Computationally Efficient Subspace-Based Method for Direction-of-Arrival Estimation Without Eigendecomposition

A computationally simple direction-of-arrival (DOA) estimation method with good statistical performance is attractive in many practical applications of array processing. In this paper, we propose a new computationally efficient subspace-based method without eigendecomposition (SUMWE) for the coherent narrowband signals impinging on a uniform linear array (ULA) by exploiting the array geometry and its shift invariance property. The coherency of incident signals is decorrelated through subarray averaging, and the null space is obtained through a linear operation of a matrix formed from the cross-correlations between some sensor data, where the effect of additive noise is eliminated. Consequently, the DOAs can be estimated without performing eigendecomposition, and there is no need to evaluate all correlations of the array data. Furthermore, the SUMWE is also suitable for the case of partly coherent or incoherent signals, and it can be extended to the spatially correlated noise by choosing appropriate subarrays. The statistical analysis of the SUMWE is studied, and the asymptotic mean-squared-error (MSE) expression of the estimation error is derived. The performance of the SUMWE is demonstrated, and the theoretical analysis is substantiated through numerical examples. It is shown that the SUMWE is superior in resolving closely spaced coherent signals with a small number of snapshots and at low signal-to-noise ratio (SNR) and offers good estimation performance for both uncorrelated and correlated incident signals.