A Measurement Matrix Design Algorithm for Ad Hoc Networks Using Phased Array Antennas

Abstract

In GPS-denied ad hoc networks equipped with single-port phased array antennas, accurate incident-angle estimation is critical for enabling reliable directional communication. Traditional methods based on the spatial covariance matrix or compressed sensing often assume uniformly distributed incident angles, which results in an elevated expected estimation error (EEE) in realistic deployments where nodes are randomly distributed (e.g., following a Poisson point process). To address this issue, this paper introduces a probability-based optimisation framework that designs the measurement matrix by leveraging the distribution of incident angles. The optimisation objective is to minimise the EEE of an orthogonal matching pursuit estimator, leading to a non-convex expectation minimisation problem. This problem is solved using a Grey Wolf Optimisation-based algorithm that determines the beam angles for the measurement matrix. Simulation results on a six-element uniform linear array show that the proposed algorithm reduces the EEE by 13.2% compared to uniform beam design when the node deployment region has an aspect ratio of 4. These results demonstrate that the algorithm effectively exploits angular distribution characteristics to achieve significant performance improvements.