  We consider the downlink of a cellular system and address the problem of
multiuser scheduling with partial channel information. In our setting, the
channel of each user is modeled by a three-state Markov chain. The scheduler
indirectly estimates the channel via accumulated Automatic Repeat Request (ARQ)
feedback from the scheduled users and uses this information in future
scheduling decisions. Using a Partially Observable Markov Decision Process
(POMDP), we formulate a throughput maximization problem that is an extension of
our previous work where the channels were modeled using two states. We recall
the greedy policy that was shown to be optimal and easy to implement in the two
state case and study the implementation structure of the greedy policy in the
considered downlink. We classify the system into two types based on the channel
statistics and obtain round robin structures for the greedy policy for each
system type. We obtain performance bounds for the downlink system using these
structures and study the conditions under which the greedy policy is optimal.
