Scheduling over time varying channels with hidden state information

We consider the problem of scheduling transmissions over a wireless downlink when channel state information (CSI) is not available to the transmitter. We assume channel states are time varying and evolve according to a Markov Chain. We show that using current QLI does not stabilize the system due to correlations between backlog and channel state. We show that the throughput optimal scheduling policy in this context must use delayed queue length information (QLI). We characterize the extent to which QLI must be delayed as a function of the channel state statistics.