Radar Waveform Design Under Communication Sum Capacity Constraint

This paper considers a joint radar and wireless communication systems where the radar transmit waveform is adaptively designed. To ensure acceptable performance of both radar and communication systems operating in the same frequency bands, the radar makes use of knowledge provided by the communication systems and vice versa. Specifically, the radar transmit waveform is designed not only to maximize radar performance such as signal-to-interference-and-noise ratio (SINR) but also to guarantee acceptable communication systems performance by ensuring a prescribed total throughput or sum capacity of communication systems. We formulate an optimization problem that maximizes the radar performance subject to the radar power constraint and the communication sum capacity constraint. Since the sum capacity constraint is not a convex constraint, the resulting optimization problem is not convex. We provide a geometric analysis of the sum capacity constraint and the solution of the SINR maximization problem in two steps: 1) obtain the optimal solution with only radar power constraints, i.e., without the sum capacity constraint, and then 2) starting from the optimal solution of the first step, find a solution satisfying the sum capacity constraint. In this process, a closed form solution to find the locally optimal point at each search is derived, which reduces computational complexity of the proposed algorithm. Numerical results are provided to verify performance of the proposed method.