REMOTE CONTROL OF TRANSMIT BEAMFORMING IN TDD/MIMO SYSTEMS

The 7th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 6) REMOTE CONTROL OF TRANSMIT BEAMFORMING IN TDD/MIMO SYSTEMS Yoshitaa Hara Kazuyoshi Oshima Mitsubishi Electric Information Technology Centre Europe B.V. (ITE), France, allée de Beaulieu, CS 86, 78 Rennes Cedex 7, France hara@tcl.ite.mee.com oshima@tcl.ite.mee.com ABSTRACT This paper propose a new control scheme that the base station (BS) controls terminal s transmit beamforming in timedivision duplex (TDD) / multi-input multi-output (MIMO) systems. In the proposed scheme, the BS transmits pilot signals using proper downlin beamforming to instruct target beamforming to the terminal. Using responses of the pilot signals, the terminal computes weight for transmit beamforming. We theoretically show that the BS can control not only a single terminal s transmit beamforming but also multiple terminals transmit beamforming simultaneously. Furthermore, efficient weight computation at the terminal is investigated to yield accurate transmit beamforming in the presence of noise. Numerical results show that the terminal can yield transmit beamforming close to the target beamforming in noise environments. I. INTRODUCTION Multi-input multi-output (MIMO) systems, which have multiple antennas at both transmitter and receiver, have been widely investigated for high data rate wireless communications ]]. In future wireless communications, multiuser MIMO system is expected to support multiple terminals access to one base station (BS). Then, it is required to optimize the system considering many aspects such as radio resource control, transmit beamforming, and modulation and coding scheme ] 8]. Usually, in the system that multiple terminals access the BS, it is difficult for a terminal to obtain information of the other terminals. Therefore, it is common that the BS collects the information related to each terminal such as channel state information (CSI) and quality of service (QoS) requirement, and performs overall system control. To realize the multiuser MIMO system, one problem lies in a terminal s transmit beamforming on uplin. Usually, on downlin, the BS can perform transmit beamforming according to the BS s system control ] ]. In contrast, on uplin, a control scheme, in which the BS controls the terminal s transmit beamforming according to the BS s system control, has not been established yet. So far, some literatures 6] 8] have presented that system performance on uplin could be improved if terminals transmit beams are determined by system optimization. To realize the performance improvement in actual environments, a control scheme that the BS remotely controls terminals transmit beamforming is needed. In this paper, we proposes a new control scheme that the BS remotely controls terminal s transmit beamforming using channel reciprocity in time-division duplex (TDD) / multi-input multi-output (MIMO) system. In the proposed system, the BS transmits pilot signals using proper downlin beamforming to instruct target beamforming to the terminal. Using responses of the downlin pilot signals, the terminal computes weight for transmit beamforming on uplin. We theoretically show that the BS can control not only a single terminal s transmit beamforming but also multiple terminals transmit beamforming simultaneously. Also, we investigate efficient weight computation method at the terminal in the presence of noise. In performance evaluation, we show that the BS can control terminals transmit beamforming with good control accuracy. II. PRELIMINARIES Throughout the paper, we define the transpose as T, the complex conjugate as, the complex conjugate transpose as, and the norm as. A. Signal Model Let us consider TDD/MIMO system, where propagation reciprocity is maintained between uplin and downlin. The system is composed of a BS with N antennas and terminals, where the -th terminal has M antennas ( =,,...). Consider that the BS transmits the p-th symbols of N signals s (p),..., s N (p) simultaneously on downlin, using different transmit beamforming based on N weight vectors w,..., w N, respectively. Here, the weights w,..., w N satisfy w +... + w N = N. Using average transmit power per beamformer,them received signal vector x (p) at the -th terminal is represented by x (p) = H N n= w n s n (p)+z (p) () where z (p) is the M interference-plus-noise vector at the -th terminal and H is the M N MIMO channel matrix. The (m, n)-th element of H represents the complex propagation gain from the BS s n-th antenna to the -th terminal s m-th antenna. The channel is assumed as quasi-stationary flat fading, which is a typical environment of low-mobility terminal using a smaller bandwidth than coherent bandwidth of multipath channels. Let a n denote the response vector of the n-th signal s n (p) at the -th terminal. Then, the response vector a n is expressed as a n = H w n. Meanwhile, on uplin, consider that the -th terminal transmits a signal r (p) using transmit beamforming based on M weight vector v ( v = ). Using the transmit power P r,then received signal vector x BS (p) at the BS is given by x BS (p) = P r H T v r (p)+z BS (p) () -444--8/6/$. c 6 IEEE

The 7th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 6) Downlin Data Pacet; Instruction slot of beamforming for next UL Uplin Data Pacet Time Channel measurement slot Figure : Frame format. where z BS (p) is the N interference-plus-noise vector at the BS. The BS s response vector of the signal r (p) is expressed as b = P r H T v. Thus, in reciprocal TDD/MIMO system, the signals on uplin and downlin are expressed by the channel matrix H. B. Condition of Terminal s Target Transmit Weight Before remote control of transmit beamforming, the BS determines the M target weight ˆv of the -th terminal s transmit beamforming and the corresponding target response vector ˆb = P r H T ˆv, according to the BS s system control. In the following, we explain condition of the weight ˆv that the BS deals with. In general, singular value decomposition (SVD) of H is expressed as Λ O H = Q d (N d) O (M d) d O (M d) (N d) ] U () where Q = q,..., q M ] is the M M unitary matrix, U =u,..., u N ] is the N N unitary matrix, Λ = diag λ,λ,..., λ d ](λ... λ d > ) is the d d real-valued diagonal matrix, and d is the ran of the matrix H. Since the arbitrary M vector ˆv is expressed as ˆv = f q + + f M q M, the target response vector ˆb satisfies ˆb = P r H T ˆv = P r d f n λ n u n. (4) n= In case of d<m, weight ˆv to achieve the target response vector ˆb has degrees of freedom in f d+,..., f M. Then, the BS deals only with the target weight ˆv with f d+ =... = f M =. The weight ˆv with f d+ =... = f M =will be most practical one among weights with arbitrary f d+,..., f M, because it minimizes the terminal s transmit power to achieve ˆb. Then, the target transmit weight ˆv is expressed as ˆv = f q + + f d q d. () Thus, the target weight ˆv that the BS deals with is restricted to subspaces of q,..., q d. In case of d = M, the BS deals with arbitrary M vector ˆv, which is also included in the expression (). III. REMOTE CONTROL OF TRANSMIT BEAMFORMING We propose a new control scheme that the BS remotely controls terminal s transmit beamforming in TDD/MIMO systems. A. Remote Control of Single Transmit Beamforming Figure shows the frame format of downlin and uplin in the proposed scheme. The downlin format includes a time period that the BS instructs the target beamforming to the terminal. Assume that the BS has nowledge of the channel matrix H. The channel matrix H is usually obtained by measuring the complex amplitude of pilot signals transmitted individually from the -th terminal s antennas on uplin in the channel measurement slot. Let us show the principle of the proposed scheme in ideal condition where the -th terminal has no noise component (z (p) =). Actual signal processing in the presence of the terminal s noise will be presented later in III.C.. Before remote control of transmit beamforming, the BS decides the -th terminal s target transmit weight ˆv and the target response vector ˆb = P r H T ˆv, according to the BS s system control. Next, the BS determines the -th transmit weight w = ˆb / ˆb and other (N ) transmit weights w n (n =,..., N, n ), such that the weights are orthogonal to each other as W W = I with W =w,..., w N ]. Then, the BS sends N pilot signals s n (p) (n =,..., N) simultaneously, using different transmit beamforming based on the weights w n, respectively. The response matrix A =a,..., a N ] of all pilot signals and the response vector a of the -th pilot signal s (p) at the -th terminal are represented by A = H W (6) a = Ps P r H w = ˆb H H ˆv. (7) Using A and a,the-th terminal computes the transmit weight v as v = (A A T ) + a (A A T ) + a = (H H T ) + H H T ˆv (H H T ) + H H T ˆv where + denotes the Moore-Penrose generalized matrix inverse. Then, v satisfies the following proposition. Proposition: v = ˆv Proof: Using () and the Moore-Penrose s generalized matrix inverse formula (8), (H H T ) + is given by (H H T ) + = Q Using (), we have Λ O (M d) d O d (M d) O (M d) (M d) (8) ] Q T. ( d ) (H H T ) + H H T ˆv = q nq T n ˆv = ˆv. (9) Therefore, v = ˆv holds. n= Since the terminal yields v = ˆv, the BS can control the - th terminal s weight v for transmit beamforming. This proposition always holds even if H H T is singular.

The 7th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 6) B. Remote Control of Multiple Transmit Beamforming When multiple terminals send uplin data signals using transmit beamforming based on space division multiple access (SDMA), the BS needs to control the multiple terminals transmit beamforming. For this purpose, we present a remote control scheme to control n max ( n max N) transmit beamforming, simultaneously. In order to control transmit beamforming of the -th terminal ( =,..., n max ), the BS decides the -th terminal s M target transmit weight ˆv and the N target response vector ˆb = P r H T ˆv, according to the BS s system control. For successful communications, the target response vectors ˆb,..., ˆb nmax are determined as non-colinear vectors. Furthermore, the BS selects vectors ˆb n (n = n max +,..., N) successively, so that ˆb n becomes orthogonal to the existing vectors ˆb,..., ˆb n. Next, the BS sends N pilot signals s (p),..., s N (p) simultaneously, using N different downlin beamforming weights w,..., w N, where W = w,..., w N ]=µ( ˆB ˆBT ) ˆB () ˆB = ˆb / ˆb,..., ˆb N / ˆb N ] () µ = N / /tr{( ˆB ˆBT ) } /. () The matrix ˆB is non-singular and the parameter µ is determined to satisfy w +... + w N = N in (). Then, the response matrix A = a,..., a N ] and the response vector a at the -th terminal are represented by A = H W () a = H w = µh ( ˆB ˆBT ) ˆb, (4) respectively. The -th terminal computes the transmit weight v as ˆb Therefore, v = ˆv holds from () and (6). Thus, the terminals ( =,..., n max ) can individually yield their target weights v = ˆv for transmit beamforming. It should be noted that the proposed method is applicable to terminals with different number of antennas. Also, the BS can control multiple transmit beamforming of one terminal remotely, supposing the -th and -th terminals as the same terminal with H = H and ˆv ˆv. The remote control of single transmit beamforming in III. A. is identical to the case of n max =in III. B.. Therefore, the -th terminal can compute the weight v using the constant formula (), whatever number of controlled transmit beamforming n max is. C. Actual Weight Computation in Terminal Following the principle, we study the terminal s actual weight computation in the presence of noise. In actual environments, N pilot signals s (p),..., s N (p) are composed of p ( N) symbols and are mutually orthogonal as s ()......... s (p ) SS = p I, S =................ (9) s N ()......... s N (p ) Using the weight matrix W =w,..., w N ] given by (), the,..., p -th symbols of the received signal at the -th terminal are totally expressed in matrix form as X =x (),..., x (p )] = H WS+ Z () where Z = z (),..., z (p )]. Using the received signal X, the terminal estimates A = H W and a = Ps H w as à =(/p )X S = H W +(/p )Z S () ã =(/p )X s = H w +(/p )Z s,() v = (A A T ) + a (A A T ) + a () = {H ( ˆB ˆB ) H T } + H ( ˆB ˆB ) H T ˆv {H ( ˆB ˆB ) H T } + H ( ˆB ˆB.(6) ) H T ˆv Then, v satisfies the following proposition. Proposition: v = ˆv Proof: From (), H ( ˆB ˆB ) H T is given by H ( ˆB ˆB ) H T = Q G G ] I : v = (à ÃT + P I) ã (4) O d (M d) Q T (à ÃT + P I) ã O (M d) d O (M d) (M d) ] where P is an appropriate constant value to represent the G = ˆB U Λ (7) quasi-noise power. Performance of the weight computations O (N d) d is evaluated by computer simulations in the next section. where G is the N d matrix with ran d. Using the formula (8), we have {H ( ˆB ˆB ) H T } + H ( ˆB ˆB ) H T = d q nq T n. (8) n= where s =s (),..., s (p )]. The terminal is required to yield weight v close to the ideal weight (). To achieve this, we consider the following two weight computation methods. : v = (à ÃT ) + ã (à ÃT ) + ã () IV. PERFORMANCE EVALUATION A. Simulation Parameters In computer simulations, we consider one BS with N =4antennas and K( 4) terminals, all of which have M antennas

The 7th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 6) Average SINR Gain 4 antennas antennas 4 antennas Figure : Average SINR gain obtained by system-based terminal s transmit beamforming. (M = M). All antennas at the BS and the terminals have the same noise power P z per antenna. The channel H is assumed as quasi-static Rayleigh fading, where elements of the matrix H are independent identically distributed ( i.i.d.) complex Gaussian random variables with zero mean and unit variance. First, the BS determines the (=,..., K)-th terminal s target weight ˆv, assuming that each terminal transmits one signal with constant power P r using transmit beamforming weight ˆv. For efficient signal transmission., the weight ˆv is decided by the following minimum total mean squared error (MSE) algorithm 8] :. Initialize i =and ˆv = e H H T ( =,..., K).. Update the weights ˆv ( =,..., K) successively by e (I/P r + H ˆΦ H T ) (H ˆΦ H T ) ˆv () where e denotes the eigenvector corresponding to maximum eigenvalue of the matrix and ˆΦ is the correlation matrix given by K ˆΦ = P r (H T n ˆv n)(h T n ˆv n) + P z I. (6) n=,n. In case of i<i max, increase i by and go bac to ), otherwise end, where i max is the the maximum iteration number. When the weight ˆv is obtained, the BS computes the target response vector ˆb = P r H T ˆv ( =,..., K, n max = K) and the transmit weights W = µ( ˆB ˆBT ) ˆB based on (). Furthermore, the BS transmits N pilot signals with 8 symbols (p =8). The -th terminal computes the weight v according to method I or method II (P = P z /), and transmits the signal r (p) with the power P r using the beamforming weight v on uplin. In the simulations, the average transmit power per beamformer on both uplin and downlin is identical as P r =. B. Effect of terminal s beamforming on system performance To understand the effect of terminal s transmit beamforming on system performance, we evaluate the BS s received SINR at the output of ideal minimum mean squared error (MMSE) combiner on uplin. We evaluate two cases : case A where each terminal uses the ideal transmit weight ˆv determined by the minimum total MSE algorithm and case B where each terminal uses locally optimized weight ˆv () = e H H T of eigenbeamforming ]. For performance evaluation, we define the average SINR gain of case A to case B Γ as Γ = E log ˆγ ] E log ˆγ () ] (7) where ˆγ and ˆγ () are the BS s received SINRs at the output of ideal MMSE combiner for the -th terminal in cases A and B, respectively, and E ] denotes the average with respect to simulation trials and all terminals. Figure shows the average SINR gain under i max =, K =,, 4 terminals, and M =,, 4 antennas. In case of one terminal (K =), the cases A and B have the same performance, whereas in case of K =4case A has more than gain in terms of average SINR. Thus, as the number of terminals increases, transmit beamforming based on system optimization achieves better performance than the locally optimized one. Since Γ, the systematically optimized transmit beamforming is always effective, although the average SINR gain depends on the number of terminals and antennas. C. Accuracy of Remote Control of Transmit Beamforming We evaluate accuracy of the proposed remote transmit beamforming control, considering the terminal s actual weight computation. For performance evaluation, we define the BS s average received SINR ˆΓ, the correlation ϕ between terminal s target transmit weight ˆv and actual weight v, and the BS s SINR error σ as ˆΓ = E log ˆγ ] ϕ = E v ˆv ] σ = E log γ log ˆγ ] where γ and ˆγ denote the BS s received SINRs for the -th terminal s signal under all terminals actual transmit weights v and under ideal transmit weights ˆv, respectively. Figure shows the average SINR ˆΓ, the weight correlation ϕ, the SINR error σ under i max =, K =,, 4, and M =. Figure 4 shows the case of M =4with the same other parameters. In these figures, method II yields transmit weight v close to ideal one, whereas a large weight error arises in method I. Specifically, in case of M =4, method I has very large weight error. This is because the method I maes wrong direction in the weight v due to noise effect when some pilot signals have small power at the terminal. In contrast, the weight of method II is not significantly affected by the noise, inserting quasi-noise power P in (4). As a result, in most cases, method II can eep the SINR error within from the target SINR ˆγ. Thus, using method II, the terminal s transmit beamforming is controlled with high accuracy.

The 7th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC 6) Average SINR Correlation of Transmit Weights.9.9 I.8.8 SINR Error I (a) (b) (c) Figure : Performance of remote transmit beam control under i max =and M =(a) Average SINR Γ (b) Weight correlation ϕ (c) SINR error σ. Average SINR Correlation of Transmit Weights.9.9 I.8.8 SINR Error I (a) (b) (c) Figure 4: Performance of remote transmit beam control under i max =and M =4(a) Average SINR ˆΓ (b) Weight correlation ϕ (c) SINR error σ. V. CONCLUSIONS In this paper, we proposed remote control scheme of transmit beamforming in TDD/MIMO systems. In theoretical parts, we presented basic principle of the remote control scheme assuming no noise component at the terminal. It is revealed that the BS can control not only single terminal s transmit beamforming but also multiple terminals transmit beamforming. Following the principle, we also investigated terminal s actual weight computation in the presence of noise. From performance evaluation, it is found that the terminal can mae accurate transmit weight close to ideal one, using appropriate weight computation. The proposed scheme is expected to support efficient space division multiplexing transmission in MIMO/TDD system, using system-based terminal s transmit beamforming. A MOORE-PENROSE GENERALIZED MATRIX INVERSE Moore-Penrose generalized matrix inverse satisfies ( ] ) + ] O E E O O O = E E O O (8) where E is the M M unitary matrix, E is the M M unitary matrix, is the m m invertible matrix (m min{m,m }). REFERENCES ] E. Telatar, Capacity of multi-antenna gaussian channels, European Transactions on Telecommunications, vol., no. 6, pp. 8 9, Nov/Dec 999. ] F. R. Farrohi, G. J. Foschini, A. Lozano, and R. A. Valenzuela, Linoptimal space-time processing with multiple transmit and receive antennas, IEEE Communications Letters, vol., no., March. ] R. L. U. Choi and R. D. Murch, A transmit pre-processing technique for multiuser MIMO systems: a decomposition approach, IEEE Trans. Wireless Commun., vol., pp. 4, Jan. 4. 4] K. K. Wong and R. D. Murch, A joint-channel diagonalization for multiuser MIMO antenna systems, IEEE Trans. on Wireless Commun., vol., pp. 77 786, July. ] Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, Zero-forcing methods for downlin spatial multiplexing in multiuser MIMO channels, IEEE Trans. on Signal Processing, vol., issue, pp. 46 47, Feb. 4. 6] K. K. Wong, R. S. K. Cheng, K. B. Letaief, and R. D. Murch, Adaptive antennas at the mobile and base stations in an OFDM/TDMA system, IEEE Trans. on Commun., vol. 49, no., pp. 9 6, Jan.. 7] E. A. Jorswiec and H. Boche, H, Transmission strategies for the MIMO MAC with MMSE receiver: average MSE optimization and achievable individual MSE region, IEEE Trans. on Signal Processing, vol., issue, pp. 87 88, Nov.. 8] S. Serbetli and A. Yener, Transceiver optimization for multiuser MIMO system, IEEE Trans. on Signal Processing, vol., issue, pp. 4 6, Jan. 4.