An Optimization Algorithm for Forward-Scatter Radar Network Node Deployment Based on BFGS and Improved NSGA-II

Recently, forward-scatter radars (FSRs) utilizing the Global Navigation Satellite System (GNSS) as a radiation source have gained increasing attention. The radar system enables aerial target surveillance by deploying multiple receiving nodes on the ground. It offers a low-cost and easily deployable solution. Therefore, how to deploy the receiving nodes to achieve efficient utilization of node resources is an urgent problem to be addressed. In this paper, a deployment method was proposed for receiving nodes in a single-transmitter and multiple-receiver configuration. First, the problem was reformulated as an optimal equal-circle covering problem via geometric approximation. A multi-objective optimization model was subsequently established with the objective functions of minimizing node cost and maximizing spatial detection area. Second, a method based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm was introduced to obtain the sub-optimal solution of node cost, thereby reducing the computational complexity of the optimization process. Finally, an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II) was proposed to derive the deployment schemes. Then, these schemes were ranked using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) based on the Entropy Weight Method (EWM). The results indicate that the proposed method can obtain the optimal deployment scheme compared to the existing method and enhance the diversity of the solutions.