Non-Cooperative Power Allocation Game in Distributed Radar Systems: A Sigmoid Utility-Based Approach

Power control algorithms using the signal-to-interference-plus-noise ratio (SINR) metric in distributed radar systems (DRS) may suffer from performance degradation in infeasible conditions. In this paper, we present a Sigmoid-based Power Allocation Game (SigPAG) algorithm for target detection in DRS to minimize total power consumption while meeting predetermined target detection performance. Firstly, a physically interpretable Sigmoid function is designed to model radar detection probability as the utility function, overcoming the performance limitations and potential deviations of SINR-based utilities. Secondly, by integrating the proposed Sigmoid utility, SigPAG is established to describe the interaction among radar nodes in the DRS. The existence and uniqueness of the Nash equilibrium (NE) solution are proven by the closed-form expressions of the best response function. Furthermore, an iterative power allocation algorithm is proposed to adjust the transmit powers towards the NE point. Finally, simulation results obtained in a 4-node DRS with Radar Cross Section (RCS) values of [1, 0.3, 2, 5] m2 demonstrate that the proposed algorithm achieves an energy efficiency improvement of 36.1% in target detection compared with the traditional SINR-based methods.