Bearings estimation by QZ and VZ decomposition

The new adaptive array processing technique that has been given in [1] is reformulated. Based on this reformulation it is shown that the number of signals present at the multiple array system and the bearings of the incoming signals are given by the nonzero eigenvalues obtained as the solution to the general matrix eigenvalue problem ACe=λ*BDe. Solution to the array processing problem is presented by using the QZ decomposition performed on two cross-cross spectral density matrices and using VZ decomposition performed directly on three data matrices obtained as the output of the multiple array system. Formulation also given to estimate the signal-signal cross spectral density matrix and hence the power of the signal corresponding to the incoming directions, whether the signals are correlated or not, and if they are correlated, amount by which they are correlated can also be obtained. Further, formulation also given in estimating the spatial noise auto-cross spectral density matrix. The reformulation presented here also gives the number of signals and the bearings concurrently and it does not demand an uncorrelated signal environment or the knowledge of the noise correlation in individual arrays. A method of obtaining the signal copy is also presented based on the Blind Reception Beamformer given in [2]. The VZ decomposition is computationally more stable than QZ decomposition since VZ directly operates on the data matrices.