Throughput Analysis of Hybrid-ARQ—A Matrix Exponential Distribution Approach

Abstract

We propose a novel performance analysis framework for lossless- and truncated-hybrid automatic repeat request (HARQ) that enables neat, general, closed-form throughput expressions in a matrix exponential (ME) distribution form. This approach is applicable to all HARQ schemes for which the probability density function of the effective channel can be characterized by a rational Laplace transform, or equivalently, an ME-distribution. This includes, for example, repetition redundancy HARQ in ME distributed channels. Throughput expressions are also given for the $K$ -truncated-HARQ $N$ -fold diversity, ARQ $N$ -fold diversity, and lossless-HARQ 2-fold diversity cases in the ME distributed channel. Schemes with effective channels of non-rational Laplace transforms, such as IR-HARQ, are explored using truncated continued fractions. A novel integration trick is developed for the integration of ME distributions with singular matrices and yields the simple throughput expression of lossless-HARQ. We also give general analytical expressions for the optimal throughput and optimal rate point that benefit from the compact ME-distribution form proposed.