Power Control with Imperfect Exchanges and Applications to Spectrum Sharing

TL;DR

This paper analyzes power control algorithms in spectrum sharing scenarios, accounting for errors in gradient exchanges, and proposes methods to bound constraint violations and suboptimality in distributed convex optimization.

Contribution

It introduces a framework for assessing and mitigating errors in gradient-based power control algorithms with applications to spectrum sharing.

Findings

Bounds on constraint violation and suboptimality derived.

Two ergodic sequences tested on spectrum sharing problems.

Effective in distributed power control with imperfect gradient exchanges.

Abstract

In various applications, the effect of errors in gradient-based iterations is of particular importance when seeking saddle points of the Lagrangian function associated with constrained convex optimization problems. Of particular interest here are problems arising in power control applications, where network utility is maximized subject to minimum signal-to-interference-plus-noise ratio (SINR) constraints, maximum interference constraints, maximum received power constraints, or simultaneous minimum and maximum SINR constraints. Especially when the gradient iterations are executed in a disributed fashion, imperfect exchanges among the link nodes may result in erroneous gradient vectors. In order to assess and cope with such errors, two running averages (ergodic sequences) are formed from the iterates generated by the perturbed saddle point method, each with complementary strengths. Under the assumptions of problem convexity and error boundedness, bounds on the constraint violation and the suboptimality per iteration index are derived. The two types of running averages are tested on a spectrum sharing problem with minimum and maximum SINR constraints, as well as maximum interference constraints.