Beam space estimation of the direction-of-arrivals of coherent signals

When the incident signals received by a phased array are correlated, spatial smoothing techniques which are used in element space (ES) to overcome the rank deficiency of the signal subspace are not able to be directly applied in beam space (BS). Recently it has been shown that an approximate ES covariance matrix with the appropriate signal and noise subspaces can be reconstructed from the BS covariance matrix thus allowing spatial smoothing to be carried out on the reconstructed ES covariance matrix and hence high resolution BS direction-of-arrival estimates to be obtained for correlated arrivals. The theory previously developed required that the beams be orthogonal and this study shows how the use of the Moore–Penrose pseudo-inverse and sector focused stability version of BS processing allows the requirement of orthogonality to be reduced to the more realistic and practical constraint that the beams used be independent. The special case of a uniform linear array is considered and it is shown that due to the Vandermonde structure of the beamforming matrix spatial smoothing can be carried out directly in BS.