Wideband delay and Direction of Arrival Estimation using sub-Nyquist sampling

Estimating the Direction of Arrival (DOA) of the signals received by a sensor array has been at the core of the array signal processing community for decades. With the advancement of the technology, the limits on the data and data transfer are increasing day by day. Such demands of the increasing bandwidths put an immense burden on the Analog to Digital Converters (ADCs). On the other hand, in the literature most of the wideband DOA estimation algorithms depend on the narrowband signal model where the signal is first decomposed into multiple signals with narrow frequency bins, the DOA is estimated for all of them and the outputs are combined together (coherent or non-coherent) to get the final result. This process is highly computational and highly susceptible to any outliers. Compressed Sensing (CS) over the last few years has shown a great promise in overcoming these problems while preserving the structure of the signal provided it is sparse in some domain. In this paper, we propose to estimate the DOA of wideband signals using CS based reconstruction recognizing that the autocorrelation of such signals is sparse in nature. The peaks in the correlation plot represent the time delays of the corresponding signals which is directly related to their DOAs. We identify and show that the relation between the cross-correlations of the sub-Nyquist signal and the Nyquist rate signal is a block sparse CS problem. By using a block sparse CS reconstruction algorithm we are able to estimate the peak locations in the Nyquist correlation vector thereby estimating the DOAs of the wideband signals.