  A cognitive radio system has the ability to observe and learn from the
environment, adapt to the environmental conditions, and use the radio spectrum
more efficiently. It allows secondary users (SUs) to use the primary users
(PUs) channels when they are not being utilized. Cognitive radio involves three
main processes: spectrum sensing, deciding, and acting. In the spectrum sensing
process, the channel occupancy is measured with spectrum sensing techniques in
order to detect unused channels. In the deciding process, sensing results are
analyzed and decisions are made based on these results. In the acting process,
actions are made by adjusting the transmission parameters to enhance the
cognitive radio performance.
  One of the main challenges of cognitive radio is the wideband spectrum
sensing. Existing spectrum sensing techniques are based on a set of
observations sampled by an ADC at the Nyquist rate. However, those techniques
can sense only one channel at a time because of the hardware limitations on the
sampling rate. In addition, in order to sense a wideband spectrum, the wideband
is divided into narrow bands or multiple frequency bands. SUs have to sense
each band using multiple RF frontends simultaneously, which can result in a
very high processing time, hardware cost, and computational complexity. In
order to overcome this problem, the signal sampling should be as fast as
possible even with high dimensional signals. Compressive sensing has been
proposed as a low-cost solution to reduce the processing time and accelerate
the scanning process. It allows reducing the number of samples required for
high dimensional signal acquisition while keeping the essential information.
