Joint power and bandwidth allocation for amplify-and-forward cooperative communications using stackelberg game

Hanan Al-Tous, Imad Barhumi

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


The amplify-and-forward (AF) cooperative communication scheme is modeled using the Stackelberg market framework, where a relay is willing to sell its resources, power, and bandwidth to multiple users to maximize its revenue. The relay determines the prices for relaying the users' information, depending on its available resources and the users' demands. Subsequently, each user maximizes its own utility function by determining the optimum power and bandwidth to buy from the relay. The utility function of the user is formulated as a joint concave function in power and bandwidth. The existence and uniqueness of the Nash equilibrium (NE) are investigated using the concavity of the utility function and the exact potential game associated with the proposed utility function. The NE solution can be obtained in a centralized manner, which requires full knowledge of all channel gains of all users, which may be difficult to obtain in practice. In this sense, a distributed algorithm can be applied to obtain power and bandwidth allocations with minimum information exchange between the relay and the users. Similarly, the optimum prices for the power and bandwidth can also be obtained in a distributed manner. The convergence of the algorithms is investigated using the Jacobian matrix at the NE. Numerical simulations are used to verify the validation of the proposed framework.

Original languageEnglish
Article number6373749
Pages (from-to)1678-1691
Number of pages14
JournalIEEE Transactions on Vehicular Technology
Issue number4
Publication statusPublished - 2013


  • Amplify-and-forward (AF) cooperative communications
  • Nash equilibrium (NE)
  • Stackelberg game
  • distributed algorithm
  • potential game

ASJC Scopus subject areas

  • Automotive Engineering
  • Aerospace Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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