Phased-Array-Based Sub-Nyquist Sampling for Joint Wideband Spectrum Sensing and Direction-of-Arrival Estimation

In this paper, we study the problem of joint wideband spectrum sensing and direction-of-arrival (DoA) estimation in a sub-Nyquist sampling framework. Specifically, considering a scenario where a number of uncorrelated narrow-band signals spread over a wide (say, several GHz) frequency band, our objective is to estimate the carrier frequencies and the DoAs associated with the narrow-band sources, as well as reconstruct the power spectra of these narrow-band signals. To overcome the sampling rate bottleneck for wideband spectrum sensing, we propose a new phased-array-based sub-Nyquist sampling architecture with flexible time delays, where a uniform linear array is employed and the received signal at each antenna is delayed by a flexible amount of time and then sampled by a synchronized low-rate analog–digital converter. Based on the collected sub-Nyquist samples, we calculate a set of cross-correlation matrices with different time lags, and develop a CANDECOMP/PARAFAC decomposition-based method for joint DoA, carrier frequency, and power spectrum recovery. Conditions for perfect recovery of the associated parameters and the power spectrum are analyzed. Simulation results show that our proposed method presents a clear performance advantage over existing methods, and achieves an estimation accuracy close to the associated Cramér–Rao bounds using only a small number of data samples.