Optimal resource allocation in fetmocell networks based on Markov modeling of interferers’ activity

Stefania Sardellitti 0 Alessandro Carfagna 0 Sergio Barbarossa 0 0 Department of Information Engineering , Electronics and Telecommunications, Sapienza University of Rome , Via Eudossiana 18, 00184 Rome, Italy Femtocell networks offer a series of advantages with respect to conventional cellular networks. However, a potential massive deployment of femto-access points (FAPs) poses a big challenge in terms of interference management, which requires proper radio resource allocation techniques. In this article, we propose alternative optimal power/bit allocation strategies over a time-frequency frame based on a statistical modeling of the interference activity. Given the lack of knowledge of the interference activity, we assume a Bayesian approach that provides the optimal allocation, conditioned to periodic spectrum sensing, and estimation of the interference activity statistical parameters. We consider first a single FAP accessing the radio channel in the presence of a dynamical interference environment. Then, we extend the formulation to a multi-FAP scenario, where nearby FAP's react to the strategies of the other FAP's, still within a dynamical interference scenario. The multi-user case is first approached using a strategic non-cooperative game formulation. Then, we propose a coordination game based on the introduction of a pricing mechanism that exploits the backhaul link to enable the exchange of parameters (prices) among FAP's. - Introduction Femtocell networks are composed of cells having a coverage radius in the order of tens of meters, providing enhanced indoor coverage through the use of femtoaccess points (FAPs) or home-enhanced node B (HeNB), in the long-term evolution (LTE) terminology [1,2]. A typical scenario is sketched in Figure 1, where we can notice the wireless links among femto user equipments (FUE), macro user equipments (MUE), macro base stations (MBSs) and FAPs. More specifically, the wireless links are classified as useful or interfering depending on whether they refer, respectively, to the useful link between a transmitter and its intended receiver or to other receivers falling within its coverage area. Being installed in residential areas, e.g., home, offices, etc., the FAPs are typically interconnected with each other through a wired link, usually an ADSL subscriber line which allows the access to a broadband Internet network, as depicted in Figure 1. One of the ideas proposed in this article is to exploit the backhaul to set up a local coordination among nearby FAPs to improve the efficiency of the radio resource management (RRM), without the presence of a centralized control. Femtocells are becoming more and more attractive due to their benefits to both cellular operators and subscribers. On the one hand, operators see femtocells as a way to improve indoor coverage and to off-load wireless traffic from the macro cellular network to the wired network, thus releasing wireless channels to additional mobile users. On the other hand, subscribers see femtocells as a way to get higher quality services, either higher data throughput or better voice quality, thanks to a better indoor coverage, and seamless connectivity. Following the current evolution of cellular standardization process, in this study we assume an LTE framework and we focus on the downlink channel, which assumes an OFDMA strategy. In this context, femtocell networks offer advantages with respect to Wi-Fi, as they avoid vertical hand-off and offer better QoS. In view of a potential massive deployment of FAPs, a special attention has to be devoted to RRM. In fact, different from MBSs, FAPs are typically installed by the subscribers and maintained without global planning, with Figure 1 Femtocell network scenario. no special consideration about traffic demands or interference with other cells, either femto or macro cells. Hence, a dense deployment of FAPs might induce an intolerable interference from FUEs to MUEs or to other FUEs. Interference management is then arguably one of the major challenges to be faced in femtocell networks. The goal of this study is to propose an algorithm for optimizing power/bit allocation over a joint time frequency domain, incorporating a statistical model of the macro-users activity. Since the interference is unknown, the proposed algorithm follows a Bayesian approach, which allocates power/bits over successive time/frequency slots depending on a preliminary sensing and estimation of the parameters of the interference model. We assume a Markov modeling for simplicity, but the approach can be generalized to more sophisticated models, like e.g., [3,4]. More specifically, in this study the interference over different frequency subchannels is modeled as a set of statistically independent homogeneous discrete-time Markov chains (DTMCs). We consider a single-user allocation first, where a single FAP finds the optimal resource allocation according to two alternative strategies: (i) maximize the expected rate, conditioned to the result of the sensing and estimation phase, under a transmit power constraint; (ii) minimize the transmit power under the expected rate constraint. Opportunistic spectrum access (OSA) in multicarrier networks where the channel occupancy follows a Markovian evolution has already been studied in the framework of cognitive radio (CR) in [5,6], for example. Chen et al. [5] develop an optimal OSA scheme aimed at optimizing spectrum sensing and access policies jointly. They assumed that the secondary transmitter receives error-free ACK signals from the secondarys receiver, whenever the transmission is successful, and this information is used to track the state of the primary channels. Interestingly enough, Chen et al. [5] establish a separation principle that decouples the design of spectrum sensor and access policy. A similar context is studied in [6,7], where the authors combine learning and dynamic spectrum access. Both Chen et al. [5] and Unnikrishnan and Veeravalli [6] consider an objective function that depends only on the available cognitive bandwidth and puts a constraint on the collision probability with the primary users. Anandkumar et al. [8] and Liu and Zhao [9] formulate the multi-user OSA problem as a decentralized multiarmed bandit problem [10]. In such a framework, each user learns the channel availability statistics and designs a channel access rule in order to maximize the transmission throughput (or equivalently minimize the system regret, defined as the loss in secondary throughput due to learning errors and collisions under distributed access). In [9], which is an extension of the single-user policy proposed in [10] to the multi-user case, Liu and Zhao propose a family of distributed learning and access policies known as time-division fair share. For these policies, they prove the minimum growth rate of the system regret, which is shown to behave logarithmically with respect to the number of time slots. Moreover, Liu (...truncated)