Vector Broadcast Channels: Optimality of Threshold Feedback Policies

TL;DR

This paper proves that threshold-based feedback policies are optimal for rate maximization in beamforming systems with limited feedback, providing a distribution-independent, practical, and robust solution that simplifies the search for optimal policies.

Contribution

It establishes the optimality of threshold feedback policies in feedback-limited beamforming systems, extending previous heuristic justifications to a rigorous, distribution-independent proof.

Findings

Threshold feedback policies are rate-wise optimal.

The result is distribution independent and robust.

Simplifies the search for optimal feedback policies.

Abstract

Beamforming techniques utilizing only partial channel state information (CSI) has gained popularity over other communication strategies requiring perfect CSI thanks to their lower feedback requirements. The amount of feedback in beamforming based communication systems can be further reduced through selective feedback techniques in which only the users with channels good enough are allowed to feed back by means of a decentralized feedback policy. In this paper, we prove that thresholding at the receiver is the rate-wise optimal decentralized feedback policy for feedback limited systems with prescribed feedback constraints. This result is highly adaptable due to its distribution independent nature, provides an analytical justification for the use of threshold feedback policies in practical systems, and reinforces previous work analyzing threshold feedback policies as a selective feedback technique without proving its optimality. It is robust to selfish unilateral deviations. Finally, it reduces the search for rate-wise optimal feedback policies subject to feedback constraints from function spaces to a finite dimensional Euclidean space.