We consider a situation where wireless service providers compete for heterogenous wireless users. The users differ in their willingness to pay as well as in their individual channel gains. We prove existence and uniqueness of the Nash equilibrium for the competition of two service providers, for a generic channel model. Interestingly, the competition of two providers leads to a globally optimal outcome. We extend some of the results to the case where more than two providers are competing. Finally, we provide numerical examples that illustrate the effects of various parameters on the Nash equilibrium.
Until recently, the heterogeneity of the users was largely ignored. The first work that explicitly takes into account the channel differences for different users is @cite_10 . To our knowledge, our work is the first one to consider the pricing competition of providers for users who are heterogenous in both willingness to pay and the channel quality for arbitrary channel coefficients. Also, most previous work considered nonatomic users, i.e., each user's influence on the network is small and negligible @cite_2 . This assumption may not be realistic in practice, which motivates us to study the atomic user case that involves resource splitting among networks (see Section for details).
@cite_10 @cite_2
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In this paper, the problem of joint multichannel cooperative sensing and resource allocation is investigated. A cognitive radio network with multiple potential channels and multiple secondary users is considered. Each secondary user carries out wideband spectrum sensing to get a test statistic for each channel and transmits the test statistic to a coordinator. After collecting all the test statistics from secondary users, the coordinator makes the estimation as to whether primary users are idle or not in the channels. When a channel is estimated to be free, secondary users can get access to the channel with assigned bandwidth and power. An optimization problem is formulated, which maximizes the weighted sum of secondary users' throughputs while guaranteeing a certain level of protection for the activities of primary users. Although the problem is nonconvex, it is shown that the problem can be solved by bilevel optimization and monotonic programming. This paper is also extended to cases with consideration of proportional and max-min fairness. We explore the performance tradeoff between opportunistic and regulated access inherent in the design of multiuser cognitive radio networks. We consider a multichannel cognitive radio system with sensing limits at the secondary users and interference tolerance limits at the primary and secondary users. Our objective is to determine the optimal amount of spectrum sharing, i.e., the number of secondary users that maximizes the total deliverable throughput in the network.We begin with the case of perfect primary user detection and zero interference tolerance at each of the primary and secondary nodes. With identical primary and secondary traffic statistics, we find that the optimal fraction of licensed users lies between the two extremes of fully opportunistic and fully licensed operation and is equal to the traffic duty cycle. When the secondary users can vary their transmission probabilities based on the number of active primary users, we find that the optimal number of opportunistic users is equal to the average number of unoccupied channels. We then consider the more involved case of imperfect sensing and non-zero interference tolerance constraints. We provide numerical simulation results to study the tradeoff between licensing and autonomy and the impact of primary user sensing and interference tolerance on the deliverable throughput for two different subchannel selection strategies at the secondary users.