Outage-optimal power adaptation and allocation for truncated HARQ

In this work, we analyze hybrid ARQ (HARQ) protocols used over independent block fading channels. We assume that the transmitter is unaware of the channel state information (CSI) at the moment of transmission but knows the statistics of the channel. We consider two scenarios with respect to the feedback received by the transmitter: (i) “conventional”, one-bit feedback carrying the message about the decoding success/failure (ACK/NACK), and (ii) the multi-bit feedback scheme when, on top of ACK/NACK, the receiver feeds back information about the state of the decoder, which is equivalent to the CSI experienced by the receiver in the past (unsuccessful) transmissions. The feedback can then be used to allocate power across the HARQ transmission attempts (in the case of one-bit feedback) or adapt the power for each re-transmission as a function of multi-bit feedback. The objective in both cases is the minimization of the outage probability under peak and long term average power constraints. We solve the optimization problems using the dynamic programming framework. The obtained results quantify the advantage of the multi-bit feedback over the conventional approach and indicate that power optimization can provide significant gains over the conventional constant-power HARQ transmission even in the presence of peak-power constraints.