Stability and Delay of Zero-Forcing SDMA With Limited Feedback

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor M >; 1. For given M → 1, the number of feedback bits per mobile is proved to be O(-log2(1-1/M)) .

[1]  Harish Viswanathan,et al.  Rate scheduling in multiple antenna downlink wireless systems , 2005, IEEE Transactions on Communications.

[2]  W. Szpankowski.  Stability conditions for some distributed systems: buffered random access systems , 1994, Advances in Applied Probability.

[3]  T. Sälzer,et al.  From Single User to Multiuser Communications : Shifting the MIMO Paradigm , 2007 .

[4]  Nihar Jindal,et al.  MIMO broadcast channels with finite rate feedback , 2006, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

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

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

[7]  Giuseppe Caire,et al.  Optimum power control over fading channels , 1999, IEEE Trans. Inf. Theory.

[8]  Robert W. Heath,et al.  Grassmannian beamforming for multiple-input multiple-output wireless systems , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[9]  Robert G. Gallager,et al.  Discrete Stochastic Processes , 1995 .

[10]  Babak Hassibi,et al.  Delay Considerations for Opportunistic Scheduling in Broadcast Fading Channels , 2007, IEEE Transactions on Wireless Communications.

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

[12]  Elza Erkip,et al.  On beamforming with finite rate feedback in multiple-antenna systems , 2003, IEEE Trans. Inf. Theory.

[13]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[14]  E. Uysal-Biyikoglu,et al.  Low Complexity Multiuser Scheduling for Maximizing Throughput in the MIMO Broadcast Channel , 2004 .

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

[16]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[17]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[18]  Horst Alzer,et al.  On some inequalities for the incomplete gamma function , 1997, Math. Comput..

[19]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[20]  Jeffrey G. Andrews,et al.  Rethinking MIMO for Wireless Networks: Linear Throughput Increases with Multiple Receive Antennas , 2009, 2009 IEEE International Conference on Communications.

[21]  Thomas L. Saaty,et al.  Elements of queueing theory , 2003 .

[22]  Kaibin Huang,et al.  Cooperative Feedback for Multiantenna Cognitive Radio Networks , 2011, IEEE Transactions on Signal Processing.

[23]  Nihar Jindal,et al.  Multi-Antenna Broadcast Channels with Limited Feedback and User Selection , 2006 .

[24]  Edmund M. Yeh,et al.  Throughput and delay optimal resource allocation in multiaccess fading channels , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[25]  Emre Telatar,et al.  Combining Queueing Theory with Information Theory for Multiaccess , 1995, IEEE J. Sel. Areas Commun..

[26]  Edmund M. Yeh,et al.  Throughput optimal power and rate control for queued multiaccess and broadcast communications , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[27]  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..

[28]  Eytan Modiano,et al.  Power allocation and routing in multibeam satellites with time-varying channels , 2003, TNET.

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

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

[31]  G.B. Giannakis,et al.  Quantifying the power loss when transmit beamforming relies on finite-rate feedback , 2005, IEEE Transactions on Wireless Communications.

[32]  Jeffrey G. Andrews,et al.  Multi-Antenna Communication in Ad Hoc Networks: Achieving MIMO Gains with SIMO Transmission , 2008, IEEE Transactions on Communications.

[33]  Lang Tong,et al.  Stability and delay of finite-user slotted ALOHA with multipacket reception , 2005, IEEE Transactions on Information Theory.

[34]  Robert W. Heath,et al.  An overview of limited feedback in wireless communication systems , 2008, IEEE Journal on Selected Areas in Communications.

[35]  Edmund M. Yeh,et al.  Multiaccess and fading in communication networks , 2001 .

[36]  Wojciech Szpankowski,et al.  Stabilty Conditions for Some Multiqueue Distributed Systems: Buffered Random Access Systems , 1992 .

[37]  Kaibin Huang,et al.  Cooperative Feedback for Multi-Antenna Cognitive Radio Networks , 2009, ArXiv.

[38]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[39]  G. Wornell,et al.  Finding NEMO: near mutually orthogonal sets and applications to MIMO broadcast scheduling , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

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

[41]  G. Wornell,et al.  MIMO Broadcast Scheduling with Limited Channel State Information , 2005 .

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

[43]  Robert W. Heath,et al.  Shifting the MIMO Paradigm , 2007, IEEE Signal Processing Magazine.

[44]  Andrea J. Goldsmith,et al.  Capacity limits of MIMO channels , 2003, IEEE J. Sel. Areas Commun..

[45]  Robert W. Heath,et al.  Grassmannian beamforming for multiple-input multiple-output wireless systems , 2003, IEEE Trans. Inf. Theory.

[46]  A. Robert Calderbank,et al.  Space-Time block codes from orthogonal designs , 1999, IEEE Trans. Inf. Theory.

[47]  Leandros Tassiulas,et al.  Resource Allocation and Cross-Layer Control in Wireless Networks , 2006, Found. Trends Netw..