Joint frequency and 2-D DOA recovery with sub-Nyquist difference space-time array

In this paper, joint frequency and 2-D direction of arrival (DOA) estimation at sub-Nyquist sampling rates of a multi-band signal (MBS) comprising of P disjoint narrowband signals is considered. Beginning with a standard uniform rectangular array (URA) consisting of M = Mx × My sensors, this paper proposes a simpler modification by adding a N — 1 delay channel network to only one of the sensor. A larger array is then formed by combining the sub-Nyquist sampled outputs of URA and the delay channel network, referred to as the difference space-time (DST) array. Towards estimating the joint frequency and 2-D DOA on this DST array, a new method utilizing the 3-D spatial smoothing for rank enhancement and a subspace algorithm based on ESPRIT is presented. Furthermore, it is shown that an ADC sampling frequency of fs ≥ B suffices, where B is the bandwidth of the narrow-band signal. With the proposed approach, it is shown that O(MN/4) frequencies and their 2-D DOAs can be estimated even when all frequencies alias to the same frequency due to sub-Nyquist sampling. Appropriate simulation results are also presented to corroborate these findings.