Optimizing the Code Rate of Energy-Constrained Wireless Communications With HARQ

Retransmissions due to decoding errors have a big impact on the energy budget of low-power wireless communication devices, which can be reduced by using hybrid automatic repeat request (HARQ) techniques. Nevertheless, this reduction comes at the cost of extra energy consumption introduced by the added computational load. No complete analysis of the tradeoff between retransmissions reduction and baseband consumption of low-power communications over fading channels has been reported so far. In this paper, we study the energy efficiency achievable by HARQ schemes when the code rate of the error-correcting code is optimized. For this purpose, we develop an energy consumption model that focuses on simple HARQ (S-HARQ) and Chase combining (HARQ-CC) transmissions, which are studied under fast-fading and block-fading scenarios with Nakagami-m fading. The retransmission statistics are analyzed, and expressions for the expected number of transmission trials are derived. Using this framework, it is shown that transmission schemes with high diversity gain are the most efficient choice for long range transmissions, which in our case correspond to HARQ-CC and codes with low code rate. On the other hand, schemes with good multiplexing capabilities are optimal for short link distances, which in our analysis correspond to S-HARQ and high code rates. It is also shown that HARQ-CC can effectively extend the transmission range of a low-power communication device.