Rotational search methods for adaptive Pisarenko harmonic retrieval

Two adaptation algorithms for adaptive Pisarenko harmonic retrieval are described. They are derived by considering the associated minimum eigenvalue problem as an optimization problem which seeks the minimum of a quadratic cost function given a hyperspherical constraint. An iterative search procedure is used in which each search path is constrained to lie on the unit hypersphere. Computational complexity per iteration is approximately one-third that of previous adaptive PHR algorithms. Simulations reveal that at low SNR the trial eigenvector can converge to the true minimum eigenvector of the sample covariance matrix, long before this matrix is a good estimate of the true covariance matrix.