Efficient subspace-based algorithm for adaptive direction estimation and tracking of narrowband signals

By exploiting the array geometry and its shift invariance property of a uniform linear array (ULA), a new computationally efficient subspace-based algorithm is investigated for estimating the constant directions adaptively and for tracking the slowly time-varying directions promptly, where the null space is estimated with the least-mean-square (LMS) or normalized LMS (NLMS) algorithm, and the directions are updated by the approximate Newton’s method. the transient analyses of LMS and NLMS algorithms are studied, where the weights are in the form of matrix, and there is the correlation between the “additive noise” and “input data” that involve the instantaneous correlation of received array data in the updating equation, and the stability conditions of step-size are derived explicitly. Additionally the analytical expressions of mean-square error (MSE) and mean-square deviation (MSD) learning curves of LMS algorithm are also clarified.