Mathematical Problems in Engineering

Volume 2015, Article ID 767649, 10 pages

http://dx.doi.org/10.1155/2015/767649

## Coalitional Game Theory for Cooperative Interference Management in Femtocell Networks

^{1}State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, No. 3 Shang Yuan Cun, Haidian District, Beijing 100044, China^{2}School of Electronic and Information Engineering, Beijing Jiaotong University, No. 3 Shang Yuan Cun, Haidian District, Beijing 100044, China

Received 5 April 2015; Accepted 2 June 2015

Academic Editor: Rafael Toledo

Copyright © 2015 Yuanyuan Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Dense deployment of femtocells can cause serious intra-tier interference in femtocell networks. In this paper, a new cooperative interference management approach which allows the femtocell user equipment (FUE) to merge into cooperative groups, that is, coalitions, for the uplink transmissions in a femtocell network is proposed, so as to reduce the intra-tier interference and improve the system performance. Taking into account the power cost for cooperation, we claim that all the FUEs are impossible to merge together, and we formulate the proposed cooperative problem as a coalitional game in partition form with an externality due to the interference between the formed coalitions. To get the solution, a novel distributed coalition formation algorithm that takes advantage of the characteristics of femtocell network and allows the FUEs to interact and individually decide on which coalitions to participate in is proposed. Furthermore, we analyze the convergence and stability of the proposed algorithm. Simulations are conducted to illustrate the behavior and the performance of the proposed coalition formation algorithm among FUEs. Results show that the proposed algorithm can improve the system performance with much lower complexity than some previously proposed coalition formation algorithms.

#### 1. Introduction

Femtocell networks have recently emerged as a key structure that shows promise in satisfying the demand for ubiquitous wireless access and higher data rates and have attracted a great attention from both academia [1] and standardization bodies such as 3GPP [2]. The basic idea of the femtocell network is to deploy plug-and-play, low power, low cost femtocell access points (FAPs) underlaying existing communication infrastructures [3, 4]. FAPs can be installed by the users or the service operators inside a home or an office and are able to connect to existing backhaul technologies through a local broadband connection [5, 6]. Subsequently, femtocells can offload traffic from the existing wireless systems (e.g., macrocell networks) and can significantly improve the spectrum efficiency and system capacity.

Nevertheless, when FAPs are deployed in a very dense manner, if interference management and resource allocation are not properly designed, the intra-tier (i.e., femtocell to femtocell) interference can be very serious, consequently affecting the achievable data rate of each FUE and the overall system performance. A lot of recent work has studied the interference problem in the femtocell network. The current solutions can be divided into two categories: noncooperative and cooperative strategies. Noncooperative approaches include power control [7, 8], interference alignment [9], interference cancelation [10], interference avoidance [11], and fractional frequency reuse [12]. In [11], the authors point out that, based on combining frequency handover and power control, the outage probability can be reduced by an interference avoidance technique for noncooperative femtocells. In [13], a two-tier femtocell network is studied by using stochastic geometric theorem, and the success probability is derived for each tier when applying disjoint and joint spectrum allocation, respectively. Cognitive femtocells perceiving the locations of scheduled macrocell users are studied in [14], and an effective macro/femto throughput tradeoff is derived. In noncooperative schemes, each femtocell just pays attention to its own quality of service (QoS) and neglects overall system performance (e.g., sum-rate of the femtocell network) which is of great importance in large scale system deployment. Furthermore, most noncooperative interference management approaches such as fractional frequency reuse and power control need a centralized controller for allocating the resource in the networks, increasing the complexity of the network structure.

To overcome this issue, cooperative methods based on the formation of the cooperative groups (i.e., coalitions) among the nodes in the femtocell network are proposed in [15–19]. The basic idea of coalition is based on the coalitional game theory [20], which aims at improving the whole utility of the game. In [15], downlink intra-tier interference is mitigated by using a game-theoretic approach. Reference [16] introduces a cooperative resource allocation algorithm for the downlink transmission system, without consideration of cost. Reference [19] proposes a cooperative model for downlink interference reduction using a cooperative game. The current schemes just focus on the downlink scenarios where FAPs can form coalitions by exchanging scheduling information through interface X2. However, such cooperative methods are not suitable for uplink scenarios, because there is no such interface for providing direct communication between any two FUEs. Besides, the current coalition formation algorithms neglect the characteristics of the networks. In fact, in a femtocell network, intra-tier interference in the uplink is often dominated by one or two FUEs located near the femtocell boundaries closest to FAP serving the desired signal. FUEs that suffered from the mutual interference have an incentive to mitigate the most serious interference with their closest interfering sources.

In this paper, by applying the coalitional game theory, we propose a new approach to mitigate the interference in the uplink transmissions in the context of femtocell networks. Specifically, to mitigate uplink intra-tier interference and improve the system performance, the neighboring FUEs which are active on the same channel, have an incentive to cooperate with each other by forming coalitions. The FUEs in the same coalition exchange some useful information in a device-to-device (D2D) mode. Based on the success of information exchange, the FUEs within one coalition share the whole transmission time, and thus the intra-tier interference is avoided in that coalition. Furthermore, we model this cooperation problem as a coalitional game in partition form with an externality in terms of the interference among disjoint coalitions. To get the solution, we propose a new algorithm for coalition formation which takes advantage of the characteristics of the femtocell network. In summary, the main contributions of this paper are the following.(i)We propose a new cooperative interference management approach for uplink transmissions in the femtocell network, aiming to improve the aggregate system utility.(ii)Taking into account the power cost for coalition formation, we show that it is impossible for all the FUEs to merge together by forming one coalition and we formulate the proposed approach as a coalitional game in partition form with an externality due to the interference among the formed disjoint coalitions.(iii)To obtain the solution of the coalitional game, we propose a new distributed coalition formation algorithm which takes advantage of the characteristics of the femtocell network to reduce the computational complexity and through which the FUEs can self-organize to reach a convergent and stable coalition structure.

The rest of this paper is organized as follows: Section 2 presents the system model and the proposed cooperative approach for interference management. Section 3 formulates the proposed cooperation problem as a coalitional game in partition form with an externality and proposes a novel algorithm to solve the cooperation problem. Simulation results and analysis are presented in Section 4. Finally, we conclude the paper in Section 5.

#### 2. System Model

Consider the uplink transmission scenario in a femtocell network with several FAPs deployed within the range of a macrocell base station (MBS). Adjacent FAPs are connected by X2 interface, and each FAP is connected to the cellular operator network via fiber backhauls. Each FAP serves several FUEs, and we assume the FUEs belonging to the same FAP are originally assigned orthogonal channels, and thus there is no interference among the FUEs which communicate with the same FAP. Let denote the set of the active FUEs in the considered network which occupy the same channel in the femtocell networks, and FAP is identified by the same label as its corresponding FUE in . Let be the maximum transmit power of FUE on channel . As shown in Figure 1(a), in the traditional noncooperative scenario, each FUE transmits its own signal on its originally assigned channel during its whole transmission time; hence, the concurrent transmission of FUEs belonging to different FAPs can generate mutual interference which constrains the transmission data rate. The intra-tier interference suffered by FAP on channel is given by where is the channel gain between FUE and FAP on channel and is the uplink transmit power of FUE on channel .