Underdetermined DOA Estimation of Quasi-Stationary Signals Exploiting Frequency Pairs

This study investigates the underdetermined wideband direction-of-arrival (DOA) estimation problem for quasi-stationary signals (QSSs) employing a sparse array with spacing designed according to the frequencies of interest. Initially, the second-order difference coarrays (SODCAs) are formed at various frequencies. Subsequently, based on the quasi-stationary nature of the signals, virtual arrays, referred to as the dual difference coarrays (DDCAs) falling in the joint spatio-spectral domain, are obtained by computing the difference coarrays of the SODCAs. Specifically, the difference coarrays of SODCAs at the same frequency are termed self-DDCAs, whereas those across different frequencies are cross-DDCAs. These DDCAs offer more degrees of freedom (DOFs) than the initial SODCAs, and it is proved that $\mathcal {O}(M^{4})$ DOFs can be provided by the cross-DDCA with $M$ physical sensors. Two DOA estimation methods based on DDCAs are then developed, showcasing enhanced capabilities in resolution and estimation accuracy.