Minimax and Maxmin Solutions to Gaussian Jamming in Block-Fading Channels under Long Term Power Constraints

Without assuming any knowledge on source's code-book 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. Under long term power constraints, the optimal power control strategies of each player for both maxmin and minimax problems are obtained. Numerical results demonstrate a sharp difference between the resulting outage probabilities of the minimax and maxmin solutions, which thus implies the non-existence of Nash equilibria.