  We introduce a new compressive power spectrum estimation approach in both
frequency and direction of arrival (DOA). Wide-sense stationary signals
produced by multiple uncorrelated sources are compressed in both the time and
spatial domain where the latter compression is implemented by activating only
some of the antennas in the underlying uniform linear array (ULA).We sample the
received signal at every active antenna at sub-Nyquist rate, compute both the
temporal and spatial correlation functions between the sub-Nyquist rate
samples, and apply least squares to reconstruct the full-blown two-dimensional
power spectrum matrix where the rows and columns correspond to the frequencies
and the angles, respectively. This is possible under the full column rank
condition of the system matrices and without applying any sparsity constraint
on the signal statistics. Further, we can estimate the DOAs of the sources by
locating the peaks of the angular power spectrum. We can theoretically estimate
the frequency bands and the DOAs of more uncorrelated sources than active
sensors using sub-Nyquist sampling.
