Performance Analysis of a Multi-Hop Communication System with Decode-and-Forward Relaying Kalpana Dhaka Department of Electrical Engineering Indian Institute of Technology - Delhi Hauz Khas, New Delhi 110016, India E-mail: kalpana.dhaka@ee.iitd.ernet.in Ranjan K. Mallik Department of Electrical Engineering Indian Institute of Technology - Delhi Hauz Khas, New Delhi 110016, India E-mail: rkmallik@ee.iitd.ernet.in Robert Schober Department of Electrical & Computer Engineering University of British Columbia Vancouver, BC, V6T 1Z4, Canada E-mail: rschober@ece.ubc.ca Abstract — This paper analyzes the performance of a multi-hop wireless communication system, consisting of a source node, N intermediate nodes or relays, and a destination node in a Rayleigh fading environment with decode-and-forward re- laying at each intermediate node. The data is therefore transmitted from source to destination through N +1 hops. Two types of modulation, namely, M -ary phase-shift keying (MPSK) and or- thogonal M -ary frequency-shift keying (OMFSK), are considered for the transmitted data. In case of MPSK, each relay performs coherent detection, while in case of OMFSK, each relay performs non- coherent detection. Using a difference equation approach, analytical expressions for the end-to- end symbol error probability are derived in both cases. We find that (1) although the performance degrades with increasing number of hops for fixed average signal-to-noise ratio per hop, the incre- mental degradation in performance with the ad- dition of each extra hop decreases, (2) when each node transmits with fixed power, multi-hop trans- mission offers significant performance improve- ment over direct transmission. Keywords – Coherent and non-coherent detec- tion, decode-and-forward (DF) relaying, M -ary phase-shift keying (MPSK), multi-hop communi- cation, orthogonal M -ary frequency-shift keying (OMFSK), symbol error probability (SEP). I. Introduction Cooperation when considered in a multi-hop wireless com- munication scenario offers lower attenuation at distant points, that helps to extend the cell coverage area. It en- ables users to act as information sources as well as relays, thus increasing data rate [1] and system throughput, and decreasing sensitivity to channel variation [2]. Multi-hop systems [3] have raised considerable atten- tion recently as they avoid severe shadowing in long dis- tance communication, or when the transmitted signal en- ergy is relatively low. They also provide broader and cheaper coverage along with large spectral efficiency. Cooperation among users can be established by using the amplify-and-forward (AF) or the decode-and-forward (DF) protocol [4]. In AF, the user transmits the data and the relay simply amplifies the signal by a scale factor so as to maintain a constant transmission power, and forwards it to the destination, whereas in DF the relay node detects (and also decodes in case of coded transmission) the user data and then forwards it to the destination. The DF protocol ensures better link reliability by hindering noise propagation to subsequent stages in a multi-hop scenario, implying that the performance analysis of multi-hop DF relaying is of considerable importance. In this paper, we analyze the performance of a multi- hop wireless communication system, consisting of a source node, N intermediate nodes or relays, and a destination node in a Rayleigh fading environment with DF relay- ing at each intermediate node. The data is therefore transmitted from source to destination through N +1 hops. Two types of modulation, namely, M -ary phase- shift keying (MPSK) and orthogonal M -ary frequency- shift keying (OMFSK), are considered for the transmit- ted data. In case of MPSK, each relay performs coherent detection, while in case of OMFSK, each relay performs non-coherent detection. Using a difference equation ap- proach, analytical expressions for the end-to-end symbol error probability (SEP) are derived in both cases. Results are presented to show the variation in performance with increasing number of hops. II. System model Consider a source node communicating data to a destina- tion node employing the DF protocol through a series of intermediate nodes or relays R 1 ,...,R N , each with a sin- gle antenna, as shown in Fig. 1. The mode of communica- tion assumed here is half duplex; alternate nodes transmit and receive at any time slot. The source node is denoted as R 0 , the destination node is denoted as R N+1 , and the link between R n-1 and R n , n =1,...,N + 1 is called the nth hop. In the first time slot, R 0 ,R 2 ,R 4 , ··· trans- mit and R 1 ,R 3 ,R 5 , ··· receive, while in the second time slot, R 2 ,R 4 , ··· receive and R 1 ,R 3 ,R 5 , ··· transmit, and the cycle repeats. We also assume that there is no inter- ference in any hop owing to transmission in surrounding hops. The channels between adjacent nodes R n-1 and R n , n =1,...,N + 1, are mutually independent and undergo flat Rayleigh fading. The additive noises at R 1 ,...,R N+1 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings