Game-Theoretic Power Allocation and the Nash Equilibrium Analysis for a Multistatic MIMO Radar Network

Abstract

We investigate a game-theoretic power allocation scheme and perform a Nash equilibrium analysis for a multistatic multiple-input multiple-output radar network. We consider a network of radars, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since there is no communication between the distributed clusters, we incorporate convex optimization methods and noncooperative game-theoretic techniques based on the estimate of the signal-to-interference-plus-noise ratio (SINR) to tackle the power adaptation problem. Therefore, each cluster egotistically determines its optimal power allocation in a distributed scheme. Furthermore, we prove that the best response function of each cluster regarding this generalized Nash game belongs to the framework of standard functions. The standard function property together with the proof of the existence of the solution for the game guarantees the uniqueness of the Nash equilibrium. The mathematical analysis based on Karush–Kuhn–Tucker conditions reveals some interesting results in terms of the number of active radars and the number of radars that over satisfy the desired SINRs. Finally, the simulation results confirm the convergence of the algorithm to the unique solution and demonstrate the distributed nature of the system.