Deterministic Beamforming for Unmanned Aerial Vehicle Array

Abstract

This paper addresses the deterministic beamforming for unmanned aerial vehicle (UAV) array (UAVA), which is equipped with an antenna for each UAV. Unlike conventional array, the UAVA can obtain extra degrees-of-freedom for beamforming by flexibly controlling the topology of UAVs, which motivates us to consider an off-grid array layout to improve the beamformer. To effectively control the load of UAVs, we incorporate the dynamic range ratio (DRR) of weighting coefficients of UAVA. On these basis, we formulate a new optimization model aiming to minimize the maximum sidelobe level under the constraints of mainlobe ripple, DRR, layout spacing and array aperture. However, the resulting NP-hard problem is quite challenging due to the exponential form of layout vector and the non-convexity of mainlobe ripple and DRR. In this respect, we reformulate this multi-constrained problem into a new iteration form of combining alternating direction penalty method and majorization-minimization via introducing a series of auxiliary variables. In each iteration, the tractable and small-sized subproblems can almost globally be solved. Numerical results confirm that our method is more suitable for deterministic beamforming of UAVA than the state-of-the-art methods.