On the impacts of lognormal-Rice fading on multi-hop extended networks

Abstract

Abstract—This paper presents an analytical model for a multi-hop two-dimensional (2-D) network with finite density of nodescommunicating with one another by forming an opportunisticlarge array (OLA). Transmission among these nodes is modeledvia Markov Chain, where the wireless channel is considered asa composite lognormal-Rice random process. We approximatethe sum distribution of the received power at a node withlognormal random variable (RV) using a moment generatingfunction (MGF)-based approach, which is acquired by usingGauss-Hermite integration. The transition probability matrix isderived to determine the one-hop success probability. Coverageaspects for different arrangement of nodes is quantified alongwith the effects of wireless channel on system performance.Index Terms —Cooperative Communication, Wireless SensorNetworks, Lognormal-Rice fading I. I NTRODUCTION Multi-hop network is a common layout nowadays for wire-less sensor networks (WSN). Data gathering, possibly in amulti-hop fashion, from a wide spread of unknown amount ofsensors to a sink node is an important application of WSN.Each sensor node in the path of a transmission is responsiblefor relaying the message to another node. However, issuesof long delays, low reliability, and increased latency raisedserious questions on the performance of single-input single-output (SISO) multi-hop networks. In addition to that, thechannel impairments like multipath fading and shadowinglimit the performance of the system.Cooperative transmission (CT), as a physical layer transmis-sion technique, was introduced to boost the system efficiencyby employing spatial diversity. The system capacity increasesby providing distributed transmit diversity as multiple nodestransmit the same message and in lieu of that a node receivesmultiple copies of the same message, which increases thelikelihood of decoding the message correctly. One of themost effective CT networks is the Opportunistic Large Arrays(OLAs) [1] that perform in a multi-hop manner where allnodes in a network form groups, and these groups of nodestransmit the same message at the same time to the other group.The promising feature of range extension [2]-[3] due to OLAbroadcasting and energy efficiency [4] makes it a desirableoption for densely populated networks.