Full length articleCooperative diversity performance of selection relaying over correlated shadowing
Introduction
Cooperative diversity systems consist of multiple nodes that share their resources in order to create multiple diversity channels and thereby improve system performance, typically in terms of availability, range and throughput. This paper considers cooperative diversity in lognormal fading channels. Lognormal channel models can be used to model indoor, as well as outdoor propagation, e.g. shadowing (see [1], [2], [3], [4, section 4.2.1], [5] and references therein). Moreover, due to various propagation effects and geometrical parameters, the fading gains of differing propagations paths can be assumed to be correlated (see e.g. [6], [7], [8] and references therein) thus following a multi-variate lognormal distribution, as described in the next Section.
A fundamental building block for cooperative diversity systems is the relaying channel [9], which has been studied in the context of fading channels in recent years [10], [11]. To the authors’ knowledge, results on the performance of diversity combining as well as cooperative diversity techniques in correlated lognormal channels are very limited. The outage probability of maximum ratio combining (MRC) and selection combining (SC) are studied in [12], [13], [14], [15], while multi-hop communications over independent lognormal fading channels have been studied in [16].
Results on cooperative lognormal systems are also very limited. In [17], several cooperative diversity systems with independent and identically distributed lognormal fading gains are studied and bounds on the pairwise error probability are provided. In [18], the impact of total power constraints are investigated through bounds of the outage probability and error probability of relaying with independent lognormal fading channel gains, while utilizing Fenton-Wilkinson’s method [19] for approximating the combiner output at the destination node. Finally, in [20] a distributed diversity system with amplify and forward [11] relays is studied, under the assumption of independent diversity channels.
In [21], the authors study a fixed relaying [11] system assuming MRC or SC at the destination. More specifically, an exact analytical expression of the outage probability is provided for both orthogonal relaying schemes utilizing time and frequency division multiple-access protocols and half-duplex relays and non-orthogonal schemes utilizing space division multiple access and full-duplex relays. In addition, the provided analytical framework is used to demonstrate the significant impact of fading correlation on the system performance and also show that the variance of the source-relay link has to be smaller than the variance of the source-destination link for cooperation to outperform non-cooperation.
In this paper, we provide exact integral expressions for the end-to-end outage probability of a cooperative diversity selection relaying [11] system. In the considered selection relaying system, a cooperative system is created whenever the signal-to-noise ratio between the source node and the relay node lies above a certain threshold; otherwise, the system falls back to direct link transmission. The two formed diversity branches are combined coherently by the destination node using either MRC or SC [4]. It should be noted that our analysis considers correlated lognormal channels, in contrast to prior art [16], [17], [18], [20] that considers uncorrelated channels, and presents a thorough investigation of the impact of correlation on cooperative system performance. In addition, some novel insights are obtained on the efficiency of cooperation by studying the impact of the multiple-access protocol on cooperation and comparing it to the performance of non-cooperation. The choice of multiple-access protocol depends on the ability of the relay to perform half-duplex or full-duplex operation.
It should also be emphasized that the final outage probability formula derived in this paper is produced using a different methodology than [11] and consists an alternative representation of the outage event of a selection relaying system. More specifically, in this paper the dual-hop part of the cooperative system is replaced by an equivalent system described by the same outage event. This equivalent system is then combined with the direct link to produce the final outage probability expression for selection relaying. Preliminary results of this analysis have been presented in [22].
This paper is organized as follows. Section 2 presents the system model and the correlated lognormal channel model including a description of the possible multiple-access protocols utilized by the cooperative diversity system. Section 3 provides exact expressions for the outage probability of selection relay systems with a single relay and MRC or SC at the destination. Section 4 establishes the energy and spectral efficiency of the cooperative protocols under consideration and proposes an appropriate direct link system for comparison purposes. Finally, Section 5 utilizes the proposed formulas and efficiency framework to numerically assess the impact of the various system parameters on the cooperative diversity system’s performance.
Section snippets
General considerations
The geometrical configuration of the considered cooperative wireless network is shown in Fig. 1. The source node S communicates with the destination node D through two different routes. The first signal is directly transmitted by the node S to the node D and the second signal is transmitted by the node S to the node D through the regenerative (decode-and-forward) relay node R (dual-hop transmission). These two signal paths form two diversity branches, which are combined by the node D using
Outage probability of cooperative diversity with SC and MRC
The relay retransmission takes place in the form of the selection relaying technique [11] where the received signal is regenerated at the relay using the full receiver-transmitter processing chain containing the sequence of demodulation, channel decoding, encoding and modulation. However, the destination only combines the relay information whenever the first hop SNR lies above a threshold; otherwise, the system falls back to a direct link system.
Considering the dual-hop part of the system
Cooperation protocol efficiency
The transmission energy as well as the spectral efficiency are two important system resources; hence, an evaluation of the overall efficiency of cooperation should consider these two parameters. This section describes the efficiency framework established in [21].
Numerical results and discussion
In this section, numerical results for the performance of the SC and MRC cooperative diversity systems are presented, using numerical evaluations of the proposed expression (12). The final expression (12) is easily calculated numerically and converges very fast due to the monotonically decreasing nature of the integrand functions. More specifically, replacing the infinite limit with a small number such as −10 results in a numerical precision that greatly exceeds the accuracy of Matlab’s erfc
Conclusions
This paper presented the study of the selection relaying channel for the decode-and-forward case and both SC and MRC at the destination. Exact analytical expressions for the probability of outage performance have been derived, which enable the evaluation of cooperative diversity for various lognormal propagation model parameters such as varying correlation and variances. Our analysis was complemented by the inclusion of the cooperative multiple-access protocol efficiency such as spectral
Acknowledgements
The authors would like to thank the National Technical University of Athens for its support with the PEBE 2009 fundamental research fund. They would also like to thank the directors of Toshiba Telecommunications Research Laboratory, Bristol, UK, for sponsoring the work presented in this paper.
Vasileios K. Sakarellos was born in France on November 27, 1980. He received the five-year engineering degree in Electrical & Computer Engineering from the Aristotle University of Thessaloniki, Greece, in 2004, and the Ph.D. Degree in Wireless Cooperative Telecommunications from the National Technical University of Athens, Greece, in 2010. His scientific interests are in the field of channel modeling, wireless link design, cooperative diversity techniques in fading channels and wireless
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Vasileios K. Sakarellos was born in France on November 27, 1980. He received the five-year engineering degree in Electrical & Computer Engineering from the Aristotle University of Thessaloniki, Greece, in 2004, and the Ph.D. Degree in Wireless Cooperative Telecommunications from the National Technical University of Athens, Greece, in 2010. His scientific interests are in the field of channel modeling, wireless link design, cooperative diversity techniques in fading channels and wireless communication network analysis. He has been awarded with the K. Karatheodoris Fund and the Fundamental Research 2009 Fund from the National Technical University of Athens, Greece. He has published 14 scientific articles in international refereed journals and proceedings of international conferences. He is a student member of the IEEE and a member of the Technical Chamber of Greece.
Dimitrios Skraparlis received the Ph.D. degree from the Department of Electrical and Computer Engineering, National Technical University of Athens, Greece in 2009, the M.Sc. in Communications and Signal Processing from University of Bristol, UK in 2003 and the 5-year Electrical & Computer Engineering Degree from Aristotle University of Thessaloniki, Greece in 2002. From June 2003 to October 2004 he was with Toshiba TREL, UK working on Multiple-Input Multiple-Output communications technology. He has also completed internships with Infineon Technologies, Munich, Germany and IBM Research, Zurich, Switzerland. He is currently with Nokia Siemens Networks, Athens, Greece working on Converged Internet Connectivity solutions for 4G systems. D. Skraparlis has filed 6 patent applications worldwide related to wireless communications technology. He has also published 15 scientific papers in international refereed journals and conference proceedings. For his work he has been awarded with a sponsorship from Toshiba TREL, UK, the K. Karatheodoris Fund and the Fundamental Research ’09 Fund from the National Technical University of Athens, Greece. His current research interests include MIMO wireless communications and multi-user diversity techniques, applied statistics, signal processing and transceiver architectures as well as applied cryptography.
Athanasios D. Panagopoulos was born in Athens, Greece on January 26, 1975. He received the Diploma Degree in Electrical and Computer Engineering (summa cum laude) and the Dr. Engineering Degree from National Technical University of Athens (NTUA) in July 1997 and in April 2002. From May 2002 to July 2003, he served the Technical Corps of Hellenic Army. From September 2003 to December 2008, he taught at School of Pedagogical and Technological Education, as part-time Assistant Professor. From January 2005 to May 2008, he was head of the Satellite Division of Hellenic Authority for the Information and Communication Security and Privacy. Since May 2008, he is Lecturer in the School of Electrical and Computer Engineering of NTUA. He has published more than 75 papers in international journals and transactions and more than 80 in conference proceedings.
He is the recipient of URSI General Assembly Young Scientist Award in 2002 and 2005. His research interests include mobile radio communication systems, wireless and satellite communications networks, channel modelling, interference problems and cross-layer optimization of communication protocols. He participates to ITU-R and to ETSI Study Groups and he is member of Technical Chamber of Greece. He is member of the TPC of many conferences. He serves on the editorial boards of the Hindawi International Journal of Antennas and Propagation and Hindawi International Journal of Vehicular Technology and Elsevier Physical Communication and since October 2008 as an Associate Editor of IEEE Transactions on Antennas and Propagation. Since 2010, he is also Associate Editor in IEEE Communication Letters.
John D. Kanellopoulos was born in Athens, Greece, on December 12, 1948. He received the Dipl. Ing. degree in mechanical and electrical engineering and the Dr. Eng. degree from the National Technical University of Athens (NTUA), Zografou, Greece, in 1971 and 1979, respectively, and the DIC and Ph.D. degrees from the Imperial College of Science, Technology, and Medicine, University of London, London, UK, in 1979. In November 1979, he joined the School of Electrical and Computer Engineering, NTUA, where he is currently a Professor. His areas of interest are microwave propagation through rain media, satellite communication systems, nonlinear optics, rough surface scattering, and waveguide propagation. He has published over 250 scientific articles in international refereed journals and proceedings of international conferences. He has also authored the books Propagation of Electromagnetic Waves above 10 GHz and Tropospheric Propagation Phenomena. He has received more than 250 references for his scientific work.