Distributed Uplink Resource Allocation in Cognitive Radio Networks -- Part II: Equilibria and Algorithms for Joint Access Point Selection and Power Allocation

The main objective of this two part paper is to formulate and address the problem of distributed uplink resource allocation in multi-carrier cognitive radio networks (CRN) with multiple Access Points (APs). When the APs operate on non-overlapping spectrum bands, such problem is essentially a joint spectrum decision and spectrum sharing problem. In this network, the cognitive users (CUs) are endowed with greater flexibility than the single AP network we considered in the first part of the paper [2]: they can optimize their uplink transmission rates by means of: 1) association to a suitable AP and 2) sharing the set of channels that belong to this AP with other CUs associated with this AP. Clearly these two steps are interdependent, and our objective is to devise suitable algorithms by which the CUs can perform these two steps in a distributed and efficient fashion. In the first part of this paper, we have studied solely the spectrum sharing aspect of the above problem, and proposed algorithms for the CUs in the single AP network to efficiently share the spectrum. In this second part of the paper, we build upon our previous understanding of the single AP network, and formulate the joint spectrum decision and spectrum sharing problem in a multiple AP network into a non-cooperative game, in which the feasible strategy of a player contains a discrete variable (the AP/spectrum decision) and a continuous vector (the power allocation among multiple channels). The structure of the game is hence very different from most non-cooperative spectrum management game proposed in the literature. We provide characterization of the Nash Equilibrium (NE) of this game, and M. Hong, A. Garcia and J. Barrera are with the Department of Systems and Information Engineering, University of Virginia, Charlottesville, VA Part of this manuscript has been accepted by the Proceedings of IEEE INFOCOM 2011[1]. January 12, 2013 DRAFT