Energyefficient downlink resource management in selforganized OFDMAbased twotier femtocell networks
 Adnan Shahid^{1},
 Saleem Aslam^{1},
 Hyung Seok Kim^{1} and
 KyungGeun Lee^{1}Email author
https://doi.org/10.1186/s1363401502279
© Shahid et al.; licensee Springer. 2015
Received: 23 June 2014
Accepted: 19 April 2015
Published: 12 May 2015
Abstract
Femtocell is a novel technology that is used for escalating indoor coverage as well as the capacity of traditional cellular networks. However, interference is the limiting factor for performance improvement due to cochannel deployment between macrocells and femtocells. The traditional network planning is not feasible because of the random deployment of femtocells. Therefore, selforganization approaches are the key to having successful deployment of femtocells. This study presents the joint resource block (RB) and power allocation task for the twotier femtocell network in a selforganizing manner, with the concern to minimizing the impact of interference and maximizing the energy efficiency. In this study, we analyze the performance of the system in terms of the energy efficiency, which is composed of both the transmission and circuit power. Most of the previous studies investigate the performance regarding the throughput requirement of the twotier femtocell network while the energy efficiency aspect is largely ignored. Here, the joint allocation task is modeled as a noncooperative game which is demonstrated to exhibit pure and unique Nash equilibrium. In order to reduce the complexity of the proposed noncooperative game, the joint RB and power allocation task is divided into two subproblems: an RB allocation and a particle swarm optimizationbased power allocation. The analysis of the proposed game is carried out in terms of not only energy efficiency but also throughput. With practical 3rd Generation Partnership Project (3GPP) LongTerm Evolution (LTE) parameters, the simulation results illustrate the superior performance of the proposed game as compared to the traditional methods. Also, the comparison is carried out with the joint allocation scheme which only considers the throughput as the objective function. The results illustrate that significant performance improvement is achieved in terms of energy efficiency with slight loss in the throughput. The analysis in regard to energy efficiency and throughput of the twotier femtocell network is carried out in terms of the performance metrics, which include convergence, impact of varying RBs, impact of femtocell density, and the fairness index.
Keywords
RB allocation Power allocation Noncooperative game Particle swarm optimization Nash equilibrium1 Introduction
Femtocell is a promising technology for expanding indoor coverage as well as the capacity of traditional cellular networks [1]. Therefore, it has attracted attention from academia, industry, and standardization forums. Although femtocell can escalate the performance of indoor users, interference is the critical factor in this regard because of the cochannel deployment of macrocell and femtocell. Femtocell is serviced by a small cellular base station (SBS), which is specifically designed for indoor users or small business. An important characteristic of femtocell is that they are installed randomly and connected to the core macrocell network by using an existing backhaul link, which could be digital subscriber line (DSL), optical fiber, etc. This backhaul link makes it possible for communication with the macrocells and femtocells. The benefits obtained by exploiting femtocell can be divided into two categories: operator and customer perspectives. From the operator’s perspective, femtocell alleviates the burden on the macrocell network by offloading the traffic from the macrocell to the femtocell network. As far as the customer is concerned, high throughput, reduced power, and reliable communication are achievable by the reduced distance between the femto users (FUEs) and the connected SBS [2].
A hierarchical twotier femtocell network is usually implemented in a cochannel environment owing to the efficient spectrum utilization. The interference in this twotier network is bottle neck in the overall performance. Principally, there are two types of interferences that exist in the twotier femtocell network: crosstier and cotier [3]. Within the context of femtocells, the former is the interference between macrocells and femtocells while the latter is among femtocells. Thereby, it is imperative and challenging to deal with the interferences in such an unplanned femtocell network.
Traditional network planning and interference management strategies are not feasible for the twotier femtocell networks. This is in accordance to the fact that prior information regarding the positions and number of femtocells is generally unknown to the operators. Therefore, selforganization provides a vital solution for the management of this unplanned femtocell network. On the other hand, the interference can also be adequately managed by employing the selforganization approaches and consequently improves the system performance [4]. The selforganization concept originates from cognitive radio technology in which there is a little or no involvement of centralized entity. Most of the existing literature on the twotier network only considers the throughput as the performance measure of the network, while the energy efficiency aspect is largely ignored [5]. For the dense deployment of femtocells, energy efficiency becomes a prime concern that needs significant attention. Besides this, the energy efficiency has recently attracted the attention from academia, industry, and standardization forums because of the rapid growth in the demand of users.
This motivates us to investigate the energy efficiency aspect for the selforganized twotier femtocell networks.
1.1 Contributions
 1.
An energyefficient resource block (RB) and power allocation task is modeled as a noncooperative game for the twotier femtocell network. Precisely, the players (SBSs) in the game interact with the environment autonomously and learn the action profile (RB and power levels) with the concern to maximizing the energy efficiency. Under the assumption of the availability of channel gains, the proposed game demonstrated to exhibit pure and unique Nash equilibrium.
 2.
The utility function of the proposed game is designed in a manner that maximizes the energy efficiency and minimizes the impact of interference in the twotier network.
 3.
The complexity of the joint RB and power allocation task of the proposed game is decomposed into two subproblems: an RB allocation and a particle swarm optimization (PSO)based power allocation. This decomposition significantly minimizes the complexity in each iteration of the proposed game.
 4.
The analysis of the proposed game is carried out regarding energy efficiency and throughput. Additionally, two different scenarios are taken into consideration for having an indepth analysis of the proposed game. The comparison of the proposed game is carried out regarding joint allocation game with throughput maximization [6] and traditional methods.
 5.
Simulation results are computed regarding energy efficiency and throughput in terms of the performance measures which include convergence, impact of varying RBs, impact of femtocell density, and the fairness index.
1.2 Related work
The related work is divided into three parts: different approaches for the selforganized resource management [610], the gametheoretic approaches for resource management [1113], and the energyefficient resource management for twotier femtocell networks [14,15].
The authors in [6] propose a joint resource and power allocation in selforganized femtocell networks by exploiting a potential game. However, the whole analysis is carried out in terms of the throughput of the macrocell and femtocell networks. The authors in [7] propose a utilitybased signal to interference and noise ratio (SINR) that reduces the crosstier interference in a femtocell network. However, they do not cater the cotier interference component, which is also termed as the bottle neck in performance enhancement for the shared channel environment. The authors in [8] propose a heuretic approach for resource allocation and power control for femtocell networks. However, the assumption of their study is that the information is thoroughly exchanged among the SBSs for performance improvement which is not practical in the real environment. The authors in [9] employ a novel docitive Qlearning for selforganized resource allocation in femtocell networks. However, it takes time to learn the learning mechanism for the optimal strategies, which makes it unsuitable for the real cases. The authors in [10] propose a joint subchannel and power allocation for the downlink of femtocell networks. Specifically, they have exploited the convex optimization and iterative approach for performance improvement of the network. However, they have only considered the throughput of the system and ignored the energy efficiency aspect that we are presenting in this study.
Gametheoretic approaches, which are appropriate for distributed resource management, have been extensively applied for the twotier femtocell networks. The authors in [11] present a joint channel allocation and power control by using game learning mechanisms for cognitive radio networks. They utilize the regret learning method for convergence to the Nash equilibrium. Moreover, the comparison with genetic algorithm in centralized framework justifies their mechanism. The results illustrate that the inculcation of noregret learning within the context of nocooperation game theory has similar performance to that of the centralized one at the cost of increased complexity. The authors in [12] propose a distributed power allocation scheme using a game theoretic framework for the overlay scenario in cognitive radio networks. More precisely, the game theoretic proposition aims for maximizing the secondary users’ throughput while keeping the interference inculcated on other secondary users and primary networks below the specified threshold. However, the uplink transmission case consideration imposes a huge burden to the FUEs in the network. The authors in [13] present a novel Stackelberg game for the resource allocation problem within the context of femtocell networks. In the game, the macro base station (MBS) which is the leader selects the resources for meeting the demand of its users followed by the allocation of followers with the concern to maximizing the throughput. They take the spectrum sharing into account while assuming the fixed power. However, the joint allocating task significantly improves the performance. All the investigation [1113] carried out only considers the throughput enhancement of the network without taking into consideration the energy efficiency.
Most of the literature focuses on the throughput enhancement of the network; however, the limited battery capacity leads to the attention on the energy efficiency aspect of the twotier femtocell networks. Although the energy efficiency aspect is largely ignored, a few efforts have been made in this domain, which includes [14] and [15]. The authors in [14] propose a noncooperative game for subcarrier allocation and power control that aims at maximizing the energy efficiency. The authors in [15] investigate the noncooperative power optimization game for enhancing energy efficiency. Both works [14] and [15] investigate the resource management for uplink case, which is indeed important for the limited power batteries. On the other hand, the growing demands of users and dense deployment of femtocells attract attention on the energy efficiency in the downlink of the femtocell networks. This will contribute to minimization of the energy consumption of the voice and data networks. Therefore, in this study, we are presenting the energyefficient downlink resource management for the twotier femtocell networks.
According to the best of the authors’ knowledge, the proposed gamebased joint RB and power allocation of the twotier femtocell networks is unique and has not been investigated so far. The exploitation of both RB and power allocation not only maximize the energy efficiency but also maximize the throughput which is shown in the results. This is in accordance to the fact that interference components are also included in the energy efficiency maximization expression which accordingly enhances the throughput also. On the other hand, the decomposition of the joint allocation task into RB allocation and PSObased power allocation makes this study a unique one. The concern of the decomposition of the joint allocation task is to minimize the complexity which makes it more appropriate for real systems. On the other hand, two different scenarios are taken into account for having an indepth analysis of the proposed game.
The rest of this paper is structured as follows: the system model and proposed framework are presented in Section 2. Energyefficient noncooperative game is presented in Section 3, which includes detailed information of the proposed game. The simulation results regarding the energy efficiency and throughput in terms of the performance measures are presented in Section 4. Finally, Section 5 concludes the article.
2 System model
2.1 Proposed framework
2.2 Energy efficiency performance criterion
The repeatedly growing demands of users attract the attention from academia, industry, and standardization forums towards the energyefficient design of wireless networks [1619]. Generally, there are two methods for computing the energy efficiency of the system. The first one considers the amount of information in bits transmitted per Joule (bits/J) [16,17], while the other takes into account the transmission power [18,19].
2.3 Problem formulation
In this study, we consider a twotier OFDMAbased femtocell network comprising of L macrocells, where each macrocell is serviced by an MBS at its center. In addition, each macrocell is overlaid with N femtocells, where each femtocell is serviced by an SBS. Specifically, we are considering the downlink case for the resource management in the twotier femtocell network along with the universal frequency reuse1 for each cell. The concern of employing the frequency reuse1 is due to the fact that each cell has access of all the pool of RBs. The total Y MUEs are randomly deployed within the coverage area of a macrocell, and X FUEs are assumed to be in the indoor environment. The closed group formation (CSG) within the femtocell is assumed in which a certain number of FUEs can only be a part of the femtocell network. Concerning the cochannel deployment, the total pool of Q RBs is taken into account here. On the other hand, the number of RBs acquired by each SBS at any time is assumed to be G such that G ≤ Q. In addition, the total R power levels are considered which can be utilized by each SBS on the acquired G RBs under the constraint of maximum power transmission. The tight synchronization amount the OFDMA subcarriers is taken into account, which correspond to the fact that interference is only inculcated when there is transmission on the same RBs.
The transmission power of lth MBS and nth FBS on acquired G RBs is given by \( {p}_l^{g,M}=\left\{{p}_l^{1,M}, \dots, {p}_l^{G,M}\right\} \) and \( {p}_n^{g,F}=\left\{{p}_n^{1,F}, \dots, {p}_n^{G,F}\right\} \). The maximum power constraint on each base station is represented as \( {P}_{\mathrm{MAX}}^M \) and \( {P}_{\mathrm{MAX}}^F \) such that \( {\displaystyle {\sum}_{g=1}^G}{p}_n^{g,M}\le {P}_{\mathrm{MAX}}^M \) and \( {\displaystyle {\sum}_{g=1}^G}{p}_n^{g,F}\le {P}_{\mathrm{MAX}}^F \), respectively.
The optimization problem in (6) aims at maximizing the energy efficiency subject to the minimum throughput requirement of the femtocells C1 and the maximum power constraint C3. Additionally, per RB power constraint is also taken into account as in C4. The performance of the macrocell users is protected by the incorporation of the constraint C2 in the problem formulation. The accumulated crosstier and cotier interference components are represented by the constraints C5 and C6. The concern of inculcating the aforementioned interference limits is that both the energy efficiency and throughput are enhanced accordingly.
2.4 Notations and assumptions
Notation and assumptions
Parameters  Meaning 

MBS  Macro base station 
SBS  Femto base station 
MUE  Macro user 
FUE  Femto user 
RB  Resource block 
L  Number of macrocells 
N  Number of femtocells or number of players 
Y  Number of macro users 
X  Number of femto users 
Q  Total pool RBs 
G  Number of RBs acquired by each SBS 
W  System bandwidth 
R  Number of power levels utilized by SBS 
\( {p}_l^{g,M} \)  Transmission power of lth MBS on th \( g \)th RB 
\( {p}_n^{g,F} \)  Transmission power of nth SBS on th \( g \)th RB 
\( {P}_{\mathrm{MAX}}^M \)  Maximum transmission power of MBS 
\( {P}_{\mathrm{MAX}}^F \)  Maximum transmission power of SBS on G RBs 
p _{ c }  Circuit power 
\( {h}_{nn,x}^{g,FF} \)  Channel gain between nth SBS and xth FUE operating on th \( g \)th RB 
\( {h}_{\ln, x}^{g,MF} \)  Channel gain between lth MBS and xth FUE of nth SBS operating on th \( g \)th RB 
\( {\varDelta}_n^F \)  Achieved throughput by nth SBS 
\( {\mathrm{EE}}_n^F \)  Achieved energy efficiency by nth SBS 
Γ _{ F }  Minimum capacity of SBS 
\( {\zeta}_n^{MF} \)  Accumulated crosstier interference limit on nth SBS 
\( {\zeta}_n^{FF} \)  Accumulated cotier interference limit on nth SBS 
A _{ n }  Action profile associated with nth player 
U _{ n }  Utility function associated with nth player 
\( {S}_n^F \)  Selection of G RBs by nth SBS 
\( {P}_n^F \)  Power allocation of G RBs by nth SBS 
\( {A}_n^{*} \)  Optimal action profile 
\( {S}_n^{*F} \)  Optimal RB allocation 
\( {P}_n^{*F} \)  Optimal power allocation 
T  Number of particles in PSObased power allocation 
O_{ j }  jth particle position of PSObased power allocation 
3 Energyefficient noncooperative gamebased resource block and power allocation
In this section, the energyefficient noncooperative game is presented, including modeling of the game as RB and power allocation, existence to the pure and unique Nash equilibrium, proposed selforganizing framework, and algorithmic details. The game theoretic approaches are the most suitable for the resource management of the selforganized femtocell network. Specifically, noncooperative game has been extensively applied for the resource allocation problems for the wireless networks [20].
3.1 Noncooperative game
We model the joint RB and power allocation problem as a noncooperative game. Generally, the game is represented by a tuple \( \mathcal{G}=\left\{N,\;\left\{{A}_n\right\},{\left\{{U}_n(.)\right\}}_{n\epsilon N}\right\} \), where N is the finite set of players, A _{ n } is the set of action or strategies (action profile) that each player can opt, and U _{ n } is the utility function that is associated with each player. In other words, the utility function corresponds to the level of satisfaction of each nth player. Moreover, the utility function depends not only on the action profile of nth player A _{ n } but also on the other ones A _{−n } = {A _{1}, A _{2},…, A _{ n − 1,} A _{ n + 1},…, A _{ N }}. Precisely, the utility function can be thought of as a function that maps the action profile A _{ n } into a real number ℝ such that U _{ n }: A _{ n } → ℝ. In a game, the general goal of each nth is to maximize its utility function while keeping the interest of other players into account.
3.2 Existence and uniqueness of Nash equilibrium
A set of action profile is termed as Nash equilibrium if the players involve in the game cannot deviate profitably given the action profile of other players [21]. For the proposed game, the Nash equilibrium is defined as:
 1)
The action profile A _{ n } is a nonempty, convex, and compact subset of some Euclidean space ℝ.
 2)
The utility function U _{ n }(A _{ n }, A _{−n }) is a continuous and quasiconcave.

Theorem 1: The Nash equilibrium point exists in the proposed game \( \mathcal{G} \).

Theorem 2: The proposed game has a unique Nash equilibrium [15].
3.3 Resource block and power allocation
In this subsection, we describe the RB and power allocation of the proposed game. Generally, the optimal joint RB and power allocation is an NPhard problem [22]. In this manner, to reduce the complexity of the proposed game, the joint allocation task is decomposed into two subproblems: an RB allocation and a PSObased power allocation. Primarily, in each iteration of the proposed game, two steps need to be carried out: RB allocation and power allocation. Firstly, the RB allocation is done given the power allocation of all the players. Secondly, the power allocation on the selected RBs is executed out which have been selected in the previous step. In both steps, the goal is to maximize the energy efficiency under the network constraints C1 to C6. The detail of the individual step is elaborated as below.
3.3.1 Resource block allocation
It can be noticed from the above expression that the concern of the RB allocation step is to maximize the utility function, which indirectly maximizes the energy efficiency. The assumption here is that power levels of the other players are acquired on each player, and this information is repeatedly acquired via control channels from the existed backhaul link.
The above expression reveals that the contiguous group of G RBs is allocated by each SBS whose accumulated \( {\displaystyle {\sum}_{g=1}^G}\frac{I_g^{g,F}}{h_{nn}^{g,FF}} \) value is minimum.
3.3.2 Power allocation
In the power allocation step, the PSO is exploited for obtaining the optimum power values on the selected RBs in the previous step. The reason for incorporating the PSO is that it is less complex and gives better results in less time. Owing to the various considered power levels, the PSObased power allocation evaluates the best power values and minimizes the complexity of the game. On the other hand, the main concern of breaking the joint allocation task into two subproblems is to minimize the complexity of the proposed game.
3.3.3 Particle swarm optimization
PSO is a populationbased biologically inspired algorithm, inspired by the bird flocking and fish schooling mechanisms. These types of algorithms are specifically useful where the sample space is very large, the parameters of interest are dynamic, and there is little information exchanged between the users (particles) [24].

a _{ 1 } and a _{ 2 } are termed as acceleration coefficients whose job is to control the influence in the search process.

T is the number of particles in a swarm.

r _{ 1 } and r _{ 2 } are two random numbers uniformly distributed in the interval from (0, 1).

O _{ j }, \( {O}_j^{\mathrm{new}} \), V _{ j }, and \( {V}_j^{\mathrm{new}} \) represent the current and updated position and velocity of the jth particle.
3.3.4 Particle swarm optimizationbased power allocation
The abovementioned power allocation is achieved by exploiting the PSObased optimization. Principally, there are three main steps in the PSObased optimization: particle encoding, fitness computation, and velocity and position upgradation. In our considered PSObased power allocation, each particle is represented by a Gdimensional vector, where each element represents the power level utilized by the SBS. In addition, R power levels can be exploited here with the concern to maximizing the utility function. As far as the fitness of the particle is considered, we use the utility function in (8) as the fitness function for the PSObased power allocation. More precisely, the PSO iteratively maximizes the utility function and yields best results in terms of power allocation on the selected group of G RBs by each SBS. The velocity and position of particles is upgraded by (15) and (16).
3.4 Proposed selforganizing framework and algorithm
Initially, the random assignment is done in terms of RBs and power levels by each SBS. In the sensing phase, each SBS interacts with the environment and acquires link gains. Here, we assume that the availability of link gains is strictly known on the SBSs, and this leads to the optimal performance of the proposed game in terms of the Nash equilibrium. In the learning phase, the proposed game is executed by each SBS based on the availability of link gains which are acquired in sensing phase. Concerning the high complexity of the joint RB and power allocation task, the joint problem is decomposed into two main tasks: an RB allocation and a PSObased power allocation. In the RB allocation step, each SBS acquires the required group of G RBs according to (14) under the available of power levels of other players. In the second step, the power allocation is carried out on the selected RBs by exploiting PSO. Because of the various choices of power levels, the PSObased optimization rules out the power levels in less time with the concern to maximizing the energy efficiency. Lastly, in the tuning phase, the decision is to be made by each SBS, i.e., whether to change the action profile or not. In addition, the changed action profile is also broadcasted to the neighbors so that they can also tune themselves accordingly.
As far as the complexity of the proposed noncooperative game is concerned, the joint allocation task that we have considered in the game is decomposed into two subproblems: an RB allocation and a PSObased power allocation. In each iteration of the proposed game, RB allocation and power allocation are carried out separately, and this significantly reduces the complexity of the original joint allocation task. Firstly, RB allocation is carried out, and then the PSObased power allocation executes on the selected RBs which decides the optimal power levels on them. The concern of exploiting PSO for power allocation is that it gives the optimal power values without parsing the whole set of power values. Under the assumption of the availability of channel gains on the SBS, the proposed noncooperative game converges to pure and unique Nash equilibrium. This information about the channel gains is repeatedly acquired on the control channels and helps in achieving the best performance. The proposed game is also scalable in the sense that any SBS can be in the part of the game any time. However, this may lead to a slightly slower convergence to the Nash equilibrium, where the convergence corresponds to the energy efficiency maximization of the femtocell networks without compromising the macrocell performance. As far as the comparison with the joint scheme is concerned, the joint optimization task is computationally intense.
4 Simulation results and analysis
In this section, the simulation setup of the considered femtocell environment is presented and then the results are presented thereafter. The analysis of the proposed game is carried out regarding energy efficiency and throughput of the femtocell networks. In addition, the performance is evaluated in terms of the performance measures such as convergence, impact of varying RBs, impact of femtocell density, and the fairness index. For the sake of comparison, the following methods have been taken into account: joint resource and power allocation game with throughput maximization (JRPAGTM) [6], proportional fairnoncooperative power optimization game (PFNPOG), and proportional fairfixed power (PFFP). In JRPAGTM, a potential game is utilized for enhancing the throughput without considering the energy efficiency. The concern of comparing the proposed game with JRPAGTM is to classify the gains and losses in energy efficiency and throughput. Furthermore, the two power levels for PFFP are incorporated: 10 and 17 dBm. In order to have an indepth analysis, two scenarios are taken into consideration: scenario 1 and scenario 2. In scenario 1, the number of SBS is taken to be N = 20, while in scenario 2 N = 40. All the simulations of the proposed game are done in MATLAB.
4.1 Simulation setup
We consider an OFDMAbased urban setting environment, operating at 1,850 MHz. For the sake of simplicity, we consider a singular macrocell environment L = 1 with a radius of 1,000 m. However, for multicell environment, the crosstier interference components also become a critical factor along with the cotier for single cell. The performance of the system degrades somehow because of the addition of this interference component. The achieved convergence for multicell environment is also reduced due to crosstier interference component. In addition, there are N femtocells underlaid in a macrocell, where each femtocell is of radius 40 m. The Y MUEs and X FUEs are randomly deployed within the coverage area of macrocell and femtocell. An important clarification is to be made here is that we are considering the average SINR computation among the X FUEs and is in accordance to (2).
In our proposed game, each SBS operates in a selforganizing manner and rules out the action profile (RB and power levels) with the concern to maximizing the energy efficiency without compromising the macrocell performance. According to the 3rd Generation Partnership Project (3GPP) LongTerm Evolution (LTE) specifications, the total system bandwidth W = 1,850 MHz is taken into consideration, which is composed of several RBs. These RBs are utilized by both macrocells and femtocells because of the cochannel deployment. Quantitatively, the total pool of RBs Q = 50 is taken into account. Furthermore, the number of RBs that SBSs can acquire any time is assumed to be G = 5. In order to have a thorough analysis, various values of G are employed such as G = {2, 4, 6, 8, and 10}. As far as the power levels are concerned, we are incorporating R = 100 power levels uniformly distributed in the range from −80 to 23 dBm. The maximum power constraint that each SBS can utilize is \( {P}_{\mathrm{MAX}}^F=23 \) dBm. Furthermore, CSG mode of operation of femtocell is concerned; in which only particular users can be part of the femtocell network. The static circuit power of p _{ c } = 100 mW is taken into account here for the computation of energy efficiency for the femtocell network.
 a)
From MBS to MUE or FUE (indoor): PL(dB) = 15.3 + 37.6 log_{10} d.
 b)
From MBS to MUE or FUE (outdoor): PL(dB) = 15.3 + 37.6 log_{10} d.
 c)
From SBS to MUE or FUE (different): PL(dB) = 7 + 56 log_{10} d + γ
 d)
From SBS to FUE (own): PL(dB) = 37 + 20 log_{10} d + γ
Particle swarm optimization parameters
Parameters  Values 

Population size, T  16 
Acceleration coefficients, a _{1} and a _{2}  2.05 
[V _{min,} V _{max}]  [−G, G] 
4.2 Simulations results
4.2.1 Convergence in terms of energy efficiency and throughput
Figure 5 illustrates the convergence in terms of throughput versus the game iterations for both the scenarios. The convergence in terms of throughput of the proposed game also increases with the increase of game iterations. Although the utility function of the game is designed by taking into account the energy efficiency, the throughput will also be adequately improved by taking into account various RBs and power levels. Similar reason for slow convergence holds for throughput in Figure 5 as in energy efficiency in Figure 4. The comparison with the PFNPOG, PFFP (10 dBm), and PFFP (17 dBm) illustrates the superior performance of the proposed game in terms of throughput. However, the comparison with JRPAGTM illustrates a slight loss in the throughput for each scenario. The reason being that in JRPAGTM, the objective is solely to enhance the throughput without considering energy efficiency. In PFNPOG, for each scenario, only power allocation is considered in the utility function of the game whereas the RBs are randomly allocated, and this corresponds to a significant inferior performance as compared to the proposed game. A similar performance trend with PFFP exists as in energy efficiency. It can be seen that a larger fixed power of 17 dBm corresponds to reduced throughput, and this is due to the fact that utility function is designed in a manner that is aligned with the energy efficiency. Therefore, a better performance is achieved for reduced power in both the scenarios.
4.2.2 Impact of varying RBs on energy efficiency and throughput
Figure 7 illustrates the impact of varying the RBs on throughput of the femtocell network for both the scenarios. Firstly, the increasing trend of the proposed game in terms of throughput is observed by the increase of acquired RBs per SBS, i.e., G. Second, 20% increase in the throughput is observed by doubling the total pool of RBs from Q = 25 to 50. This is in accordance to the fact that accumulated throughput is achieved by the increase of G. On the other hand, the increase in the pool of RBs Q also contributes to the escalation of throughput for each scenario. Therefore, the throughput is enhanced with the increase of either G or Q for each scenario. Nevertheless, a reduced throughput for scenario 2 is also observed as compared to scenario 1, and this is due to the increase competition. The comparison of the proposed game with PFNPOG, PFFP (10 dBm), and PFFP (17 dBm) in terms of throughput illustrates the superior performance of the proposed game.
Since the concern of the proposed game is to enhance the energy efficiency, a slight loss is observed while comparing with JRPAGTM. However, the gain achieved in energy efficiency illustrates the supremacy of the proposed game as compared to JRPAGTM. The throughput performance gap between proposed algorithm and PFNPOG becomes wider with the increase acquired RBs per SBS. The reason is that in the proposed game, both the RB and power allocations are taken into account in the utility function, whereas in PFNPOG, random allocation is employed which leads to reduced throughput. As far as the performance of the proposed game and PFFP is concerned, a significant performance gap of around 490% in scenario 1 and 590% in scenario 2 is observed. The reason is that in PFFP, both the RB and power levels are exploited without concerning the other players in the networks. Another important observation to be made here is that the reduced power levels in PFFP (10 dBm) help in achieving high throughput as compared to PFFP (17 dBm). This is due to the incorporation of the energyefficient resource management which leads to better performance with reduced power levels.
4.2.3 Impact of varying femtocell cell density
The comparison in terms of throughput of the proposed game with traditional methods is illustrated in Figure 8b. The loss in the throughput of the proposed game as compared to JRPAGTM is small of about 5%. The reason being that in JRPAGTM, the concern is to maximize the throughput without considering energy efficiency. The throughput of the proposed game decreases gradually to about 90% while a sharp decaying effect is observed for PFNPOG. However, an important investigation to be made here is that an PFFP (10 dBm) has high throughput as compared to PFFP (17 dBM). This is by virtue of the incorporation of energy efficiency in the utility that contributed to high throughput with reduced power values.
4.2.4 Fairness index
5 Conclusions
In this study, an energyefficient downlink resource management for twotier femtocell networks is investigated. Specifically, the joint RB and power allocation are modeled here as a noncooperative game in which the SBSs are the players and RB and power allocations are the action profiles. Most of the literature focuses only on the throughput enhancement of the twotier system, while the energy efficiency aspect is largely ignored. To this end, the utility function of the proposed game is designed in a manner that is aligned with energy efficiency of the femtocell networks. The optimization problem is modeled as the maximization of the utility function (energy efficiency) subject to the network constraints C1 to C6. These network constraints not only satisfy the minimum throughput but also include the thresholds for interference components. Under the assumption of the availability of the link gains, the proposed game converges to pure and unique Nash equilibrium. Concerning the complexity of the joint allocation task, the problem is decomposed into two subproblems: an RB allocation and a PSObased power allocation. The comparison of the proposed game with traditional methods illustrates the superior performance. In addition, the comparison with joint allocation task potential game, considering the throughput maximization, illustrates that significant performance in terms of energy efficiency with slight loss in throughput is achieved. The analysis is carried out in regard to energy efficiency and throughput.
Declarations
Acknowledgements
This research was supported by the Ministry of Science, ICT and Future Planning (MSIP), Korea, under the Convergence Information Technology Research Center (ConvergenceITRC) support program (NIPA2014H0401141006) supervised by the National IT Industry Promotion Agency (NIPA) and the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Education, Science and Technology (2012009449).
Authors’ Affiliations
References
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