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A quadratically constrained minimum dispersion (QCMD) beamformer that is robust against model uncertainties is devised for non-Gaussian signals. Different from the minimum variance based beamformers, the QCMD beamformer minimizes the lp-norm (p ≥ 1) of the output while constraining the magnitude response of any steering vector within a spherical uncertainty set to exceed unity. A gradient projection algorithmic framework is proposed to efficiently solve the resulting convex optimization problem instead of directly applying the standard optimization algorithm which has a high computational complexity. In each iteration, the gradient projection updates the solution along the gradient direction and projects it back to the constraint set. Importantly, a closed-form expression of the projection onto the constraint set is derived, which only needs a low complexity of O(M) with M being the sensor number. Therefore …