Quantifying the power loss when transmit beamforming relies on finite-rate feedback

Transmit beamforming achieves optimal performance in systems with multiple transmit antennas and a single receive antenna from both the capacity and the received signal-to-noise ratio (SNR) perspectives but ideally requires perfect channel knowledge at the transmitter. In practical systems where the feedback link can only convey a finite number of bits, transmit beamformer designs have been extensively investigated using either the outage probability or the average SNR as the figure of merit. In this paper, we study the symbol error rate (SER) for transmit beamforming with finite-rate feedback in a multi-input single-output setting. We derive an SER lower bound that is tight for good beamformer designs. Comparing this bound with the SER corresponding to the ideal case, we quantify the power loss due to the finite-rate constraint across the entire SNR range.

[1]  Mohamed-Slim Alouini,et al.  A unified approach to the performance analysis of digital communication over generalized fading channels , 1998, Proc. IEEE.

[2]  Georgios B. Giannakis,et al.  Multi-antenna adaptive modulation and transmit beamforming based on bandwidth-constrained feedback , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[3]  Holger Boche,et al.  Optimal power allocation for MISO systems and complete characterization of the impact of correlation on the capacity , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

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

[5]  N. J. A. Sloane,et al.  Packing Lines, Planes, etc.: Packings in Grassmannian Spaces , 1996, Exp. Math..

[6]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[7]  Vincent K. N. Lau,et al.  On the design of MIMO block-fading channels with feedback-link capacity constraint , 2004, IEEE Transactions on Communications.

[8]  J. Craig.  A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations , 1991, MILCOM 91 - Conference record.

[9]  R. Heath,et al.  Limited feedback unitary precoding for spatial multiplexing systems , 2005, IEEE Transactions on Information Theory.

[10]  Aris L. Moustakas,et al.  Optimizing MIMO antenna systems with channel covariance feedback , 2003, IEEE J. Sel. Areas Commun..

[11]  Mikael Skoglund,et al.  Utilizing quantized feedback information in orthogonal space-time block coding , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[12]  Georgios B. Giannakis,et al.  A simple and general parameterization quantifying performance in fading channels , 2003, IEEE Trans. Commun..

[13]  M. K. Simon,et al.  Digital communication over generalized fading channels: a unified approach to performance analysis , 2002 .

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

[15]  A. Goldsmith,et al.  On optimality of beamforming for multiple antenna systems with imperfect feedback , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[16]  John G. Proakis,et al.  Digital Communications , 1983 .

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

[18]  Sandeep Chennakeshu,et al.  Error rates for Rayleigh fading multichannel reception of MPSK signals , 1995, IEEE Trans. Commun..

[19]  Arogyaswami Paulraj,et al.  Linear precoding for space-time coded systems with known fading correlations , 2002, IEEE Communications Letters.

[20]  Georgios B. Giannakis,et al.  Multiantenna adaptive modulation with beamforming based on bandwidth-constrained feedback , 2005, IEEE Transactions on Communications.

[21]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[22]  Aris L. Moustakas,et al.  Optimizing multiple-input single-output (MISO) communication systems with general Gaussian channels: nontrivial covariance and nonzero mean , 2003, IEEE Trans. Inf. Theory.

[23]  Mikael Skoglund,et al.  Combining beamforming and orthogonal space-time block coding , 2002, IEEE Trans. Inf. Theory.

[24]  Georgios B. Giannakis,et al.  Optimal transmitter eigen-beamforming and space-time block coding based on channel correlations , 2003, IEEE Transactions on Information Theory.

[25]  Srikrishna Bhashyam,et al.  Feedback gain in multiple antenna systems , 2002, IEEE Trans. Commun..

[26]  Georgios B. Giannakis,et al.  Optimal transmitter eigen-beamforming and space time block coding based on channel mean , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  Gregory W. Wornell,et al.  Efficient use of side information in multiple-antenna data transmission over fading channels , 1998, IEEE J. Sel. Areas Commun..

[28]  Upamanyu Madhow,et al.  Space-Time transmit precoding with imperfect feedback , 2001, IEEE Trans. Inf. Theory.

[29]  Georgios B. Giannakis,et al.  Achieving the Welch bound with difference sets , 2005, IEEE Transactions on Information Theory.

[30]  Robert W. Heath,et al.  Limited feedback precoding for spatial multiplexing systems , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[31]  Liesbet Van der Perre,et al.  Performance analysis of combined transmit-SC/receive-MRC , 2001, IEEE Trans. Commun..

[32]  Rick S. Blum.  MIMO with limited feedback of channel state information , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..