Optimal Set of Multiple Relays and Distributed Self-Selection in Cooperative Networks


In this paper we derive analytically the optimal set of relays for the maximal destination signal-to-noise ratio (SNR) in a two-hop amplify-and-forward cooperative network with frequency-selective fading channels. Simple rules are derived to determine the optimal relays from all available candidates. Our results show that a node either participates in relaying with full power or does not participate in relaying at all, and that a node is a valid relay if and only if its SNR is higher than the optimal destination SNR. In addition, we develop a simple distributed algorithm for each node to determine whether participating in relaying by comparing its own SNR with the broadcasted destination SNR. This algorithm has extremely low overhead, and is shown to converge to the optimal solution fast and exactly within a finite number of iterations. The extremely high efficiency makes it especially suitable to time-varying mobile networks.

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X. Li, C. Xiong and J. Lee, "Optimal Set of Multiple Relays and Distributed Self-Selection in Cooperative Networks," Communications and Network, Vol. 5 No. 2, 2013, pp. 140-147. doi: 10.4236/cn.2013.52015.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. Bletsas, H. Shin and M. Z. Win, “Outage Optimality of Opportunistic Amplify-and-Forward Relaying,” IEEE Communications Letters, Vol. 11, No. 3, 2007, pp. 261-263. doi:10.1109/LCOMM.2007.061589
[2] D. S. Michalopoulos, G. K. Karaginannidis, T. A. Tsiftsis and R. K. Mallik, “An Optimized User Selection Method for Cooperative Diversity Systems,” Proceedings of IEEE GLOBECOM, San Francisco, 27 November-1 December 2006.
[3] Y. Li, P. Wang, D. Niyato and W. Zhuang, “A Dynamic Relay Selection Scheme for Mobile Users in Wireless Relay Networks,” Proceedings of 30th IEEE International Conference on Computer Communications (INFOCOM), Shanghai, 10-15 April 2011.
[4] G. Zheng, K.-K. Wong, A. Paulraj and B. Ottersten, “Collaborative-Relay Beamforming with Perfect CSI: Optimum and Distributed Implementation,” IEEE Signal Processing Letters, Vol. 16, No. 4, 2009, pp. 257-260. doi:10.1109/LSP.2008.2010810
[5] Y. Jing and H. Jafarkhani, “Network Beamforming Using Relays with Perfect Channel Information,” IEEE Transactions on Information Theory, Vol. 55, No. 6, 2009, pp. 2499-2516. doi:10.1109/TIT.2009.2018175
[6] Y. Jing and H. Jafarkhani, “Single and Multiple Relay Selection Schemes and Their Achievable Diversity Orders,” IEEE Transactions on Wireless Communications, Vol. 8, No. 3, 2009, pp. 1414-1423. doi:10.1109/TWC.2008.080109
[7] G. Amarasuriya, M. Ardakani and C. Tellambura, “Adaptive Multiple Relay Selection Scheme for Cooperative Wireless Networks,” IEEE Wireless Communications and Networking Conference, Sydney, 18-21 April 2010.
[8] M. Choi, J. Park and S. Choi, “Low Complexity Multiple Relay Selection Scheme for Cognitive Relay Networks,” IEEE Vehicular Technology Society Conference, San Francisco, 5-8 September 2011.
[9] H. Kartlak, N. Odabasioglu and A. Akan, “Adaptive Multiple Relay Selection and Power Optimization for Cognitive Radio Networks,” Proceedings of 9th International Conference on Communications, Bucharest, 21-23 June 2012, pp. 197-200.
[10] X. Li, “Optimal Multiple-Relay Selection in Dual-Hop Amplify-and-Forward Cooperative Networks,” Electronics Letters, Vol. 48, No. 12, 2012, pp. 694-695. doi:10.1049/el.2012.0194
[11] P. Larsson and H. Rong, “Large-Scale Cooperative Relay Network with Optimal Coherent Combining under Aggregate Relay Power Constraints,” Proceedings of Working Group 4, WWRF8 Meetings, Beijing, February 2004.
[12] I. Maric and R. D. Yates, “Bandwidth and Power Allocation for Cooperative Strategies in Gaussian Relay Networks,” Proceedings of Asilomar Conference on Signals, Systems & Computers, 7-10 November 2004, pp. 1907-1911.
[13] M. Chen, T. C.-K. Liu and X. Dong, “Opportunistic Multiple Selection with Outdated Channel State Information,” IEEE Transactions on Vehicular Technology, Vol. 61, No. 3, 2012, pp. 1333-1345. doi:10.1109/TVT.2011.2182001
[14] S. Kim, J.-H. Park and D.-J. Park, “Beamforming of Amplify-and-Forward Relays under Individual Power Constraints,” IEEE Journal on Selected Areas in Communications, Vol. 30, No. 8, 2012, pp. 1347-1357. doi:10.1109/JSAC.2012.120905
[15] M. Hong, Z. Xu, M. Razaviyayn and Z.-Q. Luo, “Joint User Grouping and Linear Virtual Beamforming: Complexity, Algorithms and Approximation Bounds,” IEEE Journal on Selected Areas in Communications, Special Issues on Virtual Antenna Systems, 2013.
[16] E. Koyuncu and H. Jafarkhani, “On the Structure of Limited-Feedback Beamforming Codebooks for Amplify-and-Forward Relay Networks,” IEEE Transactions on Information Theory, Vol. 58, No. 5, 2012, pp. 2874-2895. doi:10.1109/TIT.2011.2179116
[17] X. Li, C. Xing, Y.-C. Wu and S. C. Chan, “Timing Estimation and Resynchronization for Amplify-and-Forward Communication Systems,” IEEE Transactions on Signal Processing, Vol. 58, No. 4, 2010, pp. 2218-2229. doi:10.1109/TSP.2009.2039837
[18] E. B. Bajalinov, “Linear-Fractional Programming: Theory, Methods, Applications and Software,” Kluwer Academic Publishers, Boston, 2003.

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