Power Allocation in Wireless Multi-User Relay Networks

Transcription

1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 5, MAY Power Allocaton n Wreless Mult-User Relay Networks Khoa T Phan, Student Member, IEEE, Tho Le-Ngoc, Fellow, IEEE, Sergy A Vorobyov, Senor Member, IEEE, and Chntha Tellambura, Senor Member, IEEE Abstract In ths paper, we consder an amplfy-and-forward wreless relay system where multple source nodes communcate wth ther correspondng destnaton nodes wth the help of relay nodes Conventonally, each relay equally dstrbutes the avalable resources to ts relayed sources Ths approach s clearly sub-optmal snce each user 1 experences dssmlar channel condtons, and thus, demands dfferent amount of allocated resources to meet ts qualty-of-servce (QoS) request Therefore, ths paper presents novel power allocaton schemes to ) mze the mnmum sgnal-to-nose rato among all users; ) mnmze the mum transmt power over all sources; ) mze the network throughput Moreover, due to lmted power, t may be mpossble to satsfy the QoS requrement for every user Consequently, an admsson control algorthm should frst be carred out to mze the number of users possbly served Then, optmal power allocaton s performed Although the ont optmal admsson control and power allocaton problem s combnatorally hard, we develop an effectve heurstc algorthm wth sgnfcantly reduced complexty Even though theoretcally sub-optmal, t performs remarkably well The proposed power allocaton problems are formulated usng geometrc programmng (GP), a well-studed class of nonlnear and nonconvex optmzaton Snce a GP problem s readly transformed nto an equvalent convex optmzaton problem, optmal soluton canbeobtanedeffcently Numercal results demonstrate the effectveness of our proposed approach Index Terms Power allocaton, geometrc programmng, relay networks I INTRODUCTION RECENTLY, t has been shown that the operaton effcency and qualty-of-servce (QoS) of cellular and/or ad-hoc networks can be ncreased through the use of relay(s) Manuscrpt receved Aprl 9, 2008; revsed July 16, 2008 and November 5, 2008; accepted December 27, 2008 The assocate edtor coordnatng the revew of ths paper and approvng t for publcaton was S Shen Ths work was supported n part by the Natural Scences and Engneerng Research Councl (NSERC) of Canada, and n part by the Alberta Ingenuty Foundaton, Alberta, Canada A part of ths work was presented at the IEEE Global Communcatons Conference (Globecom), New Orleans, USA, Nov 30-Dec 4 K T Phan was wth the Department of Electrcal and Computer Engneerng, Unversty of Alberta, Edmonton, AB, Canada He s now wth the Department of Electrcal Engneerng, Calforna Insttute of Technology (Caltech), Pasadena, CA 91125, USA (e-mal: kphan@caltechedu) S AVorobyov and C Tellambura are wth the Department of Electrcal and Computer Engneerng, Unversty of Alberta, Edmonton, AB, Canada T6G 2V4 (e-mal: {vorobyov, chntha}@eceualbertaca) T Le-Ngoc s wth the Department of Electrcal and Computer Engneerng, McGll Unversty, Montreal, QC, Canada H3A 2A7 (e-mal: tho@ecemcgllca) Dgtal Obect Identfer /TWC Hereafter, the term user refers to a source-destnaton par or only the source node dependng on the context /09$2500 c 2009 IEEE [1], [2] In such systems, the nformaton from the source to the destnaton s not only transmtted va a drect lnk but also forwarded va relays Although varous relay models have been studed, the smple two-hop relay model has attracted extensve research attenton due to ts mplementaton practcablty [1] [11] The performance of a two-hop relay system has been nvestgated for varous channels, e, Raylegh or Nakagam-m, and relay strateges, e, amplfy-and-forward (AF) or decode-and-forward (DF) [1] [5] Note, however, that resource allocaton s assumed to be fxed n these works A crtcal ssue for mprovng the performance of wreless networks s the effcent management of avalable rado resources [12] Specfcally, resource allocaton va power control s commonly employed As a result, numerous works have been conducted to optmally allocate the rado resources, for example power and bandwdth to mprove the performance of relay networks [6]-[11] It s worth mentonng that a sngle source-destnaton par s typcally consdered n the aforementoned papers In [6], the authors derve closed-form expressons for the optmal and near-optmal relay transmsson powers for the cases of sngle and multple relays, respectvely The problem of mnmzng the transmt power gven an acheved target outage probablty s tackled n [7] In [8], by usng ether the sgnal-to-nose rato (SNR) or the outage probablty as the performance crtera, dfferent power allocaton strateges are developed for three-node AF relay system to explot the knowledge of channel means Bounds on the channel capacty are derved for a smlar model wth Raylegh fadng and channel state nformaton (CSI) s assumed avalable at transmtter [9] The bandwdth allocaton problem n three-node Gaussan orthogonal relay system s nvestgated n [10] to mze a lower bound on the capacty Two power allocaton schemes based on mnmzaton of the outage probablty are presented n [11] for the case when the nformaton of the wreless channel responses or statstcs s avalable at transmtter It should be noted that very few works have consdered the aforementoned two-hop relay model for more practcal case of multple users 2 Therefore, the above-mentoned analyss s applcable to only a specal case of the problem under consderaton Indeed, each relay s usually delegated to assst more than one user, especally when the number of relays s 2 Note that mult-user cooperatve network employng orthogonal frequencydvson multple-access (OFDMA) where subscrbers can relay nformaton for each other s already consdered, for example see [13], [14] and references theren

2 2536 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 5, MAY 2009 (much) smaller than the number of users A typcal example of such scenaro s the deployment of few relays n a cell at convenent locatons to assst moble users operatng n heavly scatterng envronment for uplnk transmsson Relays can also be used for helpng the base staton forwardng nformaton to moble users n downlnk mode Resource allocaton n a mult-user system usually has to take nto account the farness ssue among users, ther relatve qualtyof-servce (QoS) requrements, channel qualty and so on Mathematcally, optmzng relay networks wth multple users s a challengng problem, especally when the number of users and relays s large In ths paper, we develop effcent power allocaton schemes for mult-user wreless relay systems Specfcally, we derve optmal power allocaton schemes to ) mze the mnmum SNR among all users; ) mnmze the mum transmt power over all sources; ) mze the network throughput We show that the correspondng optmzaton problems can be formulated as geometrc programmng (GP) problems Therefore, optmal power allocaton can be obtaned effcently usng convex optmzaton technques 3 Another ssue s that due to lmted power resource, achevng QoS requrements for all users may turn out to be mpossble Therefore, some sort of admsson control where users are not automatcally admtted nto the network, wth pre-specfed obectves should be carred out Yet, none of the exstng works has consdered ths practcal scenaro n the context of relay communcatons Note, however, that the methodology for ont multuser downlnk beamformng and admsson control has been recently developed n [18] In ths paper, we also propose a ont admsson control and power allocaton algorthm for mult-user relay systems The proposed algorthm frst ams at mzng the number of users that can be admtted and QoS-guaranteed Then, the optmal power allocaton s performed Snce the aforementoned ont admsson control and power allocaton problem s combnatorally hard, we develop an effectve heurstc approach wth sgnfcantly reduced complexty Moreover, the algorthm determnes accurately the users to be admtted n most of the smulaton examples As well, ts complexty n terms of runnng tme s much smaller than that of the orgnal optmal admsson control problem A prelmnary verson of ths work has been presented n [19] Durng the revew process for ths paper, the authors also became aware of the very recent contrbutons [20], [21] In [20], the ont power and admsson control problem s solved n the context of tradtonal cellular networks, whle the same problem s consdered n [21] n the context of cogntve underlay networks The rest of ths paper s organzed as follows In Secton II, a mult-user wreless relay model wth multple relays s descrbed Secton III contans problem formulatons for three power control schemes The proposed problems are converted nto GP problems n Secton IV The problem of 3 Note that GP has been successfully appled to approxmately solve the power allocaton problem n tradtonal cellular and ad hoc networks [15], [16] The exact soluton for the same problem can be obtaned usng the dfference of two convex functons optmzaton at a prce of hgh complexty [17] ont admsson control and power allocaton s presented n Secton V The algorthm for solvng the ont admsson control and power allocaton problem s descrbed n Secton VI Numercal examplesare presented n Secton VII, followed by the conclusons n Secton VIII II SYSTEM MODEL Consder a mult-user relay network where M source nodes S, {1, M} transmt data to ther correspondng destnaton nodes D, {1,M} 4 There are L relay nodes R, {1,, L} whch are employed for forwardng the nformaton from source to destnaton nodes The conventonal two-stage AF relayng wth orthogonal transmsson through tme devson [1], [2], [11] s assumed Therefore, to ncrease the throughput (or more precsely, to prohbt decreasng of the throughput), each source S s asssted by one relay denoted by R S Sngle relay assgnment for each user also reduces the coordnaton between relays and/or mplementaton complexty at the recevers 5 The set of source nodes whch use the relay R s denoted by S (R ), e, S(R )={S R S = R } Let P S, P RS denote the power transmtted by source S and relay R S n the lnk S -R S -D, respectvely Snce unt duraton tme slots are assumed, P S and P RS correspond also to the average energes consumed by source S and relay R S For smplcty, we present the sgnal model for lnk S -R S - D only In the frst tme slot, source S transmts the sgnal x wth unt energy to the relay R S 6 The receved sgnal at relay R S can be wrtten as r SR S = P S a SR S x + n RS where a SR S stands for the channel gan for lnk S -R S, n RS s the addtve crcularly symmetrc whte Gaussan nose (AWGN) at the relay R S wth varance N RS The channel gan ncludes the effects of path loss, shadowng and fadng In the subsequent tme slot, assumng the relay R S knows the CSI for lnk S -R S, t uses the AF protocol, e, t normalzes the receved sgnal and retransmts to the destnaton node D The receved sgnal at the destnaton node D can be expressed as r SR S r D = P RS a RS D E { r SR S 2} + n D = P RS P S P S a SR S 2 + N RS a RS D a SR S x +ˆn D where E{ } denotes statstcal expectaton operator, a RS D s the channel coeffcent for lnk R S -D, n D s the AWGN at the destnaton node D wth varance N D, ˆn D s the modfed AWGN nose at D wth equvalent varance + ( ) ( ) P RS a RS D 2 N RS / PS a SR S 2 + N RS The N D 4 Ths ncludes the case of one destnaton node for all sources, for example, a base staton n cellular network, or a central processng unt n a sensor network 5 The sngle relay assgnment may be done durng the connecton setup phase, or done by relay selecton process [11] 6 We consder the case n whch the source-to-relay lnk s (much) stronger than the source-to-destnaton lnk, that s usual scenaro n practce

3 PHAN et al: POWER ALLOCATION IN WIRELESS MULTI-USER RELAY NETWORKS 2537 equvalent SNR of the vrtual channel between source S and destnaton D can be wrtten as [11] γ = P RS P S a RS D 2 a SR S 2 P S a SR S 2 N D + P RS a RS D 2 N RS + N D N RS = P S P RS η P S + α P RS + β N RS N D where η = ND a RS D, α 2 = NR S a S R S, β 2 = a S R S 2 a RS D 2 It can be seen that for fxed P RS, γ s a concave ncreasng functon of P S However, no matter how large P S s, the mum achevable γ can be shown to be equal to P RS /η Vce versa, when P S s fxed, γ s a concave ncreasng functon of P RS and the correspondng mum achevable γ s P S /α Moreover, snce γ s a concave ncreasng functon of P S, the ncremental change n γ s smaller for large P S,andγ s monotone Note that monotoncty s a useful property helpng to provde some nsghts nto optmzaton problems at optmalty In the followng sectons, we consder effcent power allocaton and admsson control schemes based on a centralzed approach wth assumed complete knowledge of channel gans Ths assumpton nvolves some tmely and accurate channel estmaton and feedback technques whch are beyond the scope of ths paper III POWER ALLOCATION IN MULTI-USER RELAY NETWORKS: PROBLEM FORMULATIONS Power control for sngle user relay networks has been popularly advocated [6]-[11] In ths secton, we extend the power allocaton framework to mult-user networks Dfferent power allocaton based crtera whch are sutable and dstnct for mult-user networks are nvestgated A Max-mn SNR Based Allocaton Power control n wreless networks often has to take nto account the farness consderaton snce the farness among dfferent users s also a maor ssue n a QoS polcy In other words, the performance of the worst user(s) s also of concern to the network operator Note that the tradtonally used mum sum SNR based power allocaton favors users wth good channel qualty Instead, we consder -mn far based power allocaton problem whch ams at mzng the mnmum SNR over all users 7 Ths can be mathematcally posed as P S,P RS subect to: mn γ =1,,M S S(R ) P RS (1a) P R,=1,,L (1b) P S P (1c) =1 0 P S PS,=1,,M (1d) where PR s the avalable power at the relay R and P s the mum total power of all sources The left-hand sde of (1b) 7 In ths way, the mnmum data rate among users s also mzed snce data rate s a monotonc ncreasng functon of SNR s the total power that R allocates to ts relayed users, and thus, t s lmted by the mum avalable power of the relay Constrant (1c) represents the possble lmt on the total power of all sources whle the constrant (1d) specfes the peak for source S We should emphasze here that n applcatons when sources are operatng ndependently, t s suffcent to have only lmts on the ndvdual source powers ndcated by (1d), and (1c) can be effectvely removed power lmt P S by smply settng P M =1 P S In ths case, sources S,=1,,M would transmt wth ther mum power PS However, there are applcatons where the total power s of concern, eg, when the sources share a common power pool as n the case of a base-staton (or access pont, access node) transmtter, or n an energy-aware system when energy consumpton and related emsson n the system are more related to total power than ndvdual peak powers In such a case, t s possble that P < M =1 P S, and both the constrants (1c) and (1d) are appled n order to control the total power consumed by all sources wthn a specfed target In other words, the constrant (1c) s ncluded n (1a) (1d) for the sake of generalty On the other hand, there s no such lmt for relay nodes snce relays are usually energyunlmted statons Note, however, that such constrant for the relays can be ncluded straghtforwardly In terms of system mplementaton, the constrant (1c) requres the sources to be coordnated n order to share the power resource It can be seen that the set of lnear nequalty constrants wth postve varables n the optmzaton problem (1a) (1d) s compact and nonempty Hence, the problem (1a) (1d) s always feasble Moreover, snce the obectve functon mn =1,,M γ s an ncreasng functon of the allocated powers P S and P RS, the nequalty constrants (1b), (1c) must be met wth equalty at optmalty when P M =1 P S Moreover, when P> M, the nequalty constrants =1 P S (1b), (1d) must be met wth equalty at optmalty It can be observed that whle the performance of user depends only on the allocated powers P S and P RS, the performance of all users nteract wth each other va shared and lmted power resource at the relays and the sources Therefore, proper power allocaton among users s necessary to mze a specfc crteron on the system performance 8 B Power Mnmzaton Based Allocaton In wreless networks, power allocaton can help to acheve the mnmum QoS and low power consumpton for users Commonly, to mprove the lnk performance, the source can transmt at ts mum avalable power whch causes tself to run out of energy quckly Fortunately, by takng nto consderaton the channel qualtes, relatve QoS requrements of users and optmal power allocaton at the relays, sources mght not always need to transmt at ther largest power Therefore, sources save ther power and prolong ts lfetme Snce the relays usually have much less severe energy constrants, resource allocaton n relay networks can explot the 8 Resource allocaton n a mult-user network s not as smple as allocatng resources for each user ndvdually, albet orthogonal transmssons are assumed

4 2538 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 5, MAY 2009 avalable power at the relays to save power at the energylmted source nodes One of the most reasonable desgn obectves s the mnmzaton of the mum transmt power over all sources Subect to the SNR requrements for each user, the resultng optmzaton problem can be posed as good users mn P S,P RS subect to: =1,,M P S (2a) γ γ mn,=1,,m (2b) The constrants (1b), (1d) (2c) SNR γ bad users where γ mn s the threshold SNR for th user 9 However, there are applcatons where the total power s of concern, eg, when the sources share a common power pool as n the case of a base-staton (or access pont, access node) transmtter, or n an energy-aware system n whch energy consumpton and related emsson are more related to total power than ndvdual peak power In such applcatons, mnmzng the total power, e, mn M PS,P RS =1 P S, can be a more approprate obectve snce t s expected to provde a soluton wth lower sum power Moreover, a weghted sum of powers may be also consdered to cover the general case of non-homogeneous users It can be observed that at optmalty, the nequalty constrants (2b) and (1b) n (2c) must be met wth equalty Ths s because γ s an ncreasng functon of P S and P RS Inorder to mnmze P S, γ and P RS must attan ther mnmum and mum values, respectvely Note that we have mplctly assumed n (2a) (2c) that none of the sources needs to transmt more than PS at optmalty C Throughput Maxmzaton Based Allocaton The -mn SNR based allocaton mproves the system performance by mprovng the performance of the worst user On the other hand, t s well-known that the -mn farness among users s assocated wth a loss n the network throughput, e, the users sum rate For some applcatons whch requre hgh data rate transmsson from any user, t s preferable to allocate power to mze the network throughput Users wth good channel qualty can transmt faster and users wth bad channel qualty can transmt slower Moreover, the network throughput, n the case of perfect CSI and optmal power allocaton, defnes the upper bound on the system achevable rates Gven the SNR γ of user, the data rate R can be wrtten as a functon of γ as R = 1 T log 2(1 + Kγ ) 1 T log 2(Kγ ) where T s the symbol perod whch s assumed to be equal to 1 for brevty, K = ζ 1 / ln(ζ 2 BER), BER s the target bt error rate, and ζ 1, ζ 2 are constants dependent on the modulaton scheme [22] Note that we have approxmated 1+Kγ as Kγ whch s reasonable when Kγ s much larger than 1 For notatonal smplcty n the rest of the paper, we set K =1 Then, the aggregate throughput for the system can 9 We assume that the threshold γ mn s not larger than the mum achevable SNR for user as prevously dscussed P R S Fg 1 SNR versus allocated power at the relay node (source powers are fxed and equal) be wrtten as [16] R = [ M R log 2 γ ] =1 =1 The power allocaton problem to mze the network throughput can be mathematcally posed as [ M ] log 2 γ (3a) P S,P RS =1 subect to: The constrants (1b), (1c), (1d) (3b) Therefore, n the hgh SNR regon, mzng network throughput can be approxmately replaced by mzng the product of SNRs 10 Here, we have assumed that there s no lower lmt constrant 11 At optmalty, the nequalty constrants (1b), (1c) n (3b) of the problem (3a) (3b) must be met wth equalty when P M =1 P S Moreover, when P > M =1 P S, the nequalty constrants (1b), (1d) must be met wth equalty at optmalty Smlar to the prevous problems, ths can be explaned usng the monotoncty of the obectve functon (3a) Note that the throughput mzaton based power allocaton (3a) (3b) does not penalze users wth bad channels and favor users wth good channels Ths s dfferent from the scenaro when network throughput mzaton s used as a crteron for power allocaton n cellular networks where some users are prevented from transmttng data [16] However n our case, as the SNR γ for a partcular user s concave ncreasng functon of allocated powers, the ncremental change n SNR s smaller for larger transmt power In Fg 1, we plot the SNRs versus allocated power at the relays when source powers are fxed and equal It can be seen that nstead 10 Note, however, that n the low SNR regon, the approxmaton of 1+γ by γ does not hold satsfactorly, and therefore, wll not gve accurate results 11 Such constrant for each user can be, however, easly ncorporated n the problem

5 PHAN et al: POWER ALLOCATION IN WIRELESS MULTI-USER RELAY NETWORKS 2539 of allocatng more power to the users wth good channel condtons at hgh SNR, the proposed scheme allocates power to the users wth bad channel condtons at low SNR It results n better mprovement n the sum throughput of the network Ths explans why the performance of the users wth bad channel condtons s not severely affected Ths fact s also confrmed n the smulaton secton IV POWER ALLOCATION IN RELAY NETWORKS VIA GP GP s a well-nvestgated class of nonlnear, nonconvex optmzaton problems wth attractve theoretcal and computatonal propertes [15], [16] Snce equvalent convex reformulaton s possble for a GP problem, there exst no local optmum ponts but only global optmum Moreover, the avalablty of large-scale software solvers makes GP more appealng A Max-mn SNR Based Allocaton Introducng a new varable t, we can equvalently rewrte the optmzaton problem (1a) (1d) as follows mn P S,P RS,t 0 subect to: 1 t (4a) P S P RS t, =1,,M(4b) η P S + α P RS + β The constrants (1b), (1c), (1d) (4c) The obectve functon n the problem (4a) (4c) s a monomal functon Moreover, the constrants n (4b) can be easly converted nto posynomal constrants The constrants (1b), (1c), (1d) are lnear on the power varables, and thus, are posynomal constrants Therefore, the optmzaton problem (4a) (4c) s a GP problem B Power Mnmzaton Based Allocaton In ths case, by usng an extra varable t, the obectve can be recast as monomal t wth monomal constrants P S t The constrants can be also wrtten n the form of posynomals Therefore, the power mnmzaton based allocaton s a GP problem C Throughput Maxmzaton Based Allocaton A smple manpulaton of the optmzaton problem (3a) (3b) gves 1 mn P S,P M RS =1 γ (5a) subect to: The constrants (1b), (1c), (1d) (5b) Each of the terms 1/γ s a posynomal n P S, P RS and the product of posynomals s also a posynomal Therefore, the optmzaton problem (5a) (5b) belongs to the class of GP problems 12 As mzng aggregate throughput can be unfar to some users, a weghted sum of data rates, e, 12 Note that the hgh operatng SNR regon s assumed If medum or low SIR regons are assumed, the approxmaton 1+γ by γ may not be accurate In ths case, successve convex approxmaton method as n [16] can be used However, t s outsde of the scope of ths paper M =1 w R where w s a gven weght coeffcent for user, can be used as the obectve functon to be mzed Usng some manpulatons, the resultng optmzaton problem can be reformulated as a GP problem as well We have shown that the three aforementoned power allocaton schemes can be reformulated as GP problems The proposed optmzaton problems wth dstnct features of relayng model are mathematcally smlar to the ones n [16] for conventonal cellular network However, the numerator and denomnator of the SNR expresson for each user consdered n [16] are lnear functons of the power varables whch s not the case n our work V JOINT ADMISSION CONTROL AND POWER ALLOCATION It s well-known that one of the mportant resource management ssues s the determnaton of whch users to establsh connectons Then, rado resources are allocated to the connected users n order to ensure that each connected user has an acceptable sgnal qualty [23] Snce wreless systems are usually resource-lmted, they are typcally unable to meet users QoS requrements that need to be satsfed Consequently, users are not automatcally admtted and only certan users can be served Our admsson control algorthm determnes whch users can be admtted concurrently Then, the power allocaton s used to mnmze the transmt power A Revsed Power Mnmzaton Based Allocaton The problem formulaton (2a) (2c) can be shown to be feasble as long as γ mn,=1,,m s less than the mum achevable value Ths s because t has been assumed that the sources are able to transmt as much power as possble to ncrease ther SNRs Ths approach s mpractcal for some wreless applcatons wth strctly lmted total transmt power, for nstance, power lmtaton of the base staton n downlnk transmsson The power mnmzaton based problem ncorporatng the power constrant can be wrtten as mn P S,P RS subect to: =1 P S (6a) P S P (6b) =1 The constrants (2b), (2c) (6c) Note that the obectve functon n the above problem s suffcently general 13, and t ams at mnmzng the overall energy consumed by the group of sources It requres the cooperaton among sources Such cooperaton can be organzed n dfferent ways The smplest example s the presence of only one source (a base staton n downlnk transmsson) wth multple antennas Also note that n some applcatons, the constrant (6b) can be effectvely excluded from the problem formulaton (6a) (6c) by settng P M =1 P S Snce the obectve functon s a sum of powers, some sources may need to transmt more power than the others at optmalty Note that 13 A more general obectve functon could be the weghted sum, e, M =1 w P S where w s a weght coeffcent for source

6 2540 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 5, MAY 2009 for some applcatons t can be more approprate to consder the followng alternatve problem formulaton mn P S,P RS =1,,M P S (7a) subect to: The constrants (6b), (6c) (7b) Our methodology can be straghtforwardly adapted to cover the above formulaton as well However, due to space lmtaton, we skp the detals here There are nstances when the optmzaton problem (6a) (6c) becomes nfeasble For example, when SNR targets are too hgh, or when the number of users M s large However, the core reason for nfeasblty s the power lmts of both the relays and/or the sources A practcal mplcaton of the nfeasblty s that t s mpossble to serve (admt) all M users at ther desred QoS requrements Some approaches to the nfeasble problem can be however used For nstance, some users can be dropped or the SNR targets could be relaxed, e, made smaller We nvestgate the former scenaro and try to mze the number of users that can be served at ther desred QoS γ mn B Mathematcal Framework for Jont Admsson Control and Power Mnmzaton Problem Followng the methodology developed n [18], the ont admsson control and power allocaton problem can be mathematcally stated as a 2-stage optmzaton problem All possble sets of admtted users S 0,S 1, (can be only one or several sets) are found n the frst stage by solvng the followng optmzaton problem arg S (8a) S {1,,M}, P S,P RS subect to: γ γ mn, S (8b) The constrants (6b), (2c) (8c) where S denotes the cardnalty of S We should note that although the sets S 0,S 1, contan dfferent users, they have the same cardnalty Gven each set S 0,S 1, of admtted users, the transmt power s mnmzed n the second stage The correspondng optmzaton problem can be wrtten, for example, for the set S k as P opt k = argmn (9a) P S,P RS subect to: S k P S γ γ mn, S k (9b) The constrants (6b), (2c) (9c) The optmal set of admtted users S k s the one among the sets S 0,S 1, whch requres mnmum P opt k Alternatvely, the ont admsson control and power mnmzaton can be regarded as a blevel programmng problem The admsson control problem s combnatorally hard, and therefore, s more dffcult Ths s because the number of possble sets of admtted users grows exponentally wth M Once the sets of admtted users are determned, the power mnmzaton problem s ust the problem (2a) (2c) Greedy algorthm(s) can be used to solve the frst stage However, t s noted that there may be many sets of admtted users wth the same mal cardnalty and dervng optmal greedy algorthm(s) s obvously a dffcult problem Due to ts combnatoral hardness, the ont admsson control and power allocaton problem admts hgh complexty for practcal mplementaton In the followng secton, we propose an effcent algorthm to sub-optmally solve (8a) (8c) and (9a) (9c) wth sgnfcantly reduced complexty VI PROPOSED ALGORITHM A A Reformulaton of Jont Admsson Control and Power Allocaton Problem Optmal admsson control (8a) (8c) nvolves exhaustvely solvng all subsets of users that s NP-hard Therefore, a better way of solvng the problem of ont admsson control and power allocaton s hghly desrable The admsson control problem (8a) (8c) can be mathematcally recast as follows s (10a) s {0,1}, P S,P RS =1 subect to: γ γ mn s,=1,,m (10b) The constrants (6b), (2c) (10c) where the ndcator varables s, = 1,,M,e,s = 0, s =1means that user s not admtted, or otherwse, respectvely The followng theorem s n order THEOREM 1: The aforementoned 2-stage optmzaton problem (8a) (8c) and (9a) (9c) s equvalent to the followng 1-stage optmzaton problem s {0,1}, P S,P RS subect to: ɛ s (1 ɛ) =1 =1 P S (11a) γ γ mn s,=1,,m (11b) The constrants (6b), (2c) (11c) where ɛ s some constant and s chosen such that P/(P +1) < ɛ<1 PROOF: The proof s a 2-step process In the frst step, we prove that the soluton of the one-stage problem (11a) (11c) and that of the admsson control problem (10a) (10c) wll both gve the same mum number of admtted users Suppose that S 0 +, P + S, P + R S s (one of) the optmal solutons of the admsson control problem (10a) (10c) wth optmal value S 0 + = n+ 14 Smlarly, suppose that S0, P S, PR S s the optmal soluton of the problem (11a) (11c) and S0 = n Thus, the optmal value of (11a) (11c) s L = ɛn (1 ɛ) M =1 P S We show that n = n + by usng contradcton Let us suppose that n <n + Snce the problems (10a) (10c) and (11a) (11c) have the same set of constrants, and thus, the same feasble set, the set S 0 +, P + S, P + R S s also a feasble soluton to (11a) (11c) wth the obectve value L + = ɛn + (1 ɛ) M =1 P + S Wehave ( M ) L + L = ɛ(n + n )+(1 ɛ) PS P + S =1 =1 ɛ (1 ɛ)p > 0 (12) 14 We should note that n + s some unknown but t s a fxed number

7 PHAN et al: POWER ALLOCATION IN WIRELESS MULTI-USER RELAY NETWORKS 2541 The frst nequalty corresponds to the assumpton that n + n 1 and the fact that PS P + S P =1 =1 The latter fact holds true because M =1 P S P and M =1 P + S P The second nequalty s vald due to the choce of P/(P +1) <ɛ<1 Ths obvously contradcts the assumpton that S0, P S, PR S s the optmal soluton of (11a) (11c) Therefore, we conclude that n cannot be less than n + On the other hand, we also have S0, PS, PR S s a feasble soluton of (10a) (10c) Therefore, the optmal value of (10a) (10c) s at least equal to S0 = n, e, n + n By the vrtues of two mentoned facts, we conclude that n = n +, or equvalently, the soluton of the one-stage optmzaton problem (11a) (11c) gves the same number of admtted users as that of the soluton of the admsson control problem (10a) (10c) In the second step, we prove that the user set obtaned by solvng (11a) (11c) s the optmal set of admtted users wth mnmum transmt power Agan, suppose that S 0, P S, P R S s another feasble soluton to (11a) (11c) such that S 0 = S 0 = n wth the obectve value L = ɛn (1 ɛ) M =1 P S SnceS0, P S, PR S s the optmal soluton of (11a) (11c), we must have L < L, or equvalently, M =1 P S < M =1 P S Therefore, among sets whch have the same mum number of admtted users, the one obtaned by solvng (11a) (11c) requres the mnmum transmt power Ths completes the proof Careful observaton reveals some nsghts nto the optmzaton problem (11a) (11c) whch s n rather smlar form as the one n [18] For example, t s smlar to a mult-obectve optmzaton problem, e, mzaton of the number of admtted users and mnmzaton of the transmt power, wth ɛ beng the prorty for the former crteron Therefore, t s reasonable to set ɛ large to mze number of admtted users as a prorty The formulaton (11a) (11c) provdes a compact and easy-to-understand mathematcal framework for the ont optmal admsson control and power allocaton However, as well as the orgnal 2-stage problem, the formulaton (11a) (11c) s NP-hard to solve Moreover, t s easy to see that the optmzaton problem (11a) (11c) s always feasble Ths s due to the fact that no users are admtted n the worst case, e, s =0,=1,,M To ths end, we should menton that the optmzaton problem (11a) (11c) s extremely hard, f possble, to solve It belongs to the class of nonconvex nteger optmzaton problems Therefore, we next propose a reduced-complexty heurstc algorthm to perform ont admsson control and power allocaton Albet theoretcally sub-optmal, ts performance s remarkably close to that of the optmal soluton for most of the testng nstances (see Secton VII) B Proposed Algorthm The followng heurstc algorthm can be used to solve (11a) (11c) Step 1 Set S := {S =1,,M} 200 m Y-Axs Fg 2 Source 2 Source M Source 1 Source 3 Relay 3 Relay 2 Relay m X-Axs 150 m A wreless relay system Destnaton 1 Destnaton 3 Destnaton M Destnaton m Step 2 Solve GP problem (6a) (6c) wthout the constrant (6b) for the sources n S LetPS, PR S denote the resultng power allocaton values Step 3 If S P S S P, then stop and PS, PR S beng power allocaton values Otherwse, user S wth largest } requred power value, e, S = arg S S{ P S s removed from S and go to step 2 We can see that after each teraton, ether the set of admtted users and the correspondng power allocaton levels are determned or one user s removed from the lst of most possbly admtted users Snce there are M ntal users, the complexty s bounded above by that of solvng M GP problems of dfferent dmensons It worths mentonng that the proposed reduced complexty algorthm always returns one soluton VII SIMULATION RESULTS Consder a wreless relay network as n Fg 2 wth 10 users and 3 relays dstrbuted n a two-dmensonal regon 200m 200m The relays are fxed at coordnates (100,50), (100,100), and (100,150) The ten source nodes and ther correspondng destnaton nodes are deployed randomly n the area nsde the box areas [(0, 0), (50, 200)] and [(150, 0), (200, 200)], respectvely In our smulatons, each source s asssted by a random (and then fxed) relay For smulaton smplcty, we assume that there s no mcroscopc fadng and the gan for each transmsson lnk s computed usng the path loss model as a =1/d where d s the Eucldean dstance between two transmsson ends 15 The nose power at the recever ends s assumed to be dentcal and equals to N 0 = 50 db Although each relay node may assst dfferent number of users, they are assumed to have the same mum power level P R Smlarly, all users are assumed to have equal mnmum SNR thresholds γ mn We have used software package [24] for solvng convex programs n our smulatons 15 If fadng s present, the proposed technques can also be straghtforwardly appled assumng that the nstantaneous channel fadng gans are known and not vared durng the tme requred to compute the solutons In ths case, the average performance computed over a long tme nterval for dfferent sets of channel fadng gans can serve as a performance measure

8 2542 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 5, MAY Worst User Data Rate Optmal Power Allocaton Equal Power Allocaton 3 P R Worst User Data Rate Transmt Power Optmal Power Allocaton Equal Power Allocaton Network Throughput Optmal Power Allocaton Equal Power Allocaton 44 P R Network Throughput Transmt Power Optmal Power Allocaton Equal Power Allocaton Fg 3 Max-mn SNR based allocaton: data rate versus P R Fg 4 Max-mn SNR based allocaton: data rate versus P A Power Allocaton wthout Admsson Control 1) Max-mn SNR based allocaton: Fgs 3 and 4 show the mnmum rate of the users and the network throughput when the mum power levels of the relays PR and sources P are vared The performance of the equal power allocaton (EPA) scheme s also plotted In ths case, the power s allocated equally among all sources, e, P S = P/10, S and each relay dstrbutes power equally among all relayed users For P =50(see Fg 3), the optmal power allocaton (OPA) scheme acheves about 08 bts performance mprovement over the EPA scheme for the worst user data rate The performance mprovement of both schemes s hgher when PR s small (less than 30) The EPA scheme provdes a slght performance mprovement for the worst user(s) for PR 35 However, the OPA scheme s able to take advantage from larger PR Ths demonstrates the effectveness of OPA scheme n general and our proposed approach n partcular In Fg 4, we fx PR = 50 It can be seen that the OPA scheme also outperforms the EPA scheme The mprovement s about 08 bts and ncreases when P ncreases In both scenaros, t can be seen that snce our obectve s to mprove the performance of the worst user(s), there s a loss n the network throughput Ths confrms the well-known fact that achevng -mn farness among users usually results n performance loss for the whole system 2) Power mnmzaton based allocaton: Fgs 5 and 6 dsplay the total transmt power and the mum power of all users for two scenaros, where n the frst scenaro the obectve s to attan a mnmum SNR γ mn wth fxed P R =50, whle n the second scenaro t s assumed that PR s vared wth fxed γ mn =10dB We plot the results for both the mnmzaton of the mum power based power allocaton (mn- scheme) and the mnmzaton of sum power based power allocaton (mnmum sum power scheme) For the frst scenaro, the OPA mnmum sum power scheme allocates less power than that of the EPA and OPA mn- schemes Moreover, when γ mn 18 db, the EPA scheme can not fnd a feasble power allocaton (n fact, suggests negatve power allocaton) whch s represented by the werd part n the EPA curve It s because the threshold γ mn 18 db exceeds Sum Transmt Power Maxmum Power Fg 5 Optmal Power Allocaton Mn Power Allocaton Equal Power Allocaton mn γ Optmal Power Allocaton Max mn Power Allocaton mn γ Power mnmzaton based allocaton: transmt power versus γ mn the mum value of γ for some users as dscussed n Secton II We can see that by approprate power dstrbuton at the relays, OPA scheme can fnd power allocaton to acheve larger target SNR γ mn Ths further demonstrates the advantages of our proposed approach over the EPA scheme Moreover, the OPA mn- scheme needs sgnfcantly larger total transmt power than the OPA mnmum sum power scheme Therefore, the latter scheme s preferable when applcable For the second scenaro, the OPA mnmum sum power scheme agan requres less total power than that of the EPA and OPA mn- scheme, especally when PR s small The transmt power requred by the -mn scheme s sgnfcantly larger than that requred by the other two schemes It can be observed that as there s more avalable PR,less sum power s requred to acheve a target SNR 3) Throughput mzaton based allocaton: In the last example, we use the OPA to mze the network throughput Fg 7 shows the performance of our proposed approach when P =50 The OPA scheme outperforms the EPA for all values of PR It s notceable that OPA scheme acheves better performance n terms of both worst user data rate and network throughput Comparng wth the results n Fgs 3 and 4, we can see the tradeoff between achevng versus P R

9 PHAN et al: POWER ALLOCATION IN WIRELESS MULTI-USER RELAY NETWORKS 2543 Sum Transmt Power Maxmum Power P R Equal Power Allocaton Mn Power Allocaton Optmal Power Allocaton Optmal Power Allocaton Mn Power Allocaton 22 P R Fg 6 Worst User Data Rate Network Throughput Power mnmzaton based allocaton: transmt power versus P R 3 P R Optmal Power Allocaton Equal Power Allocaton Optmal Power Allocaton Equal Power Allocaton 46 P R Fg 7 Throughput mzaton based allocaton: data rate versus P R farness and sum throughput P =50, P R TABLE I =50,RUNNING TIME IN SECONDS Enumeraton Proposed Algorthm SNR 17 db 17 db # users served 8 8 Users served 1, 2, 4, 5, 7, 8, 9, 10 1, 2, 4, 5, 7, 8, 9, 10 Transmt power Users served 1, 2, 3, 4, 5, 8, 9, 10 - Transmt power Users served 1, 2, 3, 4, 7, 8, 9, 10 - Transmt power Users served 1, 2, 4, 5, 6, 8, 9, 10 - Transmt power Users served 1, 2, 4, 6, 7, 8, 9, 10 - Transmt power Runnng tme SNR 18 db 18 db # users served 7 7 Users served 1, 2, 4, 5, 8, 9, 10 1, 2, 4, 7, 8, 9, 10 Transmt power Users served 1, 2, 3, 4, 8, 9, 10 - Transmt power Users served 1, 2, 4, 7, 8, 9, 10 - Transmt power Users served 1, 4, 5, 7, 8, 9, 10 - Transmt power Runnng tme SNR 19 db 19 db # users served 6 6 Users served 1, 2, 4, 8, 9, 10 1, 2, 4, 8, 9, 10 Transmt power Users served 1, 4, 7, 8, 9, 10 - Transmt power Runnng tme SNR 20 db 20 db # users served 5 5 Users served 1, 4, 8, 9, 10 1, 4, 8, 9, 10 Transmt power Users served 1, 2, 4, 8, 10 - Transmt power Users served 1, 2, 8, 9, 10 - Transmt power Users served 2, 4, 8, 9, 10 - Transmt power Runnng tme B Jont Admsson Control and Power Allocaton In ths secton, we provde several testng nstances to demonstrate the performance of the proposed admsson control scheme For such purpose, the performance of the optmal admsson control s used as benchmark results 16 The convenent and nformatve method of representng results as n [18] s used In Tables I and II, PR are taken to be equal to 50 and 20, respectvely whle P s fxed at P =50 Dfferent values of γ mn are used To gan more nsghts nto the optmal admsson control and power allocaton problem, all feasble subsets of users whch have mum possble number of users are also provded n Table I 17 The optmal subset of users s the one whch requres the smallest transmt power The runnng tmes requred for the optmal exhaustve search based algorthm and the proposed algorthm are also shown 16 Optmal admsson control s done by solvng the problem (8a) (8c) for all possble combnatons of users 17 In Tables II and III, only the optmal set of users and ts correspondng transmt power are provded As we can see, our proposed algorthm determnes exactly the optmal number of admtted users and the users themselves n all cases except for the case when PR =20, γ mn =19dB The transmt power requred by our proposed algorthm s exactly the same as that requred by the optmal admsson control usng exhaustve search However, the complexty n terms of runnng tme of the former algorthm s much smaller than that of the latter Ths makes the proposed approach attractve for practcal mplementaton Moreover, t s natural that when γ mn ncreases, less users are admtted wth a fxed amount of power For example, when PR =50, eght users and sx users are admtted wth SNR γ mn =17dB and 19 db, respectvely Smlarly, when more power s avalable, more users are lkely to be admtted for a partcular γ mn threshold For nstance, when γ mn = 19 db, sx and four users are admtted wth PR =50and 20, respectvely Table III dsplays the performance of the proposed algorthm when PR =50and P =20 The proposed algorthm s able to decde correctly (optmally) whch users should be

10 2544 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 5, MAY 2009 TABLE II P =50, P R =20 Enumeraton Proposed Algorthm SNR 17 db 17 db # users served 7 7 Users served 1, 2, 4, 5, 8, 9, 10 1, 2, 4, 5, 8, 9, 10 Transmt power SNR 19 db 19 db # users served 4 3 Users served 1, 4, 8, 10 8, 9, 10 Transmt power SNR 21 db 21 db # users served 3 3 Users served 4, 8, 10 8, 9, 10 Transmt power TABLE III P =20, P R =50 Enumeraton Proposed Algorthm SNR 17 db 17 db # users served 4 4 Users served 1, 8, 9, 10 1, 8, 9, 10 Transmt power SNR 19 db 19 db # users served 3 3 Users served 8, 9, 10 8, 9, 10 Transmt power SNR 21 db 21 db # users served 2 2 Users served 8, 10 8, 10 Transmt power admtted and assgn an optmal amount of power for each admtted user As before, less users are admtted when the requred SNR threshold s larger Moreover, as P ncreases, more users can be admtted For example, when PR =50 and γ mn = 17 db, four and eght users are admtted for P =20and P =50, respectvely VIII CONCLUSIONS In ths paper, we have proposed the power allocaton schemes for wreless mult-user AF relay networks Partcularly, we have presented three power allocaton schemes to ) mze the mnmum SNR among all users; ) mnmze the mum transmt power over all sources; ) mze the network throughput Although the problem formulatons are nonconvex, they were equvalently reformulated as GP problems Therefore, obtanng optmal power allocaton can be done effcently va convex optmzaton technques Smulaton results demonstrate the effectveness of the proposed approaches over the equal power allocaton scheme Moreover, snce t may not be possble to admt all users at ther desred QoS demands due to lmted power resource, we have proposed a ont admsson control and power allocaton algorthm whch amed at mzng the number of users served and mnmzng the transmt power A hghly effcent GP heurstc algorthm s developed to solve the proposed nonconvex and combnatorally hard problem In ths paper, the GP problems are solved n a centralzed manner usng the hghly effcent nteror pont methods However, whether dstrbuted power allocaton va GP s possble s an nterestng research area ACKNOWLEDGEMENTS We would lke to thank the anonymous revewers for comments and suggestons whch helped to mprove the qualty of the paper We are also grateful to Mr Duy H N Nguyen from the Unversty of Saskatchewan, Dr Long Le from the Massachusetts Insttute of Technology, and Dr Ncholas D Sdropoulos from Techncal Unversty of Crete for helpful dscussons and comments REFERENCES [1] J N Laneman, D N C Tse, and G W Wornell, Cooperatve dversty n wreless networks: effcent protocols and outage behavor, IEEE Trans Inform Theory, vol 50, pp , Dec 2004 [2] M O Hasna and M S Aloun, End-to-end performance of transmsson systems wth relays over Raylegh fadng channels, IEEE Trans Wreless Commun, vol 2, pp , Nov 2003 [3] P A Anghel and M Kaveh, Exact symbol error probablty of a cooperatve network n a Raylegh-fadng envronment, IEEE Trans Wreless Commun, vol 3, pp , Sept 2004 [4] S Ikk and M H Ahmed, Performance analyss of cooperatve dversty wreless networks over Nakagam-m fadng channel, IEEE Commun Lett, vol 11, pp , July 2007 [5] N C Beauleu and J Hu, A closed-form expresson for the outage probablty of decode-and-forward relayng n dssmlar Raylegh fadng channels, IEEE Commun Lett, vol 10, pp , Dec 2006 [6] Y L, B Vucetc, Z Zhou, and M Dohler, Dstrbuted adaptve power allocaton for wreless relay networks, IEEE Trans Wreless Commun, vol 6, pp , Mar 2007 [7] M Chen, S Serbetl, and A Yener, Dstrbuted power allocaton for parallel relay networks, n Proc IEEE Global Commun Conf (GLOBECOM 05), St Lous, MO, USA, Nov 2005, pp [8] X Deng and A M Hamovch, Power allocaton for cooperatve relayng n wreless networks, IEEE Commun Lett, vol 9, pp , Nov 2005 [9] A H Madsen and J Zhang, Capacty bounds and power allocaton for wreless relay channels, IEEE Trans Inform Theory, vol 51, pp , June 2005 [10] Y Lang and V Veeravall, Gaussan orthogonal relay channel: optmal resource allocaton and capacty, IEEE Trans Inform Theory, vol 51, pp , Sept 2005 [11] Y Zhao, R S Adve, and T J Lm, Improvng amplfy-and-forward relay networks: optmal power allocaton versus selecton, IEEE Trans Wreless Commun, vol 6, pp , Aug 2007 [12] L B Le and E Hossan, Multhop cellular networks: potental gans, research challenges, and a resource allocaton framework, IEEE Commun Mag, vol 45, pp 66-73, Sept 2007 [13] T C-Y Ng and W Yu, Jont optmzaton of relay strateges and resource allocatons n a cooperatve cellular network, IEEE J Select Areas Commun, vol 25, pp , Feb 2007 [14] Z Zhang, W Zhang, and C Tellambura, Improved OFDMA uplnk frequency offset estmaton va cooperatve relayng: AF or DF? 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11 PHAN et al: POWER ALLOCATION IN WIRELESS MULTI-USER RELAY NETWORKS 2545 [19] T K Phan, T Le-Ngoc, S A Vorobyov, and C Tellambura, Power allocaton n wreless relay networks: a geometrc programmng based approach, n Proc IEEE Global Commun Conf (GLOBECOM08), New Orleans, LA, USA, Nov 2008, pp 1-5 [20] E Karpds, N D Sdropoulos, and L Tassulas, Jont QoS multcast power/admsson control and base staton assgnment: a geometrc programmng approach, n Proc IEEE Sensor Array and Multchannel Sgnal Process Workshop (SAM08), Darmstadt, Germany, July 2008, pp [21] I Mtlagkas, N D Sdropoulos, and A Swam, Convex approxmaton-based ont power and admsson control for cogntve underlay networks, n Proc IEEE Wreless Commun and Moble Computng Conf (IWCMC08), Lmn Hersonssou, Crete, Greece, Aug 2008, pp [22] A Goldsmth, Wreless Communcatons Cambrdge Unversty Press, 2004 [23] C C Wu and D P Bertsekas, Admsson control for wreless networks, IEEE Trans Veh Technol, vol 50, pp , Mar 2001 [24] M Grant and S Boyd, CVX: Matlab software for dscplned convex programmng (web page and software), boyd/cvx, Feb 2008 Khoa T Phan (S 05) receved the BSc degree wth Frst Class Honors from the Unversty of New South Wales (UNSW), Sydney, NSW, Australa, n 2005 and the MSc degree from the Unversty of Alberta, Edmonton, AB, Canada, n 2008 He s currently at the Department of Electrcal Engneerng, Calforna Insttute of Technology (Caltech), Pasadena, CA, USA Hs current research nterests are mathematcal foundatons, control and optmzaton of communcatons networks He s also nterested n network economcs, applcatons of game theory, mechansm desgn n communcatons networks He has been awarded several prestgous fellowshps ncludng the Australan Development Scholarshp, the Alberta Ingenuty Fund Student Fellowshp, the CORE Graduate Student Award, and most recently the Atwood Fellowshp to name afew Tho Le-Ngoc (F 97) obtaned hs BEng (wth Dstncton) n Electrcal Engneerng n 1976, hs MEng n Mcroprocessor Applcatons n 1978 from McGll Unversty, Montreal, and hs PhD n Dgtal Communcatons n 1983 from the Unversty of Ottawa, Canada Durng , he was wth Spar Aerospace Lmted and nvolved n the development and desgn of satellte communcatons systems Durng , he was an Engneerng Manager of the Rado Group n the Department of Development Engneerng of SRTelecom Inc, where he developed the new pont-to-multpont DA-TDMA/TDM Subscrber Rado System SR500 Durng , he was a Professor at the Department of Electrcal and Computer Engneerng of Concorda Unversty Snce 2000, he has been wth the Department of Electrcal and Computer Engneerng of McGll Unversty Hs research nterest s n the area of broadband dgtal communcatons wth a specal emphass on Modulaton, Codng, and Multple-Access Technques He s a Senor Member of the Ordre des Ingeneur du Quebec, a Fellow of the Insttute of Electrcal and Electroncs Engneers (IEEE), a Fellow of the Engneerng Insttute of Canada (EIC), and a Fellow of the Canadan Academy of Engneerng (CAE) He s the recpent of the 2004 Canadan Award n Telecommuncatons Research, and recpent of the IEEE Canada Fessenden Award 2005 Sergy A Vorobyov (M 02-SM 05) receved the MS and PhD degrees n 1994 and 1997, respectvely Snce 2006, he has been wth the Department of Electrcal and Computer Engneerng, Unversty of Alberta, Edmonton, AB, Canada, as Assstant Professor Snce hs graduaton, he also occuped varous research and faculty postons n Kharkv Natonal Unversty of Radoelectroncs, Ukrane, Insttute of Physcal and Chemcal Research (RIKEN), Japan, McMaster Unversty, Canada, Dusburg-Essen and Darmstadt Unverstes, Germany, and Jont Research Insttute, Herot-Watt and Ednburgh Unverstes, UK Hs research nterests nclude statstcal and array sgnal processng, applcatons of lnear algebra and optmzaton methods n sgnal processng and communcatons, estmaton and detecton theory, samplng theory, mult-antenna communcatons, and cooperatve and cogntve systems He s a recpent of the 2004 IEEE Sgnal Processng Socety Best Paper Award, 2007 Alberta Ingenuty New Faculty Award, and other research awards He currently serves as an Assocate Edtor for the IEEE TRANSAC- TIONS ON SIGNAL PROCESSING and IEEE SIGNAL PROCESSING LETTERS He s a member of Sensor Array and Mult-Channel Sgnal Processng Techncal Commttee of IEEE Sgnal Processng Socety Chntha Tellambura (SM 02) receved the BSc degree (wth frst-class honors) from the Unversty of Moratuwa, Moratuwa, Sr Lanka, n 1986, the MSc degree n electroncs from the Unversty of London, London, UK, n 1988, and the PhD degree n electrcal engneerng from the Unversty of Vctora, Vctora, BC, Canada, n 1993 He was a Postdoctoral Research Fellow wth the Unversty of Vctora ( ) and the Unversty of Bradford ( ) He was wth Monash Unversty, Melbourne, Australa, from 1997 to 2002 Presently, he s a Professor wth the Department of Electrcal and Computer Engneerng, Unversty of Alberta Hs research nterests nclude dversty and fadng countermeasures, multple-nput multple-output (MIMO) systems and spacetme codng, and orthogonal frequency dvson multplexng (OFDM) Prof Tellambura s an Assocate Edtor for the IEEE TRANSACTIONS ON COMMU- NICATIONS and the Area Edtor for Wreless Communcatons Systems and Theory n the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONSHe was Char of the Communcaton Theory Symposum n Globecom05 held n St Lous, MO