Analysis and optimization of adaptive multicopy transmission ARQ protocols for time-varying channels

This paper outlines an efficient method to concurrently optimize a multiplicity of design variables for continuous selective-repeat (SR) and go-back-N (GBN) automatic repeat request (ARQ) strategies, both in noiseless and noisy feedback channels. For these ARQ protocols, we adapt either the number of identical message blocks sent in each transmission (in the case of GBN scheme) or the number of copies of a block retransmitted to handle a NACKed codeword (for the SR protocol) dynamically to the estimated channel condition. The channel state information is obtained by counting the contiguous acknowledgment (ACK or NACK) messages. Exploiting the asymptotic properties of the steady state probability expressions, we show analytically that the optimum solution indeed lies in the infinite space. Subsequently, a simple expression to estimate the suboptimal design parameters is suggested. Our approach of minimizing the mean-square error function yields to a quantitative study of the appropriateness of the selected parameters. Exact analytical expressions that allows us to compute the throughput crossover probability between any two arbitrary multicopy transmission modes are derived. The results provide fundamental insights into how these key parameters interact and determine the system performance.