  Spectrum sensing, which aims at detecting spectrum holes, is the precondition
for the implementation of cognitive radio (CR). Collaborative spectrum sensing
among the cognitive radio nodes is expected to improve the ability of checking
complete spectrum usage. Due to hardware limitations, each cognitive radio node
can only sense a relatively narrow band of radio spectrum. Consequently, the
available channel sensing information is far from being sufficient for
precisely recognizing the wide range of unoccupied channels. Aiming at breaking
this bottleneck, we propose to apply matrix completion and joint sparsity
recovery to reduce sensing and transmitting requirements and improve sensing
results. Specifically, equipped with a frequency selective filter, each
cognitive radio node senses linear combinations of multiple channel information
and reports them to the fusion center, where occupied channels are then decoded
from the reports by using novel matrix completion and joint sparsity recovery
algorithms. As a result, the number of reports sent from the CRs to the fusion
center is significantly reduced. We propose two decoding approaches, one based
on matrix completion and the other based on joint sparsity recovery, both of
which allow exact recovery from incomplete reports. The numerical results
validate the effectiveness and robustness of our approaches. In particular, in
small-scale networks, the matrix completion approach achieves exact channel
detection with a number of samples no more than 50% of the number of channels
in the network, while joint sparsity recovery achieves similar performance in
large-scale networks.
