Mutual Information Games in Multi-user Channels with Correlated Jamming

TL;DR

This paper analyzes a non-cooperative game involving two users and a jammer in AWGN channels, exploring optimal strategies and the impact of channel fading and correlation on solution existence.

Contribution

It introduces a game-theoretic framework for mutual information maximization in multi-user channels with correlated jamming, including solutions for non-fading and fading scenarios.

Findings

Optimal strategies are Gaussian signaling and linear jamming in non-fading channels.

Solutions exist when the jammer is uncorrelated in fading channels.

When the jammer is correlated, optimal strategies may not exist, but max-min strategies are characterized.

Abstract

We investigate the behavior of two users and one jammer in an AWGN channel with and without fading when they participate in a non-cooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop the channel and can use the information obtained to perform correlated jamming. Under various assumptions on the channel characteristics, and the extent of information available at the users and the jammer, we show the existence, or otherwise non-existence of a simultaneously optimal set of strategies for the users and the jammer. In all the cases where the channel is non-fading, we show that the game has a solution, and the optimal strategies are Gaussian signalling for the users and linear jamming for the jammer. In fading channels, we envision each player's strategy as a power allocation function over the channel states, together with the signalling strategies at each channel state. We reduce the game solution to a set of power allocation functions for the players and show that when the jammer is uncorrelated, the game has a solution, but when the jammer is correlated, a set of simultaneously optimal power allocation functions for the users and the jammer does not always exist. In this case, we characterize the max-min user power allocation strategies and the corresponding jammer power allocation strategy.