On the Optimal Set of Channels to Sense in Cognitive Radio Networks

In the channel selection problem, a secondary user (SU) senses a subset of size
$M$
out of
$N$
existing channels, and then accesses up to
$K$
sensed-free channels. Given
$M$
,
$N$
,
$K$
, and some estimates on the rates of channels, and the sensing accuracy, the channel selection problem asks what set of channels SU should sense to maximize its throughput. The intuitive answer is the set of
$K$
channels with the highest rewards, where the reward of a channel is defined as the expected number of bits that can be successfully transmitted on that channel. Surprisingly, the above-mentioned intuitive solution is not optimal when
$M>K$
. In this letter, we study the case
$M>K$
, and propose polynomial-time optimal solutions for special cases where
$K=1$
or where
$M$
or
$N-M$
are small. We also derive an upper bound on the maximum achievable throughput, and propose a generic near-optimal heuristic algorithm.