A Power Allocation Technique for Fairness and Enhanced Energy ...

0 downloads 0 Views 617KB Size Report
Enhanced Energy Efficiency in Future Networks. Hanifa Nabuuma1 ... and energy efficiency without reducing the minimum data rate of an established resource.
A Power Allocation Technique for Fairness and Enhanced Energy Efficiency in Future Networks 1

Hanifa Nabuuma1 , Emad Alsusa1 , Wahyu Pramudito1 , and Mohammed W. Baidas2 School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, UK 2 Electrical Engineering Department, College of Engineering and Petroleum, Kuwait University, Kuwait Email: [email protected], [email protected], [email protected], [email protected].

Abstract—In this paper, we present a power allocation technique that improves the sum rate and energy efficiency without reducing the minimum data rate of an established resource block allocation technique. To achieve this, the technique is implemented in two stages where the first is for ensuring that the minimum data rate remains unchanged. The second stage is for increasing the sum rate by ensuring that more resource blocks are reused by the femtocells that reduce their power. The algorithm is iterative with changes in transmit power resulting in changes in resource block allocation. It will be shown that at the expense of some delay, the proposed technique can result in significant energy savings while maintaining the minimum data rate when compared to equal power allocation. Further, relative to optimal allocation techniques, the proposed technique results in better fairness.

I. I NTRODUCTION Femtocells have been proposed as one of the solutions to combat the rising demand for high data rates by users of the cellular networks [1]. They are also an attractive option for mobile network operators because they have lower operational cost [1]. However, the deployment of femtocells comes with a number of challenges; interference being one of the major ones [1], [2]. Femtocell deployment results in co-tier interference between collocated femtocells and crosstier interference between the femtocells and the macrocell [2]. This paper considers a femtocell only network with only cotier interference in the downlink. The access control employed by femtocells has an impact on the level of interference. Open access femtocells allow all user equipments (UEs) in their coverage to connect to them resulting in better network capacity while degrading the quality of service of the femtocell owner [3]. Closed access femtocells only allow access to pre-registered UEs resulting in “dead zones” for other UEs [4]. Co-tier interference in orthogonal frequency division multiple access (OFDMA) networks can be mitigated and in some cases eliminated through resource allocation i.e. subcarrier and power allocation. Self-organising network (SON) capabilities can be used by femtocells to improve resource allocation. SON capabilities enable UEs to monitor their environment and report back to their serving femtocell which will then have an accurate representation of the interference environment of its UEs and adapt its resource allocation strategy accordingly [5]. In the downlink, power allocation in femtocells is mainly carried out to mitigate cross-tier interference to nearby macro-

978-1-5090-0304-4/16/$31.00 ©2016 IEEE

cell UEs while maximising femtocell throughput [2]. In [6] a distributed resource allocation algorithm that allocates subcarriers using graph colouring is presented. Based on the signal to interference and noise ratios (SINRs) of the UEs, the power is adjusted by each femtocell so that its users attain a target SINR and for UEs where it is infeasible, they are scheduled for the next subframe [6]. In [7], the aim of power allocation is to minimise power consumption while meeting the target UE data rates. UEs are assigned subchannels with higher SINR so as to use less power and higher modulation and coding. UEs that can’t meet their data rates are scheduled for the next frame [7]. A distributed technique in [8] mitigates both cross-tier and co-tier interference by modelling femtocells as players in a potential game whose utility function simultaneously maximises capacity and minimises interference caused to neighbouring UEs. [6] and [8] require femtocells to have the channel gains of all UEs in the network to all basestations (BSs) which may result in excessive overhead. In [9], given a subchannel allocation, power is allocated using a non-cooperative game whose utility is to maximise the energy efficiency per subchannel. Similarly, [10] allocates power using a non-cooperative game whose utility function aims at maximising throughput while minimising interference. Ngo et. al. developed a joint subcarrier and power allocation technique to minimise cross-tier interference while maximising femtocell throughput [11]. Specifically, the technique is iterative and successive convex approximation is used to determine the power allocation to each subcarrier. In [12] power is allocated to maximise throughput while ensuring that macrocell UEs attain their minimum data rate and that delay sensitive UEs are not in outage. This technique assumes co-tier interference is very low; however, this is not always the case. In this paper we tackle the problem of improving the sum rate of an established resource block (RB) allocation technique in a femtocell network without reducing the minimum data rate, which is the measure of fairness adopted by this paper. To address this problem, we generate an interference map from the measurement reports submitted by UEs to their serving BSs. This interference map is used by two algorithms to determine the power allocation iteratively. Unlike the techniques discussed above where the power allocated to each RB is different, in our technique each femtocell allocates equal power to each RB however, some femtocells may allocate more power than others to the RBs.

244

The rest of this paper is organized as follows. Section II describes the system model while Section III describes the construction of the interference map. RB allocation, the power allocation algorithm and evaluation of its performance are presented in Sections IV, V and VI respectively. Finally, Section VII presents the conclusion. II. S YSTEM M ODEL A perfectly synchronous N subcarrier long term evolution/time division duplex femtocell network. We assume that there are 12 RBs for data transmission in each time slot. Further, a UE is allocated an RB for the duration of one transmission time interval (TTI). The allocation is done on a frame by frame basis and because there are 10 TTIs in a frame, B = 120 RBs are allocated in each allocation cycle [13]. The femtocells are connected to a Femtocell Gateway (FGW) with operation and management (OAM) functionality in order to manage resource allocation. It is assumed that there is no cross-tier interference. Furthermore, we assume that the femtocells are able to establish their neighbours through information exchange via the IP backhaul. Therefore, all femtocells and UEs have a neighboring femtocell list in their memory. Finally the femtocells are assumed to operate in open access mode. The scenario considered is of an l × l building with M uniformly distributed femtocells. An equal number of UEs is uniformly distributed in a circle around each femtocell. There are Q UEs in total. .

the signal wavelength by λ. Assuming free space path loss (PL) and ignoring shadowing and fading, Φq,i and Φq,j are estimated by  2  η λ 1 · , (3) Φq,i = p · 4π dq,i η  2  λ 1 · . (4) Φq,j = p · 4π dq,j Assuming equal transmitted power, p, by all femtocells, a 1/η femtocell interferes with a UE if dq,j < (γth ) dq,i . IV. R ESOURCE B LOCK (RB) A LLOCATION RB allocation is done using the technique in [5] and is described here. From the aggregated MoC, ζ, the number of UEs detected by each femtocell m is given by um =

Q 

ζ (q, m) > 0.

(5)

q=1

To establish the minimum number of RBs to be allocated to each UE, we first calculate the minimum RB vector, S ∈ R1×M , using S(m) = B/um  ,

(6)

where · denotes the floor function. The minimum number of RBs allocated to a UE q is given by

III. I NTERFERENCE M AP

Smin (q) = min ((ζ(q, : ) > 0)  S) ,

An interference map is constructed from the measurement reports (MRs) generated by UEs and is referred to as the matrix of conflict (MoC) [5]. Each UE sends its MR to its serving femtocell indicating the Reference Signal Received Power from neighbouring femtocells. The number of UEs served by a femtocell i is denoted by Qi and its local interference map, ζi ∈ RQi ×M is generated as follows [5]

where  is the component wise multiplication of vectors and Smin ∈ R1×Q . The minimum data rate of the network is dependent on the minimum value in S and it is denoted by εmin . Once Smin is determined for all UEs, RB allocation commences and is done in three stages. In the first stage, each UE q is allocated Smin (q) RBs which are not forbidden to it. It is forbidden to RBs allocated to UEs detected by its serving BS in the MoC and UEs served by femtocells in the set {m | ζ(q, m) = 1 ∧ m = 1 : M } where ∧ denotes “AND”. When allocating RBs to a UE, priority is given to allocated RBs as opposed to empty RBs to ensure maximum reuse. In the second stage, UEs that are not interfered by any femtocell, referred to as inner UEs, are allocated to all the remaining RBs to which they are not forbidden. The third stage allocates to UEs that are not inner UEs any remaining RBs to which they are not forbidden. The UEs are allocated in descending order of the number of UEs forbidden to share RBs with them.

ζi (q, j) =

⎧ ⎪ ⎪ ⎨1, ⎪ ⎪ ⎩0,

Φq,i < γth , Φq,j Φq,i > γth , Φq,j

(1)

where Φq,i is the power received by UE q served by femtocell i, Φq,j is the power received from a neighbouring femtocell j and γth is the signal to interference ratio (SIR) threshold. Therefore if the SIR, γj , with respect to femtocell, j, is less than γth , it is considered an interferer to q and q cannot reuse an RB allocated by that femtocell. The FGW aggregates the local MoCs to form an aggregated MoC ζ ∈ RQ×M given by [5] ⎧ ⎪ ⎨2, if m serves q, (2) ζ (q, m) = 1, if m inteferes q, ⎪ ⎩ 0, otherwise. We denote the distance between the UE and its serving femtocell by dq,i , the distance between the UE and another femtocell by dq,j , the indoor pathloss exponent by η and

(7)

V. P OWER A LLOCATION A LGORITHM The aim of power allocation is to improve the sum rate and energy efficiency without reducing the minimum data rate of the network. To do this, the power allocation algorithm is executed in two steps: a) detected UE minimisation, and b) inner UE throughput maximisation. When the transmit powers of the femtocells are different, the condition for a femtocell to be an interferer to a UE q is

245

 dq,j
γth . The femtocell that reduces power reduces detected UEs and if it is the highest interferer it will increase εmin . A. Detected UE Minimisation Let U denote the number of detected UEs by each femtocell, uinit denotes the maximum value in U when equal power is allocated by all femtocells while umax denotes the maximum value after power allocation starts. Moreover, Un denotes the number of detected UEs in the updated MoC after power allocation, Fmax denotes the femtocells with umax detected UEs and F denote the femtocells in the network. For each femtocell m, um = usm + uim where usm are the UEs served by femtocell m and uim are UEs interfered by femtocell m. Additionally usm and uim are given by usm = |{q | ζ(q, m) = 2}| ,

(9)

uim = |{q | ζ(q, m) = 1}| ,

(10)

where |·| is the cardinality of the parameter set. Detected UE minimisation is performed using Algorithm 1. Femtocells in Fmax reduce their power in steps of δ dB. After each iteration, the new MoC and U are generated. UEs served by femtocells in set Fmax have reduced SIRs with respect to other femtocells. When the SIR, γm , with respect to femtocell m drops below γth then the UE becomes a detected UE of that femtocell. If a UE served by femtocell i ∈ Fmax becomes a detected UE of femtocell m ∈ / Fmax making um ≥ umax , then femtocell m is considered dependent on femtocell i. Such femtocells are denoted as Fdep , which is given by Fdep = {m | m ∈ / Fmax ∧ um ≥ umax } .

(11)

M ×M

This dependency is depicted in  ∈ R as (i, m) = 1.  is initialised as a zero matrix and whenever a new dependency is identified it is updated. If (i, m) = 1, then when femtocell i reduces power then so should femtocell m. After each power reduction iteration, changes in the MoC and U are used to update . Further, if any of following three checks is true, then power reduction should stop,

{m | um

= Fmax ⊆ Ui = usm ∧ m ∈ Fmax } =

F Us Ø,

B. Inner UE Throughput Maximisation Inner UE throughput maximisation boosts system throughput by letting inner UEs access more RBs and is performed using Algorithm 2. Let S(q) denote the number of RBs allocated to a UE q so that the total Q RB utilisation St = q=1 S(q). The number of inner UEs m that serves

of femtocell Qm UEs is uin,m = M



q | q ∈ Qm ∧ k=1 ζ(q, k) = 2 . Let Finner denote femtocells with inner UEs i.e. {m | uin,m > 0 ∧ m ∈ M }. Each femtocell in Finner will take a turn to reduce power in steps of δ dB to reduce um until any of these exit criteria are met, umax um uin,m

(12)

where Us denotes all UEs served by femtocells in Fmax and Ui denotes all UEs interfered by femtocells in Fmax . If Fdep = Ø, then in the next iteration the femtocells reducing power are denoted by Fpc which is given by Fpc = Fmax ∪ Fdep .

Algorithm 1 Detected UE Minimisation 1: while max (U) ≥ umax 2: if it is the first iteration 3: Fpc = Fmax i.e. only BSs in Fmax reduce power 4: else 5: Fpc = Fmax ∪ Fdep i.e. BSs in  also reduce power 6: end if 7: for k = 1 : M 8: if k ∈ Fpc 9: reduce femtocell k’s power by δ dB 10: end if 11: end for 12: update the MoC using new measurement report 13: generate Un using (5) 14: update unmax by unmax = max (Un ) 15: if unmax ≥ umax // if detected UEs increase 16: update Fmax by Fmax = Un ≥ umax 17: update Us and Ui based on new MoC 17: update  using changes in MoC 18: generate Fdep from  and Fmax 19: Fpc = Fmax ∪ Fdep 20: if conditions in (12) are all false 21: update U such that U = Un 22: else 23: exit while loop 24: end if 25: else // if detected UEs decrease 26: umax = unmax i.e. umax is reduced for next while loop 27: U = Un // detected UEs are updated 28: end if 29: end while

(13)

The power reduction continues until the exit criteria is met.

= = =

uinit usm,m Ø.

(14)

If fpc is the femtocell currently reducing power, then m = fpc in (14). Each time the detected UEs of fpc are reduced, St and the total power reduction are noted in T and D respectively. When the femtocell reaches an exit criterion, the FGW will find the maximum value of St , Tmax , and the power reduction, β, when T = Tmax . If the transmit power of femtocell m before the start of Algorithm 2 is denoted by pm , then the final transmit power is pm = pm − β. Two or

246

more femtocells may simultaneously reduce power if none of them interferes with the UEs served by the other femtocell. C. Distributed Power Allocation The number of iterations required by the proposed power allocation technique makes it impractical for centralised allocation. Therefore we suggest exchange of measurements between femtocells at the start of the power allocation process to enable distributed allocation. To minimise the exchanged data, instead of sharing the pathloss measurements, the SIR difference, γm = γm − γth is shared and an aggregate MoC

= RQ×M is generated by each femtocell using the shared information. The MoC is generated as follows, ⎧ ⎪ ⎨ 2, ζ (q, m) = 1, ⎪ ⎩0,

q,m = −γth ,

q,m < 0 ∧ q,m > −γth ,

q,m > 0.

(15)

Algorithms 1 and 2 are then implemented and with each power reduction step, δ, is updated by (Qm , :) = (Qm , : ) − δ for UEs Qm served by power reducing femtocell m and

(q, m) = (q, m) + δ for UE q not served by femtocell m. D. Convergence Analysis The exit criteria ensure that Algorithms 1 and 2 converge. In a scenario where all femtocells have the same number of detected UEs, it is impossible for all of them to simultaneously reduce detected UEs because they are all reducing power by the same step. This is the same reason why when Ui ⊆ Us , the power reduction is stopped. It is also critical to identify relationships in between femtocells as depicted in . This is to avoid an infinite loop where one femtocell may cause another to join Fmax while it leaves Fmax and then this femtocell also does the same to another femtocell and so on. With identification of these relationships, all such femtocells reduce power simultaneously. If these relationships result in a situation where all femtocells are reducing power simulataneously, the power reduction is halted to avoid infinite power reduction. E. Received SINR Model We denote with Pt the total transmit power of the femtocell and it is constrained to maximum value denoted by Pmax . pi = Pt /N is the downlink transmission power of femtocell i on each subcarrier. pi is constrained to a maximum power pmax = Pmax /N . We denote the link gain between the transmitting femtocell j and the receiving UE of femtocell i allocated subcarrier s in subframe r by hiji,s,r , and with hiii,s,r the link gain between the transmitting femtocell i and its UE, allocated subcarrier s in subframe r. The SINR of UE q served by femtocell i is ψq,s,r = M

j=1, j=i

pi hiii,s,r pj hiji,s,r χj,s,r + σ 2

,

(16)

where σ 2 is additive white Gaussian noise power and χj,s,r is a binary multiplier equal to 1 if γj > γth and 0 otherwise.

Algorithm 2 Inner UE throughput maximisation 1: for m = 1 : M 2: T = 01×um // intialise RB utilisation tracker 3: D = 01×um // initialise power tracker 4: ϑ = 1;  = 1; // initialise counters 6: T (ϑ) = sum (S) // initialise total RB utilisation 7: if m ∈ Finner // if m has inner users 8: while umax < uinit 9: update counter to track power reduced,  =  + 1 10: reduce femtocell m’s power by δ dB 11: update the MoC using new measurement report 12: generateUn using (5) 13: update unmax by unmax = max (Un ) 14: if unmax < uinit 15: if detected UEs decrease,Un (m) < U(m) 16: update counter, ϑ = ϑ + 1 17: allocate RBs and calculate St 18: update total RB utilisation,T (ϑ) = St 19: update power reduction, D(ϑ) =  × 0.5 20: end if 21: update umax for next iteration, umax = unmax 22: update detected users for next iteration, U = Un 23: else 24: find maximum utilisation,Tmax = max (T ) 25: find β at which D(T = Tmax ) 26: final transmit power is pm = pm − β 27: exit while loop 28: end if 29: end while 30: end if 31: end for The capacity of a UE q served by femtocell i is Cq =

F N sub  

log2 (1 + ψq,s,r ) ,

(17)

r=1 s=1

where Fsub is the number of subframes in a frame. The system sum rate Ctot is given by (18), where T0 is the OFDM symbol period.

 Q q=1 Cq . (18) Ctot = T0 Fsub F. Power Consumption Model The radio frequency (RF) power consumption for downlink transmission of femtocell m is modelled as [5]   Pt,m , (19) Pc = μpa μps where Pc is the power consumed by the femtocell, Pt,m is the power transmitted by the femtocell m, μpa is the power amplifier efficiency and μps is the power supply efficiency. The energy consumption ratio (ECR) is modelled by (20), where Psp is the power used by the BS for signal processing.   M

Pt,m 1 m=1 μpa + Psp μps ECR = . (20) Ctot

247

90

Table I S YSTEM L EVEL S IMULATION PARAMETERS

MoC − IMIM MoC − EP NPAG POT

80

Value 256 4 per BS 2.3 GHz 15 kHz 10 × 10−3 s 8 dB 10% of symbols Rayleigh

Parameter η σ

Value 3 -174 dBm/Hz

μpa μps

20% 85%

T0 Fsub

1.43 × 10 10

Pmax Psp

−4

70 Sum rate (Mbps)

Parameter Subcarriers, N UEs, Qm Carrier Bandwidth Frame period Shadowing Delay spread Fading

s

60

50

100 mW 3.35 W

δ = 2 dB

40 δ = 0.5 dB 30

5

6

7

8

600 MoC − IMIM MoC − EP NPAG POT

δ = 0.5 dB

12

13

14

15

13

14

15

Figure 2. Sum Rate

400 34 δ = 2 dB

300

MoC − IMIM MoC − EP NPAG POT

33 32

200

RF power consumption (dBm)

Minimum data rate (kbps)

500

9 10 11 Number of base stations

100

0

5

6

7

8

9 10 11 Number of base stations

12

13

14

15

31 30 29 28 27 δ = 0.5 dB

26

Figure 1. Minimum Data Rate

δ = 2 dB

25 24

VI. P ERFORMANCE E VALUATION The number of femtocells randomly placed within a 60 m by 60 m area with uniform distribution is varied. UEs are placed uniformly in a circle of radius 10 m around the femtocells. A single omnidirectional antenna femtocell system with a full buffer is assumed. The rest of the simulation parameters are shown in Table I. The performance of our technique, denoted by MoC-IMIM, is evaluated for the 20 dB threshold because it results in the right balance of sum rate, minimum data rate and resource utilisation ratio [5]. Results are compared to the noncooperative game (NPAG) in [10], the potential game based allocation (POT) in [8] and MoC RB allocation with equal power allocation (MoC-EP). The impact of δ is also assessed. Figure 1 shows that the minimum data rate is slightly improved with MoC-IMIM and that it is roughly the same for 0.5 dB and 2 dB steps. Algorithm 1 increases εmin while Algorithm 2 increased interference by increasing reuse of RBs. Therefore the result is a tradeoff between increased εmin and increased interference. MoC-IMIM maintains the fairness of MoC based RB allocation. NPAG and POT have a minimum data rate of zero because cell-edge UEs are not allocated RBs. Figure 2 shows increased sum rate with MoC-IMIM compared to MoC-EP resulting from increased reuse of RBs by inner UEs which have high SINRs. The 0.5 dB step has a higher sum rate than the 2 dB step because it enables finer tuning of SIRs before any of the exit criteria is met. The sum rate is much less than that attained by NPAG and POT because

5

6

7

8

9 10 11 Number of base stations

12

Figure 3. RF Power Consumption

the MoC-IMIM allocates RBs to low data rate UEs in order to improve fairness. Further, NPAG and POT have a reuse factor of 1 which also increases sum rate compared to MoC-IMIM. Figure 3 shows that with MoC-IMIM, the RF power consumed by the network reduces, with nearly 4 dBm reduction when there are fifteen femtocells in the network. NPAG consumes the least power and this is as result of its utility function which aggressively minimises transmitted power to combat interference while maximising sum rate. Figure 4 shows that MoC-IMIM has a better ECR than MoC-EP due to increased sum rate and lower transmit power. The 0.5 dB step has better ECR than 2 dB because of the higher sum rate. NPAG and POT have a better ECR than MoCIMIM because they have higher sum rates. Figure 5 shows the fraction of UEs that do not achieve a specified data rate. MoC-IMIM has nearly identical performance to MoC-EP but always has a smaller fraction of UEs not meeting the specified data rate than NPAG and POT. All UEs are able to receive at least 100 Kbps irrespective of BS density with MoC-IMIM which is consistent with the minimum data rate results in Figure 1. However, as the data rates are increased the fraction of UEs that doesn’t meet the data rate increases with BS density. This is because as the number of BSs and UEs increase, fewer RBs are allocated to each UE and fewer

248

1

250 MoC−IMIM MoC−EP NPAG POT

0.8 δ = 2 dB

0.7

δ = 0.5 dB

δ = 1 dB

δ = 2 dB

0.6

0.4

50

5

6

7

8

9 10 11 Number of base stations

12

13

14

0

15

Figure 4. Energy Consumption Ratio 100 Kbps

Fraction of UEs 5

10 Number of base stations

12

13

14

15

R EFERENCES

0.2 5

10 Number of base stations

15

1 Mbps

10 Number of base stations

15

Fraction of UEs

MoC − IMIM MoC − EP NPAG POT 5

9 10 11 Number of base stations

0.4

0.9

0.2

8

0.6

700 kbps

0.4

7

then each BS would implement the power allocation technique and determine how much power to transmit.

0.8

0

15

0.8 0.6

6

400 Kbps 1

0.5

0

5

Figure 6. Iterations

1 Fraction of UEs

150

100

0.5

Fraction of UEs

δ = 0.5 dB

200

Iterations

ECR (microjoules/bit)

0.9

0.8 0.7 0.6 0.5 0.4

5

10 Number of base stations

15

Figure 5. Fraction of UEs below Specified Data Rate

RBs implies lower data rate. NPAG and POT have the same fraction of UEs in outage for all data rates because the UEs allocated RBs all have data rates greater than 1Mbps. Figure 6 shows that smaller δ requires more iterations to reach convergence despite resulting in higer sum rate. During each iteration, all BSs send their updated MoC to the FGW which then instructs the relevant BSs to reduce power for the next iteration. Forty or more iterations of such updates would introduce significant delay. However, with distributed power allocation, measurements are exchanged once and each BS determines its power allocation. This reduces the delay significantly. VII. C ONCLUSION In this paper, an iterative power allocation algorithm that improves system sum rate and energy efficiency while maintaining fairness of the underlying RB allocation technique has been presented. The high number of iterations required by the power allocation technique suggests that implementing the technique in a distributed manner is more practical because it would minimise the associated delay. Distributed allocation would require only one iteration of updates from each BS and

[1] A. Damnjanovic, J. Montojo, Y. Wei, T. Ji, T. Luo, M. Vajapeyam, T. Yoo, O. Song, and D. Malladi, “A survey on 3gpp heterogeneous networks,” Wireless Communications, IEEE, vol. 18, no. 3, pp. 10–21, June 2011. [2] N. Saquib, E. Hossain, L. B. Le, and D. I. Kim, “Interference management in ofdma femtocell networks: issues and approaches,” Wireless Communications, IEEE, vol. 19, no. 3, pp. 86–95, June 2012. [3] J. Andrews, H. Claussen, M. Dohler, S. Rangan, and M. Reed, “Femtocells: Past, present, and future,” Selected Areas in Communications, IEEE Journal on, vol. 30, no. 3, pp. 497–508, April 2012. [4] K. Zheng, Y. Wang, W. Wang, M. Dohler, and J. Wang, “Energy-efficient wireless in-home: the need for interference-controlled femtocells,” Wireless Communications, IEEE, vol. 18, no. 6, pp. 36–44, December 2011. [5] W. Pramudito and E. Alsusa, “A hybrid resource management technique for energy and qos optimization in fractional frequency reuse based cellular networks,” Communications, IEEE Transactions on, vol. 61, no. 12, pp. 4948–4960, December 2013. [6] G. Cao, D. Yang, and X. Zhang, “A distributed algorithm combining power control and scheduling for femtocell networks,” in Wireless Communications and Networking Conference (WCNC), 2012 IEEE, April 2012, pp. 2282–2287. [7] D. Lopez-Perez, X. Chu, A. Vasilakos, and H. Claussen, “Power minimization based resource allocation for interference mitigation in ofdma femtocell networks,” Selected Areas in Communications, IEEE Journal on, vol. 32, no. 2, pp. 333–344, February 2014. [8] L. Giupponi and C. Ibars, “Distributed interference control in ofdmabased femtocells,” in Personal Indoor and Mobile Radio Communications (PIMRC), 2010 IEEE 21st International Symposium on, Sept 2010, pp. 1201–1206. [9] Z. Zhang, H. Zhang, Z. Lu, Z. Zhao, and X. Wen, “Energy-efficient resource optimization in ofdma-based dense femtocell networks,” in Telecommunications (ICT), 2013 20th International Conference on, May 2013, pp. 1–5. [10] H. Kwon and B. G. Lee, “Distributed resource allocation through noncooperative game approach in multi-cell ofdma systems,” in Communications, 2006. ICC’06. IEEE International Conference on, vol. 9. IEEE, 2006, pp. 4345–4350. [11] D. T. Ngo, S. Khakurel, and T. Le-Ngoc, “Joint subchannel assignment and power allocation for ofdma femtocell networks,” Wireless Communications, IEEE Transactions on, vol. 13, no. 1, pp. 342–355, 2014. [12] 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 Global Communications Conference (GLOBECOM), 2012 IEEE, Dec 2012, pp. 4572–4577. [13] E. Dahlman, S. Parkvall, and J. Skold, 4G: LTE/LTE-advanced for mobile broadband. Academic press, 2013.

249