Optimal linear array orientation design for 3D direct position determination via semi-Definite relaxation

Abstract

This paper presents an optimization strategy for array orientations in a three-dimensional (3D) direct position determination (DPD) system. Specifically, we consider a scenario in which uniform linear arrays (ULAs) are used to locate emitters, and we seek to optimize the array orientations in terms of localization accuracy. The E-optimality criterion, which minimizes the spectral norm of the Cramér-Rao lower bound (CRLB), is exploited to formulate this problem. As the objective function is non-convex with bilinear structures, we leverage semi-definite relaxation (SDR) to transform it into a convex semi-definite programming (SDP) problem by substituting the bilinear terms with a matrix variable. In addition, we tackle the array orientation configuration problem in the context of multi-emitter scenarios and develop an SDR solution for large-scale antenna array systems. Simulation results validate that the ULAs with array orientations designed by the proposed SDR-based method have near-optimal localization performance.