基于二维Markov链和中继聚合方法的多跳ARQ系统吞吐量的分析

Throughput Analysis of Multi-Hop ARQ System Based on Two-Dimensional Markov Chain and Relay Aggregation

摘要: 本文主要基于中继聚合的研究方法对多跳ARQ系统的吞吐量进行了分析。首先，对由一对收发节点和一个中继节点组成的两跳ARQ系统的节点状态进行了定义，通过建立二维的Markov链得到了四阶的状态转移矩阵，并因而求得两跳ARQ系统中继节点的状态转移概率。其次，在讨论由一对收发节点和N个中继节点组成的N + 1跳ARQ系统时，我们采用中继聚合将N个中继节点合并成一个超级中继并使得N + 1跳系统在原理上等效于两跳系统，从而求得N + 1跳ARQ系统中继节点的状态转移概率。最后，把多跳ARQ系统自身的状态定义为“G”和“B”，结合超级中继和直传链路的状态我们得到了多跳ARQ系统状态转移过程的八个状态，并通过稳态方程求得了多跳ARQ系统吞吐量的解析式。事实上，我们的结果也证实了多中继和多跳ARQ系统的吞吐量研究有统一的方法，有利于后续研究的统筹规划。

Abstract: In this paper, we analyzed the throughput of multi-hop ARQ system based on the method of relay aggregation. Firstly, we defined the node-state of two-hop ARQ system which consisted of a pair of transceivers and one relay node, and obtained the four-state transition matrix by establishing a two-dimensional Markov chain, then obtained the state transition probability of relay nodes in two hop ARQ system. Secondly, in the N + 1-hop ARQ system composed of a pair of transceivers and N relay nodes, we used relay aggregation to merge N relay nodes into a super relay and made the N+1-hop system equivalent to the two-hop system in principle, then obtained the state transition probability of relay nodes in N + 1-hop ARQ system. Finally, we defined the state of the multi-hop ARQ system as “G” and “B”, and got eight-state of state transfer processes of multi-hop ARQ system by combining with the state of the super relay and direct channel, and obtained the analytical solution for the throughput of multi-hop ARQ systems based on the steady-state equation. In fact, it was shown that there was a unified method to study the throughput performance of multi-relay and multi-hop ARQ system.