Robust beampattern synthesis algorithm for arrays with sensor position error

A new robust beampattern synthesis algorithm is presented which can be used to find array weight coefficients. The algorithm synthesizes the beampattern with a given look direction and sidelobe regions when there are sensor positioning errors. The new method minimizes the mean squared error between the actual beamformer response and the desired one in the sidelobe regions. The weight coefficients are calculated based on the solution of a linearly constrained minimum variance technique with the unity gain response and phase-independent derivative constraints. The novelty in the approach is that the minimization takes into account the distribution of the one-dimensional and two-dimensional errors in sensor locations. The constraints ensure to find the precise direction of arrival of the desired signal and avoid an undesirable high sidelobes phenomenon because of the choice of a reference point. Unlike an array calibration algorithm, the method does not require any a priori information on the sensor locations. The mathematical formulae for the proposed algorithm are derived in detail for three different types of errors. We also extend the synthesis algorithm to the iterative method for achieving equiripple beampattern. Simulation results show the performance of the new algorithm compared to the current algorithm without error compensation for the different types of errors.