Sparse Channel Estimation Based on Compressed Sensing for Massive MIMO Systems

Transcription

1 Sparse Channe Estimation Based on Compressed Sensing for Massive MIMO Systems Chenhao Qi, Yongming Huang, Shi Jin and Lenan Wu Schoo of Information Science and Engineering, Southeast University, Nanjing , China Emai: Abstract The sparse channe estimation which sufficienty expoits the inherent sparsity of wireess channes, is capabe of improving the channe estimation performance with ess piot overhead. To reduce the piot overhead in massive MIMO systems, sparse channe estimation exporing the joint channe sparsity is first proposed, where the channe estimation is modeed as a joint sparse recovery probem. Then the boc coherence of MIMO channes is anayzed for the proposed mode, which shows that as the number of antennas at the base station grows, the probabiity of joint recovery of the positions of nonzero channe entries wi increase. Furthermore, an improved agorithm named boc optimized orthogona matching pursuit (BOOMP) is aso proposed to obtain an accurate channe estimate for the mode. Simuation resuts verify our anaysis and show that the proposed scheme exporing joint channe sparsity substantiay outperforms the existing methods using individua sparse channe estimation. Index Terms Compressed sensing (CS); sparse channe estimation; massive MIMO; arge-scae MIMO; I. Introduction In order to improve the data rate as we as the reiabiity of wireess systems, the muti-antenna technoogy, termed as mutipe-input mutipe-output (MIMO), has been extensivey investigated in the ast two decades. In a typica muti-user MIMO system, a base station (BS) equipped with some antennas simutaneousy communicates with severa users each equipped with a singe antenna. Recenty, it has been shown that as the number of BS antennas grows to be infinity, the effect of additive noise and rayeigh fading is negigibe and a very high data rate can be achieved [1]. Therefore, we may construct a massive MIMO or arge-scae MIMO system by equipping the BS with orders of magnitude more antennas, e.g., 128, which is even arger than the number of users that the BS serves [2]. In this way, the BS can sufficienty expoit the spatia degree of freedom to simutaneousy communicate with severa users using the same tempora and frequency resource [3]. The researchers from Rice University estabish a BS equipped with 64 antennas serving 15 users, which is demonstrated to achieve up to 6.7 fod capacity gains whie using a mere 1/64th of transmission power [4]. One of the chaenges in massive MIMO systems is the piot overhead that grows ineary with the number of channes to be estimated. In massive MIMO systems, the number of wireess ins and channes is very arge, eading to the proiferation of piot overhead and thus the reduced resource for data. To reduce the piot overhead, one potentia choice is to expore the inherent sparsity of wireess channes and to use the sparse channe estimation [5], [6], [7]. Wireess channe is essentiay sparse, where ony a sma number of channe coefficients are nonzero. By appying recenty emerged compressed sensing (CS) technique, sparse channe estimation can be used to estimate the channe impuse response (CIR) based on the received and transmitted piot symbos. Compared to the east squares (LS) and minimum mean square error (MMSE) methods, sparse channe estimation is capabe of improving the channe estimation performance and reducing the piot overhead [8], [9], [10], [11]. In [5], distributed compressive channe estimation and feedbac schemes are considered for frequency-division dupex (FDD) massive MIMO Systems. In [12], superimposed piot design for downin FDD massive MIMO systems is proposed based on structured CS. In [13], sparse channe estimation with structured CS is proposed for muti-input singe-output (MISO) systems. In [14], based on the idea that the degree of freedom of the channe matrix is smaer than the number of free parameters, a ow-ran matrix approximation is proposed and soved via semidefinite programming (SDP). In [15], upin channe estimation exporing joint channe sparsity is investigated for massive MIMO systems. It is shown in [16] that the CIR from different BS antennas to the same user antenna shares a common support, because the time of arriva (ToA) is simiar whie the paths ampitudes and phases are distinct. In other words, the nonzero positions of different CIRs are the same, exhibiting the joint sparsity. So it is beneficia to expoit the joint sparsity so that the number of piots for channe estimation can be substantiay reduced. In this paper, we first consider the sparse channe estimation exporing the joint channe sparsity, where the channe estimation is modeed as a joint sparse recovery probem. Then the boc coherence of MIMO channes is anayzed for the proposed mode, which shows that as the number of BS antennas grows, the probabiity of joint recovery of the positions of nonzero channe entries wi increase. Furthermore, an agorithm named boc optimized orthogona matching pursuit (BOOMP) is aso proposed to obtain a reiabe soution to this mode. The remainder of this paper is organized as foows. Section II provides the system mode for sparse channe estimation expoiting joint sparsity, which is then formuated as a joint sparse recovery probem. Section III anayzes the boc coherence for the proposed mode. In Section IV, an agorithm named BOOMP is proposed to get a soution to the /15/$ IEEE 4558

2 mode. Simuation resuts are provided in Section V. Finay, Section VI concudes this paper. The notations used in this paper are defined as foows. Symbos for matrices (upper case) and vectors (ower case) are in bodface. ( ) T, ( ) H, diag{ }, I L, a 2, CN and, denote the matrix transpose, conjugate transpose (Hermitian), the diagona matrix, the identity matrix of size L, 2 -norm of a vector a, the compex Gaussian distribution and the empty set, respectivey. II. System Mode As shown in Figure 1, we give a three-ce massive MIMO system. We iustrate three different configuration of BS antennas, e.g., inear antenna configuration on an edge of a buiding, rectanguar antenna configuration at a wa of a buiding, and cyindrica antenna configuration on a tower. Therefore, it is fexibe to depoy BS for different scenarios in practice. With the arge number of antennas, the energy can be focused on extremey sharp beams, where the beamforming wi be more efficient and the spatia degree of freedom can be fuy expoited. cyindrica rectanguar BS. With the downin CSI, the BS designs the beamforming vector for each user so that the spatia degree of freedom in the massive MIMO system can be fuy expoited. In order to distinguish M different downin channes, the BS has to use M orthogona piots, either in time domain, frequency domain, or sequence domain. According to current wireess standards [17], frequency-orthogona piots are usuay empoyed. With the increased number of BS antennas, i.e., growing M, these orthogona piots wi occupy increased resource, resuting in reduced resource for data transfer. So in the foowing, we wi expore the joint sparsity of downin channes and reduce the piot overhead. The positions of piot subcarriers mae up a piot pattern, which is a positive integer vector. Suppose the piot pattern used by the ith BS antenna is p (i), i = 1, 2,..., M. The piot patterns used by different antennas are frequency-orthogona to each other, i.e., p (i) p ( j) = if i j, where represents the intersection of two sets. Suppose the OFDM symbo transmitted by the ith BS antenna is x (i), i = 1, 2,..., M. The piot vector transmitted by the ith BS antenna can be denoted as x (i) (p (i) ), i = 1, 2,..., M. After the user receives an OFDM symbos y, it can extract the received piot vectors y(p (i) ), i = 1, 2,..., M, corresponding to different transmit piot vectors, because the transmit piot vectors are orthogona in the frequency domain. To ease the notation, we define y (i) y(p (i) ), i = 1, 2,..., M. We then formuate the channe estimation probem as y (i) = D (i) F (i) h (i) + η (i), i = 1, 2,..., M (1) Fig. 1. systems. beam inear Three different configuration of BS antennas in massive MIMO To overcome the frequency-seective fading and improve the spectra efficiency, orthogona frequency division mutipexing (OFDM) is usuay adopted for downin transmission in current wireess standards, e.g., LTE-A [17]. OFDM transforms the frequency-seective wireess channe into severa parae fat-fading narrowband subchannes. Each subchanne ony needs a singe-tap equaizer, and therefore the high compexity associated with the ong equaizer to combat inter-symbo interference (ISI) is substantiay mitigated. We consider a massive MIMO system incuding a BS e- quipped with M antennas and severa users each equipped with a singe antenna. We use OFDM for downin transmission. Suppose the tota number of OFDM subcarriers is N. From N subcarriers, K(0 < K N) subcarriers are seected to transmit piot symbos for piot-assisted channe estimation. In FDD systems, each user first performs channe estimation for each downin channe and then feeds bac the quantized CSI to the where D (i) diag{x (i) (p (i) )} denotes a diagona square matrix, with the diagona entries being the entries of x (i) (p (i) ); η (i) CN(0, σ 2 I K ) denotes the noise term of the ith downin channe; F (i) is a K by L submatrix indexed by p (i) in row and [1, 2,..., L] in coumn from a standard N by N DFT matrix; and h (i) = [h (i) (1), h (i) (2),..., h (i) (L)] T denotes the CIR of the ith downin channe. Due to the inherent sparsity of wireess channes, most entries of h (i) are zero, and the number of the nonzero entries of h (i) equas the number of mutipath in the ith downin channe. It is shown in [16] that the CIR of different downin channes shares a common support, because the ToA from different transmit antennas to the same receive antenna is simiar whie the path ampitudes and phases are distinct. In other words, the nonzero positions of h (i) are the same for i = 1, 2,..., M, whie their nonzero coefficients are different. We define the measurement matrix A (i) D (i) F (i), then (1) can be rewritten as y (i) = A (i) h (i) + η (i), i = 1, 2,..., M (2) which is essentiay to use y (i) and A (i) to estimate h (i) under the perturbation of η (i). In order to expore the joint sparsity of MIMO downin channes, we define w as a stac vector w [w T 1, wt 2,..., wt L ]T (3) where w [h (1) (), h (2) (),..., h (M) ()] T denotes the th boc of w, = 1, 2,..., L. Since the nonzero positions of h (i) are the 4559

3 same for i = 1, 2,..., M, the entries of w i wi be either a zero or a nonzero, exhibiting the boc sparsity. Correspondingy, we define a stac vector of received piots as where z [z T 1, zt 2,..., zt K ]T (4) z [y (1) (), y (2) (),..., y (M) ()] T (5) denotes the th boc of z, = 1, 2,..., K. In the same way, we define a stac vector of noise terms as where n [n T 1, nt 2,..., nt K ]T (6) n [η (1) (), η (2) (),..., η (M) ()] T (7) denotes the th boc of n, = 1, 2,..., K. We generate a new measurement matrix B based on a matrix E. Given any matrix E with K rows and L coumns, we substitute the throw jth-coumn entry of E, denoted as E(, j), by a diagona matrix diag{a (1) (, j), A (2) (, j),..., A (M) (, j)}, = 1, 2,..., K, j = 1, 2,..., L. We thus construct a boc-diagona matrix B with MK rows and ML coumns. The sparse channe estimation exporing joint sparsity can be finay formuated as z = Bw + n. (8) Recent wors in CS show that the sparse recovery performance of (8) is determined by two factors, incuding the structure of B and the sparse recovery agorithm, which wi be discussed in Section III and Section IV, respectivey. III. Anaysis of Boc Coherence Assuming that each coumn of B in (8) is normaized. This assumption is reasonabe because we can normaize B by simpy decomposing it into a normaized matrix Q and a diagona matrix G so that B = QG. And after the sparse recovery, we can obtain the soution to the origina probem by mutipying the resuts with G 1. We define the coherence of A (i), i = 1, 2,..., M for (2) as µ(a (i) ) = max (a (i) ) H a (i) (9) where a (i) denotes the th coumn of A (i), = 1, 2,..., L. To improve the sparse recovery performance of (2), it is better to minimize µ(a (i) ) [8]. We represent B in (8) as a concatenation of bocs B, = 1, 2,..., L, as B [ b 1, b 2,..., b } {{ M, b } M+1, b M+2,..., b 2M,..., } {{ } B 1 B 2 ] b LM M+1, b LM M+2,..., b } {{ LM} B L (10) where b j denotes the jth coumn of B, j = 1, 2,..., LM. It s observed that the coumns within each boc of B are orthogona to each other, meaning that the ran of each boc is M. Simiary, we define the coherence of B as µ(b) = max bh b. (11) Considering that the sparse w in (8) exhibits boc sparsity, we further define the boc coherence of B according to [18] as µ B (B) = 1 M max ρ(bh B ) (12) where we denote the spectrum norm of a given matrix R as ρ(r) λ 1/2 max(r H R), (13) with λ max (R H R) representing the argest eigenvaue of the positive-semidefinite matrix R H R. Theorem 1: For sparse channe estimation exporing the joint sparsity which is formuated in (8), we have Proof: From (8) and (10), we observe that µ B (B) = 1 µ(b). (14) M µ(b) = According to (12), we have max i=1,2,...,m µ(a(i) ). (15) µ B (B) = 1 M max ρ(bh B ) = 1 ( M max ρ diag { ( a (1)) H a (1), ( a (2) ) H a (2),..., ( a (M) ) H }) a (M) = 1 ( M max λ1/2 max diag { ( a (1)) H a (1) 2, ( a (2) ) H a (2) 2,..., ( a (M) ) H a (M) 2 }) = 1 M max max ( a (i) ) H i=1,2,...,m a (i) = 1 M max ( a (i) ) H a (i) max i=1,2,...,m = 1 M max i=1,2,...,m µ(a(i) ) = 1 µ(b). (16) M If M grows to be infinity, µ B (B) wi be zero, which means that the bocs B, = 1, 2,..., L, in (10) wi be orthogona to each other, eading to the unique recovery of bocs. So as the number of BS antennas grows, the probabiity of joint recovery of the positions of nonzero channe entries wi increase. In this way, we can reduce the piot overhead and therefore eave more resource for data transfer in the massive MIMO system. IV. Boc Optimized Orthogona Matching Pursuit (BOOMP) Existing methods for soving (8) can be roughy divided into two casses, incuding convex optimization agorithms and greedy agorithms. The convex optimization agorithms incude BP agorithms such as 1 -LS, YALL1, SpaRSA and other optimization sovers. The greedy agorithms construct a sparse soution by iterativey seecting the matrix coumns and eventuay forming a inear combination of them cosest to the 4560

4 origina signa, and they incude methods such as orthogona matching pursuit (OMP), CoSaMP, subspace pursuit and Homotopy. However, a of these agorithms did not expoit the joint sparsity. Now we propose a BOOMP agorithm exporing the joint sparsity for the proposed mode in (8). Note that the BOOMP agorithm presented in this wor is based on the optimized OMP agorithm (OOMP) [19] instead of the basic OMP agorithm. Agorithm 1-Boc Optimized Orthogona Matching Pursuit 1: Input: B, z, M, L, σ. 2: Initiaizations: r z. T 0. Λ 3: whie r 2 > Mσ and T L 4: T T : Obtain J via (17). 6: Λ Λ {J}. 7: r z B Λ (B H Λ B Λ) 1 B H Λ z. 8: end 9: Output: ĥ (i) Λ (A H Λ A Λ) 1 A H Λ y(i), i = 1, 2,..., M. At first, we initiaize a residue vector r z and a oop counter T 0. At each iteration, we obtain an index of the nonzero entry of h (i) by J = arg max (B H j B j) 1 B H j r 2 (17) j {1,2,...,L}\Λ and eep J in an active set Λ. Since h (i) shares a common support for i = 1, 2,..., M, we ony need one active set to eep the common support. We denote the submatrix indexed by Λ in bocs from B and the submatrix indexed by Λ in coumns from A as B Λ and A Λ, respectivey. We iterativey update the residue r by the LS estimation in step 7 of Agorithm 1, where (B H Λ B Λ) 1 B H Λ is the pseudo inverse of B Λ. Once the power of residue is comparabe to the noise or the number of iterations is greater than L, we stop the iterations. Meanwhie we output the estimated CIR as ĥ (i), with the coefficients of nonzero entries denoted as ĥ (i) Λ, i = 1, 2,..., M. V. Simuation Resuts We consider a massive MIMO system incuding a BS equipped with M = 8 antennas. The BS uses N = 256 OFDM subcarriers for downin transmission, where K = 16 subcarriers are seected to transmit piot symbos. QPSK is empoyed for moduation. The ength of the CIR vector is set to be L = 60. The number of channe mutipath is set to be S = 12, which means that there are ony S = 12 nonzero entries in the CIR vector. Since different channes share a common support [16], the positions of nonzero entries in the CIR vector are the same whie the coefficients of these nonzero entries are different. A. With the fixed positions of nonzero entries of CIR We first consider the fixed positions of nonzero entries of CIR. The positions of nonzero entries are fixed to be [2, 13, 21, 24, 29, 33, 41, 42, 43, 53, 54, 60]. In order to estimate the downin channe, each BS antenna transmits a piot symbo and the user wi simutaneousy receive M = 8 different piot symbos, meaning that the user has to estimate M = 8 channes. In order to distinguish different downin channes, frequency-orthogona piots are used. In Tabe I, we provide M = 8 frequency-orthogona piots via piot optimization [8]. Each piot in Tabe I is used by a BS antenna for downin sparse channe estimation. TABLE I Frequency-orthogona piots for sparse channe estimation in the massive MIMO system. Positions of piot subcarriers 1st antenna 8, 40, 48, 52, 72, 82, 99, 142, 145, 154, 158, 161, 183, 209, 212, 230 2nd antenna 9, 41, 49, 53, 73, 83, 100, 143, 146, 155, 159, 162, 184, 210, 213, 231 3rd antenna 10, 42, 50, 54, 74, 84, 101, 144, 147, 156, 160, 163, 185, 211, 214, 232 4th antenna 17, 25, 47, 56, 59, 63, 75, 111, 115, 130, 141, 149, 153, 174, 200, 250 5th antenna 12, 34, 55, 64, 67, 109, 112, 148, 173, 215, 222, 233, 238, 241, 249, 252 6th antenna 2, 15, 45, 58, 62, 66, 96, 103, 107, 132, 165, 181, 186, 189, 204, 206 7th antenna 18, 22, 33, 68, 76, 80, 88, 91, 95, 116, 133, 167, 198, 205, 229, 246 8th antenna 7, 79, 92, 117, 120, 152, 168, 180, 187, 197, 219, 223, 239, 243, 251, 255 Now we compare the individua sparse channe estimation using OMP and the joint sparse channe estimation using BOOMP. Since K 2S, the individua sparse channe estimation can not succeed, from information theoretica point of view, because K = 16 equations are not enough to sove 24 unnown variabes incuding S = 12 unnown positions and S = 12 unnown coefficients of nonzero entries. As shown in Tabe II, the positions of nonzero entries individuay estimated for h (i), i = 1, 2,..., 8, named as individua for ith antenna, are a incorrect. Then we use 2 of 8 antennas, 4 of 8 antennas, 6 of 8 antennas and a 8 antennas, respectivey, for joint sparse channe estimation, named as joint for x antennas with x = 2, 4, 6, or 8. It is seen from Tabe II that we can not obtain the true positions exacty as those of the origina CIR uness we use a x = 8 antennas for joint sparse recovery, which verifies the anaysis of boc coherence in Section III. Moreover, the estimation performance wi further increase if we use more antennas and expore the joint sparsity. We further compare the performance of individua sparse channe estimation and joint sparse channe estimation in terms of mean square error (MSE). We define the MSE as MS E = 1 V h (i) ĥ (i) 2 2. (18) V i=1 h (i) 2 2 where ĥ (i) is the estimate of h (i) and V is the number of a possibiities for the averaging. For exampe, in individua sparse channe estimation, V = 8. In joint sparse channe 4561

5 TABLE II Comparisons of individua sparse recovery and joint sparse recovery in terms of estimated nonzero positions for downin channes. Positions of nonzero entries True positions 2,13,21,24,29,33,41,42,43,53,54,60 Individua for 1st antenna 2,8,15,21,24,33,41,42,47,53,54,60 Individua for 2nd antenna 1,2,13,24,35,40,44,46,50,53,54 Individua for 3rd antenna 2,5,11,13,20,24,33,37,42,53,54,55,60 Individua for 4th antenna 1,8,13,17,24,27,33,41,43,46,53,60 Individua for 5th antenna 5,6,13,15,20,21,24,29,31,32,38,41,51,60 Individua for 6th antenna 2,7,12,21,24,26,33,41,42,49,54,60 Individua for 7th antenna 3,8,10,17,21,26,36,41,42,43,50,55,59 Individua for 8th antenna 2,6,15,18,20,21,24,29,32,41,49,56,60 Joint for 2 antennas 8,9,10,12,13,15,21,25,36,43,44,50,56,60 Joint for 4 antennas 2,10,12,13,19,21,24,41,47,50,53,54,57,60 Joint for 6 antennas 3,6,7,13,14,23,29,33,40,41,42,43,51,53,60 Joint for 8 antennas 2,13,21,24,29,33,41,42,43,53,54,60 B. With random positions of nonzero entries of CIR Now we consider the random positions of nonzero entries of CIR. For MIMO channe reaization where the positions of nonzero entries of CIR are randomy generated, we execute the routine described in the previous subsection. In this way we repeat it 1000 times and mae an average of them. As shown in Figure 3, the joint estimation using BOOMP outperforms the individua estimation using OMP. Moreover, as the number of BS antennas for joint sparse channe estimation increases, the MSE can be further reduced MSE 10 1 MSE Individua sparse channe estimation for each BS antenna Using 4 of 8 antennas for joint sparse channe estimation Using a 8 antennas for joint sparse channe estimation SNR / db 10 2 Individua sparse channe estimation for each BS antenna Using 2 of 8 antennas for joint sparse channe estimation Using 4 of 8 antennas for joint sparse channe estimation Using 6 of 8 antennas for joint sparse channe estimation Using a 8 antennas for joint sparse channe estimation SNR / db Fig. 2. Comparisons of individua sparse channe estimation and joint sparse channe estimation in terms of MSE with the fixed positions of nonzero entries of CIR. estimation using 2 of 8 antennas, V = ( 8 2) = 28. It is seen from Figure 2 that the joint estimation using BOOMP notaby outperforms the individua estimation using OMP. Moreover, we can further improve the MSE performance by empoying more BS antennas for joint sparse channe estimation, which shows that our scheme is beneficia for massive MIMO systems. We aso evauate the piot reduction of joint sparse channe estimation, supposing that the individua sparse channe estimation and joint sparse channe estimation achieve the same MSE performance. The resuts show that when the number of piots increases up to K = 28, the MSE performance of the individua sparse channe estimation and joint sparse channe estimation is the same. Therefore, the piot reduction of (28 16)/16 = 75% can be achieved. Fig. 3. Comparisons of individua sparse channe estimation and joint sparse channe estimation in terms of average MSE with random positions of nonzero entries of CIR. VI. Concusions In this paper, we have investigated the sparse channe estimation based on CS for massive MIMO systems. We have proposed a system mode for sparse channe estimation exporing the joint channe sparsity. We have anayzed the boc coherence for the proposed mode, which has shown that as the number of BS antennas grows, the probabiity of joint recovery of the positions of nonzero channe entries wi increase. We have aso proposed an agorithm named BOOMP to get a soution to the mode. Simuation resuts have verified our anaysis and shown that the proposed sparse channe estimation exporing joint sparsity substantiay outperforms the existing methods using individua sparse channe estimation. Acnowedgment This wor is supported in part by the Nationa Natura Science Foundation of China (NSFC) under Grant and , by the Nationa Science and Technoogy Major Project of China under Grants 2013ZX and 2012ZX , by the Ph.D. Programs Foundation of the Ministry of Education of China under Grant , and by the Fundamenta Research Funds for the Centra Universities under Grant K

6 References [1] E. G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta, Massive MIMO for next generation wireess systems, IEEE Commun. Mag., vo. 52, no. 2, pp , Feb [2] F. Ruse, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, Scaing up MIMO: Opportunities and chaenges with very arge arrays, IEEE Signa Process. Mag., vo. 30, no. 1, pp , Jan [3] H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, Energy and spectra efficiency of very arge mutiuser MIMO systems, IEEE Trans. Commun., vo. 61, no. 4, pp , Apr [4] C. Shepard, H. Yu, N. Anand, L. E. Li, T. L. Marzetta, R. Yang, and L. Zhong, Argos: Practica many-antenna base stations, in Proc. ACM Int. Conf. Mobie Computing and Networing (MobiCom), Istanbu, Turey, Aug. 2012, pp [5] X. Rao and V. Lau, Distributed compressive CSIT estimation and feedbac for FDD muti-user massive MIMO systems, IEEE Trans. Signa Process., vo. 62, no. 12, pp , June [6] L. Dai, J. Wang, Z. Wang, P. Tsiafais, and M. Moonen, Spectrumand energy-efficient OFDM based on simutaneous muti-channe reconstruction, IEEE Trans. Signa Process., vo. 61, no. 23, pp , Dec [7] G. Gui and F. Adachi, Stabe adaptive sparse fitering agorithms for estimating mutipe-input-mutipe-output channes, IET Commun., vo. 8, no. 7, pp , May [8] C. Qi and L. Wu, A study of deterministic piot aocation for sparse channe estimation in OFDM systems, IEEE Commun. Lett., vo. 16, no. 5, pp , May [9] C. Qi, G. Yue, L. Wu, Y. Huang, and A. Naanathan, Piot design schemes for sparse channe estimation in ofdm systems, IEEE Trans. Veh. Techno., vo. 64, to appear in [10] Z. Gao, L. Dai, Z. Lu, C. Yuen, and Z. Wang, Super-resoution sparse MIMO-OFDM channe estimation based on spatia and tempora correations, IEEE Commun. Lett., vo. 18, no. 7, pp , Juy [11] C. Qi and L. Wu, Optimized piot pacement for sparse channe estimation in OFDM systems, IEEE Signa Process. Lett., vo. 18, no. 12, pp , Dec [12] Z. Gao, L. Dai, and Z. Wang, Structured compressive sensing based superimposed piot design in downin arge-scae MIMO systems, Eectron. Lett., vo. 50, no. 12, pp , June [13] W. Hou and C. W. Lim, Structured compressive channe estimation for arge-scae MISO-OFDM systems, IEEE Commun. Lett., vo. 18, no. 5, pp , May [14] S. L. Nguyen and A. Ghrayeb, Compressive sensing-based channe estimation for massive mutiuser MIMO systems, in Proc IEEE Wireess Communications and Networing Conference (WCNC), Shanghai, China, Apr. 2013, pp [15] C. Qi and L. Wu, Upin channe estimation for massive MIMO systems exporing joint channe sparsity, Eectr. Lett., vo. 50, no. 23, pp , Nov [16] Y. Barbotin, A. Hormati, S. Rangan, and M. Vetteri, Estimation of sparse MIMO channes with common support, IEEE Trans. Commun., vo. 60, no. 12, pp , Dec [17] A. Ghosh, R. Ratasu, B. Monda, N. Mangavedhe, and T. Thomas, LTE-Advanced: Next-generation wireess broadband technoogy, IEEE Wireess Commun., vo. 17, no. 3, pp , June [18] Y. C. Edar, P. Kuppinger, and H. Bocsei, Boc-sparse signas: Uncertainty reations and efficient recovery, IEEE Trans. Signa Process., vo. 58, no. 6, pp , June [19] L. R. Neira and D. Lowe, Optimized orthogona matching pursuit approach, IEEE Signa Process. Lett., vo. 9, no. 4, pp , Apr