On the Minimum Differential Feedback for Time-Correlated MIMO Rayleigh Block-Fading Channels

TL;DR

This paper derives the minimum differential feedback rate for MIMO Rayleigh block-fading channels to maximize ergodic capacity, revealing an optimal feedback interval and validating results through simulations.

Contribution

It provides a closed-form expression for the minimum differential feedback rate considering channel errors and quantization, and identifies the optimal feedback interval for capacity maximization.

Findings

Existence of an optimal differential feedback interval.

Closed-form expression for minimum feedback rate.

Validation through simulations with Lloyd's quantization.

Abstract

In this paper, we consider a general multiple input multiple output (MIMO) system with channel state information (CSI) feedback over time-correlated Rayleigh block-fading channels. Specifically, we first derive the closed-form expression of the minimum differential feedback rate to achieve the maximum erdodic capacity in the presence of channel estimation errors and quantization distortion at the receiver. With the feedback-channel transmission rate constraint, in the periodic feedback system, we further investigate the relationship of the ergodic capacity and the differential feedback interval, and we find by theoretical analysis that there exists an optimal differential feedback interval to maximize ergodic capacity. Finally, analytical results are verified through simulations in a practical periodic differential feedback system using Lloyd's quantization algorithm.