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Performance Comparison Analyses of the \(N\)th Best Relay Selection Schemes Over Independent and Non-identically Distributed Nakagami-\(m\) Fading Channels

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Abstract

In this work, we study the \(N\)th best relay selection schemes with the consideration that in some case the best relay is unavailable due to the restriction of practical implementation. With amplify-and-forward relaying protocols, the interested \(N\)th best relay schemes are investigated over independent and non-identically distributed (i.ni.d) Nakagami-\(m\) fading channels. For such opportunistic relaying schemes, we first obtain the closed-form expressions to the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous end-to-end signal-to-noise ratio with appropriate mathematical proof. Then, with the obtained CDF and PDF, three main measurements are investigated as well as the corresponding explicit solutions, \(i.e.\), outage probability, average symbol error ratio (SER), and ergodic capacity. At the same time, as a byproduct, the corresponding performance metrics over Rayleigh fading are also derived. Finally, the detailed performance comparison analyses are presented under different values of \(N\) and different Nakagami-\(m\) channel fading severity parameters. The numerical results show that the increase of \(N\) incurs the very severe loss in performance such outage probability, SER, and ergodic capacity. However, the loss in performance can be decreased greatly when the \(N\)th systems have bigger fading severity factors. The derivations are of significance because the Nakagami-\(m\) fading spans via the fading severity parameters a wide range of fading scenarios that are typical in realistic wireless relay networks.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their constructive comments and suggestions, which helped to improve the quality of this paper. This work was supported by the Natural Science Foundation of China under Grant 61261015, the 973 project 2013CB329104, the Natural Science Foundation of China under Grant 61372124 and 61171093, the key projects 2011ZX03005-004-003 and BK2011027, the China Postdoctoral Science Foundation 2012M521105, Research Fund for the Doctoral Program of Higher Education of China 20113223110001, and by the project 11KJA510001 and PAPD.

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Authors and Affiliations

  1. College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Xiangdong Jia

  2. Wireless Communications Key Lab of Jiangsu province, Nanjing University of Posts and Telecommunications, Nanjing, 210003, People’s Republic of China

    Xiangdong Jia, Longxiang Yang & Hongbo Zhu

  3. Key Lab of Broadband Wireless Communication and Sensor Network Technology, Ministry of Education, Nanjing University of Posts and Telecommunications, Nanjing, 210003, People’s Republic of China

    Xiangdong Jia, Longxiang Yang & Hongbo Zhu

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  1. Xiangdong Jia
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Correspondence to Xiangdong Jia.

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Jia, X., Yang, L. & Zhu, H. Performance Comparison Analyses of the \(N\)th Best Relay Selection Schemes Over Independent and Non-identically Distributed Nakagami-\(m\) Fading Channels. Wireless Pers Commun 75, 1355–1372 (2014). https://doi.org/10.1007/s11277-013-1428-x

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