A non-zero sum game of a joint radar and communication system and a jammer.

In this paper, we model a joint (dual) system maintaining both radar task and communication task under the worst environmental conditions caused by hostile interference of the jammer. This model involves two maxmin problems formulated and solved in zero-sum game framework between system and jammer as players. The first problem is to find the equilibrium power allocation strategy of the system in the spectrum band to maximize communication signal-to-interference-plus-noise ratio (SINR) and radar’s SINR depending on the task the system focuses on. The second problem is to find a trade-off between the expected system’s SINR and fairness in using radar mode and communication mode by the system with $\alpha$-fairness as such criteria. Also, here we consider the jammer as an adversary supporting artificial intelligence (AI) which allows the adversary not just to obstruct the system’s functionality but also might achieve it in a less predictable way for the system. The derived solution is numerically illustrated. Moreover, we suggest an approach allowing us to find an optimal fairness coefficient, in other words, to find the most fair fairness criteria, to support both communication task and radar task.