  Spectrum sensing research has mostly been focusing on narrowband access, and
not until recently have researchers started looking at wideband spectrum.
Broadly speaking, wideband spectrum sensing approaches can be categorized into
two classes: Nyquist-rate and sub-Nyquist-rate sampling approaches.
Nyquist-rate approaches have major practical issues that question their
suitability for realtime applications; this is mainly because their high-rate
sampling requirement calls for complex hardware and signal processing
algorithms that incur significant delays. Sub-Nyquist-rate approaches, on the
other hand, are more appealing due to their less stringent sampling-rate
requirement. Although various concepts have been investigated to ensure
sub-Nyquist rates, compressive sampling theory is definitely one concept that
has attracted so much interest. This paper explains and illustrates how
compressive sampling has been leveraged to improve wideband spectrum sensing by
enabling spectrum occupancy recovery with sub-Nyquist sampling rates. The paper
also introduces new ideas with great potential for further wideband spectrum
sensing enhancements, and identifies key future research challenges and
directions that remain to be investigated.
