  In this paper, the problem of opportunistic channel sensing and access in
cognitive radio networks when the sensing is imperfect and a secondary user has
limited traffic to send at a time is investigated. Primary users' statistical
information is assumed to be unknown, and therefore, a secondary user needs to
learn the information online during channel sensing and access process, which
means learning loss, also referred to as regret, is inevitable. In this
research, the case when all potential channels can be sensed simultaneously is
investigated first. The channel access process is modeled as a multi-armed
bandit problem with side observation. And channel access rules are derived and
theoretically proved to have asymptotically finite regret. Then the case when
the secondary user can sense only a limited number of channels at a time is
investigated. The channel sensing and access process is modeled as a bi-level
multi-armed bandit problem. It is shown that any adaptive rule has at least
logarithmic regret. Then we derive channel sensing and access rules and
theoretically prove they have logarithmic regret asymptotically and with finite
time. The effectiveness of the derived rules is validated by computer
simulation.
