Ergodic and Outage Performance of Fading Broadcast Channels with 1-Bit Feedback

TL;DR

This paper analyzes the ergodic sum-rate and outage probability of a fading broadcast channel with K users using only 1-bit CSI feedback, revealing that sum-rate scales as loglogK and exploring the effects of feedback delay.

Contribution

It provides a closed-form expression for ergodic sum-rate with 1-bit feedback, examines the impact of feedback delay, and characterizes outage performance and DMT under limited feedback.

Findings

Sum-rate scales as loglogK, matching full CSI schemes.

Feedback delay degrades sum-rate, especially at large K or low SNR.

Power allocation with instantaneous feedback doubles the DMT.

Abstract

In this paper, the ergodic sum-rate and outage probability of a downlink single-antenna channel with K users are analyzed in the presence of Rayleigh flat fading, where limited channel state information (CSI) feedback is assumed. Specifically, only 1-bit feedback per fading block per user is available at the base station. We first study the ergodic sum-rate of the 1-bit feedback scheme, and consider the impact of feedback delay on the system. A closed-form expression for the achievable ergodic sum-rate is presented as a function of the fading temporal correlation coefficient. It is proved that the sum-rate scales as loglogK, which is the same scaling law achieved by the optimal non-delayed full CSI feedback scheme. The sum-rate degradation due to outdated CSI is also evaluated in the asymptotic regimes of either large K or low SNR. The outage performance of the 1-bit feedback scheme for both instantaneous and outdated feedback is then investigated. Expressions for the outage probabilities are derived, along with the corresponding diversity-multiplexing tradeoffs (DMT). It is shown that with instantaneous feedback, a power allocation based on the feedback bits enables to double the DMT compared to the case with short-term power constraint in which a dynamic power allocation is not allowed. But, with outdated feedback, the advantage of power allocation is lost, and the DMT reverts to that achievable with no CSI feedback. Nevertheless, for finite SNR, improvement in terms of outage probability can still be obtained.