Regularization approach to direction estimation of coherent narrow-band signals

This paper addresses the problem of estimating the directions of coherent narrow-band signals impinging on a uniform linear array when the number of signals is unknown. By incorporating the linear prediction (LP) model with a subarray scheme, the directions of coherent signals can be estimated from the zeros of the corresponding prediction polynomial. To obtain a reliable estimation of the LP coefficients, we introduce multiple regularization parameters into the corrected least squares (CLS) estimation. The analytical expressions of the mean-squares-error (MSE) of the regularized CLS estimate and the optimal regularization parameters are derived. It is clarified that the number of signals can be determined by comparing the optimal parameters with the eigenvalues. An iterative regularization algorithm is developed for direction estimation without any a priori knowledge, where the number of coherent signals and the noise variance are estimated from the noisy data simultaneously.