Phase-Only Robust Minimum Dispersion Beamforming

A phase-only robust minimum dispersion (PO-RMD) beamformer is devised for non-Gaussian signals. Unlike conventional beamformers that adjust the complex-valued weights, including both amplitude and phase, of each antenna to fulfill spatial filtering, the proposed PO-RMD employs a unit-modulus constraint on the weights, which is equivalent to simply phase shifting at each antenna. Instead of the widely used minimum variance criterion, the PO-RMD adopts the minimum dispersion criterion, which minimizes the ℓ_p-norm of the array output to utilize the non-Gaussianity of the signals. To achieve robustness against model uncertainty, the magnitude response of any steering vector within an uncertainty region is forced to exceed the threshold. A gradient projection (GP) algorithmic framework is developed to solve the resulting nonconvex optimization problem. In order to find a feasible point in the intersection of the unit-modulus, and robustness constraint sets in each iteration, an alternating projection algorithm is also devised. More importantly, the closed-form expressions of the projection onto the two sets are derived, which only need a low complexity of O(M) with M being the number of antennas. Convergence of the alternating projection is analyzed, and the local linear convergence rate is established. Simulation results demonstrate the fast convergence rate, and accuracy of the GP, as well as the simplicity and robustness of the PO-RMD.