Nonconventional least squares optimization for DOA estimation

An optimization technique based on the nonconventional least squares approximation to the direction-of-arrival (DOA) estimation problem is presented. In contrast to the conventional least squares problem, where the number of equations is greater than the number of unknowns, in this nonconventional optimization procedure, the number of unknowns is much greater than the number of equations and hence it is a very underdetermined problem. The proposed method utilizes signal steering vector as a function of azimuth angles similar to the discrete Fourier transform (DFT) concept. Various electromagnetic effects, such as mutual coupling between array elements, antenna element failure, the use of dissimilar antenna elements, the use of nonplanar and nonuniformly spaced array elements, and coupling from near-field scatterers can be automatically taken into account in the preprocessing. After carrying out the electromagnetic optimization through a preprocessing, the DOA estimation reduces to a simple matrix multiplication, which reduces the computational complexity in the estimation. Hence, this procedure is ideally suited for deployment in a complex environment and the entire computation can be done in real time. Sample numerical results are presented to demonstrate the performance and accuracy of this procedure. This is a good procedure for the DOA estimation but not very accurate in estimation of the amplitudes due to the classical picket fence effect produced by a DFT-based methodology.