Distributed Design of Joint Transmit and Receive Beamforming for MIMO Radar Networks Using Game Theory

This article investigates the problem of joint transmit and receive beamforming for a colocated multiple-input multiple-output radar network with multiple targets and signal-dependent interferences. At first, a distributed beamforming design scheme is developed using noncooperative game theory. The basis of this scheme is to minimize the maximum transmit power of antennas for each radar while adhering to the constraint of signal-to-interference-plus-noise ratio for the targets. By transforming the formulated optimization problem into a convex problem, the Lagrangian duality theory is utilized to decompose the original problem into two sub-problems. Then, a subgradient projection method and an equivalent receive beamforming optimization method are developed to tackle the two sub-problems, yielding the optimal transmit beamformers for the radars. After obtaining the transmit and receive beamformers iteratively, the game relationship among radars is then formulated as a power control game, and the paper proves the existence and uniqueness of the Nash equilibrium. Furthermore, a centralized beamforming design problem is explored for comparative analysis, where the beamformers of all radars are jointly optimized to suppress power fluctuations among transmit antennas. Simulation results are provided to validate the effectiveness of the proposed schemes.