Underdetermined DOA estimation of deterministic signals using high order statistics and noncircularity

Abstract

Sensor arrays play important roles in signal transmission/reception, estimation, and tracking, and have been successfully applied to many engineering fields such as radar, sonar, wireless communications to name a few. Practically, sensor array systems usually suffer from nonideal factors such as signal coherency, spatially coloured noise, and a limited number of sensors. In this thesis, problems of direction of arrival (DOA) estimation in the presence of nonideal factors are addressed, and new algorithms to tackle these problems are developed that achieve improved performance with a limited number of sensors. Under multipath propagation, independent and coherent signals coexist, resulting in rank deficiency of the cumulant matrix. To tackle this problem, two methods for DOA estimation of mixed independent and coherent signals using fourth-order cumulants (FOC) are proposed, and both algorithms can make efficient use of the array degrees of freedom (DOFs). The first algorithm implements the estimation via two-stage processing by separating the independent and coherent signals. In this method, new matrix reconstruction techniques for independent signal cumulants and rank restoration are developed, and the DOAs of both the independent and coherent signals can be estimated by polynomial rooting without performing a spectral grid search. Its superiority over existing methods is demonstrated by simulation results. The second algorithm considers the case when a large number of coherent signals, greater than the number of sensors, exist due to the propagation channel. Here, we exploit temporal correlation in the signals to form an array output matrix with pseudo snapshots, spanning the same signal subspace as the one using real snapshots. By incorporating this property, new augmented cumulant matrices are constructed and the corresponding method for coherent group separation is derived. Compared with the existing method, the proposed one achieves better performance in terms of estimation accuracy and robustness of the spatial signature, especially for weak signals. Apart from signal with circular statistics discussed above, we study the noncircularity embedded in modern wireless communication signals to further extend the effective aperture, enhance DOFs, and improve the estimation performance. A new FOC-based direction finding method which can extend the array aperture as well as maximise the DOFs is proposed. By combining noncircularity with high order cumulants and optimising geometric arrangement of the virtual array arising accordingly, the resultant identifiability of DOA estimation can be up to twice larger compared with the using the same order cumulants for circular signals. Simulation results validate that the proposed method offers better performance in terms of identifiability as well as accuracy. Last, we revisit the case when uncorrelated and coherent signals coexist and utilise the noncircularity of signals in this scenario. To the best of our knowledge, there are no publications addressing the class of DOA estimation problem, and a novel two-stage second order statistics (SOS) estimator is introduced accordingly to further increase the DOFs. In this method, a more robust approach is presented to identify the true DOA estimates from the pseudo ones, the estimates of noncircular phases are derived in closed-form, and a novel spatial smoothing technique based on the eigenvectors is developed to restore the rank deficiency. Additionally, new deterministic Cram´er- Rao lower bounds (CRLBs) are derived for the considered mixture model of noncircular signals. The theoretical analysis justifies that the number of identifiable signals is larger than the current algorithms. Extensive simulation results show that the proposed method offers sufficient DOFs as well as improving the estimation accuracy of both the uncorrelated and coherent signals.