A multi-link communication connectivity game under hostile interference

In this paper, we consider a communication connectivity problem involving a primary user (transmitter, for example, a Ground Control Station (GCS)) servicing a group of secondary users (receivers, for example, drones) under hostile interference. We formulate this multi-link communication connectivity problem, where the channels are affected by Rayleigh fading, as a zero-sum power resource allocation game between a transmitter and an adversary (jammer). The transmitter's objective is to maximize the probability of communication connectivity with all the receivers. It is proven that the problem has unique equilibrium in power allocation strategies, and the equilibrium is derived in closed form. Moreover, we reduce the problem of designing the equilibrium in power resource allocation strategies to the problem of finding a fixed point of a real-valued function. An algorithm based on the bisection method to find the fixed point (and so equilibrium strategies) is developed, and its convergence is proven.