  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 few uncorrelated narrowband
signals spread over a wide (say, several GHz) frequency band, our objective is
to estimate the carrier frequencies and the DoAs associated with the narrowband
sources, as well as reconstruct the power spectra of these narrowband signals.
To overcome the sampling rate bottleneck for wideband spectrum sensing, we
propose a new phased-array based sub-Nyquist sampling architecture with
variable time delays, where a uniform linear array (ULA) is employed and the
received signal at each antenna is delayed by a variable amount of time and
then sampled by a synchronized low-rate analog-digital converter (ADC). Based
on the collected sub-Nyquist samples, we calculate a set of cross-correlation
matrices with different time lags, and develop a CANDECOMP/PARAFAC (CP)
decomposition-based method for joint DoA, carrier frequency and power spectrum
recovery. Perfect recovery conditions for the associated parameters and the
power spectrum are analyzed. Our analysis reveals that our proposed method does
not require to place any sparse constraint on the wideband spectrum, only needs
the sampling rate to be greater than the bandwidth of the narrowband source
signal with the largest bandwidth among all sources. Simulation results show
that our proposed method can achieve an estimation accuracy close to the
associated Cram\'{e}r-Rao bounds (CRBs) using only a small number of data
samples.
