A Multi-Index Policy for Joint Selection of Subarrays and Operational Mode of Distributed Coherent Aperture Radars

The joint selection of subarrays and operational mode plays a crucial role in distributed coherent aperture radar (DCAR) with multiple subarrays, which has received limited attention despite its significance in multi-target tracking. We model the joint selection problem of subarrays and operational mode as a restless multi-arm bandit (RMAB) process, aiming to minimize the expected total discounted error covariance trace value over an infinite time horizon. This paper generalizes the conventional binary-action RMAB to the more complex multi-action RMAB (MA-RMAB) process with multi-constraints. The Whittle relaxation with two distinct Lagrange multipliers is utilized to relax the constraints on subarrays and computing resources over an infinite time horizon. A multi-index policy is proposed as a computable suboptimal heuristic for the MA-RMAB model, where the multi- indices are calculated by using the optimal value of the Lagrangian dual problem. The effectiveness of the proposed multi-index policy is validated through numerical simulation.