Abstract
In this paper, the process of the Nth-best relay selection strategy with outdated feedback is given in the selection cooperative system. The performance of the proposed Nth-best relay selection with outdated channel state information is investigated in Rayleigh fading scenarios. The exact closed-form expression for the outage performance is derived. In the high signal-to-noise ratio regime, the asymptotic outage behavior is also analyzed. In addition, based on the asymptotic analysis, the diversity-multiplexing tradeoff of the considered system is obtained. At last, simulation results show that even a small deviation of the channel estimates from the actual values will lead to a severe degradation of the outage performance of the considered system.
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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 Shandong Provincial Natural Science Foundation, China under Grant Nos. ZR2014FQ012 and ZR2014FP003, Qingdao Municipal Applied Basic Research Project of China under Grant No. 15-9-1-111-jch, the Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LN25, and the National Science and Technology Pillar Program of China during the 12th Five-Year Plan Period under Grant No. 2014BAK12B06.
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Appendices
Appendix 1
In the case of \(0 \le \rho < 1\), satisfying \({\gamma _{{k^*}D}} \ne {\tilde{\gamma } _{{k^*}D}}\). Based on our problem formulation we can write the PDF \({f_{{\gamma _{{k^*}D}}}}\left( x \right)\) as follows
Substituting (8) and \({f_{{\gamma _{SD}}}}\left( x \right) = {{\exp ( - {x /{{{\bar{\gamma } }_{SD}}}})} /{{{\bar{\gamma } }_{SD}}}}\) into (24), after some algebraic manipulations, we can obtain
After some integral manipulations, (11) can be easily obtained from (25).
Appendix 2
In the case of \(0 \le \rho < 1\), satisfying \({\gamma _{{k^*}D}} \ne {\tilde{\gamma } _{{k^*}D}}\). Based on our problem formulation we can write the PDF \({f_{{\gamma _{{k^*}D}}}}\left( x \right)\) as follow
Using the Bayes rule, it is well known that the conditional probability density function can be expressed as
Substituting (27) into (26), the PDF of \({\gamma _{{k^*}D}}\) can be rewritten as
Substituting (4) and (9) into (28), after some simpler manipulations, we can obtain (12).
Appendix 3
In case of \(0 \le \rho < 1\), the term \(P\left\{ {{\gamma _{SD}} + {\gamma _{{k^*}D}} < {g_T}} \right\}\) in (10) can be written as
Substituting (13) and \({f_{{\gamma _{SD}}}}\left( x \right) = {{\exp ( - x /{{\bar{\gamma } }_{SD}}}}\) into (29), after some simple manipulations, we obtain
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Li, E., Wang, X., Dong, Y. et al. Research on the Nth-best Relay Selection with Outdated Feedback in Selection Cooperation Systems. Wireless Pers Commun 89, 45–59 (2016). https://doi.org/10.1007/s11277-016-3251-7
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DOI: https://doi.org/10.1007/s11277-016-3251-7