Algebraic Method for Deterministic Blind Beamforming with Unknown Receiver Gain and Phases

Conventional methods for signal reconstruction which first estimate the directions of arrival (DOA) in order to compute the beamformer weights are sensitive to calibration errors. Blind methods are preferable as the signals are separated without array calibration and DOA estimation. In this work we present a non-iterative method for blind beamforming avoiding a multidimensional search as for Maximum Likelihood estimators. Only a two-dimensional search for the minima of a cost function in the differential wavenumber vector plane has to be accomplished. The antenna may have arbitrary but known element positions whereas the receivers gains and phases are unknown. The sensor array elements are assumed to have up to a multiplicative constant the same, angle dependent, unknown gain pattern and negligible small inter element couplings. In simulations we compare our method with a weighted Least Squares (WLS) estimator.