Joint Use of H-inf Criterion in Channel Estimation and Precoding to Mitigate Pilot Contamination in Massive MIMO Systems

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1 Joint Use of H-inf Criterion in Channel Estimation and Precoding to Mitigate Pilot Contamination in Massive MIMO Systems Peng Xu 1,, Dongming Wang 3, Jinkuan Wang 1 1. School of Information Science and Engineering, Northeastern University, Shenyang, China. School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, China {xup, wjk}@neuq.edu.cn 3. National Mobile Communications Research Laboratory, Southeast University, Nanjing, China {wangdm}@seu.edu.cn Abstract In this paper, a channel estimation (CE and precoding scheme by using H-infinity (H-inf criterion for mitigation of pilot contamination (PC in Massive multiple input multiple output (MIMO orthogonal frequency division multiplexing (OFDM systems is reconsidered. Firstly, different thresholds in H-inf CE and precoding are considered. Secondly, asymptotic analysis of the large system is applied to simplify the H-inf precoding, which shows that the complexity of an order of magnitude is reduced. Thirdly, approximate downlink achievable data rates per user are presented for different CE and precoding schemes, such as H-inf and minimum mean square error (MMSE CE, MMSE, zero-forcing (ZF and H-inf precoding. The analytic work shows that the proposed scheme can provide dual mitigation to the PC. That is, the H-inf CE mitigates the PC by adjusting its thresholds, and the H-inf precoding is utilized to suppress the PC by considering inter-cell interference. The numerical results show that the joint use of H-inf CE and H-inf precoding outperforms existing several schemes in terms of mitigation to the PC. Keywords Massive MIMO, pilot contamination, channel estimation, precoding, H-inf I. INTRODUCTION Multiple-input multiple-output (MIMO technology has been widely studied for many years and applied to wireless systems either centralised [1-3] or distributed [4-11]. In order to achieve more dramatic gains as well as to simplify the required signal processing, Massive MIMO has been proposed [1]. With perfect channel state information (CSI, Massive MIMO provides multiple advantages compared to traditional MIMO [13]. To avoid the high overhead of pilots, channel estimation (CE in Massive MIMO is generally performed in time division duplex (TDD mode [13]. Due to the mobility of users and the limited bandwidth, the reuse of pilots is necessary for users in different cells. One of the main consequences of pilot reuse is pilot contamination (PC. In this case, the achievable rate of system is saturated when the number of antennas at the BS increases even to infinite [1]. In recent years, CE and precoding have been investigated to mitigate the PC in Massive MIMO systems [14]-[15]. The existing researches generally addressed these two issues separately. Since CE is an indispensable part of precoding, it is crucial to consider them jointly to mitigate the impact of PC. H-infinity (H-inf filter which can achieve an acceptable performance without accurate knowledge of statistical information has been applied to estimate the channels in traditional wireless communication systems [19, 0]. In [1], the H-inf CE was designed in multi-cell multi-user MIMO systems to render a substitute for traditional CE methods investigated in [16-18], and the PC impacts on mean square error (MSE of CE were analyzed. Due to effective computing and performance in CE, H-inf criterion was applied again to design multicell precoding in Massive MIMO OFDM systems []. It has been shown that the downlink achievable rate obtained by using H-inf precoding outperforms that of rates by using singlecell precoding methods. However, in our previous works, the identical thresholds in H-inf CE and precoding were assumed for simplicity, and the proposed H-inf precoding involves high complexity because of pseudo-inverse operations. Furthermore, the analysis of downlink achievable rate for joint use of H-inf criterion in CE and precoding was not given. In this paper, the joint use of H-inf criterion in CE and precoding is investigated further. Different from our previous works in [], the scheme here is designed to take into account the effect of different thresholds in H-inf CE and precoding on downlink achievable rate. Also, a low-complexity approximate solution of H-inf precoding is obtained by applying the asymptotic analysis of large system dimension. In order to assess the performance of joint scheme, approximations of downlink achievable rate for several precoding and CE methods (i.e., ZF, MMSE and H-inf precoding methods in the downlink, MMSE and H-inf CE methods in the uplink are analyzed. From the results given herein, by using the H-inf precoding, the downlink achievable rate can be enhanced because the PC is suppressed by considering the inter-cell interference. The performance of H-inf percoding can be improved by adjusting the thresholds of H-inf CE, which suppresses the PC and further enhance downlink achievable rate. Numerical results show that joint use of H-inf criterion in CE and precoding exhibits significant rate gains compared to many popular combination of CE and precoding. Notations: (, ( T and ( H denote the conjugate, transpose and the Hermitian transpose operations, respectively. ( stands for the pseudo inverse operations, respectively. denotes the two-norm operation. tr{ } denotes the trace operation, E [ ] and var [ ] stand for expectation and variance /15/$ IEEE

2 operations. I N denotes an N N identity matrix, and diag{ } denotes a diagonal matrix. CN(Γ, Υ denotes complex Gaussian distribution with mean Γ and covariance matrix Υ. II. SYSTEM MODEL Consider a multi-cell multi-user MIMO OFDM system with Q cells, each of which consists of one BS with M antennas and K single-antenna terminals. The number of OFDM subcarriers is N [3-6]. The frequency selective channel is modelled as a finite-duration channel impulse response (CIR with L paths. All BSs and users are assumed to be perfectly synchronized with a TDD protocol, where uplink channel is used as an estimation of downlink channel. For users in each cell, phase shift orthogonal pilot sequences are used [16]. There are two phases in this communication scheme: pilot transmission and precoded data transmission. In the first phase, pilots are embedded in the uplink OFDM symbol sent by the users in order for BS to estimate the downlink channels. In the second phase, based on channel estimation, the signals are precoded and then transmitted from the BS to the users. A. Uplink pilots transmission The received N 1 signal vector on all N subcarriers at the r-th antenna at the j-th BS can be expressed as (for simplicity, the antenna index r is neglected Y j = Q q=1 k=1 K X qk H qjk + Z j (1 where Y j = [y j0,,y jn 1 ] T, X qk is N N diagonal signal matrix from the k-th user in the q-th cell, its diagonal entries are CN(0, 1, Z j =[z j0,,z jn 1 ] T is CN(0, I N noise vector. H qjk is N 1 channel frequency response vector between the j-thbsandthek-thuserintheq-th cell, H qjk = F NL C qjk, where F NL is 1/ N times the first L columns of Discrete Fourier Transform (DFT matrix, C qjk is the L 1 vector representing the CIR between the j-th BS and the k-th user in the q-th cell, and is given by C qjk = D 1 qjk G qjk ( where G qjk is the L 1 fast fading coefficients vector, and let g qjkl be the l-th element of G qjk, g qjkl CN(0, 1. D qjk is L L diagonal matrix whose diagonal elements are d qjkl, where d qjkl is assumed to be non-negative constant with respect to l and k, corresponding to path-loss and shadow fading coefficients. Since d qjkl changes slowly, it is rewritten as d qj for simplicity, and d qj is assumed to be less than 1. B. Downlink precoded data transmission The received signal U jn of all K users at the n-th subcarrier in the j-th cell is given by (for simplicity, the subscripts about the subcarrier index n are dropped U j = Q λqh qja qe q + V j (3 q=1 where A q is M K precoding matrix, E q =[e q1,,e qk ] T is K 1 signal for the K users in the q-th cell, E q CN(0, I K, and V j =[v j1,,v jk ] T is K 1 CN(0, I K noise vector. λ q = 1 E[ 1 K tr{aqah q }] is introduced to keep the average power constraint. H qj = [h qj1,, h qjk ] T is K M channel propagation matrix between the K users in the q-th cell and the BS in the j-th cell, and h qjk = h qjk d 1 qj, h qjk is fast fading coefficients vector, h qjk =[h qjk1,,h qjkm ] T, h qjkm CN(0, 1. The signal received by the k-th user is given by Q K u jk = λqh qjk a qpe qp + v jk (4 q=1 p=1 where a qp is the p-th column of A q. The achievable rate R jk of the k-thuserincellj is expressed as [7, Theorem 1] ( R jk =log 1+ρ DL (5 where ρjk DL is the associated signal-to-interference-plus-noise ratio (SINR, and is given by ρ DL jk = III. λ j E [h jjk a jk ] 1+λ jvar [h jjk a jk ]+ (q,p (j,k λqe [ h ] (6 jqpa qp MULTI-CELL H-INF CHANNEL ESTIMATION AND PRECODING A. Multi-cell H-inf channel estimation As for CE in Massive MIMO systems, the idea of the H- inf is to find a CE method so that the ratio between the CE error and the input noise/interference less than a prescribed threshold. Considering all the users in the j-th cell, given a positive scalar s jj,ul, the objective function of the H-inf CE in the j-th cell to satisfy sup Z j jk Ĉ jj C jj W Z j <s jj,ul (7 where Ĉ jj is a LK 1 vector, denoting the CIR vector to be estimated between all the users in the j-th cell and the BS in the j-th cell, C jj =[Cjj1, T, CjjK] T T, W > 0 is a weighting matrix, and Ĉ jj C jj W =(Ĉ jj C jj H W(Ĉ jj C jj. The H-inf CE can be described as [1] Ĉ jj = r jj,ult jyj (8 where T j =[T j1,, T jk ], T jk = X jk F N,L. Remark: The channels in current cell (C jj isestimated by (8, while the channels between cells (C qj can also be obtained directly via the similar process, just by using different signal from other cells (T q. If multi-cell precoding is considered, the achievable rate does not depend only on the threshold of current cell. Thus, it is assumed that the thresholds between cells (s qj,ul are not the same as the thresholds within the same cell (s jj,ul. B. Multi-cell H-inf precoding Consider the signal and interference terms corresponding to the BS in the j-th cell. Following the concept of H-inf criterion, the H-inf precoding is to find a CE based precoding matrix A j, so that the ratio between the precoding error and the noise/interference from all the other cells is less than a prescribed positive threshold s jj,dl. The objective function of the H-inf precoding is expressed as [] λjh jja je j λ je j W sup λj H qj A j E j +V j <sjj,dl (9 Q q j λjh qja je j + V j

3 where λ j H jj A j E j λ j E j W = H W, = λj H jj A j E j λ j E j, W > 0 is a weighting matrix. Solving (9, a closed-form solution to the precoding matrix A j is given by []  j = Ĥ jj (r jj,dlδ 1 + Δ (10 where Δ 1 = I K + Q q j ĤqjĤ jj, Δ = rjj,dl Δ 1 +4r jj,dl λ 1 j V j Ej H, and r jj,dl is a positive scalar. Note that Ĥ jj is a K M estimated channel matrix of n-th subcarrier between the K users in the j-th cell and the j-th BS, which is obtained by applying (8. The similar process for Ĥ qj is straightforward. In order to obtain an ideal solution in (10, V j and Ej H should be given. When the value of M is close to infinity, the effects of small-scale fading will vanish [1], and the approximate expression ignoring V j and Ej H can be given by  app j = r jj,dl Ĥ jj + r jj,dl Q q j Ĥ jjĥqjĥ jj (11 }{{} considering inter-cell interference As a result of making use of the user information from the other cells in (9, the solution of precoding matrix  j subsequently considers the inter-cell interference. In order to reduce the high complexity caused by pseudo-inverse in (11, the following well-known Lemma 1 is applied [1]. Lemma 1. LetX be K M matrix, and the elements of X are CN (0, 1, when M is large and M K, then ( X H X I K (1 M M K By applying Lemma 1, (10 can be simplified as  app j = r jj,dl Md jjr jj,ul Ĥ H jj + r jj,dl (Md jjr jj,ul Q Ĥ jjĥqjĥh H jj (13 Considering the number of complex multiplications for each estimated precoding matrix as a complexity metric, the inversion of a n n matrix requires n 3 operations, the pseudoinverse of a n r matrix requires r n + r 3 operations, and the product of a m r matrix with a r n matrix requires mrn operations. Assuming Q = K = 4, a comparison of complexities between our proposed H-inf precoding in (10 and (13 is given in Fig. 1. Seen from (13, by using the approximation of large system dimensions, the pseudoinverse operations of (10 are eliminated, and the complexity is reduced by an order of magnitude. IV. PERFORMANCE ANALYSIS A. Analysis of matrix W, s jj,dl and s jj,ul Firstly, according to [1, ], W is a diagonal matrix. Define W = wi K, where w is a scale factor, denoting the diagonal elements of W, and then w<s jj,dl is required. In addition, different our previous works in [], the threshold s jj,dl of H-inf precoding is defined as a different value compared to the threshold of H-inf CE s jj,ul. This is because whether these two thresholds in the uplink and downlink q j Number of complex multiplications reduced by an order of magnitude 10 5 H inf precoding (10 H inf precoding ( Number of BS antennas (M Fig. 1. Complexity comparisons between our proposed H-inf precoding schemes (10 and (13 both have benefit for the performance of system needs further investigation. Secondly, when W is fixed, the monotonic relations between s jj,ul and r jj,ul is generally presented [1]. A smaller s jj,ul is made, a better CE performance is achieved, which is the intrinsic characteristic of H-inf CE. Besides, in this paper, the same W is used in the uplink and downlink, and it is not difficult to find w<s jj,ul. B. Analysis of proposed scheme in finite system dimension The existing researches characterized their proposed schemes by analyzing the achievable rate mainly based on the assumption of infinite system dimension [7]. However, in practice, the number of antennas at the BS cannot be infinite. When finite system dimension is considered, although the exact achievable rate is hard to derive, an approximate lower bound shown in the Theorem 1 can be derived. Theorem 1: Considering finite system dimension, by using H-inf criterion in CE and precoding, the lower bound of the asymptotically achievable rate of the k-th user in the j-th cell during downlink transmission is given by R H inf d jjrjj,ul jk > log (14 q j dqjr qj,ul Remark: Since r jj,ul (r qj,ul and s jj,ul (s qj,ul have the monotonic relations [1], adjusting the value of s jj,ul (s qj,ul is equivalent to adjusting r jj,ul (r qj,ul. Accordingly, the mitigation to PC can be implemented by adjusting the u- plink thresholds s jj,ul and s qj,ul. Furthermore, it seems that the performance is irrelevant to the downlink threshold s jj,dl (s qj,dl. C. Analysis of different CE and precoding schemes To assess the performance of the above-mentioned scheme, different CE and precoding schemes will be analyzed based on the following three cases.

4 1 The H-inf CE in the uplink: Single-cell ZF and singlecell MMSE precoding methods in the downlink are introduced, and the case when SNR is considered. The following Theorem can be obtained. Theorem : By using H-inf CE and single-cell ZF(MMSE precoding, considering SNR, the asymptotically achievable rate of the k-th user in the j-th cell during downlink transmission is given by lim SNR RZF jk,rjk MMSE d jjrjj,ul =log q j dqjr qj,ul (15 Remark: Similar to Theorem 1, when the H-inf CE is used, the PC can also be mitigated by adjusting the values of uplink thresholds, even if the H-inf precoding is not used. Since the inter-cell interference is not considered in this precoding scheme, the achievable rate is worse than that of rate by using H-inf precoding. Referring to Theorem 1-, no matter what kind of precoding methods are used, the H-inf CE is an essential way to suppress the PC. The H-inf precoding in the downlink: The MMSE CE is introduced, and for the finite system dimension case the following Theorem 3 can be obtained. Theorem 3: By using MMSE CE and H-inf percoding, considering finite system dimension, the lower bound of the asymptotically achievable rate of the k-thuserinthej-th cell during downlink transmission is given by R MMSE CE jk > log ( 1+ d jj Q q j d qj (16 Remark: When MMSE CE is used, the achievable rate depends only on the values of direct gain d jj and cross gain d qj, however, these two parameters which exist forever in practice cannot be controlled by the designer. 3 MMSE CE and single-cell MMSE precoding: We assess the achievable rate when MMSE CE and single-cell MMSE precoding are adopted, and the case when SNR is considered. The following Theorem 4 can be obtained. Theorem 4: By using MMSE CE and single-cell MMSE precoding, considering SNR, the asymptotically achievable rate of the k-th user in the j-th cell during downlink transmission is given by d jj lim SNR RMMSE jk = log Q q j d (17 qj Remark: Similar to Theorem 3, when MMSE CE is used, the achievable rate also depends only on the values of d jj and d qj. Without considering the inter-cell interference from other cells in this precoding scheme, the worse achievable rate is obtained compared to that of rate by using H-inf precoding. Referring to Theorem 1-4, no matter what kind of CE method is used, the H-inf precoding is another way to suppress the PC. Note: Due to limited space, the proof of Theorem 1-4 is omitted. D. Summary of achievable rate for different CE and precoding schemes To assess the achievable rate of the proposed H-inf criterion scheme, Table I is given for clear comparisons. According to Table I, the following conclusions can be drawn: (1 By using H-inf precoding, the achievable rate can be improved by mitigating the PC due to considering inter-cell interference. ( Introducing the H-inf CE can mitigate the PC, by adjusting the uplink thresholds within the same cell (s jj,ul and between cells (s qj,ul. (3 Joint use of H-inf criterion in CE and H-inf precoding, a dual suppression to the PC is provided, compared to other existing schemes. Moreover, the performance of precoding only depends on the uplink thresholds s jj,ul and s qj,ul. TABLE I. ACHIEVABLE RATE FOR DIFFERENT CE AND PRECODING SCHEMES CE Precoding Approximate achivable rate per user d jj r jj,ul H-inf single-cell ZF(MMSE log q j d qj r qj,ul d jj r jj,ul H-inf multi-cell H-inf > log q j d qj r qj,ul d MMSE multi-cell H-inf > log jj Q q j d qj d MMSE single-cell MMSE log jj Q q j d qj V. SIMULATION RESULTS In this section, some representative simulation results are given. It is assumed that the number of cells Q =4, and the number of users K =4in each cell. The same set of phase shifted orthogonal pilot sequences are reused in all the cells. The channel is assumed to have 8 multi-path components. It is assumed the scale factor w =0.1 for all simulations. The thresholds s jj,dl of H-inf precoding is 1, and the thresholds of H-inf CE s jj,ul and s qj,ul are set to be not larger than 1. 1 Furthermore, for all k, d jqk =1(direct gain if j = q, d jqk = a (cross gain in case j q, and a = 0.1. The SNRs from uplink and downlink phases are 10dB and 0dB, respectively. For OFDM symbols, the number of subcarriers is 18, the length of cyclic prefix (CP is 16, and QPSK is adopted. Average achievable rate per user is considered as performance metric of interest. In the following simulations, each scheme simulated is simply expressed as a combination of X CE + Y, which means that X CE and Y precoding are considered respectively in uplink and downlink. Specifically, for precoding methods, single-cell and multi-cell methods are expressed as s-y and m-y respectively. A. Selection of s jj,ul and s qj,ul As analyzed in Section IV, the performance of our proposed schemes is relevant to the selection of s jj,ul and s qj,ul. Thus, the simulation experiments are performed in the following case, where for several fixed values of s qj,ul, the effect of varying s jj,ul will be evaluated. Fig. shows the achievable 1 In our simulations, we observe the performance of H-inf CE and precoding are not very sensitive when the thresholds is larger than 1.

5 rates per user for different values of s qj,ul as a function of s jj,ul at M = 00. It can be seen that when the value of s qj,ul is 0., 0.5, 0.7 or 1, the achievable rates are not sensitive to the value of s jj,ul which ranges from 0. to 1. On the other hand, the performance of our proposed scheme can be improved with decreasing the value of s qj,ul. When the value of s jj,ul is fixed, the achievable rate per user decreases as the value of s qj,ul increases. Average rate per user (bits/s/hz threshold between cells 0. threshold between cells 0.5 threshold between cells 0.7 threshold between cells Threshold within same cell Fig.. Average per-user rate for different thresholds between cells (s qj,ul versus thresholds within same cell (s jj,ul at M = 00 In Fig., s qj,ul can be considered as a filter performance level of the H-inf CE towards the channels between cells. Since multi-cell precoding mitigates the PC by utilizing the channels information between cells, when the value of s qj,ul is decreased, that is, the performance of H-inf CE between cells is enhanced, the performance of H-inf precoding will be improved, and thus for the system performance. Therefore, in a multi-cell scenario, the performance, to a great extent, depends on the mitigation to the inter-cell interference. Furthermore, it is observed that the H-inf CE is a good way for multi-cell scenario to mitigate the PC. B. Performance comparisons between different schemes From the above, it is observed that the performance of our proposed scheme increases with decreasing the value of s qj,ul, and the minimum and maximum can be obtained respectively in the given range. In order to compare our proposed scheme to the existing schemes, the experiments will be performed in two cases: s qj,ul =1and s qj,ul =0.. Fig. 3 illustrates the achievable rates under different CE and precoding schemes as a function of the number of BS antennas at s qj,ul =1. It can be seen that the performance of the H-inf precoding (13 is the same as the H-inf precoding (10 as M 100. This is because the effects of small-scale fading vanish for large M at each BS. Thus, the approximation given in (13 can be considered as a substitute for (10 in Massive MIMO systems. Compared to the schemes which use single-cell ZF and single-cell MMSE precoding, the multi-cell H-inf precoding exhibits significant advantage by considering inter-cell interference, which suppresses the PC and improve the achievable rate. It is also observed in those multi-cell precoding designs that when s qj,ul =1the performance of Average rate per user (bits/s/hz multi cell precoding single cell precoding MMSE CE + m H inf (10 H inf CE + m H inf (10 H inf CE + m H inf (13 MMSE CE + s MMSE 1 H inf CE + s MMSE H inf CE + s ZF Number of BS antennas Fig. 3. Average per-user rate for different CE and precoding schemes versus the number of BS antennas at s qj,ul =1 using H-inf CE is much worse than that of using MMSE CE which provides the optimal filter performance. This phenomenon means that the performance of the H-inf CE is not always good for any values of s qj,ul. Since the performance of H-inf CE depends on the value of thresholds and the signals from adjacent cells are assumed to be sent synchronously, the filter performance level to the channels between cells should be enhanced, that is, the values of s qj,ul should be decreased. Average rate per user (bits/s/hz multi cell precoding single cell precoding 3 H inf CE + m H inf (10 H inf CE + m H inf (13 MMSE CE + s MMSE H inf CE + s MMSE 1 H inf CE + s ZF MMSE CE + m H inf ( Number of BS antennas Fig. 4. Average per-user rate for different joint CE and precoding schemes versus the number of BS antennas at s qj,ul =0. Fig. 4 shows the achievable rates for different CE and precoding schemes as a function of the number of BS antennas at s qj,ul = 0.. As expected, the scheme which adopts CE and single-cell precoding gets worse performance without considering the mitigation to inter-cell interference. Similar to Fig. 3, it can be seen from Fig. 4 that the performance of the H-inf precoding (13 is the same as the H-inf precoding (10 as M 100. It is shown in those multi-cell precoding designs that when s qj,ul =0.the filter performance level to the channels between cells is enhanced, the performance of using H-inf CE is improved obviously compared to Fig., which indicates that the PC can be suppressed dramatically by

6 adjusting the value of s qj,ul. In this case, the dual mitigation by utilizing the H-inf criterion in both uplink and downlink exhibits significant gains compared to nearly all the schemes. Furthermore, its performance is almost the same as the scheme of using optimal MMSE CE. All the results shown in this figure validate the analysis in Section IV, indicating that the use of H-inf criterion in both uplink and downlink provide a better mitigation to the PC than other schemes. VI. CONCLUSIONS This paper reinvestigated the CE and precoding scheme by applying H-inf criterion in Massive MIMO systems. Different our prior work, the effect of different thresholds on downlink achievable rate for H-inf CE and precoding is considered. The asymptotic analysis of large system dimension is used to simplify the high complexity of H-inf precoding. The achievable rate per user for different CE and precoding schemes were assessed. The following conclusions are drawn: (1 The H-inf CE is capable of mitigating the PC by adjusting the thresholds for different cells. Specifically, the performance of the H-inf CE is not sensitive to the threshold within same cell (s jj,ul and depends mainly on the decreasing value of thresholds between cells (s qj,ul. In a multi-cell scenario, the mitigation to the inter-cell interference plays an important role in improving the performance. ( By using the approximation of large system dimension, the computational complexity is reduced by an order of magnitude. Moreover, when the number of antennas at the BS is large, the performance loss of the approximate solution is negligible. (3 Joint use of H-inf criterion in CE and precoding can provide dual mitigation to the PC. Furthermore, the performance of precoding depends only on uplink thresholds s jj,ul and s qj,ul. VII. ACKNOWLEDGMENT This work was supported by China High-Tech 863 Program under Grant No.014AA01A706, the National Natural Science Foundation of China under Grants , , and , the Program for New Century Excellent Talents in University No. NCET , and the Program of Science and Technology Research of Hebei University No. ZD REFERENCES [1] D. Gesbert, M. Shafi, D. Shiu, and P. J. Smith, From theory to practice: an overview of MIMO space-time coded wireless systems, IEEE J. Sel. Areas Commun., vol. 1, no. 3, pp , Apr [] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bolcskei, An overview of MIMO communications-a key to gigabit wireless, Proc. IEEE, vol. 9, no., pp , Feb [3] D. Gesbert, M. Kountouris, R. W. Heath Jr., C. B. Chae, and T. Sälzer, From single user to multiuser communications: shifting the MIMO paradigm, IEEE Signal Process. Mag., vol. 4, No. 5, pp , Oct [4] H. Zhu, Performance comparison between distributed antenna and microcellular systems, IEEE J. Sel. 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