Determination of the angular coordinates of sources of radiation with a planar equidistant antenna array using the maximum-likelihood method

A method of constructing maximum-likelihood estimates in the problem of determining the angular coordinates of the sources of a known number K of monochromatic signals from a single sample of observations from the outputs of a plane equidistant antenna array is considered. The solution of the problem is reduced to obtaining the roots of two K-degree polynomials, which determine the maximum-likelihood estimates of the direction cosines. The maximum-likelihood estimates of the vectors of the coefficients of these polynomials are determined by the eigenvectors corresponding to the minimum eigenvalues of two Hermitian matrices, the elements of which are known functions of the sufficient statistics in this problem. The results of an analysis of the quality of the estimates obtained are given.