Power-Controlled Feedback and Training for Two-way MIMO Channels

TL;DR

This paper investigates the impact of power-controlled feedback and training on the diversity-multiplexing tradeoff in two-way MIMO channels, revealing that one-bit feedback suffices for optimal asymptotic performance despite practical imperfections.

Contribution

It introduces novel power-controlled feedback and training schemes that achieve optimal diversity-multiplexing tradeoff with minimal feedback bits in realistic noisy conditions.

Findings

One-bit feedback achieves the same diversity order as more feedback bits.

More than one feedback bit does not improve performance asymptotically.

Proposed protocols perform optimally despite imperfect channel estimation and noisy feedback.

Abstract

Most communication systems use some form of feedback, often related to channel state information. The common models used in analyses either assume perfect channel state information at the receiver and/or noiseless state feedback links. However, in practical systems, neither is the channel estimate known perfectly at the receiver and nor is the feedback link perfect. In this paper, we study the achievable diversity multiplexing tradeoff using i.i.d. Gaussian codebooks, considering the errors in training the receiver and the errors in the feedback link for FDD systems, where the forward and the feedback are independent MIMO channels. Our key result is that the maximum diversity order with one-bit of feedback information is identical to systems with more feedback bits. Thus, asymptotically in $\mathsf{SNR}$, more than one bit of feedback does not improve the system performance at constant rates. Furthermore, the one-bit diversity-multiplexing performance is identical to the system which has perfect channel state information at the receiver along with noiseless feedback link. This achievability uses novel concepts of power controlled feedback and training, which naturally surface when we consider imperfect channel estimation and noisy feedback links. In the process of evaluating the proposed training and feedback protocols, we find an asymptotic expression for the joint probability of the $\mathsf{SNR}$ exponents of eigenvalues of the actual channel and the estimated channel which may be of independent interest.