Jounal of Communicaions Vol., No. 7, July 015 Comensaion Esimaion Mehod fo Fas Fading MIMO- OFDM Channels Based on Comessed Sensing Xiaoing. Zhou 1,, Zhongxiao. Zhao 1, Li. Li 1, and Si. Li 1 1 College of Infomaion, Mechanical and Elecical Engineeing, Shanghai Nomal Univesiy, Shanghai 0007, China De. of Eleconic Engineeing a Shanghai Jiao ong Univesiy, Shanghai, 0040, China Email: {zxshnu, gouwuyizu911, lisishnu}@163.com; lilyxuan@shnu.edu.cn Absac In his ae, a comensaion esimaion algoihm is develoed fo Mulile-Inu Mulile-Ouu (MIMO) Ohogonal Fequency-Division-Mulilexing (OFDM) sysems oeaing in a fas fading envionmen. In ode o saisfy he consain fequency mask, he ulse signal secum mus be limied in he mask band. We invesigae a channel esimao ha exloi channel sasiy in he ime and/o Dole domain, whee he channel is descibed by a limied numbe of ahs, each chaaceized by a delay, Dole scale, and aenuaion faco, and deive he exac ine-caie-inefeence aen. he algoihm woks wih channel sasiy by joinly esimaing he sase coefficiens veco and by econsucing dynamic mahemaical model of ulse wave funcions. he oosed mehod exlois he ininsic elaionshi beween he sase channels and he mahemaical model. A dynamic mahemaical model of ulse wave funcions is used o consuc he sase channels. he dynamic mahemaical model econsucion is used o udae he sensing maix. he ulse signal which is band and ime concenaed disibuion, is conducive o oimizaion design of sase MIMO- OFDM channel. he simulaion esuls show ha he oosed channel esimao can ovide a consideable efomance imovemen in esimaing doubly selecive channels wih few ilos and comuaional comlexiy. Index ems Comessed sensing, sase channel, channel esimaion, fas fading I. INRODUCION Ohogonal Fequency Division Mulilexing (OFDM) is a oula echnique widely used fo boadband wieless communicaion sysems due o is high secal efficiency [1]. Howeve, he heoeical efomance of Mulile-Inu Mulile-Ouu (MIMO) [] and OFDM sysems may be degaded seveely in boadband mobile alicaions due o he doubly selecive channels. hus, channel esimaion which is emloyed o eliminae he disoion of he signals a he eceive is a ciical comonen ha affecs he efomance of MIMO- OFDM sysems. he convenional channel esimaion mehods fo MIMO-OFDM sysems have focused on ilo-assised aoaches [1]-[3] based on a quasi-saic fading model ha allows he channel o be invaian duing an OFDM block. Howeve, a loss of subchannel ohogonaliy due Manusci eceived Febuay 5, 015; evised July 18, 015. Coesonding auho email: zxshnu@163.com. doi:.170/jcm..7.466-473 o ime-vaian muliah channels in ohogonal OFDM leads o ine-caie inefeence (ICI) which inceases he eo of sysem [4]-[5]. heefoe, he channel ime vaiaion duing a symbol block mus be consideed o suo high-seed mobile channels. Many ilo-aided channel esimaion mehods [3]-[5] usually esimae he channel esonse fo a few seleced subcaies fis. hose obsevaions ae used o ineolae he es subcaies. In such schemes, he equied numbe of ilos deends on he coheence bandwidh of he channel, since he sacing of he ilo sequence has o saisfy he Nyquis samling heoem o oely samle he fas fading channels. Howeve, hese schemes jus conside he ich scaeing envionmen, wih he sasiy of he MIMO-OFDM channels being ignoed. A numbe of sase channel esimaion schemes [6]-[17] have been oosed fo ime-fequency fading channels. he ime-fequency join sase channel esimaion scheme [17] fis elies on a seudoandom ime-domain eamble, which is idenical fo all ansmi anennas. he sase common suo oey of he MIMO channels is uilized o acquie he aial common suo. hen, fequency-domain ohogonal ilos ae used fo he channel ecovey. Howeve, he common suo and he equied numbe of ilos deend on he coheence bandwidh of channels and ime of ansmi anennas. he ovehead of he equied ilos o eamble will significanly incease as he numbe of ansmi anennas. he blocks of ansmied OFDM symbols become lage, which deceases he secal efficiency. I may lead o he unacceable high comuaional consumion, ine symbol inefeence and low fequency mask [18]. Accoding o he Heisenbeg unceainy incile [19], he ulse signal is concenaed disibuion in fequency domain and mus disese in he ime domain. he sensing maix of is udaed by highseed mobile channels [0]. I is no easy o obain sase channels ha mee he equiemens of band and ime limied [1]. he soluion of oblem o consuc he sase channels equies he use of a dynamic mahemaical model of ulse wave funcions. Howeve, such models ofen involve eos due o a vaiey of causes, including fas fading envionmens, amosheic effecs, and hadwae limiaions. In his ae, we focus on he comensaion esimaion of mahemaical model in comessed sensing (CS) based fas fading MIMO-OFDM channels. In ode o achieve 015 Jounal of Communicaions 466
Jounal of Communicaions Vol., No. 7, July 015 few ilos, few comuaional comlexiy and low ine symbol inefeence, he ulse signal duaion should be as sho as ossible, and be limied in he ime. A he same ime, in ode o saisfy he consain fequency mask, he ulse signal secum mus is limied in he mask band. When he fequency mask changes, ulse wavefom can be flexibly adjused and coeced. he ulse signal which is band and ime concenaed disibuion, is conducive o oimizaion design of sase MIMO-OFDM channel. he oosed mehod exlois he ininsic elaionshi beween he sase channels and he dynamic mahemaical model of ulse wave funcions. he oosed mehod woks by joinly esimaing he sase coefficiens veco and by econsucing he dynamic mahemaical model. hen, he dynamic mahemaical model of ulse wave funcions econsucion is used o udae he sensing maix, and he algoihm asses o he nex ieaion. he mahemaical model is exloied o ack aidly MIMO- OFDM channels by avoiding deending on he coheence X 1 [ n,0] X 1 [ n, K 1] N X N X [ n,0] Fig. 1. MIMO-OFDM sysem models [ n, K 1] IFF IFF CP CP Paallel/Seial Paallel/Seial x 1 [ n, k] N x [ n, k] N1 h 1N h 11 h NN h bandwidh and ime of channels. We oose a CS-based fas fading channels esimao fo MIMO-OFDM sysems wih as few measuemens as ossible. he comuaional comlexiy is significanly educed by avoiding he invese comuaion of he lage ilo maices. he oganizaion of his lee is as follows. he MIMO-OFDM sysem model is inoduced in Secion II. he CS-based channel comensaion esimaion is esened in Secion III. Secion IV deics he exeimens based on channel comensaion esimaion and he lee is summaized in Secion V. Noaion:,, H,, 1 and denoe he F comlex conjugaion, ansose, conjugae-ansose, invese, seudo-invese oeaions and Fobenius nom, esecively. diag V is diagonal maix whose diagonal is he veco V ; min is o ge minimum elemens of an aay; I denoes a ideniy maix; I N 1 is an N 1 veco. y 1 [ n, k] N y [ n, k] Seial/Paallel Seial/Paallel CP CP FF FF 1 [ n,0] N 1 [ n, K 1] N [ n,0] [ n, K 1] II. SSEM MODEL Conside a MIMO-OFDM sysem wih anennas, NR N ansmi eceive anennas in Fig. 1. he OFDM sysem conains K subcaies. he samle ineval is s. he K 1 veco X denoes he OFDM symbols ansmied fom he ih anenna coesonding o he nh duaion ime. X X (1), X (),, X ( K) (1) Befoe hese symbols ae ansmied, his veco is fis modulaed by he invese comlex Fouie ansfom (IDF), and a cyclic efix is aended a he head of each OFDM symbol. Afe emoving he cyclic efix a he h eceive anenna, we obain he K 1 veco y ( ) whee n, which can be wien as () N, H y H F X N 1 y y (1), y (),, y ( K) (3), H is a ciculan maix [4,5] wih fis column given by, h,0 1 ( KL ) in slow fading envionmens. he, L 1 veco h denoes he imulse esonse of a channel wih L ahs beween he h ansmi anenna and he h eceive anenna, and is he owe allocaed o he subcaies. L is chosen o exceed he maximum delay sead. F denoes K K he uniay comlex Fouie ansfom (DF) maix. is veco of he noise. I is easy o show, H, H F diag K F h,0 1 ( KL ) F aking he DF of y ( n ), we obain (4) N, diag K F h,0 1 ( KL) X N 1 whee F. Fo fas fading envionmens, he channel maix model defined in (4) is no longe valid. (5) N, X Fh N 1 whee F is K imes he fis L columns of F. 015 Jounal of Communicaions 467
Jounal of Communicaions Vol., No. 7, July 015 Due o he aid ime vaiaion of he channel, he KL( Q 1) channel maix, H canno be consideed as a ciculan maix. Whee Q eesens he basis exansion, ode. heefoe, he channel maix H canno be diecly alied o fas fading channels wihou aying a efomance enaly. III. CS-BASED CHANNEL COMPENSAION ESIMAION A. Channel Model Fo he n h symbol, he h ansmi anenna sends ilos in M subcaies and he emaining K M subcaies ae used fo daa ansmission. he se of ilos chosen fo diffeen ansmi anennas need no be he same o disjoin. he ih anenna ansmi demodulaed baseband daa maix is X ( n ).he ansmi symbols maix can be denoed as X X G (6) whee he K 1veco G ( n ) fequency ulse wavefom is G G (1), G (),, G ( K) (7) hen, he eceived signal of he h eceive anenna in he nh obsevaion symbol can be exessed as N, diag X G Fh (8) N 1 In many cases such as he nonline-of-sigh scenaio, he mean angle of deaue and angle of aival of he cluses of muliah comonens end o be unifomly disibued ove all subcaies. hus, when he numbe of cluses is elaively lage, he channel esimaion echnique [3]-[5] may hadly imove a consideable efomance in esimaing fas fading channels, because nealy all he elemens of saial domain channel maices may no aoach zeo. o conside wide alicaions, we will focus on echniques in which he sase channel coefficiens wih mahemaical model. One of he mos salien chaaceisics of muliah wieless channels is signal oagaion ove mulile saially disibued ahs. he channels beween diffeen ansmi-eceive anenna ais ae ime fequency sase. he ime domain channel veco fo he h eceive anenna is,1, N, ( ) ( ), ( ),, ( ) h n h n h n h n (9) whee he muliah channels h by L1,, l0, can be eesened h h ( n, l) ( l ) (), whee h ( n, l ) and l eesen he gain, he delay of he ah l, esecively, and () is he Diac dela funcion. L is imulse esonses of equal maximum esolvable, ahs. he ah l channel h ( n, l) is eesened by as Q j ( qq/) k,, WK h ( n, l) h ( n, l, q) e (11) q0 wheew is a osiive inege, and he vaiaion of W is associaed wih he maximum Dole fequency. Q can max s be se o ode, whee f K, eesening he basis exansion f max he caie fequency offse maix is is he maximum Dole fequency. j ( qq ) j ( qq )( K 1), WK WK Ψ q e,, e (1) he muliah channels, h is he nh symbol comlex imulse esonse of he all ah, and can is be wien in maix fom as,,, h Ψ (13) whee he caie fequency offse maix is Ψ, Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ,,, 0,0 0,1 0, Q,,, 1,0 1,1 1, Q,,, L,0 L,1 L, Q (14) he sase coefficiens veco of comlex imulse esonse is h ( n, ), h ( n, ),, h ( n, ) (15),,,, 0 1, Due o he unknown of, we use he comlex basis including all ime fequencies o sasely eesen he eceived channel in (15). Equaion (15) means ha he eceived signals ae sase in he ime and fequency domain. Fo esimaion of such channels, he efomance can be imoved hough exloiaion of sasiy. Exied MIMO-OFDM channel esimaion echniques ea channels as saial ich muliah. Howeve, in many siuaions, MIMO-OFDM channels may end o be ime fequency sasiy due o limied scaeing. Using he ime fequency exansion and a measuemen maix, he samling scheme based on CS can be designed o educe he samling ae in heoy. B. Subsamled a he Pilo Posiion he following is esened o design he measuemen maix wih finie bases. he sase coefficiens veco of channel esonses ae esimaed a he ilo locaions. Defining X (1), (),, diag diag X X X ( K) L, he se of eceive vecos a he ilo osiions using he known ilo maix ae chosen by (16) N, S X diag S S G Fh N 1 015 Jounal of Communicaions 468
Jounal of Communicaions Vol., No. 7, July 015 whee S (n) is he M (n) K ilo selecion maix ha his secion. he feaue used o deec he channel is fisly esened in he following. Afe he CS eceive, he maximal elemen is assumed o be he dominae scae, which is coesonding o he basis. A he eceive, he dominae scae is deiced as chooses he M (n) ows of he X diag maix accoding o he kh subcaies ilos chosen in he nh symbol, M (n) N KL(Q 1). I can be noiced ha he aining sage enails a oal of M (n) ilos o esimae (n) N KL(Q 1) channels. Fo adiional channel esimaion schemes, he sacing of he ilo sequence has o saisfy he Nyquis samling heoem o oely samle he fas fading channels. I is necessay o esablish a heoeical limi on he numbe of ilos equied fo efec channel ecovey in a noise sysem. Accoding o he heoy of comessed sensing, a sase signal can be exacly econsuced fom is measuemen maix. Based on he CS heoy, (16) can be samled by a measuemen maix. he measuemen maix saisfies he so-called esiced isomey oey (RIP). Accoding o he RIP heoems, he goal hen is o design he aining maix using minimum numbe of ilo vecos and ocess he eceived signal maix (n) o obain an esimae hˆ (n) ha is close, S (n, M (n)) s g ( ) s (17) v sin D max 1 s g ( ) v sinh( D max ) 1 s sinh( locaion of he M (n) ilo subcaies ae escibed by vd max 1 ) e vd max e g ( ) u( ) ansmie fo obing a channel. A he ansmie, he andom sequence {x } is geneally used o obe a vd max () (3) whee channel. he numbes of ilo ae v sin D max 1 u ( ) v sinh( D max ) 1 K (18) 1 k 1 of ode and aamee s wih obabiliy a leas 1 e, whee, C 1 is he ovesamling faco. We have diffeen obsevaions fo diffeen ansmi-eceive anenna ais. Fuhe he lengh M (n) of he obsevaion is no same fo all anennas. CM (4) he fequency ulse wave funcions can be wien as G (n) U(n) (5) whee U (n) is he Fouie ansfom of U(n) Fu( ). I can be obseved ha he enegy of ime concenaes along (0). Dole lines vd max shaes he same fequency as he dominae scae. Equaion (5) shows ha channels funcion is limied by angula fequency and C. Esimaion and Comensaion Using he saisical chaaceisic and he dominae scae, a comensaion esimaion deeco is oosed in 015 Jounal of Communicaions (1) he ime ulse wave funcions can be exessed as a andom sequence {x } ha is geneaed a he RIP (0) whee viual caies. he enies of S (n) which deemine he saisfies sin( ( )vd max ) d ( ( )) Based on he definiion of equaion (0), g ( ) can be shown as follows: ansmission while he es K M (n) ones ae daa and M C log( N N KL(Q 1) / ) f maxs. he ime ulse whee is he eigenvalues of ulse wave funcions. he nh symbol. he M (n) subcaies ae used fo ilo (19) wave funcions mee he oduc diffeenial equaion selecing andomly M (n) subcaies of K subcaies in M (n, k ) (n) S (n)g (n) F 1 bandwidh vd max, whee vd max he selecion maix selecs andomly he ilo symbol M In ode o avoid he inefeence of he wieless sysem and imove channels sasiy, an effecive mehod is o design aoiae ulse wavefom G (n). he channels funcion is limied by angula fequency and ime domain. he ime ulse wave funcions can be he mos of concenaion in a given ime ineval s, s and maximum nomalized Dole locaions. he nh column S (n) is consuced by N N N S (n)xdiag S Ψ,, (n) (n) o h (n) in ems of he mean squaed eo (MSE). he measuemen maices saisfy he RIP [8]. he h ansmi anenna selecion maix S (n) S (n,1), S (n, ), 469
Jounal of Communicaions Vol., No. 7, July 015 ime domain. Accoding o he ime domain wavefom and amliude secum, he se of eceive vecos ae N,, S X diag S S U FΨ N 1 ( n ) (6) Equaion (6) can be exessed in maix fom as whee (7) ( n,0),, ( n, M ) (8) 1 1 1 N N N Φ S X diag S,, S X diag S N 1,1 N, N ( ) ( ( )U( ) Ψ,, ( )U( ) Ψ ) (9) n diag S n n F S n n F (30),1, N,,,, (31) Convenional mehods assume ha he channels don' include ime and fequency consains. he following oimizaion oblem is used o channel econsucion [13]-[17]: ag min 1 (3) whee is he egulaizaion aamee. In consideaion of he ime and fequency sasiy, we also need o econsucion he eigenvalues of aoiae ulse wavefom. hen, he sase channels ae esimaed by using aoiae ulse wave funcions. We ose he oblem of join channels esimaion and eigenvalues econsucion as he minimum cos soluion of he following cos funcion:,1 ( ), ( ) ( ) ( ) ( ) ( ) 1 J n n n n n n (33) he channels esimaion and eigenvalues econsucion can be obained as, ag min J,, (34) By solving (34), boh he channels esimaion and eigenvalues econsucion can be joinly obained. he emaining oblem is how o solve (34). Using a simila join mehod oosed in [17], (34) can be solved by an ieaive algoihm wih channels esimaion, eigenvalues econsucion and comensaion of ulse wave funcions. he cos funcion is minimized wih esec o he sase coefficiens esimaion. he eigenvalues ae econsuced by he channels esimaion. he ulse wave funcions ae udaed using he econsuced eigenvalues. he sensing maix of is udaed by he ulse wave funcions. he sasiy and accuacy of he channel esimaion ae comensaed o imove by he new sensing maix in nex ieaive ocess. he algoihm flow is oulined as follows: Fisly, he oblem of esimaing he sase comlex basis exansion channel h coefficiens is ansfomed ino he oblem of esimaing. ( ) i n 1 i 1 i ag min J, (35) is he sase coefficiens of he comlex ime fequency basis aamee wih ulse wavefom. Fuhemoe, when some saial domain bins conain few hysical ahs due o limied scaeing, he coesonding channel coefficiens should aoach zeo. Equaion (35) is acually comosed of comlex ulses, which means ha he eceived signals in (35) is sase in he ime fequency domain. he cos funcion is minimized wih esec o he sase coefficiens esimaion. Secondly, he eigenvalues ae econsuced by he channels esimaion. Reconsucion of eigenvalues fo ulse wave funcions is: i i J n 1 1 ag min ( ), (36) hidly, he ulse wave funcions ae udaed using he econsuced eigenvalues i 1 funcions v D max, U( ). he ulse wave n ae udaed by using i 1 Fouhly, he sensing maix G of is udaed by he ulse wave funcions U( n ). Finally, he sasiy and accuacy of he channel esimaion ae comensaed o imove by he new sensing maix in nex ieaive ocess. he comensaion sase comlex basis exansion eesens band and ime limied sequences wih he ulse wave funcions. Le ii 1 and eun o esimaion of sase coefficiens. eminae when i 1 i i. (37) Equaion (37) is less han a ese heshold. his allows us o choose a suiable heshold fo ignoing he small-valued channel as and eaining only he mos significan as o educe he effec of noise in he esimaion. he enegy mainly concenaes in he saial ime fequency, heeby imoving he efomance of he channel esimaion echnique. I can be obseved ha he enegy of ( ) i n 1 seads ove he enie ambiguiy domain, so he enegy in an adjacency of he dominan ime fequency, coesonding o he mached signal. When he fequency mask changes, ulse wavefom can be flexibly adjused and coeced. he ulse signal which is band and ime concenaed disibuion, is conducive o oimizaion design of sase MIMO- OFDM channel. he oosed mehod exlois he 015 Jounal of Communicaions 470
Jounal of Communicaions Vol., No. 7, July 015 ininsic elaionshi beween he sase channels and he dynamic mahemaical model. he oosed mehod woks by joinly esimaing he sase coefficiens veco and by econsucing he dynamic mahemaical model. hen, he dynamic mahemaical model econsucion is used o udae he sensing maix, and he algoihm asses o he nex ieaion. he mahemaical model is exloied o ack aidly MIMO-OFDM channels by avoiding deending on he coheence bandwidh and ime of channels. MSE of he channel esimae, and he bi eo ae (BER) vesus SNR. Fig. esens he coec channel imulse esonse ecovey obabiliy when diffeen numbes of ilos [M (n) ( N K )]% ae used unde he fas fading channel wih he fixed SNR of 60 db in a 4 4 MIMO sysem. Hee, he coec ecovey is defined as he esimaion Mean Squae Eo (MSE) is lowe han. I can be seen fom Fig. ha by uilizing he obained ininsic elaionshi beween he sase channels and he dynamic mahemaical model, he equied numbe of ilos in he oosed mehod is less han ha in he MIMO FOFDM [17] algoihm and fa less han ha in SOMP algoihm. D. Pefomance Evaluaion We define dominan non-zeo channel coefficiens (n) s as hose which conibue significan channel owe, ha is, he coefficiens fo which E h, (n, 1 ) fo some escibed heshold 0 N E 1 (n) N KL(Q 1) Recovey Pobabiliy 0. hus, he channels ae sase (38) 0 I is easily seen ha he fas fading channels encouneed in acice ae sase MIMO-OFDM channels wih mos of he muliah enegy localized o elaively small egions. he channels imulse esonses ae dominaed by a elaively small numbe of dominan esolvable ahs wihin he sase comlex basis exansion. hus, he goal is o econsuc he sase channel coefficiens (n) fom few ilo measuemens. Using he sase comlex basis exansion and a measuemen maix, he samling scheme based on CS can be designed o educe he samling ae in heoy. When adiional channel esimaion mehods ae used fo he doubly selecive MIMO OFDM channels, he M N KL(Q 1) maix will be designed o have full column ank N KL(Q 1), which Poosed MIMO F-OFDM SOMP - 0 0 Numbe of Pilos(%) 30 Fig.. Comaison of he ecovey obabiliies a he SNR = 60 db. -1 MSE - Poosed MIMO F-OFDM FRI-PERK IJEP equies -3 M N KL(Q 1), whee N KL(Q 1) is he numbe of ah. he main comuaional cos is fom of sase coefficiens esimaion and eigenvalues econsucion. In each ieaion, he fis se econsuc he ages, whose comlexiy is ode O MN K. he comuaional comlexiy of eigenvalues econsucion is ode O N K. 5 15 0 SNR(dB) 5 30 Fig. 3. MSE agains SNR -1 - -3 BER IV. SIMULAIONS -4-5 In ode o demonsae he efomance of he oosed channel esimaion, he simulaions wee esened in his secion. he simulaion aamees ae chosen o be deicive of a communicaion sysem wih caie fequency o be.3ghz, symbol duaion and guad ineval o be.4 s and 1.8 s, subcaies o Poosed MIMO F-OFDM FRI-PERK IJEP -6 5 15 SNR(dB) 0 5 Fig. 4. BER agains SNR. be4 and FF size o be 4. he efomance of he MIMO-OFDM sysem is measued in ems of he 015 Jounal of Communicaions -1 Fig. 3 shows MSE of channel esimaion eo vs. Signal-o-Noise Raio (SNR). he BER of each daa 471
Jounal of Communicaions Vol., No. 7, July 015 seam is shown in Fig. 4. Fig. 3 and Fig. 4 illusae he MSE and BER efomance of diffeen schemes unde he fas fading channel wih he mobile seed of 00 km/h in a 66 MIMO sysem, esecively. he join esimaion mehods of IJEP [5], FRI-PERK [13] and MIMO F-OFDM ae also evaluaed fo comaison. I could be seen ha fo he mobile channel, he oosed mehod yields bee efomance comaed wih IJEP, FRI-PERK and MIMO F-OFDM. Since he sacing of he ilo sequence doesn saisfy he Nyquis samling heoem o oely samle he fas fading channels. he join channel esimaion schemes of IJEP, FRI-PERK and MIMO F-OFDM ely on a seudoandom imedomain eamble, which is idenical fo all ansmi anennas. Howeve, he equied numbe of ilos deend on he coheence bandwidh of channels and ime of ansmi anennas. he ovehead of he equied ilos o eamble will significanly incease as he numbe of ansmi anennas and he blocks of ansmied OFDM symbols becomes lage, which deceases he secal efficiency. he oosed mehod exlois he ininsic elaionshi beween he sase channels and he dynamic mahemaical model. he oosed mehod woks by joinly esimaing he sase coefficiens veco and by econsucing he dynamic mahemaical model. When he fequency mask changes, ulse wavefom can be flexibly adjused and coeced. he ulse signal which is band and ime concenaed disibuion, is conducive o oimizaion design of sase MIMO-OFDM channel. he mahemaical model is exloied o ack aidly MIMO-OFDM channels by avoiding deending on he coheence bandwidh and ime of channels. V. CONCLUSIONS We oosed he CS-based channel comensaion esimaion fo MIMO-OFDM wih fas fading channels. he oosed esimaion mehod has much bee efomance han adiional channel esimaion mehod. We invesigae a channel esimao ha exloi channel sasiy in he ime and Dole domain, whee he channel is descibed by a limied numbe of ahs, each chaaceized by a delay, Dole scale, and aenuaion faco, and deive he exac ine-caie-inefeence aen. he algoihm woks wih channel sasiy by joinly esimaing he sase coefficiens veco and by econsucing he mahemaical model. he oosed mehod exlois he ininsic elaionshi beween he sase channels and he mahemaical model. ACKNOWLEDGMEN his wok was suoed by he Naional Naual Science Foundaion of China (6113004, 61), he key discilines of Shanghai Nomal Univesiy (DZL16), he Shanghai Municial Educaion Commission funding scheme fo aining young eaches of Colleges and univesiies in 01, and he geneal ojec of Shanghai Nomal Univesiy (SK0131, A-7001-15-0005). REFERENCES [1] C. E. 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Jounal of Communicaions Vol., No. 7, July 015 [19] S. A. Hosseini and N. Amjady, A fouie based wavele aoach using heisenbeg's unceainy incile and shannon's enoy cieion o monio owe sysem small signal oscillaions, IEEE ansacions on Powe Sysems, no. 99,. 1-13, 015. [0] X. P. Zhou, Sasiy adaive channel sensing esimaion of fas fading MIMO-OFDM sysems, Signal Pocessing, vol. 6, no. 1,. 1833-1839. 0 [1] X. P. Zhou, Comessed sensing esimaion mehods fo fas fading channel of MIMO-OFDM sysems, Chinese Jounal of Radio Science, vol. 5, no. 6,. 19-1115, 0. Xiao-Ping Zhou was bon in shanghai Povince, China, in 1978. He eceived he B.S. degee fom he Nanchang Univesiy of China (NCUC), Nanchang, in 001 and he M.S. degee fom he Chongqing Univesiy of Poss and elecommunicaions (CUFP), Chongqing, in 006, boh in elecical engineeing. He eceived he Ph.D. degee fom Shanghai Univesiy (SU), Shanghai in 011. He held an aoinmen as associae ofesso Shanghai Nomal Univesiy. He is cuenly a Posdocoal Reseach Fellow a he Shanghai Jiao ong Univesiy. His eseach inees include boadband wieless communicaions, channel modeling, secal esimaion, aay signal ocessing, and infomaion heoy, ec. Zhong-Xiao Zhao was bon in henan Povince, China, in 1988. He eceived he B.S. degee fom he shanghai nomal univesiy, Shanghai, in 013. He is cuenly usuing his M.S a shanghai nomal univesiy. He was in he wieless newoking and communicaions gou. Li Li was bon in henan Povince, China, in 196. He eceived he B.S. degee fom singhua univesiy of China, beijing, in 1985 and he M.S. degee fom china eseach insiue of adio wave oagaion, henan, in 1988. He eceived he Ph.D. degee fom eking univesiy, beijing in 1997. She held an aoinmen as ofesso and mase insuco, he eseach inees is mainly coding and digial synchonizaion, ec. Si Li was bon in wuhan Povince, China, in 1993. He eceived he B.S. degee fom he hubei engineeing univesiy, hubei, in 014. She is cuenly usuing his M.S a shanghai nomal univesiy. He was in he wieless newoking and communicaions gou. 015 Jounal of Communicaions 473