Optimal Strategies for Gaussian Jamming in Block-Fading Channels under Delay and Power Constraints

TL;DR

This paper models Gaussian jamming in block-fading channels as a zero-sum game, deriving optimal power control strategies under various constraints and analyzing the existence of equilibrium solutions.

Contribution

It formulates the jamming problem as a game without source code knowledge and provides complete solutions for maxmin and minimax strategies under different power constraints.

Findings

Optimal strategies are derived for both short-term and long-term power constraints.

No Nash equilibrium exists under long-term constraints, but maxmin and minimax solutions are characterized.

Numerical results show significant differences in outage probabilities between strategies.

Abstract

Without assuming any knowledge on source's codebook and its output signals, we formulate a Gaussian jamming problem in block fading channels as a two-player zero sum game. The outage probability is adopted as an objective function, over which transmitter aims at minimization and jammer aims at maximization by selecting their power control strategies. Optimal power control strategies for each player are obtained under both short-term and long-term power constraints. For the latter case, we first prove the non-existence of a Nash equilibrium, and then provide a complete solution for both maxmin and minimax problems. Numerical results demonstrate a sharp difference between the outage probabilities of the minimax and maxmin solutions.