Limited Feedback Beamforming Over Temporally-Correlated Channels

TL;DR

This paper analyzes limited feedback beamforming in temporally-correlated MIMO channels, deriving analytical models and proposing a feedback compression algorithm to optimize throughput.

Contribution

It introduces a Markov chain model for quantized CSI in correlated channels and develops a new feedback compression method for beamforming.

Findings

Feedback delay exponentially reduces throughput gains.

Derived source bit rate and feedback channel requirements.

Proposed a CSI feedback compression algorithm.

Abstract

Feedback of quantized channel state information (CSI), called limited feedback, enables transmit beamforming in multiple-input-multiple-output (MIMO) wireless systems with a small amount of overhead. Due to its efficiency, beamforming with limited feedback has been adopted in several wireless communication standards. Prior work on limited feedback commonly adopts the block fading channel model where temporal correlation in wireless channels is neglected. This paper considers temporally-correlated channels and designs single-user transmit beamforming with limited feedback. Analytical results concerning CSI feedback are derived by modeling quantized CSI as a first-order finite-state Markov chain. These results include the source bit rate generated by time-varying quantized CSI, the required bit rate for a CSI feedback channel, and the effect of feedback delay. In particular, based on the theory of Markov chain convergence rate, feedback delay is proved to reduce the throughput gain due to CSI feedback at least exponentially. Furthermore, an algorithm is proposed for CSI feedback compression in time. Combining the results in this work leads to a new method for designing limited feedback beamforming as demonstrated by a design example.