Estimaton of the number of signals based on orthogonal projection of forward-backward covariance matrix

A fast algorithm for estimating the number of multiple spatial signals with uniform linear array based on forward-backward sample covariance matrix orthogonal projection (SCMOP) is proposed. Firstly, a unitary transform is performed on the forward-backward sample covariance matrix, and then the column vectors of the transformed matrix are orthogonalized via Gram-Schmidt (GS) orthogonalization algorithm. The number of signal sources is estimated by comparing the modulus of the orthogonalized vectors with an adaptive threshold, which is derived from the asymptotic distribution properties of the estimation errors of the sample covariance matrix. Computer simulations are given to illuminate the correctness and efficiency of the algorithm.