Robust Beamforming with Phase Response Fixed and Magnitude Response Constraint

The conventional magnitude constraints beamformer is a non-convex issue which is reformulated as a linear programming issue. A robust beamformer with Phase response Fixed and Magnitude response Constraint (PFMC) is proposed for Uniform Linear Array (ULA). Making use of the property that there is only a phase factor difference between the transfer function of the inverse sequence of the weight vector and the array response function, the phase response is set to be linear and the real magnitude response is constrained. Thus, a convex optimization cost function is established whose optimal solution can be found out by highly efficient interior point method. The PFMC-WC method against covariance matrix error is proposed based on Worst Case (WC) performance optimization to improve the performance of PFMC. Compared with the conventional magnitude response constraint beamformer, the proposed method reduces the number of constraints and leaves out the processing of recovering the weight vector, therefore, the calculation cost is reduced. In addition, due to the guarantee of the phase response, the proposed beamformer has better performance than the traditional magnitude constraint beamformer. Simulation results demonstrate the effectiveness of the proposed beamformer.