  This paper focuses on the design of medium access control protocols for
cognitive radio networks. The scenario in which a single cognitive user wishes
to opportunistically exploit the availability of empty frequency bands within
parts of the radio spectrum having multiple bands is first considered. In this
scenario, the availability probability of each channel is unknown a priori to
the cognitive user. Hence efficient medium access strategies must strike a
balance between exploring (learning) the availability probability of the
channels and exploiting the knowledge of the availability probability
identified thus far. For this scenario, an optimal medium access strategy is
derived and its underlying recursive structure is illustrated via examples. To
avoid the prohibitive computational complexity of this optimal strategy, a low
complexity asymptotically optimal strategy is developed. Next, the
multi-cognitive user scenario is considered and low complexity medium access
protocols, which strike an optimal balance between exploration and exploitation
in such competitive environments, are developed.
