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A Cooperative Strategy for Trustworthy Relay Selection in CR Network: A Game-Theoretic Solution

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Abstract

The non-symmetric type of game is Stackelberg, where one player or a specific set of players has the advantage of making moves ahead of the other players. These games are being used to aid administrative decisions in telecommunications and computational systems. Stackelberg games have increasingly been helpful in systems where security is a key decision consideration. The authors have suggested a cooperative and novel framework for selection of relays within Cognitive Radio (CR) System utilizing Stackelberg game-theoretic approach through this correspondence. The cooperation is based on the trustworthiness of the Secondary Users (SUs) while getting selected as a relay. Additionally, the strategy of the Secondary Transmitter (ST) is always to increase its own utility function by selecting the best available SU (as a relay) satisfying the rules of the Stackelberg game. The Nash equilibrium strategies for Secondary Relays (SR) have been analyzed in this paper at the suggested approach, as well as the Stackelberg competitive game with successive moves has been justified in the process. To our experience, no work on the trustworthy selection process of the relay to aid transmission of secondary users in the CR network using the game-theoretic method by Stackelberg has yet been published. Results obtained from simulation confirm that ST, as well as SR, gain more utilities if compared with the non-cooperative transmission scheme. Further, the relay which gets selected in this process even reduces the secondary outage loss in comparison to few non-game-theoretic approaches.

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Abbreviations

PT, ST:

Primary transmitter, secondary transmitter

\(P_{PT}\), \(P_{ST}\) :

Transmission power of PT and ST

\(r_{PT}\), \(r_{ST}\) :

Data rate of PT and ST

\(SR_{i}\) :

‘i’ th Secondary Relay

K:

Total number of relay nodes

\(\Re\) :

Set of secondary relays \(\Re = \left\{ {\left. {SR_{i} } \right| \, i = 1, \, 2,{ 3 }\ldots \, K} \right\}\)

\(c_{u, \, v}\) :

Channel impulse response of the link between u and v nodes

\(\alpha_{u, \, v}\) :

Instantaneous channel gain between nodes u and v

\(\Phi_{D}\) :

Decoding set \(\Phi_{D} \, = \, \left\{ {\varphi \, \left| { \, \varphi \, \in \, \phi \, \cup \varphi_{{\text{K }}} {\text{ , k}} = { 1, 2 }\ldots{, 2}^{{\text{K}}} - 1} \right.} \right\}\)

\(\gamma\) :

Path loss coefficient

\(d_{u, \, v}\) :

Path length connecting elements u and v

\({\text{g}}_{{u,{\text{ v}}}}\) :

Fading coefficient with zero-mean

\(U_{ST} ,{\text{U}}_{{{\text{SR}}}}\) :

Utility of ST and SR

\({\text{I}}()\) :

Status of packet delivery

\({\text{p}}_{{{\text{SR}}_{{\text{i}}} }}\) :

Packet forwarding probability

\(\omega_{{SR_{i} }}\) :

Willingness of \(SR_{i}\) node to cooperate in a transmission

\({\text{f}}_{{{\text{SD}}}}^{{\text{i}}}\) :

Feedback from SD for ‘i’ th relay’s packet delivery

\(\mu\), \(\nu\) :

Observed number of well and misbehavior over the time T

\(\Gamma_{{{\text{SR}}_{{\text{i}}} }}\) :

Trust factor of \(SR_{i}\)

\({\text{ C}}_{{\text{V}}}\) :

Equivalent cost of achieving +ve trust factor

\(\Im_{{{\text{SR}}_{{\text{i}}} }}\) :

Trust utility

\(\eta_{{{\text{thr}}}}\) :

Predefined outage threshold

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Authors and Affiliations

  1. Department of ECE, Bengal Institute of Technology, Kolkata, 700150, India

    Jyoti Sekhar Banerjee & Arpita Chakraborty

  2. Department of ECE, University of Engineering and Management, Kolkata, 700156, India

    Abir Chattopadhyay

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Banerjee, J.S., Chakraborty, A. & Chattopadhyay, A. A Cooperative Strategy for Trustworthy Relay Selection in CR Network: A Game-Theoretic Solution. Wireless Pers Commun 122, 41–67 (2022). https://doi.org/10.1007/s11277-021-08888-0

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