Advances in MIMO Techniques for Mobile Communications A Survey

Transcription

1 Int. J. Communcatons, Network and System Scences, 010, 3, 13-5 do:10.436/jcns Publshed Onlne March 010 ( Advances n MIMO echnques for Moble Communcatons A Survey Abstract Farhan Khald, Joachm Spedel Insttute of elecommuncatons, Unversty of Stuttgart, Stuttgart, Germany Emal: {khald, spedel}@nue.un-stuttgart.de Receved December, 009; revsed January 5, 010; accepted February 6, 010 hs paper provdes a comprehensve overvew of crtcal developments n the feld of multple-nput multple-output (MIMO) wreless communcaton systems. he state of the art n sngle-user MIMO (SU-MIMO) and multuser MIMO (MU-MIMO) communcatons s presented, hghlghtng the key aspects of these technologes. Both open-loop and closed-loop SU-MIMO systems are dscussed n ths paper wth partcular emphass on the data rate maxmzaton aspect of MIMO. A detaled revew of varous MU-MIMO uplnk and downlnk technques then follows, clarfyng the underlyng concepts and emphaszng the mportance of MU-MIMO n cellular communcaton systems. hs paper also touches upon the topc of MU-MIMO capacty as well as the promsng convex optmzaton approaches to MIMO system desgn. Keywords: Multple-Input Multple-Output (MIMO), Multuser MIMO, Wreless Communcatons, Beamformng, Dversty, Precodng, Capacty 1. Introducton Multple-nput multple-output (MIMO) wreless systems employ multple transmt and receve antennas to ncrease the transmsson data rate through spatal multplexng or to mprove system relablty n terms of bt error rate (BER) performance usng space-tme codes (SCs) for dversty maxmzaton [1]. MIMO systems explot multpath propagaton to acheve these benefts, wthout the expense of addtonal bandwdth. More recent MIMO technques lke the geometrc mean decomposton (GMD) technque proposed n [] am at combnng the dversty and data rate maxmzaton aspects of MIMO n an optmal manner. hese advantages make MIMO a very attractve and promsng opton for future moble communcaton systems especally when combned wth the benefts of orthogonal frequency-dvson multplexng (OFDM) [3,4]. he capacty of an M N sngle-user MIMO (SU- MIMO) system wth M transmt and N receve antennas, n terms of the spectral effcency.e. bts per second per z, s gven by [1] C log det IN M (1) where s the N M MIMO channel matrx and ρ s the sgnal to nose rato (SNR) at any receve antenna. Equaton (1) assumes that the M nformaton sources are uncorrelated and have equal power. Expressed n terms of the egenvalues, Equaton (1) can be wrtten as [1] C m 1 log 1 M () where λ represent the nonzero egenvalues of or for N M and M < N respectvely and m = mn(m, N). herefore, MIMO systems are capable of achevng several-fold ncrease n system capacty as compared to sngle-nput sngle-output (SISO) systems by transmttng on the spatal egenmodes of the MIMO channel. Equaton () also shows that the performance of MIMO systems s dependent on the channel egenvalues. Very low egenvalues ndcate weak transmsson channels whch may make t dffcult to recover the nformaton from the receved sgnals. Optmal power allocaton based on the water-fllng algorthm can be used to maxmze the system capacty subject to a total transmt power constrant. Water-fllng provdes substantal capacty gan when the egenvalue spread,.e., the condton number λ max /λ mn s suffcently large. he MIMO concept becomes even more attractve n multuser scenaros where the network capacty can be ncreased by smultaneously accommodatng several users Copyrght 010 ScRes.

2 14 F. KALID E AL. wthout the expense of valuable frequency resources. hs paper s arranged as follows: Secton provdes an overvew of the current wreless standards whch support MIMO technologes. Sectons 3 and 4 nclude detaled dscusson and performance analyss of varous mportant SU-MIMO and multuser MIMO (MU-MIMO) technques respectvely that are proposed for the next generaton wreless communcaton systems. In-depth descrpton of several MU-MIMO uplnk and downlnk schemes s gven n Secton 4 followed by a bref dscusson of the MU-MIMO capacty. Secton 5 provdes an overvew of convex optmzaton whch has become an mportant tool for desgnng optmal MIMO beamformng systems. Secton 6 concludes ths work and dentfes the areas for future research.. Current Implementaton Status here has been a lot of research on MIMO systems and technques. MIMO-OFDM WLAN products based on the IEEE 80.11n standard are already avalable. he IEEE wreless MAN standard known as WMAX also ncludes MIMO features. Fxed WMAX servces are beng offered by operators worldwde. Moble WMAX networks based on 80.16e are also beng deployed whle 80.16m s under development. IEEE 80.0 moble broadband wreless access (MBWA) standard s also beng formulated whch wll have complete support for moblty ncludng hgh-speed moble users e.g., on tran networks. For other applcatons lke cellular moble communcatons whch supports both voce and data traffc, MIMO systems are yet to be deployed. owever, the 3GPP s long term evoluton (LE) s under development and adopts MIMO-OFDM, orthogonal frequency-dvson multple access (OFDMA) and sngle-carrer frequency-dvson multple access (SC-FDMA) transmsson schemes. he followng text presents a more detaled dscusson of the varous techncal aspects of these standards and technologes..1. IEEE 80.11n W-F he IEEE 80.11n WLAN standard ncorporates MIMO- OFDM as a compulsory feature to enhance data rate. Intal target was to acheve data rates n excess of 100 Mb/s [5]. owever, current WLAN devces based on 80.11n Draft.0 are capable of achevng throughput up to 300 Mb/s utlzng two spatal streams n a 40 Mz channel n the 5 Gz band [6]. Intally, there were two man proposals one form the WWSE consortum and the other from the GnSync consortum competng for adopton by the IEEE Gn. owever, another proposal by the Enhanced Wreless Consortum (EWC) was fnally accepted as the frst draft for IEEE 80.11n [7]. he IEEE 80.11n standard proposes the use of the legacy 0 Mz channel and also an optonal 40 Mz channel. he avalable modulaton schemes nclude BPSK, QPSK, 16-QAM and 64-QAM [5,6]. Convolutonal codng wth dfferent code rates s specfed and use of low-densty party-check (LDPC) codes s also supported [5,8]. he MIMO technques adopted nclude both spatal multplexng and dversty technques. Open-loop MIMO (OL-MIMO) technques whch do not requre channel state nformaton (CSI) at the transmtter seem to have been preferred [9]. Non-teratve lnear mnmum mean square error (LMMSE) detecton has prmarly been consdered so as to mnmze the complexty assocated wth MIMO detecton whle ensurng reasonably good performance [10]. Spatal spreadng mentoned n [11] s an open-loop MIMO spatal multplexng technque where multple data streams are transmtted such that the dversty s maxmzed for each of the streams. he MIMO dversty technques ntroduced n the standard nclude space-tme block codng (SBC) and cyclc shft dversty (CSD) whch extend the range and recepton of 80.11n devces. In addton, conventonal recever spatal dversty technques lke maxmum rato combnng (MRC) are also specfed. ransmt beamformng s also specfed as an optonal feature [6]. he Csco Aronet 150 seres access pont based on 80.11n draft.0 supports open-loop transmt beamformng [1] n draft.0 specfes a maxmum of 4 spatal streams per channel. hus, a maxmum throughput of 600 Mb/s can be acheved by usng 4 spatal streams n a 40 Mz channel. In addton to spatal multplexng and doubled channel bandwdth, more effcent OFDM wth shorter guard nterval (GI) and new medum access control (MAC) layer enhancements (e.g. closed-loop rate adaptaton [13]) have also contrbuted to the ncreased throughput of 80.11n [6]... IEEE WMAX he IEEE worldwde nteroperablty for mcrowave access (WMAX) s a recently developed wreless MAN standard that employs MIMO spatal multplexng and dversty technques. In addton to fxed WMAX, the IEEE 80.16e Moble WMAX standard has also been developed and was approved n December 005 [14]. Fxed WMAX networks have already been deployed around the world and Moble WMAX deployments have also started e-005 s bascally an amendment to the standard for fxed WMAX wth addton of new features to support moblty e specfes the 6 Gz frequency band for moble applcatons and the 11 Gz band for fxed applcatons (he sngle-carrer WrelessMAN-SC PY specfcaton for fxed wreless Copyrght 010 ScRes.

3 F. KALID E AL. 15 access however specfes the Gz frequency band [15].). It also specfes a lcense-exempt band between 5 6 Gz. A cellular network structure s specfed wth support for handoffs and moble users movng at vehcular speeds are also supported, thus enablng moble wreless nternet access [14,16]. In addton to sngle carrer transmsson, the standard specfes OFDM transmsson scheme wth 18, 56, 51, 104 or 048 subcarrers. Both DD and FDD duplexng s specfed whle the multplexng/multple access schemes nclude OFDMA n addton to burst DM/ DMA. owever, scalable OFDMA s specfed n all moble WMAX profles as the physcal layer multple access technque. he varous channel bandwdths specfed n the standard nclude 1.5, 1.75, 3.5, 5, 7, 10, 8.75, 10, 14 and 15 Mz. WMAX supports adaptve modulaton and codng schemes. he supported modulaton schemes nclude BPSK, QPSK, 16-QAM and 64-QAM [14,16]. Optonal 56-QAM support s provded n the WrelessMAN-SCa PY [15]. Convolutonal codes at rate1/, /3, 3/4 or 5/6 are specfed as mandatory for both uplnk and downlnk. In addton, convolutonal turbo codes, repetton codes, LDPC and concatenated Reed-Solomon convolutonal code (RS-CC) are specfed as optonal. he supported data rates range from 1 Mb/s to 75 Mb/s [14,16]. IEEE 80.16e supports both open-loop and closedloop MIMO. Open-loop MIMO technques nclude spatal multplexng (SM) and space-tme codng (SC) [14,17,18] e ncludes support for up to four spatal streams and therefore a maxmum of 4 4 MIMO confguraton [14,18]. SC s based on the Alamout scheme (also SBC) and s also called space-tme transmt dversty (SD). It s an optonal feature and may be used to provde hgher order transmt dversty on the downlnk [14]. In closed-loop MIMO, full or partal CSI s avalable at the transmtter through feedback. Egenvector steerng s employed to approach full capacty of the MIMO channel and water fllng can be used to maxmze throughput by allocatng power n an optmal manner [9,19]. IEEE 80.16e supports closed-loop MIMO precodng for SM and also closed-loop SC [14,17]. owever, closed-loop MIMO s not yet supported n the latest WMAX Forum Wave profles [18]. Another MIMO mode called collaboratve spatal multplexng s also specfed where two subscrber statons (SS), each havng a sngle antenna, use the same subchannel for uplnk transmsson n order to ncrease the throughput [14,15, 17,0]. he adaptve antenna systems (AAS) supported n 80.16e also nclude closed-loop adaptve beamformng, whch uses feedback from the SS to the base staton (BS) to optmze the downlnk transmsson [14,15,18]. IEEE ask Group m (Gm) has also been set up to develop the IEEE 80.16m standard whch wll enable nteroperablty between WMAX and 3GPP s Long erm Evoluton (LE) standard for next generaton moble communcatons [1,] m s expected to support hgh-speed moble wreless access (up to 350 km/h) and peak data rates of over 300 Mb/s usng 4 4 MIMO []..3. IEEE 80.0 MBWA he IEEE 80.0 workng group was establshed to draft the IEEE 80.0 Moble Broadband Wreless Access (MBWA) standard whch s also ncknamed as MobleF. IEEE 80.0 proposes a complete cellular structure and s desgned and optmzed for moble data servces at speeds up to 50 km/h. owever, t can also support voce servces due to very low transmsson latency of ms (better than the 5 40 ms for 80.16e). User data rates n excess of 1 Mb/s can be supported at 50 km/h [3 5]. MBWA s desgned to operate n the lcensed bands below 3.5 Gz [4,5]..5 Mz to 0 Mz of uplnk/downlnk transmsson bandwdth can be allocated per cell [5]. For a bandwdth of 5 Mz, peak aggregate data rate of around 16 Mb/s can be supported n the downlnk [3,4] whch obvously would be much greater for hgher bandwdths. he transmsson scheme s based on OFDM, wth OFDMA used for downlnk transmsson whle both OFDMA and code-dvson multple access (CDMA) are specfed for the uplnk. Rotatonal OFDM s specfed as an optonal scheme. he standard supports both FDD and DD operaton. he supported modulaton schemes nclude QPSK, 8-PSK, 16-QAM and 64-QAM. Support of herarchcal (layered) modulaton nvolvng the superposton of two modulaton schemes s also ncluded for broadcast and multcast servces. he specfed FEC codng schemes nclude convolutonal codes, turbo codes and LDPC codes [5]. Varous MIMO schemes are also supported. SD (based on SBC) and SM are specfed for SU-MIMO transmsson, utlzng up to 4 transmt antennas. SD s partcularly mportant for hgh speed moble access. wo dfferent stream multplexng schemes namely sngle codeword (SCW) and multple codeword (MCW) may be employed for MIMO transmsson. hese schemes also support closed-loop MIMO downlnk transmsson wth rank adaptaton. Both schemes utlze lnear precodng at the BS for transmt beamformng based on the feedback of a sutable precodng matrx from the user equpment s (UE s) codebook to the BS. he standard also supports MU-MIMO or space-dvson multple access (SDMA) transmsson n the downlnk whch nvolves multuser schedulng and precodng at the BS dependng upon the feedback of the preferred precodng matrx ndex and dfferental channel qualty ndcator Copyrght 010 ScRes.

4 16 F. KALID E AL. (CQI) reports from the UEs [5]. he IEEE 80.0 standard was supposed to be avalable n 006 but was delayed due to lack of support from some of the key vendors and the poltcal turmol wthn the standards forum [3]. owever, t was fnally approved n June 008 and made avalable by the end of August 008 [5]..4. 3GPP LE he 3 rd generaton partnershp project s (3GPP) long term evoluton (LE) project s amed at developng a new moble communcatons standard for gradual mgraton from 3G to 4G. LE physcal layer s almost near completon. It specfes an OFDM based system wth support for MIMO. Downlnk transmsson s based on OFDMA whle SC-FDMA s used for the uplnk due to ts low PAPR characterstcs. It supports both DD and FDD operaton. A packet swtchng archtecture s specfed for LE [6,7]. LE supports scalable bandwdths of 1.5,.5, 5, 10 and 0 Mz. Peak data rates of 100 Mb/s and 50 Mb/s are supported n the downlnk and the uplnk respectvely, n 0 Mz channel. he standard specfes full performance wthn a cell up to 5 km radus and slght degradaton from 5 30 km. Operaton up to 100 km may be possble. It also supports hgh-speed moblty wth hgh performance at speeds up to 10 km/h whle the E-URAN (Evolved Unversal errestral Rado Access Network.e., LE s RAN) should be able to mantan the connecton up to 350 km/h, or even up to 500 km/h. LE also specfes very low latency operaton wth control plane (C-plane) latency of < ms and user plane (U-plane) latency of < 10 ms [7,8]. he sngle-user MIMO technques supported nclude SBC and SM. Closed-loop multple codeword (MCW) SM wth codebook based precodng and wth support for cyclc delay dversty (CDD) s specfed. A maxmum of two downlnk spatal streams are specfed. LE also supports MU-MIMO n the downlnk as well as n the uplnk. Closed-loop transmt dversty usng MIMO beamformng wth rank adaptaton s also supported. he supported antenna confguratons for the downlnk nclude 4,, 1 and 1 1 whereas 1 and 1 1 confguratons are supported n the uplnk [7,9,30]. owever, multple UE antennas n the uplnk may be supported n future. lkely canddates for the next generaton wreless systems V-BLAS he vertcal Bell Laboratores Layered Space-me (V- BLAS) [31] s one of the very frst open-loop spatal multplexng MIMO systems whch has been practcally demonstrated to acheve much hgher spectral effcences than SISO systems, n rch scatterng envronments. In V-BLAS, a sngle data stream s demultplexed nto multple substreams whch are mapped on to symbols and then transmtted through multple antennas. Intersubstream codng s not employed n V-BLAS, however channel codng can be appled to the ndvdual substreams for reducton of bt error rate (BER). CSI n a V-BLAS system s avalable at the recever only by means of channel estmaton. Fgure 1 shows the smple block dagram of a V-BLAS system. V-BLAS detecton can be accomplshed by usng lnear detectors lke zero-forcng (ZF) or mnmum mean square error (MMSE) detector along wth symbol cancellaton (also called successve nterference cancellaton). Symbol cancellaton s a nonlnear technque whch enhances the detecton performance by subtractng the detected components of the transmt vector from the receved symbol vector [31]. hs technque, however, s prone to error propagaton. he QR decomposton of the MIMO channel matrx can be used to represent the ZF nullng n V-BLAS []. Assumng a frequency-flat fadng MIMO channel, the correspondng sampled baseband receved sgnal for a V-BLAS system wth M transmt and N receve antennas (M N) s therefore gven by y x n (3) QRx n where Q s an N M untary matrx wth orthonormal columns, R s a M M upper trangular matrx, x s the transmtted sgnal and n represents the nose vector. he 3. Sngle-User MIMO echnques Varous open-loop and closed-loop SU-MIMO technques are dscussed n the followng text along wth performance analyss and comparson. Some of the technques mentoned heren have already been adopted for the current standards whle other advanced methods are Fgure 1. V-BLAS system block dagram [31]. Copyrght 010 ScRes.

5 F. KALID E AL. 17 dscrete-tme ndex s dropped to smplfy notaton. Multplyng both sdes of Equaton (3) by Q gves y Rxn (4) he sequental sgnal detecton n V-BLAS can be accomplshed as follows []: for M : 1:1 M xˆ ˆ C y r / j 1 jx j r end where C represents mappng to the nearest modulaton symbol. he results for an ntal V-BLAS prototype mentoned n [31] yelded spectral effcences of 0 40 bps/z n ndoor scenaros whch s qute mpressve. owever, later has shown that V-BLAS also performs reasonably well n moble scenaros and can be employed for MIMO- OFDM systems as well and further mprovements have been suggested n the lterature. [3] proposes an extenson of V-BLAS ncorporatng power and rate feedback whch approaches closed-loop MIMO capactes. Equal power allocaton wth per-antenna rate control (PARC) produces the best results for the proposed system. PARC enables the transmtter to select the approprate data rate and the assocated modulaton and codng scheme (MCS) for each transmt antenna based on the feedback of channel qualty nformaton from the recever [33]. It presents a comparson between a modfed V-BLAS system wth lmted feedback (ncludng the modulaton ndex and the number of streams to be used) and closed-loop MIMO (CL-MIMO) n [34]. CL-MIMO shows 15.1% throughput mprovement for Raylegh fadng channel, 48.1% for spatally correlated channel and 104% for the case of a realstc channel model, at SNR of 5 db. Fgure shows these results. (a) (b) (c) Fgure. hroughput for (a) Raylegh fadng channel, (b) Spatal correlaton channel and (c) Realstc channel model [34]. Copyrght 010 ScRes.

6 18 F. KALID E AL. 3.. Spatal Multplexng wth Cyclc Delay Dversty Spatal multplexng (SM) can be combned wth a smple dversty technque such as cyclc delay dversty (CDD) to obtan much better performance as compared to regular SM systems lke V-BLAS. Such a system whch combnes SM and MIMO dversty s referred to as a jont dversty and multplexng (JDM) system [35]. SM wth CDD s also specfed n the 3GPP LE standard [30]. It proposes a cyclc delay asssted SM-OFDM (CDA-SM-OFDM) system whch does not requre any CSI at the transmtter, however complete CSI s requred at the recever [35]. Fgure 3 shows the transmtter and recever block dagram. he blocks denoted 1,,, perform the cyclc delay operaton whch nvolves cyclc shftng of the sgnal wthn each group of transmt antennas per SM branch. If there are P SM branches then the total number of transmt antennas s P. he recever for CDA-SM-OFDM system s smlar to V-BLAS. CDD ncreases the channel frequency-selectvty snce cyclc shftng of the OFDM sgnal and then addng those shfted sgnals lnearly at the recever nserts vrtual echoes on the channel response. he resultng hgher order frequency dversty can be exploted by any coded OFDM (COFDM) system [35]. Fgure 4 shows a comparson of the CDA-SM-OFDM system capacty wth and 4 SM-OFDM systems. ere t can be seen that the capacty of the CDA-SM- OFDM system les between that for the two SM-OFDM systems. owever, the capactes for the SM-OFDM systems are plotted for the deal case.e. wth the best possble SC and channel codng schemes. It can also be seen that the outage capacty.e. the capacty obtaned below 10% of the tmes, for the CDA-SM-OFDM system s much hgher than the SM-OFDM and closer to the 4 SM-OFDM. hus the system performance for the CDA-SM-OFDM system shows a sgnfcant ncrease just by employng a smple SC.e. CDD. It has also be shown n [35] that the egenvalue spread for the CDA-SM-OFDM system s generally hgher than both the SM-OFDM schemes and ths means that egen-beamfomng can be employed for CDD based SM systems. In fact, the 3GPP LE standard ncorporates CDD based SM wth precodng and specfes precodng matrces for small and large delay CDD [30]. Fgure 5 provdes a comparson of the average spectral Fgure 4. Comparson of system capacty for 4 CDA- SM-OFDM system wth and 4 SM-OFDM system [35]. (a) CDA-SM-OFDM transmtter (b) CDA-SM-OFDM recever Fgure 3. CDA-SM-OFDM system transmtter and recever [35]. Fgure 5. Average spectral effcences n bps/z [35]. Copyrght 010 ScRes.

7 F. KALID E AL. 19 effcences of SM-OFDM systems and 4 CDA-SM-OFDM systems for a low user moblty ndoor WLAN scenaro. ere t can be seen that the 4 CDA-SM-OFDM systems provde much hgher spectral effcences at low SNR values Sngular Value Decomposton Based MIMO Precodng Sngular value decomposton (SVD) based MIMO precodng s a closed-loop MIMO scheme where the precodng flter at the transmtter s desgned by takng the SVD of the MIMO channel matrx. [36] provdes an analyss of the classcal SVD based MIMO precodng scheme, SVD based precodng wth ZF equalzaton, SVD based precodng wth MMSE equalzaton and also an mproved SVD based precodng technque. All of these schemes are analyzed wth realstc channel knowledge at the transmtter. Fgure 6 shows the block dagram of the SVD based MIMO-OFDM transmtter and recever Classcal SVD Precodng and Equalzaton In SVD based technques, the channel matrx of a MIMO system wth Nt transmt antennas and Nr receve antennas, s decomposed as UDV (5) NrNt NtNt where U and V are untary matrces Nt Nt whle D s a dagonal matrx consstng of the ordered sngular values d. he classcal SVD approach utlzes matrx V for precodng at the transmtter. he columns v of matrx V are the egenvectors of. he receved sgnal s gven by r Vs n (6) where s s a vector of nformaton symbols s and n s the nose vector correspondng to an addtve whte Gaussan nose (AWGN) process wth varance n for each element. At the recever, matrx U s employed for equalzaton and the detected sgnal vector s gven by y U r U VsU n U UDV VsU n (7) y DsU n Each ndvdual receved sgnal can be wrtten as y ds n (8) (a) (b) Fgure 6. SVD based MIMO-OFDM system (a) ransmtter and (b) Recever [36]. Copyrght 010 ScRes.

8 0 F. KALID E AL. where ' n represents the -th element of correspondng SISO SNR values are then gven by n U n. he s SNR d (9) Equatons (8) and (9) show that the sngular values represent the MIMO processng gan for each of the egenmodes. herefore, SVD based MIMO precodng requres adaptve modulaton and bt loadng technques for capacty maxmzaton [36] SVD Precodng wth ZF Equalzaton Lnear ZF equalzaton can also be used at the recever whch s based on the nverson of the estmated MIMO channel matrx. ZF equalzaton requres the estmaton of the product of V at the recever. Assumng deal channel knowledge at the recever, the detected sgnal can then be gven by y V r (10) V Vs V n y s UD n (11) where 1 represents the pseudo nverse SVD Precodng wth MMSE Equalzaton MMSE equalzaton s based on mnmzng the mean square error (MSE) between the transmtted and detected symbols. he mnmum mean square error s gven by emn sˆ s (1) where s s the transmtted symbol and sˆ represents the receved symbol. he detected sgnal for SVD based MIMO MMSE equalzaton s gven by y 1 I V V V r (13) K n wth K Nt utlzed egenmodes. As seen from Equaton (13), MMSE MIMO equalzaton also requres the precodng matrx V at the recever Improved SVD Precodng echnque wth Realstc Channel Knowledge An mproved SVD based MIMO precodng technque s also proposed n [36] whch maxmzes MIMO capacty whle consderng realstc channel knowledge at the transmtter rather than the deal one. he MIMO capacty for realstc channel knowledge s gven by where d C N t s log 1d (14) 1 n represent the sngular values for the case of realstc channel knowledge. he mproved technque consders the K strongest egenmodes for transmsson wth K N f the followng statement s fulflled. t (15) N t s K N s t log 1d log 1 d 1 n 1 K n he remanng egenmodes whch correspond to the Nt K unused egenvectors of the precodng matrx V are not utlzed Performance Comparson Fgure 7 shows the BER performance comparson of the classcal SVD, ZF and MMSE equalzaton schemes for a 4 4 MIMO-OFDM system. A curve for deal ZF equalzaton s also provded for reference. It s clear from the comparson that MMSE equalzaton provdes the best results wth realstc channel estmaton. Fgure 8 shows the performance comparson of the Fgure 7. BER performance of uncoded 4 4 SVD based MIMO systems [36]. Fgure 8. BER performance of an uncoded 4 4 SVD based MIMO system wth MMSE equalzaton [36]. Copyrght 010 ScRes.

9 F. KALID E AL. 1 MMSE equalzaton scheme wth dfferent values of K x should satsfy (utlzed egenmodes) for an uncoded 4 4 MIMO system wth realstc channel knowledge at the transmtter. dagr s R x (0) he BER curve for the case of deal channel knowledge where the left-hand sde represents the element-wse s also provded. he MMSE equalzaton scheme provdes the best performance for K = utlzed egen- elements of s. he soluton to Equaton (0) s then multplcaton of the dagonal elements of R wth the modes selected accordng to Equaton (15). 1 x R dag Rs (1) 3.4. Geometrc Mean Decomposton (GMD) Based MIMO he ZFDP scheme, unlke V-BLAS, does not suffer from the error propagaton problem. owever, due to the GMD based MIMO [] s also a closed-loop jont transcever desgn scheme whch ams at optmally combnng sgnfcantly amplfed resultng n ncreased transmtter matrx nverson n Equaton (1) the norm of x can be the benefts of MIMO dversty and spatal multplexng. power consumpton. hs problem can be resolved by hs technque utlzes the GMD of the MIMO channel usng the omlnson-arashma precoder to restrct the matrx for precoder and equalzer desgn when the CSI s transmt sgnal level wthn acceptable lmts []. avalable at both the transmtter and the recever. It s also applcable to MIMO-OFDM systems Combnng GMD wth V-BLAS and ZFDP GMD calculaton algorthm n [] starts from the SVD he GMD-VBLAS scheme can be mplemented begnnng wth the GMD of the channel matrx, QRP. of the channel matrx whch s gven accordng to Equaton (5) he nformaton symbol vector s s then encoded by UDV the lnear precoder P resultng n the transmt sgnal x Ps. he resultng sgnal at the recever s then gven he GMD s then gven by by UURRVRV y QRs n () (16) QRP whch can be decoded smply by usng the V-BLAS where Q and P are sem-untary matrces, P beng recever. GMD-ZFDP scheme can be also be mplemented n a smlar way. he resultng K ndependent K K the lnear precoder at the transmtter. R s an and dentcal subchannels are gven by upper trangular matrx whose dagonal elements are the geometrc mean of the K nonzero sngular values of y x n ; 1,, K (3). he GMD scheme thus decomposes the MIMO channel nto dentcal parallel subchannels whch makes the symbol constellaton selecton and the overall system desgn much smpler. GMD can also be seen as an extended QR decomposton. GMD MIMO can be mplemented wth the V-BLAS recever and also wth the zero-forcng drty paper precoder (ZFDP). he V-BLAS technque has been dscussed earler n the text. he ZFDP technque also nvolves sequental nullng and cancellaton but at the transmtter and utlzes CSI at the transmtter only. he ZFDP scheme combnes QR decomposton and drty paper precodng. he QR decomposton for ZFDP s gven by QR (17) he sampled baseband receved sgnal s then gven by y R Q x n (18) Substtutng x Qx we have y R xn (19) K1 Let s be the transmtted symbol vector then where represent the subchannel gan and are n fact the dentcal dagonal elements of the matrx R [] Performance Some smulaton results from [] depctng the performance of GMD based MIMO schemes are presented n the followng text, assumng ndependent dentcally dstrbuted (..d) Raylegh flat fadng channels. Fgure 9 shows a comparson of the capacty of GMD-MIMO wth other schemes for 4 4 MIMO confguraton. he nformed transmtter (I) curve corresponds to the Shannon channel capacty when CSI s avalable at both the transmtter and the recever whle the unnformed transmtter (U) curve corresponds to the channel capacty when CSI s not avalable at the transmtter. MM and MMD are both lnear precoder desgn schemes for lnear transcevers. MM s based on the mnmzaton of the trace of the MSE matrx whle MMD mnmzes the maxmum dagonal elements of the MSE matrx resultng n nearoptmal performance. Clearly, GMD outperforms both MM and MMD at hgh SNR and approaches optmal capacty. he capacty loss of GMD at low SNR s due to Copyrght 010 ScRes.

10 F. KALID E AL. the ZF recever. Based on GMD, the authors of [] have also proposed another scheme called unform channel decomposton (UCD) whch can decompose a MIMO channel nto dentcal subchannels n a strctly capacty lossless manner [37]. Fgures 10 and 11 show the BER performance comparson of GMD-MIMO wth ordered MMSE-VBLAS, MM and MMD for 4 and 4 4 MIMO confguratons respectvely. GMD acheves much hgher performance partcularly at hgh SNR. Fgure 1 shows a performance comparson of GMD- VLBAS and GMD-ZFDP when combned wth OFDM for ISI suppresson. GMD-VBLAS results n performance loss of about db because of error propagaton urbo-mimo Systems urbo-mimo systems represent a class of MIMO com- Fgure 11. BER performance for 4 4 MIMO confguraton []. Fgure 9. Average capacty for 4 4 MIMO confguraton []. Fgure 10. BER performance for 4 MIMO confguraton []. Fgure 1. BER performance of GMD based MIMO-OFDM systems []. muncaton systems that combne the turbo-processng prncple used n turbo codng wth MIMO. hese systems am at attanng channel capacty close to the Shannon lmt for MIMO channels wth manageable complexty and can be mplemented from dversty maxmzaton or SM aspects [38]. A turbo-mimo archtecture known as urboblas s presented n [39]. hs MIMO system s based on random layered space-tme (RLS) codng whch s a combnaton of ndependent block-tme codng and space-tme nterleavng. he recever uses teratve turbo-processng for RLS decodng and estmaton of the flat fadng MIMO channel matrx. A smlar turbo-mimo system based on space-tme bt-nterleaved coded modulaton (S-BICM) s presented n [38]. S-BICM codes are formed by concatenaton of a turbo encoded sequence and S nterleavng. Copyrght 010 ScRes.

11 F. KALID E AL. 3 Fgure 13 shows the block dagram of a S-BICM MIMO system transmtter. he nformaton bts are turbo encoded based on a lnear forward error correcton (FEC) code represented as the outer code. he encoded sequence s then bt-nterleaved usng a space-tme pseudorandom nterleaver denoted by n the fgure. Each nterleaved substream s then ndependently mapped onto M-ary PSK or QAM symbols and transmtted usng a separate antenna. he nner code bascally represents a lnear space-tme mapper whch allows for a flexble MIMO desgn wth optmal dversty order and multplexng gan or a desred tradeoff between the two. SBCs can be used to obtan the maxmum dversty order whle a symbol multplexer can be used f full multplexng gan s desred [38]. Fgure 14 shows a double teratve decodng recever for the S-BICM MIMO system. It operates n two stages consstng of nner and outer teratve decodng loops. he nner and outer decoders are separated by an nterleaver and a denterleaver represented by and 1 respectvely. hs arrangement decorrelates the correlated outputs between the two stages. he decorrelator compensates for the nterleavng operaton at the transmtter. he two stages teratvely exchange nformaton, producng a better estmate of the transmtted symbols after each teraton, untl the recever converges [38]. he nner decoder s n fact a MIMO detector, the optmal choce beng the maxmum a posteror probablty (MAP or APP) detector/decoder. owever, due to the excessve computatonal complexty of APP detecton, reduced-complexty near-optmal detectors lke MMSE- SIC or reduced-complexty APP detectors e.g. the lstsphere detector (LSD), teratve tree search (IS) and multlevel bt mappng IS (MLM-IS) detectors can be used. he outer decoder conssts of a channel turbo decoder wth two decodng stages separated by an nterleaver and a denterleaver denoted by α and α -1 respectvely n Fgure 14. hs arrangement forms the outer teratve decodng loop of the S-BICM MIMO recever [38]. Fgure 13. S-BICM MIMO system transmtter [38]. Fgure 14. Recever structure for the S-BICM MIMO system [38]. Copyrght 010 ScRes.

12 4 F. KALID E AL Performance Fgure 15 shows the BER performance of a smulated 8 8 S-BICM MIMO system usng a rate-1/, memory turbo code as the outer channel code, wth feed-forward and feedback generators 5 and 7 (octal) respectvely. A block fadng channel s assumed for the nner encoder whch remans constant for a block sze of 19 nformaton bts wth each block representng a statstcally ndependent channel realzaton. A rch scatterng Raylegh MIMO model s used to select the elements of the MIMO channel matrx. 4 teratons are used n the nner decoder loop whle 8 teratons are used n the outer channel decoder loop. he fgure shows a comparson for dfferent modulaton schemes wth MMSE-SIC and MLM-IS nner detectors. he performance of MLM- IS detecton ncreases wth larger lst sze M however, at the cost of ncreased complexty. he respectve capacty lmts for QPSK, 16-QAM and 64-QAM are also shown. At BER = 10-5 and M = 64, he S-BICM systems usng QPSK, 16-QAM and 64-QAM operate 1, 4 and 6 db away from ther respectve capacty lmts [38]. Fgure 16 shows the BER performance of the S- BICM system usng MLM-IS detector as the no. of teratons n the outer decoder ncrease from 1 to 5. Clearly the performance mproves wth the no. of teratons whch pertans to only a lnear ncrease n complexty. owever, t can also be seen that the performance gan between successve teratons dmnshes somewhat due to the feedback of correlated nose. Further ncrease n teratve gan can be acheved by usng larger nterleavers [38]. CSI feedback s not desrable and may not even be possble e.g. n case of rapdly varyng moble channels. Furthermore, results have shown that performance close to that wth full CSI can be acheved by usng lmted feedback strateges utlzng only a few bts of feedback. Fgure 17 shows the block dagram of a lmted feedback MIMO system [40]. Fgure 15. BER performance of 8 8 S-BICM MIMO system wth dfferent modulaton and nner detecton schemes [38] Lmted Feedback Strateges for Closed-loop MIMO Systems Certan closed-loop MIMO systems lke the SVD and GMD based systems assume the avalablty of full CSI at the transmtter. Full CSI s avalable at the transmtter n a DD system wth duplex tme less than the channel coherence tme due to the recprocty of the channel whle n a FDD system a feedback channel for CSI s requred thus consumng addtonal bandwdth. owever, n practcal scenaros the extra load resultng from large Fgure 16. BER performance of 8 8 S-BICM MIMO system wth dfferent no. of teraton n the outer decoder [38]. Fgure 17. Lmted feedback closed-loop MIMO system [40]. Copyrght 010 ScRes.

13 F. KALID E AL. 5 he feedback may be based on channel quantzaton or quantzaton of some propertes of the transmtted sgnal. Channel quantzaton nvolves vector quantzaton (VQ) of the channel matrx as depcted n Fgure 18. he quantzed verson of the MIMO channel can then be fed back to the transmtter. owever, t has been observed that quantzaton of the entre channel may not be necessary and t may be suffcent to nclude only some part of the channel structure lke the channel sngular vectors. For example, the optmal precodng matrx for an..d MIMO channel conssts of the egenvectors of the channel covarance matrx, as columns. he feedback overhead may be further reduced by usng only a lmted number of quantzed weghtng vectors or matrces for precodng. hs collecton of precodng matrces s known as a precodng codebook and s shared by the transmtter and the recever. he feedback conssts of bts representng a partcular precodng matrx wthn the codebook [40,41]. A large codebook length for vector quantzaton schemes results n ncreased complexty at the recever due to the exhaustve search requred for selectng a precodng matrx. In such cases, when the codebook length and therefore the correspondng no. of feedback bts B s large, scalar quantzaton of the elements of the precodng matrx can be employed nstead. owever, for small values of B, scalar quantzaton may become too naccurate. In such cases, performance of scalar quantzaton can be mproved by usng the reduced rank approach where the columns of the precodng matrx are constraned to le wthn a subspace of dmenson less than the no. of transmt antennas N t [40]. Fgure 19 shows the symbol error rate (SER) performance of a smulated 4 5 lmted feedback MIMO beamformer wth dfferent feedback strateges. he system uses 16-QAM modulaton for transmsson and MRC at the recever. Optmal BF n the fgure represents the optmal beamformer wth unquantzed feeback and full CSI at the transmtter. Grassmannan BF (6-bt) represents sgnal adaptve beamformng usng a 6-bt feedback VQ codebook and results n the best performance, lyng wthn 0.7 db of the optmal BF and approxmately 1dB better than the 40-bt channel quantzaton whch suffers from large quantzaton error. he 6-bt quantzed reduced rank (RR) beamformer wth dmenson D = 3, performs close to the 40-bt channel quantzaton [40]. Fgure 18. Channel Quantzaton [40]. Fgure 19. Lmted feedback beamformer performance for 4 5 MIMO confguraton [40] Lnk Adaptaton wthout Precodng In addton to the precodng matrx, other nformaton e.g. the receved sgnal to nterference and nose rato (SINR) may also be ncluded n the feedback for lnk adaptaton. owever, some MIMO schemes lke the modfed V- BLAS schemes n [3,34] rely solely on ths type of feedback wthout any precodng nformaton. Another example s the -codeword multple codewords (CW-MCW) scheme for FDD MIMO-OFDM cellular systems proposed n [41] that uses SINR feedback for each stream to select a sutable modulaton and codng scheme (MCS) for each of the two smultaneously transmtted codewords. he two codewords are mapped onto and 4 streams respectvely for and 4 4 antenna confguratons. he mappng may ether be fxed or adaptve. Adaptve mappng also makes use of the SINR feedback. Precodng s not used n ths scheme resultng n reduced feedback overhead Partal Feedback Schemes Partal feedback schemes for MIMO systems are based on the feedback of statstcal channel nformaton along wth some nstantaneous channel qualty ndcator (CQI) e.g. SNR, SINR etc. to the transmtter. A partal feedback scheme for MIMO-OFDM systems nvolvng the decomposton of MIMO channel covarance matrx s presented n [4]. he covarance matrx R s calculated from the estmated MIMO channel matrx (for the k-th subcarrer) at the recever and s gven by E R (4) he matrx R s then decomposed usng SVD whch s gven by where R U Λ V (5) Stat Stat Stat s a dagonal matrx contanng the sngular Λ Stat Copyrght 010 ScRes.

14 6 F. KALID E AL. values whle and are untary matrces. he U Stat V Stat feedback ncludes the matrx Λ Stat and the column vectors of VStat for power allocaton and spatal processng (precodng) at the transmtter [4]. Fgure 0 shows the block dagram of a N N R MIMO-OFDM system based on ths partal feedback scheme whch transmts N S spatal streams usng N C OFDM subcarrers. he receved sgnal vector for the k-th subcarrer s gven by y = QAx (6) where x s the transmt data vector, s the MIMO channel matrx for the k-th subcarrer, A s a dagonal matrx wth N S dagonal elements determned by the matrx ΛSt at feedback for power allocaton to the actve spatal streams, and the N N S matrx Q represents a spatal processng transformaton whch maps the spatal streams to the transmt antennas. he Q matrx s constructed from the vectors of V Stat receved at the transmtter va feedback and s used to maxmze the receved energy for each transmtted spatal stream. hs enables maxmum rato transmsson (MR) and SVD beamformng along wth trackng of spatal varatons of the MIMO channel [4]. he MIMO channel covarance and the correspondng channel sngular values do not vary rapdly wth tme even at vehcular speeds around 100 km/h [4]. hs greatly reduces the feedback load on the system and makes ths closed-loop MIMO-OFDM system sutable for moble envronments. Fgures 1 and show the smulated frame error rate (FER) performance of the proposed MIMO-OFDM system n comparson wth open-loop SM and perfect CSI feedback MIMO-OFDM systems, for and 4 4 MIMO confguratons respectvely. he fgures nclude FER performance curves for QPSK and 64-QAM modulaton n a low speed moble scenaro usng the IU PB channel profle wth vehcular speeds of 3 km/h. he OFDM scheme s based on 51-pont FF wth 15 subchannels for data transmsson each consstng of 0 contnuous subcarrers, for a total bandwdth of 5 Mz. he frame duraton s about 0.5ms. urbo codng s employed for FEC and MMSE detecton s used at the recever. Fgure 0. MIMO-OFDM system wth partal feedback [4]. Fgure 1. FER performance for coded MIMO confguraton [4]. Fgure. FER performance for coded 4 4 MIMO confguraton [4]. Copyrght 010 ScRes.

15 F. KALID E AL. 7 Equal power allocaton s used for the open-loop SM system whle water-fllng s used for the closed-loop systems. Ideal channel knowledge s assumed at the recever for all systems and antenna correlatons are not consdered [4]. As seen from the results, the proposed system operates qute close to the perfect CSI feedback system and shows substantal performance gan over the open-loop system. he small performance loss n comparson wth the perfect feedback system s prmarly due to the quantzaton error assocated wth lmted feedback [4]. Effcent feedback reconstructon algorthms for mprovement of the closed-loop transmt dversty scheme consttutng the mode 1 of 3GPP s wdeband code-dvson multple access (WCDMA) 3G standard are presented n [43]. hese algorthms effcently reconstruct the beamformng weghts at the transmtter whle consderng the effect of feedback error. Performance results for vehcular speeds up to 100 km/h are provded. he proposed technques are applcable to closed-loop MI- MO dversty systems and may possbly be extended to 4G systems. In [44], the optmal MIMO precoder desgns for frequency-flat and frequency-selectve fadng channels are presented, assumng partal CSI at the transmtter consstng of transmt and receve correlaton matrces. he elements of transmt and receve correlaton matrces are determned from the respectve transmt and receve antenna spacng and angular spread. It s shown that from the capacty maxmzaton perspectve, the optmal precoder for a frequency-flat fadng channel s an egen-beamformer. On the other hand, the optmal precoder for a frequency-selectve fadng channel represented by L uncorrelated effectve paths conssts of P + L parallel egen-beamformers where P s an arbtrary value dependng on the no. of vectors n a transmsson data block [44]. A closed-loop lmted feedback MIMO scheme called mult-beam MIMO (MB-MIMO) s proposed n [45] for 3GPP LE E-URA downlnk. MB-MIMO employs multple fxed beams at the base staton (Node B) to transmt multple data streams. he no. of beams and data streams to be used are adaptvely selected usng a codebook at the UE. he selected precodng vectors or beam ndces consttutng a precodng matrx are then fed back to the Node B. he MB-MIMO scheme can adaptvely swtch between MIMO SM and transmt beamformng (x-bf) modes. x-bf s used f a sngle beam s selected and SM s used f multple beams are selected. he proposed scheme elmnates the need for a hardware calbrator (W-CAL) at Node B that was requred for a prevously proposed MB-MIMO mplementaton. W-CAL compensates the phase varatons caused by RF components and was needed to algn the phase condton of each transmt antenna element for maxmzng the transmt beamformng gan. he proposed scheme uses a larger codebook based on an extended precodng matrx whch ncludes phase terms that can be controlled to algn the phase condton of the 4 node B antenna elements. hs results n hgh beamformng gan even wthout W-CAL. owever, 4 addtonal bts or a total of 8 bts are requred for feedback, whch s stll a small number MIMO over gh-speed Moble Channels Open-loop MIMO dversty technques lke SC and space frequency codng (SFC) are approprate choces for hgh-speed moble channels that vary rapdly wth tme. In such scenaros, mantanng a relable lnk becomes the foremost prorty rather than maxmzng system throughput. gh-speed moble channels undergo fast fadng whch may cause tme varaton of the fadng channel wthn an OFDM symbol perod. hs results n the loss of subchannel orthogonalty and leads to nterchannel nterference (ICI) due to the dstrbuton of leakage sgnals over other OFDM subcarrers. he error floor assocated wth ICI ncreases wth the speed of the moble termnal [46]. An mproved MIMO-OFDM technque for hgh-speed moble access n cellular envronments s proposed n [46]. hs technque reduces ICI and provdes dversty gan as well as nose averagng even for hghly correlated channels. ICI s reduced by transmttng weghted data on adjacent subcarrers. he weghts are selected such that the mean ICI power s mnmzed. he adopted weght selecton procedure however results n suboptmal weghts. Dversty gan n [46] s acheved by usng space-frequency block codng (SFBC) whch s based on Alamout code but the codng s appled n frequency doman.e. to OFDM subcarrers rather than to OFDM symbols n tme doman [47]. Fgure 3 shows the data assgnment scheme for the 1 SFBC-OFDM system, wthout the weghtng factors. he transmt data s assgned to subcarrer groups each consstng of two adjacent subcarrers, as shown n the fgure. Instead of SFBC, other dversty technques such as SBC, space-frequency trells codng (SFC), maxmal- Fgure 3. Data assgnment scheme for ICI reducton n 1 SFBC-OFDM system [46]. Copyrght 010 ScRes.

16 8 F. KALID E AL. rato receve combnng (MRRC) etc. can also be used. he proposed technque operates wthout CSI at the transmtter and does not requre any plot sgnals for channel trackng. owever, t s sutable for OFDM systems wth subcarrer group spacng less than the channel coherence bandwdth because the channel coeffcents are assumed to be dentcal for adjacent subcarrers. Fgure 4 shows the smulated BER performance of the proposed SFBC-OFDM scheme n comparson wth conventonal SFBC MIMO-OFDM schemes for 1 antenna confguraton usng I-MERA MIMO channel model Case A for downlnk transmsson wth moble speed of 50 km/h. Case A corresponds to a frequencyflat Raylegh fadng channel wth uncorrelated antennas. 5 Mz of downlnk channel bandwdth s used at Gz wth 048 OFDM subcarrers. Performance results for QPSK and 16-QAM are provded. Fgure 5 shows the performance comparson usng I-MERA Case B whch corresponds to a frequencyselectve fadng channel wth correlated transmt antennas n an urban macro cellular envronment. he proposed SFBC-OFDM scheme clearly outperforms the conventonal SFBC-OFDM schemes n both cases. he conventonal SFBC-OFDM scheme referred to as Alamout n the fgures s severely performance lmted due to the error floor phenomenon resultng from ICI ntroduced by the hgh-speed moble user at 50 km/h. 4. Multuser MIMO Multuser MIMO (MU-MIMO) systems consst of multple antennas at the BS and a sngle or multple antennas at each UE. MU-MIMO enables space-dvson multple access (SDMA) n cellular systems whch ncreases the system capacty by explotng the spatal dmenson (.e. the locaton of UEs) to accommodate more users wthn a cell. It also provdes beamformng or array gan as well as dversty gan due to the use of multple antennas. In case of multple antennas at the UE, spatal multplexng can also be employed to further enhance the spectral effcency [48]. he uplnk and the downlnk of a MU-MIMO system represent two dfferent problems whch are dscussed n the followng text he MU-MIMO Uplnk Fgure 4. BER Performance of SFBC-OFDM systems usng I-MERA Case A channel [46]. he MU-MIMO uplnk channel s a MIMO multple access channel (MIMO-MAC) [49] where the users smultaneously transmt data over the same frequency channel to the BS equpped wth multple antennas. he BS must separate the receved user sgnals by means of array processng, multuser detecton (MUD), or some other method [48]. Fgure 6 shows varous lnear and nonlnear MUD schemes for MIMO-OFDM systems, some of whch are dscussed n the later sectons Classc SDMA-OFDM MUDs An overvew of some classc MUDs for MU-MIMO- OFDM s presented n [3]. he dscusson s based on the Fgure 5. BER Performance of SFBC-OFDM systems usng I-MERA Case B channel [46]. Fgure 6. Varous multuser detectors (MUDs) for MIMO- OFDM systems [3]. Copyrght 010 ScRes.

17 F. KALID E AL. 9 uplnk MIMO SDMA-OFDM system model of Fgure 7 where each of the L UEs uses a sngle transmt antenna whle the BS s equpped wth P antennas. he complex-valued P 1 receved sgnal vector at the BS antenna array for the k-th subcarrer of the n-th OFDM symbol s gven by x=s+n (7) where s s the L 1 transmtted sgnal vector, n s the P 1 AWGN nose vector and s the P L channel transfer functon matrx consstng of L column vectors, each contanng the transfer functons for a partcular UE. herefore, can be represented as where 1 L,,, (8) l l l l 1 P,,,, l 1,, L (9) s a P 1 vector whose elements are the channel transfer functons for the transmsson paths between the transmt antenna of the l-th UE and the P BS antennas. It s assumed that the complex sgnal s transmtted by the l-th user has zero mean and varance whle l l the AWGN sgnal n p he channel transfer functons has zero mean and varance l p n. are assumed to be ndependent, statonary, complex Gaussan dstrbuted processes wth zero mean and unt varance. he classc MUD schemes [3] are dscussed n the followng text. 1) MMSE MUD: Fgure 8 shows the schematc dagram of a MMSE SDMA-OFDM MUD. he multuser sgnals receved at each BS antenna are multpled by a complex-valued l array weght w p and then summed up. he superscrpt l represents a partcular user whch means that a separate set of weghts s used for detecton of each user s sgnal. he combner output yt () s subtracted from a user specfc reference sgnal rt () known at the BS and the UE, resultng n an error sgnal є() t. he error sgnal s used for weght estmaton accordng to the MMSE crteron. he steepest descent algorthm can be used n ths regard for stepwse weght adjustment for each subcarrer of each user. he performance of the MMSE MUD mproves as the no. of antennas P n the BS antenna array s ncreased and degrades when the no. of users ncrease. Fgure 7. Uplnk MIMO SDMA-OFDM system model wth sngle antenna at each UE [3]. Fgure 8. MMSE SDMA-OFDM MUD [3]. Copyrght 010 ScRes.

18 30 F. KALID E AL. ) Successve Interference Cancellaton (SIC) MUD: he successve nterference cancellaton (SIC) MUD enhances the MMSE MUD usng SIC. For each subcarrer, the detecton order of the users s arranged accordng to ther estmated total receved sgnal power at the BS antenna array and the strongest user s sgnal wth the least multuser nterference (MUI) s detected usng the MMSE MUD. he detected user sgnal s then subtracted from the composte multuser sgnal and the next strongest user s detected by the same procedure. hs process contnues tll the detecton s completed for all users. SIC results n hgh dversty gan at the MMSE combner, whch mtgates the effects of MUI as well as channel fadng. he SIC MUD s also effectve n near-far scenaros that result from naccurate power control. owever, t s prone to errors n power classfcaton of user sgnals and also to nteruser error propagaton. Fgure 9 shows the BER performance comparson of MMSE MUD and SIC MUD (M-SIC wth M = ) for an SDMA- OFDM scenaro wth four sngle-antenna UEs and a four-antenna BS antenna array usng QPSK modulaton. he ndoor short wreless asynchronous transfer mode (SWAM) channel model s used. 3) Parallel Interference Cancellaton (PIC) MUD: he PIC MUD does not requre any power classfcaton of the receved user sgnals. he detecton procedure conssts of two teratons for all subcarrers. In the frst teraton, MMSE detecton s used to estmate all user l sgnals y from the receved composte multuser sgnal vector x. In case of channel encoded transmsson, all user sgnals must be decoded, slced, channel encoded Fgure 9. BER performance of MMSE MUD and SIC MUD [3]. agan and also remodulated onto subcarrers. In the second detecton teraton, sgnal vectors x for all L us- l k ers are reconstructed and an estmate y of each user sgnal s generated by subtractng the sgnal vectors l x, l k of all other users followed by MMSE combnng. he estmated user sgnals are then channel decoded and slced. he PIC MUD scheme s also vulnerable to nteruser error propagaton. 4) Maxmum Lkelhood (ML) MUD: he ML MUD employs the ML detecton prncple to fnd the most lkely transmtted user sgnals through an exhaustve search. It provdes the optmal detecton performance but also has the hghest complexty of any other MUD. For an OFDM-SDMA system wth L smultaneous users, the ML MUD produces the estmated L 1 symbol vector ŝ ML consstng of the most lkely transmtted symbols of the L users for a partcular OFDM subcarrer, as gven by sˆ ML arg mn L xs (30) sm where M L s a set contanng ml tral vectors, m beng the no. of bts per symbol dependng on the modulaton scheme used resultng n m constellaton ponts. herefore, the computatonal complexty of the ML MUD ncreases exponentally wth the no. of users L thus makng t prohbtve for practcal mplementaton. 5) Sphere Decodng (SD) aded MUD: SD-aded MUDs use SD for reduced-complexty ML multuser detecton wth near-optmal performance. SD reduces the ML search to wthn a hypersphere of a certan radus around the receved sgnal. he radus of ths search sphere determnes the complexty of the MUD. Varous SD algorthms have been proposed n lterature lke the complex-valued SD (CSD) and multstage SD (MSD) whch sgnfcantly reduce the complexty by reducng the requred search radus [3] Layered Space-me MUD A V-BLAS based MUD scheme referred to as layered space-tme MUD (LAS-MUD) s presented n [50] for CDMA uplnk. hs scheme s somewhat smlar to the SIC MUD snce V-BLAS detecton also ncorporates SIC. Fgure 30 shows the layered space-tme MU-MIMO system block dagram. ere the sngle antenna users are arranged n G groups each contanng M users for a total of K G M. he UEs wthn each group are treated as the multple transmt antennas of a V-BLAS system. he users wthn each group share the same unque spreadng code whch dstngushes the groups from one another. herefore, out of the K total spreadng codes, only G are unque. he N K random spreadng matrx consstng of K length N code vectors s denoted by Copyrght 010 ScRes.

19 F. KALID E AL. 31 Fgure 30. LAS MU-MIMO system [50]. S S,, S, S,, S,, S,, S 1 1 system can also accommodate users wth multple antennas thus enablng spatal multplexng for achevng hgh data rates. In that case each user wth multple transmt antennas wll be consdered as one group. he K 1 transmtted symbol vector s represented as,, b b1 b K where each element represents the bt transmtted by a partcular user. he channel between the users and the BS s consdered to be a frequency-flat fadng MIMO channel and s denoted by the channel,, matrx h1 hp where h p s the K 1 channel coeffcent vector between all K users and the p-th BS antenna. he BS s equpped wth a total of P antennas. he N 1 receved baseband sgnal at the p-th BS antenna for a certan symbol perod after chp-matched flterng s gven by where C rp SCpbn p dag p h p G G. he proposed (31) s the complex dagonal channel matrx for the p-th BS antenna and n p s the correspondng complex-valued AWGN nose vector wth zero mean and varance. A frequency-flat fadng MIMO channel s assumed as well as perfect channel estmaton and symbol synchronzaton. he users are assumed to be separated by a consderable dstance so that the antennas of dfferent users are not correlated. he channel estmaton and symbol synchronzaton at the BS s also assumed to be deal. he BS employs space-code matched flterng to separate the dfferent user groups. he K 1 suffcent statstc vector Y MU s then fed to the layered spacetme decorrelator whch elmnates the remanng nteruser nterference to produce the estmated symbol vector b ˆ bˆ,, ˆ 1 b K. he vector Y MU s gven by where R matrx, MU P MU p p MU p1 Y C S r R b n (3) s the K K space-code cross-correlaton P R MU Xp X p (33) p1 wth Xp SC p. he K 1 real Gaussan nose vector n wth covarance matrx R MU s gven by P n Xp np (34) p1 he detecton algorthm s teratve and conssts of three steps: 1) computaton of the nullng vector, ) user Copyrght 010 ScRes.

20 3 F. KALID E AL. sgnal estmaton and 3) nterference cancellaton (SIC). For the -th teraton, the frst step conssts of calculatng the pseudonverse R of MU R MU. he user sgnals are then ranked accordng to ther post detecton SNRs (followng the space-code matched flterng) and the user havng the hghest SNR, gven by k arg max 1,, 1 RMU j, j j k k b j (35) s selected. he subscrpts and j n ths equaton denote the elements of an array, vector or matrx. he nullng vector for the selected user s wk MU,.e., the R k -th gven by column of R MU k. he slcer output s then z w Y (36) k k MU resultng n the estmated symbol ˆ b k. he fnal step s nterference cancellaton where the detected symbol s subtracted from the receved sgnal vector resultng n the symbol vector for the next teraton 1, gven by bˆ 1 rp rp Xp k k where X s the k -th column of p k 1 (37) X p Smlarly, X p and R MU 1 are obtaned by strkng out the k -th column of X p and the k -th row and column of R MU respectvely. Y MU 1 s then gven by P Y 1 X 1 r 1 MU p p p1. (38) hs process s repeated untl all K user sgnals are detected. wo reduced complexty versons of LAS-MUD called seral layered space-tme group multuser detector (LASG-MUD) and parallel LASG-MUD are also presented n [50]. Fgure 31 shows the SER performance of the LAS- MUD scheme usng 4-QAM modulaton wth 1 smultaneous users (sngle-antenna) and 6 BS antennas, as the no. of user groups s ncreased. Fxed spreadng factor of N = 15 s used. he performance mproves as the users are dstrbuted nto more (smaller) groups snce the no. of unque spreadng codes also ncreases. For G = 1, the performance s equvalent to V-BLAS and represents the worst case. Fgure 3 shows the SER performance as the no. of users s ncreased by addng more user groups wth M = 4 users per group. he LAS-MUD scheme provdes substantal ncrease n network capacty by accommodatng a large no. of smultaneous users wth good SER performance SMMSE SIC MUD A MUD scheme for MIMO-OFDM systems referred to as successve MMSE receve flterng wth SIC (SMMSE SIC) s presented n [51]. he MMSE SIC MUD suffers from performance loss n scenaros wth multple closely spaced antennas located at the same UE. he proposed scheme tackles ths problem by successvely calculatng the rows of the receve matrx at the BS for each of the UE transmt antennas, followed by SIC thus transformng the uplnk MU-MIMO channel nto a set of parallel SU-MIMO channels. Fgure 31. Groupng effect on SER performance of LAS-MUD [50]. Fgure 3. SER performance of LAS-MUD wth ncreasng number of users [50]. Copyrght 010 ScRes.

21 F. KALID E AL. 33 Fgure 33 shows the MU-MIMO uplnk employng SMMSE SIC detecton. he system conssts of K smultaneous users, each equpped wth M transmt antennas for 1,, K and therefore, a total of K M M 1 transmt antennas. he BS has M R receve antennas. s and r represent the -th user data vector and the receve vector respectvely whereas and F are the respectve UE transmt matrx and the BS receve matrx. he MIMO channel matrx s represented as M M 1 K D (39) R where s the MIMO channel matrx between user and the BS for 1,, K. he M R M receve flter matrx at the BS s gven by M M 1 F F F F (40) R where F corresponds to the -th user. Each row of F corresponds to one of the M transmt antennas at the UE. he proposed algorthm successvely calculates the rows of each F usng the MMSE crteron such that the users are ordered accordng to ther respectve total MSE n ascendng order (startng wth the mnmum MSE). he total MSE of user s obtaned by summng up the MSE correspondng to each of ts ndvdual transmt antennas. Followng the receve flterng by the receve flter matrx F, SIC s performed to elmnate the MUI. hs process has the effect of transformng the multuser uplnk channel nto a set of parallel M M SU MIMO channels represented as F. K he SMMSE SIC detecton n [51] has been consdered for SBC based MIMO transmsson.e. the Alamout scheme and also for domnant egenmode transmsson (DE). he open-loop Alamout scheme provdes MIMO dversty wthout the need for any CSI at the UEs. On the other hand, DE requres full CSI at both the transmtter and the recever, whch means that the UE transmt matrces D need to be computed at the BS and then fed forward to the UEs. owever, besde the full dversty gan equal to that of SBC, DE also provdes the maxmum array gan by transmttng over the strongest egenmode of the MIMO channel [49,51,5]. Fgure 34 shows the BER performance of SMMSE SIC Alamout n comparson wth V-BLAS. he mpact of channel estmaton errors s also shown. he smulated MIMO-OFDM system conssts of 6 BS antennas and 3 UEs equpped wth antennas each, denoted as 6 {,, } MU-MIMO confguraton. he MIMO channel s assumed to be frequency selectve wth the power delay profle defned by IEEE 80.11n - D for non-lne-of-sght (NLOS) condtons. he channel model for each user s channel takes nto account the antenna correlaton at the BS. owever, the antennas at each UE are consdered to have low spatal correlaton assumng large angular spread at the user. A total of 64 OFDM subcarrers are used wth subcarrer spacng of 150 kz. he user data s encoded usng a 1/ rate convolutonal code. 4-QAM modulaton s used for each subcarrer of SMMSE SIC Alamout system whle BPSK s used for V-BLAS so that the data rate remans the same for both systems. Clearly, the SMMSE SIC Alamout system outperforms V-BLAS by a large margn partcularly when the channel estmaton errors are taken nto account. Fgure 33. Block dagram of SMMSE SIC MUD based MU- MIMO system [51]. Fgure 34. BER performance of SMMSE SIC Alamout and V-BLAS for 6 {,, } confguraton [51]. Copyrght 010 ScRes.

22 34 F. KALID E AL. Fgure 35 shows the performance gan of SMMSE SIC DE over SMMSE SIC Alamout. SMMSE SIC DE shows substantal gans n the hgh SNR regon and these become more sgnfcant as the no. of users n the system ncreases urbo MUD An teratve urbo MMSE MUD scheme s presented n [53] for sngle-carrer (SC) space-tme trells-coded (S- C) SDMA MIMO systems n frequency-selectve fadng channels. hs scheme can jontly detects multple UE transmt antennas whle cancellng the MUI from undetected users along wth co-channel nterference (CCI) and ISI through soft cancellaton. Unknown co-channel nterference (UCCI) from other nterferers not known to the system s also consdered. It s also shown that the no. of BS antennas requred to acheve the correspondng lower performance bound of sngle-user detecton s equal to the no. of users rather than the total no. of transmt antennas. he recever dervatons n [53] are provded for M-PSK modulaton but can be extended to QAM as well. Fgure 36 shows the system model whle the UE transmtter block dagram s gven n Fgure 37. he system has a total of K KI smultaneous users, each ndexed by k 1, K, K 1, K I where the frst K are the users to be detected at the BS whle the remanng K I are unknown nterferng users representng the source of UCCI. Each UE s equpped wth N transmt antennas. owever, the system can also support unequal no. of antennas at the UEs. Each UE encodes the bt sequence ck () for 1,, BN usng a rate k / 0 N SC code, where B represents the frame length n symbols. he encoded sequences b (), 1,, BN are Fgure 35. BER performance of SMMSE SIC Alamout and SMMSE SIC DE for 6 {,, } confguraton [51]. k Fgure 36. System model of urbo MUD based SC MU-MIMO system [53]. Fgure 37. UE transmtter block dagram [53]. grouped nto B blocks of N symbols, where 1,, k 0 represents the modulaton alphabet of M-PSK, and then nterleaved by user-specfc permutaton of blocks of length N wthn a frame, such that the postons wthn each block reman unchanged. hs nterleavng process preserves the rank propertes of the SC code. User-specfc tranng sequences of length N are then attached at the start of the nterleaved sequences. After seral-to-parallel (S/P) converson of the n entre frame, the resultng sequences bk for n 1,, N, 1,, B are transmtted over the frequency-selectve MIMO channel usng the N transmt antennas. he transmt sgnals from all users are receved at the N R BS receve antennas. he space-tme sampled receved sgnal vector R LN 1 y at tme nstant s gven by y u IuI n, 1,, B (41) desred UCCI nose whch can also be represented as L1,, y r r (4) Copyrght 010 ScRes.

23 F. KALID E AL. 35 where each vector N R 1 r conssts of R N eleme- nts rm, m 1,, NR representng the receved sgnal sample after matched flterng at the m-th receve antenna and L s the no. of paths of the frequency-selectve LNRKN L1 MIMO channel. he channel matrx has the structure 0 L 1) L 1) NR KN Each element l s gven by l where 1 N 1 N 1,1 1,1 K,1 K,1 (43) h l h l h l h l 1 N 1 N h1, N l h1,,, R N l h R K N l h R K N l R h n km, l (44) represents the complex gan for the l-th path between the n-th transmt antenna of user k and the m-th BS receve antenna. he channel matrx LNR KIN L 1 correspondng to UCCI has a smlar I NR KIN structure as, and conssts of matrces I l he vectors 1 1 KN L u and. u consst of the respectve transmt sequences I b KN L1 1 I n k of the desred and the unknown users, and are expressed as L1,,,, L1 L1,,,, L1 u b b b u b b b I I I I where the vectors are gven by n KN 1 b and 1 N K b I N K (45) KIN1 b b,, b, b, b 1 N 1 N bi bk 1,, bk 1, bkk, b I KK I (46) s the AWGN vector wth covarance ma- trx I. LN R 1 he urbo recever block dagram s shown n Fgure 38. For the k-th user, the recever frst assocates the sgnals from the user s transmt antennas to N / n sets N of equal sze n 0 such that the antennas n 1,, n0 represent the frst set and so on. he tranng sequence u, 1,, s used to obtan an estmate Ĥ of the channel matrx. he UCCI-plus-nose covarance matrx R s then estmated. he estmate for the frst teraton s gven by ˆ 1 R y u ˆ y u ˆ (47) 1 0 Fgure 38. Block dagram of the teratve urbo multuser recever [53]. Copyrght 010 ScRes.

24 36 F. KALID E AL. From the second teraton onward, the soft feedback vector u from the APP (also MAP) SISO decodng s used to obtan the covarance matrx estmate Vector ˆ 1 R y u ˆ y u ˆ 1 y u y u B 1 ˆ ˆ. B 1 u conssts of the sequences n b k (48) cal- APP culated usng the a posteror probablty P. he n SISO sgnals bk, n 1,, n0 for user k are jontly detected usng a ln ear MMSE MUD whch flters the sgnal vector y 1 k where the vector sc probablty and 1 1 k y u, 1,, B (49) P 1 k ext SISO u s calculated usng the extrnobtaned after APP SISO decodng denotes the frst set of n 0 antennas for user k. he weghtng matrx satsfes the crteron, 1 W k f or the MMSE MUD, argmn k k k k, W A W y A (50) WA subject to the constrant, 1 j j avod the trval soluton he vector 1 n0 1 k s gven by 1 1 n0 k k k A, j 1,, n to, 1 1 Wk Ak 0, 0. b,, b. 0 (51) 1 n0 he correspondng output MUD s gven by z z k W y Ω ψ 1 k k k k k k 0 0 of the MMSE (5) where the matrx 1 n Ω n k conssts of the 1 equvalent channel gans after flterng and ψ k 0 n 1 s the fltered AWGN vector. he MMS E MUD outputs z k along wth the parameters Ω k and ψ k for all antenna sets 1,, N / n0 of user k, are pass ed on to the APP SISO detector whch calculates the extrnsc probabltes for SISO decodng. hs teratve procedure s contnued for all antenna sets of the remanng users untl all users are detected. he complexty of ths recever s prmarly assocated wth the MMSE and APP blocks and s on the order of O max L N, kn. R wo specal cases of the proposed recever archtecture are consdered n [53]. Recever 1, wth n0 1, detects the transmt antennas of user k one by one. hs recever type has the lowest complexty snce the complexty depends exponentally on n 0. Recever, wth n0 N, jontly detects all N transmt antennas of user k and has the hghest complexty. he smulated SER and FER performance of the two recever types vs. per-antenna Es / N 0 s shown n Fgure 39 and Fgure 40, for a par tcular user referred to as user 1. Performance comparson wth optmal jont ML (a) (b) Fgure 39. Recever 1 s (a) SER and (b) FER performance, (K, K I, N R) = (3, 0, 3) and ( 1, 0, 3), N = [53]. Copyrght 010 ScRes.

25 F. KALID E AL. 37 detecton of all N antennas of user 1 followed by MAP SISO decod ng assumng perfect feedback (FB), s also provded. he results are provded for 1 and 10 teratons for K, KI, NR 3,0,3 and for 1 and 7 teratons for K, KI, NR 1,0,3 wth N transmt antennas per user. K, K I and N R represent the no. of desred users, unknown nterferer s (UCCI) and BS receve antennas. QPSK modulaton s used for transmsson and frequency-selectve fadng s assumed wth L = 5 uncorrelated Raylegh dstrbuted paths. For a suffcent no. of teratons, both recevers perform reasonably close to the ML recever, partcularly n the hgh SNR regon. Recever shows slghtly better performance than recever 1. Fgure 41 shows the SER and FER performance of the tw K, K, N,1,3 wth N o recevers for I transmt antennas per desred user and a sngle t ransmt antenna for the unknown nterferer (UCCI).e. N I 1. wo cases of sgnal-to-ucci nterference rato (SIR) are consdered. For SIR = 3 db, the sgnal transmtted from UCCI s antenna s assumed to have the same power as that of the sgnal from one antenna of the desred user whereas, for SIR = 0 db, UCCI s antenna transmts at R (a) (b) Fgure 40. Recever s (a) SER and (b) FER performance, (K, K I, N R ) = (3, 0, 3) and (1, 0, 3), N = [53]. (a) (b) Fgure 41. Recever 1 s and s (a) SER and (b) FER performance, (K, K I, N R ) = (, 1, 3), N =, N I = 1 [53]. Copyrght 010 ScRes.

26 38 F. KALID E AL. twce the transmt power of a desred user s antenna. he performance of both recevers s obvously better for the 3 db SIR case. owever, the UCCI has a consderable mpact on performance and more teratons are needed to acheve a reasonably low SER or FER. he performance wll degrade further n case of multple UCCI antennas and also as the UCCI sources.e. the no. of unknown nterferers ncrease Genetc Algorthm (GA) Asssted MUDs Genetc algorthms (GAs) are based on the theory of evoluton s concept of survval of the fttest, where the genes from the fttest ndvduals of a speces are passed on to the next generaton through the process of natural selecton. When appled to MUDs, an ndvdual represents the L-dmensonal MUD weght vector correspondng to the L users. hese MUD weghts are then optmzed usng GA by genetc operatons of matng and mutaton to get a new generaton of ndvduals.e. the MUD weghts. he ntal populaton (MUD weghts) s typcally obtaned from the MMSE soluton whch s retaned throughout the GA search process as an alternate soluton n case of poor convergence [3]. Consderng the SDMA-OFDM system model of Fgure 7 wth a sngle transmt antenna at each UE and P receve antennas at the BS, the ML-based decson metrc or objectve functon (OF) for a GA-asssted MUD correspondng to the p-th receve antenna can be wrtten as s x s (53) p p p where x p s the receved symbol correspondng to the p-th BS antenna for a specfc OFDM subcarrer and p s the p-th row of the channel transfer functon matrx. he estmated symbol vector of the L users correspondng to the p-th BS antenna s then gven by sˆ GA arg mn p p s (54) s he combned decson metrc for the P receve antennas can therefore be wrtten as P s p1 p s xs (55) herefore, the decson rule for the GA-asssted MUD s to fnd an estmate ŝ GA of the L 1 transmtted symbol vector such that Ωs s mnmzed [3]. Revew and analy ss of varous GA-asssted MUDs s provded n [3] for the SDMA-OFDM uplnk consstng of a sngle transmt antenna at each UE. Fgure 4 shows the schematc dagram of the SDMA-OFDM uplnk system based on the concatenated MMSE-GA MUD. he concatenated MMSE-GA MUD uses the MMSE estmate L1 sˆ MMSE of the transmtted symbol vector of the L users as ntal nformaton for the GA. ŝ MMSE s gven by sˆ W MMSE MMSE x (56) P L where W MMSE s the MMSE MUD weght matrx, expressed as W MMSE 1 n I (57) Fgure 4. SDMA-OFDM uplnk system based on concatenated MMSE-GA MUD [3]. Copyrght 010 ScRes.

27 F. KALID E AL. 39 Usng ths MMSE estmate, the 1 st GA generaton, y = 1 contanng a populaton of X ndvduals, s created. he x-th ndvdual s a symbol vector denoted as 1 L,,, yx yx yx yx, s s, s,, s, x 1,, X y 1,, Y where each element l yx, (58) s called a gene, belongs to the set of complex-valued modulaton symbols correspondng to the partcular modulaton scheme used. he GA search procedure shown n Fgure 43 s then ntated, whch nvolves several GA operatons lke matng, mutaton, eltsm etc. leadng to the next generaton. hs process s repeated for Y generatons and the ndvdual wth the hghest ftness value s consdered to be the detected L 1 multuser symbol vector for the correspondng OFDM subcarrer. All users are jontly detected by the concatenated MMSE-GA MUD and therefore, no error propagaton exsts between the detected users. Enhanced GA MUDs, utlzng an advanced mutaton technque called based Q-functon-based mutaton (BQM) nstead of the conventonal unform mutaton (UM), and ncorporatng the teratve turbo trells coded modulaton (CM) scheme for FEC decodng, are also dscussed n [3]. Fgure 44 shows the schematc dagram of an MMSE-ntalzed teratve GA (IGA) MUD ncorporatng CM. he P 1 receved symbol vector x s detected by the MMSE MUD to get the estmated symbol vector ŝ MMSE of the L users consstng of the symbols s ˆ l MMSE, l 1,, L. Each of these symbols are then Fgure 43. GA search procedure for one generaton [3]. Fgure 44. Schematc dagram of an IGA MUD [3]. Copyrght 010 ScRes.

28 40 F. KALID E AL. decoded by a CM decoder to get a more relable estmate. he resultng symbol vector s then used as the ntal nformaton for the GA MUD. he GA-estmated symbol vector ŝ GA s then fed back to the CM decoders for further mprovement of the estmate. hs optmzaton process nvolvng the GA MUD and the CM decoders s contnued for a desred no. of teratons. he fnal estmates s ˆ l of the L users symbols are then obtaned at the output after the fnal teraton. Fgure 45 shows the BER performance comparson of varous MMSE-ntalzed CM-asssted GA and IGA MUD based SDMA-OFDM systems consstng of L = 6 (sngle-antenna) users and P = 6 BS antennas. 4-QAM modulaton and SWAM channel model s used. GA populaton sze of X = 0 (also X = 10 for CM, MMSE-IGA ()) and a total of Y = 5 generatons are consdered. UM and BQM mutaton schemes are employed. Performance curves for 1 1 SISO AWGN, 1 6 MRC AWGN, CM-MMSE SDMA-OFDM and CM-ML SDMA-OFDM systems are also provded for reference. he CM-MMSE-GA MUDs and the IGA MUDs n partcular provde exceptonally good BER performance. he performance of the CM-MMSE- IGA scheme wth teratons and X = 0 (represented as CM, MMSE-IGA () n the fgure), s n fact dentcal to the optmum CM-ML MUD. he BER performance comparson for rank-defcent scenaros where the no. of users exceeds the no. of BS antennas resultng n nsuffcent degrees of freedom for separatng the users, s gven n Fgure 46. Performance curves for L = 6, 7 and 8 users and P = 6 BS antennas are provded. he IGA MUD schemes stll perform reasonably good wth relatvely small performance degradaton. Fgure 47 compares the complexty of the CM- MMSE-GA and CM-ML MUDs n terms of the no. of Fgure 46. BER performance of CM-MMSE-GA/IGA SDMA-OFDM systems, L = 6, 7, 8 and P = 6 [3]. Fgure 47. Complexty of CM-MMSE-GA and CM- ML SDMA-OFDM systems vs. no. of users, L = P [3]. OF calculatons, as the no. of users ncrease. he no. of BS antennas s kept equal to the no. of users.e. L = P. he complexty of the GA MUD ncreases very slowly wth the number of users as compared to the ML MUD, resultng n a huge dfference as more users are added to the system. 4.. he MU-MIMO Downlnk Fgure 45. BER performance of CM-MMSE-GA/IGA SDMA-OFDM systems, L = 6, P = 6 [3]. he MU-MIMO downlnk channel s referred to as the MIMO broadcast channel (MIMO-BC) [49] where the BS equpped wth multple antennas, smultaneously transmts data to multple UEs consstng of one or more antennas each, as shown n Fgure 48. he multuser nterference (MUI) (also called multple access nterference, MAI) can be suppressed by means of transmt beamformng or drty paper codng. herefore, CSI Copyrght 010 ScRes.

29 F. KALID E AL. 41 feedback from each user s requred for precodng at the BS. Varous lnear and nonlnear precodng technques for MU-MIMO downlnk systems are dscussed n the followng text Channel Inverson Channel nverson s a lnear precodng technque for MU-MIMO downlnk systems where each UE s equpped wth a sngle receve antenna. As the name sug- the nverse of the channel gests, channel nverson uses matrx for precodng to remove the MUI, as llustrated n Fgure 49. Assumng that the no. of receve antennas M R M, the no. of transmt antennas, ZF precodng can be used for ths purpose. he M 1 transmtted sgnal vector s then gven by x d 1 d (59) where d s the vector of data symbols to be precoded and s the pseudonverse of the M R M channel matrx. Vector d can have any dmenson up to the rank of [48]. he -th column of the preflterng or precodng matrx P s gven by [49] ZF p ZF, h h (60) where h s the -th column of. he combned receved sgnal vector can be expressed as Fgure 48. he MU-MIMO downlnk [48]. y d w (61) where w s the nose vector. herefore, ZF precodng s only sutable for low-nose or hgh transmt power scenaros [48]. MMSE precodng, also called regularzed channel nverson provdes a better alternatve. In ths case, the transmtted sgnal vector s gven by 1 x I d (6) where s the loadng factor. For a MU-MIMO downlnk system wth total transmt power P and K smultaneous users, K / P maxmzes the SINR at the recevers [48] Block Dagonalzaton Block dagonalzaton (BD) or block channel nverson, whch was frst proposed n [54], s a generalzaton of channel nverson to mult-antenna UEs [48]. BD also requres the total no. of receve antennas M R to be less than or equal to the no. of transmt antennas M.e. M R M. Consder the system model of Fgure 50. he system conssts of K smultaneous us ers each havng M R receve antennas for 1,, K such that the total no. of K receve antennas M R M 1 R. he combned channel matrx s gven M R M by M 1 K ( 63) M R where represents the MIMO channel from the M BS antennas to user. he combned M S precodng matrx P can be expressed as P P P P (64) 1 K MS where P s the precodng matrx for the -th user, S M R s the total no. of transmtted data streams and S MR s the no. of data streams transmtted to user. P ne eds to be selected n such a way that P becomes block dagonal. o ths end, a matrx s defned as Fgure 49. Channel nverson [48]. Fgure 50. System model for MU-MIMO downlnk transmsson [55]. Copyrght 010 ScRes.

30 4 F. KALID E AL K (65) whch contans all but the -th user s channel matrx. herefore, P les n the null space of and conssts of untary column vectors whch are obtaned by the SVD of, gv en by 1 0 U D V V ( 66) he rghtmost M L sngular vectors V form an orthogonal bass for the null space of where L s the rank of dmensons M R M L. he product 0 MM L 0 V wth represents the equvalent channel matrx for user after elmnatng the MUI. hus, BD transforms the MU-MIMO downlnk system nto a set of K parallel M L M R SU-MIMO systems. Usng SV D, 0 V can be expressed as V D U V V (67) 0 0 where D s an L L dagonal matrx, assumng L 0 to be the rank of V 0. he product of V and the frst L sngular vectors V 1 produces an orthogonal bass of dmenson L and represent the transmsson vectors whch maxmze the nformaton rate for the -th user whle elmnatng the MUI. herefore, the precodng 0 1 matrx P for user conssts of V V wth appro- of prate power scalng. Optmal power allocaton s acheved by water-fllng, usng the dagonal elements the matrces D and can ether be mplemented global ly to maxmze the overall nformaton rate of the system or on a per-user bass [54,56,57] Successve Optmzaton Successve optmzaton (SO) [54,56,57] s a successve precodng algorthm whch addresses the power control problem n BD where capacty loss occurs due to the nullng of overlappng subspaces of dfferent users. Frst, an optmum orderng of the users s determned lke n case of V-BLAS detecton. he precodng matrx for each user s then desgned n a successve manner so that t les n the null space of the channel matrces of the prevous users only. In other words, the transmt power of user s optmzed n such a manner that t does not nterfere wth users 1,, 1. owever, nterference wth the successve users s allowed. he combned channel matrx for the prevous 1 users can be wrtten as and ts SVD s gven by ˆ 1 1 (68) ˆ ˆ ˆ ˆ 1 ˆ 0 U D V V (69) ˆ 0 V contans the M ˆ L rghtmost sngular vectors where L ˆ s the rank of Ĥ. he precodng matrx P that les n the null space of ˆ s then determned as ˆ 0 ' ' P V P for som e choce of P Drty Paper Codng Drty paper codng s a nonlnear precodng technque and s based on the concept ntroduced by Costa [58] where the AWGN channel s modfed by addng nter- to wrtng on drty paper where the wrt- ference whch s known at the transmtter. hs concept s analogous ng s the desred sgnal and the drt represents the nterference. Snce the transmtte r knows where the drt or nterference s, wrtng on d rty paper s the same as wrtng on clean paper [48]. In addton to SU-MIMO systems, e.g. the GMD- ZFDP scheme mentoned n Subsecton 3.4, drty paper codng s also applcable to MU-MIMO downlnk trans- of the channel ma- msson. In a MU-MIMO downlnk system, CSI feedback from the users s avalable at the BS and t can fgure out the nterference produced at a partcular user by the sgnals meant for other users. herefore, drty paper codng can be appled to each user s sgnal at the BS so that the known nterference from other users s avoded. Varous drty paper codng technques for the MU- MIMO downlnk are dscussed n [48]. A well-known approach s to use QR decomposton trx, gven by LQ, where L s a lower trangular matrx and Q s a untary matrx. Q s then used for transmt precodng whch results n the effectve channel L. herefore, the frst user does not see any nterference from the other users and no further processng of ts sgnal s requred at the BS. owever, each of the subsequent users sees nterference from the precedng users and drty paper codng s appled to elmnate ths known nterference. Another technque called vector precodng jontly precodes the users sgnals rather than applyng drty paper codng to the users sgnals ndvdually. he vector precodng technque s shown n Fgure 51. he desred sgnal vector d s offset by a vector l of nteger values and ths operaton s followed by channel nverson, resultng n the transmtted sgnal x, gven by 1 x d l (70) where the vector l s chosen to mnmze the power of x,.e. Copyrght 010 ScRes.

31 F. KALID E AL. 43 Fgure 51. Vector precodng [48]. l 1 arg mn d ' l (71) ' l he sgnal receved at the k-th user s expressed as y d l w k k k where wk represents the Gaussan nose. A modulo operaton s then appled to remove the offset l k, as gven by y mod d l w k k k k k mod d k w k mod (7) (73) Regularzed vector precodng s a modfcaton of vector precodng whch uses regularzed (MMSE) chan- nel nverson n place of smple channel nverson. he transmtted sgnal vector s then gven by 1 x I d l where the vector l s chosen to mnmze the norm of x and K / P. Drty paper codng technques based on vector precodng approach the sum capacty of the MU-MIMO downlnk channel, whch s defned as the maxmum system throughput acheved by maxmzng the sum of the nformaton rates of all the users [48]. Fgure 5 shows the performance comparson of var- (74) ous channel nverson and drty paper codng technques for uncoded MU-MIMO downlnk transmsson wth M 10 BS transmt antennas and M R 10 sngleantenna UEs, usng QPSK modulaton. h e vector pre- clearly outperform the others at hgh codng technques SNR. owever, regularzed channel nverson performs even better than regularzed vector precodng n the low SNR regon. A possble reason for the performance loss of regularzed vector precodng at low SNR s the use of a fnte cubcal lattce n ths algorthm [48]. Use of dfferent lattce strateges may result n mproved performance omlnson-arashma Precodng omlnson-arashma precodng (P) s a nonlnear precodng technque orgnally developed for SISO systems for temporal pre-equalzaton of ISI and s equvalent to movng the decson feedback part of the decson feedback equalzer (DFE) to the transmtter [59]. owever, P can also be appled to MU-MIMO downlnk systems for MUI mtgaton n the spatal doman. wo MU-MIMO downlnk transmsson schemes utlzng P are descrbed n [57]. he frst one called SO P combnes SO and P to mprove performance by elmnatng resdual MUI. SO P nvolves successve BD, reorderng of the users and fnally, P. Fgure 53 shows the block dagram of the SO P system (taken from [57] wth a slght notatonal change). ere P represents the combned precodng matrx for all users generated by SO, gven by Equaton 64. s the channel matrx and D represents the combned demodulaton (receve flterng) matrx. he lower trangular feedback matrx B s generated n the last step and s used for P. In order to generate matrx B, the users are frst arranged n the reverse order of precodng and then the lower dagonal Fgure 5. Performance comparson of varous channel nverson and drty paper codng technques [48]. Fgure 53. SO P system block dagram [57]. Copyrght 010 ScRes.

32 44 F. KALID E AL. equvalent combned channel matrx (whch ncludes precodng and demodulaton) s calculated, wth sngular values on the man dagonal. he elements n each row of ths matrx are then dvded by the correspondng sngular values to obtan the feedback matrx B. he order n whch P precodng s appled to the users data streams s opposte to the order n whch ther precodng matrces are generated. herefore, P precodng starts wth the data stream of the frst user whose precodng matrx P 1 was generated last. Use of P results n ncreased transmt power and for ths reason, a modulo operator s ntroduced at the transmtter and the recever so that the constellaton ponts are kept wthn certan boundares. At the recever, each data stream s dvded by the correspondng sngular value before applyng the modulo operator, whch ensures that the constellaton boundares reman the same as at the transmtter. Detaled descrpton of SO P s provded n [60]. he other scheme called MMSE P [61] combnes MMSE precodng and P to elmnate the MUI below the man dagonal of the equvalent combned channel matrx. MMSE P s an teratve precodng technque. he users are frst arranged accordng to some optmal orderng crteron and the precodng matrx P s calcu- lated column by column startng from the last user K. he -th column of P correspondng to the -th user s obtaned usng the corespondng rows (frst rows for user K) of the channel matrx accordng to the MMSE crteron, gven by where 1 M P I (75) tr P Pxx P, M R n P mult-antenna UEs. SMMSE nvolves successvely cal- precodng matrx culatng the columns of the combned P, where each column represents a beamformng vector correspondng to a partcular receve antenna. Consder the system model of Subsecton 3. 7 where each of the K users s equpped wth M receve antennas for 1,, K and P represents the precodng matrx for the -th user consstng of M R columns, each correspondng to a receve antenna. For the j-th j receve antenna of the -th user, the matrx s defned as j, j K h (76) where h, j represents the j-th row of the -th user s channel matrx. he correspondng column of P s then calculated usng the MMSE crteron and s equal to the frst column of the matrx 1 j j j, j M P I (77) All columns of P are calculated n ths manner and ths process s repeated for all users to obtan the combned precodng matrx P. After precodng, the equvalent combned channel matrx s gven by P M R M R whch s block dagonal for hgh SNR values, resultng n a set of K SU-MIMO channels. herefore, any SU- MIMO technque e.g. egen-beamformng for capacty maxmzaton or DE for maxmum dversty and array gan can be appled to the -t h user s equvalent channel matrx P. SMMSE precodng has slghtly hgher complexty than BD [57]. A reduced complexty verson called per-user SMMSE (PU-SMMSE) s proposed n [6]. R P represents the total transmt power, x s the data vector to be transmtted and n represents the varance of the zero-mean crcularly symmetrc complex Gaussan (ZMCSCG) nose. P s then appled to elmnate the MUI seen by the -th user from the prevous 1 users. Fgure 54 compares the 10% outage capacty of SO P and MMSE P schemes for a MU-MIMO downlnk system consstng of 4 sngle-antenna users and 4 BS transmt antennas, denoted as {1, 1, 1, 1} 4 antenna confguraton. Results for ZF channel nverson and a {, } 4 DMA system are also provded Successve MMSE Precodng he Successve MMSE (SMMSE) precodng scheme proposed n [57] addresses the problem of performance degradaton assocated wth MMSE precodng when closely spaced receve antennas are used, lke n case of Fgure % outage capacty of SO P and MMSE P for {1, 1, 1, 1} 4 confguraton [57]. Copyrght 010 ScRes.

33 F. KALID E AL. 45 Fgure 55 shows the BER performance comparson of SMMSE, SO P and BD for {,, } 6 and MMSE P for {1, 1, 1, 1, 1, 1} 6 antenna confguraton, n a spatally whte flat fadng channel. hese results are based on dversty maxmzaton for the ndvdual users and water-fllng s used for power allocaton. SMMSE provdes the best performance for the case of mult- antenna users whle BD surpasses SO P. Fgure 56 shows the BER performance of SMMSE, SO P and BD for {1, 1,, } 6 and MMSE P for {1, 1, 1, 1, 1, 1} 6 confguraton. ere SO P outperforms the others. owever, SMMSE performs better than MMSE P and even SO P at low SNR. Fgure 55. BER performance of SMMSE, SO P, BD for {,,} 6 and MMSE P for {1,1,1,1,1,1} 6 confguraton [57] Iteratve Lnear MMSE Precodng wo teratve lnear MMSE precodng schemes are dscussed n [55] for users wth multple antennas. Consder the system model of Fgure 50 where P s the combned precodng matrx at the BS and V s the block-dagonal combned decodng matrx consstng of the decodng matrces V of all the users. In case of lnear MMSE precodng whch mnmzes the MSE between â and a, V s the lnear MMSE recever for user and can be estmated locally at the correspondng UE. he frst scheme called drect optmzaton, teratvely computes the MMSE soluton usng a numercal me thod. he SMMSE soluton can be used as an ntal guess for the free varables V wth 1 for the free varable. An teratve process s then used whch can lead to a true MMSE soluton but not n all cases. he BD soluton can also be used as an ntal guess but that would result n slower convergence. he other scheme explots the uplnk/downlnk dualty [63] to obtan the true MMSE soluton usng an teratve algorthm. he resultng objectve functon s convex n ths case. Detaled descrpton as well as a practcally mplementable algorthm for ths dualty-based scheme s presented n [64]. he uncoded BER performance of BD, SMMSE, drect optmzaton and the dualty-based scheme s compared n Fgure 57 for {1,, 3} 6 antenna confguraton. he bt error rates are averaged over all users. DE s appled for BD and SMMSE whle sngle stream (SS) transmsson (consstng of a sngle data stream per user) s used for drect optmzaton and the dualty-based scheme based on the algorthm from [64]. Independent Raylegh fadng channel perturbed by complex Gaussan nose s consdered and QPSK modulaton s used for transmsson. Both teratve lnear MMSE schemes outperform the other two by a large margn. he dualty-based scheme shows slghtly better performance than Fgure 56. BER performance of SMMSE, SO P, BD for {1,1,,} 6 and MMSE P for {1,1,1,1,1,1} 6 confguraton [57]. Fgure 57. Uncoded BER performance of BD, SMMSE, drect optmzaton and dualty-based scheme [55]. Copyrght 010 ScRes.

34 46 F. KALID E AL. drect optmzat on. hs dfference s due to the nonconvex objectve functon used for drect optmzaton whch occasonally causes the optmzaton routne to undesred mnma. BD provdes the worst performance because of the zero-forcng constrant. Fgure 58 shows the coded BER performance of these precodng schemes. A rate 1/ turbo code s used for error correcton. OFDM based transmsson s consdered where the precodng s appled on a per-subcarrer bass. he IU Vehcular A channel model s used. Drect optmzaton and the dualty-based scheme provde almost dentcal performance n ths case, far better than BD and SMMSE Partal CSI Feedback ransmt precodng for downlnk MU-MIMO transmsson requres CSI feedback from the users. owever, feedback nformaton consstng entrely of the current state of the channel may not be accurate enough n case of rapdly varyng channels. Downlnk transmsson schemes that utlze partal CSI consstng of long-term channel statstcs along wth some nstantaneous channel nformaton lke SNR, SINR etc. provde a soluton to ths problem whle reducng the feedback overhead. An nterestng MU-MIMO downlnk transmsson scheme based solely on nstantaneous channel norm feedback s proposed n [65]. MU-MIMO confguraton wth multple base staton (BS) antennas and a sngle antenna at each UE s consdered. he proposed scheme can provde hgh multuser dversty gan by optmzng resource allocaton at the BS whle smply utlzng the nstantaneous channel norm feedback from the UEs. Fgure 59 shows the operaton of the proposed system at the transmtter (BS). he BS ntally transmts orthogonal plot sgnals on all transmt antennas whch are used by each UE to estmate the receved sgnal energy.e. the squared norm of the channel vector gven by Fgure 58. Coded BER performance of BD, SMMSE, drect optmzaton and dualty-based scheme [55]. Fgure 59. System operaton at the transmtter [65]. k k h (78) where h k represents the channel vector for the k-th UE from the UEs scheduled for transmsson. k s categorzed as channel gan nformaton (CGI) n [65]. hs quantty s then fed back to the BS. he BS estmates the long-term channel statstcs ncludng the channel mean and the channel covarance matrx, defned as hˆ E h (79) k k k ˆ Q E h h (80) k k k k hs slow varyng statstcal nformaton s referred to as channel dstrbuton nformaton (CDI). he CGI feedback along wth the CDI s used to estmate the SINR and the optmzed beamformng weght vectors for each of the UEs scheduled for transmsson. he SINR for user k s estmated as ˆ SINR wk Qkwk k (81) w Q w \ k k k where w k s the correspondng beamformng vector, ˆ ˆ k w Qkw s the MMSE estmate of the sg- power rato (SIR) k w hkhk w nal-to-nterference and k s the AWGN power. he actual data transmsson to the scheduled users then begns. Another set of users can later be scheduled to acheve better farness and ths process goes on untl the CGI becomes outdated. At ths pont, BS transmts the plot sgnals agan and the whole process s repeated Multuser Schedulng he BS can only support a lmted no. of smultaneous users for MU-MIMO downlnk transmsson wth acceptable performance. he performance degrades n rankdefcent scenaros and also when the users are spatally correlated. In case of mult-antenna users, the no. of us- ers that can be supported smultaneously becomes even lesser. In practcal stuatons, the BS would generally serve a larger no. of users than t can smultaneously support. herefore, an effcent schedulng algorthm s requred to select the group of users that wll be spatally multplexed by the BS at a certan tme and frequency. he schedulng algorthm should avod groupng spatally correlated users and maxmze system performance whle mantanng farness toward all users. Farness Copyrght 010 ScRes.