  This paper considers a widely studied stochastic control problem arising from
opportunistic spectrum access (OSA) in a multi-channel system, with the goal of
providing a unifying analytical framework whereby a number of prior results may
be viewed as special cases. Specifically, we consider a single wireless
transceiver/user with access to $N$ channels, each modeled as an iid
discrete-time two-state Markov chain. In each time step the user is allowed to
sense $k\leq N$ channels, and subsequently use up to $m\leq k$ channels out of
those sensed to be available. Channel sensing is assumed to be perfect, and for
each channel use in each time step the user gets a unit reward. The user's
objective is to maximize its total discounted or average reward over a finite
or infinite horizon. This problem has previously been studied in various
special cases including $k=1$ and $m=k\leq N$, often cast as a restless bandit
problem, with optimality results derived for a myopic policy that seeks to
maximize the immediate one-step reward when the two-state Markov chain model is
positively correlated. In this paper we study the general problem with $1\leq
m\leq k\leq N$, and derive sufficient conditions under which the myopic policy
is optimal for the finite and infinite horizon reward criteria, respectively.
It is shown that these results reduce to those derived in prior studies under
the corresponding special cases, and thus may be viewed as a set of unifying
optimality conditions. Numerical examples are also presented to highlight how
and why an optimal policy may deviate from the otherwise-optimal myopic sensing
given additional exploration opportunities, i.e., when $m<k$.
