Point-to-point scheduling over a wireless channel with costly channel state information

In this work, we are interested in understanding the trade-off between the cost of acquiring accurate information and the improvement in the system performance because of accuracy of information. Specifically, we consider the wireless scheduling scenario where a scheduler residing at the transmitter can acquire the channel state information (CSI) at various levels of accuracy, but at a cost which increases with accuracy. The scheduler is, therefore, required to make CSI acquisition as well as scheduling decisions to minimize the total cost over an infinite horizon. We pose this problem as a partially observable Markov decision problem. We analyze it by converting it into a perfect state Markov decision problem (MDP) with belief distribution as the state and provide structural properties of the optimal policy. Under a special case, where CSI is either known perfectly or is not known, we show that the problem can be simplified and posed as an MDP in which the policy determines a sampling interval for each channel state. We present a numerical technique to compute these sampling intervals and numerical results based on it.