This paper analyses the data rate achieved by various relay selection schemes in a single-user multi-hop relay network with decode-and-forward (DF) relaying. While the single-user relay selection problem is well studied in the literature, research on achievable rate maximization is limited to dual-hop networks and multi-hop networks with a single relay per hop. We fill this important gap by focusing on achievable rate maximization in multi-hop, multi-relay networks. First, we consider optimal relay selection and obtain two approximations to the achievable rate. Next, we consider three existing sub-optimal relay selection strategies namely hop-by-hop, ad-hoc and block-by-block relay selection and obtain exact expressions for the achievable rate under each of these strategies. We also extend the sliding window based relay selection to the DF relay network and derive an approximation to the achievable rate. Further, we investigate the impact of window size in sliding window based relay selection and show that a window size of three is sufficient to achieve most of the possible performance gains. Finally, we extend this analysis to a noise limited multi-user network where the number of available relay nodes is large compared to the number of users and derive approximations to the achievable sum-rate.

翻译：本文分析了在采用解码转发（DF）中继的单用户多跳中继网络中，不同中继选择方案所实现的数据速率。尽管单用户中继选择问题在文献中已有充分研究，但关于可达速率最大化的研究仅限于双跳网络以及每跳仅有一个中继的多跳网络。我们通过聚焦多跳、多中继网络中的可达速率最大化来填补这一重要空白。首先，我们考虑最优中继选择，并获得了可达速率的两种近似表达式。接着，我们考察了三种现有的次优中继选择策略，即逐跳、即席和逐块中继选择，并得到了每种策略下可达速率的精确表达式。我们还将基于滑动窗口的中继选择扩展到DF中继网络，并推导了可达速率的一种近似表达式。此外，我们研究了滑动窗口选择中窗口大小的影响，并表明窗口大小为三已足够实现大部分可能的性能增益。最后，我们将此分析扩展到噪声受限的多用户网络，其中可用中继节点数量远大于用户数量，并推导了可达总速率的近似表达式。