PERFORMANCE EVALUATION OF C-BLAST MIMO SYSTEMS USING MMSE DETECTION ALGORITHM

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1 53 EFOACE EVALUATIO OF C-BLAST IO SYSTES USIG SE DETECTIO ALGOITH urhayat * * hyscs Departemet, FIA, Surabaya State Uversty Jl. Kettag Surabaya 603 d@grad.ts.ac.d ABSTACT C-BLAST system s detecto algorthm of the IO (ultple-iput ultple Output systems that s desged to acheve good multplexg ga. I the C-BLAST systems, every atea trasmts has ts ow depedetly coded wth power cotrol. I ths paper we use SE (mum ea Square Error detecto to acheve the performace of error rate for the C-BLAST systems. Smulato results show that the C-BLAST system wth the proposed TA (trasmt ower Allocato scheme ad wth SE detecto algorthm ca provde a sgfcat reducto the ucoded BE compared wth the covetoal V- BLAST system. I ths system we also aalze the performace of C-BLAST by combato varous umber of ateas, detecto orderg, C-BLAST correlated chael ad C-BLAST wth mperfect chael estmato. Key Word: C-BLAST, Trasmt ower Allocato,,SE, Chael estmato.. ITODUCTIO ultple Iput ultple Output (IO techques ca provde sgfcat performace ehacemets wreless commucato systems. Vertcal-Bell Laboratores Layered Space Tme(V- BLAST s techque of data processg IO to get the trasmsso sgal that has smple codg ad smple detecto structure compared wth the system Dagoal- Bell Laboratores Layered Space Tme (D-BLAST. I ths letter to mprove the trasmsso qualty of V-BLAST we use trasmt power allocato to mmze the error rate ad t eed feed bac chael formato. That system called C-BLAST(Close loop system. It s dfferet by covesoal V-BLAST thet use uform power each atea. I ths system trasmt power allocato deped o chael codto[]. ODEL, AALYSIS, DESIG, AD ILEETATIO I IO systems there are trasmt ateas ad receve ateas. I the trasmtter, a data stream s demultplexed to depedet substreams, ad the each substream s ecoded to trasmt symbols usg same modulato scheme. I ths system we use 4 QA. Based o the feedbac formato the trasmt power s the assged to the data smbol x ad the symbol s trasmted through the -th trasmt atea. I the recever the C-BLAST detector estmated the receve sgal from atea trasmt ad determes S ad trasmt power. The basebad equvalet of the dmetoal receved sgal vector may be expressed as Y H x. ( H s the IO chael model. The IO chael model s the quas-statc, frequecy o-selectve, aylegh fadg chael model. Uder the quas-statc assumto,the chael rema costat over the legth of frame, chagg depedetly betwee cocecutve frames. The chael udergoes frequecy o selectve fadg whw the coherece badwdth of the chael s large compared to the badwdth of the trasmtted sgal. I equato ( x [x x. a ] T deotes the trasmt symbol vector wth each elemet havg the ut average power, ad H deotes the x chal matrx, whose elemet h m at the th row ad m th colum s the chael ga from the mth trasmt atea to the th receve atea, H matrx are Gaussa radom varabels. The elemets of the -dmetoal ose vector [... ] T are assumed to be..d. complex Gassa radom varabels wth zero mea ad varace of. It s assumed that the chael estmato at the recever s perfect.the trasmt for trasmt ateas power (,,... wth the total power costrat ad seds the power to the trasmtter through a error free feedbac chael. I C-BLAST system, A dagoal matrx dag (,,... represet the trasmt power. I V-BLAST wthout feedbac for all ad thus s detty matrx I. Ths pcture s the C-BLAST system wth ISS ICTS

2 54 4 th Iteratoal Coferece Iformato & Commucato Techology ad System feedbac of chaelm formato by power allocato the tramtter[]. Iput Data DEULTI LEXE X X X OWE ALLOCATIO T X T X T X ch Scatterg Chael H X X X Feedbac Chael Fgure. IO C-BLAST system y y y V-BLAST DETEC TO ower calculato. Detecto algorthm for Zero Forcg (ZF ullg[] Isalzato: (a y y (b G (H - H (c argm <H > (d ecurto w <G > (e z w y x Q(z (g y y - x y - G ([H] [H] x [H] argm <([H] > {.. } (h ( X X X (f ( ( where (. deotes oore-erose pseudo verse,. s the orm of the vector, <.> s the th row of matrx ad, [.] the th colum of a matrx, ad [.] s a matrx formed by zerog the,,,.. Q(.s the slcg operator assocated wth a modulato scheme, ad x s the estmated value of x. symbol dex detected at the th stage, detecto order s determed based o the sgal-to-terferece-plus-ose rato (SI of trasmt symbols wth I The ullg vector (e ca be rewrtte as: w < G > < ([ H ] > / v / the performace of each stage, as the SI of the decso statstc z. The terferece compoet s zero for zero-forcg (ZF, but ozero for mmum mea-square error (SE. the postdetecto SI ρ f or the th symbol ca be calculated as ρ (3 w v ρ adalah varabel radom, v adalah bobot vetor da adalah daya trasms utu smbol e-. erformas rata-rata dar tgat detes e- dtetua dar ρ. v... Detecto algorthm for SE ullg Ule the ZF ullg that removes the terferece compoets completely but results ose ehacemet, the SE ullg compromses terferece suppresso ad ose ehacemet, such that the mea-square error (SE betwee the trasmt symbol ad estmate of the recever s mmzed.. I the case of SE, (c da ( should be chaged as : G (H H ((H(H H I - (4 G ([H] H (([H] ([H] H [I ] - where (. H deotes the cougate traspose.. ( G H arg max G whre ( G H ( G [ H ] arg max {,..., } G ( G G G I [ H ] (5 s the ullg matrx, I the post detecto SI for the th symbol s[]: ( w [ H] (6 ρ w w [ H] (.3. ower feedbac wth the perfect chael estmato Trasmt power allocato ca be derved by post detecto S from chael matrx. ote that I Zero Forcg ad SE detecto algorthm ZF ths detecto order s determed based o the sgal-to-terferece-plus-ose rato (SI of trasmt symbols wth I tal codto where the vector v ([ H ] > correspods to the ullg vector of the th detecto stage, whe I. The postdetecto SI, whch determes ISS ICTS

3 089 erformace Evaluato of C-BLAST IO Systems Usg SE Detecto Algorthm-urhayat ( ( l3.5 λ (,,3..., (8 dmaa v v l ( v H l l ( v H.6 ( λ exp l l ZF SE ( 3.5λ( (9 (0 Ths power allocato ca be dfferet each sub chael deped o chael codto. Ad the total power s as much as trasmt ateas. Ths power wll dfferet for the ew chael matrx,for ew burst. []..7. C-BLAST to chael correlato I ths system we use correlato coefse cosdered by the early research [4] For the spacg betwee ateas λ Tx x,00 0,68 0,4,00 0,68 0,68,00 0,4 0,68 0,09,00 For the ear spacg for the ateas of 5λ Tx x,00 0,09 0,0,00 0,09 0,09,00 For the ear spacg atea s 7λ Tx x,00 0,3 0,0 0,00 0,0 0,09,00 0,3 0,0 0,00,00 0,3 0,0 0,3,00 0,3 0,0 0,3,00 To geerate chael correlato as flowchart fg. s[5].4. C-BLAST system by detecto orderg System wth detecto orderg s system by order of detecto s decded by S, trasmt atea wth largest S s selected each terato. System wthout orderg s order of detecto s selected radomly ad wthout cosder S post detecto,,3,..,-, arg max G ( G H ( G H (.5. C-BLAST wth varato of modulato level. I ths system we use BSK, 4 QA, ad 6 QA modulato, System that use 4 trasmt ateas ad 4 recever ateas [3] [6]..6. C-BLAST wth varaty of dmeto ateas Atea trasmt ad recever has dmeso x, 4x4 da 4x8. I ths system we use 4 QA level modulato. S erala roecer [ IO ] [A] BS [a] I.I.D Spetrum dopler Fg 3. Flowchart for geerate chael correlato cooefse.8. power feedbac mperfect chael estmato I C-BLAST system by mperfect chael estmato we use Least Square methode by sedg trag symbol ad the legth of trag symbol s L [].I ths paper we use equatos : ISS ICTS

COCLUSIO I ths paper we have show that C-BLAST wth SE detecto have better performace compared wth V-BLAST ZF.

4 56 4 th Iteratoal Coferece Iformato & Commucato Techology ad System Y X ( Y Y ( HX V X H ( X H ( HX V ( X X Where s the receve sgal. X s trag sgal., V AWG ose matrx, H s chael matrx of C-BLAST mperfect chael estmato by varous of trag symbols. 4. COCLUSIO I ths paper we have show that C-BLAST wth SE detecto have better performace compared wth V-BLAST ZF. We have also derved the performace of C-BLAST SE wth detecto orderg ad by creasg the umber of ateas. I ths paper we also compare the performace of C-BLAST chael wth perfect ad mperfect estmato, varous level modulato, ad the correlato chael. EFEECE Fgure : Trag symbols mperfect chael formato 3. ESULT From the fg 5. we ca see that V-BLAST wth SE detecto ca acheve performace tha V-BLAST detecto by Zero Forcg detecto. I the ZF the system oly waste terfereto compoet wthout cosder ose. I the SE detecto t happe compromze betwee ose ad terferece. I BE 0-3 t ca be creasg S as 3dB C-BLAST ad V- BLAST wth SE detecto algorthm. I fg 6 shows that C-BLAST wth perfect chael estmato has better performace error rate compare wth C-BLAST system by mperfect chael estmato. Loger trag sysmbol t mae the performace of mperfect chael estmato closer to perfect chael estmato. But loger trag symbol ca reduce the spectral efcecy of badwdth ad more complcated. I fg 7 by detecto orderg ad wth trasmt power allocato has better performace error rate compare wth C-BLAST wthout detecto orderg. I fg 6. deote C-BLAST system has better performace of error rate where dmeto of ateas s, because IO system (, the orthogoal chael s recever, So that more of recever the system wll be good. I fg 8 we ca see that the smaller modulato level t mae the performace of error rate s better. It cause of the smaller costellato ad t mae lttle error rate ca be happe. I fg 9. deote the performace chael correlato. I small chael correlato the performace of error rate s better compare wth the system wth strogest chael correlato.it mea the C-BLAST system s better appled chael correlato. I fg 0 ad shows the performace [] Seug Hoo am, Kwag Bo Lee (004, Trasmt ower Alocato For Exteded V-BLAST System, IEEE, Vol 5, o 7. [] T.L.arzetta(999, BLAST:Trag:Est mato Chael Characterstcs for Hgh Capcty Space Tme Wreless, roc, Aual Allerto Cofereces o Commucato, Cotrol ad Computg, otcello [3] Joh G. roas, asoud Saleh (000, Cotemporary Commucato System Usg ATLAB, Broos/Cole [4] yoma ramata, Aalsa Uu Kera Sstem V-BLAST pada aal flat fadg yag berorelas, Tess Jurusa Te Eletro FTI - ITS, Jauar 003. [5] Je hlppe Kermoal, Lauret Schumacher, A Stochastc IO ado Chael odel Wth Expermetal Valdato, IEEE Joural, Vol 0, o.6, [6] Goldsmth, A. J, Soo Ghee Chua, October (997, Varable ate Varable ower QA for Fadg Chaels. IEEE Tras. Comm., vol.45, o. 0. Fg 4. C-BLAST ad V-BLAST wth SE ad ZF detecto algorthm ISS ICTS

089 erformace Evaluato of C-BLAST IO Systems Usg SE

C-BLAST wth orderg Fg.9. C-BLAST correlato chael Fg 7.

5 089 erformace Evaluato of C-BLAST IO Systems Usg SE Detecto Algorthm-urhayat 57 Fg 5. C-BLAST SE detecto perfect ad mperfect chael estmato Fg 8. C-BLAST wth varous of modulato level Fg 6. C-BLAST wth orderg Fg.9. C-BLAST correlato chael Fg 7. C-BLAST Wth varous dmeto ateas Fg.0. C-BLAST perfect ad mperfect chael estmato ISS ICTS

6 58 4 th Iteratoal Coferece Iformato & Commucato Techology ad System Fg.. C-BLAST wth varous trag symbols ISS ICTS

Functions of Random Variables

Functions of Random Variables Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,