Uplink bit combining for multiple base-stations MIMO with applications to CoMP systems

Transcription

1 WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 016; 16:19 08 Publised online 19 August 014 in Wiley Online Library (wileyonlinelibrary.com)..504 RESEARCH ARTICLE Uplin bit combining for multiple base-stations MIMO wit applications to CoMP systems Harry Leib 1 * and Wenjing Lin 1 Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec H3A A7, Canada Telus mobility, Calgary, Alberta, Canada ABSTRACT Tis wor considers a simple bit level combining tecnique, aided by robust bit reliability information, for uplin collaborating multiple-input multiple-output (MIMO) base-stations (also nown as macrodiversity MIMO), operating over composite Rayleig-lognormal fading cannels. Bit reliability weigts based on a robust modification of te logaritmic lieliood ratio, combined wit instantaneous symbol signal-to-noise ratio information, are derived for different local MIMO detection scemes. Tis bit reliability information is used at te fusion center, togeter wit locally detected data, for combining and producing final information bits delivered to te destination. Computer simulation results confirm tat suc bit level combining tecniques, wen used wit minimum mean squared error ordered successive interference cancelation and also wit spere decoding maximum lieliood local detectors, provide significant performance improvements over non-collaborative base-stations systems. Performance gains are maintained even wen tese scemes suffer from cannel estimation errors and also in te presence of space correlation. Low bacaul overead and performance advantages mae tese bit level combining tecniques attractive for applications in next generation cellular systems employing coordinated multi-point (CoMP) tecnology, as well as for oter collaborative MIMO communication scemes. Copyrigt 014 Jon Wiley & Sons, Ltd. KEYWORDS MIMO systems; multi-antenna communication; data fusion; sadowing; cellular communication; collaborative communication *Correspondence Harry Leib, Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec H3A A7, Canada. arry.leib@mcgill.ca 1. INTRODUCTION Multiple-input multiple-output (MIMO) transmission tecniques constitute a powerful performance enancing tecnology in wireless communications [1,]. Because of its ig bandwidt efficiency [3], MIMO tecnology is crucial to broadband wireless access. Increasing te number of antennas in a MIMO system yields significant capacity gains in absence of spatial correlation [3]. However in realistic systems, increasing te number of antennas in a restricted space reduces te inter-antenna spacing increasing spatial correlation and ence could limit te capacity gain of traditional co-located MIMO (C-MIMO) [4 6]. Furtermore, wen C-MIMO is used for cellular communications, it is affected significantly by te sadowing penomenon [4,7]. Distributed MIMO (D-MIMO) scemes for cellular communication systems, were antennas are distributed between different base stations, can circumvent some of tese problems. To acieve suc performance benefits, D-MIMO systems need to employ some form of collaboration between base-stations, a paradigm tat constitutes te next major advance in wireless telecommunications [8]. Te main feature of D-MIMO tecnology for uplin cellular systems consists of multiple receive antennas distributed among widely-separated radio ports (RPs) (or base stations) tat collaborate in decoding user data [4,5]. Te benefits of D-MIMO over a composite cannel model are considered in [9], were it is sown tat multiple RPs are essential to acieving ig capacity. Te capacity loss due to spatial correlation and sadowing as been analyzed in [4] revealing te advantage of D-MIMO over C-MIMO. Mean spectral efficiency (MSE) and mean outage spectral efficiency (MOSE) metrics for D-MIMO and C-MIMO ave been introduced in [10], were it is sown tat D-MIMO as a significant larger MOSE tan C-MIMO. In [11], it is sown tat te instantaneous mutual information in a D-MIMO systems is asymptotically equivalent to a Gaussian random variable, and using tis results, it is 19 Copyrigt 014 Jon Wiley & Sons, Ltd.

2 H. Leib and W. Lin Uplin bit combining for multiple base-stations demonstrated tat D-MIMO can provide trougput gains over C-MIMO. D-MIMO tecnology can increase te robustness of cellular communication against sadowing troug macrodiversity [1]. An important parameter in any combining macrodiversity system is te extra information required to be transmitted by te RPs to te fusion center (FC) [13] (or central combining unit (CCU) [8]), taing into account te finite capacities of te lins between tese entities [14]. Assuming tat te FC performs optimal MIMO detection jointly on all RPs, requiring complete cannel state information (CSI), [7] sows tat D-MIMO provides capacity gains wit respect to C-MIMO over sadowed cannels tat are also affected by spatial correlation. Due to te large amount of overead information required to implement suc an optimal combining sceme, and ence required to be transmitted to te FC, its application in practical systems is very bandwidt demanding from te bacaul lin. Tis wor considers a D-MIMO sceme based on uplin fusion of data from RPs. Tese RPs locally process received signals transmitted by a mobile station (MS) and send detected data as well as reliability information to a FC for combining and final decision maing. We assume igly reliable lins between RPs and FC, wic can be modeled as error-free. For example, suc condition can be acieved by using fiber optic lins, or suitable automatic repeat request protocols. Te FC can be located in an RP as proposed in [15] for 3GPP LTE or can be part of te mobile switcing center (MSC). In general, te FC can be located at any point accessible troug te bacaul. Robust bit reliability metrics are derived for RPs employing minimum mean square error ordered successive interference cancelation (MMSE OSIC) and spere decoding maximum lieliood (SD ML) wen used as local MIMO detectors. Performance analysis employs extensive computer simulations using a cannel model tat includes small-scale Rayleig fading as well as lognormal sadowing taing into account propagation loss. Wile te application in tis paper aims at uplin cellular MIMO systems, te proposed combining tecnique can be adapted to oter collaborative scemes suc as in [16]. Te rest of tis paper is structured as follows. Te system model is presented in Section. Te combining sceme and robust reliability weigts are derived in Section 3. Performance analysis results troug computer simulations are presented in Section 4. Complexity issues and bacaul rates required to realize te proposed sceme are considered in Section 5. Finally, te conclusions are presented in Section 6.. SYSTEM MODEL Consider a D-MIMO system consisting of one transmit node, or MS, and N geograpically dispersed receive nodes, or RPs, as in [9] and illustrated in Figure 1. Te MS transmitter employs M co-located antennas, and te RP n receiver as L.n/ co-located antennas. Suc a system is referred to as an M, N, n L.1/, L./, :::, L.N/o D-MIMO sceme. For te equal number of antenna case, wen L.1/ D L./ DDL.N/ D L, we use te more compact notation from [9] and term te system as (M,N,L) D-MIMO. A data stream, or transmitted bit vector b in a single cannel use, as components b f0, 1g, D 1, :::, MQ 0,wereQ 0 D log Q and Q is te symbol constellation size. Te data stream b is demultiplexed into M substreams, eac Gray mapped into a cannel symbol s i, i D 1, :::, M, tat is fed to its respective transmit antenna [17]. Define L TOT D P N L.n/. Te uplin received signal at all N RPs can be written as [9]: r D Hs C n (1) were r C L TOT 1 is te received signal vector at all RPs, H is te L TOT M composite cannel matrix, s D Œs 1, :::, s M T is te MS transmitted symbol vector satisfying E ss H D s I M D 1 M I M,andn C L TOT 1 is Additive Wite Gaussian Noise (AWGN) vector wit EŒn D 0 Figure 1. Multi-cell (M,N,L) distributed-mimo system model. Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 193

3 Uplin bit combining for multiple base-stations H. Leib and W. Lin and E nn H D n I L TOT. Te composite cannel matrix H is determined by all te L.n/ M cannel matrices between te MS and RP n, denoted as H.n/, n D 1, :::N, troug H D H.1/ T, :::, H.N/ T T. Wile at tis stage we want to remain as general as possible, in Section 4, we will present in detail te specific cannel model employed for computer simulations, wic considers Rayleig smallscale fading as well as lognormal sadowing, and taes into account distance dependent propagation losses. Essentially, (1) represents a MIMO system wit M transmit and L TOT receive antennas, and ence, it can be decoded jointly involving all RPs. Tis would demand a large amount of overead information be circulated between RPs over te bacaul. Instead, we assume eac RP decodes separately based only on its received signal r.n/ D H.n/ s C n.n/ () tat is related to (1) troug r D r.1/ T, :::, r.n/ T T, n D n.1/ T, :::, n.n/ T T, and produces te detected bit vector Ob D b O.1/ i T,aswell as reliability indication weigts for eac bit, if needed. Let w.n/ be a bit level reliability weigt vector at RP n, of dimension MQ 0, associated wit Ob.n/. Eac RP passes Ob.n/ and if necessary also w.n/ to te FC were te output bit vector Ob of dimension MQ 0 is produced. We assume a flat-fading cannel tat is static during a symbol duration and perfect CSI available at all RP receivers. Te effects of imperfect CSI are also investigated troug computer simulations. 3. ROBUST BIT LEVEL COMBINING WITH RELIABILITY INFORMATION In tis section, we present an algoritm for bit combining at te FC and derive robust bit reliability weigts forwarded by te local MIMO detectors at RPs A bit combining tecnique Let Ob.n/ be te t detected bit at RP n,forn D 1, :::, N, and D 1, :::, MQ 0.Let be te probability tat Ob.n/ is in error (i.e., te bit error probability at RP n ), and assume 1= (i.e., te bit error rate tat a local detector produces at an RP is not larger tan 0.5 indicating proper operation). Let b f0, 1g, and denote by b f0, 1g te t transmitted information bit. Define ( d H.Ob.n/ 1 Ob.n/ b, b/ D 0 Ob.n/ D b as te Hamming distance between Ob.n/ P i jb D b because Ob.1/ on b,and P i b O.n/ jb D b 8 < D : D NY D P NY D and b. Ten, i b O.n/ jb D b 1 i dh b O.n/,b i 1 dh b O.n/,b NY i D 1 " # NY.n/ dh b O.n/,b p 1 (3) are independent wen conditioned 1 i dh.ob.n/, Ob.n/, Ob.n/ Taing te logaritm of (3), we ave log P were D n i jb D b o i, b NX D 1=, we ave D Because Te final detected bit b D b,b/ 1 NX D D log n i 1 dh b O.n/,b 1 d H b O.n/, b log n i (4) o i, b (5) ".n/ 1 p o # (6) i, b 0. Ob is generated at te FC by implementing te ML decision rule Ob D arg max log P bf0,1g n D arg min D b O.1/ bf0,1g i jb D b o i (7), b Wen tere is a tie, ten Ob D 1 wit probability 1= and Ob D 0 wit probability 1=. Wit equal a-prior 194 Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

4 H. Leib and W. Lin Uplin bit combining for multiple base-stations probabilities for b, tis will result in minimizing te probability of error. Defining i n o D D b O.1/ n D b O.1/ i,1 o,0 i (8) te decision rule is 8 < 0, Ob D 1 iˆ< b O.1/ > 0, Ob D 0 D 0, Ob D 1 wit probability 1=and ˆ: Ob D 0 wit probability 1= (9) From (6) and (8), we ave i NX b O.1/ D log log d H O b.n/,1 ".n/ 1 p ".n/ 1 p i d H b O.n/,0 # NX b D. 1/ O.n/ # (10) In order to implement (10), eac RP must send to te FC, in addition to Ob.n/ also te associated probability of error tat in practice as to be estimated. To reduce complexity, we adopt a sub-optimal approac, were instead of eac RP sends anoter variable tat it is easier to 1 p compute. Recognizing tat log.n/ can be considered as reliability indication, because decreasing increases tis term, we consider te following class of decision rules: Q were Q 8 < 0, Ob D 1 i ˆ< > 0, Ob D 0 D 0, Ob D 1 wit probability 1=and ˆ: Ob D 0 wit probability 1= (11) i NX D b. 1/ O.n/ w.n/ (1) and w.n/ are bit reliability weigts satisfying w.n/ 0. Te larger is w.n/ te more reliable is Ob.n/. Essentially, (1) provides a general metod for combining locally detected bits at eac RP, Ob.n/, using reliability information represented by w.n/, and retaining te general form of te optimal sceme given by (10). It is seen tat (1) depends only on te locally detected bits Ob.1/ and te associated reliability weigts w.1/, :::, w.n/, regardless of te local detection metods at RPs or te number of received antennas. Hence, (1) applies also wen te number of antennas at te RPs is not te same, and wen te RPs employ different local detection tecniques. An important consequence of w.n/ being non-negative is tat wen all te local decisions agree ten (11) produces a result tat is identical to te local decisions. In order to tae advantage of tis property to reduce bacaul information rates, te system operates in two pases. During pase I, te locally detected bits Ob.1/ are transmitted to te FC. If te FC determines tat Ob.1/ D Ob./ D D Ob.N/, ten te final decision is taen as Ob.1/. Oterwise, pase II is initiated were te FC requires te RPs to send te reliability weigts w.1/, :::, w.n/,and wen received it uses (11) and (1) to produce te final decision. Tere is no need to forward CSI or samples of te received signals, and ence, te overead information tat is circulated troug te bacaul is reduced. Next, we derive suitable forms for te reliability weigts w.n/. 3.. Robust bit reliability information Consider a signal space constellation composed of te set of points A D fa 1, :::, a Q g and a mapping of Q 0 D log Q information bits b 1, :::, b Q0 into tese constellation points. We consider quadrature amplitude modulation (QAM) wit Gray mapping. Define A.0/ i as te set of constellation points for wic b i D 0, and A.1/ i as te set for wic b i D 1. Ten, for i D 1,, :::, Q 0,weave A.0/ T.1/ i A i D;and A.0/ S.1/ ˇ i A i D A, wit ˇA.0/ i ˇ D ˇ ˇA.1/ i ˇ D Q=, were jjdenotes te cardinality of a set. Let b be te t transmitted bit and Qs a symbol estimate. For MMSE OSIC detection Qs will be te variable used in te quantization procedure (te decision variable) at eac layer yielding te output symbol [18]. For SD ML detection Qs will be te center of te spere at eac layer [19,0]. Te a posterior probability ratio for te t bit is ƒ D P.b D 1jQs/ P.b D 0jQs/ (13) were P.b D bjqs/ is te a posterior probability of b D b given Qs. Using Bayes rule wit equally liely b, (13) can be written as ƒ D p.qsjb D 1/ (14) p.qsjb D 0/ were p.qsjb D b/ is te PDF of Qs given b D b. Te reliability metrics for b are calculated from te logaritmic lieliood ratio (LLR) [1], Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 195

5 Uplin bit combining for multiple base-stations H. Leib and W. Lin L D ln ƒ D ln P.Qsjb D 1/ P.Qsjb D 0/ D ln P P aa.1/ aa.0/ were p.qsjs D a/ is te PDF of Qs wen s D a. p.qsjs D a/ p.qsjs D a/ (15) Complex generalized Gaussian model. Because of te igly nonlinear detection structures used for MIMO systems, deriving te exact form of p.qsjs D a/ is cumbersome. On te oter and assuming a Gaussian PDF for p.qsjs D a/ seems to be an over simplification tat may result in outliers (large associated wit errored locally ). To counteract tis penomenon, we adopt a robust approac tat aims at reducing te cance of suc outliers occurring, witout actually aving to identify tem. Te idea is to use a model for p.qsjs D a/ wose PDF as tails suc tat wen we move away from a tey decay at just te rigt rate, not too fast or too slow. Tis can be acieved by using a Complex Generalized Gaussian PDF [] wose tails can be controlled by a parameter, and investigating te resulting forms for reliability information. Hence, using [], we assume reliability weigts w.n/ detected bits Ob.n/ p.qsjs D a/ D c.1=c/ e jqs ajc (16) were./ is te Gamma function and c is a constant determining te sape of te PDF. For c D 1, we obtain te conventional circular complex Gaussian PDF. As c decreases, te PDF becomes more eavy tailed. From [], we ave EŒjQs aj D.=c/=.1=c/. Substituting (16) in (15) yields P L D ln P aa.1/ aa.0/ exp jqs aj c exp jqs ajc (17) Employing te max-log approximation ln P j exp.a j/ max.a j / in (17) results in j n L min aa.0/ jqs aj co min aa.1/ n jqs aj co (18) Because reliability information must be positive, we could use n ˇ min jqs aj co n min jqs aj coˇˇˇˇˇ (19) aa.0/ aa.1/ for te t bit, yielding a class of bit reliability metrics parametrized by te constant c. Forc D 1, we ave reliability information based on te popular squared distance metric [1,3] tat is obtained by assuming tat Qs a is circular complex Gaussian. Tere are several reservations concerning te use of te squared distance metric in an application suc as ours. Firstly, because of te nonlinearity of te detection sceme we cannot establis tat Qs a is indeed circular complex Gaussian, and ence a more robust alternative is preferable. Secondly, even if Qs a is circular complex Gaussian tere is no indication tat te squared distance metric in (19) yields te best performance wen used as bit reliability weigts in (1). Notice tat te use of te squared distance metric in [1,3] is different tan in our system. Tirdly, te use of te max-log approximation resulting in (18) introduces some sub-optimality features even wen Qs a is circular complex Gaussian, opening te possibility tat in (19) values of c oter tan 1 could result in better performance. Indeed, [4] points out te deficiency of using te squared metric for MIMO detection in presence of non-gaussian noise. Furtermore, [5] sows te nonrobust nature of te squared metric in context of Viterbi decoding of convolutional codes Robustness of te absolute value metric. Next, we compare te absolute distance metric wit te squared distance metric from a robustness point of view. Let X DQs a ave te PDF of (16) and define D 1 DjXj, (0) D DjXj (1) Following [6], we use te asymptotic relative efficiency (ARE) of D 1 wit respect to D to quantify robustness as a function of te sape parameter c from (16). We use te notation for i D 1, i D EŒD i, i D EŒ.D i i /.From [6], we ave ARE.c/ D = 1 D = 1 EŒjXj 4 E ŒjXj 1 EŒjXj E ŒjXj 1 () Wen ARE.c/ >1, ten D 1 is advantageous over D [6]. From [], we ave tat wen X as te PDF of (16) ten and ence p jxj.r/ D EŒjXj n D cr.1=c/ e rc, r 0 (3) c.1=c/ From [7, p. 398, ], we ave Z 1 r nc1 e rc dr (4) 0 nc EŒjXj n c D (5) 1c 196 Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

6 H. Leib and W. Lin Uplin bit combining for multiple base-stations Using () wit (5), we ave ARE.c/ D. 1 c /. 3 c / 1. c /. 1 c /. c / 1. 3 c / (6) Te function ARE.c/ from (6) is illustrated in Figure, revealing tat it is significantly larger tan 1 over a wide range of interest for te parameter c. Hence, te absolute distance metric is advantageous wit respect to te squared distance metric from a robustness point of view. We investigate now te function ARE.c/ from (6) for small values of te parameter c, wen (16) becomes eavily tailed. Using te asymptotic expression for te Gamma function for large argument values,.z/ e z z z.=z/ 1=, in (6), we ave for c << 1 ARE.c/ =c =c 1 (7) Hence, for c << 1, te function ARE.c/ increases fast wit decreasing c (approximately as 1.4 1=c ), an effect also illustrated in Figure. Tis beavior of ARE.c/ sows te significant advantage of te absolute value distance over te squared distance wen (16) is eavily tailed, revealing its resistance to outliers. To understand tis effect better, we compare te increase rate wit respect to jxj of D 1 from (0) wit tat of D from (1). It is easily found tat dd 1 djxj D 1and dd djxj D jxj sowing tat wile te increase rate of D 1 is bounded, tat of D is linear in jxj and ence unbounded. Terefore, an outlier will ave a bigger effect on D tan on D 1. We will ARE c Figure. Asymptotic relative efficiency of te absolute value metric wit respect to te squared metric, as a function of te sape parameter c. see in te next section tat in our system, tese robustness related advantages of D 1 over D are translated into significant SNR performance gains Te form of reliability weigts. Anoter possible measure to bit reliability could be based on te SNR associated wit te cannel symbol containing te information bit. Te output of te MIMO cannel from te MS to RP n, represented by H.n/,canbe written as H.n/ s D MX id1.n/ i s i (8) were.n/ i indicates te it column of H.n/. We see tat.n/ i s is te received power of symbol s i. Because te transmit power is equally divided among transmit antennas, we ave s symbol s i D 1, resulting in te received SNR for M i D 1.n/ i _.n/ i (9) M tat is te same for all bits associated wit tis symbol. We see tat.n/ i is te factor in i tat depends on te cannelfrommstorp n, providing an indication to te quality of wic s i is received at RP n. We propose to use as reliability weigt a function tat depends on te bit reliability information as well as on te SNR of te corresponding cannel symbol. Using (9) and (19) wit c D 0.5 (corresponding to te more robust absolute value metric) we define te t bit reliability weigt associated wit te it symbol at RP n as w.n/,i D.n/ i f n o ˇ min jqs.n/ aa.0/ i aj n g (30) min jqs.n/ aa.1/ i ajoˇˇˇˇˇ were Qs.n/ i is te it layer symbol estimate at RP n, i D 1, :::, M, D 1, :::, Q 0 and n D 1, :::, N. Te parameters f and g, wic assume te values 0,1, are used to isolate a single factor in (30), allowing to adjust te form of te reliability weigt to a particular local MIMO detection sceme. Wen f D 0, g D 1, ten (30) assumes te form of (19) wit c D 0.5 corresponding to te more robust absolute distance metric. Wen f D 1, g D 0, ten (30) assumes te form (9). Te complete form tat integrates (19) (c D 0.5) wit (9) into one reliability weigt is obtained by using f D 1, g D 1 in (30). Te best form of (30) assuming tese options for f, g will be determined in te next section by using computer simulations. We will see tat coosing a rigt reliability form for a local detection metod provides significant performance gains. Te optimization of te more general form of reliability Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 197

7 Uplin bit combining for multiple base-stations H. Leib and W. Lin weigts, obtained by te product of (19) and (9), over te entire parameter space c > 0, f 0, g 0 is beyond te scope of te present paper. Te bit reliability information vector at RP n is w.n/ D w.n/ 1,1, :::, w.n/ Q 0,1, w.n/ 1,, :::, w.n/ Q 0,, :::, i w.n/ T (31) 1,M, :::, w.n/ Q 0,M. 4. COMPUTER SIMULATIONS PERFORMANCE RESULTS We present computer simulation results for bit error rate () performance of D-MIMO and C-MIMO systems, were = 1 MQ X 0. Pr.Ob b /. Monte Carlo simulations are used to obtain Pr.Ob b /. At eac simulation MQ 0 D1 point, te is averaged over at least 1 million cannel realizations and a minimum of 500 frame errors are accumulated. A frame error is defined as te event Os s were Os is te symbol vector detected at te FC. Two local MIMO detection scemes are considered: MMSE OSIC [18] and SD ML [19]. For simulations purposes, we assume all RPs employ te same number of receive antennas L, and ence L TOT D NL. Te NL M composite cannel matrix H.d/ is parameterized by te vector d D Œd.1/, d./, :::, d.n/ T were d.n/ is te distances from MS to RP n. Wit small-scale as well as large-scale fading, we ave [8] H.d/ D H SH.d/H SSF (3) were H SSF is an NL M matrix representing small-scale fading, and H SH.d/ is an NL NL matrix representing large-scale fading including te pat loss penomenon. We use te Kronecer model for small-scale fading accounting for spatial correlation at te transmitter and receiver as in [8]. Wit tis model H SSF D R 1= R H wr 1= T (33) were H w is an NL M random matrix wit i.i.d. entries modeled as zero mean circular complex Gaussian wit unit variance, and R T, R R are te transmit and receive space correlation matrices. Using te exponential correlation model of [9], te M M transmit correlation matrix is t ::: t.m 1/ t 1 ::: t.m / R T D C (34) A t.m 1/ t.m / ::: 1 were t Œ0, 1 is te transmit fading correlation coefficient. At D-MIMO receivers, we assume independent small-scale fading between RPs due to te large distance between base-stations. At eac RP, te small-scale fading between antennas may be space correlated due to small spacing between antennas. Hence, te NL NL receive correlation matrix can be expressed as R R D diag.r.1/ R, R./ R, :::, R.N/ R / (35) were diag./ denotes a bloc diagonal matrix wit main diagonal consisting of te L L square matrices R.1/ R, R./ R, :::, R.N/ R. Te receive correlation matrix at RP n also follows te exponential correlation model R.n/ R r ::: r.l 1/ D r 1 ::: r.l / C A r.l 1/ r.l / ::: 1 (36) were r Œ0, 1 is te receive fading correlation coefficient. Hence, using (33) and (35), we ave te small-scale fading matrix given by were H.n/ w 0 R.1/ 1= 1.1/ R H w.r T / 1= R./ 1=./ R H w.r T / 1= H SSF D C A R.N/ 1=.N/ R H w.r T / 1= is a L M submatrix of H w,and R.n/ R (37) 1= H.n/ w.r T/ 1= D H.n/ SSF (38) is an L M small-scale fading matrix between te MS and RP n. Due to large spacing between base stations, we assume tat sadowing affecting te RPs are independent penomena, wile all antennas at te same RP are experiencing same sadowing [4,9]. Te combined pat loss and sadowing effects can be represented as a power decrease versus distance penomenon wit random attenuation due to sadowing. From [30,31], te received signal power at te nt base station P.n/ R is given in terms of te transmitted signal power P T by P.n/ R D A d.n/ d 0 n P T (39) were A is te pat gain at reference distance d 0, d.n/ is te distance between MS and RP n, is te pat loss exponent tat strongly depends on te base station antenna eigt and te terrain category [30] wit typical values in urban macrocells [31]. Furtermore, n is a lognormal random variable representing sadowing at RP n,were 198 Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

8 H. Leib and W. Lin Uplin bit combining for multiple base-stations 10 log 10 n is zero mean Gaussian wit variance db. Empirical studies support db ranging from 4 to 13 db [31] for outdoor cannels. At 1.9 GHz, te constant A is close to te free-space pat loss at d 0 D 100m [30], and ence from [31] A D (40) 4d 0 were D c is te wavelengt in meters, c is te speed of f c ligt, and f c is te carrier frequency. Combining (39) and (40), we ave P.n/ R c D f c 4d 0 c d.n/ n P T D f c 4 d 0 d. / n 0 d.n/ P T (41) c Defining D d. / f c 4 0,weavetesadowing and pat loss coefficient associated wit RP n s,n.d.n/ / D s n d.n/ (4) Tis model applies to base station antenna eigts from 10 to 80 m, and RP-to-MS distances from 0.1 to 8 m [30]. Finally, te matrix representing large-scale fading is H SH.d/ D diag s,1 d.1/ I L, s, d./ I L,, s,n d.n/ i I L were I L is te L L identity matrix. From (3), (37), (38), and (43), we ave (43) H.d/ D H.1/ d.1/ T, H./ d./ T, :::, H.N/ d.n/ T T (44) were H.n/ d.n/ D s,n d.n/ H.n/ SSF (45) is te L M cannel matrix associated wit te lin from MS to RP n. Te cannel, specified by (44), varies randomly and independently from one use to anoter. In tis wor, for simulations purposes, te large-scale fading parameters are set to f c D 1.9 GHz, d 0 D 100 m, D 4and db D 4. In order to avoid aving to present results as a function of several receiver SNRs (one for eac RP), we plot te against E btr D s,were Q 0 n E btr D s Q 0 is te transmit bit energy at te MS and n D is te discrete noise variance at te RP receivers. Using tese numerical values and d.n/ D1 m, we ave A tat in (39) te attenuation coefficient d.n/ D d (= db). For comparison purposes, we point out tat at a distance of 1 m, measurements results at f c D 1.9 GHz indicate pat losses in te range 118 to 140 db [30]. Hence, in tis case, te values of E btr must be large enoug to compensate for te pat loss. To ave an idea wat values for E btr we can expect, assume te pat loss is 15 db, and let E b be te average received bit energy. For E b Œ5, 50 db, wit suc pat loss we need E btr Œ15 C 5, 15 C 50 db, or equivalently E btr Œ130, 180 db. In tis paper, all scemes employ 16QAM or 64QAM wit Gray mapping. Wile in our wor we ave performed extensive simulations also wit QPSK and 3QAM, te results could not be included because of space limitations. Te conclusions based on tese additional modulation scemes are essentially te same as tose tat can be drawn from te presented results Effects of te reliability weigt form Assuming perfect CSI at MIMO local detectors, we first present simulation results to illustrate te effect of te reliability information forms. Two types of reliability information forms are considered: reliability information using te absolute metric c D 0.5 and reliability information using te squared metric c D 1. Two D-MIMO systems are considered: (4,,4) D-MIMO wit d.1/ D d./ D 1m and (4,,4) D-MIMO wit d.1/ D 1 m, d./ D 1. m. For 16QAM Figure 3 presents results wit reliability parameter settings f D 1, g D 1, and Figure 4 wit f D 0, g D 1. For 64QAM Figure 5 presents results for f D 1, g D 1 and Figure 6 for f D 0, g D 1. We see tat in all cases, te performance corresponding to reliability information based on absolute value metric is better tan tat based on squared value. For SD ML, te performance wit f D 1, g D 1 is better, and for MMSE OSIC, te performance wit f D 0, g D 1 is better. At D 10 5, for SD ML wit f D 1, g D 1, te E btr = gain of reliability information wit absolute value metric over tat wit squared value is around 0.8 db for 16QAM and 1. db for 64QAM. For MMSE OSIC wit f D 0, g D 1, te E btr = gain of reliability information based on absolute value metric over tat based on squared value metric is around 6 db for 16QAM and 5. db for 64QAM. Tis confirms te improvement of te reliability information sceme proposed in Section 3. sowing tat it is more significant for MMSE OSIC detection. It was found tat wit SD ML, te performance wit f D 1, g D 1 is essentially te same as te performance wit f D 1, g D 0, and ence for simplicity, we continue wit te latter values of f and g wen considering tis local MIMO detection sceme. Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 199

9 Uplin bit combining for multiple base-stations H. Leib and W. Lin DMIMO d (1) =1m d () =1m DMIMO d (1) =1m d () =1.m absolute value absolute square value DMIMO d (1) =1m d () =1m DMIMO d (1) =1m d () =1.m absolute value absolute square value Figure 3. Performance wit absolute and squared reliability metrics: D-MIMO(4,,4), 16QAM, (f D 1,g D 1), perfect CSI. DMIMO d (1) =1m d () =1m DMIMO d (1) =1m d () =1.m absolute value absolute square value Figure 5. Performance wit absolute and squared reliability metrics: D-MIMO(4,,4), 64QAM, (f D 1, g D 1), perfect CSI. DMIMO d (1) =1m d () =1m DMIMO d (1) =1m d () =1.m absolute value absolute square value Figure 4. Performance wit absolute and squared reliability metrics: D-MIMO(4,,4), 16QAM, (f D 0,g D 1), perfect CSI. 4.. Performance gains over C-MIMO wit perfect cannel information Assuming perfect CSI at local MIMO detectors we consider two types of D-MIMO systems: (4,,4) D-MIMO wit d.1/ D d./ D 1 m and (4,,4) D-MIMO wit d.1/ D 1 m, d./ D 1. m. We also consider two types of C-MIMO systems: 44 C-MIMO wit d D 1mand Figure 6. Performance wit absolute and squared reliability metrics: D-MIMO(4,,4), 64QAM, (f D 0, g D 1), perfect CSI. C-MIMO wit d D 1. m. For brevity, we present results for 16QAM only. Figure 7 presents results wit reliability parameter settings f D 1, g D 0 tat are better for RPs employing SD ML local detectors, and Figure 8 wit f D 0, g D 1 tat are better for RPs wit MMSE OSIC detection. We see tat D-MIMO provides significant E btr = gains over C-MIMO for SD ML detection wit f D 1, g D 0 and for MMSE OSIC detection wit f D 0, g D 1. Furtermore, at ig E btr =, te performance gain for MMSE OSIC detection wit f D 0, g D 1 is larger tan tat wit SD ML detection wit f D 1, g D Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

10 H. Leib and W. Lin Uplin bit combining for multiple base-stations CMIMO d=1m DMIMO d (1) =1m d () =1m CMIMO d=1.m DMIMO d (1) =1m d () =1.m SD ML MMSE OSIC are acieved witout any diversity gains in te range explored in tis paper Effects of cannel estimation errors Next, we investigate te effects of cannel estimation errors on te performance of D-MIMO. Assume an L M estimated cannel matrix OH.n/, modeled as in [3] by OH.n/ D H.n/ C QH.n/, (46) Figure 7. Performance wit perfect CSI for D-MIMO(4,,4) and 4 4 C-MIMO wit 16QAM, (f D 1,g D 0). CMIMO d=1m DMIMO d (1) =1m d () =1m CMIMO d=1.m DMIMO d (1) =1m d () =1.m SD ML MMSE OSIC were H.n/ is te true cannel matrix from MS to RP n, and QH.n/ is a L M matrix representing cannel estimation errors. Te matrix QH.n/ is independent of H.n/ and as i.i.d. zero mean circular complex Gaussian entries of variance n, wit te constant indicating te relative error variance wit respect to te cannel noise. We consider a (4,,4) D-MIMO system wit d.1/ D d./ D 1m and a 4 4 C-MIMO system wit d D 1 m. Figures 9 and 10 present results for 16QAM employing SD ML detection wit f D 1, g D 0, and MMSE OSIC wit f D 0, g D 1. We see tat E btr =N o gains of D-MIMO over C-MIMO are maintained even in te presence of cannel estimation errors. We found tat also wit 64QAM te gains of D-MIMO over C-MIMO are maintained in te presence of cannel estimation errors. However, from Figures 9 and 10, we see tat cannel estimation errors cause performance degradations, for D-MIMO as well as C-MIMO, tat increase wit.at=10 5,forSD ML wit f D 1, g D 0, te degradation is 3 db for D 1 and 10.3 db for D 10. For MMSE OSIC wit f D 0, g D 1 te degradation is 3.1 db for D 1and 13 db for D CMIMO d=1m DMIMO d (1) =1m d () =1m SD ML SD ML γ =1 SD ML γ =10 Figure 8. Performance wit perfect CSI for D-MIMO(4,,4) and 4 4 C-MIMO wit 16QAM (f D 0,g D 1). At =10 5, using SD ML wit f D 1, g D 0, D- MIMO wit d.1/ D 1md./ D 1. m provides E btr = gains of 4.7 and 6. db over C-MIMO wit d D 1m and C-MIMO wit d D 1. m, respectively. Employing MMSE OSIC wit f D 0, g D 1, D-MIMO wit d.1/ D 1md./ D 1. m provides E btr = gains of 6.3 and 8.9 db over C-MIMO wit d D 1mandC-MIMOwit d D 1. m, respectively. Significant performance gains of D-MIMO over C-MIMO were obtained also wit QPSK, 3QAM, and 64QAM. All tese performance advantages Figure 9. Effect of cannel estimation errors on D-MIMO(4,,4) wit d.1/ D d./ D 1 m, and on 4 4 C-MIMO wit d D 1m for 16QAM wit SD ML. Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 01

11 Uplin bit combining for multiple base-stations H. Leib and W. Lin CMIMO d=1m DMIMO d (1) =d () =1m MMSE OSIC MMSE OSIC γ =1 MMSE OSIC γ =10 CMIMO t=r=0 DMIMO t=r=0 CMIMO t=0.6,r=0 DMIMO t=0.6,r=0 CMIMO t=r=0.6 DMIMO t=r= Figure 10. Effect of cannel estimation errors on D-MIMO(4,,4) wit d.1/ D d./ D 1 m, and on 4 4 C-MIMO wit d D 1m for 16QAM wit MMSE OSIC Effects of spatial correlation Now, we investigate te impact of cannel spatial correlation on te performance of D-MIMO. We consider a (4,,4) D-MIMO system wit d.1/ D d./ D 1manda4 4 C-MIMO system wit d D 1 m. Te local detection sceme is SD ML wit f D 1, g D 0. Te cannel model for spatial correlation is given by (3) (36). Two situations for spatial correlation are considered in tis paper: spatial correlation at transmitter only, and spatial correlation at transmitter and receiver. We found tat te performance wit spatial correlation at receiver only is very close to tat wen spatial correlation exits at te transmitter only, and ence due to space limitations, te simulation results for tis case are not included in tis paper. Furtermore, we present results only for 64QAM wit Gray mapping. Figure 11 presents results for t D 0.6 and r D 0.6. We see tat te performance improvement of D-MIMO over C-MIMO is maintained. At = 10 5 te improvement is 4.6 db witout spatial correlation, 4. db wit spatial correlation at transmitter only, and 4 db wit spatial correlation at transmitter and receiver. We also observe tat in general spatial correlation degrades te performance of D-MIMO as well as C-MIMO Comparison between (M,N,L) D-MIMO and M NL C-MIMO We present simulation results for a (4,,4) D-MIMO system wit d.1/ D d./ D 1manda4 8 C-MIMO system wit d D 1 m. Hence, bot systems ave te same number of transmit and receive antennas. We consider 16QAM Figure 11. Effect of cannel spatial correlation on D-MIMO(4,,4) wit d.1/ D d./ D 1 m, and on 4 4 C-MIMO wit d D 1 m for 64QAM wit SD ML local detection. wit Gray mapping and SD ML detection wit f D 1, g D 0. Te correlation coefficients in (34) and (36) in a given wave-field [33] are approximated as cor.coef. exp 3 d (47) were is te angular spread [33], and d is te distance in wavelengts between adjacent antennas [9]. We assume uniform linear arrays wit equidistant antenna spacing. Using (47) for 4 8 C-MIMO we ave tat wen doubling te number of receive antennas in te same space ten d is alved, and ence r 0 D exp 3 d =4 D r 1=4 (48) were r is te correlation coefficient in te original 4 4 MIMO system. Figure 1 presents te performance for (4,,4) D-MIMO and 4 8 C-MIMO systems wit te same correlation coefficient at transmitter and receiver. We see tat te performance of an uncorrelated 4 8 C-MIMO is better tan an uncorrelated (4,,4) D-MIMO and te difference is.1 db at D Te performance for bot C-MIMO and D-MIMO deteriorates as spatial correlation increases. However wit same spatial correlation at te transmitter and receiver, te performance of C-MIMO is better tan tat of D-MIMO and te difference increases as spatial correlation increases. At D 10 5, te difference is.5 db wen t D r D 0.3,.9 db wen t D r D 0.5 and 3.75 db wen t D r D 0.8. It is seen tat despite te performance gain of 4 8 C-MIMO over (4,,4) D-MIMO, te former acieves a diversity order of only 4, te same as te D-MIMO system. From [34], we 0 Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

12 H. Leib and W. Lin Uplin bit combining for multiple base-stations C t=r=0 D t=r=0 C t=r=0.3 D t=r=0.3 C t=r=0.5 D t=r=0.5 C t=r=0.8 D t=r=0.8 C t=r=0 D t=r=0 C t=0.3, r=0.74 D t=r=0.3 C t=0.5, r=0.84 D t=r=0.5 C t=0.8, r=0.95 D t=r= Figure 1. Comparison between D-MIMO(4,,4) wit d.1/ D d./ D 1 m (D in te legend), and 48 C-MIMO wit d D 1m (C in te legend) for 16QAM wit SD ML local detection. ave tat te asymptotic diversity order of 4 8 C-MIMO wit SD ML detection sould be 8. However suc a large asymptotic diversity order is acieved at muc lower tan considered in tis wor. Hence, tis potential diversity gain of C-MIMO wit large number of received antennas is not realized at practical values. We see tat te inability of our simple combining tecnique to provide diversity gains is not manifested as a loss wit respect to optimal joint detection because te potential large diversity gains of te later sceme is not realized in te practical range wen te total number of receive antennas is large. Furtermore, ere we assumed tat te 4 8C- MIMO system experiences same spatial correlation as a 4 4 MIMO sceme in eac RP, meaning tat it requires twice te space to accommodate 8 antennas instead of 4. Next, we consider te case wen we ave a restriction on te space used by receive antennas, resulting in alving te inter-antenna spacing d wen moving from a 44 to a 48 C-MIMO system and ence increasing space correlation (48). Figure 13 presents te performance of (4,,4) D-MIMO and 48 C-MIMO were te 8 antennas occupy te same space as te 4 antennas of eac RP in te D- MIMO system. Wit same spatial correlation at transmitter for bot 4 8 C-MIMO and (4,,4) D-MIMO systems, te performance of C-MIMO is only sligtly better tat of D- MIMO. At D 10 5, te difference between C-MIMO wit t D 0.3, r D 0.74 and D-MIMO wit t D r D 0.3 is 0.43 db, and te difference between C-MIMO wit t D 0.5, r D 0.84 and D-MIMO wit t D r D 0.5 is 0.6 db. Te performance of D-MIMO wit t D r D 0.8 becomes essentially te same as tat of C-MIMO wit t D 0.8, r D We see tat in realistic systems wit Figure 13. Comparison between D-MIMO(4,,4) wit d.1/ D d./ D 1 m (D in te legend), and 48 C-MIMO wit d D 1m wen te spacing of adjacent receive antennas is reduced to alf (C in te legend) for 16QAM wit SD ML local detection. restricted space for receiver antennas, space correlation is an important factor. D-MIMO systems allow for spreading of antennas between RPs and ence reducing space correlation effects. Wit SD ML local detection, te proposed bit combining sceme for a (4,,L) D-MIMO system provides a comparable performance to a 48 C-MIMOsystem employing joint SD ML detection, wen space correlation increases due to limited spacing for receiver antennas. 5. COMPLEXITY AND BACKHAUL RATES COMPARISON In tis section, we compare our sceme wit joint MIMO detection performed at te FC. We first consider complexity issues and ten analyze te bacaul rates required wen suc tecniques are employed for uplin cellular systems using coordinated multi-point (CoMP) [8, pp ] tecnology SD ML In tis subsection, we assume our sceme employs MIMO SD ML detection at local RP tat forward to FC locally detected bits, as well as bit reliability information if needed. For joint MIMO detection at FC, te RPs need to forward samples of te received signals, as well as CSI if necessary. In our sceme, te MIMO system from te MS to eac RP is specified by (), and ence from [35], we ave tat te average complexity of SD wen employed at eac RP depends on te SNR and in general is O.Q M /. In [35], Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 03

13 Uplin bit combining for multiple base-stations H. Leib and W. Lin te average complexity is defined as te average number of nodes in te tree searc employed by te SD, owever also in terms of average number of floating point operations (FLOPS) its beavior wit M remains te same. In [36], it is sown tat te average complexity of SD becomes close to polynomial in M for large SNR. Te important conclusions for our case is te significant role tat M, te number of MS transmit antennas, plays in determining te average complexity of SD decoding at one RP. Wit N RPs te average complexity results scale linearly wit N. In our sceme, RP n could be required to generate reliability information weigts (30) tat from te results of Section 4.1 are better wit f D 1, g D 0, sowing tat actually in tis case w.n/,i D.n/ i (49) tat is te same for all bits associated wit a symbol. Taing into account tat.n/ i is of dimensionality L.n/ and as complex components, to generate (49) requires 4L.n/ 1 FLOPS for eac symbol yielding a total of M.4L.n/ 1/ FLOPS, and sowing tat it is linear in M and ence negligible wen compared to te complexity of SD at eac RP. Finally, te complexity of forming te fusion rule (1) at te FC and performing te final decision is only linear in N. Hence, te overall complexity in our sceme is determined by te complexity of SD for M transmit antennas. Considering now te case wen te FC performs joint SD, ten te MIMO system in tis situation is given by (1) tat also as M transmit antennas, and ence, it is equivalent from average complexity point of view to tat of SD at eac RP. An important factor in CoMP systems is te information rate troug te bacaul. Assume a cannel use rate R.In our sceme, at rate R, eac RP must forward Q 0 M locally detected bits. In addition, if te locally detected bits from all RPs are not te same, ten te FC requires also te reliability weigts (49) tat are real analog quantities and ence ave to be quantized to Qq bits. Te reliability weigts (49) are te same for all bits associated wit one symbol and ence for eac cannel use only M ave to be sent. Te number of bits tat RP n mustsendatrater is a random variable A n specified by PrŒA n D Q 0 M D 1 O Q 0 M, PrŒA n D Q 0 M CQqM D 1 1 O Q 0 M were O is te bit error probability at RP n from (4) (for simplicity te dependency on is not indicated) tat for a specific local detection metod at RP n it depends on E b. For simplicity, we do not include in our notation tis dependency on E b. Taing into account all N RPs, te average bacaul information rate in our system is given in units of [bit/sec] by R SDL D R NX EŒA n NX D R 1 O Q 0 M Q0 M C 1 1 O Q 0 M.Q 0 M CQqM/ (50) and normalizing by te transmitted information rate RQ 0 M gives r SDL D NX 1 O Q 0 M C 1 1 O Q 0 M.1 CQq=Q 0 / (51) In (51), r SDL represents te fractional increase in bacaul rate due to te collaboration of N RPs in te uplin. We see tat wen tere are no local errors (i.e., Op.1/ D Op./ D D Op.N/ D 0/ and ence te FC does not require bit reliability weigts to be sent, we ave r SDL D N. Tis represents te increase in bacaul rate due to te fact tat for eac transmitted information bit, eac one of te N RPs forwards a locally detected bit to te FC. Wen we use ard decision combining at FC, tat does not require reliability information and ence Qq D 0, we also ave r SDL D N. However, wen te reliability information as to be forwarded to te FC, we ave r SDL > N. Consider now te case wen joint MIMO detection (tat includes SD) is performed at te FC. In tis case, eac RP as to forward samples of te received signals and also CSI if necessary. Assuming tat eac RP employs a receiver tat discretizes te signal from eac receive antenna at te symbol rate and ten its real and imaginary components are quantized to Qq bits, te resulting rate in te bacaul due to RP n is RL.n/ Qq. Te rate at wic te ML.n/ complex components of te cannel matrix H.n/ ave to be sent to te FC is r CSI R,were0 r CSI 1 is a constant tat depends on te Doppler rate in te cannel. Te lower is te Doppler rate, te less is te frequency tat CSI as to be updated at te FC, and ence r CSI is smaller. Te case wen te FC obtains CSI from te signal samples, and ence no separate cannel information as to be sent, is represented by r CSI D 0. Taing into account all N RPs, te rate in te bacaul wit joint detection at te FC is R JDF D RQq.1 C r CSI M/ NX L.n/ D RQq.1 C r CSI M/L TOT (5) 04 Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

14 H. Leib and W. Lin Uplin bit combining for multiple base-stations Relative bacaul rate QAM 8bit quant. Joint16QAM 8bit quant. 64QAM 8bit quant. Joint64QAM 8bit quant. 16QAM 4bit quant. Joint16QAM 4bit quant Ebtr/No (db) Figure 14. Comparison between bacaul rates of te proposed combining scemes wit SD ML local detection at RPs, and joint MIMO detection at FC. Te results correspond to a system wit RPs. Normalizing by te transmitted information rate RQ 0 M yields r JDF D QqL TOT 1 Q 0 M C r CSI (53) From (53), we see tat for small enoug Doppler rates, wen we can ave r CSI 1=M, transferring CSI as a only a small effect on te bacaul rate. From (51), we see tat te bacaul rate does not depend on te number of RP antennas L TOT wen our combining metod is used at te FC. However, (53) sows tat wit joint detection at FC, te bacaul rate increases linearly wit L TOT, indicating tat suc tecnique may not be adequate for base stations wit many receive antennas. A sample of numerical results for r SDL and r JDF wit two RPs is presented in Figure 14 for 16QAM and 64QAM. Te values for O/ in (51) were obtained by computer simulations. It is seen tat for E btr values associated wit 10 3 our proposed combining sceme requires a bacaul rate tat is less tan.5, tat furter decreases toward (te minimum for two RPs) wit increasing E btr. Joint detection at te FC, owever, requires a significantly larger bacaul rate tat is constant wit E btr. 5.. MMSE OSIC Now, we assume for our sceme MMSE OSIC detection at RPs tat forward locally detected bits, and wen necessary also bit reliability information to te FC. For simplicity of analysis, we assume M L.n/, n D 1,., N (i.e., te number of antennas at eac RP is not less tan te number of antennas at te MS). At RP n, te system is given by (), and ence from [37,38], we ave tat te complexity of MMSE OSIC detection is O.M L.n/ /. Wen using N RPs, te complexity is O M P.n/ L.n/.EacRPcould be required to generate reliability information weigts (30) tat from our results of Section 4.1 are better wit f D 0, g D 1, and consume 7 Q FLOPS for eac bit. Hence, for all MQ bits, te reliability weigt calculations at eac RP require 7 MQ FLOPS. Furtermore, te complexity of forming (1) at te FC is linear in N. Considering te case wen te FC employs joint MMSE OSIC detection, ten te MIMO system is given by (1) sowing tat it as M transmit and P N L.n/ receive antennas. From [37,38], te complexity of tis system is O.M P.n/ L.n/ /,andit is equivalent to te complexity of MMSE OSIC at all N RPs. However, in tis case, tere is no need to calculate reliability weigts (30). Tis saving comes at te expense of an increase in bacaul information rates, a subject tat is considered next. Wit our sceme, as in Subsection 5.1, eac RP must send to te FC a frame of Q 0 M locally detected bits for eac cannel symbol vector. If te locally detected bits are not te same, ten te FC requires also Q 0 M reliability weigts. Notice tat in Subsection 5.1 due to te fact tat all reliability weigts for te bits associated Relative bacaul rate QAM 8bit quant. Joint16QAM 8bit quant. 64QAM 8bit quant. Joint64QAM 8bit quant. 16QAM 4bit quant. Joint16QAM 4bit quant Ebtr/No (db) Figure 15. Comparison between bacaul rates of te proposed combining scemes wit MMSE OSIC local detection at RPs, and joint MIMO detection at FC. Te results correspond to a system wit RPs. Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd. 05

15 Uplin bit combining for multiple base-stations H. Leib and W. Lin wit te same symbol are identical, only M suc weigts ave to be transmitted. Using te same derivation as in Subsection 5.1, wile taing into account tat in tis case Q 0 M reliability weigts are transmitted to te FC, we ave tat te fractional increase in bacaul rate is given by r OSICL D NX 1 O Q 0 M C 1 1 O/ Q 0 M (54).1 CQq/ Wen te FC employs joint MMSE OSIC detection, te fractional bacaul rate is given by (53). A sample of numerical results for r OSICL and r JDF wit two RPs are presented in Figure 15 for 16QAM and 64QAM. Te values for O in (54) were obtained by computer simulations. Similarly to te findings for SD ML, we see tat for E btr values associated wit 10 3 our proposed combining sceme wit MMSE OSIC at RPs requires a fractional increase in bacaul rate of less tan.5, tat is significantly lower tan wat joint detection at FC requires, and furter decreases wit increasing E btr.itisalsoseenfromfigure15tatfor smaller values of E btr,wen> and using eigt quantization bits for digitization, our sceme wit MMSE OSIC at RPs requires a larger bacaul rate tan joint detection at FC does. However, suc large is not te usual operation regime of a communication system. 6. CONCLUSIONS Tis wor considers bit level combining aided by reliability information for multiple base-stations D-MIMO systems operating over a composite Rayleig-lognormal fading cannel. Robust bit reliability weigts are derived by modifying te LLR at local detectors and including symbol SNR information. It is sown tat using te absolute value metric for weigts results in significant performance gains over te squared metric. Ten, tis compounded bit reliability information is adjusted for different local MIMO detection scemes to improve performance. Wile not providing diversity order advantages, tis paper sows tat significant performance gains over C-MIMO can be obtained wit te proposed combining sceme for D-MIMO wit perfect, as well as imperfect, cannel estimation at local detectors. Furtermore, significant performance gains are also obtained in presence of space correlation. Tis paper also sows tat te proposed combining metod requires a muc lower bacaul rate tan joint detection at FC. Terefore, suc a bit level combining tecnique could be attractive for uplin D-MIMO cellular systems employing CoMP tecnology, yielding significant performance gains wit small bacaul overead bandwidt. REFERENCES 1. Paulraj AJ, Gore DA, Nabar RU, Bolcsei H. An overview of MIMO communications: a ey to gigabit wireless. Proceedings of te IEEE 004; 9(): Raycaudari D, Mandayam NB. Frontiers of wireless and mobile communications. Proceedings of te IEEE 01; 100(4): Telatar E. Capacity of multi-antenna Gaussian cannels. European Transactions on Telecommunication (ETT) 1999; 10(6): Dai H. Distributed versus co-loacted MIMO systems wit correlated fading and Sadowing. In IEEE International Conference on Acoustics, Speec and Signal Processing, 006. ICASSP 006 Proceedings, Toulouse, France, May 006; Hanzo L, El-Hajjar M, Alamari O. Near-capacity wireless transceivers and cooperative communication in te MIMO era: evolution of standards, waveform design and future perspectives. Proceedings of IEEE 011; 99 (8): Ozdemir MK, Arvas E, Arsalan H. Dynamics of spatial correletion, and implications on MIMO systems. IEEE Communications Magazine 004; 4(6): Jeong W-C, Cung J-M. Analysis of macroscopic diversity combining of MIMO signals in mobile communication. AEU International Journal of Electronics and Communication 005; 59: Marsc P, Fettweis GP (eds.) Coordinated Multi-Point in Mobile Communications: From Teory to Practice. Cambridge University Press: Cambridge, UK, Ro W, Paulraj A. MIMO cannel capacity for te distributed antenna systems. In IEEE 56t Veicular Tecnology Conference Proceedings, VTC 00-Fall, Vancouver, Canada, September 00; Wang D, You X, Wang J, Wang Y, Hou X. Spectral efficiency of distributed MIMO cellular systems in a composite fading cannel. In IEEE International Conference on Communications, ICC 008, Beijing, Cina, May 008; Heliot F, Hosyar R, Tafazolli R. An accurate closedform approximation of te distributed MIMO outage probability. IEEE Transactions on Wireless Communications 011; 10(1): Bernardt RC. Macroscopic diversity in frequency reuse radio-systems. IEEE Journal on Selected Areas in Communications 1987; 5(5): Martin F, Leib H. Distributed detection for macrodiversity enanced cellular communication systems. IEEE Transactions on Aerospace and Electronic Systems 009; 45(4): Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.

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17 Uplin bit combining for multiple base-stations H. Leib and W. Lin AUTHORS BIOGRAPHIES Harry Leib received te BSc (cum laude) and MSc degrees in electrical engineering from te Tecnion - -Israel Institute of Tecnology, Haifa, Israel in 1977 and 1984 respectively. In 1987 e received te P.D. degree in electrical engineering from te University of Toronto, Canada. During e was wit te Israel Ministry of Defense, woring in te Communication Systems area. After completing is PD studies, e was wit te University of Toronto as a post-doctoral researc associate and as an assistant professor. Since September 1989 e as been wit te Department of Electrical and Computer Engineering at McGill University in Montreal, were e is now as a full professor. He spent part of is Sabbatical leave at Bell Nortern Researc in Ottawa, Canada ( ). During te oter part of is Sabbatical leave (1996) e was a visiting professor in te Communications Lab of te Helsini University of Tecnology in Finland. At McGill, e teaces undergraduate and graduate courses in Communications and directs te researc of graduate students. His current researc activities are in te areas of digital communications, wireless communication systems, detection, estimation, and information teory. Dr. Leib was an editor for te IEEE Transactions on Communications and an associate editor for te IEEE Transactions on Veicular Tecnology He as been a guest co-editor for special issues of te IEEE Journal on Selected Areas in Communication on Differential and Noncoerent Wireless Communication , and on Spectrum and Energy Efficient Design of Wireless Communication Networs Wenjing Lin was born in Sangai Cina and obtained er B.Eng. degree from Sangai University in 000. After graduation se wored as a GSM engineer at Alcatel-Lucent Sangai Bell during During se was a graduate student and researcer at McGill University in Montreal Canada, woring in te area of MIMO wireless communication systems. Se obtained te M.Eng. degree from McGill University in 011. Since 01 se as been wit TELUS, first as a customer system engineer and ten as an RF engineer (Capacity planning) for TELUS Mobility in Calgary Alberta Canada. 08 Wirel. Commun. Mob. Comput. 016; 16: Jon Wiley & Sons, Ltd.