Vector Broadcast Channels: Optimal Threshold Selection Problem

TL;DR

This paper addresses the problem of selecting optimal thresholds for feedback in vector broadcast channels, revealing that uniform thresholds are not always optimal and providing conditions for optimal threshold policies.

Contribution

It introduces a novel analysis of threshold selection using majorization theory, showing when homogeneous thresholds are optimal in finite feedback systems.

Findings

Homogeneous thresholds are not always rate-wise optimal.

Majorization theory reveals a Schur-concave structure in the rate function.

Results apply to various fading channel models, including Rayleigh fading.

Abstract

Threshold feedback policies are well known and provably rate-wise optimal selective feedback techniques for communication systems requiring partial channel state information (CSI). However, optimal selection of thresholds at mobile users to maximize information theoretic data rates subject to feedback constraints is an open problem. In this paper, we focus on the optimal threshold selection problem, and provide a solution for this problem for finite feedback systems. Rather surprisingly, we show that using the same threshold values at all mobile users is not always a rate-wise optimal feedback strategy, even for a system with identical users experiencing statistically the same channel conditions. By utilizing the theory of majorization, we identify an underlying Schur-concave structure in the rate function and obtain sufficient conditions for a homogenous threshold feedback policy to be optimal. Our results hold for most fading channel models, and we illustrate an application of our results to familiar Rayleigh fading channels.