1. Introduction
Femtocell networks provide enhanced indoor coverage for cellular systems through the use of low-power indoor base stations, named femto-access points (FAP) or Home Base Stations (HBS) [1], which are connected to the cellular operator's network via a digital subscriber line (DSL) or cable modem. The femto mobile user communicates with a FAP via a wireless link, while the FAP forwards traffic to the macro base stations (MBS) through a wired line. Deployment of femtocell networks induces benefits to both operators and subscribers: Femtocells are seen by operators as a way to off-load traffic from the macro cellular network to the wired lines and to have better reuse of resources; subscribers see femtocells as a way to get higher quality services, either higher data throughput or better voice quality, thanks to the capillary indoor coverage of femtoaccess points, which avoid the wall penetration losses. Since FAPs are typically installed by the subscribers without any consideration about traffic demands or interference with other femto and macro cells, a potential massive deployment of FAPs might induce an intolerable interference. Interference management is then one of the major challenges to be faced by femtocell networks. An accurate global planning would be the optimal solution to interference management. However, a centralized management is unfeasible as it requires an excessive amount of signaling among the many FAPs and the macro base stations. It is then of special interest to devise decentralized mechanisms able to adapt resource allocation dynamically in order to limit interference adequately and get the advantages offered by the capillary deployment of FAPs. An important aspect of FAPs is the possibility to exploit the user's Digital Subscriber Line (DSL) or other broadband wired backhaul links to send data to the Macro Base Stations (MBS) and, possibly, to communicate with other FAPs. As proposed in the European project FREEDOM [2], depending on the quality of the backhaul link three different kinds of scenario have to be considered: i) the backhaul link is either absent or of low-quality, so that FAPs are in competition with each other; ii) the backhaul link allows a local exchange of signaling information among FAPs, so that local coordination is possible; iii) the backhaul link is of sufficient quality to allow FAPs to share the data to be transmitted, so that cooperative communications becomes possible. In this work, we concentrate on the first two scenarios, which are the less demanding in terms of backhaul link quality. In this framework, decentralized mechanisms for resource allocation based on Game Theory (GT) become fundamental tools. Game theoretic approaches have been proposed for the multicarrier interference channel [3], [4] and, lately, for cognitive radios [5]. Those works focused on purely competitive games and the achievement of a Nash Equilibrium (NE) was taken as the design criterion for resource allocation. We recall that a NE indicates the condition in which every player (FAP) has no incentive to unilaterally deviate from his strategy, given the strategies of the others. However, a NE, just because of its purely competitive nature, could be Pareto-inefficient. In particular, the inefficiency is more likely to occur when the interference is high and the channels are flat. It is then of interest to check if the game formulation can be modified in order to move the NE's of the modified game towards the Pareto optimal boundary. One of the mechanisms to be used to achieve such a goal is pricing, which requires some exchange of information among players. In femtocell such a form of local coordination among FAPs is made possible through the backhaul link, which creates an underlying wired network connecting FAPs and MBSs, as proposed in [6]. Aimed at allocating power optimally in the joint time-frequency domain, following the current trend in 3G systems and their evolution like WiMax and LTE, it is of particular interest to have a model for the interference activity in the time-frequency plane. As suggested in previous works on cognitive radios, a useful statistical model for the interference activity is the Markov model, see, e.g. [7] and its references.