Performance of Multiuser MIMO-OFDM downlink system with ZF-BF and MMSE-BF linear precoding

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1 Iteratioal Joural of Iovatio ad Applied Studies ISS Vol. 3 o. 4 Aug. 013 pp Iovative Spae of Sietifi Resear Jourals ttp://.issr-jourals.org/ijias/ Performae of Multiuser MIMO-OFDM dolik system it ZF-BF ad MMSE-BF liear preodig Mouir Esslaoui ad Moammed Essaaidi Iformatio ad eleommuiatio Systems Laboratory Faulty of Siees Abdelmalek Essaadi Uiversity etoua Moroo Copyrigt 013 ISSR Jourals. is is a ope aess artile distributed uder te Creative Commos Attributio Liese i permits urestrited use distributio ad reprodutio i ay medium provided te origial ork is properly ited. ABSRAC: e fortomig ireless ommuiatio etorks ommoly referred to as fourt geeratio (4G) systems are expeted to support extremely ig rates as lose as possible to te teoretial ael apaity ile satisfyig quality of servie (QoS) ostraits. e developmet of tese systems must take ito aout te problem of limited radio resoures ad te arsess of ireless ael oditios. o emergig teologies tat are potetial adidates for 4G ireless etorks are multiuser multiple-iput multiple-output (MU-MIMO) ireless systems ad ortogoal frequey divisio multiplexig (OFDM). e MU-MIMO teique allos te spatial multiplexig gai at te base statio to be obtaied itout te eed for multiple atea termials tereby alloig multiple users to reeive over te dolik simultaeously. e use of OFDM provides protetio agaist itersymbol iterferee (ISI) ad allos ig rates to be aieved. Liear preodig semes for MU-MIMO ireless systems e.g. zero forig beamformig (ZF-BF) ad miimum mea squared error beamformig (MMSE-BF) ave bee idely oered for teir ig performae i sigle-arrier MU- MIMO etorks ere a base statio attempts to ommuiate simultaeously it multiple users. I tis paper e evaluate ad exted te ZF-BF ad MMSE-BF semes from sigle-arrier MU-MIMO to multiarrier MU-MIMO ariteture based o OFDM i.e. MU-MIMO-OFDM system assumig te availability of ael state iformatio (CSI) at te trasmitter. umerial results demostrate tat bot itrodued liear preodig strategies provide a iger sum-rate apaity improvemet ompared to a ovetioal MU-MIMO-OFDM system ere te users are served o a time divisio multiple aess (DMA) basis. EYWORDS: Multiuser MIMO OFDM zero forig miimum mea squared error beamformig preodig. 1 IRODUCIO e mai allege of te fortomig ireless ommuiatio systems ommoly referred to as fourt geeratio (4G) systems is to satisfy te ireasig demad for ig rates ile satisfyig quality of servie (QoS) ostraits. I partiular te use of multiple-iput multiple-output (MIMO) ireless systems a improve te apaity by a fator depedet o te miimum umber of trasmit ad reeive ateas if perfet ael state iformatio (CSI) is available at te base statio [1]. O oter ad ortogoal frequey divisio multiplexig (OFDM) is a popular metod for ig rate ireless trasmissio. It is a effetive teique to mitigate te effets of itersymbol iterferee (ISI) i frequeyseletive aels by overtig a frequey-seletive ael ito a parallel olletio of frequey flat subaels []. Combiig MIMO atea ofiguratios it OFDM results i a poerful ariteture MIMO-OFDM tat is able to exploit spatial as ell as frequey diversity ad allo ig rates it large degrees of freedom available i te ireless eviromet [3]. Reetly multiuser MIMO (MU-MIMO) as bee osidered a key teology for system apaity improvemet i moder ireless etorks itout te eed for multiple ateas ad expesive sigal proessig at user equipmets. I otrast to sigle-user MIMO (SU-MIMO) ere a base statio a oly ommuiates it a sigle user MU-MIMO allos Correspodig Autor: Mouir Esslaoui (mouir.ess@gmail.om) 946

2 Mouir Esslaoui ad Moamed Essaaidi multiple mobile statios to be served simultaeously by meas of spae divisio multiple aess (SDMA) [4]. Iformatio teory reveals tat if CSI is fully ko at te trasmitter dirty paper odig (DPC) is te optimal trasmit strategy for te MU-MIMO broadast ael from a system apaity poit of vie [5]. oever deployig tis teique i pratie is ard to implemet beause of te ig omputatioal omplexity it requires espeially e te umber of users is large. erefore suboptimal liear preodig strategies su as zeroforig beamformig (ZF-BF) [6] [7] ad miimum mea square error beamformig (MMSE-BF) [8] ave bee ivestigated to provide te apaity gai promised by DPC ile removig te multiuser iterferee amog te simultaeously trasmitted users. I tis paper ZF-BF ad MMSE-BF liear preodig semes are evaluated ad exteded i ligt of te available CSI at te trasmitter from sigle-arrier to multiarrier MU-MIMO systems ere te users trasmit stritly usig OFDM (i.e. frequey is ot used for multiple aess). Simulatios results ave so tat ompared to a ovetioal MU-MMO-OFDM based time divisio multiple aess (DMA) strategy ere te BS trasmits to te best user at ea time slot osiderable sum-rate apaity improvemet a be aieved by bot proposed liear preodig teiques. e remaider of tis paper is orgaized as follos. Setio presets te MU-MIMO-OFDM system model. Setio 3 presets te proposed preodig semes. umerial results are so i Setio 4. Fially Setio 5 summarizes te mai outomes of te paper. OAIOAL REMAR Boldfae letters deote matrix-vetor quatities ile o-bold letters are used for salars. e operatio (.) ad (.) represet te traspose ad te ermitia traspose of a matrix respetively. E(.) deotes te expetatio operator r(.) is te trae ad C is te set of omplex umbers. I is te idetity matrix ad a deotes te Eulidea orm of a vetor a. SYSEM MODEL User 1 Codig Modulatio Liear IFF FF Detetio Demodulatio Deodig User 1... Preodig User Codig Modulatio IFF FF Detetio Demodulatio Deodig User Base Statio M Cael state iformatio Mobile termials Fig. 1. Blok diagram of MU-MIMO-OFDM dolik system it trasmit ateas ad sigle atea mobile users We osider te dolik of a sigle-ell MU-MIMO-OFDM system i i a sigle base statio (BS) equipped it M trasmit ateas ommuiates it M mobile users ea equipped it a sigle reeive atea. e system operates i a total badidt W tat is exploited by meas of OFDM subarriers. e BS broadasts to all users simultaeously over all OFDM subarriers. e system blok diagram is depited i Fig. 1. Let s be te symbol of user k over te t subarrier. e 1 all users is M overall vetor of trasmitted symbols from te BS ateas o subarrier for s s s. x (1) 1 Assumig perfet frequey syroizatio betee te trasmitter ad reeiver ad yli prefix duratio exeedig te ael delay spread te reeived sigal y k for user k o subarrier for a arbitrary OFDM symbol is give by k ISS : Vol. 3 o. 4 Aug

3 Performae of Multiuser MIMO-OFDM dolik system it ZF-BF ad MMSE-BF liear preodig y k k k x () ere k C 1xM represets te ael gai respose orrespodig to userk over te subarrier ad k is a zeromea additive ite Gaussia oise (AWG) sample it variae. e base statio (BS) as full ad istataeous koledge of te ael state iformatio (CSI) of all users. e trasmitter is subjet to a average poer ostrait P i.e. r( E ( xx )) P i implies tat te total trasmit poer is ot depedet o te umber of trasmit ateas. e trasmitter multiplies te symbol s for ea user k o ea subarrier by a preodig vetor C Mx1 so tat te trasmitted sigal o ea subarrier is a liear futio at a be ritte as k k k k k 1 k x P s (3) ere P deotes te poer alloated to te k t user o te t subarrier satisfyig k k Pk P (4) 1 k 1 ad tus te resultig reeived sigal for user k o subarrier may be reritte as y k k s j 1 (5) Pk k k k k j k j1 j k s P s (6) ere te seod-term i (6) orrespods to te multi-user iterferee tat represets te major impairmet i tis seario. e allege o is o to perform te preodig operatio i order to elimiate all multiuser iterferee. 3 PRECODIG ECIQUES FOR MU-MIMO-OFDM SYSEMS I MU-MIMO-OFDM dolik system a BS ommuiates simultaeously it multiple reeivers usig te SDMA teique. o aieve tis goal preodig strategies sould be desiged i ligt of te available CSI i order to irease system apaity ad/or redue te omplexity of te reeiver. I tis setio e preset ad evaluate liear preodig semes usig eiter ZF-BF ad MMSE-BF. For ompariso e also preset a ovetioal MU-MIMO-OFDM based DMA system ere te base statio trasmits oly to best user at a give time slot. 3.1 ZERO-FORCIG BEAMFORMIG Let us defie te respetively as M ael gai matrix ad M preodig matrix o subarrier for all users 1 (7) 1 W. (8) I Zero-Forig Beamformig (ZF-BF) te preoder is desiged to aieve te zero iterferee oditio betee te users ISS : Vol. 3 o. 4 Aug

4 Mouir Esslaoui ad Moamed Essaaidi i.e. k k 0 for j k. (9) 1 for j k e ZF-BF preodig matrix for ea subarrier is give by te pseudo-iverse of te ael gai matrix [7] tat is 1 ere te preodig vetor k aievable sum-rate apaity usig ZF-BF over all subarriers is expressed as P W (10) for ea user k o subarrier is obtaied by ormalizig te k t olum of 1 P R ZF-BF log 1 k k 1 k 1 ere k maximum sum-rate apaity is give by te aterfillig algoritm [9]. W. e (11) deotes te poer alloated to user k o subarrier. e optimal poer alloatio tat aieves te 3. MIIMUM MEA SQUARED ERROR BEAMFORMIG e ZF-BF preoder ompletely elimiates multi-user iterferee at te expese of oise eaemet ad tus te system a be treated as a group of parallel SU-MIMO ommuiatios at ea subarrier. oever if some of te aels are i bad oditio te system eeds large poer to ompesate te bad ael oditio. e miimum measquare-error beamformig (MMSE-BF) preoder a rea a good tradeoff betee oise ad iterferee ad is suitable to be used to overome tis problem. I presee of CSI at te trasmitter te MMSE-ZF preoder at ea subarrier is give as follos: W 1 I (1) ere is a regularizatio fator ommoly ose as M /P motivated by te results i [10] soig tat for sigle arrier systems te performae of MMSE-BF is ertaily sigifiatly better at lo-medium SR ad overges to tat of ZF-BF at ig SR. oever MMSE-BF does ot provide parallel aels ad tus poer alloatio teiques aot be performed i a straigtforard maer. ere e aievable sum-rate apaity usig MMSE-BF over all subarriers it equal poer alloatio is give by k 1 k1 1 R MMSE-BF log 1 SIR (13) SIR k represets te sigal to iterferee plus oise ratio of userk o subarrier ad a be expressed as SIR k j1 jk k k k / P. (14) 3.3 IME DIVISIO MULIPLE ACCESS I a ovetioal MU-MIMO-OFDM etork ere user multiplexig takes plae usig DMA teiques te base statio selets te best user at a time o ill be alloated all te spetrum ad poer resoures [11]. I tis seario it is easy to so tat oe a user as bee seleted te preodig operatio o ea subarrier is simply implemeted by meas of maximum ratio trasmissio (MR) [1] tat is ISS : Vol. 3 o. 4 Aug

5 Performae of Multiuser MIMO-OFDM dolik system it ZF-BF ad MMSE-BF liear preodig ere k k x P s (15) k k k. e maximum sum-rate apaity aieved by sedig to te user it te largest ael orm is 1 R DMA P max log 1 k k {1 } 1. (16) 4 UMERICAL RESULS I tis setio e evaluate te performae of ZF-BF ad MMSE-BF liear preodig semes i MU-MIMO-OFDM searios assumig te availability of CSI at trasmitter ad ompare tem to ovetioal MU-MMO-OFDM based DMA system. e simulatios osider te use of parameters urretly foud i te latest WLA stadard IEEE e system as bee ofigured to operate at 5.5Gz arrier frequey o a badidt of W0Mz it 64 OFDM subarriers ere te subael gais are idepedet ad idetially distributed for ea user. e ael profile used to geerate te frequey-seletive ael resposes orrespod to profiles B (residetial) from ael models developed iti te IEEE stadard [13]. e base statio is assumed to ommuiate it a total of M mobile users ea equipped it a sigle reeive atea. Fig. sos a performae ompariso i terms of sum-rate apaity as a futio of te average SR for MMSE-BF ZF- BF ad te ovetioal DMA etork i a system it M 4 trasmit ateas ad M mobile users. As expeted it a be see tat te performae of MMSE-BF is ertaily sigifiatly better at lo-medium SR regime ad overges to tat of ZF-BF at ig SR regime. Moreover te gai i sum-rate apaity gap betee bot liear preodig semes ad te ovetioal DMA system exibits a liear irease it SR values reaig more tat 10 bits/s/z for a SR30 db. Sum-rate apaity [bits/s/z] DMA ZF-BF MMSE-BF SR [db] Fig.. Sum-rate apaity versus te average SR. M 4 I Fig. 3 e ompare te sum-rate apaity versus te umber of trasmit ateas M for M mobile termials ad a average SR10 db. It a be observed tat ireasig te umber of trasmit ateas M i.e. ireasig te umber of simultaeously trasmittig users as te detrimetal effet of providig a liear sum-rate apaity grot for bot liear preodig semes ere te sum-rate apaity of MMSE-BF outperforms tat of te ZF-BF. oever for te ovetioal ase ere te best user is seduled te sum-rate apaity saturates at 7.7 bits/s/z. is a be explaied by te fat tat addig more trasmit ateas does ot improve te performae of te DMA teique. ISS : Vol. 3 o. 4 Aug

6 Mouir Esslaoui ad Moamed Essaaidi DMA ZF-BF MMSE-BF Sum-rate apaity [bits/s/z] M Fig. 3. Sum-rate apaity versus te umber of trasmit ateas M. M users SR10 db 5 COCLUSIO I tis paper zeroforig beamformig (ZF-BF) ad miimum mea square error (MMSE-BF) liear preodig semes ave bee aalyzed ad exteded from sigle-arrier MU-MIMO to a multiarrier MU-MIMO ariteture based o OFDM. Simulatio results ave so tat e ael state iformatio (CSI) is available at te trasmitter ad for pratial average SR values te performae of bot proposed liear preodig teiques is sigifiatly better ta te ovetioal DMA etork ad aieve a liear sum-rate grot it te umber of trasmit ateas. I additio for a fixed umber of trasmit ateas at te base statio te performae of MMSE-BF is sigifiatly better at lo-medium SR regime ad overges to tat of ZF-BF at ig SR regime. ACOWLEDGME e autors ould like to tak te editor ad te aoymous revieers ose areful osideratio of te mausript improved te presetatio of te material. REFERECES [1] E.elatar Capaity of multi-atea Gaussia aels Eur. ras.eleommu. vol. 10 o. 6 pp ov [] R. va ee ad R. Prasad OFDM for ireless multimedia ommuiatios. Arte ouse 000. [3] A. J. Paulra D. A. Gore R. U. abar ad. Bolskei A overvie of MIMO ommuiatios a key to gigabit ireless Proeedigs of te IEEE vol. 9 o. pp [4] D. Gesbert M. outouris R. eat C.-B. Cae ad. Salzer Siftig te MIMO paradigm IEEE Sig. Proes. Mag. vol. 4 o. 5 Sep [5] M. Costa Writig o dirty paper IEEE ras. Ifo. eory vol. 9pp May [6] G. Caire ad S. Samai O te aievable trougput of a multiatea Gaussia broadast ael IEEE ras. Iform.eory vol. 49 o. 7 pp Jul [7]. Yoo ad A. Goldsmit O te optimality of multiatea broadast sedulig usig zero-forig beamformig IEEE Joural o Seleted Areas i Commuiatios vol. 4 o. 3 pp Mar [8] M. Joam W. Utsik ad J. A. Utsik Liear trasmit proessig i MIMO ommuiatios systems IEEE Sig. Proes. Mag. vol. 53 o. 8 pp Aug [9]. Jidal W. Ree S. Visaat S. A. Jafar ad A. Goldsmit Sum poer iterative ater-fillig for multi-atea gaussia broadast aels IEEE ras. o Iformatio eory vol. 51 o. 4 pp April 005. ISS : Vol. 3 o. 4 Aug

7 Performae of Multiuser MIMO-OFDM dolik system it ZF-BF ad MMSE-BF liear preodig [10] C. B. Peel B. M. oald ad A. L. Sidleurst A vetor-perturbatio teique for ear-apaity multiatea multiuser ommuiatio-part I: ael iversio ad regularizatio IEEE ras. Commu. vol. 53 o. 1 pp Ja [11] D. se ad P. Visaat Fudametals of ireless ommuiatios. Cambridge Uiversity Press 005. [1] P. Visaat D. se ad R. Laroia Opportuisti beamformig usig dumb ateas IEEE ras. o If. eory vol. 48 o. 6 Ju. 00. [13] J. ermoal L. Sumaer. Pederse P. Mogese ad F. Frederikse A stoasti MIMO radio ael model it experimetal validatio IEEE JSAC vol. 0 o. 6 pp Aug 00. ISS : Vol. 3 o. 4 Aug