Channel State Acquisition in FDD Massive MIMO: Rate-Distortion Bound and Effectiveness of "Analog" Feedback

TL;DR

This paper derives fundamental bounds on channel estimation accuracy in FDD massive MIMO systems using rate-distortion theory, and demonstrates the effectiveness of an 'analog' feedback strategy that achieves near-optimal performance without channel covariance knowledge.

Contribution

It introduces a rate-distortion bound for channel estimation in FDD massive MIMO and shows that simple 'analog' feedback can attain optimal scaling without prior channel knowledge.

Findings

Optimal bounds on estimation error derived using rate-distortion theory

'Analog' feedback achieves the optimal quality scaling exponent in diverse scenarios

Numerical simulations validate the theoretical bounds and effectiveness of the proposed feedback strategy

Abstract

We consider the problem of estimating channel fading coefficients (modeled as a correlated Gaussian vector) via Downlink (DL) training and Uplink (UL) feedback in wideband FDD massive MIMO systems. Using rate-distortion theory, we derive optimal bounds on the achievable channel state estimation error in terms of the number of training pilots in DL ($\beta_{tr}$) and feedback dimension in UL ($\beta_{fb}$), with random, spatially isotropic pilots. It is shown that when the number of training pilots exceeds the channel covariance rank ($r$), the optimal rate-distortion feedback strategy achieves an estimation error decay of $\Theta (SNR^{-\alpha})$ in estimating the channel state, where $\alpha = min (\beta_{fb}/r , 1)$ is the so-called quality scaling exponent. We also discuss an "analog" feedback strategy, showing that it can achieve the optimal quality scaling exponent for a wide range of training and feedback dimensions with no channel covariance knowledge and simple signal processing at the user side. Our findings are supported by numerical simulations comparing various strategies in terms of channel state mean squared error and achievable ergodic sum-rate in DL with zero-forcing precoding.