Optimal Transmission Rate Control Policies in a Wireless Link Under Partial State Information

We consider the problem of PHY layer transmission rate control for maximum throughput on a wireless link over a finite time horizon. For each link state there exists a most advantageous transmission rate for the controller. The controller needs to rely on incomplete link state information in the form of positive acknowledgements (ACKs) and negative acknowledgements (NACKs) for transmitted packets. We cast the problem as a partially observed Markov decision processes (POMDP). We focus on the special case of time-invariant or slowly time varying link quality with two states and two control options. In that case, the optimal control problem is a state estimation one and the optimal strategy is of threshold structure, where the thresholds are certain values of the belief of being in one of the two states. The policy admits a simple interpretation: increase rate when the number of successive ACKs exceeds a threshold, and decrease rate when the number of successive NACKs exceeds a threshold.