第40卷第3期上海交通大學(xué)學(xué)報(bào)Vol. 40 No. 32006年3月OURNAL OF SHANGHAI JIAOTONG UNIVERSITYMar.2006文章編號(hào):1006-2467(2006)03039405種適用于快速雙選衰落信道的時(shí)頻雙差分空時(shí)編碼正交頻分復(fù)用技術(shù)姜海寧,羅漢文,田繼鋒,宋文濤,徐友云(上海交通大學(xué)電子工程系,上海200240)摘要:為了保誣在快速雙選衰落信道下的有效數(shù)據(jù)傳輸,提岀了一種新穎的時(shí)頻雙差分空時(shí)編編碼正交頻分復(fù)用(OFDM)技術(shù).該技術(shù)通過分別在OFDM系統(tǒng)的子載波之間和OFDM符號(hào)之間引入差分空時(shí)編碼,實(shí)現(xiàn)了在系統(tǒng)時(shí)域和頻域上的差分調(diào)制,文中同時(shí)給出了相應(yīng)的準(zhǔn)最優(yōu)譯碼算法,并對(duì)系統(tǒng)性能進(jìn)行了分析和計(jì)算機(jī)仿真.結(jié)果表明,該技術(shù)在快速雙選衰落信道下能夠保持良好的誤碼率性能關(guān)鍵詞:差分空時(shí)編碼;雙選衰落;正交頻分復(fù)用中圖分類號(hào):TN914.3文獻(xiàn)標(biāo)識(shí)碼:ATime-Frequency Double Differential Space-Time Coded OFDMTechnique for Fast Doubly-Selective Fading ChannelJIANG Hai-ning, LUO Han-wen, TIAN Ji-feng, SONG Wen-tao, XU You-yun(Dept. of Electronic Eng, Shanghai Jiaotong Univ, Shanghai 200240, ChinAbstract: Doppler shift gives rise to time-selectivity, while multipath propagation introduces frequencyselectivity in mobile links. In order to guarantee the effect data transmission in fast time-selective andfrequency-selective(or doubly-selective) fading channel, a novel time-frequency double differential space-time coded OFDM technique was proposed. In this technique, double differential space-time coding isintroduced into both time domain and frequency domain in an OFDM system. A corresponding sub-optimaldecoding algorithm was also derived. The performance analysis and computer simulation prove therobustness of the new system to fast doubly-selective fading.Key words: differential space-time coding: doubly-selective fading; orthogonal frequency division modula-隨著移動(dòng)通信技術(shù)的發(fā)展,人們對(duì)無線信號(hào)傳的研究大都假設(shè)接收端完全已知信道信息(3.然而,輸?shù)乃俣群唾|(zhì)量提出了越來越高的要求.為了在獲信道容量的增加迫使天線數(shù)目遞增,移動(dòng)速度的提得更高信道容量的同時(shí)有效提高系統(tǒng)的性能增益,高也加強(qiáng)了信道參數(shù)反饋的及時(shí)性要求,這些將大人們提出了空時(shí)編碼技術(shù):3.目前,有關(guān)空時(shí)編碼大增加信道估計(jì)的難度和復(fù)雜度.為了解決這個(gè)問收稿日期:200504-16基金項(xiàng)目:國家自然科學(xué)基金資助項(xiàng)目(60272079);國家高技術(shù)研究發(fā)展計(jì)劃(863)項(xiàng)目(2003AA123310)作者簡介:姜海寧(1977),女,哈爾濱人,博士生,主要從事空時(shí)編碼技術(shù)及正交頻分復(fù)用技術(shù)的研究羅漢文(聯(lián)系人)男,教授,電話(Tel.):021-62932159; E-mail: heluo@sjtu,edu,cn第3姜海寧,等:一種適用于快速雙選衰落信道的時(shí)頻雙差分空時(shí)編碼正交頻分復(fù)用技術(shù)395題,文獻(xiàn)[4,5]中提出了差分空時(shí)編碼方案,該方案為了描述方便,定義N2個(gè)OFDM符號(hào)為一個(gè)無需知道信道信息也可達(dá)到信道容量OFDM符號(hào)塊,那么第k個(gè)子載波,第i個(gè)OFDM高速數(shù)據(jù)傳輸和多徑延遲將導(dǎo)致無線信道的頻符號(hào)塊對(duì)應(yīng)的 TF-DDST矩陣C(k,)可表示為率選擇性衰落,而載波頻率偏移和多普勒偏移將引起移動(dòng)信道的時(shí)間選擇性衰落.在移動(dòng)信道中,時(shí)間選擇性衰落和頻率選擇性衰落(或稱雙選衰落)往往c1(N2+N-1)…c(iN2+N-1)同時(shí)出現(xiàn).為了有效克服雙選衰落對(duì)系統(tǒng)性能的影響,文獻(xiàn)[6~8]中通過將差分空時(shí)編碼方案引入到(1)正交頻分復(fù)用(OFDM)系統(tǒng)中的每個(gè)子載波中,提第m個(gè)發(fā)送天線和第n個(gè)接收天線間的信道出了差分空時(shí)編碼OFDM( Differential Space-Time模型可以用帶抽頭的延遲線來模擬,其時(shí)域信道沖擊響應(yīng)為Coded OFDM. DST-OFDM)方案.但是,該方案只適用于慢速雙選衰落信道,當(dāng)信道多普勒擴(kuò)展較大(2)時(shí),該系統(tǒng)性能急劇惡化式中:6(·)表示 Kronecker函數(shù);L表示非零抽頭為了保證在快速雙選衰落信道下的有效數(shù)據(jù)傳數(shù);am(p;)表示第p個(gè)非零抽頭所對(duì)應(yīng)的衰落幅輸本文提出了一種新穎的時(shí)頻雙差分空時(shí)編碼度,其延遲為n/(N△∫),n為整數(shù),△為OFDMOFDM(Time-Frequency Double Differential Space-系統(tǒng)的子載波間隔.假設(shè)多普勒頻移在最大信道延Time Coded OFDM, TF-DDST-OFDM)技術(shù)在發(fā)遲時(shí)間內(nèi)保持不變,則am(p;t)可表示為送端,通過分別在OFDM系統(tǒng)的子載波之間和ama (p; t)=hm(P)exp(j2f, t) (3)OFDM符號(hào)之間引入差分空時(shí)編碼,實(shí)現(xiàn)了在系統(tǒng)式中:1≤p≤L;1≤m≤N將式(3)代入式(2),再時(shí)域和頻域上的差分調(diào)制.在接收端,為了保證較低的譯碼復(fù)雜度,采用了一種準(zhǔn)最優(yōu)的譯碼算法.本文對(duì)hn(τ;t)作離散傅里葉變換,得頻域信道響應(yīng)為對(duì)該技術(shù)的系統(tǒng)性能進(jìn)行了分析,推導(dǎo)出成對(duì)誤碼H-a (k: 0)=2am. (p: )exp(Na)概率,并據(jù)此給出了相應(yīng)的編碼設(shè)計(jì)準(zhǔn)則.與傳統(tǒng)的DST-OFDM技術(shù)相比,本文所提 TF-DDST-OFDMar m(p)exp(- j2rkmne)exp(j2x/)=技術(shù)在雙選衰落信道下更具魯棒性,而且能夠保證在快速雙選衰落信道下的有效數(shù)據(jù)傳輸Hm(k)exp(j2f,t)在接收端,對(duì)第n個(gè)接收天線上的時(shí)域信號(hào)作1系統(tǒng)模型離散傅里葉變換,所得第k個(gè)子載波,第i個(gè)OFDM時(shí)頻雙差分空時(shí)編碼OFDM系統(tǒng)框圖如圖1符號(hào)塊對(duì)應(yīng)的接收信號(hào)為X(k, i)=Aexp(j2xfiN,)X所示,該系統(tǒng)采用N個(gè)子載波,N,個(gè)發(fā)送天線和A C(k,i)H (k)+Z,(k,i) (5)N個(gè)接收天線.在發(fā)送端,每一個(gè)信息符號(hào)被映射成一個(gè)雙差分空時(shí)編碼矩陣,該矩陣在時(shí)域上持續(xù)式中:A為發(fā)送信號(hào)的幅度;個(gè)OFDM符號(hào),在頻域上占用一個(gè)子載波A.:=diag(1,exp(2xfn),…,exp(12πfn(N-1));Hn(k):=(H1,(k),莊2n(k),…,HNn(k)Z (k,i):=(z, (k,iN,)符號(hào)FDsTZn(k,i)為噪聲矩陣,服從CN(0,Na)分布編碼器2TF-DDST編譯碼方案2.1 TF-DDST編碼方案輸出TF-DDST矩陣C(k,)中各列保持正交,即符號(hào)| TF-DDSTH譯碼器C(k,i)C(k,D)=NIN(6)式中:1≥1,k=1,2,…N;IN為N階單位矩陣.為保證最大數(shù)據(jù)傳輸率,定義N2=N=N.為了將圖1時(shí)頻雙差分空時(shí)編碼OFDM系統(tǒng)框圖DDST同時(shí)引入時(shí)域和頻域, TF-DDST碼字矩陣須Fig. 1 Block diagram of TF-DDST-OFDM system滿足:上海交通大學(xué)學(xué)報(bào)第40卷C(k,i)=G(k,i)C(k,i-1)(7)重寫為式中:i≥2,k=1,2,…,N;生成矩陣G(k,i)滿足diag(X, 2-Zx2)(XH-ZH)G(k, i)= FCk,i)GCk-1,i)diag[(Xn1-Zn1)(X-2)]F(12)k=2,3,…,N;i≥1將式(12)中的噪聲量置于右端,可得G(k,1)=INk=1,2,…,Ndiag(X, 2 XH)= diag(X, XH)FH +N, (13)F(k,)為信息矩陣,它根據(jù)信息符號(hào)從酉矩陣群g2式中:中選擇生成,即N,=diaglX 2 ZH+Z,2XH+Z, ZHF(k, i)F(k, i)= IN(V F(k, i)E32) (8)Zn2H-Xn器-ZnX2.2準(zhǔn)最優(yōu) TF-DDST譯碼方案為便于描述,將式(13)重寫為根據(jù) TF-DDST編碼方案和式(5),第n個(gè)接收,(i)=r,(i-1)FH+N(14)天線在時(shí)頻域上相鄰4個(gè)接收矩陣可表示為式中:(i)= diag(X,XH)C(k-1,t-1)Hn(k-1)+Zn(k-1,i-1)diag(X, (k-1,i)XH(k,i))X k-1,i)= Aexp(2If,iN,)G(k-1, i)AXr(i-1)= diag(X, X)=C(k-1,-1)Hn(k-1)+Zn(k-1,)diag(X(k-1,-1)Xm(k,-1))(k, i-1)= Aexp(j2f (i-1)N,)A,X則N,個(gè)接收天線上的信號(hào)可表示為C(k,-1)Hn()+Zn(k,i-1)R(i)=R(i-1)(L.②F)+N(15)X, (k,i)= Aexp(inin)G(k, i)4, X式中:⑧表示 Kronecker乘積;C(k,i-1H(k)+Z (k,i(i)(9)R(i)考慮到最大似然譯碼算法較高的實(shí)現(xiàn)復(fù)雜度Tn(i)本文提出一種準(zhǔn)最優(yōu)譯碼方案為獲得準(zhǔn)最優(yōu)譯碼準(zhǔn)則,忽略噪聲矩陣N的二首先,消除式(9)中未知衰落成份Hn(k-1)和階量,所得噪聲矩陣仍記為N,服從復(fù)高斯分布,均Hn(k),可得值為零,協(xié)方差矩陣定義為X, (k-l, i)-Z(k-l,i)= exp(j2x N,)XG(k-1,)[X(k-1,i-1)一Zn(k-1,-1)]X, (k, i)-Z,(k, i)= exp(2I,N)G(k,i)x其中:[Xn(k,-1)一Zn(k,i-1)]En= No diag(X, XM +X,2 XM2+ XmX.3+ XMX)(10)因?yàn)镹服從復(fù)高斯分布,所以R(i的條件概率可表然后,通過外積運(yùn)算消除多普勒成份示為exp(j2πfnNx),即Pr(R(i)|R(i-1),F)=diagIlX (k-1, i)-Z,(k-1,i)I[XH(k, i)NNi-exp(-trI[R(i)ZH(k,i))=G(k-1, i)diag([X, (k-1,i-1)-Zn(k-1,i-1)]X(k,-1)R(-1)(I⑧F)x[R(i)zH(k,i-1)]}G"(k-1,i)F"(k,i)=R(i-1)(I⑧F)]}(16)dag{X(k-1,-1)-Zn(k-1,-1)]×式中:“tr”表示“跡”運(yùn)算;“det”表示行列式運(yùn)算.由[X#(k,-1)-zH(k,-1)]}F(k,)(11)式(16)可知:信息矩陣的估計(jì)值F為使概率函數(shù)式中 diag(A表示對(duì)角矩陣,該矩陣可通過將矩陣P(R()R(-1),F)達(dá)到最大值的F值,即A中的非對(duì)角元素置零獲得.為描述方便,將F(k,F=arg max Re trL(IN O FR(i-1)E-R(i]i)簡寫成F并作如下定義:X, (k-l, i-1)= X,, X, (k-l, i)=Xarg max>Re tr(F[diag(X, xt )]'[diag(X,,Xt+X (k,i-1)=X3, X(k,i)=XX+黜X+ⅫX)]dag(X2)(17)以同樣的方法定義Z、Z2、Z和Zn,則式(11)可以根據(jù)信息符號(hào)和信息矩陣F之間的一一對(duì)應(yīng)關(guān)系,第3期姜海寧,等:一種道用于快速雙選衰落信道的時(shí)頻雙差分空時(shí)編碼正交頻分復(fù)用技術(shù)397不難從估計(jì)值F恢復(fù)出原信息符號(hào)比較,可以看出:如果一個(gè)對(duì)角酉群對(duì) DST-OFDM2.3性能分析系統(tǒng)是最優(yōu)的,那么它對(duì)于本文所提的 TF-DDST下面對(duì)TF-DDST-OFDM系統(tǒng)性能進(jìn)行分析.OFDM系統(tǒng)同樣是最優(yōu)的.因此,在設(shè)計(jì)TF首先,計(jì)算該系統(tǒng)的成對(duì)誤碼概率( Pairwise Error DDST-OFDM信息碼字過程中,可采用文獻(xiàn)[3,4,Probability,PEP.系統(tǒng)的PEP定義為在接收端將9]中提出的最優(yōu)碼群.發(fā)送端信息矩陣F譯碼成F的概率(F,F∈g,F≠F).根據(jù)式(14),條件成對(duì)概率P(F3仿真結(jié)果F|rn(i-1)的 Chernoff上限可近似為為了驗(yàn)證所提 TF-DDST-OFDM技術(shù)在快速P(F→F|rn(i-1)≤雙選衰落信道下的良好性能,下面利用 Matlab軟件式中,“么xp(-a(F,F)A2N2/(16N)(18)對(duì)其性能進(jìn)行仿真仿真中采用N=2個(gè)發(fā)送天,F)=‖rn(-1)(F-F)H‖2=線,N=1個(gè)接收天線.不同收發(fā)天線間的子信道相互獨(dú)立,且為兩抽頭等功率衰落信道,延遲擴(kuò)展為·‖表示 Frobenius范數(shù);e=F-F5ps,歸一化多普勒頻移為∫aT,其中f為最大多當(dāng)接收端信噪比SNR足夠高時(shí),式(9)中的噪普勒頻移,T為OFDM符號(hào)時(shí)間間隔.系統(tǒng)帶寬為聲項(xiàng)可忽略.此時(shí)d2(F,F)可近似為1MHz,子載波數(shù)為128.對(duì)于每個(gè)OFDM符號(hào),插d(F,F)≈trH" e CcLc,C2e"H)(19)人一段20s的循環(huán)前綴作為保護(hù)間隔以避免符號(hào)式中:間干擾信道衰落系數(shù)根據(jù) Jakes模型生成10).TFC1=C(k-1,-1),C2=C(k,i-1)DDST-OFDM系統(tǒng)和 DST-OFDM系統(tǒng)采用相同的h= diag H ( k-1)H(k)群碼(4;1,1)4,編碼效率為1令vec{A}表示矩陣A中的對(duì)角元素構(gòu)成的列圖2給出快速衰落信道(f4T=0.03)下兩系統(tǒng)向量,則式(19)可寫成:性能隨信噪比變化曲線圖.由圖可見, TF-DDSTd(F,F)≈H"( eC2CiCC2e")h(20)OFDM系統(tǒng)性能優(yōu)于 DST-OFDM系統(tǒng),尤其在高式中:h=vec(H).由式(6)可得:CHC=CC2信噪比情況下.當(dāng)SNR=30dB時(shí), DST-OFDM系NIN.因此,有統(tǒng)呈現(xiàn)出較高的誤碼平層,對(duì)應(yīng)的比特誤碼率約為d2(F,F)≈(h')φ(h)(21)0.01,而此時(shí)TF- DDST-OFDM系統(tǒng)仍然保持較低式中:h'=h/2;=2Nee",根據(jù)文獻(xiàn)[9]和式(3),的比特誤碼率,約為3×10并假設(shè)式(3)中的h(p)服從獨(dú)立同復(fù)高斯分布,每維方差為1/(2L),均值為零,不難推導(dǎo)得:h亦為復(fù)高斯變量,其均值為零,協(xié)方差矩陣為E{h'(h')"}=E{hh"}/2=IN將式(21)代入式(18),并對(duì)h取統(tǒng)計(jì)平均,可得P(F→F)≤(16N(22)DST-OFDM-tTF-DDST-OFD式中:G= min rank(),為分集增益;G[det()]mk,為編碼增益.為保證良好的系SNR/dB統(tǒng)性能要求P(F→F)的上限值盡可能小,即G4圖2快速衰落信道下 TF-DDST-OFDM與和G。的取值盡可能大,據(jù)此可得到 TF-DDSTDST-OFDM性能比較OFDM系統(tǒng)的編碼設(shè)計(jì)準(zhǔn)則Fig 2 Performance comparison of TF-DDST-OFDMand dST-OFDM in fast fading channel準(zhǔn)則1(分集增益準(zhǔn)則)設(shè)計(jì)最優(yōu)的對(duì)角酉群g使得對(duì)于任意的F,F∈g(F≠F),矩陣e=圖3給出高速衰落信道(∫T=0.1)下兩系統(tǒng)F一F保持滿秩性能隨信噪比變化曲線圖.對(duì)于 DST-OFDM系統(tǒng)準(zhǔn)則2(編碼增益準(zhǔn)則)設(shè)計(jì)最優(yōu)的對(duì)角酉群即使在高信噪比情況下其比特誤碼率仍然非常高,使得對(duì)于任意的F,F∈(F≠F),行列式這說明 DST-OFDM系統(tǒng)不適用于高速衰落信道de(F一F)|的取值盡可能大與之相反, TF-DDST-OFDM仍然保持良好性能,當(dāng)將以上編碼設(shè)計(jì)準(zhǔn)則與文獻(xiàn)[5,6]中的準(zhǔn)則相SNR=30dB時(shí),其比特誤碼率為4×10398上海交通大學(xué)學(xué)報(bào)第40卷formance criterion and code construction [J]. 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