  In this paper, to jointly estimate the frequency and the
direction-of-arrival(DOA) of the narrowband far-field signals, a novel array
receiver architecture is presented by the concept of the sub-Nyquist sampling
techniques. In particular, our contribution is threefold. i) First, we propose
a time-space union signal reception model for receiving array signals, where
the sub-Nyquist sampling techniques and arbitrary array geometries are employed
to decrease the time-domain sampling rate and improve the DOA estimation
accuracy. A better joint estimation is obtained in the higher time-space union
space. ii) Second, two joint estimation algorithms are proposed for the
receiving model. One is based on a trilinear decomposition from the third-order
tensor theory and the other is based on subspace decomposition. iii) Third, we
derive the corresponding Cram\'er\text{-}Rao Bound (CRB) for frequency and DOA
estimates. In the case of the branch number of our architecture is equal to the
reduction factor of the sampling rate, it is observed that the CRB is robust in
terms of the number of signals, while the CRB based on the Nyquist sampling
scheme will increase with respect to the number of signals. In addition, the
new steer vectors of the union time-space model are completely uncorrelated
under the limited number of sensors, which improves the estimation performance.
Furthermore, the simulation results demonstrate that our estimates via the
receiver architecture associated with the proposed algorithms closely match the
CRB according to the noise levels, the branch number and the source number as
well.
