Game theoretical framework for clustering and resource allocation in macro-femtocell networks

Abstract

We address the femtocell clustering together with the resource allocation in macro-femtocell networks. The clustering schemes allow the implementation of distributed approaches that can run locally within each cluster. Nevertheless, several limitations should be addressed for dense femtocell deployment, such as: lack of clustering schemes that encourage femtocells to grant service to public users and to become cluster members while guaranteeing their subscriber satisfaction, inefficient bandwidth usage due to the lack of bandwidth adaptation per tier when the cluster configuration changes, and lack of power control mechanisms to reduce interference. In this paper, we propose a distributed clustering model based on a cooperative game, where femtocells are encouraged to cooperate by forming clusters and rewarded with resources from macrocell. Our solution consists of: a cluster formation based on a coalitional game among femtocells and the macrocell to determine the subcarrier distribution per tier, a base station selection for public users and a resource allocation algorithm using Particle Swarm Optimization. We compare our solution with a centralized clustering approach and our cooperative clustering model using the well-known Weighted Water Filling resource allocation algorithm. Simulation results show that our proposal obtains throughput values similar to the centralized approach, satisfies the service requirements for both types of users and reduces the interference in comparison with the benchmark models.

Introduction

Femtocell (FC) technology has been used to solve the main limitations of the traditional cellular networks, such as: poor indoor coverage, degraded signal at cell-edge, offloading traffic and the inefficient use of spectrum. However, there are still several challenges such as base station (BS) selection, resource allocation, power control and interference mitigation due to the dense deployment of femtocells.

Femtocells are connected to the mobile core network by means of an Internet backhaul (e.g. DSL connection) [1]. A femtocell supports all cellular standard protocols such as CDMA, GSM, WCDMA, LTE, WiMAX, and also all the protocols standardized by 3GPP, 3GPP2 and IEEE/WiMAX [2].

In a macro-femtocell network, mobile users are classified as public users (PUs) or subscribers (SUs). The public users are the traditional users of the wireless network while the FC subscribers are the authorized users that can connect to their own femtocells. Three access control modes are defined for the public users access to FCs. These are the closed, open and hybrid access modes [1]. In closed access mode, only FC subscribers can connect to their femtocells and these users get full benefit of their own FCs. However, the network capacity is limited and the interference caused by FCs to nearby macro users is increased. Open access mode allows any mobile user to use FCs, which requires a tight coordination between the macrocell (MC) and FCs. Hybrid access mode allows public users to access FCs but FCs reserve some resources for their own subscribers. Valcarce et al. [3], [4] demonstrated that the hybrid access mode outperforms the closed and the open access modes due to its ability to reduce the interference while guaranteeing the performance of their own subscribers.

The resource allocation problem for macro-femtocell networks was proved to be NP-hard due to the non-convexity of the signal-to-interference-plus-noise ratio (SINR) [5]. In the literature, some centralized approaches have addressed different challenges such as interference mitigation [6] and resource allocation [7] for non-dense FC deployment. Nevertheless, these solutions require global knowledge in real-time and long running times which make these approaches unfeasible for dense deployment.

The complexity of the resource allocation problem is still a very challenging issue for dense femtocell deployment. Recently, FC clustering schemes have attracted the attention of researchers in order to reduce this complexity. The main goal is to form FC groups that allow the implementation of distributed resource allocation approaches within each FC group. The majority of these approaches focuses on FCs deployed in the closed access mode (e.g. [8]), despite the benefits of the hybrid access mode.

To the best of our knowledge, there are no related works that dynamically change the bandwidth allocated per tier taking into account the offloading traffic from macrocell and the cooperative femtocell networks. The main issues that need to be addressed when combining clustering and resource allocation for the hybrid access FCs are: (1) the bandwidth starvation in macrocell or cluster, (2) guarantees for the FC subscriber transmissions; and (3) inter-cluster interference mitigation.

The limitations of the previous works can be summarized as follows:

• Lack of appropriate clustering schemes that encourage FCs to grant service to the public users while guaranteeing the quality of service of FC subscriber transmissions without depriving the macro user transmissions.

• Lack of dynamic bandwidth allocation per tier when the public user distribution changes with the cluster configuration.

• Lack of appropriate FC power control mechanisms to reduce not only co-tier interference but also inter-cluster interference.

To overcome these limitations, we propose a distributed clustering model using a game theoretical framework for cooperation between macrocell and femtocells that is able to determine the amount of MC resources (i.e. subcarriers) that can be allocated to the femto-tier without depriving macro user transmission of resources. Our cooperative game determines first the top-coalition C* formed by a set of femtocells and the macrocell such that FCs maximize their subscribers satisfaction and the network operator maximizes the satisfaction of the public users. Then, other coalitions are formed using a fair portion of the allocated bandwidth to femto-tier. Finally, a distributed resource allocation algorithm is run locally within each cluster. The objective of this algorithm is to maximize the cluster throughput. We use Particle Swarm Optimization (PSO) technique for the resource allocation algorithm due to its ability to obtain a satisfying near-optimal solution while speeding up the optimization process.

In this section, we use a motivating example to demonstrate that all entities of the macro-femtocell network (i.e. network, macrocell, femto-tier, clusters and femtocells) can effectively enhance their throughput by means of the clustering.

Fig. 1 shows a macrocell with eleven deployed femtocells ($F{C}_1,F{C}_2,\dots ,F{C}_{11}$) represented by houses. Each FC is serving one subscriber (i.e. a total of 11 subscribers) and 17 public users are located within the FCs’ vicinity. We assume equal demand for subscribers and the public users (e.g. 1 Mbps). The macrocell has 22 available channels for both tiers and each channel reaches a maximum data rate of 1 Mbps if it is not reused. Spectrum partitioning approach [9] is assumed among tiers. This means that a dedicated number of subcarriers is allocated for each tier. The number of subcarriers allocated to the femto-tier should satisfy at least the average demand requested by FCs, $\overline{D_{SUE}^f},$ that is defined as the sum of FC’s data rate demands divided by the FC number.

The network utility can be defined as the sum of all user data rates:

$$U^N=\sum _{i\in MS}{\alpha }_i^m{R}_i^m+U^{FT}$$

where the first term corresponds to the throughput delivered by macrocell m and the binary variable ${\alpha }_i^m$ indicates if user i is served by macrocell m. U^FT is the femto-tier utility, which is the sum of the data rates of the users served by FCs and is given by

$$U^{FT}=\sum _{c\in C}\sum _{f\in F^c}{U}^c+\sum _{f\in F^{sa}}{R}_{SU}^f$$

where F^c, F^sa, C are the sets of femtocells in coalition or cluster c, stand-alone femtocells, and clusters, respectively. The first term in (2) represents the sum of clusters’ utilities, U^c, and the second term is sum of the stand-alone FCs’ utilities. The cluster utility is estimated as the sum of data rate of both type of users being served by cluster members (i.e. ${\sum }_{f\in F^c}(R_{PU}^f+R_{SU}^f)$).

$R_{PU}^f$ represents the sum of the data rate of public users being served by the femtocell f, i.e. ${\sum }_i^{PU}{\alpha }_i^f{R}_i^f$. $R_{SU}^f$ corresponds to the sum of the data rate of the subscribers of femtocell f, i.e. ${\sum }_i^{SU}{\alpha }_i^f{R}_i^f$. $R_i^f$ is the achievable data rate offered by femtocell f to user i and ${\alpha }_i^f$ is the binary variable indicating the allocation of user i to the femtocell f. Finally, FC’s utility is given by

$$U^f=\{\begin{array}{cc}{\displaystyle \sum _{j\in PU}{\alpha }_j^f{R}_j^f+\sum _{i\in SU}{\alpha }_i^f{R}_i^f}\hfill & f\text{in}\text{a}\text{cluster}\hfill \\ \\ {\displaystyle \sum _{i\in SU}{\alpha }_i^f{R}_i^f}\hfill & \text{otherwise}\hfill \end{array}$$

Let us consider three scenarios: (i) FCs work in closed access mode, (ii) FCs work in hybrid access and they are cooperative forming clusters of equal size, and (iii) FCs work in hybrid access but they form clusters of different size.

In the first scenario, each FC serves only its own subscriber because of its closed access mode. To reach the maximum data rate provided by a channel (i.e. 1 Mbps), dedicated channels are allocated to the users such that the cross-tier and co-tier interferences are avoided. Thus, the femto-tier needs 11 channels to satisfy the total demand required by subscribers while the macro-tier needs 17 Mbps (1 Mbps per PUs) to fulfill the PUs demand. However, the available channels are not enough to satisfy the total users’ demand. To maximize the femto-tier throughput, the macrocell should allocated 11 channels to the femto-tier, grant access to 11 PUs and block 6 PUs. Table 1 summarizes the channel distribution per BSs and their respective utilities. Table 2 shows the throughput values for the scenarios with coalition. In the second scenario, 9 FCs ($F{C}_2,\dots ,F{C}_{10}$) choose to form three clusters of equal size while FC₁ and FC₁₁ work in the closed access mode. The macrocell rewards with one additional channel to each FC belonging to clusters. These two channels can reach the maximum data rate owing to the fact that the clusters are far from each other and the inter-cluster interference can be considered negligible. Each cluster reaches an utility of 6 Mbps and the femto-tier utility is 20 Mbps using only 6 channels. The femto tier serves 9 public users and 11 subscribers while the macrocell serves 8 public users. The macrocell and network utilities are equal to 8 Mbps and 28 Mbps respectively while keeping 8 available channels for new arriving users. Fig. 1depicts the third scenario where only femtocell FC₁₁ is working alone and the remaining FCs form three clusters of different size. Table 2(b) summarizes the utility of the network entities. The femto-tier utility is increased to 21 Mbps in comparison with the second scenario, the overall utility is the same while the number of available channels is lower than the scenario with cluster of equal size.

In summary, the coalitions allow the network to increase the throughput by means of rewarding FC with extra resources to grant service to PU and reduce the power consumption due to the proximity of the serving BSs. There is no gain for subscribers when their FCs become cluster members through the additional allocated channel but the co-tier interference reduction. This motivates our work to investigate how to reward cooperative femtocells with additional resources from the unused channels in the network to improve the subscribers satisfaction. For example, three additional channels could be easily allocated to FC clusters in the second scenario and the FCs can increase the subscriber throughput to 2 Mbps and still keep some available channels for new arriving users.

We propose a new framework that consists of three components: a distributed clustering model, a BS selection algorithm for public users, and a distributed resource allocation. In particular, our contribution is a model that provides:

• Bandwidth adaptation per tier based on the bandwidth allocated to a top coalition that maximizes the throughput of public users of the network.

• Enhanced subscriber satisfaction and reduction of the inter-cluster interference owing to the fact that FCs can choose to join or leave their current coalition depending on their SU satisfaction and the inter-cluser interference.

• Improved public user satisfaction by means of a BS selection algorithm, where each PU prefers to be connected to a FC, which is member of a cluster and provides higher data rate than the MC.

• Enhanced throughput per cluster by means of a cluster based resource allocation algorithm that maximizes its throughput using PSO technique.

Moreover, extensive simulations are carried out to perform a comparison between the proposed solution and two benchmark models: (1) its modified version using the same proposed distributed clustering scheme with a resource allocation algorithm based on the Weighted Water Filling (WWF) applied within each cluster, and (2) a centralized clustering model proposed in [10].

The rest of the paper is organized as follows: Section 2 presents an overview of related works. Section 3 describes the system model and problem formulation. Section 4 presents the components of the game theoretical framework for clustering and resource allocation as well as the benchmark models. Section 5 presents and analysis the numerical results obtained for the proposed and benchmark models. Finally, Section 6 concludes the paper.