Abstract

In this work, we tackle the estimation of elevation and azimuth direction of arrival (DOA) of uncorrelated wideband (WB) and statistically non-stationary (NS) sources located in the far-field of a sensor array in both free-field and multipath propagation environments. For the case of free-field propagation, we derive the closed-form expression of the Cramer-Rao Bound (CRB) that is applicable to both the overdetermined and underdetermined cases of DOA estimation. We also establish the condition for the existence of the CRB along with a discussion on the dependence of CRB on the signal-to-noise ratio and the upper bound on the total number of WB and NS sources that can be resolved theoretically. Further, we develop a coarray-based DOA estimation algorithm that uses the enhanced degrees of freedom (DOF) of the difference coarray of a non-uniform planar array to localize more uncorrelated WB and NS sources than the number of physical sensors. In the multipath scenario, the correlation between the direct signal and the reflected signal is tackled by proposing a new focusing method based on the decomposition of the array steering function using 2D Fourier basis functions. The proposed focusing approach can be applied to any realworld arbitrary planar array and does not require the initial estimate of the DOAs of the WB and NS sources. After focusing, frequency smoothing is performed to decorrelate the direct and reflected signals. After decorrelation, we propose two coarraybased techniques to identify the time-frequency bins that are dominated by the direct signals which are then used to estimate the DOA of the sources emitting the direct signals. Numerical examples verify the effectiveness of the proposed methods.