Resource Allocation in Multiple Access Channels

TL;DR

This paper develops efficient algorithms for rate allocation in Gaussian multiple-access channels with general concave utility functions, leveraging polymatroid structure and approximate projections for computational tractability.

Contribution

It introduces a novel approximate projection method using polymatroid properties, enabling scalable rate allocation for complex utility functions.

Findings

The proposed algorithms efficiently handle exponentially many constraints.

Approximate projections are implemented via recursive algorithms with polynomial complexity.

Rate-splitting improves convergence bounds of the projection method.

Abstract

We consider the problem of rate allocation in a Gaussian multiple-access channel, with the goal of maximizing a utility function over transmission rates. In contrast to the literature which focuses on linear utility functions, we study general concave utility functions. We present a gradient projection algorithm for this problem. Since the constraint set of the problem is described by exponentially many constraints, methods that use exact projections are computationally intractable. Therefore, we develop a new method that uses approximate projections. We use the polymatroid structure of the capacity region to show that the approximate projection can be implemented by a recursive algorithm in time polynomial in the number of users. We further propose another algorithm for implementing the approximate projections using rate-splitting and show improved bounds on its convergence time.