Low-Complexity Rate Selection of HARQ With Chase Combining in Rayleigh Block-Fading Channels

We consider hybrid automatic repeat request with Chase combining (HARQ-CC) in a Rayleigh block-fading channel, where rate adaptation is based on long-term channel statistics instead of instantaneous channel information because the latter may be outdated. In the HARQ-CC with long-term rate adaptation, optimal selection of the transmission rate for each HARQ round requires a two-step numerical search procedure with heavy computational burden. In this paper, we propose two suboptimal rate-selection algorithms that substantially reduce the computational burden: In the first scheme, the solution of the second-step numerical search is approximated by using a closed-form Lambert
$W$
function, and in the second scheme, additionally, the solution of the first-step numerical search is approximated by a closed-form lower bound. Analytical and numerical results are presented to show that the proposed algorithms yield the performance of the long-term average transmission rate tightly approaching that of the optimal numerical search algorithm.