Distributed MPDR Beamforming in Virtual Arrays

This paper extends the distributed minimum power distortionless response (MPDR) beamformer to 3D virtual arrays with heterogeneous node geometries. We first present a system model of cooperative nodes-each with its own arbitrary array-and generalize the distributed MPDR, originally designed for λ/2-spaced linear arrays, to 3D arrays. We then evaluate beam pattern shape, directivity, beam efficiency, and bit error rate (BER), benchmarking these metrics against the centralized MPDR. Simulations reveal grating lobes for antenna-element spacings larger than λ/2, but the array gain mitigates their BER impact. The slow convergence speed of the distributed MPDR indicates the necessity of searching for techniques to improve it. With sufficient snapshots, its performance nearly matches centralized MPDR, confirming its promise for practical virtual arrays, including satellite swarms.