Optimal Power and Retransmission Control Policies over Fading Channels with Packet Drop Penalty Costs

We present a power and retransmission control policy that achieves an optimal tradeoff between transmission power, delay, and packet drop penalty costs over a radio fading channel. We formulate the underlying power and retransmission control as a Markov decision problem (MDP). Under certain sufficient conditions, we show that the optimal transmission power monotonically decreases in the channel quality and the number of retransmission slots left. These structural results lead to power allocation policies that are computationally inexpensive for on-line implementation and are scalable in terms of transmission parameters. Numerical examples confirm the monotonicity results and demonstrate the improvement in the transmission cost enabled by the optimal policy.