Truncated HARQ-Based Multi-Hop Systems: Outage and Related Performance Metrics

In this paper, we focus on the analysis of the end-to-end outage probability of hybrid automatic repeat request (HARQ) in a multi-hop, block-fading channel. First, we use a Markov chain to model the multi-hop system with truncated HARQ type-I (HARQ-I) and derive closed-form expressions for the outage probability and throughput; we also obtain lower and upper bounds on the energy efficiency of the system. Then, we extend the analysis to cover HARQ with packet combining where we provide a general formulation of the outage probability; in special cases, closed-form expressions for outage probability and throughput are obtained. Finally, for a multi-hop system with opportunistic routing, we present recursive formulas to obtain outage probability and throughput. The expressions we derived allow us to draw conclusions about the outage diversity of different multi-hop protocols. In particular, we show that the diversity order is improved for opportunistic multi-hop system and is linearly increasing with the number of allowed transmissions for each packet. Numerical results illustrate how the analytical expression can be used to compare various multi-hop HARQ transmission strategies.