Outage Minimization via Power Adaptation and Allocation for Truncated Hybrid ARQ

In this work, we analyze hybrid ARQ (HARQ) protocols over the independent block fading channel. We assume that the transmitter is unaware of the channel state information (CSI) but has a knowledge about the channel statistics. We consider two scenarios with respect to the feedback received by the transmitter: i) ''conventional'', one-bit feedback about the decoding success/failure (ACK/NACK), and ii) the multi-bit feedback scheme when, on top of ACK/NACK, the receiver provides additional information about the state of the decoder to the transmitter. In both cases, the feedback is used to allocate (in the case of one-bit feedback) or adapt (in the case of multi-bit feedback) the power across the HARQ transmission attempts. The objective in both cases is the minimization of 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. A simplified solution for the high signal-to-noise ratio (SNR) regime is presented using a geometric programming (GP) approach. The obtained results quantify the advantage of the multi-bit feedback over the conventional 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.