Game Theoretic Power Allocation and Antenna Selection for Target Detection in Hybrid Active and Passive MIMO Radar

In this paper, a hybrid active and passive (HAP) multiple-input multiple-output (MIMO) radar network is considered, where target returns from both active radar transmitters and illuminators of opportunity (IOs) are employed to complete target detection. With consideration for the active radar power limitation and the total available number constraint for the IOs, the joint discrete power allocation and antenna selection for target detection in HAP MIMO radar is studied. A game-theoretic framework is proposed to solve the problem where the target probability of detection (PD) of the HAP MIMO radar is utilized to build a common utility. The formulated discrete game is proven to be a potential game that possesses at least one pure strategy Nash equilibrium (NE) and an optimal strategy profile that maximizes the PD of HAP radar. The properties of the formulated game, including the feasibility, existence and optimality of NE, are also analyzed. The proposed game’s pure strategy NE is determined to be an optimal scheme under certain conditions. An iterative algorithm is then designed to achieve the pure strategy NE. The designed algorithm’s convergence and complexity are discussed. It is demonstrated that the designed algorithm can achieve almost optimal target detection performance while maintaining low complexity. Under certain conditions, the designed algorithm can obtain optimal performance.