Tracking A Dynamic Sparse Channel Via Differential Orthogonal Matching Pursuit

Transcription

1 Mlcom 2015 Track 1 - Waveforms and Sgnal Processng Trackng A Dynamc Sparse Channel Va Dfferental Orthogonal Matchng Pursut Xudong Zhu 1, Lnglong Da 1, We Da 2, Zhaocheng Wang 1, and Marc Moonen 3 1 Tsnghua Natonal Laboratory for Informaton Scence and Technology (TNlst), Tsnghua Unversty, Chna 2 Department of Electrcal and Electronc Engneerng, Imperal College, UK 3 Department of Electronc Engneerng, Katholeke Unversty Leuven, Belgum Emal: zhuxd12@mals.tsnghua.edu.cn, we.da1@mperal.ac.uk, marc.moonen@esat.kuleuven.be Abstract Ths paper consders the problem of trackng a dynamc sparse channel n a broadband wreless communcaton system. A probablstc sgnal model s frstly proposed to descrbe the specal features of temporal correlatons of dynamc sparse channels: path delays change slowly over tme, whle path gans evolve faster. Based on such temporal correlatons, we then propose the dfferental orthogonal matchng pursut (D-OMP) algorthm to track a dynamc sparse channel n a sequental way by updatng the small channel varaton over tme. Compared wth other channel trackng algorthms, smulaton results demonstrate that the proposed D-OMP algorthm can track dynamc sparse channels faster wth mproved accuracy. I. INTRODUCTION In a broadband wreless communcaton system, channel state nformaton (CSI) s requred at the recever due to the fact that the multpath fadng channel dstorts the receved sgnals, especally when the channel s dynamcally changng. Hence, accurate channel estmaton and trackng become an mportant problem for communcaton over a dynamc wreless channel [1]. Varous lnear channel estmaton methods wth low computatonal complexty have been proposed [2], but ther performance s often not robust enough to meet the requrement of communcaton systems wth hgh rate and hgh moblty. Recently, a lot of physcal channel measurements have verfed that wreless channels exhbt sparsty,.e., the dmenson of a wreless channel may be large, but the number of actve taps wth sgnfcant power s usually small, especally n a broadband wreless communcaton system [3]. By explotng ths channel sparsty, many nonlnear channel estmaton methods based on classcal compressve sensng (CS) algorthms have been proposed to mprove the estmaton performance, such as orthogonal matchng pursut (OMP), compressve samplng matchng pursut (CoSaMP), and subspace pursut (SP) [4]-[7]. Compared wth the conventonal lnear methods, CS-based channel estmaton methods are able to acheve mproved accuracy wth reduced tranng resources [4]. Further studes have uncovered addtonal channel characterstcs, e.g., the temporal correlatons of practcal wreless channels: path delays have been shown to change slowly over tme, whle path gans evolve faster [8]. However, the CS-based channel estmaton methods gnore these temporal correlatons of dynamc sparse channels and have to estmate them ndependently. By takng the temporal correlaton nto account, the adaptve smultaneous OMP (A-SOMP) algorthm has been proposed n [9] to obtan smultaneous mult-channel estmates based on the assumpton that the dynamc channel estmates n several consecutve tme slots share the same path delay set. However, the path delays of a dynamc sparse channel wll change over tme, or even there maybe some mutatons, so the assumpton n [9] s not always true n practce. Another attractve soluton for trackng a dynamc sparse channel s the herarchcal Bayesan Kalman (HB-Kalman) flter based on Bayesan CS (BCS) [10], whereby the teratve re-estmaton of the posteror covarance [11] s used to acheve accurate channel estmaton when sudden changes happen to the dynamc sparse channel, but t suffers from slow trackng speed and hgh computatonal complexty. In ths paper, we propose a dynamc CS algorthm called dfferental orthogonal matchng pursut (D-OMP) based on the standard OMP algorthm to track a dynamc sparse channel wth fast trackng speed and low computatonal complexty. By explotng the temporal correlaton of a dynamc sparse channel, the proposed D-OMP algorthm only needs to detect the small varaton of the dynamc sparse channel n a sequental way. Furthermore, an adaptve threshold based on the statstcal analyss of the equvalent nose s proposed to accurately dstngush true,.e., non-zero channel taps wth low power from thermal nose. Ths s essentally dfferent from the standard OMP algorthm n whch the ncorrect channel taps chosen n one teraton wll never be removed, whch fnally leads to performance degradaton. The performance analyss ndcates that a non-zero channel tap can be detected wth a hgh probablty, whle the nose n the estmate can be removed almost completely. Numercal smulatons show that the proposed D-OMP algorthm can track dynamc channels faster and acheve more accurate channel estmates than other trackng algorthms. The remander of ths paper s organzed as follows. The system model of dynamc sparse channels s descrbed n Secton II. Secton III addresses the proposed D-OMP algorthm, together wth the threshold based on nose statstcs. Secton IV presents the performance analyss, and smulaton results are provded n Secton V. Fnally, conclusons are drawn n Secton VI. Notaton: We use upper-case and lower-case boldface letters to denote matrces and vectors, respectvely; ( ) T, ( ) H, ( ) 1, /15/$ IEEE 792

2 Mlcom 2015 Track 1 - Waveforms and Sgnal Processng Path Gan Path gans evolve smoothly over tme A burst tap n tme slot 3 Sparse Channel n Tme slot 1 Sparse Channel n Tme slot 2 Sparse Channel n Tme slot 3 A dsappeared tap n tme slot 2 and Path Delay Fg. 1. Illustraton of the dynamc Vehcular B channel wth a velocty of 120 km/h n three consecutve tme slots. ( ), and p denote the transpose, conjugate transpose, matrx nverson, Moore-Penrose matrx nverson, and l p norm operaton, respectvely; Γ denotes the number of elements n set Γ; h Γ denotes the entres of the vector h n the set Γ; Φ Γ denotes the submatrx comprsng the Γ columns of Φ. II. SYSTEM MODEL In ths paper, we consder the problem of trackng a dynamc sparse channel {h (t) } T t=1 from under-sampled nosy measurements {y (t) } T t=1 n T tme slots, n a broadband wreless communcaton system. The sngle tme slot measurement vector y (t) = [y (t) 1, y(t) 2,, y(t) M ]T s usually obtaned through the lnear measurement process y (t) = Φ (t) h (t) + n (t), t = 1, 2,, T, (1) where h (t) = [h (t) 1, h(t) 2,, h(t) N ]T denotes the tme-doman dscrete channel vector wth N taps, where N > M, and the addtve whte Gaussan nose (AWGN) s modeled as n (t) CN (0, σni 2 M ), where I M denotes the dentty matrx of sze M M. The measurement matrx Φ (t) of sze M N s a Toepltz matrx determned by the tranng sequence c = [c 0, c 1,, c M ] T n the tme or frequency doman, e.g., the well known pseudo nose (PN) sequence used n CDMA systems [4]. Thus the measurement matrx Φ (t) becomes tme-nvarant [9],.e., Φ (1) = Φ (2) = = Φ (T ) = Φ = [ϕ 1, ϕ 2,, ϕ N ]. Snce the tranng sequence s usually desgned n a random way,.e., c CN (0, σc 2 ), we can obtan that ϕ (t),j CN (0, σϕ 2), where σ2 ϕ = σ2 c and ϕ (t),j denotes the element of the matrx Φ (t). Furthermore, based on ths Gaussan assumpton, the columns of the Φ matrx are semorthogonal,.e., ϕ H ϕ j 0, j. The temporal correlatons of practcal wreless channels have been verfed through analyss and experments, even when the channels are varyng fast [8]. Fg. 1 llustrates the tme-doman mpulse response of the dynamc Raylegh fadng Vehcular B channel wth a velocty of 120 km/h n three consecutve tme slots [12]. It s clear that path delays of such dynamc sparse channels change slowly, whle path gans evolve faster. In order to characterze the temporal correlatons of a dynamc sparse channel, we adopt a probablstc sgnal model wth two tme seres vectors {s (t) } T t=1 and {a (t) } T t=1, where the bnary vector s (t) = [s (t) 1, s(t) 2,, s(t) N ]T s used to descrbe the temporal evoluton of the channel paths, whle the complex-valued vector a (t) = [a (t) 1, a(t) 2,, a(t) N ]T characterzes the temporal varaton of the path gans. Hence, the dynamc sparse channel can be modelled as h (t) where the bnary s (t) = s (t) a (t), t = 1, 2,, T, 1 N (2) {0, 1} denotes whether there s a nonzero channel tap at ndex n the tth tme slot, and a (t) denotes the correspondng path gan. Thus, the path delay set Λ (t) of the dynamc sparse channel can be represented as Λ (t) = { : s (t) = 1}. We model the tme seres {s (t) } T t=1 as a dscrete Markov process wth two transton probabltes [13]: p 0 1 = P {s (t) = 1 s (t 1) = 0} and p 1 0 = P {s (t) = 0 s (t 1) = 1}. Wthout loss of generalty, {s (1) } N =1 s ntalzed as ndependent Bernoull random varables based on the probablty p 1,.e., s (1) Bernoul(p 1 ), = 1, 2,, N. Smlarly, we model the tme seres {a (t) } T t=1 as a Gauss-Markov process, and each path gan evolves ndependently as a (t) = a (t 1) + w (t), t = 1, 2,, T, 1 N (3) where w (t) = [w (t) 1, w(t) 2,, w(t) N ]T CN (0, σai 2 N ) controls the temporal correlaton of the path gans [13]. We model the ntal dstrbuton of path gans as a Gaussan dstrbuton,.e., {a (1) } N =1 CN (0, σ2 h I N). The probabltes p 0 1 and p 1 0 are usually small to model the slow changng of the path delays, whle {a (t) } T t=1 changes n each tme slot to model the faster changng of the path gans. Furthermore, the aforementoned parameters wll be gven n detal n Secton V. III. PROPOSED D-OMP ALGORITHM In ths secton, the proposed D-OMP algorthm s explaned n detal. Then the threshold used n the algorthm s derved based on nose statstcs. A. D-OMP Algorthm We propose the D-OMP algorthm to track a dynamc sparse channel, whch obtans the fnal estmates n a sequental way by updatng the small varaton of the dynamc sparse channel. The key dea of the proposed D-OMP algorthm s that, the major nformaton of the channel n the current tme slot can be obtaned from the estmaton results n prevous tme slots due to the temporal correlatons of the dynamc sparse channel, and then the small varaton of the channel can be estmated wth low complexty to refne the fnal estmate result. Ths s essentally dfferent from the standard OMP algorthm whch gnores any temporal correlaton of the channel taps [5]. The proposed algorthm also dffers from the HB-Kalman 793

3 Mlcom 2015 Track 1 - Waveforms and Sgnal Processng algorthm utlzng the teratve re-estmaton of the posteror covarance to obtan channel estmaton, whch leads to a slow trackng speed and hgh computatonal complexty. Algorthm 1 D-OMP Algorthm Input: Receved sgnals: {y (t) } T t=1; Measurement matrx: Φ = [ϕ 1, ϕ 2,, ϕ N ]; Threshold: P th. Output: Channel estmates: {ĥ (t) } T t=1. 1: Intalzaton : 2: ˆΛ(0) =, ĥ(0) = 0. 3: for t = 1 to T do 4: y + = y (t) Φĥ(t 1). 5: Λ + = arg max {λ = ϕ H y + : / ˆΛ (t 1) }. 6: ˆΛ(t) = ˆΛ (t 1) Λ +. 7: ĥ (t) = arg mn h { Φh y (t) 2 : supp(h) ˆΛ (t) }. 8: Λ = { : ĥ(t) P th, ˆΛ (t) }. 9: ĥ (t) Λ = 0, ˆΛ (t) = ˆΛ (t) Λ. 10: end for 11: return {ĥ (t) } T t=1. The pseudocode of the proposed D-OMP algorthm s provded n Algorthm 1, and each loop s comprsed of the followng three parts: 1) Incremental Support Detecton (step 4 6): Frstly, we obtan the ncremental observatons y + by subtractng Φĥ(t 1) from y (t) n step 4, where ĥ(t 1) denotes the estmate of h (t 1). Here we use Φĥ(t 1) nstead of y (t 1) to avod the mpact of the nose n (t 1). Dfferent from the way used n the standard OMP algorthm whch teratvely detects the canddate supports by selectng the element that correlates best wth the resdual sgnal [5], here we only detect the ncremental support Λ + n step 5, whch s able to acqure the appearng channel tap as s (t 1) = 0 s (t) = 1. Then, the temporary estmate of the path delays set ˆΛ (t) s obtaned by mergng ˆΛ (t 1) whch contans the persstent channel taps,.e., Λ (t 1) Λ (t), and Λ + whch contans the appearng channel tap. 2) Channel Estmate Update (step 7): Step 7 ams to update the channel estmate based on the temporary estmate of the path delays set ˆΛ (t). Intutvely, the varaton of the channel estmate s comprsed of three parts: a) The appearng channel tap a (t) when s (t 1) = 0 s (t) = 1; b) The dsappearng channel tap a (t 1) j when s (t 1) j = 1 s (t) j = 0; c) The smooth varaton of the path gans w (t) ( ˆΛ (t) ). The mnmzaton problem n step 7 corresponds to the man computatonal burden of the D-OMP algorthm, whch can be realzed by the standard least-squares (LS) technque wth low complexty [14]. 3) Dsappearng Channel Taps Removal (step 8 9): When a tap h (t 1) dsappears as s (t 1) = 1 s (t) = 0, the estmated tap n the prevous (t 1)th tme slot wll stll reman n the estmated path delay set of the current tme slot snce ˆΛ (t) = ˆΛ (t 1) Λ +. The path gan of ths dsappearng channel tap ĥ(t) wll be small. Therefore, we propose a threshold P th to judge whether the nonzero elements n ĥ(t) are nonzero channel taps or nose n step 8. After removng the dsappearng channel taps, the fnal channel estmate can be obtaned n step 9. Unlke the standard OMP algorthm whch needs to solve the mnmzaton problem for many tmes accordng to the sparsty level of the wreless channel [6], the proposed D- OMP algorthm only needs to solve the mnmzaton problem once, so the computatonal complexty can be dramatcally reduced. Furthermore, unlke the hard threshold [4] or the rough crteron [9], we rely on the nose analyss to select the threshold P th, whch wll be derved n the followng subsecton. B. Threshold Based on Nose Statstcs Here we consder a sngle tme slot (we omt the tme slot superscrpt t), and rewrte (1) as y = Φh + n = Φ(h + Φ n) = Φ(h + n ), (4) where Φ = Φ H (ΦΦ H ) 1 denotes the pseudonverse of Φ. Generally, lnear channel estmaton methods are desgned to drectly approach h + n, so ther performance s lmted by the contamnaton of the equvalent nose n = Φ n n (4). The advantage of CS-based nonlnear estmaton methods s that they reconstruct the sparse channel h and avod part of the nterference caused by the equvalent nose n. Snce the basc dea of the greedy CS methods s to teratvely search the channel taps from the strongest one to the weakest one [4], [9], t s dffcult for these algorthms to judge whether the searched taps are true,.e., non-zero channel taps or nose, when they are weak. In order to further reduce the nterference caused by n under the CS framework, we desgn the threshold P th based on the statstcal propertes of the nose n for the proposed D-OMP algorthm to separate non-zero channel taps from nose as much as possble. Accordng to (4), we have n = Φ n. The mean of the vector n can be easly obtaned as E{n } = E{Φ }E{n} = 0 due to the fact that the measurement matrx Φ and the nose vector n are ndependent. Then, the covarance of the elements n equvalent nose n can be derved as Var{n } = Var{ϕ n} = MVar{ϕ,j }Var{n j} = MσnVar{ϕ 2,j }, (5) where ϕ denotes the th row of the matrx Φ and ϕ,j s the jth element of ϕ. Furthermore, we have Φ = Φ H (ΦΦ H ) 1 Φ H (NσϕI 2 M ) 1 = 1 Nσϕ 2 Φ H, (6) where we use Nσ 2 ϕ I M to approxmate ΦΦ H due to the randomness of the matrx Φ. Then we can obtan the varance 794

4 Mlcom 2015 Track 1 - Waveforms and Sgnal Processng of n as Var{n } Mσ2 n (Nσϕ 2)2 Var{ϕ,j} = Mσ2 n N 2 σϕ 2. (7) Fnally, the statstcal propertes of the elements n n can be represented as n CN (0, σ 2 n ) CN (0, Mσ2 n N 2 σϕ 2 ). (8) Wth the help of the statstcal propertes of the nose vector n, the threshold P th can be selected as P th = ασ n ασ n M σ ϕ N, (9) where the varance σn 2 of the nose vector n can be usually obtaned at the recever [15]. The coeffcent α can be set as α = 3 so that the strength of the nose element n wll be smaller than P th wth hgh probablty of 99.73%, based on the assumed Gaussan dstrbuton. IV. PERFORMANCE ANALYSIS A. Persstent Channel Tap Detecton In secton III-B, the proposed threshold P th = ασ n s used to remove the dsappearng channel taps from the channel estmate result wth hgh probablty. On the other hand, as the proposed scheme may also remove a persstent channel tap by mstake, the correct detecton probablty of the persstent tap for the scheme s also mportant to guarantee ts performance n practce, whch wll be analyzed below. Frstly, the SNR γ at the recever can be obtaned [15] and represented as γ = 10log Var{Φh} Var{n} = 10logKσ2 ϕ σ2 h σ 2 n = 10log MKσ2 h N 2 σ 2 n, (10) where K = Np 1 denotes the sparsty level of the dynamc sparse channel. Thus, the threshold P th can be obtaned as P th = ασ n = ασ h MK 10 γ 10 N 2. (11) After the threshold has been obtaned, we can calculate the detecton probablty of a persstent channel tap as P (h (t) Λ), whch can be derved by usng the normal Gaussan dstrbuton probablty functon Ψ as P (h (t) Λ) = P ( h (t) > P th ) ( ) MK = 2 1 Ψ(α 10 γ 10 N ). (12) 2 For example, n a typcal wreless communcaton system wth M = 200, N = 400, K = 5, and γ = 15 db, the probablty of a persstent tap beng larger than P th s about 96.64%. B. Appearng Channel Tap Detecton As the D-OMP algorthm s proposed to track a dynamc channel, the condton of appearng channel tap detecton s mportant to be analyzed. For the sake of a smplfed analyss, we assume that the channel estmate n tme slot (t 1) s accurate wthout loss of generalty,.e., ĥ (t 1) = h (t 1). When there s an appearng channel tap from tme slot (t 1) to (t) (for smplcty, we assume other channel taps stay unchanged,.e., h (t) k = h (t 1) k, k Λ (t 1) ), the step 4 n Algorthm 1 can be rewrtten as y + = y (t) Φh (t 1) = ϕ h (t) + n, (13) where h (t) ( / Λ (t 1) ) denotes the appearng channel tap at the tme ndex durng the tth tme slot of the dynamc sparse channel. Accordng to the detecton rule n step 5 of Algorthm 1, the appearng channel tap h (t) s successfully detected f and only f λ j < λ, j, j / ˆΛ (t 1), (14) where λ can be derved as λ = ϕ H y + = ϕ H (ϕ h (t) Then λ j can be smlarly derved as + n) ϕ H ϕ h (t) ϕ H n. (15) λ j = ϕ H j y + = ϕ H j (ϕ h (t) + n) ϕ H j ϕ h (t) + ϕ H j n. (16) Usng (14), we can obtan the condton under whch the appearng channel tap h (t) s successfully detected: h (t) ϕh n + ϕ H j n ϕ H ϕ ϕ H j ϕ, j, j / ˆΛ (t 1), (17) whch means the path gan of the appearng channel tap should be larger than a mnmum value. Intutvely, the dea behnd the ncremental support detecton of the proposed D-OMP algorthm s to fnd the elements Λ + that correlate best wth the ncremental observatons y +, but the prevously detected support ˆΛ (t 1) wll not be consdered. Due to the fact that the appearng channel tap can be detected mmedately f t s larger than a certan value derved n (17), whle the posteror covarance matrx of the HB-Kalman method [10] needs several tme slots to converge, the condton of ncremental support detecton of the proposed D-OMP algorthm s much easer to satsfy than that of the HB-Kalman method. C. Computatonal Complexty The computatonal complexty of the proposed D-OMP algorthm n terms of the requred number of complex multplcatons ncludes the followng three parts: 1) In the ncremental detecton part, the complexty s O(NM) for the calculaton of Φĥ(t 1) and ϕ H y +. 2) In the channel estmate update part, the LS problem arg mn h { Φh y + 2 : supp(h) ˆΛ (t) } can be 795

5 Mlcom 2015 Track 1 - Waveforms and Sgnal Processng 1 MSE Lnear Method [2] Standard OMP [6] A SOMP [9] HB Kalman [10] Proposed D OMP Correct Detecton Probablty Hard Threshold [4] Rough Crteron [9] Proposed Threshold Theoretcal bound (12) Tme SNR (db) Fg. 2. MSE performance comparson aganst tme slot t. Fg. 3. The correct detecton probablty comparson aganst SNR. mplemented wth the O(MK 2 ) complexty by usng the Gram-Schmdt algorthm [14]. 3) In the dsappearng taps removal part, the complexty s O(M) for the comparson of taps wth the threshold P th. To sum up, the total complexty of the proposed D- OMP algorthm s O(M(N + K 2 + 1)T ) to track a dynamc sparse channel over T tme slots. Compared wth the O(KM(N + K 2 )T ) complexty of the standard OMP algorthm, the complexty of the proposed D-OMP algorthm s reduced approxmately by a factor of K. Consderng the re-estmaton of the posteror covarance matrx wth J teratons n each tme slot [11], the computatonal complexty of HB-Kalman flter [10] s O(JKM(N + K 2 )T ), whch s much hgher than the complexty for both the standard OMP algorthm and the proposed D-OMP algorthm. The complexty reducton comes from the fact that the proposed D-OMP algorthm obtans the major nformaton of the current channel from the estmaton results n prevous tme slots, and then refnes the fnal estmaton result by detectng the small varaton of the channel. V. SIMULATION RESULTS AND DISCUSSION Ths secton nvestgates the performance of the proposed D-OMP algorthm compared wth the conventonal lnear algorthm [2], standard OMP algorthm [6], A-SOMP algorthm [9], and HB-Kalman algorthm [10]. The parameters mentoned n Secton II (system model) are set as follows: 1) The sze of the matrx Φ s N = 400 and M = 200; 2) The probablty p 1 s set as 0.025, whch means the average channel sparsty level s K = Np 1 = 10; 3) A channel tap wll appear or dsappear over every 1/(Kp 1 0 ) = 1/((N K)p 0 1 ) = 10 tme slots on average correspondng to probabltes p 1 0 = 0.01 and p 0 1 = p 1 p 1 0 /(1 p 1 ); 4) σ a = 0.05, σ n = 0.05, σ h = 1, σ ϕ = 1. Fg. 2 shows the mean squared error (MSE) performance aganst tme slot t for the fve channel estmaton methods MSE Lnear Method [2] Standard OMP [6] A SOMP [9] HB Kalman [10] Proposed D OMP SNR (db) Fg. 4. MSE performance comparson aganst SNR. mentoned above. It s clear that A-SOMP and HB-Kalmam acheve lower error levels than the standard OMP algorthm, whle the conventonal lnear method performs worst. The MSE performance of the proposed D-OMP algorthm s the best, as the temporal correlatons of the dynamc sparse channel are effcently exploted. More mportantly, when two channel taps suddenly dsappear n tme slot t = 80, the HB- Kalman algorthm requres about 20 tme slots to detect ths, whle the proposed D-OMP algorthm s able to detect the change mmedately, whch confrms the trackng capablty of the proposed scheme as dscussed n secton IV-B. Fg. 3 shows the correct detecton probablty of a persstent channel tap aganst SNR. It s evdent that the hard threshold used n many CS-based channel estmaton methods [4] s not adapted to the SNR. The rough crteron [9] can mprove the correct detecton probablty by usng the statstcal nformaton of the channel. For the proposed threshold P th based on nose statstcs, the correct detecton probablty can be mproved further, whch s close to the theoretcal bound 796

6 Mlcom 2015 Track 1 - Waveforms and Sgnal Processng derved n (12). Fg. 4 shows the MSE performance comparson aganst SNR for the fve channel estmaton methods. It s clear that the standard OMP algorthm outperforms the lnear method by about 1 db, where the beneft comes from utlzng the channel sparsty. Further, A-SOMP and HB-Kalman are better than the standard OMP algorthm by about 2 db, snce they partally consder the temporal correlatons of the dynamc sparse channel. For the proposed D-OMP algorthm, t s evdent that another 2 db SNR gan can be acheved due to ts capablty to track the dynamc sparse channel rapdly and detect the non-zero channel taps accurately as dscussed n Secton IV. VI. CONCLUSION In ths paper, we have proposed a novel dynamc CS algorthm called D-OMP to rapdly track a dynamc sparse broadband communcaton channel n a sequental way by updatng only the small channel varaton over tme. An adaptve threshold based on nose statstcs s used n the proposed D-OMP algorthm to remove the dsappearng channel taps. Moreover, the performance analyss provdes the correct detecton probablty of persstent channel taps as well as the condton of appearng channel tap detecton for the dynamc sparse channel wth low computatonal complexty. Fnally, smulaton results demonstrate that the proposed D- OMP algorthm s able to rapdly detect appearng channel taps, and acheves about 2 db gan compared wth the recently proposed dynamc channel trackng algorthms. ACKNOWLEDGMENT Ths work was supported by Natonal Key Basc Research Program of Chna (Grant No. 2013CB329203) and Natonal Natural Scence Foundaton of Chna (Grant Nos and ). REFERENCES [1] J. Ln, Least-squares channel estmaton for moble OFDM communcaton on tme-varyng frequency-selectve fadng channels, IEEE Trans. Veh. Technol., vol. 57, no. 6, pp , Nov [2] S. Coler, M. Ergen, A. Pur, and A. Baha, Channel estmaton technques based on plot arrangement n OFDM systems, IEEE Trans. Broadcast., vol. 48, no. 3, pp , Sep [3] N. Cznk, X. Yn, H. Ozcelk, M. Herdn, E. Bonek, and B. Fleury, Cluster characterstcs n a MIMO ndoor propagaton envronment, IEEE Trans. Wreless Commun., vol. 6, no. 4, pp , Apr [4] C. Berger, Z. Wang, J. Huang, and S. Zhou, Applcaton of compressve sensng to sparse channel estmaton, IEEE Commun. Mag., vol. 48, no. 11, pp , Nov [5] J. Tropp, Greed s good: Algorthmc results for sparse approxmaton, IEEE Trans. Inf. Theory, vol. 50, no. 10, pp , Oct [6] G. Gu, A. Mehbodnya, Q. Wan, and F. Adach, Sparse sgnal recovery wth OMP algorthm usng sensng measurement matrx, IEICE Electroncs Express, vol. 8, no. 5, pp , Mar [7] G. Gu, W. Peng, and F. Adach, Improved adaptve sparse channel estmaton based on the least mean square algorthm, IEEE WCNC 2013, pp , Apr [8] S. Borade and L. Zheng, Wrtng on fadng paper, drty tape wth lttle nk: Wdeband lmts for causal transmtter CSI, IEEE Trans. Inf. Theory, vol. 58, no. 8, pp , Aug [9] L. Da, J. Wang, Z. Wang, P. Tsaflaks, and M. Moonen, Spectrum- and energy-effcent OFDM based on smultaneous mult-channel reconstructon, IEEE Trans. Sgnal Process., vol. 61, no. 23, pp , Dec [10] E. Karseras, K. Leung, and W. Da, Trackng dynamc sparse sgnals usng Herarchcal Bayesan Kalman flters, IEEE ICASSP 2013, pp , May [11] S. J, Y. Xue, and L. Carn, Bayesan compressve sensng, IEEE Trans. Sgnal Process., vol. 56, no. 6, pp , Jun [12] Gudelne for Evaluaton of Radon Transmsson Technology for IMT- 2000, Recommendaton ITU-R M. 1225, [13] C. Tan and N. Beauleu, On frst-order Markov modelng for the Raylegh fadng channel, IEEE Trans. Commun., vol. 48, no. 12, pp , Dec [14] K. Seung-Jean, K. Koh, M. Lustg, S. Boyd, and D. Gornevsky, An nteror-pont method for large-scale l1-regularzed least squares, IEEE J. Sel. Areas Sgnal Process., vol. 1, no. 4, pp , Dec [15] G. Png and C. Tepedelenloglu, SNR estmaton for nonconstant modulus constellatons, IEEE Trans. Sgnal Process., vol. 53, no. 3, pp , Mar