Direction of arrival estimation of wideband signals using sub-Nyquist samples

This work is dedicated towards finding the Direction of Arrival (DOA) of Wideband signals using Sub-Nyquist samples. In a sensor array, the time delay between two sensors depends on the position of sources and thus its estimate could be used in finding the DOA of the sources. In this paper, we propose to estimate the time delay among sensors using cross-correlation of the signals received at the sensor array. The wider the bandwidth of the signal, the sharper will be the peak of its autocorrelation. Thus, it would be safe to assume that the autocorrelation of a wideband signal is sparse. The number of sharp peaks in the autocorrelation will be the same as the number of uncorrelated sources. The strength of Compressive Sampling (CS) lies in solving an underdetermined problem with a very high probability, provided the solution is sparse. This fits our wideband DOA problem very well, and is used to estimate the autocorrelation and hence the DOA of the signals with sub-Nyquist sampling. Simulations are given to support this concept.