Diversity for Wireless Communications

Transcription

1 Dverst for Wreless Commucatos For AWG caels, te probablt of error decas epoetall wt SR c.f. Q. fucto P e Q SR SR e For fadg caels, te deca s muc slower. For Raleg-fadg caels cael coeffcet s comple Gaussa=>ampltude s Raleg te probablt of error decas versel wt SR P e K SR

2 Proof

3 Proof 3

4 Sce power s a lmted ad precous resource wreless commucatos, t s udesrable to crease trasmt power to compesate for fadg power cotrol eve f cael s ow at trasmtter wc s ot realstc. Oter problems wt creasg te power are creased terferece to oter users ad creased pea to average rato wc would crease amplfer bac off to operate te lear rego

5 A alteratve more desrable soluto to ts fadg problem s troug dverst trasmsso/recepto were we sed te same formato over D depedet caels wc are ulel to all fade togeter Ts dverst tecque reduces probablt of error to P e SR e D.As D we aceve epoetal deca wt SR same as Gaussa. I practce, eve D=-4 results sgfcat performace mprovemet

6 Dverst ca be aceved several forms cludg Tme Dverst: Trasmt same formato smbols at tmes separated b more ta te coerece tme of te cael=> same smbols wll eperece depedet fadg=> temporal dverst Frequec Dverst: est were ee we trasmt ta t same fo over frequec carrers separated b more ta te coerece badwdt of te cael

7 Bot tme ad frequec dverstes are aceved at te epese of rate loss 3Spatal Dverst : trasmt or receve formato to/from depedet ateas separated b more ta te coerece dstace of te cael. Does t volve rate loss but addtoal ateas & RF cas. Icludes polarzato dverstt To esure depedece, ateas are separated b more ta alf wavelegt at termal ad b more ta wavelegts at base stato

8 Remar: Multple trasmt ateas ca be used to Icrease spatal dverst of sstems b sedg te same formato stream over depedet spatal caels Space-Tme Codg Or crease rate of sstem b spatall multpleg depedet formato streams BLAST 3Aceve a sutable tradeoff of rate ad dverstt

9 Sgle Iput Multple Output g p p p Receve DverstSIMO M r r r r M M M r M to mamze SR at recever => use matced r r r M M M flter also ow as mamal rato comber

10 Sgle Iput Multple Output z r... M dverst order M r ~ Cael assumed perfectl ow at recever REMARK: Receve dverst s more sutable for upl moble to base stato were we ca mplemet multple ateas more easl ta at user termal

11 Spato-Temporal Equalzato To mtgate sgal fadg effects o wreless caels, multple receve ateas are used for dverst ad ter outputs are combed Select sgal wt gest SR selecto dverst Sum wt equal wegtg equal-ga combg Sum wt wegtg proportoal to SR mamal- rato combg O frequec-selectve caels, atea outputs are fltered b tapped-dela-les TDL ad ter outputs are combed b tapped-dela-les TDL ad ter outputs are combed. TDL FIR wegts optmzed to mmze MSE

12 Spato-Temporal Equalzato H H I I w w - Dec ˆ H M r M r M r M r w b I M r j j j z I : j,,..., r Sgle-Iput Multple-Output SIMO Cael M were s o. of receve ateas

13 bloc Ts structure ca be geeralzed to perform mult-user detecto usg full cross-coupled mult-put mult-output feedforward & feedbac flters 3

14 Trasmt Dverst MISO I cellular sstems, dowl from base stato to termal s te bottleec Iteret traffc asmmetr To mprove dowl performace, trasmt same formato usg multple ateas at base stato Trasmt Dverst Trasmt dverst eeps user termals cost effectve small sze ad low power Trasmt ateas are separated wde eoug to esure depedet fadg over multple trasmsso caels Sce o cael formato s assumed at trasmtter, total trasmt power dvded equall amog ateas Smplest form of spatal trasmt dverst s dela dverst dverst ga ol. Advaced forms ow as space-tme codg aceve codg & dverst gas 4

15 Dela Dverst over Flat-Fadg Caels Here, we assume cael s OT ow at trasmtter Dela Dverst Sceme D D D D D D D D D Y Dela dverst creates a artfcal ISI cael tat ca be equalzed e.g. usg D Vterb algortm to get performace mprovemet secod-orderorder dverst

16 Dela Dverst over ISI Caels D D D D Preflter D L D D MLSE Equalzer Aceves dverst b creatg cotrolled ISI Bacward compatble wt estg SISO stadards ad user termals Equalzer sees a equvalet SISO cael wt more taps spatal dverst trasformed to temporal dverst D D D D D D L D D D D D How to coose L? D D D eq 6

17 Te Alamout Sceme Code over two cosecutve b l d l - smbols ad assume cael s fed over tese smbols * * H Aceves dverst order H le dela dverst but at lower decodg complet

18 Alamout Sceme Cot d REMARK: Te equvalet cael matr s ortogoal, ece matced flter s ML optmal H H HH I Performace of Trasmt/Receve atea dverst s degraded te presece of atea a correlato 3 Te Alamout sceme falls uder te class of space-tme bloc codg STBC scemes

19 Alamout Sceme Decodg: Matced flter s optmal ere! z H H H H ~ ~ d order dverst ~ s stll Gaussa, zero mea ad as varace SR mproved b factor

20 Alamout Sceme Advatages of Alamout Sceme Mamumdverst d order Rate formato smbols tme slots=> full- rateuder restrcto of o costellato epaso Ope loop o eed for cael owledge at T Low decodg complet lear Drawbac: more o ts later Caot be eteded to more ta trasmt ateas for comple sgal costellatos wtout rate loss.e. rate < or sacrfcg smple lear decodg complet or costellato epaso

21 Te Alamout Sceme for ISI Caels For ISI Caels, te Alamout sceme sould be mplemeted at a bloc ot smbol level as flat-fadgfadg case order to realze multpat dverst addto to te d order spatal dverst. Tere are at least 3 was of dog ts te tme doma called tme-reversal spacetme bloc codg TR-STBC or te frequec- doma usg sgle-carrer FDE or usg multcarrer OFDM trasmsso. I te sequel, sgle carrer FDE-STBC wll be descrbed

22 Te Alamout SC-FDE Sceme for ISI Caels CP CP Remove CP FFT ˆ ˆ SBS IFFT FDE

23 ECODIG RULE Deote te t smbol of te t trasmtted bloc of legt from atea "" b were deotes,.te te modulo dl - for operato. Tag te DFT of te put blocs, we get tme de,,.. -,,4,... wc s m m m m for frequec b m te Alamout sceme at te bloc level.,,.. -,,4,...

24 Iput-Output Relatosp p p p z H H j j j j j j j j cclc pref due to te use of crculat matrces are ad H H were cclc pref due to te use of :dagoal matr : FFT Q Q Q H Q Q H j j j j g Q Q

25 Recever Operatos p FFT : j j j j j j j Z Q Y Z Y blocs : Processg pars of Z - Z Y - Y Y cosecutve blocs matrces are assumed fed over were te cael

26 Recever Operatos Z ~ ~ Appl space tme matced flter 3 Y f f l d Z ~Z ~ ~ Y Y Y Y blocs are decoupled te two formato ow,. to ortogoalt of due : Z ~ ~ ~, : Z ~ ~ Y Y wc ca be equalzed as SISO FDE -STBC, : Z Y : Z ~ ~ Y ~ b s frequec m m m m m

27 3 MIMO Case B sedg depedet formato streams from multple trasmt ateas ad detectg tem at recever usg multple receve ateas acevable trougput o,we crease Assumptos: FIR Cael from t trasmt atea to j t receve atea wt memor j deoted b j

28 MIMO - Assumptos to use flterg based equalzato at recever to detect fo streams. Groupg te Y were H ad m cael H m m m ma, j, j m m outputs, m m we ave

29 MIMO - Assumptos p Over a bloc of f output smbols Y H H H H H f f f f f f f Y Y f f f f Y Bl T lt C l M d l Bloc Toepltz Cael Model

30 MIMO - DFE Cosder te case W, + + SBS ˆ W,, W, W + + SBS ˆ Feedforward Matr Flter +, e b, b, b Feedbac Matr Flter +, e b

31 MIMO Equalzato To crease te data rate over wreless ls, depedet formato streams are trasmtted ad receved smultaeousl usg multple trasmt & receve ateas. Ts spatal multpleg creates a MIMO cael MIMO caels also arse we multple l users eac equpped wt atea trasmt same cell ad same tme slot to a base stato equpped w/ multple l ateas but trasmt ateas are o colocated ts case! For MIMO case, MLSE Vterb equalzer requres M b states epoetal o. put ateas also! 3 All SISO equalzato scemes studed ts course ca be eteded to te MIMO case

32 3

33 33

34 MIMO - DFE Remars: Te MIMO DFE ca also be used for sgle atea mult-user commucatos Ts model ca also be used to develop a MIMO Cael sorteg sceme, e, for detals see,. Al-Dar, FIR Cael Sorteg Equalzers for MIMO ISI Caels, IEEE Tras. Comm. Feb

35 Matr Feed Forward Flter f W W W W Feedbac Flter Matr b b b b B B B - O I - B* O I b b B B B I,, were W w w,, were W w w

36 B, b,, b, b b Furtermore, defe B ~ O B were f -s te decso dela

37 Performace Aalss : Error Vector ~ * Y W B E f f : : Y W B E f f f f correlato matr : Error Auto - ee E E E R ~ ~ ~ ~ YY YY Y Y YY Y R R B W R R R B W B R R R R B YY R Y R B W

38 Usg te Ortogoalt Prcple ~ W * B * R R opt R ee p ~ B ~ B opt ~ * R R R B * R H * R H * R ~ B R ~ B ~ B 38

39 Performace Aalss Assumptos: Ol prevous decsos o all formato streams are avalable,.e. all 4 feedbac flters for te eample are strctl causal B I We ave te cove optmzato problem m tracer m traceb R B ee ~ B were I b ~ B ad C ~ * ~ * subject to B ~ * C I

40 It ca be sow tat te soluto s gve b ~ R R C Remar: B opt, C R C R ee m We stll eed to optmze decso dela. I fact, we ca allow for dfferet for eac formato stream but t would crease computatoal complet

41 Specal Case: FIR MIMO MMSE-LE Set B I ad B for,,... defe g I R ee,mmse-le,mimo R s : cose to g Equalzer Coeffcets : R g, mmze : W MMSE-LE f trace b of R R R ee g

42 Oter Specal Cases: SISO DFE/LE = = SIMO DFE/LE = 3MISO DFE/LE o = 4Zero-Forcg MIMO/MISO/SIMO SISO DFE/LE σ = Referece:.Al-Dar ad A.H.Saed Te Fte Legt Multple Iput Mult-Output MMSE-DFE, IEEE Tras o Sgal Processg, OCT