In this paper, we study the problem of joint wideband spectrum sensing anddirection-of-arrival (DoA) estimation in a sub-Nyquist sampling framework.Specifically, considering a scenario where a few uncorrelated narrowbandsignals spread over a wide (say, several GHz) frequency band, our objective isto estimate the carrier frequencies and the DoAs associated with the narrowbandsources, as well as reconstruct the power spectra of these narrowband signals.To overcome the sampling rate bottleneck for wideband spectrum sensing, wepropose a new phased-array based sub-Nyquist sampling architecture withvariable time delays, where a uniform linear array (ULA) is employed and thereceived signal at each antenna is delayed by a variable amount of time andthen sampled by a synchronized low-rate analog-digital converter (ADC). Basedon the collected sub-Nyquist samples, we calculate a set of cross-correlationmatrices with different time lags, and develop a CANDECOMP/PARAFAC (CP)decomposition-based method for joint DoA, carrier frequency and power spectrumrecovery. Perfect recovery conditions for the associated parameters and thepower spectrum are analyzed. Our analysis reveals that our proposed method doesnot require to place any sparse constraint on the wideband spectrum, only needsthe sampling rate to be greater than the bandwidth of the narrowband sourcesignal with the largest bandwidth among all sources. Simulation results showthat our proposed method can achieve an estimation accuracy close to theassociated Cram'{e}r-Rao bounds (CRBs) using only a small number of datasamples.
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