Spectrum optimization in multi-user multi-carrier systems with iterative convex and nonconvex approximation methods

TL;DR

This paper introduces a new class of iterative approximation methods for spectrum optimization in multi-user multi-carrier systems, focusing on per-user iterative implementation to achieve faster convergence and better solutions.

Contribution

It proposes a systematic design framework for novel iterative approximation methods that relax convexity requirements, improving convergence speed and solution quality in spectrum optimization.

Findings

New methods converge faster than existing ICA approaches.

Proposed methods require lower computational cost.

Methods effectively avoid poor local optima.

Abstract

Several practical multi-user multi-carrier communication systems are characterized by a multi-carrier interference channel system model where the interference is treated as noise. For these systems, spectrum optimization is a promising means to mitigate interference. This however corresponds to a challenging nonconvex optimization problem. Existing iterative convex approximation (ICA) methods consist in solving a series of improving convex approximations and are typically implemented in a per-user iterative approach. However they do not take this typical iterative implementation into account in their design. This paper proposes a novel class of iterative approximation methods that focuses explicitly on the per-user iterative implementation, which allows to relax the problem significantly, dropping joint convexity and even convexity requirements for the approximations. A systematic design framework is proposed to construct instances of this novel class, where several new iterative approximation methods are developed with improved per-user convex and nonconvex approximations that are both tighter and simpler to solve (in closed-form). As a result, these novel methods display a much faster convergence speed and require a significantly lower computational cost. Furthermore, a majority of the proposed methods can tackle the issue of getting stuck in bad locally optimal solutions, and hence improve solution quality compared to existing ICA methods.