Outage Analysis of Myopic Multi-hop Relaying: A Markov Chain Approach

Abstract

In this paper, a cooperative protocol is investigated for a multi-hop network with buffers of finite size at the relay nodes. The protocol is based on the myopic decode-and-forward coding strategy, where each node of the network cooperates with a limited number of neighboring nodes for the transmission of the signals. Each relay stores in its buffer the messages that were successfully decoded, in order to forward them through the appropriate channel links. A complete theoretical framework is investigated that models the evolution of the buffers as a state Markov chain (MC). We analyze the performance of the proposed protocol in terms of outage probability and diversity gain by using the state transition matrix and the related steady state of the MC. Our results show that the proposed protocol outperforms the conventional multi-hop relaying scheme and the system's outage probability as well as the achieved diversity order depend on the degree of cooperation among neighboring nodes. Index Terms-Cooperative networks, multi-hop relaying, myopic coding, outage probability, diversity, Markov chain.

A Markov Chain Approach for Myopic Multi-hop Relaying: Outage and Diversity Analysis

“…• Decoding process: Every relay combines all the received signals x(t − j + 1), acquired at the transmission phase, and attempts to decode the message. The first element of its buffer b i [1] is used for the outcome of the decoding process: it stores the signal if it is successfully decoded, otherwise it becomes an empty element. It is important to note that, an empty element indicates that the decoding of the signal failed (i.e.…”

“…If at least one of these equalities does not hold, then the transition is not possible. The first element of each array at the new buffer state β i,l [1] indicates if an outage occurred at the corresponding relay, while the elements of the new relay state indicate which dual-mode relays are active. As the decoding is handled separately by each relay, these probabilities are independent and therefore the transition probability is given as their product.…”

“…where P o (j, m) is the probability that the j-th node has an outage event, given that the network instance is derived by the state s m . Note that, due to the two possible values that the elements λ H(i),l and β j,l [1] can take, the aggregate number of all possible transitions from every state are 2 ν+N . The analytical expressions for the outage probability are given in Section V.…”

“…Nicolaides, C. Psomas and I. Krikidis are with the IRIDA Research Centre for Communication Technologies, Department of Electrical and Computer Engineering, University of Cyprus, Cyprus, e-mail:{anicol09, psomas, krikidis}@ucy.ac.cy. Part of this work was presented at the IEEE Global Communications Conference, Taipei, Taiwan, December 2020 [1].…”

“…The proof of the maximum diversity order that is achieved for the specific scenario can be found in[1].…”