Optimal Routing for Multi-User Multi-Hop Relay Networks Via Dynamic Programming

Abstract

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 suboptimal 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.

Sum-Rate Optimal Relay Selection and Power Control in Multi-Hop Networks

“…Therefore, we consider four sub-optimal relay selection strategies used in literature namely, the hop-by-hop relay selection [4], ad-hoc relay selection, block-by-block relay selection [5] and sliding window based relay selection [6]. In addition, we evaluate the achievable sum-rate obtained by the optimal relay selection when the objective is maximizing the minimum SINR [17]. These strategies are detailed in the following.…”

“…Under this strategy, we consider the optimal relay selection when the objective is maximizing the minimum SINR across all users. We use the dynamic programming based algorithm, which has a linear complexity with respect to L, proposed in [17]. Once the relay selection is completed, we compute the achievable sum-rate according to the objective function in (5).…”

“…For example, in an ad-hoc sensor network, if idle nodes serve as relays, then they may cause severe interference to other transmissions in the area [14]. In the literature, this problem has been mainly analyzed with considerations to outage probability thus maximizing the minimum signalto-interference-plus-noise-ratio (SINR) of all user pairs [15]- [17]. In [17], the authors propose a dynamic programming based efficient algorithm to obtain the optimal relay assignment of DF relay networks when the objective is maximizing the minimum SINR.…”

“…In the literature, this problem has been mainly analyzed with considerations to outage probability thus maximizing the minimum signalto-interference-plus-noise-ratio (SINR) of all user pairs [15]- [17]. In [17], the authors propose a dynamic programming based efficient algorithm to obtain the optimal relay assignment of DF relay networks when the objective is maximizing the minimum SINR. Multi-user relay selection problem with the focus of maximizing the overall network sum-rate has been mostly analyzed for AF relay networks [18]- [20] while such analysis of DF relay networks are limited to dualhop relay networks.…”

“…The Proposed Iterative Joint Relay Selection and Power Control Algorithm Input : Instantaneous channel state information (CSI), P Output: Maximum achievable sum-rate R * , optimum relay assignment X opt and power allocation P [r i,l ], ∀i, l 1 n = 1, X opt ← {}, R * ← 0, P [r i,l , l] ← P, ∀i ∈ {1, ..., N}, l ∈ {0, ..., L − 1} X, R(n) ] ← solution to relay selection problem via[17, Algorithm 1] …”