The normal operations of radar systems and communication systems under the condition of spectrum coexistence are facing a huge challenge. This paper uses game theory to study power allocation problems between multistatic multiple-input multiple-output (MIMO) radars and downlink communication. In the case of spectrum coexistence, radars, base station (BS) and multi-user (MU) have the working state of receiving and transmitting signals, which can cause unnecessary interferences to different systems. Therefore, when they work together, they should try to suppress mutual interferences. Firstly, the signal from BS is considered as interference when radar detects and tracks targets. A supermodular power allocation game (PAG) model is established and the existence and uniqueness of the Nash equilibrium (NE) in this game are proved. In addition, the power allocation problem from BS to MU is also analyzed, and two Stackelberg PAG models are constructed. It is proved that the NE of each game exists and is unique. Simultaneously, two Stackelberg power allocation iterative algorithms converge to the NEs. Finally, numerical results verify the convergence of the proposed PAG algorithms.
Keywords: game theory; nash equilibrium; power allocation; radar and communication; spectrum coexistence.