Direction finding via joint diagonalization

An approach to array processing (i.e., direction-finding, signal separation and reconstruction, and calibration) based on the Analytical Constant Modulus Algorithm is considered. The main advantage of this approach is that the multidimensional search associated with Maximum Likelihood based estimators or the single dimensional search associated with MUSIC type methods are eliminated. The sensor array elements are assumed to have the same, up to a multiplicative constant, angle dependent, unknown gain pattern. We show that under this assumption it is possible to estimate the array response matrix and then use the result for direction finding, if the nominal array manifold is known, at least approximately. It is also possible to use the estimated array response matrix in order to separate and reconstruct the signals, or calibrate the array shape or response.