Semi-blind Channel Estimation for MIMO-OFDM Systems Based on Received Signal Reconstruction Weijia Cui 1, You Zhou 2, a 3, b,*

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1 Ieaial Cfeece Aumai, Mechaical Cl ad Cmuaial Egieeig (AMCCE 15) Semi-blid Chael Eimai f MIMO-OFDM Syem Baed Receied Sigal Recuci Weijia Cui 1, Yu Zhu, a 3, b,*, Sg Che 1 Ifmai Sciece ad echlgy Iiue, Zhegzhu, 451, Chia Ifmai Sciece ad echlgy Iiue, Zhegzhu, 451, Chia 3 Ifmai Sciece ad echlgy Iiue, Zhegzhu, 451, Chia a 39734@qq.cm, b wielemac@16.cm,*cedig auh Keywd: MIMO-OFDM; Blid chael eimai; Subace; Sigal ecuci; QR decmii; Gam-Schmid hgalizai; Abac. Blid chael eimai f MIMO-OFDM yem wa dicued, ad a ubace baed blid chael eimai algihm by e-cucig he eceied igal ad i imlified e wee ed. he algihm chaged he chael maix f he afe fuci i a blck eliz high maix exliig OFDM cyclic efix, ad he chael eimai chaaceiic equai wa baied wih he hgaliy bewee he igal ubace ad he ie ubace f he ecuced igal. I de elimiae he ifluece f iual caie, he igula alue decmii f he equiale ami igal wa imed. he imlified algihm exlied a QR decmii ad Gam-Schmid hgalizai ce aimig a educig he cmlexiy f baiig he ie ubace. Simulai eul illuae he efmace f he ed algihm ia umeical exeime cmaed wih he he e, ad i ieiie eeimae f he ue chael de. Iduci Chael eimai he e-cdii f chee deeci i MIMO-OFDM yem. adiial mehd i ie il i he amiig daa [1]. I de ime fequecy ecum efficiecy, blid chael eimai ha becme h ic i ece yea []~[7]. Amg he blid algihm, ubace baed algihm eceie gea aei becaue f i bee accuacy efmace [8]. A OFDM ubace algihm exliig CP i ed i [9]. Alhugh wih a gd accuacy efmace, i i alicable yem wih exiece f iual ub-caie. adiial OFDM ubace baed algihm i exaded MIMO-OFDM yem i [1] wih lw cegece ae. he ae ay aei fa emi-blid chael eimai i MIMO-OFDM yem wih exiece f iual ub-caie. Lea fm [9], a emi-blid algihm baed eceied igal ecuci ad i imlified e ae ed. Sme ai ae illuaed a fllw: (), () ad () ae aii, cjugae ad cjugae ae eeciely. I i ui maix. E[] i aiical aeage. x [1: k] i he f k eleme i x. X [:, k] ad X [ k,:] ae he k -h clum ad k -h w f X. X [: i jm, : ] i he ub-maix f X fm w i j ad clum m. a( X ) ad ak( X ) ae he clum ace f maix X ad i ak eeciely. ec( X) i ecizai f maix X. i l m. i Kecke duc. Defie w ex( j / ). C (, σ ) i cmlex Gauia diibui. MIMO-OFDM Syem Mdel Aume ha he umbe f amiig ad eceiig aea i MIMO-OFDM yem ae ad eeciely wih. hee ae ub-caie wih D daa ub-caie ad ( D) iual ub-caie. he idice f daa ub-caie ae deed by k k + D 1. CP ad OFDM legh ae P ad Q= + P 15. he auh - Publihed by Alai Pe 189

2 eeciely. Daa be amied i x ( k, ) = [ x1( k, ), x( k, ),..., x ( k, )], whee xi ( k, ) i he daa he k -h ub-caie f aea i i -h OFDM ymbl. Accdigly, he al -h daa be mdulaed ca be deed by x = [ x( k, ), x( k, + 1),..., x ( k, + D) ]. i he mdulaed daa afe iei f CP. Defie ( k, ) = [ ( k, ), ( k, ),..., ( k, )], whee ( k, ) he k -h daa afe IFF aea i. We hae 1 i = [ (, P),..., (, ), (,), (,1),..., (, ) ]. Defie: 1 ki ( k+ 1) i ( k+ D ( ) [,,..., 1) i F i = w w w ] F= [ F( P),..., F( ), F(), F(1),..., F( ) ] Γ = F I S we hae = Γx. Chael mdel bewee amiig ad eceiig aea i deed by FIR file, ad L i maximum chael de. he l -h chael cefficie i deed by h11() l h1() l h1 () l h1() l h() l h () l h() l = () h1() l h () () l h l We ake a he eceied igal. Defie ( k, ) = [ 1( k, ), ( k, ),..., ( k, )], whee j ( k, ) i he k -h eceied daa eceiig aea j i -h ymbl. Accdigly, we. Aume ha L P hae = [ (,),..., (,1),..., (, + P) ], he chael be eimaed i deed by h= [ h(), h(1),..., h ( P)]. Whei > L, h() i =. Defie h() h( P) h(1) =, 1 = h( P) h( P) h( P) h() (3) we hae = + 1 +, whee ~ C (, σ I ) i he cmlex whie Guaia ie. Q (1) Subace Algihm baed Receied Sigal Recuci A. Algihm Deduci Deide, ad i 3 ub-ec: = [ 1,, 3], = [ 1,, 3], = [ 1,, 3]. F ad, he dimei f he 1 ad he 3 d ub-ec i P 1, while f, he dimei i P 1. Defie 1 ( ) = [ ( ), ( )3, 1], ( ) = [ 1,, 3], ad ecuc he eceied igal accdig ( ) = 1( ) ( ). Exliig CP chaaceiic, we hae ( ) = ( ) + ( ), whee, ( ) ad ( ) ae deed a fllw: h() ( ) 1 ( ) 1 = h( P) h(), ( ) =, ( ) = ( )3 (4) ( )3 1 3 h( P) 1891

3 Aaely, i a Q ak h () =. R = E[ ( ) ( ) ], R = E[()()] ad R = E[ ( ) ( ) ] ae caiace maixe f ( ), ( ) ad ( ) eeciely. Aume ha he ie ad amiig igal ae muual ideede wih each he, we hae R = R + R (5) full clum ak eliz high maix wih ( ) Defie F1 = [ F(), F(1),..., F( ) ] F = [ F( P),..., F( ), F(), F(1),..., F( P) ] We hae ( ) = ( F I ) x ( F I ) x 1 Aume ha all he amiig daa i muual ideede, we hae Rx = E[ xx ] = I D, he R = E[()()] = ( FF + FF ) I D SVD R 1 1 R = AΛ A (9) Whee Λ i he diagal maix cmed by -ze eigealue f R, A i he cedig eigeec. he algihm i alicable yem wih exiece f iual ub-caie wih hi decmii. A i a fixed maix wih he ame, P ad, which mea ly a mall amu f addiial calculai i equied. Mee, IP I P R = E[ ( ) ( ) ] = σ I( P) (1) IP I P I ca be ee ha ( ) i cl ie. Aaely, R i a iie defiie maix which ca be whieed hugh Chleky decmii R = σ ww, whee w i a lwe iagula maix wih iie diagal eleme. Al, w i a fixed maix wih he ame, P ad, which mea eal-ime calculai f he maix i equied. I ca be baied ha R = w Rw = ( w A) Λ σ( w A) + σ IQ M (11) Λ i a full ak maix, ad ak( w A) = ak( A). Wih cai ak( h ()) =, eigealue decme equai (11) R = Λ + (1) Whee he dimei f eeciely. ad w A = Λ, ad ae igal ad ie ace f ae D D R (7) (8) (6), Q D ad Q ( Q D) eeciely. Al (13) he abe equai i he chaaceiic equai f he chael eimai. Defie = [ ()[:, i], (1)[:, i],..., ( P)[:, i] ],1 i = [ h, h,..., h ] ad h = ec( ). he hi h h h, 1 diffeece bewee h ad he acual chael i a ieible ca maix which ca be baied hugh iei f mall amu f il [1]. B. Algihm Decii R i eimaed by Q D C( ) = Vˆ [:, k] A k = 1 b ˆ = ( ( ) ( ) )/ = R, ad i al a eimaed maix. Defie c fuci wih Vˆ = w b ˆ ˆ. Accdig equai(13), eimaed Ĥ i he alue which 189

4 ca miimize C( ). Equally Diide V ˆ [:, k] i Q egme ad deed ( ) ( ) ( ) by ˆ ˆ k [:, ] [( ),( ˆ k ),...,( ˆ k V k = V V V ) ]. Defie he fllwig maix: κ k 1 Q ˆ ( k) ˆ ( k) ˆ ( k) V V1 V Q P ˆ ( k) ˆ ( k) ˆ ( k) V1 V VQ P = ˆ ( k) ˆ ( k) ˆ ( k) VP VP+ 1 VQ 1 Q D ( k ) ( ) k k = 1 Θ = κ I AA κ I w, C( ) ca be ewie a C( ) = h Θh.I de aid all ze lui, add a limiai f h i = 1. Defie h h h ˆ = ag mi h Θh, whee he eimaed h i he liea, he eimai ca be accmlihed by ( ) hi = 1 cmbiai f eigeec cedig he miimum eigealue. C. Simlified Algihm Calculae he ie ace i a ieaie mae. If Φ ( ) i a ca maix, we hae [13] ( ) = Φ( ) Q( 1), ( ) = Q( ) R ( ) (15) Fially Q( ) will cege he eigeec cedig he mai eigealue f Φ ( ) R i accmlihed a fllw: R( ) = αr( 1) + (1 α) w ( ) ( ) w Whee α i he fgeig fac. Subiue Φ ( ) i equai (15) wih R ( ) aximai[14] ( w ) ( ) α ( 1) + (1 α) w ( ) Q ( ) ( ) (14). he udaig f (16), we hae he fllwig (17) Ad Q ( ) will fially cege. he cmlexiy i abu O( QD ) [14]. ca be calculaed by Schmid hgalizai exliig he hgaliy bewee ad. Make ( 1) hgal Q ( ) ia Schimid hgalizai, ad he ceed ec will be eaed a he ie ace f he cue ieai. Fially ( ) will cege. he cmlexiy i abuo( Q( Q D)). Simulai ad Aalyi le hewie ed, we che =, =, = 16, D = 16, P = 3, L = 3, b = 1, l hij ()~ l C (, σ l ) wih σ /1 l = ae, l =,..., L, a i we malizai fac[11]. Simulai 1: Pefmace f he ed algihm ad algihm i [1] i cmaed i Fig.1 chig J = i [1]. he accuacy ad cegece efmace ae hw i (a) ad (b) eeciely. he ed algihm ha bee efmace bh way. 1893

5 1 RMSE db 3dB 1-3 4dB b (a) Accuacy efmace (b) Cegece efmace Fig.1 Pefmace camai Simulai : he accuacy efmace wih diffee iual ub-caie i hw i Fig.. We ca ee ha he ed algihm ca wk well wih diffee iual ub-caie. Simulai 3: he accuacy efmace f he ed algihm wih diffee eceiig aea i hw i Fig.3. he efmace ime gadually wih he iceae f eceiig aea. he ea i ha he umbe f he ie ace bai iceae wih he iceaig f eceiig aea, which mea a bee ai-iefeece abiliy f he ed algihm D= D=1 D= = =3 =4 RMSE 1 - RMSE SR(dB) SR(dB) Fig. Pefmace wih diffee Fig.3 Pefmace wih diffee iual ubcaie eceiig aea Simulai 4: he accuacy efmace wih diffee CP i hw i Fig. 4. We ake he CP legh a chael de, he umbe f chael cefficie be eimaed iceae wih he iceaig f CP. Alhugh he efmace degade lighly wih lg CP, he algihm ill wk well, which mea i i bu chael de eeimai. Simulai 5: he accuacy efmace f imlified algihm i hw i Fig. 5, whee SR=4 db, J =. Alhugh he imlified algihm accuacy deceae lighly, i ill ha bee efmace cmaed wih algihm i [1]. he cmlexiy f algihm i [1], SVD ad he imlified e ae O (343), O (5487) ad O (584) eeciely. 1894

6 1 1-1 P=3 P=4 P=8 RMSE SR(dB) Fig.4 Pefmace wih diffee CP Fig.5 Pefmace f imlified algihm Cclui Exliig he chaaceiic f CP, he ed algihm ecuc he eceied igal ad chage he chael maix i eliz high maix. Alhugh addiial ie whieig ad SVD decmii ae equied, hey ae all yem aamee elaed, which mea eal-ime calculai i eeded. he imlified algihm ca effeciely educe he cmlexiy hugh a ieaie mehd. Simulai hw ha he ed algihm ha bee accuacy ad cegece efmace, ad i eiie chael de. Refeece [1] Lae, M.D.. Pefmace bud f MIMO-OFDM chael eimai [J]. IEEE aaci Sigal Pceig, 9, 57(5): [] Miyajima,., Zhi Dig. Subcaie ullig algihm f chael heig i ulik OFDMA yem [J]. IEEE aaci Sigal Pceig, 1, 6(5): [3] Feg Wa, Wei-Pig Zhu, Swamy, M..S.. Semiblid ae chael eimai f MIMO- OFDM yem [J]. IEEE aaci Vehicula echlgy, 11, 6(6): [4] Al-affui,.Y., Dahma, A.A., Shail, M.S., e al.. Lw-cmlexiy blid equalizai f OFDM yem wih geeal cellai [J]. IEEE aaci Sigal Pceig, 1, 6(1): [5] Al-Bayai, A.K.S.. Subace-baed blid chael eimai i ealy auaed dwlik mulicaie cde diii mulile acce yem [J]. IE Cmmuicai, 1, 6(4): [6] Zha Zhi-ji, Wag Bai-chua, Shag Ju-a, e al.. A eimai algihm f MIMO-OFDM chael baed RS [J]. Jual f Elecic & Ifmai echlgy, 33(): [7] Feg Wa, Wei-Pig Zhu, M.. S. Swamy. Semiblid ae chael eimai f MIMO- OFDM yem [J]. IEEE aaci Vehicula echlgy, 11, 6(6): [8] Zhag Lig, Zhag Xia-da. A eiew f blid chael eimai algihm f MIMO- OFDM yem [J]. ACA Elecic Siica, 7, 35(6A): 1-6. [9] uag Xue-ju. Blid chael eimai algihm i OFDM yem [D]. Shaghai Jiag ieiy,

7 [1] Chagyg Shi, Rbe W. eah, J., e al.. Blid chael eimai f MIMO-OFDM yem [J]. IEEE aaci Vehicula echlgy, 7, 56(): [11] Wei-Chieh uag, Chu-ie Pa, Chih-Peg Li, e al.. Subace-baed emi-blid chael eimai i ulik OFDMA yem [J]. IEEE aaci Badcaig, 1, 56(1): [1] Y. Zeg,. S. g. A emi-blid chael eimai mehd f muliue muliaea OFDM yem [J]. IEEE aaci Sigal Pceig, 4, 5(5): [13] G.. Glub, C. F. Va La. Maix Cmuai, Secd edii [M]. Balime, MD: Jh ki ieiy Pe, [14] Pee Sbach. Lw-Rak adaie file [J]. IEEE aaci Sigal Pceig, 1996, 44(1):