Rate Constrained Random Access over a Fading Channel

TL;DR

This paper introduces a game-theoretic approach with a stochastic gradient algorithm for managing random access in fading channels, ensuring rate constraints and convergence to equilibrium without centralized coordination.

Contribution

It proposes a novel two timescale stochastic gradient algorithm with a waterfilling mechanism for rate-constrained random access in fading channels, guaranteeing convergence and rate satisfaction.

Findings

Algorithm converges to Nash equilibrium.

Rate constraints are satisfied in simulations.

Users' power consumption is minimized at equilibrium.

Abstract

In this paper, we consider uplink transmissions involving multiple users communicating with a base station over a fading channel. We assume that the base station does not coordinate the transmissions of the users and hence the users employ random access communication. The situation is modeled as a non-cooperative repeated game with incomplete information. Each user attempts to minimize its long term power consumption subject to a minimum rate requirement. We propose a two timescale stochastic gradient algorithm (TTSGA) for tuning the users' transmission probabilities. The algorithm includes a 'waterfilling threshold update mechanism' that ensures that the rate constraints are satisfied. We prove that under the algorithm, the users' transmission probabilities converge to a Nash equilibrium. Moreover, we also prove that the rate constraints are satisfied; this is also demonstrated using simulation studies.