Analysis of Feedback Overhead for MIMO Beamforming over Time-Varying Channels

TL;DR

This paper quantifies the feedback overhead reduction in MIMO beamforming over time-varying channels by analyzing the entropy of phase tracking information, demonstrating how temporal correlation can be exploited for efficient feedback encoding.

Contribution

It introduces entropy-based bounds for feedback overhead in MIMO beamforming, leveraging phase tracking information and channel temporal correlation for improved efficiency.

Findings

Feedback overhead can be significantly reduced using phase tracking information.

Entropy bounds depend on the channel's temporal correlation parameter.

Simulation shows SNR gains with phase tracking over phase steering feedback.

Abstract

In this paper, the required amount of feedback overhead for multiple-input multiple-output (MIMO) beamforming over time-varying channels is presented in terms of the entropy of the feedback messages. In the case that each transmit antenna has its own power amplifier which has individual power limit, it has been known that only phase steering information is necessary to form the optimal transmit beamforming vector. Since temporal correlation exists for wireless fading channels, one can utilize the previous reported feedback messages as prior information to efficiently encode the current feedback message. Thus, phase tracking information, difference between two phase steering information in adjacent feedback slots, is sufficient as a feedback message. We show that while the entropy of the phase steering information is a constant, the entropy of the phase tracking information is a function of the temporal correlation parameter. For the phase tracking information, upperbounds on the entropy are presented in the Gaussian entropy and the von-Mises entropy by using the theory on the maximum entropy distributions. Derived results can quantify the amount of reduction in feedback overhead of the phase tracking information over the phase steering information. For application perspective, the signal-to-noise ratio (SNR) gain of phase tracking beamforming over phase steering beamforming is evaluated by using Monte-Carlo simulation. Also we show that the derived entropies can determine the appropriate duration of the feedback reports with respect to the degree of the channel variation rates.