Dynamic Rate Allocation in Fading Multiple-access Channels

TL;DR

This paper introduces low-complexity approximate rate allocation policies for fading Gaussian multiple-access channels, analyzing their ability to track optimal rates amid channel variations, and providing bounds on their performance.

Contribution

It presents novel low-complexity approximate gradient-based rate allocation schemes for fading MACs, with explicit analysis of their tracking performance under channel dynamics.

Findings

Proposed policies implement a single gradient projection per measurement.

Explicit bounds on tracking neighborhood size are derived.

Policies are computationally efficient with polynomial complexity.

Abstract

We consider the problem of rate allocation in a fading Gaussian multiple-access channel (MAC) with fixed transmission powers. Our goal is to maximize a general concave utility function of transmission rates over the throughput capacity region. In contrast to earlier works in this context that propose solutions where a potentially complex optimization problem must be solved in every decision instant, we propose a low-complexity approximate rate allocation policy and analyze the effect of temporal channel variations on its utility performance. To the best of our knowledge, this is the first work that studies the tracking capabilities of an approximate rate allocation scheme under fading channel conditions. We build on an earlier work to present a new rate allocation policy for a fading MAC that implements a low-complexity approximate gradient projection iteration for each channel measurement, and explicitly characterize the effect of the speed of temporal channel variations on the tracking neighborhood of our policy. We further improve our results by proposing an alternative rate allocation policy for which tighter bounds on the size of the tracking neighborhood are derived. These proposed rate allocation policies are computationally efficient in our setting since they implement a single gradient projection iteration per channel measurement and each such iteration relies on approximate projections which has polynomial-complexity in the number of users.