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Multi-relay selection in energy-harvesting cooperative wireless networks: game-theoretic modeling and analysis

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A Correction to this article was published on 25 November 2019

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Abstract

This paper studies distributed multi-relay selection in energy-harvesting cooperative wireless networks and models it as an Indian Buffet Game (IBG). Particularly, the IBG is utilized to model the multi-relay selection decisions of network source nodes, while accounting for negative network externality. Two scenarios are considered: (1) constrained selections (CS), and (2) unconstrained selections (US). In the former scenario, each source is constrained to a maximum number of relay selections; while in the latter scenario, the source nodes can select as many relays as possible. Since the relays are energy-harvesting—and thus intermittently harvest random amounts of energy—the accumulated energy at each relay is unknown to the source nodes, leading to uncertain relays’ energy states. In turn, a non-Bayesian learning (NBL) algorithm is devised for the source nodes to learn the relays’ energy states. After that, two distributed best-response (BR) recursive algorithms, namely BR-CS and BR-US, are proposed to allow the source nodes to make multi-relay selection decisions, while guaranteeing subgame perfect Nash equilibrium. Simulation results are presented to verify the efficacy of the proposed distributed NBL and multi-relay selection algorithms. Specifically, the NBL is shown to efficiently learn the true relays’ energy states. More importantly, the BR-CS algorithm is shown to be comparable to the centralized multi-relay selection—and superior to other relay selection schemes—in terms of network sum-rate improvement (and utility). Lastly, the number of relay selections of the BR-CS algorithm must be constrained to the minimum so as to reduce complexity and fully exploit diversity gains.

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Change history

  • 25 November 2019

    Unfortunately, the original publication contains errors.

Notes

  1. Perfect CSI is assumed at the source and relay nodes.

  2. Power and energy terms can be used interchangeably due to the normalized time-slots.

  3. Due to hardware limitations, it is assumed that no energy is harvested during the multiple-access time-slot, as the relays may be involved in cooperative transmission.

  4. The case for i.i.d continuous uniform random variables can be straightforwardly incorporated [28, 29].

  5. In general, there could be more than two relay states, but this setting is beyond the scope of this paper.

  6. It is noteworthy the learning process of each relay state \(\theta _{r_k}\) is independent of the other relays, which significantly decreases computational costs.

  7. The more accurate the belief is, the better the relay selections of each source node are (i.e. better utility).

  8. The source nodes are assumed to be rational, and thus have an incentive to share their true belief information so as to improve the overall network learning. Moreover, the existence of malicious nodes in the network may lead the learning algorithm to be vulnerable to attacks; however, this is beyond the scope of this paper, and may be pursued in future work.

  9. The C-MRS optimization problem is solved using MIDACO [38], with tolerance set to 0.001.

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Authors and Affiliations

  1. Department of Electrical Engineering, College of Engineering and Petroleum, Kuwait University, Kuwait City, Kuwait

    Mohammed W. Baidas

  2. School of Electrical and Electronic Engineering, University of Manchester, Manchester, UK

    Emad Alsusa

  3. Department of Electrical Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Motasem Alfarra

  4. Department of Electrical and Computer Engineering, Ohio State University, Columbus, OH, US

    Mubarak Al-Mubarak

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  1. Mohammed W. Baidas
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  2. Emad Alsusa
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  3. Motasem Alfarra
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  4. Mubarak Al-Mubarak
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Correspondence to Mohammed W. Baidas.

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This work was partially supported by the Kuwait Foundation for the Advancement of Sciences (KFAS), under Project Code PN17-15EE-02.

The original version of this article was revised: The co-author “Mubarak Al-Mubarak” email address is corrected. The equations 5, 14, 17, 19, 25, 26, 27, 32, 36, 40, 42, 46, 48, 49 and equations in the algorithm 2, 3 alignments are corrected.

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Baidas, M.W., Alsusa, E., Alfarra, M. et al. Multi-relay selection in energy-harvesting cooperative wireless networks: game-theoretic modeling and analysis. Telecommun Syst 73, 289–311 (2020). https://doi.org/10.1007/s11235-019-00611-6

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