Capacity of a multiple-antenna fading channel with a quantized precoding matrix
IEEE Transactions on Information Theory
Why does the Kronecker model result in misleading capacity estimates?
IEEE Transactions on Information Theory
Asymptotic performance of MIMO wireless channels with limited feedback
MILCOM'03 Proceedings of the 2003 IEEE conference on Military communications - Volume I
IEEE Transactions on Signal Processing
Performance Analysis of Quantized Beamforming MIMO Systems
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Design and analysis of transmit-beamforming based on limited-rate feedback
IEEE Transactions on Signal Processing
On the performance of random vector quantization limited feedback beamforming in a MISO system
IEEE Transactions on Wireless Communications
On beamforming with finite rate feedback in multiple-antenna systems
IEEE Transactions on Information Theory
Grassmannian beamforming for multiple-input multiple-output wireless systems
IEEE Transactions on Information Theory
Transmit beamforming in multiple-antenna systems with finite rate feedback: a VQ-based approach
IEEE Transactions on Information Theory
Feedback rate-capacity loss tradeoff for limited feedback MIMO systems
IEEE Transactions on Information Theory
Semiunitary Precoding for Spatially Correlated MIMO Channels
IEEE Transactions on Information Theory
What is the value of limited feedback for MIMO channels?
IEEE Communications Magazine
Capacity limits of MIMO channels
IEEE Journal on Selected Areas in Communications
Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels
IEEE Journal on Selected Areas in Communications
An overview of limited feedback in wireless communication systems
IEEE Journal on Selected Areas in Communications
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Codebooks based on Random Vector Quantization (RVQ) are popular in limited feedback beamforming applications over MIMO channels because of their low-complexity design properties. The goal of this work is on understanding the performance of an ensemble of RVQ codebooks as a function of the number of bits of feedback (B), antenna dimensions, and spatial correlation. We analyze the case of correlated MIMO channels and arbitrary choice of B. Towards this goal, we first study the distribution function of weighted norms of isotropically distributed beamforming vectors. From this, we compute the received SNR loss and mutual information loss of a B-bit RVQ scheme relative to a perfect channel information benchmark. Our computation reveals the following: i) The loss terms are a product of two factors. The first factor, which is also common to analysis of i.i.d, channels, decays as B increases at the rate 2-B/(Nt-1) where Nt is the number of transmit antennas; ii) The second factor reflects the condition number of the channel. A channel that minimizes/maximizes the condition number on average also minimizes/maximizes the performance loss, respectively. Such behavior is typical of channels that correspond to rich (i.i.d.) spatial scattering, and poor (rank-1 channels) spatial scattering, respectively.