  We consider a cognitive radio network with multiple primary users (PUs) and
one secondary user (SU), where a spectrum server is utilized for spectrum
sensing and scheduling the SU to transmit over one of the PU channels
opportunistically. One practical yet challenging scenario is when \textit{both}
the PU occupancy and the channel fading vary over time and exhibit temporal
correlations. Little work has been done for exploiting such temporal memory in
the channel fading and the PU occupancy simultaneously for opportunistic
spectrum scheduling. A main goal of this work is to understand the intricate
tradeoffs resulting from the interactions of the two sets of system states -
the channel fading and the PU occupancy, by casting the problem as a partially
observable Markov decision process. We first show that a simple greedy policy
is optimal in some special cases. To build a clear understanding of the
tradeoffs, we then introduce a full-observation genie-aided system, where the
spectrum server collects channel fading states from all PU channels. The
genie-aided system is used to decompose the tradeoffs in the original system
into multiple tiers, which are examined progressively. Numerical examples
indicate that the optimal scheduler in the original system, with observation on
the scheduled channel only, achieves a performance very close to the
genie-aided system. Further, as expected, the optimal policy in the original
system significantly outperforms randomized scheduling, pointing to the merit
of exploiting the temporal correlation structure in both channel fading and PU
occupancy.
