Adaptive array beamforming with robust capabilities under random sensor position errors

The problem of adaptive array beamforming with multiple-beam constraints in the presence of steering error caused by random sensor position errors is considered. First the statistical relationship between the random sensor position errors and the induced random phase perturbation is derived. Based on the result, a cost function consisting of terms which utilise a posteriori information owing to the received array data and a priori information owing to the probabilistic distribution of the resulting phase perturbation, respectively, is constructed. Then, an appropriate estimate of the actual phase angle vector associated with each of the desired signals can be obtained by performing a nonlinear optimisation problem. An implementation algorithm is further presented to solve iteratively the problem. Theoretical analysis regarding the convergence property of the iterative procedure is also investigated. Finally, several computer simulation examples are provided for demonstrating the effectiveness of the proposed technique.