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Adaptive array beamforming with robust capabilities under random phase perturbations

The problem of adaptive array beamforming with multiple-beam constraints in the presence of steering error caused by random phase perturbations is considered. We first construct a cost function consisting of terms that utilize a posteriori information due to the received array data and a priori information due to the probabilistic distribution of phase perturbation, respectively. Then, an appropriate estimate of the actual phase angle vector associated with each of the desired signals can be obtained by performing a nonlinear optimization problem based on the cost function. An implementation algorithm is further presented to iteratively solve the problem. Theoretical analysis regarding the convergence property of the iterative procedure is also investigated. Finally, several computer simulation examples are provided for illustration.