Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 6, Pages 3251-3271Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2043138
Keywords
Cognitive radio; distributed algorithms; game theory; Gaussian interference channel; Nash equilibrium; pricing games; temperature-interference constraints; variational inequality theory
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Funding
- U. S. A. National Science Foundation [DMS 0754374, CMI 0802022]
- Air Force Office of Sponsored Research
- NSFC/RGC [N_HKUST604/08]
- Italian project MIUR-PRIN [20079PLLN7]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0802022] Funding Source: National Science Foundation
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The concept of cognitive radio (CR) has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper, we propose a novel Nash equilibrium (NE) problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate. The formulation contains constraints on the transmit power (and possibly spectral masks) as well as aggregate interference tolerable at the primary users' receivers. The coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of Nash games that cannot be addressed using the game theoretical models proposed in the literature. For this purpose, we need the framework given by the more advanced theory of finite-dimensional variational inequalities (VI). This provides us with all the mathematical tools necessary to analyze the proposed NE problem (e. g., existence and uniqueness of the solution) and to devise alternative distributed algorithms along with their convergence properties.
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