρ ( H ) T, then the matrx [ I Γ H ] s nvertble and P * T I H u (.) = Γ s the soluton of the optmzaton problem posed n (.)-(.3). There are nether guarantees that T * Γ γ nor guarantees that the power vector P * s wthn the constrants (.3). In ths case a removal algorthm wll be needed to reduce the number of users n the cell lke the Stepwse Removal Algorthm (SRA) []. Power control n CDMA moble communcaton system wll be llustrated by the followng example. In the example we assume addtve Gaussan whte nose rado channel wth propagaton loss and shadowng. The receved sgnal power at base staton j due to user s assumed to follow power law Pˆ j S j 0 P α d =, (.3) j where S j s the shadowng varable n the path from -th moble staton to j-th base staton and t s assumed to be a random varable wth log-normal dstrbuton and 5 db varance. d j s the dstance between user and base staton j. We assume that all the users are unformly dstrbuted n a crcular cell wth radus of r = 500 m. The loss factor α s assumed to be constant for all users wth α=4. Also the varance of the addtve whte nose s assumed to be -0dBm. In the smulatons we have calculated the number of users, whch can acheve the specfed CIR. Fgure. shows the number of users (y-axs) wth the acheved CIR (x-axs) n two cases. In the frst case centralzed power control and n the second case no power control s used. The mprovement n the channel capacty s clear, when power control has been used. If the target CIR s 5 db n Fgure., then the number of users, whch can be supported usng centralzed power control, s 33. Only 3 users can be supported, when no power control s used.

29 Chapter Two Power Control Algorthms 7 The result of ths example can not be generalzed because t shows one scenaro of the moble communcaton system. It gves only a general mpresson of the mportance of usng power control n CDMA cellular communcaton systems. 40 The number of users wth the target CIR Usng Ideal Power Control The Number of Users Wthout Power Control CIR (db) Fgure.. System capacty wth and wthout power control The computaton of the optmum power vector usng the centralzed power control algorthm needs the lnk gans of all users. Ths s computatonally ntensve; moreover t s not feasble partcularly n mult-cell cases. Therefore t s common n practce to use a dstrbuted power control technque. Centralzed power control can be appled to test the upper bound performance usng a dstrbuted technque n smulaton..3 Two-User power control The power control problem can be descrbed graphcally for a smple case. Consder two users wthn one cell. The frst user has the lnk gan G (t) and the second user the lnk gan G (t). The lnk gans are functons n tme due to the dynamcal behavor of the moble communcaton system. Assume that N s the average nose power. Recall the optmum power control problem (.)-(.3). The problem s to determne the mnmum transmtted power vector that satsfes the requred QoS. Then, we can wrte

30 Chapter Two Power Control Algorthms 8 P P * P * P Fgure.3. Black area conssts of feasble power par values satsfyng QoS. P() t G() t () () + P t G t N Γ T for the frst user and Solvng the prevous nequaltes we obtan () P t () () () () () T G t NΓ Γ P () t + G t G t T P t T () T G t NΓ Γ P() t + G t G t () P( t) G( t) () () + P t G t N Γ T for the second user. (.4) In practce, the gans are random varables due to slow fadng, and fast fadng behavor. To solve the system of lnear equatons (.4), t s easer to assume that the gans are constant,.e. they are frozen at tme t. Ths s termed snapshot assumpton. Wth that assumpton the problem can be solved by centralzed or dstrbuted lnear technques, as we wll descrbe later. Fgure.3 llustrates the graphcal nterpretaton of power control wth the snapshot assumpton. The shaded area shows the set of feasble power par values to acheve the requred QoS..4 Dstrbuted Power Control Algorthms For dstrbuted power control, only local nformaton s needed for a specfc transmtter to transmt the optmum power. The transmtted power of all users can be descrbed mathematcally as

31 Chapter Two Power Control Algorthms 9 ( t + ) = ( ( t) ) P Ψ P t=0,, (.5) where Ψ ( P () t ) = Ψ ( P () t ),..., ΨQ ( P () t ) s the nterference functon. There are dfferent types of nterference functons n the lterature as we wll see later. The nterference functon Ψ( ) s called standard when the followng propertes are satsfed for all components of the nonnegatve power vector P [7]: Postvty Ψ ( P ) > 0 ; Monotoncty, f ( ) ( ) P P then Ψ P Ψ P > 0 ; Scalablty, for all α >, α ( ) > ( α ) Ψ P Ψ P. Theorem () If the standard power control algorthm (.5) has a fxed pont, then that fxed pont s unque. Proof: See [7]. Theorem () If Ψ(P) s feasble, then for any ntal power vector P o, the standard power control algorthm converges to a unque fxed pont Proof: See [7]. Theorem (3) * P. If Ψ(P) s feasble, then from any ntal power vector P o, the asynchronous standard power control algorthm converges to a unque fxed pont Proof: See [7]. * P..4. Dstrbuted Balancng Algorthm (DBA) Zander has proposed a Dstrbuted Balancng Algorthm []. The method s based on the power method for fndng the domnant egenvalue (spectral radus) and ts correspondng egenvector. The DBA algorthm s as follows ( 0 ) P = P P > (.6) P( t + ) = βp( t) +, β > 0, t=0,,..., =,...,Q Γ () t The algorthm starts wth an arbtrary postve vector P(0). The CIR level Γ (t) s

32 Chapter Two Power Control Algorthms 0 measured n lnk. If the power control s for downlnk, then the measurement of the CIR s made at the moble. The result s to be reported back to the base staton. The transmtter power at the base staton s then adjusted accordng to the DBA n (.6). If the power control s for uplnk, then the measurement of the CIR has to be made at the base staton. The result has to be reported back to the moble, and each moble staton wll adjust ts transmtted power accordng to the DBA. Practcally, to reduce the feedback bandwdth as well as the sgnalng data, only quantzed (one or few bts) CIR s reported. We call power control algorthms based on the quantzed CIR as totally dstrbuted power control algorthms. These types of algorthms wll be dscussed later. Proposton (.) Usng the DBA algorthm (.6) the system wll converge to CIR balance wth probablty one,.e., where () () lm P t * = P t = 0,,... t * lm Γ t =γ t =,...,Q * γ s the maxmum achevable CIR, whch s equal to (.7) * λ. As before, λ * s the spectral radus of the nonnegatve matrx H, and P * s the correspondng egenvector representng the optmum transmtted power. Proof: See [] It s clear that the DBA uses only local CIR nformaton and utlzes an teratve scheme to control the transmtted power. The man dsadvantage of the DBA s that ts convergence speed s not satsfactory. If the allowed speed of the teratons s not hgh enough, then the dstrbuted algorthm may result n an outage probablty much greater than the optmum value [3]. The DBA requres a normalzaton procedure after each teraton (n noseless case) to determne the transmtted power; hence t s not fully dstrbuted [3]..4. The Dstrbuted Power Control (DPC) It has been shown that the dstrbuted power control scheme for satellte systems can be appled to cellular systems []. The results presented n [] ndcate that the DPC scheme has the potental to converge faster than the DBA scheme at hgh CIR s. The power adjustment made by the th moble at the t th tme slot s gven by

33 Chapter Two Power Control Algorthms () () t P t P ( t+ ) = β ( t) =,...,Q, t = 0,,... Γ (.8) where β(t) s some postve coeffcent chosen to acheve the proper power control vector (not too large or too small). In addtve nose envronment, t s very common to select β(t)= Γ T. Proposton (.) For a system wth M 3 (necessary condton for convergence) that uses the DPC scheme of (.8) wth β(t), t 0 chosen so that we have lm t t * t ( λ ) β( k ) <, (.9) k = 0 t () * ( * t lm P t = P blm λ ) β( k) (.0) t t k = 0 * () t γ lm Γ =, =,,Q, (.) t where b s a postve constant determned by P(0). Proof : See [] We can see from proposton (.) that as t ncreases we approach the optmum power * * control P multpled by a common factor. It s clear that P s the egenvector of the gan matrx assocated wth the largest egenvalue. β(t) can be selected as follows (n noseless case) β () t = (.) max { P ()} Q t = Equaton (.) further shows that the DPC algorthm s not a fully dstrbuted algorthm..4.3 Dstrbuted Constraned Power Control (DCPC) The transmtted power of a moble staton or a base staton s lmted by some maxmum value P max. The constraned power control generally takes the followng form

34 Chapter Two Power Control Algorthms { max ( )} ( ) ( ) P t+ = mn P, Ψ P t, t = 0,,,...; =,..., Q (.3) where Ψ (), =,..., Q s the standard nterference functon. The dstrbuted constraned power control DCPC algorthm suggested n [6] has the followng form ( ) () t T P t P ( t+ ) = mn Pmax, Γ, t = 0,,,...; =,..., Q Γ Proposton (.3) (.4) Startng wth any nonnegatve power vector P(0), the DCPC scheme descrbed n (.4) converges to the fxed pont * P of { max ( )} T ( ) ( ) P t+ = mn P, Γ HP t + u, t = 0,,,... (.5) where u s a vector wth postve elements u specfed by (.). If the target CIR s T * greater than the maxmum achevable CIR,.e., Γ γ then the fxed pont P * wll converge to P max. Proof : see [6]..4.4 Fully Dstrbuted Power Control (FDPC) Algorthm The Fully Dstrbuted Power Control (FDPC) has been proposed n [3]. The FDPC algorthm can be specfed as follows: ( ) P 0 = ( ) ( Γ () t ξ ) Γ () t mn, P t+ = P t 0 < ξ <, t=0,,... () (.6) Note that there s one parameter ξ n the above FDPC algorthm. Clearly, when ξ, the FDPC algorthm becomes the fxed power control algorthm (.e., wthout power control). For very small values of ξ the proposed FDPC reduces to the dstrbuted power control DPC algorthm (n noseless case). The man advantage of ths algorthm s that no normalzaton s requred as s the case n the other dstrbuted algorthms. In smulaton part we show that the FDPC fals to converge n dynamcal channel envronment. Proposton (.4) * * If ξ γ, then lmγ () t = γ for all. Proof: See [3]. t

35 Chapter Two Power Control Algorthms Foschn s and Mljanc s Algorthm (FMA) Foschn and Mljanc have proposed a smple and effcent dstrbuted power control algorthm [4]. The proposed algorthm s based on the followng contnuous tme dfferental equaton: ( ) ( ) T Γ τ = β[ Γ τ Γ ], β > 0, τ 0 (.7) The steady state soluton of the above dfferental equaton for user s T Γ =Γ. The speed of the convergence depends on the coeffcent β. Defne the total nterference of user : Q I ( τ ) = G ( τ) P ( τ) + N( τ) (.8) kj j j Then Γ from (.) becomes ( ) ( ) ( τ) ( τ) + ( τ) ( ) ( ) I ( τ ) Gk τ P τ Gk τ P τ Γ ( τ ) = =, =,..., Q, k =,..., M. Q G P N j kj j (.9) Assumng that I (τ) and G k (τ) are constant, substtutng (.9) nto (.7) gves GP ( τ) GP( τ) = β Γ, =,..., Q, k =,..., M. (.30) I k k T Usng (.8) becomes I T Q Γ P ( τ) = β P( τ) Gkj( τ) Pj( τ ) + N, =,..., Q, k =,..., M. (.3) Gk j Usng matrx notaton one can wrte (.3) as T ( ) ( ) P τ = β[ I Γ H] P τ + β u. (.3) At the steady state, we have P * T I H u. (.33) = Γ Proposton (.5) If there s a power vector * P, for whch the target what s the ntal P ( 0), each of the ( τ) * P of (.33). Proof: see [4]. T Γ values are attaned, then no matter P evolvng accordng to (.3) wll converge to

36 Chapter Two Power Control Algorthms 4 The dscrete form of (.3) s T P( t+ ) = β I+ Γ H P() t + β u, β t = 0,,... (.34) and the teratve power control for each user s T β Γ P ( t+ ) = ( β ) P ( t) +, t = 0,,,...; =,..., Q ( β ) Γ () t (.35) Proposton (.6) Whenever a centralzed gene can fnd a power vector then for ( 0,], to * P. * P meetng the desred crteron, β the soluton of (.35) startng from any ntal vector ( 0) P, converges Proof: See [4] Actually, the Foschn and Mljanc algorthm s a specal case of the general lnear teratve method of numercal lnear algebra, whch has been used to solve the dstrbuted power control problem [56]. The power control problem wth consderable addtve whte nose can be descrbed as Now defne T [ I Γ HP ] = u (.36) I Γ T H = M N, (.37) where M and N are Q Q matrces, M nonsngular. Then (.37) could be solved teratvely as Ths leads to ( t ) ( t) P + = M NP + M u. (.38) t t () t = ( ) () t + ( ) k. P M N P M N M u (.39) k= 0 If ( ) ( t t k ρ M N < then lm M N) 0 and snce lm ( M N) ( I M N) then t t, k 0 =

37 Chapter Two Power Control Algorthms 5 T () t ( ) = ( ) P I M N M u I Γ H u, (.40) whch s the soluton of power control problem. The foregong analyss shows that for any ntal power vector P ( 0), the lnear teratve method converges wth probablty one to the fxed pont soluton spectral radus of ( M N) T e.., Γ < ρ ( ) H. Settng * P, provdng that the s less than one, and that there s a feasble postve soluton T M = I, N= I+ ΓΗ (.4) β β n (.38) results n FMA n (.34)..4.6 Constraned Second Order Power Control (CSOPC) Jäntt and Km have proposed a second order algorthm, whch sgnfcantly enhances the convergence speed of power control [9]. The algorthm s based on the framework of the general teratve method shown n (.38). What dffers of the exstng algorthms, however, s that t has a second order teratve form gven by T Γ P( t+ ) = mn Pmax,max 0, a( t) P() t + ( a() t ) P( t ), t =,, Γ () t (.4) where P (0) and P () are chosen arbtrarly n the range nonncreasng sequence of control parameters, where a( ) < smulatons of [9], the followng relaxaton factor s employed [0, P ]. The term a(t) s a max < and lm a() t =. In a() t = + (.43).5 t * Proposton (.7) If the system s feasble, CSOPC converges to P. Proposton (.8) If the system s feasble, CSOPC s asymptotcally faster than DCPC. Proofs: See [9]. t

38 Chapter Two Power Control Algorthms Estmated Step Power Control Algorthm (ESPC) Perfect estmaton of the moble s CIR at the base staton s assumed n the prevous dstrbuted power control algorthms. In the exstng cellular communcaton system only quantzed verson of the CIR s avalable at the moble staton. To reduce the bandwdth of the feedback channel only one bt s used to represent the CIR (two or three bts are used as repettve code). In the exstng CDMA cellular system, the power control s performed as follows: ) Measure and estmate the CIR of user at ts assgned BS. ) Compare the estmated CIR wth the target. 3) If the estmated CIR s less than the target CIR, then send (+) command to ask the moble to ncrease ts transmtted power by one step. 4) If the estmated CIR s larger than the target CIR, then send (-) command to ask the moble to decrease ts transmtted power by one step. From the above steps, t s clear that the MS does not know the actual CIR value at the BS. The MS transmtted power follow the nstructons of the BS blndly. Ths type of power control s called bang-bang power control or Fxed Step Power Control (FSPC). Mathematcally, ths s represented as (all the values are n db) where ( T ) P ( t+ ) = P ( t) + δ sgn Γ Γ ( t), t = 0,,,...; =,..., Q (.44), FSPC, FSPC P FSPC mn P ( t) Pmax s the transmtted power at tme slot t, mn P and P max are the mnmum and maxmum transmtted powers respectvely, δ s the step sze of the power T update, Γ s the target CIR whch s determned by the outer loop power control, and Γ (t) s the measured CIR at tme slot t. The sgn functon s gven by ( ) sgn x = +, x 0, x < 0 (.45) It s clear from (.44) that the MS s commanded to ncrease or decrease ts transmtted power wthout detaled nformaton about the channel stuaton,.e., the MS does not know how large s the dfference between the target CIR and the measured CIR. If the measured CIR s much greater than the target CIR then t wll take a relatvely long tme to adjust the transmtted power to the proper value to make the actual CIR close to the target CIR. Ths can reduce the performance and the capacty of the system. The DCPC algorthm (.4) can be rewrtten n db scale as

39 Chapter Two Power Control Algorthms 7 ( T ) P ( t+ ) = P ( t) + Γ Γ ( t), t = 0,,,...; =,..., Q (.46) where () mn DPC, max, DPC, DPC P P t P, and all the values are n decbels. It s clear that the DCPC algorthm assumes no quantzaton dstorton so more nformaton about the channel s avalable. For ths reason the DCPC performance s better than the FSPC algorthm. In ths secton we ntroduce a new power control T algorthm based on the estmaton of the dfference ( () t ) Γ Γ by usng one bt sgnalng. We call t Estmated Step Power Control (ESPC) algorthm [93]-[94]. In what follows we consder only uplnk, but the proposed method s applcable also to downlnk. The ESPC algorthm s based on a smple trackng method, whch uses one memory locaton for the prevous BS power command. Defne for all users =,,Q, and t=0,,, T e () t =Γ Γ () t, (.47) ( e t ) ν tr, () t = sgn (), (.48) ν () t = ν () t E () t, (.49) tr, PC, where EPC, () t s wth probablty PPCE, () t and - wth probablty PPCE, ( t). PPCE, () t s the probablty of bt error n power control command transmsson at tme t. Let the estmate of the error sgnal e ( t ) be e ( t). We propose a smple form for the estmate: e () t = [ + ν() t ν( t ) ] e ( t ) + δν () t, (.50) where δ s the adaptaton step sze of user. The ESPC algorthm s gven by P ( t+ ) = P ( t) + e ( t), (.5) ESPC, ESPC, P P () t P, and all the values are n decbels. Fgure.4 shows the where mn ESPC, max block dagram of the suggested algorthm.