Power control scheme for spectral coexisting multistatic radar and massive MIMO communication systems under uncertainties: A robust Stackelberg game model

In this paper, we study the problem of robust Stackelberg game-based power control (RSG-PC) for spectral coexisting multistatic radar and massive multiple-input multiple-output (MIMO) communication systems. Recognizing that the path propagation gains cannot be assumed to be constant, the column-wise model is employed to describe the uncertainty of the parameters. The primary objective of the RSG-PC scheme is to minimize the worst-case radiated power of each radar with uncertain path gains for a specified signal-to-interference-plus-noise ratio (SINR) requirement for target detection, while the massive MIMO communication base station (MIMO-CBS) is protected from the interference of radar transmissions. The hierarchical competition between the massive MIMO-CBS and multiple radars are modeled as a robust single-leader multi-follower Stackelberg game. In the considered game model, the massive MIMO-CBS plays as the leader to decide the prices first through the maximization of its own utility. The radars act as the followers, who compete with each other in a non-cooperative Nash game according to the released interference prices from the massive MIMO-CBS subsequently. Based on the theoretical findings on the existence and uniqueness of the robust Nash equilibrium (RNE) in the formulated game, we present an iterative power control approach that guarantees the convergence to the RNE. Finally, the numerical simulations are provided to verify that our RSG-PC scheme can provide efficient power resource utilization, guarantee a predefined target detection performance, and also protect the quality of service (QoS) of massive MIMO-CBS with uncertainties in path propagation gains.