Optimal rate selection scheme in a two-hop relay network adopting Chase combining HARQ in Rayleigh block-fading channels

In Rayleigh block fading channels which represent fast-varying channels, long-term rate adaptation is required instead of instantaneous rate adaptation because the channel information fed back may be outdated. We maximize the long-term average transmission rate (LATR) in a two-hop relay network which adopts Chase combining (CC) type Hybrid Automatic-Repeat-reQuest (HARQ). The round transmission rate, i.e. the transmission rate of each HARQ round in each hop, is optimally selected based on the channel statistics of two hops. Two constraints are considered: the outage probability and the maximum number of HARQ rounds, L. In an infinite L case, we show that the optimal round transmission rate of one hop is determined only by the channel statistics of that hop, and can be expressed as a Lambert W function. In a finite L case, we propose a numerical search algorithm to find the optimal round transmission rate. If HARQ is not adopted, the LATR performance becomes very poor. As L increases in the two-hop relay with CC-based HARQ, the LATR performance becomes close to the LATR performance in the infinite L case. We also show the benefits of the proposed rate selection method compared to a non-optimal rate selection method in terms of the LATR.