Scheduling for Multiuser MIMO Broadcast Systems: Transmit or Receive Beamforming?

In this paper, we present an approximation formula and the close-form expression for the sum rate of the transmit and the receive zero-forcing (ZF) multiple-input multiple-output (MIMO) broadcast systems with user selection, respectively. Instead of assuming a large number of users to obtain a scaling law as most current work, we derive the sum rate formulas of the ZF MIMO broadcast systems with a small number of scheduled users. By analysis and simulations, we find that when taking the variations of feedback channel into account, the receive ZF MIMO broadcast system is more robust to feedback errors and can deliver equal or even higher sum rate than the transmit ZF MIMO broadcast system. We discuss whether a feedback channel is suitable to send channel state information (CSI) for calculating transmit antenna beamforming weights, or suitable to send CSI for selecting users in the receive ZF MIMO broadcast system. Our results show that as the variation of feedback channel errors increases from 0.5 to 1.5, the receive ZF 3 × 3 MIMO broadcast system can provide 36% to 116% higher sum rate than the transmit ZF 3 × 3 MIMO broadcast system in the case of 20 users at signal to noise ratio (SNR) equal to 20 dB. Providing that more feedback bandwidth and an error-free feedback channel are available, the transmit ZF MIMO broadcast system can achieve higher sum rate than the receive ZF MIMO broadcast system.

[1]  Shlomo Shamai,et al.  On the achievable throughput of a multiantenna Gaussian broadcast channel , 2003, IEEE Transactions on Information Theory.

[2]  Martin Haardt,et al.  Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels , 2004, IEEE Transactions on Signal Processing.

[3]  A.J. Paulraj,et al.  Multiuser diversity for MIMO wireless systems with linear receivers , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[4]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[5]  Andrea J. Goldsmith,et al.  Multi-Antenna Downlink Channels with Limited Feedback and User Selection , 2007, IEEE Journal on Selected Areas in Communications.

[6]  Naresh Sharma,et al.  A study of opportunism for multiple-antenna systems , 2005, IEEE Transactions on Information Theory.

[7]  Babak Hassibi,et al.  Differentiated Rate Sceduling for MIMO Broadcast Channels , 2005 .

[8]  Jeffrey G. Andrews,et al.  Uplink SDMA with Limited Feedback: Throughput Scaling , 2008, EURASIP J. Adv. Signal Process..

[9]  Joonho Lee,et al.  A scheduling algorithm combined with zero-forcing beamforming for a multiuser MIMO wireless system , 2005, VTC-2005-Fall. 2005 IEEE 62nd Vehicular Technology Conference, 2005..

[10]  R.W. Heath,et al.  Multiuser diversity for the multiple antenna broadcast channel with linear receivers: asymptotic analysis , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[11]  Jeffrey G. Andrews,et al.  Multimode Transmission for Multiuser MIMO Systems With Block Diagonalization , 2008, IEEE Transactions on Signal Processing.

[12]  David Gesbert,et al.  Orthogonal Linear Beamforming in MIMO Broadcast Channels , 2007, 2007 IEEE Wireless Communications and Networking Conference.

[13]  Jeffrey G. Andrews,et al.  Low Complexity User Selection Algorithms for Multiuser MIMO Systems with Block Diagonalization , 2006, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[14]  David Tse,et al.  Opportunistic beamforming using dumb antennas , 2002, IEEE Trans. Inf. Theory.

[15]  Alireza Bayesteh,et al.  On the User Selection for MIMO Broadcast Channels , 2005, IEEE Transactions on Information Theory.

[16]  David Tse,et al.  Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality , 2003, IEEE Trans. Inf. Theory.

[17]  Michael D. Zoltowski,et al.  Multiple Antenna Broadcast Channels With Shape Feedback and Limited Feedback , 2007, IEEE Transactions on Signal Processing.

[18]  Babak Hassibi,et al.  On the capacity of MIMO broadcast channels with partial side information , 2005, IEEE Transactions on Information Theory.

[19]  Giuseppe Caire,et al.  Multiuser MIMO Achievable Rates With Downlink Training and Channel State Feedback , 2007, IEEE Transactions on Information Theory.

[20]  D. Gesbert,et al.  Low Complexity Scheduling and Beamforming for Multiuser MIMO Systems , 2006, 2006 IEEE 7th Workshop on Signal Processing Advances in Wireless Communications.

[21]  Babak Hassibi,et al.  A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users , 2007, IEEE Transactions on Communications.

[22]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[23]  Robert W. Heath,et al.  Transmit selection in spatial multiplexing systems , 2002, IEEE Communications Letters.

[24]  Li-Chun Wang,et al.  Multi-user MIMO broadcast systems with imperfect feedbacks , 2009, IWCMC.

[25]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[26]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[27]  Jeffrey G. Andrews,et al.  Performance of Orthogonal Beamforming for SDMA With Limited Feedback , 2006, IEEE Transactions on Vehicular Technology.

[28]  N.D. Sidiropoulos,et al.  On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm , 2005, IEEE Transactions on Signal Processing.

[29]  Jeffrey G. Andrews,et al.  Mode Switching for the Multi-Antenna Broadcast Channel Based on Delay and Channel Quantization , 2008, EURASIP J. Adv. Signal Process..

[30]  Andrea J. Goldsmith,et al.  Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels , 2003, IEEE Trans. Inf. Theory.

[31]  Andrea J. Goldsmith,et al.  On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming , 2006, IEEE Journal on Selected Areas in Communications.

[32]  Rohit U. Nabar,et al.  Introduction to Space-Time Wireless Communications , 2003 .

[33]  Shlomo Shamai,et al.  The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel , 2006, IEEE Transactions on Information Theory.

[34]  Gregory W. Wornell,et al.  MIMO Broadcast Scheduling with Quantized Channel State Information , 2006, 2006 IEEE International Symposium on Information Theory.

[35]  Harish Viswanathan,et al.  Downlink capacity evaluation of cellular networks with known-interference cancellation , 2003, IEEE J. Sel. Areas Commun..

[36]  David Gesbert,et al.  Enhanced multiuser random beamforming: dealing with the not so large number of users case , 2008, IEEE Journal on Selected Areas in Communications.

[37]  B. Hassibi,et al.  Differentiated Rate Scheduling for MIMO Broadcast Channels with Estimation Errors , 2006, 2006 Fortieth Asilomar Conference on Signals, Systems and Computers.

[38]  Andrea J. Goldsmith,et al.  Dirty-paper coding versus TDMA for MIMO Broadcast channels , 2005, IEEE Transactions on Information Theory.

[39]  Witold A. Krzymien,et al.  Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink , 2009, IEEE Transactions on Vehicular Technology.

[40]  Martin Haardt,et al.  Low-Complexity Space–Time–Frequency Scheduling for MIMO Systems With SDMA , 2007, IEEE Transactions on Vehicular Technology.

[41]  Chiung-Jang Chen,et al.  Enhancing coverage and capacity for multiuser MIMO systems by utilizing scheduling , 2006, IEEE Transactions on Wireless Communications.

[42]  Chiung-Jang Chen,et al.  Performance Analysis of Scheduling in Multiuser MIMO Systems with Zero-Forcing Receivers , 2007, IEEE Journal on Selected Areas in Communications.

[43]  Rick S. Blum,et al.  Multiuser diversity for a dirty paper approach , 2003, IEEE Communications Letters.