Abstract
To overcome the loss in the outage probability and symbol error ratio (SER) caused by the Nth single relay opportunistic relaying (OR), in this paper, we present the N–Rth dual best relays OR schemes in which there are two relays selected out of the available relays to forward the received signals to destination over orthogonal channels by using amplify-and-forward protocols. For the proposed N–Rth OR schemes, we obtain firstly the closed-form expressions to the probability density function (PDF) and cumulative distribution function of the instantaneous end-to-end signal-to-noise ratio (SNR) by using the appropriate mathematical manipulations over independent and non-identically distributed Rayleigh fading channels. Then, based on the derived statistical descriptions, the outage probability, average SER, and ergodic capacity of the proposed dual relays OR schemes are investigated as well as the corresponding closed-form analytical solutions. The fair comparison analyses between the Nth schemes and the N–Rth schemes show that the proposed N–Rth schemes can improve greatly the outage probability and average SER of the considered OR schemes in medium and high power transmission regions (or SNR). Especially, the proposed dual relays OR schemes can provide more improvement on SER than outage probability. At the same time, the presented numerical results indicate clearly the improvement on the outage probability and average SER is at the price of the loss in the ergodic capacity, which is due to the constrain of diversity and multiplexing tradeoff in cooperative communications.
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Jia X., Yang L. (2011) Interaction of multiplexing gains and power exponents allocation of two-level superposition coding relaying. European Transactions on Telecommunications 22(7): 352–366
Haiyang D., Jianhua G., Benevides D., Zhuoqin J. (2012) Two birds with one stone: Exploiting direct links for multiuser two-way relaying systems. IEEE Transactions on Wireless Communications 11(1): 54–59
Jia X., Yang L., Fu H. (2011) Tight performance bounds for two-way opportunistic amplify-and-forward wireless relaying networks with TDBC protocols. Eurasip Journal on Wireless Communications and Networking 2011(1): 1–8
Jia X., Fu H., Yang L., Zhao L. (2011) Superposition coding cooperative relaying communications: Outage performance analysis. International Journal of Communication Systems 24(3): 384–397
Sendonaris A., Erkip E., Aazhang B. (2003) User cooperation diversity. Part I. System description. IEEE Transactions on Communications 51(11): 1927–1938
Laneman J., Tse D., Wornell G. (2004) Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory 50(12): 3062–3080
Bletsas A., Khisti A., Reed D. P., Lippman A. (2006) A simple cooperative diversity method based on network path selection. IEEE Journal on Selected Areas in Communications 24(3): 659–672
Laneman J. N., Wornell G. W. (2003) Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks. IEEE Transactions on Information Theory 49(10): 2415–2425
Haifang J., Sihai Z., Wuyang Z. (2011) Outage analysis of distributed scheme on opportunistic relaying with limited CSI. IEEE Communications Letters 15(9): 935–937
In-Ho L., Dongwoo K. (2012) Outage performance of opportunistic cooperation in amplify-and-forward relaying systems with relay selection. IEEE Communications Letters 16(2): 224–227
Xiaowen, G., Chandrashekhar, T. P. S., Junshan, Z., Poor, H. V. (2012). Opportunistic cooperative networking: To relay or not to relay?. IEEE Journal on Selected Areas in Communications 30(2), 307–314.
MinChul J., Il-Min K., Dong In K. (2012) Joint relay selection and relay ordering for df-based cooperative relay networks. IEEE Transactions on Communications 60(4): 908–915
Zhou M., Cui Q., Jantti R., Tao X. (2012) Energy-efficient relay selection and power allocation for two-way relay channel with analog network coding. IEEE Communications Letters 16(6): 819
Ubaidulla P., Aissa S. (2012) Optimal relay selection and power allocation for cognitive two-way relaying networks. IEEE Wireless Communications Letters 1(3): 816–819
Jia X., Yang L., Fu H., Feng B., Qi Y. (2012) Two-way denoise-and-forward network coding opportunistic relaying with jointing adaptive modulation relay selection criterions. IET Communications 6(2): 194–202
Xu C., Ting-wai S., Zhou Q., Lau F. (2010) High-SNR analysis of opportunistic relaying based on the maximum harmonic mean selection criterion. IEEE Signal Processing Letters 17(8): 719–722
Krikidis I., Thompson J., McLaughlin S., Goertz N. (2009) Max-min relay selection for legacy amplify and forward systems with interference. IEEE Transactions on Wireless Communications 8(6): 3016–3027
Ikki S. S., Ahmed M. H. (2010) On the performance of cooperative-diversity networks with the Nth best-relay selection scheme. IEEE Transactions on Communications 58(11): 3062–3069
Ikki, S. S., & Ahmed, M. H. (2009). On the performance of amplify-and-forward cooperative diversity with the Nth best-relay selection scheme. In Proceeding of IEEE ICC, June 2009 (pp. 1–6).
Ikki, S. S., & Ahmed, M. H. (2009). On the performance of adaptive decode-and-forward cooperative diversity with the Nth best-relay selection scheme. In Proceeding of IEE GLOBECOM, Nov. 2009 (pp. 1–6).
Kyunbyoung, K., & Woo, C. (2011). Another closed-form expression of average error rate for the N th best relay selection AF relaying over Rayleigh fading channels. In Proceeding of ICTC, 2011 (pp. 106–109).
Ko, K., & Woo, C. (2011). More accurate ASER bound for opportunistic amplify-and-forward relay systems. Wireless Personal Communications (first published online, Dec. 2011). doi:10.1007/s11277-011-0471-8.
Ko, K., & Woo, C. (2012). More tractable average error rate expression for the N th best relay selection scheme of DF relaying over Rayleigh fading channels. International Journal of Communication Systems (first published online, Jan. 2012). doi:10.1002/dac.1397.
Yonghui L., Louie R. H. Y., Vucetic B. (2010) Relay selection with network coding in two-way relay channels. IEEE Transactions on Vehicular Technology 59(9): 4489–4499
Krikidis I., Charalambous T., Thompson J. (2012) Buffer-aided relay selection for cooperative diversity systems without delay constraints. IEEE Transactions on Wireless Communications 11(5): 1957–1967
Ikhlef A. D., Michalopoulos S., Schober R. (2012) Max-max relay selection for relays with buffers. IEEE Transactions on Wireless Communications 11(3): 1124–1135
Alamouti S. M. (1998) A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications 16(8): 1451–1458
Ferdinand N. S., Rajatheva N., Latva-aho M. (2012) Effects of feedback delay in partial relay selection over Nakagami-m fading channels. IEEE Transactions on Vehicular Technology 61(4): 1620–1634
David H. A., Nagaraja H. N. (2003) Order statistics, 3rd edn. Wiley, New York
Gradshteyn I. S., Ryzhik I. M. (2007) Table of integrals, series, and products, 7th edn. Acdemic, San Diego, CA
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Jia, X., Zhu, H., Yang, L. et al. Performance Analyses of the N–Rth Dual Best Relays Opportunistic Cooperation with Amplify-and-Forward Protocols. Wireless Pers Commun 71, 2361–2377 (2013). https://doi.org/10.1007/s11277-012-0942-6
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DOI: https://doi.org/10.1007/s11277-012-0942-6