Two-Stage Detector for SC-FDMA Transmission over MIMO ISI Channels

Transcription

1 Two-Stage Detector for SC-FDMA Transmsson over MIMO ISI Channels Marcel Jar Eml Matúš Esther Pérez-Adeva Eckhard Ohlmer and Gerhard Fettwes Vodafone Char Moble Communcaton Systems Technsche Unverstät Dresden Dresden Germany Abstract In ths paper a two-stage detector s proposed for sgnals transmtted usng multple antenna confguratons over frequency-selectve channels For the frst stage a frequency doman equalzer applyng the mnmum mean-squared error crteron s used to mtgate the ntersymbol nterference ntroduced by the channel s non-flat frequency response Followng the output of ths frequency doman equalzer assumed to be ntersymbol nterference free s used as an nput for a sphere detector The sphere detector then processes ts nput returnng log-lkelhood ratos for all transmtted bts from all transmttng antennas These log-lkelhood ratos can be used for nstance as nputs for decoders followng the sphere detector n the recevng chan The proposed method s shown to be well suted for the uplnk scenaro of the Long Term Evoluton (LTE) Advanced standard where hgh-modulaton order sgnals can be transmtted by multple antennas usng a sngle-carrer frequency dvson multplexng access (SC-FDMA) scheme that s prone to suffer from the effects of ntersymbol nterference I INTRODUCTION In order to accommodate a growng demand for hgher data rates n wreless communcatons new standards have been proposed and deployed over the past few years Currently wreless provders worldwde are ncreasng ther capacty by swtchng from Thrd Generaton (3G) technologes to the Long Term Evoluton (LTE) standard 1 Some of the most mportant characterstcs of ths standard are the use of multple-nput multple-output (MIMO) antenna systems 1 frequency-dvson modulaton schemes usng large bandwdths and hgh-order modulatons Multple antenna technologes can theoretcally ncrease the throughput by a factor of mn (N T x N Rx ) where N T x and N Rx denote the number of transmttng and recevng antennas respectvely 3 However each recevng antenna perceves a combnaton of the sgnal transmtted by all transmttng antennas resultng n mult-antenna nterference (MAI) Moreover although the capacty scales lnearly wth the bandwdth large bandwdths frequently result n experencng channels wth a non-flat frequency response resultng n the appearance of ntersymbolc nterference (ISI) ISI ntroduces correlaton between symbols transmtted over dfferent tme nstants makng the task of estmatng the transmtted sgnal more computatonally ntensve 1 MIMO systems were frst proposed only for the downlnk scenaro However they were later extended to the uplnk scenaro for the LTE Advanced standard 2 ISI s crcumvented n the LTE downlnk e base staton (enodeb) to moble user equpment (UE) by makng use of orthogonal frequency-dvson multplexng access (OFDMA) OFDMA dvdes the frequency spectrum n sub-bands and assgns a dfferent subcarrer to each band effectvely transformng ISI MIMO channels nto a set of parallel frequencyflat hence ISI-free MIMO sub-channels 4 Snce each sub-channel s flat powerful detecton methods lke sphere detecton 5 can be used for each channel ndvdually Despte ts great potental OFDMA presents two major drawbacks Frst t s very senstve to carrer frequency synchronzaton Second and more mportantly t results n a hgh peak-to-average power rato (PAPR) makng t ll suted for the uplnk scenaro of cellular networks where the transmtter s normally a battery powered devce 6 In order to mantan the PAPR at approprate levels for moble devces the LTE standard employs a sngle-carrer frequency dvson multplexng access (SC-FDMA) nstead of OFDMA for the uplnk scenaro SC-FDMA shares many characterstcs wth OFDMA beng able to dynamcally allocate frequency bands to ts users whle resultng n a much lower PAPR 6 However as opposed to OFDMA SC-FDMA transmssons are prone to suffer from ISI For SC-FDMA recevers to keep the computatonal complexty low a lnear frequency doman equalzer (FDE) s normally employed 2 A lnear FDE normally uses the mnmum mean-squared error (MMSE) crteron to mtgate both ISI and MAI at the same tme However the nose ntroduced by the channel whch s assumed here to be addtve whte Gaussan nose (AWGN) s also fltered resultng n an undesrable nose-enhancement effect and correlaton whch shfts the channel memory from the mpulse response nto the nose In ths work a novel two-stage detector scheme s proposed It employs a lnear FDE to suppress the ISI whle leavng the task of mtgatng the MAI to a more robust detector (n ths work a sphere detector) It wll be shown n what follows that as long as the nterference s largely domnated by the MAI ths two-stage detector can result n a sgnfcant gan n performance Ths paper s organzed as follows In Secton II a descrpton of the basc recever for the uplnk scenaro of the LTE Advanced standard s presented Followng a two-stage recever s proposed and analyzed n Secton III Monte-Carlo /12/$ IEEE 391

2 Fg 1 Schematcs dagram for a SC-FDMA LTE uplnk scenaro transmtter smulaton results are presented n Secton IV ndcatng the sgnfcant gans n performance that the proposed two-stage recever has over FDE detecton Concludng remarks are lad down n Secton V II BASIC SYSTEM MODEL For the sake of smplcty the man processng steps for SC-FDMA transmsson for the LTE uplnk scenaro are presented here for a 2 2 MIMO system as shown n Fg 1 Nevertheless all results can be straghtforwardly extended to other MIMO confguratons The process starts for the th layer wth the encoder recevng a vector of bts and outputtng an encoded vector c Followng the encoded vector passes through a rate matchng devce that wll puncture or repeat some bts n order to accommodate the transmtted sgnal to the avalable resources resultng n c After puncturng/repeatng the sgnal s nterleaved and modulated resultng n a vector of symbols s Denotng by s N the output of the seral to parallel converter for the th layer n Fg 1 and by F N a Fourer matrx of sze N the output of the dscrete Fourer transforms (DFT) of sze N s gven by S N F N s N The vector S N s mapped to N among M > N possble subcarrers va a resource mapper Ths mappng can be represented by an M N matrx D MN wth N ones correspondng to the used frequences and zeros elsewhere Hence S M D MN SN D MN F N s N Followng the sgnal s sent back to the tme doman usng an nverse DFT of sze M F M resultng n s M F M S M F M D MN F N s N where the operator denotes the Hermtan of a matrx Pror to transmsson the sgnal s M s converted back from parallel to seral and a cyclc prefx s added resultng n s M Stackng up the output of both cyclc prefx adders s M0 and s M1 and dong the same for the receved sgnal at each recevng antenna r and r the relatonshp between M0 M1 transmtted and receved sgnal s gven by r M0 H00 H r s M0 M1 H 10 H s M1 n0 n 1 where n s a vector of addtve whte Gaussan nose components of sze M and varance σ 2 and each sub-channel matrx H j denotes the M M channel matrx between the th transmttng and the jth recevng antenna Assumng that there are at most L echoes these matrces have the format h 0 j 0 0 h 0 j H j h L 1 j 0 h L 1 j 0 0 h 0 j At the recever as shown n Fg 2 the cyclc-prefx s removed and the sgnal s converted from seral to parallel resultng for each layer n r M The overall effect of addng a cyclc prefx at the transmtter and removng t at the recever s that t makes the channel to appear crcular to the recever 6 Ths crcular property as t wll be shown later greatly smplfes the task of the FDE To smplfy notaton the sub-channels wll be assumed to be crcular from now on and have the cyclc prefx attached to t resultng n rm0 sm0 r M1 H 00 H H 10 H s M1 n0 n 1 After the sze M DFT and resource remapper the recever sgnal n the frequency doman s gven by R H00 H S R N1 H S N1 N 1 where each sub-channel matrx H j obtaned accordng to (1) s a dagonal matrx due to the DFT egenstructure property of crculant matrces 4 For ths scenaro there s stll spatal couplng n the frequency doman between sgnals transmtted by dfferent antennas however there s no more couplng between sgnals transmtted at dfferent subcarrers For the th subcarrer the relatonshp between transmtted and receved sgnal s R R N1 h 00 h S h 10 h } {{ } H S N1 N N N1 Hence the outputs of a FDE usng the MMSE crteron for the th sub-carrer are obtaned as S SN1 H ( ) 1 H H σ 2 R I 2 RN1 (2) From the result n (2) t can be seen that snce there s no couplng between sgnals transmtted at dfferent frequences 392

3 Fg 2 H00 H D MN 0 NM H 0 NM D MN Schematcs dagram for a SC-FDMA LTE uplnk scenaro recever FM 0 M H 00 H 0 M F M H 10 H F M 0 M 0 M F M DMN 0 MN 0 MN D MN (1) the FDE can operate by nvertng N matrces of sze 2 2 nstead of the much more costly task of nvertng one matrx of sze 2N 2N n the tme doman Followng the recever processng chan n Fg 2 each one of the outputs of the FDE s sent back to the tme doman and converted from parallel to seral resultng n ŝ Ths sgnal s demodulated resultng n log-lkelhood ratos (LLRs) for each transmtted bt denterleaved and the results from all layers are combned Ths results at the output of the rate rematcher n a detected vector ĉ that s sent to a turbo decoder Due to ts low-complexty and ease of analyss FDE has been wdely studed and mplemented for SC-FDMA recevers 2 However as dscussed before FDE leads to noseenhancement effects whch for some channels can result n unsatsfactory performance III TWO-STAGE DETECTOR A schematcs dagram for the the two-stage detector proposed here s shown n Fg 3 Ths systems dffers from the conventonal detector depcted n Fg 2 for ts lnear FDE suppresses only the ISI leavng the task of elmnatng the MAI to be performed by a sphere detector n the tme doman Ths scheme was envsaged based on the observaton that for small to medum bandwdths most of the energy at the receved sgnal s concentrated n the frst tap For such scenaros the channel s frequency response s almost flat and the ISI s small Hence a lnear flter to remove only the ISI does not ncur a large nose enhancement Pror to determnng the lnear flter to be used n the frst stage a target channel H tg s defned Ths channel s equal to the channel matrx H wth the excepton of the coeffcents correspondng to echoes whch are set to zero Then the MMSE lnear flter Ω should be chosen n order to mnmze: { ( E Ω ( H00 H S H S N1 Htg ) N 1 } (3) )2 S S N1 where all matrces j and H j are obtaned accordng to (1) It s shown n 7 that the flter Ω that mnmzes (3) can be obtaned by multplyng the target channel by the MMSE flter for the whole channel Ie the lner flter s gven by Ω Ψ (4) where Ψ corresponds to the MMSE soluton Ψ H ( H H σ 2 I) 1 Followng the fltered sgnal s sent back to the tme doman resultng n ˆν and ˆν N1 for the 2 2 MIMO scenaro depcted n Fg 3 whch are to be processed by a sphere detector The choce of sphere detector n ths work s a tuple search detector (TSD) wth matched canddate determnaton 8 applyng a sorted QR decomposton wth MMSE bas reducton 9 Ths sphere detecton shown n 10 to be able to delver close to optmal performance whle requrng a small computatonal effort works as follows Frst for the th tme nstant the N Rx N T x channel coeffcents correspondng to each par of transmttng and recevng antennas are grouped nto a matrx () Then a sorted QR decomposton s appled to an extended channel matrx H ext Htg () σ 2 I Q Q3 Q 2 Q 4 R 0 Ths extenson ensures that the varance of the nose at the recever s taken nto account reducng the number of closeto-sngular dagonal entres n R and thus the detecton complexty Followng for the th tme nstant a vector contanng the detected sgnals from each transmttng antenna ˆν () and ˆν N1 () s multpled by Q resultng n y Q ˆν () ˆν N1 () Snce Q has untary energy ths procedure does not alter the statstcs of the nose Fnally the sphere detector searches for the ML soluton mn y R x (5) x takng advantage of the upper trangular property of R Parallel to the search for the ML soluton n (5) the sphere detecton algorthm stores the statstcs of other possble transmtted sgnals These statstcs are used together wth the ML soluton to determne LLRs for each transmtted bt 2 The same way as n the conventonal system the LLRs at the output of the sphere detector are converted from parallel 2 For a more detaled descrpton of the tuple sphere detector used n ths work the reader s referred to 393

4 Fg 3 Schematcs dagram for the proposed two-stage processng recever to seral and denterleaved 3 The results from all layers are combned resultng at the output of the rate rematcher n a detected vector ĉ to be sent to a turbo decoder A Adequacy of sphere detecton for fltered sgnals In the second stage of the proposed recever the sgnal at the th tme nstant s processed by the sphere detector as f t had been transmtted over a target channel H tg Ths clearly dffers from the real scenaro where a sgnal s transmtted over a channel H and fltered n the frequency doman by Ω Hence the successful applcaton of a sphere detecton scheme for ths scenaro depends on the approprateness of the followng approxmaton Ω ( H S S N1 N N N1 ) S S N1 whch usng (4) can be shown to be equvalent to N N N1 Fg 4 Hstogram showng the percentage of the total transmtted power receved n the form of echoes (or ISI) for a thousand 4 4 MIMO channels assumng an EPA delay profle 3 MHz bandwdth and a SNR of 20 db H ( H H σ 2 I) 1 H Htg (6a) H ( H H σ 2 I) 1 I (6b) Clearly (6a) s equvalent to assumng that the FDE has successfully removed all the ISI To verfy ths a thousand 4 4 MIMO channels were generated accordng to the gudelnes set for the LTE standard n 12 usng the EPA delay profle at 3 MHz and a SNR of 20 db It s shown n Fg 4 the percentage of the total transmtted power receved n the form of echoes before and after FDE For ths scenaro the resdual ISI e after the FDE accounts for less than one percent of the total energy Also (6b) s equvalent to assumng that the FDE does not sgnfcantly alter the statstcs of the nose To verfy ths the autocorrelaton of the nose at the output of the FDE for a random 4 4 MIMO EPA channel wth a bandwdth of 3MHz s plotted as a functon of the frequency-space τ dstance 4 As one can see there s a sgnfcant autocorrelaton at and 384 for the classcal FDE These values correspond to multples of the chosen value of N 128 For the FDE used n the two-stage processor on the other hand no notceable autocorrelaton exsts Makng use of (6a) and (6b) the two-stage system proposed here does not need to use a whtenng nose flter at the output of the FDE as done n 7 resultng n a sgnfcant computatonal complexty reducton 3 Note that snce the sphere detector returns LLRs t acts as both detector and demodulator Hence as shown n Fg 3 there s no need for a separate demodulator block as n the case of the conventonal system depcted n Fg 2 4 Frequency and space are combned snce the vectors R N n (2) are stacked on top of each other Fg 5 Correlaton between nose samples as a functon of the tme-space dstance τ for the two-stage FDE as well as for the conventonal FDE IV SIMULATION RESULTS To assess the mprovement n performance obtaned by the presented two-stage detector over the classcal FDE for the uplnk scenaro of the LTE Advanced standard Monte Carlo smulatons were carred out For all smulatons a CQI of 10 s assumed resultng n a code rate of 0455 and a modulaton choce of 64-QAM The sgnal s transmtted over a 4 4 MIMO system usng a bandwdth of 14 MHz The subcarrer mappng operaton maps 60 subcarrers nto 128 avalable frequences n a localzed fashon Fnally three power delay profles are used extended pedestran A (EPA) extended vehcular A (EVA) and extended typcal urban (ETU) A thousand transport blocks were transmtted by each MIMO layer accordng to the processng steps depcted n Fg 1 For each transport block the channel s assumed constant (block-fadng) These transport blocks are receved accordng to the processng steps depcted n Fg 2 for the classcal FDE detector or the processng steps depcted n Fg 3 for the proposed two-stage detector The obtaned block 394

5 Fg 6 Block error rate curves for FDE and Two-Stage detectors for the LTE uplnk scenaro over 4 4 MIMO channels assumng a CQI of 10 an EPA delay profle and a 14 MHz bandwdth Fg 8 Block error rate curves for FDE and Two-Stage detectors for the LTE uplnk scenaro over 4 4 MIMO channels assumng a CQI of 10 an ETU delay profle and a 14 MHz bandwdth performance and computatonal complexty For large bandwdths the proposed method can stll result n large gans n performance as long as multple users are beng served by parttonng the total bandwdth n sub-bands and assgnng dfferent bands for each users ACKNOWLEDGMENT The authors would lke to acknowledge the fnancal support from NEC Corporaton Fg 7 Block error rate curves for FDE and Two-Stage detectors for the LTE uplnk scenaro over 4 4 MIMO channels assumng a CQI of 10 an EVA delay profle and a 14 MHz bandwdth error statstcs are presented n Fgs 6 7 and 8 for the EPA EVA and ETU delay profles respectvely As t can be seen for all scenaros the proposed two-stage detector results n sgnfcant performance gans Nomnally at a block error rate (BLER) of 10 1 gans n performance of 7 db 4 db and 1 db were obtaned for the EPA EVA and ETU scenaros respectvely Further smulatons not shown here due to space constrants showed that sgnfcant gans n performance can stll be obtaned for the EPA profle for bandwdths up to 5 MHz and for bandwdths up to 3 MHz for the EVA profle For the ETU profle the proposed scheme dd not result n sgnfcant gans for hgher bandwdths V CONCLUSIONS In ths work a two-stage detector was proposed to replace FDE detectors normally employed n the LTE Advanced uplnk scenaro for MIMO channels It was shown va Monte Carlo smulatons that the proposed method results n a sgnfcant performance gan for small to average bandwdths n realstc scenaros allowng a very postve trade-off between REFERENCES 1 H Holma and A Toskala LTE for UMTS: Evoluton to LTE-Advanced John Wley and Sons 20 2 E Dahlman S Parkvall and J Sköld 4G: LTE/LTE-Advanced for Moble Broadband Academc Press 20 3 E Bgler R Calderbank A Constantndes A Goldsmth A Paulraj and H V Poor MIMO Wreless Communcatons Cambrdge A Goldsmth Wreless Communcatons Cambrdge E Vterbo and J Boutros A unversal lattce code decoder for fadng channels IEEE Transactons on Informaton Theory vol 45 no 5 pp H Myung J Lm and D Goodman Sngle-carrer FDMA for uplnk wreless transmsson IEEE Vehcular Technology Magazne pp J Ketonen J Karjalanen M Juntt and T Hännnen MIMO detecton n sngle carrer systems n Proceedngs of the European Sgnal processng Conference Barcelona 20 pp B Mennenga A von Borany and G Fettwes Complexty reduced soft-n soft-out sphere detecton based on search tuples n IEEE Internatonal Conference on Communcatons 2009 pp E Zmmermann and G Fettwes Unbased MMSE tree search detecton for multple antenna systems n Proceedngs of the Internatonal Conference on Wreless Personal and Multmeda Communcatons E Adeva B Mennenga and G Fettwes Survey on an effcent lowcomplex tuple search based sphere detector n Sarnoff Symposum 20 34th IEEE may 20 pp 1 6 E Zmmermann W Rave and G Fettwes On the complexty of sphere decodng n Proceedngs of the Internatonal Conference on Wreless Personal and Multmeda Communcatons Abano 2004 p GPP TS 361 V930 Evolved unversal terrestral rado access (E- UTRA); user equpment (EU) rado transmsson and recepton (release 9)