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Energy-Saving Resource Allocation Scheme with. QoS Provisioning in OFDMA Femtocell Networks. Wenpeng Jing. †. ,Zhaoming Lu. †. ,Haijun Zhang. ††.
ICC'14 - W14: Workshop on Energy Efficiency in Wireless Networks & Wireless Networks for Energy Efficiency

Energy-Saving Resource Allocation Scheme with QoS Provisioning in OFDMA Femtocell Networks Wenpeng Jing† ,Zhaoming Lu† ,Haijun Zhang†† ,Zhicai Zhang† ,Jun Zhao† ,Xiangming Wen† †

Beijing Key Laboratory of Network System Architecture and Convergence School of Information and Communication Engineering Beijing University of Posts and Telecommunications, Beijing †† College of Information Science and Technology Beijing University of Chemical Technology, Beijing Email: [email protected]

Abstract—In this paper, the resource allocation problem is studied in downlink femtocell networks to minimize the energy consumption of femtocell base stations (FBSs), provide delayaware quality-of-service (QoS) guarantees for femtocell users and limit the cross-tier interference. Specifically, by integrating the concept of effective capacity, users’ delay-aware QoS requirements are characterized by the QoS exponent and minimum effective capacity constraints. The problem of minimizing transmit power of FBSs is formulated as a mixed integer programming problem and is decomposed into two subproblems in order to reduce the complexity. Accordingly, a suboptimal subchannel allocation algorithm and a QoS-driven optimal power allocation algorithm are proposed respectively. Simulation results demonstrate that the proposed algorithms can use the lowest transmit power to satisfy diverse delay-aware QoS requirements of femtocell users, which show great advantages in energy saving and QoS provisioning.

I. I NTRODUCTION The femtocell is considered as a promising technology, which can enhance the network coverage of indoor environment, provide ubiquitous high speed connectivity to end users and offload traffic from the macrocell [1] [2]. However, with the co-channel deployment of femtocells and macrocells, severe cross-tier interference may be introduced, and this will dramatically degrade users’ QoS and network performance [3] [4]. Therefore, the interference management is a critical technical challenge that has to be coped with for femtocell networks. Besides, energy saving is one of the most important issues in wireless networks due to environmental and financial considerations. As the deployment number of FBSs is increasing rapidly worldwide, the energy consumption of all the femtocell network can not be neglected. It is reported that over 80% of the energy consumption in mobile networks takes place in radio access part, especially base stations [5]. For the base station, 50-80% of energy is consumed in the power amplification [6]. Hence, mitigating the transmit power of FBSs is of great importance for energy saving. Furthermore, providing reliable delay provisioning is an urgent task for delay-sensitive traffic in mobile networks. However, imposing deterministic delay guarantees is impractical for mobile services because of the time-varying nature of wireless channels. Therefore, the effective capacity, which is

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defined by Wu and Negi in [7], has been adopted widely to provide statistical delay provisioning. In [8], a QoS-driven energy-efficient resource allocation algorithm is proposed for orthogonal frequency division multiple access (OFDMA) networks with the statistical delay provisioning based on effective capacity. In [9], a joint power and subcarrier assignment policy is proposed for vehicular communication networks, which can satisfy users’ delay-aware QoS requirements with a minimized power consumption. In [10], a distributed energy-efficient power optimization scheme is developed for interferencelimited multi-cell OFDMA networks. However, all the above works can not be applied to femtocell networks directly, because the severe cross-tier interference problem is not solved. In [11], a power allocation policy based on game theory is proposed to maximize the effective capacity of femtocell networks as well as control the co-channel interference. However, the power saving is not taken into consideration. In view of the existing literature, it is necessary to solve the energy saving, delay provisioning as well as interference mitigation jointly for femtocell networks. In this paper, we investigate the energy-saving radio resource allocation problem for femtocell networks in the downlink, by jointly considering three major challenges in OFDMA femtocell networks, namely, 1) minimizing the transmit power of FBSs, 2) providing delay-aware QoS guarantees for users and 3) limiting cross-tier interference. The effective capacity theory is introduced and users’ delay-aware QoS requirements are characterized by the QoS exponent and minimum effective capacity constraints. Considering protecting macrocell users from severe cross-tier interference, a cross-tier interference threshold is set. The minimizing transmit power problem is then formulated as a mixed integer programming problem and decomposed into two subproblems in order to reduce the complexity. A suboptimal subchannel allocation algorithm is proposed by assuming an equal power distribution. Subsequently, a QoS-driven optimal power allocation algorithm is devised based on the Lagrangian dual decomposition approach. Simulation results demonstrate that our algorithms have significant advantages over other algorithms in terms of energy-saving and QoS provisioning. The rest of the paper is organized as follows. Section

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II describes the system model and problem formulation. In Section III, by decomposing the original problem into two subproblems, the subchannel allocation and power allocation algorithms are proposed respectively. In Section IV, the performance of the algorithm is evaluated by simulation. The conclusion is given in Section V. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION A. System Model We consider the downlink of a two-tier femtocell network, which consists one central macrocell overlaid by K femtocells. It is assumed that F active femtocell users camp in each femtocell and M active macrocell users in macrocell. Let K = {1, 2, · · · , K} denote the set of FBSs in the network, and Fk = {1, 2, · · · , F } denote the set of femtocell users in FBS k. Femtocells are assumed to operate in closed access mode [3] and share the whole available spectrum with the macrocell. The system bandwidth is divided equally into N subchannels, each with a bandwidth of B. The subchannel set is denoted as N = {1, 2, · · · , N }. The fading of all subchannels assigned to the same user is assumed to be independent and identically distributed (i.i.d.) and perfect channel state information (CSI) can be available for both the transmitters and the receivers. Specifically, this paper considers the sparse deployment scenario of femtocells, e.g., the scenario of suburban area. Thus, the co-tier interference between neighboring FBSs is negligible compared with the cross-tier interference, and is assumed as part of the thermal noise in this paper. Then, the channel gain-to-interference-plus-noise ratio of user u in FBS k on subchannel n can be expressed as n = γk,u

n gk,u FM + σ pnw gk,u,n

, 2

arrival data rate that the wireless channel can support with a statistical delay constraint. The effective capacity of the block fading channel is defined as 1 EC (θ) = − ln E(e−θr[i] ), (3) θ where E(·) denotes the expectation operator; {r[i], i = 1, 2, · · ·} corresponds to the uncorrelated, discretetime, stationary and ergodic stochastic service process; the θ is the QoS exponent [12]. The QoS exponent θ characterizes the steady-state delay violation probability of the user by Pr(D > Dmax ) ≈ e−θcD

B. Statistical Delay-QoS Guarantee It is assumed that active femtocell users are being providing all kinds of services that have different delay-aware QoS requirements. Due to the time varying nature of the wireless channel, to impose deterministic delay guarantees for femtocell users is impractical. Therefore, the statistical delay guarantee, which is based on the effective capacity, is introduced. The effective capacity characterizes the maximum

(4)

C. Problem Formulation Our target is to minimize the total transmit power of all FBSs in the femtocell network while satisfying users’ delayaware QoS requirements in terms of effective capacity and limiting the cross-tier interference. Hence, the corresponding optimization problem is formulated as follows, K ∑ F ∑ N ∑

minn n

ρk,u ,pk,u

where pnk,u denotes the transmit power of FBS k on subchannel n to user u.

,

where D is the delay user suffering, Dmax is the delay bound, and c is determined by the arrival and service processes [13]. It is obvious that a small θ corresponds to a loose delay limit, while a large θ corresponds to a stringent delay requirement. Define Emin to be the minimum effective capacity requirement with QoS exponent θ that the user should achieve, then, the delay-aware QoS requirement can be satisfied only on the condition that EC (θ) > Emin holds.

(1)

where pnw denotes the transmit power of the macrocell base n station (MBS) on subchannel n to its serving user w; gk,u is the channel power gain of subchannel n from FBS k to user FM u and gk,u,n denotes the interference channel power gain of subchannel n from MBS to the femtocell user u in FBS k. σ 2 is the power of additive white Gaussian noise (AWGN) per subchannel. As a result, the ideal achievable data rate of user u in FBS k on subchannel n in one frame with duration Tf can be denoted as n n rk,u = Tf Blog2 (1 + pnk,u γk,u )(bits/f rame), (2)

max

s.t. −

E(ρnk,u pnk,u )

k=1 u=1 n=1 N ∑ n ρn −θk,u k,u rk,u

1 ln E(e θk,u K ∑ F ∑

n=1

) > Ek,u , ∀k, u,

MF ρnk,u pnk,u gw,k,n ≤ Inth , ∀n,

k=1 u=1 pnk,u ∈ [0, pmax ], ∀k, u, n, ρnk,u ∈ {0, 1}, ∀k, u, n,

(5a)

(5b) (5c) (5d) (5e)

where ρ = [ρnk,u ]K×F ×N is the subchannel assignment indication matrix, being ρnk,u = 1 if subchannel n of FBS k is assigned to user u, and ρnk,u = 0 otherwise; pmax is the maximum transmit power on each subchannel for all FBSs; MF is the channel power gain of subchannel n from FBS k gw,k,n to macrocell user w who is occupying the subchannel n; θk,u is the QoS exponent of user u in FBS k; Ek,u is the required minimum effective capacity of user u in FBS k. The objective function in problem (5) is the sum of the mean transmit power of all FBSs in the network. Constraint (5b) guarantees the QoS requirements of the femtocell users in terms of the effective capacity. Constraint (5c) represents that cross-tier interference macrocell users tolerating on each subchannel can not exceed the interference threshold Inth .

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III. S UBCHANNEL A LLOCATION AND P OWER A LLOCATION S CHEME

Algorithm 1: Subchannel Allocation Algorithm 1

Considering the integer variable ρnk,u and continuous variable pnk,u , the problem (5) falls into the scope of a mixed binary integer programming problem, in which the nonlinear constraints are also involved. It is prohibitive to find the global optimizer of problem (5) because the integer constraints generate an exponential complexity. In order to make the problem tractable, we first decompose it into two subproblems of subchannel allocation and power allocation. Then, the subchannel allocation algorithm and power allocation algorithm are proposed respectively.

2 3 4 5 6 7 8 9 10 11 12 13 14

A. Subchannel Allocation In this subsection, a subchannel allocation algorithm is developed by modifying the algorithm in [14]. The details of the algorithm are shown in algorithm 1. The main difference between our work and [14] is that at the second step of the algorithm, the metric for users’ priorities of getting extra subchannels is not the achieved data rates, but the ratio of achieved effective capacity to minimum effective capacity requirement. Equal initial power pini is assumed for all subchannels during the initialization. In the first step, each femtocell user will be assigned the subchannel with the highest signalto-interference-plus-noise-ratio (SINR), where the SINR of n user u in FBS k on subchannel n is denoted as ηk,u and n n ηk,u = pini γk,u mathematically. Then, the achieved effective capacity of user u in FBS k can be calculated based on EC (θk,u ) = − =−

1 θk,u 1 θk,u

ln E(e ln E(e

−θk,u

N ∑ n=1

−θk,u

N ∑ n=1

n ρn k,u rk,u

) (6)

n ρn k,u Tf Blog2 (1+ηk,u )

)

At the second step, the rest of the subchannels will be allocated based on the ratio of the achieved effective capacity E (θk,u ) to minimum effective capacity requirement, i.e., CEk,u . The user with the minimum ratio will get the assignment opportunity. This choosing and updating iteration procedure will continue until no subchannels are left. It should be noted that this subchannel allocation algorithm is suboptimal because of the assumption of equal power distribution in the initialization step.

Initialize pnk,u = pini , Ak = N , Nk,u = ∅ for n ∈ N , u ∈ Fk , k ∈ K for k = 1 : K do for u = 1 : F do n j = arg maxn {ηk,u |n ∈ Ak }; update Nk,u = Nk,u + {j} and Ak = Ak − {j}; calculate EC (θk,u ) according to (6); end for while Ak ̸= ∅ do i = arg minu {EC (θk,u )/Ek,u |u ∈ Fk }; n j = arg maxn {ηk,i |n ∈ Ak }; update Nk,i = Nk,i + {j} and Ak = Ak − {j}; update EC (θk,u ) according to (6); end while end for

problem, which can be denoted as follows, min n pk,u

s.t. −

θk,u

ln E(e

k=1

E(pnk,u )

k=1 u=1 n∈Nk,u ∑ n −θk,u rk,u n∈Nk,u

K ∑ ∑

(7a)

) > Ek,u , ∀k, u,

(7b)

MF pnk,u gw,k,n ≤ Inth , ∀n,

(7c)

u∈Fkn

pnk,u ∈ [0, pmax ], ∀k, u, n,

(7d)

where Nk,u is the set of subchannels assigned to user u in FBS k and Fkn is the set of users to whom subchannel n is allocated in FBS k. As each subchannel can only be allocated to one user, the set Fkn has at most one element for all k ∈ K and n ∈ N . The objective function of problem (7) is still the sum of the mean transmit power of all FBSs and is convex obviously. Besides, all the constraints of problem (7) can be proved to be convex easily, thus the feasible set of the objective function is convex. As a result, the problem (7) is a convex optimization problem, which has a unique global optimal solution and can be solved by the Lagrangian dual decomposition method [15]. The Lagrangian function for (7) can be given by L({pnk,u }, λ, µ)

+

+

B. QoS-Driven Power Allocation

= [

K ∑ F ∑

K ∑ F ∑ ∑

µn (

E(pnk,u )

k=1 u=1 n∈Nk,u ∑ n −θk,u rk,u

λk,u E(e

k=1 u=1 N K ∑ ∑ n=1

Given a certain determined subchannel assignment, binary variable ρnk,u ’s are fixed to be 0’s or 1’s, so that the original optimization problem (5) is converted into a power allocation

1

K ∑ F ∑ ∑



n∈Nk,u

] ) − e−θk,u Ek,u

(8)

MF pnk,u gw,k,n − Inth ),

k=1 u∈Fkn

where λk,u and µn are the Lagrangian multipliers for constraints (7b) and (7c) respectively. The constraint (7d) will be absorbed in Karush-Kuhn-Tucker (KKT) conditions [15],

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which will be shown later. Then, the Lagrangian dual function is defined as g(λ, µ) = min L({pnk,u }, λ, µ). n

(9)

pk,u

The Lagrangian dual problem can be expressed as

∗ With a recursive method, the optimal subchannel set Nk,u can i−1 i ∗ be got until Nk,u = Nk,u = Nk,u . Then, the optimal transmit power policy can be denoted as [ ]pmax ∗ Wk,u 1 n(∗) pk,u = − n , (17) MF + 1 γk,u µn gw,k,n 0

max g(λ, µ) λ,µ

(10)

s.t. λ, µ ≽ 0.

where

L({pnk,u }, λ, µ) = −

λk,u e−θk,u Ek,u −

k=1 u=1

N ∑

µn Inth ,

n=1

(11) where the subproblem Lk ({pnk,u }, λ, µ) =

+

F ∑

λk,u E(e

Lk ({pnk,u }, λ, µ)

F ∑ ∑

is

E(pnk,u )

u=1 n∈Nk,u ∑ n −θk,u rk,u n∈Nk,u

)+

u=1

N ∑ ∑ n=1

MF . µn pnk,u gw,k,n

u∈Fkn

(12) According to the KKT optimality conditions, the optimal solution of subproblem (12) can be obtained by setting the derivative of Lk equal to 0, i.e., ∂Lk ({pnk,u }, λ, µ) = 0. ∂pnk,u

Wk,u = (λk,u βk,u )

 1 1+Nk,u βk,u

 ∏  

n∈Nk,u

(

n γk,u

) 1+N−βk,uβ

k,u k,u

MF µn gw,k,n

+1

k,u k,u

MF µn gw,k,n

+1

λk,u (t + 1) =λk,u (t)

[

−θk,u

+Γk,u (t) E(e

∑ n∈N ∗ k,u

]

n rk,u

−θk,u Ek,u

)−e

,

(19) µn (t + 1) = µn (t) + Γn (t)(

K ∑ ∑ k=1

MF pnk,u gw,k,n − Inth ), (20)

u∈Fkn

where Γk,u (t) and Γn (t) are the step sizes of the tth iteration and the step sizes should satisfy the following conditions

 , 

t=1 ∞ ∑

Then, the original solution (14) should be updated by replacing 1 1 Nk,u by Nk,u and converting Nk,u into Nk,u respectively.

(18)

After solving all the subproblems in (11), the value of Lagrangian dual function (9) can be obtained. By updating the Lagrangian dual multipliers (λ, µ), the optimal (λ∗ , µ∗ ) of the problem (10) can be derived readily. The subgradient method can be used to calculate the optimal (λ∗ , µ∗ ) and the dual multipliers are updated according to the following expressions

∞ ∑

Note that the transmit power can not be non-positive, so pnk,u should be set 0 if the derived pnk,u is non-positive. We define 1 as the set of subchannels which satisfy the following Nk,u equality { } 1 Nk,u = n ∈ Nk,u pnk,u > 0, ∀n . (16)

 , 

Obviously, the optimal transmitting power scheme in (17) is similar with the classical water-filling policy, but has significant differences. The water level in the water-filling scheme is a constant, on the contrary, the water level of the scheme in this paper is a variable, which is dependent on users’ delayaware QoS requirements as well as the cross-tier interference to the macrocell users.



(15) Nk,u is the number of subchannels assigned to user u in FBS k, βk,u = θk,u T B/ ln(2).



) 1+N−β∗ k,uβ

(13)

Then, the transmit power of FBS k on subchannel n to user u can be derived as Wk,u 1 pnk,u = − n , (14) MF + 1 γk,u µn gw,k,n where

∗ n∈Nk,u

n γk,u

∗ ∗ is the number of elements in set Nk,u . and Nk,u

Lk ({pnk,u }, λ, µ)

k=1 K ∑ F ∑

(

1  ∏ ∗ ∗ Wk,u = (λk,u βk,u ) 1+Nk,u βk,u  

With the help of the Lagrangian relaxation in (8), the dual function can be decomposed into K subproblems. The Lagrangian function (8) is rewritten as K ∑



t=1

Γk,u (t) = ∞, lim Γ2k,u (t) < ∞, ∀k, u; t→∞

(21) Γn (t) = ∞, lim

t→∞

Γ2n (t)

< ∞, ∀n.

Having the above optimal power allocation scheme, we design a distributed power allocation algorithm, which is summarized in the algorithm 2. (λini , µini ) is the initial value of the Lagrangian multipliers, and Tmax is the maximum iteration MF number. It should be noted that gw,k,n can be estimated by the macrocell users and reported to the MBS, then broadcasted to all the FBSs by air interference or the backhaul link. It could also be estimated directly by each FBS based on the assumption of symmetry between the uplink and the downlink.

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Algorithm 2: Power Allocation Algorithm 2 3 4 5 6 7 8 9

10

Initialize t = 1, (λini , µini ), pnk,u = 0, ∀k, u, n; repeat for k = 1 : K do for u = 1 : F do ∗ FBS updates pnk,u according to (17) for n ∈ Nk,u ; FBS updates λk,u according to (19); end for end for MBS updates µ according to (20), and broadcasts µ to all FBSs, t = t + 1; until Convergence or t = Tmax ;

Multiplier λ

0.12

1,1

Multiplier λ

3,1

Multiplier µ

0.1 Lagrange Multiplier Values

1

1

0.08

0.06

0.04

0.02

0 0

10

15

20

25 30 Iterations

35

40

45

50

Fig. 1: Convergence of Lagrangian multipliers

In this section, the performance of the proposed resource allocation algorithm is evaluated. The numerical results of two other resource allocation algorithms, namely the energyefficient resource allocation scheme (EE) and classical waterfilling scheme (WF), are also presented for comparison purpose. Both of the algorithms follow with the same subchannel allocation policy proposed in this paper, but the power allocation of EE is based on the algorithm proposed in [10] and that of the WF is based on the classical water-filling power allocation scheme. During the simulation process, FBSs are randomly distributed in the macrocell coverage area and femtocell users are uniformly distributed within the coverage of their femtocells. The detailed simulation parameters are listed in Table I. Note that all the subchannels are assumed to undergo i.i.d. Rayleigh fading.

20 PA, Emin=1Mbps PA, Emin=0.8Mbps

15

Transmission Power of FBS 1 (dBm)

IV. S IMULATION AND N UMERICAL A NALYSIS

EE Algorithm WF Algorithm 10

5

0

−5

−10 −5

−4

10

TABLE I: Simulation Parameters

10

−3

10 QoS Exponent θ

−2

10

−1

10

Fig. 2: Minimum Transmit Power versus θ

Value 2GHz/0.15MHz 10 1ms 8 10 2 30dBm/20dBm 10dBm -61dBm

5

14

x 10

13 12

Fig. 1 shows the convergence of the proposed algorithm, where three Lagrangian multipliers are chosen arbitrarily to be taken as examples. It is assumed that all the femtocell users have the same delay exponents of θ = 10−3 and same minimum effective capacity requirements of Emin = 1Mbps. From Fig. 1, it can be observed that all the three multipliers get stable after about 20 iterations. Thus, we can conclude that the convergence of the proposed algorithm is guaranteed. The minimum transmit power of FBS 1 and the achieved average effective capacity of users in FBS 1 is evaluated with

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Effecitve Capcacity (Bit/s)

Parameter Carrier frequency/System bandwidth Subchannel number K Frame duration Tf Femtocell number per cell-site K Active macrocell users M Active femtocell users per femtocell F MBS/FBS maximum transmit power FBS constant circuit power Pc Interference temperature threshold Inth

5

11 10 9 8 7

PA, E

=1Mbps

min

6

PA, Emin=0.8Mbps

5

EE Algorithm WF Algorithm

4 −5 10

−4

10

−3

10 QoS Exponent θ

−2

10

−1

10

Fig. 3: Average Effective Capaicty versus θ

ICC'14 - W14: Workshop on Energy Efficiency in Wireless Networks & Wireless Networks for Energy Efficiency

different QoS exponent θ in Fig. 2 and Fig. 3 respectively. It is assumed that users in FBS 1 has the same QoS exponent, i.e., θ1,1 = θ1,2 , and the QoS exponent of all the other femtocell users are fixed to be θ = 10−3 . Besides, all femtocell users are assumed to have the same minimum effective capacity requirements. From Fig. 2, it can be observed that with the increase of θ, the minimum transmit power of the proposed algorithm increases. This is because larger θ is, more stringent the delay requirement is, with which FBSs need to spend more transmit power to satisfy. Specifically, when the θ > 4 × 10−2 , the minimum transmit power of the proposed algorithm increases sharply to the maximum transmit power of FBS, and the corresponding effective capacity of users achieved reduces to a low level. This demonstrates that increasing the transmit power solely is insufficient to satisfy users’ strict delay constraints if the spectrum resource is limited. From Fig. 2 and Fig. 3, it can be observed that the WF algorithm always works in the maximum transmit power mode and can sustain a fixed effective capacity of 1.4Mbps when θ is not too large. Thus, the WF is not quite energyefficient if the minimum effective capacity requirement is lower than 1.4Mbps. On the contrary, the EE algorithm works at a lower transmit power mode, but can only sustain an effective capacity of 0.9Mbps, which cannot provide sufficient delay-aware QoS provisioning when the minimum effective capacity requirement is larger than 0.9Mbps. However, from Fig. 2 and Fig 3, it can be found that the proposed algorithm has a capability to adapt the minimum transmit power to different exponents θ and users’ minimum effective capacity requirements, i.e., spending minimum transmit power to satisfy different delay-aware QoS requirements of femtocell users. As a result, we can conclude that the proposed algorithm can strike a good balance of energy saving and QoS provisioning. V. C ONCLUSIONS In this paper, we investigate energy-saving radio resource allocation problem in downlink femtocell networks, taking both statistical delay constraints and cross-tier interference limit into consideration. By integrating the theory of effective capacity, users’ delay-aware QoS requirements are characterized by the QoS exponent and the minimum effective capacity constraints. The whole energy-saving optimization problem is decomposed into two subproblems, where a suboptimal subchannel allocation algorithm and an optimal power allocation algorithm are proposed respectively. The proposed algorithms can ensure that FBSs consume minimum transmit power while

still satisfying users’ delay-aware QoS requirements. Numerical results show that the proposed algorithms have great advantages in power saving and delay provisioning compared with the existing schemes of EE and WF. ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundation of China (61271179) and the fundamental research funds for the central universities (2013RC0110). R EFERENCES [1] T. Zahir, K. Arshad, A. Nakata, and K. Moessner, “Interference management in femtocells,,” IEEE Commun. Surveys and Tutorials, vol. 15, no. 1, pp. 293–311, 2013. [2] H. Zhang, W. Zheng, X. Chu, X. Wen, M. Tao, A. Nallanathan, and D. Lopez-Perez, “Joint subchannel and power allocation in interferencelimited ofdma femtocells with heterogeneous qos guarantee,” in IEEE ICC’12, Dec 2012, pp. 4572–4577. [3] N. Saquib, E. Hossain, L. B. Le, and D. I. Kim, “Interference management in OFDMA femtocell networks: issues and approaches,” IEEE Wireless Commun. Mag., vol. 19, no. 3, pp. 86–95, 2012. [4] H. Zhang, W. Zheng, X. Chu, X. Wen, M. Tao, A. Nallanathan, and D. Lopez-Perez, “Joint subchannel and power allocation in interferencelimited ofdma femtocells with heterogeneous qos guarantee,” in IEEE GLOBECOM’12, Dec 2012, pp. 4572–4577. [5] G. Fettweis and E. Zimmermann, “Ict energy consumption-trends and challenges,” in WPMC’08, vol. 2, no. 4, 2008, p. 6. [6] L. Correia, D. Zeller, O. Blume, D. Ferling, Y. Jading, I. Godor, G. Auer, and L. Van der Perre, “Challenges and enabling technologies for energy aware mobile radio networks,” IEEE Commun. Mag., vol. 48, no. 11, pp. 66–72, 2010. [7] D. Wu and R. Negi, “Effective capacity: a wireless link model for support of quality of service,” IEEE Trans. Wireless Commun., vol. 2, no. 4, pp. 630–643, 2003. [8] C. Xiong, G. Li, Y. Liu, and S. Xu, “QoS driven energy-efficient design for downlink OFDMA networks,” in IEEE GLOBECOM’12, 2012, pp. 4320–4325. [9] H. Zhang, Y. Ma, D. Yuan, and H.-H. Chen, “Quality-of-service driven power and sub-carrier allocation policy for vehicular communication networks,” IEEE J. Sel. Areas in Commun., vol. 29, no. 1, pp. 197–206, 2011. [10] G. Miao, N. Himayat, G. Li, and S. Talwar, “Distributed interferenceaware energy-efficient power optimization,” IEEE Trans. Wireless Commun., vol. 10, no. 4, pp. 1323–1333, 2011. [11] C. Lin, M. Tao, G. Stuber, and Y. Liu, “Distributed cross-layer resource allocation for statistical qos provisioning in femtocell networks,” in IEEE ICC’13, 2013, pp. 5000–5004. [12] J. Tang and X. Zhang, “Quality-of-service driven power and rate adaptation over wireless links,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 3058–3068, 2007. [13] ——, “Cross-layer-model based adaptive resource allocation for statistical qos guarantees in mobile wireless networks,” IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2318–2328, 2008. [14] W. Rhee and J. Cioffi, “Increase in capacity of multiuser ofdm system using dynamic subchannel allocation,” in IEEE VTC 2000 Spring,2000, vol. 2, 2000, pp. 1085–1089 vol.2. [15] S. P. Boyd and L. Vandenberghe, Convex optimization. Cambridge university press, 2004.

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