UPLINK SPATIAL SCHEDULING WITH ADAPTIVE TRANSMIT BEAMFORMING IN MULTIUSER MIMO SYSTEMS

Transcription

1 UPLINK SPATIAL SCHEDULING WITH ADAPTIVE TRANSMIT BEAMFORMING IN MULTIUSER MIMO SYSTEMS Yoshitaka Hara Loïc Brunel Kazuyoshi Oshima Mitsubishi Electric Information Technology Centre Europe B.V. (ITE), France 1, allée de Beaulieu, CS 0, 3570 Rennes Cedex 7, France ABSTRACT This paper presents uplink spatial scheduling with adaptive transmit beamforming, where terminals perform system-based transmit beamforming in multiuser multi-input multi-output (MIMO) systems. In the presented spatial scheduling, the base station (BS) selects appropriate combination of terminals and their transmit beamforming among possible terminals. In the selection process, a terminal and its transmit beamforming for a are successively selected, considering the effect of the other predetermined s. In performance evaluation, we show that the spatial scheduling achieves much larger system throughput than the system without spatial scheduling. We also present a basic system configuration in which the BS reports the target transmit beamforming to the selected terminal efficiently in time-division duplex (TDD) system downlink. I. INTRODUCTION Multi-input multi-output (MIMO) systems, which have multiple antennas at both transmitter and receiver, have been widely investigated for higher data rate wireless communications [1][]. In future wireless communications, multiuser MIMO system is expected to support multiple terminals accessing one base station (BS). Then, it is required to optimize the system considering many aspects of radio resource control, transmit beamforming, and modulation and coding scheme (MCS) [3] []. So far, in uplink of multiuser MIMO systems, many papers have investigated efficient terminal s transmit beamforming, assuming a fixed number of s for each terminal [5][]. In future multiuser MIMO systems, spatial scheduling would be also essential to improve the system performance. In the spatial scheduling, the terminals with good channel conditions are selected to send s among possible terminals in each subband and time frame. The terminals send s based on space division multiple access (SDMA) on uplink. Selecting appropriate terminals, the spatial scheduler is expected to achieve higher spectrum efficiency than the system in which terminals continue to send a fixed number of s. The SDMA transmission performance depends not only on s propagation gains but also on spatial correlation of the multiplexed s. Since the transmission performance deteriorates in case of high spatial correlation at the BS, it is required to select the terminals and their transmit beamforming, so that the multiplexed s have low spatial correlation. Thus, the spatial scheduler is required to optimize combination of the terminals and the transmit beamforming under complex characteristics of SDMA transmission performance. The optimum solution to this problem is obtained by examining all possible combinations of terminals and transmit beamformers, but it requires huge and unrealistic complexity. Up to now, appropriate combination of terminals has been sought by non-linear optimization algorithm or grouping terminals based on spatial correlation [7][], assuming terminal s eigenbeamforming. However, it is not guaranteed that the terminal s eigenbeamforming achieves good performance in multiuser MIMO system. The terminal s adaptive transmit beamforming based on system optimization might achieve better performance. In this paper, we investigate uplink spatial scheduling with adaptive transmit beamforming, where terminals perform system-based transmit beamforming in multiuser MIMO systems. In the presented scheduling, appropriate combination of terminals and their transmit beamforming is selected among all possible transmit beams. In the selection process, the BS determines a terminal and its transmit beamforming successively in the presence of the already determined s. We also present a system configuration in which the BS reports the determined transmit beamforming to the selected terminals efficiently in time-division duplex (TDD) system. Using the scheduling algorithm, the terminal is expected to have more efficient transmit beamforming than eigenbeamforming, considering the spatial correlation of multiplexed s. In the performance evaluation, we show that the spatial scheduler achieves much higher system throughput than the system without spatial scheduling. It should be noted that successive determination of transmit beamforming have been dealt with in papers [][11] for downlink. In case of downlink, it was difficult to nullify interference among multiplexed s perfectly, because the previously determined s give interference to the newly added s. In contrast, the successive determination presented here for uplink nullifies all mutual interference among multiplexed s easily. II. SYSTEM MODEL Throughout the paper, we define the transpose as T, the complex conjugate as, the complex conjugate transpose as,the norm as, and the trace as tr{ }. A. Uplink MIMO channel Let us consider the multiuser MIMO system which is composed of a base station with N antennas and K terminals, where the k-th terminal has M k antennas (k =1,..., K). Fig. 1 shows the image of the multiuser MIMO system on uplink. The /0/$0.00 c 00 IEEE

2 Downlink Uplink MT1 M 1 antennas MT M antennas BS MT k M k antennas Figure 1: Image of multiuser MIMO system on uplink. base station can receive at most N s simultaneously on uplink and determines terminal k = k(n) to send the n-th multiplexed (n =1,..., N) and the M k(n) 1 weight vector v n ( v n =1)forthek(n)-th terminal s transmit beamforming in each subband and time frame. The BS informs the k(n)-th terminal of the transmit weight v n in advance and the terminal performs transmit beamforming based on the weight v n. Assuming that the k(n)-th terminal transmits the n-th s n (p) (E[ s n (p) ]=1) with a constant power P s,thep-th sample of the BS s received vector x BS (p) =[x BS,1 (p),..., x BS,N (p)] T is given by x BS (p) = max n=1 Ps H T k(n)v n s n (p)+z(p) (1) where n max ( N) is the number of spatially multiplexed s, z(p) is the N 1 BS s noise vector with E[z(p)z (p)] = P z I. The matrix H k is the M k N channel matrix, where the (m, n)-th element of H k represents the complex propagation gain from the BS s n-th antenna to the k-th terminal s m-th antenna. The channel is assumed as quasi-stationary flat fading, which is a typical environment for a low-mobility terminal using a small subband of block subcarriers in OFDMA systems. Assume that the BS has knowledge of the channel matrix H k (k =1,..., K) and the noise power P z. The channel matrix H k is usually obtained by measuring responses of pilot s transmitted individually from the k-th terminal s antennas on uplink. Using the knowledge of H k and P z, the BS determines the terminal k(n) to send the n-th, the transmit beamforming weight v n, and the corresponding MCS. We refer to this transmission control scheme as uplink spatial scheduling and study efficient control method. B. Basic Control Structure for Uplink Spatial Scheduling Let us explain the basic control structure of uplink spatial scheduling, supposing TDD/MIMO systems. Fig. shows the downlink and uplink frame formats to achieve uplink spatial scheduling. On downlink, a scheduling instruction slot is placed and the BS reports the terminal number k(n), the transmit weight v n, and the corresponding MCS information (n =1,..., n max ) to the existing terminals. Fig. 3 shows the structure of scheduling instruction slot on downlink. In the instruction slot, N different instructions are spatially multiplexed by different transmit beamforming based on N 1 weight w DL n (n =1,..., N). One instruction contains pilot of fixed pattern, terminal s identifier (ID), and MCS information, where the pilot s are mutually orthogonal in Data Packet Scheduling instruction slot Data Packet Time Channel measurement slot Figure : Downlink and uplink frame formats for spatial scheduling. Downlink (Scheduling Instruction slot) Uplink (Data packet) Pilot Terminal's MCS Pilot Pilot Terminal's Terminal's ID MCS for Tx weight w ID ID MCS N for Tx weight w 1 Pilot Data Figure 3: Instruction format on downlink and data packet format on uplink. different instructions 1. According to [9], the k(n)-th terminal can yield the target transmit weight v n using responses of the N pilot s if the weights w DL n (n =1,..., N) are determined as [w DL 1,..., w DL N ] = N 1/ (B B T ) 1 B tr{( ˆB () ˆBT ) 1 } 1/ B = [b 1 / b 1,..., b N / b N ] where b n = P s H T k(n)v n (n = 1,..., n max ) and b n (n = n max +1,..., N) is successively selected to be orthogonal to b 1,..., b n 1. Consequently, the BS has the following control procedures on downlink : 1. The BS determines the terminal k(n),them k(n) 1 transmit weight v n, and the MCS to send the n-th uplink (n =1,..., N) based on scheduling algorithm.. The BS determines w DL n (n =1,..., N) from (). 3. The BS sends N instructions using different transmit weights w DL n (n =1,..., N), respectively. When the instructions arrive at a terminal, the terminal performs receive beamforming using pilot s individually for each instruction. At the output of beamformer, the terminal checks the terminal ID in each instruction. If the terminal ID does not correspond to the terminal, the terminal checks the other instructions. If the terminal ID corresponds to the terminal, the terminal recognizes the instruction to send a packet on the next uplink frame. Then, the terminal reads MCS information and obtains the instruction number n from the pilot pattern. Using the responses of N pilot s, the terminal yields the M k(n) 1 target weight v n [9]. Fig. 3 shows the packet structure on uplink. Each packet includes pilot and data s, and at most N packets are multiplexed based on SDMA. The k(n)-th terminal sends the n-th packet using the instructed MCS and the transmit beamforming 1 The N instructions are always sent on downlink. In case of n max <N, terminal ID and MCS information in n max +1,..., N-th instructions become blank.

3 weight v n. The pilot pattern is determined by the instruction number n and the pilot patterns in different packets are mutually orthogonal. Consequently, the terminal has the following control procedures : 1. The terminal checks the n-th instruction (n =1,..., N)on downlink. If the terminal ID corresponds to the terminal, the terminal reads MCS and obtains the instruction number n. The terminal yields the weight v n using responses of pilot s in instructions.. The terminal sends a packet using the instructed MCS and the transmit beamforming weight v n on uplink. The BS receives the spatially multiplexed packets using receive beamforming. Even though a packet does not include terminal s ID and MCS, the BS can identify the terminal ID and MCS by checking the pilot pattern of the n-th packet and referring the n-th instruction information stored at the BS. In spatial scheduling, the terminal ID, the transmit weight, and MCS vary in subbands and time frames. The terminal can follow the system control checking instructions in each subband and time frame. Since spectrum efficiency depends on the strategy to determine the terminal ID, the transmit weight, and MCS, we study efficient scheduling algorithm for uplink. III. UPLINK SPATIAL SCHEDULING We present uplink spatial scheduling algorithm to determine terminals to send s, their transmit beamforming, and the corresponding MCSs. A. Characteristics of Received Signal Consider that the k(1),..., k(n)-th terminals send the 1,..., n- th packets, respectively, on uplink. Then, the received at the BS is expressed as x BS (p) = Ps H T k(l)v l s l (p)+z(p). (3) The BS receives the l-th s l (p) using receive beamforming based on MMSE weight w l =(R 1 n Ps H T k(l)v l ), where R n is the correlation matrix of x BS (p) given by R n = P s H T k(l)v l v l H k(l) + P z I. () The -to-interference-plus-noise power ratio (SINR) γ l n of the l(= 1,..., n)-th s l (p) at the output of MMSE beamformer is given by [5] γ l n = P s v l H k(l)φ 1 l n HT k(l)v l (5) Φ l n = R n P s H T k(l)v l v l H k(l). () Also, the total mean-square-error (TMSE) TMSE n for all multiplexed s is expressed as [] TMSE n E[ w l x BS(p) s l (p) ] = C l P z v l H k(l)φ l n HT k(l)v l v l (I/P s + H k(l)φ 1 l n HT k(l))v l (7) where C l is the term independent of H k(l) and v l. In (5), the SINR γ l n is maximized to γ l n =P s ρ H k(l) Φ 1 l n HT k(l) by using v l = e H k(l)φ 1 l n HT k(l), under fixed v 1,..., v l 1, v l+1,..., v n, where ρ A and e A are the maximum eigenvalue and the corresponding eigenvector of the matrix A, respectively. Also, TMSE n is minimized to C l ˆρ P z H k(l)φ l n H T k(l), I/P s + H k(l)φ 1 l n HT k(l) by using v l = ê P z H k(l) Φ l n HT k(l), I/P s + H k(l)φ 1 l n HT k(l), under fixed v 1,..., v l 1, v l+1,..., v n, where ˆρ A 1, A and ê A 1, A are the maximum generalized eigenvalue and the corresponding generalized eigenvector of A 1 and A, respectively. B. Spatial Scheduling Algorithm We present uplink spatial scheduling algorithm that decides the terminal k(n) to send the n-th (n =1,..., n max ), successively. The presented scheduler selects the terminal to achieve the largest received SINR among terminals in the presence of the1to(n 1)-th s as follows : [Uplink Spatial Scheduling Algorithm] 1. Initialize n = 1, Ξ(0) = 0.. Compute ρ k = ρ H kφ 1 n n HT k for all terminals k = 1,..., K and select the terminal k which has largest ρ k as the terminal k(n). Decide the k(n)-th terminal s transmit weight as v n = e H k(n)φ 1 n n HT k(n). 3. Compute system throughput Ξ(n) in the presence of n multiplexed s. If Ξ(n) > Ξ(n 1), go to ), otherwise n max = n 1 and end.. If n<n, go back to ), otherwise n max = n and end. Thus, the terminal k(n) and the transmit weight v n (n = 1,..., n max ) are determined successively, maximizing the SINR for new. After all procedures, the scheduler decides MCS for each packet, referring the predetermined lookup table of the SINR to MCS and using γ l nmax. In step 3), the system throughput Ξ(n) is computed as Ξ(n) = n ξ(γ l n), where ξ(γ) is throughput of one packet. The throughput ξ(γ) is a function of the SINR γ and the lookup table of throughput versus the SINR is prepared in advance. In step 3), the n-th is admitted if the system throughput under n s is higher than that under n 1 s. The presented scheduling algorithm selects the terminals and the transmit weights to maximize SINR for the new, so we refer to the algorithm as Max SINR algorithm. Similarly, the terminals and the transmit weights can be selected based on TMSE minimization in step ), replacing ρ k and v n by ρ k =ˆρ P z H kφ n n HT k, I/P s + H kφ 1 n n HT k and v n = ê P z H k(n)φ n n HT k(n), I/P s + H k(n)φ 1 n n HT k(n), respectively. Here, we considered only second term of TMSE n in (7), because all terminals have the same first term C n (l = n). This algorithm is referred to as Min TMSE algorithm. The presented scheduler successively selects the terminals to achieve the maximum SINR (or minimum TMSE). Therefore,

4 the scheduler is expected to have higher spectrum efficiency than the system without spatial scheduling. Moreover, since the scheduler decides the terminal s transmit weight considering the effect of the other multiplexed s, it is expected to have higher spectrum efficiency than the case in which terminals perform transmit eigenbeamforming In the presented scheduler, a newly added may degrade the other multiplexed s. However, the newly added which achieves high SINR is likely to have low spatial correlation with the other existing s. In this case, the performance deterioration in the existing first to (n 1)-th packets is expected to be small. If the n-th greatly deteriorates performance of the existing s, the scheduler rejects the n-th and keeps the system throughput in 3). C. Iterative Transmit Weight Computation After spatial scheduling procedures, we examine the effect of the following iterative transmit weight computation shown in [5][] to refine weights v l, because the SINR or the TMSE may be degraded by new s. [Iterative Transmit Weight Computation] 1. Initialize i =1.. Update the weight v l (l =1,..., n max ) successively by e H k(l)φ 1 H T k(l) v l () 3. If i<i max, increase i by 1 and go back to ), otherwise end, where i max is the the maximum iteration number. MCS is determined after this algorithm. In case of Min TMSE algorithm, () is replaced by ê P z H k(l)φ H T k(l), I/P s + H k(l)φ 1 H T k(l) v l. IV. PERFORMANCE EVALUATION The uplink spatial scheduler is evaluated by simulations. A. Simulation Parameters In computer simulations, we consider one BS with N =antennas and K terminals, all of which have the same number of antennas M k = M. The terminals have low-mobility and the MIMO channels H k, where elements of H k are independent identically distributed ( i.i.d.) complex Gaussian random variables with zero mean and unit variance. One data packet consists of convolutionally encoded 150 symbols based on the instructed MCS. From packet error rate (PER) results in single-input single-output (SISO)-additive white Gaussian noise (AWGN) channel, the required SNR to meet PER= 1 is given by Table 1. Accordingly, the BS decides appropriate MCS based on the SINR γ n nmax. The throughput ξ(γ) is also determined by Table 1. For comparison purpose, we evaluate the case without spatial scheduling, where constant four terminals send one individually on uplink. In case of no iterative transmit weight computation, the k(n)-th terminal (k(n) =n = 1,..., ) sends the n-th using eigenbeanforming v (0) n = Table 1: Selection of MCS based on received SINR and the corresponding throughput (TP). SINR [db] Modulation Coding Rate TP [b/s/hz] -5.0 No use QPSK 1/ QPSK 1/ QPSK 1/ QPSK / QAM 1/ QAM / QAM 1/ QAM / QAM QAM 7/ 5.5 e H k(n)h T k(n). In case of the iterative transmit weight computation, the transmit weight v (0) n is updated i max times. MCS is selected in the same manner as in spatial scheduling. B. System Throughput Fig. shows system throughput in spatial scheduling with iterative transmit weight computation under P s /P z =0dB. In the figure, the system throughput is enhanced by spatial scheduling, as the number of terminals K increases. This is because the scheduler can maintain lower spatial correlation of multiplexed s under a larger number of terminals. It is also found that Min TMSE algorithm has a slightly better system throughput than Max SINR algorithm. Basically, Max SINR algorithm optimizes quality of the new, whereas TMSE algorithm optimizes quality of all multiplexed s. Therefore, Min TMSE algorithm takes into account the performance of all multiplexed s more deeply and will lead to better performance. However, Min TMSE algorithm has larger complexity than Max SINR algorithm, due to a larger number of matrix inversion operations. Fig. 5 shows the average number of multiplexed s E[n max ] in spatial scheduling under P s /P z =0dB. In the figure, more s can be spatially multiplexed in a larger number of terminal s antennas M. Since the terminal with larger M can control s arrival angle at the BS in wider range, more s can be accommodated maintaining low spatial correlation. Fig. shows the system throughput versus P s /P z db under terminals (K =). Comparing with the case without spatial scheduling, the spatial scheduler has large superiority specifically under a small number of antennas M. The spatial scheduler has at least db gain under M. Fig. 7 shows the system throughput in spatial scheduling without iterative transmit weight computation under P s /P z = 0 db. Comparing Fig. with Fig. 7, the iterative transmit weight computation has little effect on the system throughput of spatial scheduling. It implies that the spatial scheduler has good spatial relation between multiplexed s without the iterative transmit weight computation. In contrast, system throughput of no spatial scheduling greatly deteriorates without the iterative transmit weight computation. This result shows that the terminals eigenbeamforming v (0) n = e H k(n)h T k(n) is not necessarily good in multiuser MIMO system. Thus, the system-based transmit beamforming, which considers overall system performance, will make better performance. Thus, it is

5 1 M= M= Figure : System throughput under P s /P z =0dB and iterative decision of terminal s transmit beamforming i max =3. Average n max M= M= Figure 5: Average number of multiplexed s under P s /P z = 0 db and iterative decision of terminal s transmit beamforming i max =3. essential to decide the terminal s transmit beamforming, considering overall system performance. In the performance evaluation, each terminal has fair throughput, since the same number of antennas M is assumed in terminals. The scheduling algorithm for fair throughput under different types of terminals is subject for future study. V. CONCLUSION This paper studied uplink spatial scheduling using adaptive transmit beamforming in multiuser MIMO systems. The presented spatial scheduler selects terminals and their transmit beamforming under all possible terminal s transmit beamforming. From the numerical results, it is found that the system throughput is greatly enhanced by the use of spatial scheduling. Also, the system-based terminal s transmit beamforming improves the transmission performance effectively. Thus, the spatial scheduling is a promising technology for future wireless communications. REFERENCES [1] E. Telatar, Capacity of multi-antenna gaussian channels, European Transactions on Telecommunications, vol., no., pp , M= M= P s /P z [db] Figure : System throughput under K =with iterative decision of terminal s transmit beamforming i max =3. 1 M= M= Figure 7: System throughput under P s /P z = 0 db without iterative decision of terminal s transmit beamforming. Nov/Dec [] F. R. Farrokhi, G. J. Foschini, A. Lozano, and R. A. Valenzuela, Linkoptimal space-time processing with multiple transmit and receive antennas, IEEE Communications Letters, vol. 5, no. 3, March 001. [3] 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. 3, pp. 0, Jan. 00. [] K. K. Wong and R. D. Murch, A joint-channel diagonalization for multiuser MIMO antenna systems, IEEE Trans. on Wireless Commun., vol., pp , July 003. [5] 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. 9, no. 1, pp , Jan [] S. Serbetli and A. Yener, Transceiver optimization for multiuser MIMO system, IEEE Trans. on Signal Processing, vol. 5, issue 1, pp. 1, Jan. 00. [7] K. N. Lau, Analytical framework for multiuser uplink MIMO spacetime scheduling design with convex utility functions, IEEE Trans. Wireless Commun., vol. 3, issue 5, pp , Sept. 00. [] Y. J. Zhang and K. B. Letaief, An efficient resource-allocation scheme for spatial multiuser access in MIMO/OFDM system, IEEE Trans. on Commun., vol. 53, no. 1, pp. 7 11, Jan [9] Y. Hara and K. Oshima, Remote control of transmit beamforming in TDD/MIMO system, Proc. of IEEE PIMRC 0, Sept. 00. [] Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, IEEE Transactions on Signal Processing, vol. 5, no., pp. 1 71, Feb. 00. [11] P. Tejera, W. Utschick, G. Bauch, and J.A. Nossek, Sum-rate maximizing decomposition approaches for multiuser MIMO-OFDM, Proc. of IEEE PIMRC 05, Sept. 005.