A joint array resource allocation and transmit beampattern design approach for multiple targets tracking

Abstract In this paper, we consider a joint array resource allocation and transmit beamforming approach to track multiple targets using phased array radar. Firstly, array allocation is accomplished by solving a constrained optimization problem formulated to minimize total tracking Cramer-Rao Lower Bound with antenna number as a constraint. A procedure to solve this problem is developed by checking Karush-Kuhn-Tucker conditions. Based on the allocated array resource, we develop a novel transmit beampattern design with null steering capability. The emitted signal model and objective functions of optimization are presented with a given power budget and null steering constraint. The resulted problem is revealed to be hard to tackle, therefore, we propose a cyclic algorithm scheme for solving it. The scheme separates the optimization into two problems, where each problem is transformed into simpler convex problems. Lastly, the projected gradient decent method with a penalty function is applied for the optimal design of beamforming with null steering. Simulation results show that the proposed array allocation solution provides better tracking accuracy, and the proposed beampattern design method outperforms conventional optimization methods in the optimal beamforming by achieving much deeper null steering and more accurate peak power in the given directions.