TY - JOUR

T1 - Capacity of a multiple-antenna fading channel with a quantized precoding matrix

AU - Santipach, Wiroonsak

AU - Honig, Michael L.

N1 - Funding Information:
Manuscript received December 22, 2006; revised July 17, 2008. Current version published February 25, 2009. This work was supported by the U.S. Army Research Office under Grant DAAD19-99-1-0288 and the National Science Foundation under Grant CCR-0310809. The material in this paper was presented in part at the IEEE Military Communications (MILCOM), Boston, MA, October 2003, IEEE International Symposium on Information Theory (ISIT), Chicago, IL, June/July 2004, and the IEEE International Symposium on Spread Spectrum Techniques and Applications (ISSSTA), Sydney, Australia, August 2004.

PY - 2009

Y1 - 2009

N2 - Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of random vector quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are independent and identically distributed (i.i.d.) and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using B bits. We first derive the large system capacity of beamforming (rank-one precoding matrix) as a function of B, where large system refers to the limit as B and the number of transmit and receive antennas all go to infinity with fixed ratios. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and minimum mean squared error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback.

AB - Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of random vector quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are independent and identically distributed (i.i.d.) and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using B bits. We first derive the large system capacity of beamforming (rank-one precoding matrix) as a function of B, where large system refers to the limit as B and the number of transmit and receive antennas all go to infinity with fixed ratios. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and minimum mean squared error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback.

KW - Beamforming

KW - Large system analysis

KW - Limited feedback

KW - Multiple-input multiple-output (MIMO)

KW - Precoding

KW - Vector quantization

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U2 - 10.1109/TIT.2008.2011437

DO - 10.1109/TIT.2008.2011437

M3 - Article

AN - SCOPUS:62749191475

VL - 55

SP - 1218

EP - 1234

JO - IRE Professional Group on Information Theory

JF - IRE Professional Group on Information Theory

SN - 0018-9448

IS - 3

ER -