Outage Minimization via Power Adaptation and Allocation in Truncated Hybrid ARQ

In this work, we analyze hybrid ARQ (HARQ) transmission over the independent block fading channel. We consider two scenarios with respect to the message sent by the receiver via the feedback channel: i) “conventional”, one-bit feedback used to inform the transmitter about the decoding success/failure (ACK/NACK), and ii) the multi-bit feedback message, where on top of ACK/NACK, the transmitter is provided with additional information about the state of the receiver. To minimize the outage probability under long-term average and peak power constraints, we cast the problems into the dynamic programming (DP) framework and solve them for Nakagami-m fading channels. An approximate, closed-form solution for the high signal-to-noise ratio (SNR) regime is proposed using geometric programming (GP). The obtained results quantify the advantage of the multi-bit feedback over the conventional one-bit approach, and show that the power optimization can provide significant gains over conventional power-constant HARQ transmissions even in the presence of peak-power constraints.