Pseudo-Handover Based Power and Subchannel Adaptation for ...

IEEE WCNC 2011 - Network

Pseudo-Handover Based Power and Subchannel Adaptation for Two-tier Femtocell Networks Hongjia Li, Xiaodong Xu, Dan Hu, Xin Chen, Xiaofeng Tao and Ping Zhang Wireless Technology Innovation Institute Key Laboratory of Universal Wireless Communication, Ministry of Education Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China. Email: [email protected]

Abstract—The two-tier femtocell network is comprised of a central macrocell underlaid with shorter range femtocell hotspots. Due to the universal frequency reuse, this kind of new system architecture brings about urgent problems of the interference management and the resource allocation. Motivated by these problems, the following contributions are made in this paper: 1) a novel joint power and subchannel allocation problem for Orthogonal Frequency Division Multiple Access (OFDMA) downlink based femtocells is formulated on the premise of minimizing Femto BSs’ radiating interference; 2) a pseudohandover based scheduling information exchange method is proposed to avoid the collision interference; 3) an iterative scheme of subchannel allocation and power control is proposed to solve the formulated problem, which is an NP-complete problem. Through simulations and comparisons with three other schemes, the proposed scheme shows better performance in reducing interference and the Femto BS’s transmit power, and improving the spectrum efficiency.

I. I NTRODUCTION Femtocell, as a green radio technique, processes characteristics of lower power and superior indoor experience for users. So a significant interest has focused on the femtocell, also known as Home NodeB (HNB) or Home enhanced NodeB (HeNB) in the 3GPP standardization [1] [2]. In two-tier femtocell networks, femtocells are underlaid in the coverage of the macrocell, which brings many urgent challenges to the architecture of current cellular systems. The co-tier co-channel interference among femtocells and the cross-tier co-channel interference between the femtocell tier and the macrocell tier is one of the most urgent challenges. Interference level splitting results in [2] show that the co-tier interference and cross-tier interference have severe impact on the capacity and coverage of femtocell networks. In order to address the aforementioned problem, different schemes have been proposed in the prior art. In [3]- [5], contributions are made on the basis of the frequency partitioning scheme, in which orthogonal frequency bands are allocated to the femtocell tier and the macrocell tier respectively. However, spectrum efficiency is the key problem of these schemes, and hence the universal frequency reuse scheme [6] is preferable both in the industry area and the research area. In the universal frequency reuse scheme, how to avoid interference through effective resource management and interference management schemes are critical requirements for

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the femtocell configuration. In [7], the authors utilize a timehopped CDMA scheme with universal frequency reuse in its uplink system capacity analysis, which is in fact equivalent to splitting the resource in the time domain instead of splitting it in the frequency domain. In [8], the authors present a Dynamic Frequency Planning (DFP) that takes Femto users (FUEs) as Macro users (MUEs) to operate conventional resource allocation. In [9], the authors proposed a decentralized resource allocation scheme for the OFDMA downlink of the two-tier femtocell networks, where each femtocell randomly selects a subset of available OFDMA resources for transmission. But many problems still need to be addressed: 1) Many schemes of prior literatures are on the basis of the provision of co-tier and cross-tier information exchange, which has potential benefits in allowing femtocells to take account of uplink and downlink conditions at nearby the Macro Base Station (MBS) and other Femto Base Station (FBSs) when configuring power and resources to be used in uplink and downlink [10]. But how to implement the information exchanging procedure, considering the cost of overhead, the cross-tier and co-tier synchronization and compatibility with LTE and LTE-A systems, is not well discussed in prior works. 2) Available researches focus on improving the performance of the overall system. In the femtocell networks, however, it is important to improve the performance not only of the overall system, but also of the specific non-CSG [10] MUEs which are in the femtocell coverage. 3) Since Macrocell is the infrastructure of mobile communications, the service quality of MUEs should be guaranteed as a priority, which means that femtocell should adjust its resources, e.g., power and subchannels, to meet the macro cellular link quality when its links interfere macro cellular links. This paper firstly formulates a novel resource allocation problem, the objective of which is to minimize the co-tier and cross-tier interference. Then, a co-tier and cross-tier scheduling information exchange procedure based on the proposed pseudo-handover method is designed, considering the cost of overhead and compatibility. Finally, based on the pseudohandover information exchange scheme, this paper proposes an iterative scheme to solve the formulated problem. Without loss of generality, the rest of this paper focuses on the downlink and

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is organized as follows. Section II describes the system model and the formulated problem. Section III depicts the proposed scheme, together with important practical issues. Section IV provides the setup of the simulation scenario and performance results of the proposed scheme compared with three other schemes. Finally, Section V wraps up the conclusion. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION The system bandwidth is divided into orthogonal subcarriers, which are in turn combined into N groups, known as resource blocks or subchannel. The subchannel set shared by the macrocell and femtocells is defined as Nc and the bandwidth of each subchannel is equal to B. In the following, femtocell k is taken as the femtocell of interest to elaborate the proposed scheme. Define Nku as the active FUEs in femtocell k. MUEs in the vicinity of femtocell k can be interfered by the co-channel FUEs camping on femtocell k, the set of which is defined as SM . Correspondingly, the interference power received by any MUE in set SM can be represented as  n Pkn gˆk, ¯ ∈ SM , (1) ζcr (m, n) = m ¯ , ∀m

where SˆM and SˆF are sets of MBSs and FBSs that cause con and Pfn channel interference to femtocell k, respectively; Pm are the transmit powers of MBSs and FBSs on subchannel n in n is the path gain from MBS set SˆM and SˆF respectively; gm,k ˆ m (m ∈ SM ) to the FUE using subchannel n in femtocell k; n gf,k is the path gain from FBS f (f ∈ SˆF ) to the FUE using subchannel n in femtocell k. In essence, the formulated problem (3), which is to minimize the interference radiated from every femtocell, is to jointly allocate subchannel and power according to the FUEs’ data rate requirements. However, to obtain the optimal solutions is restricted by the following reasons: n n ˆk, 1) Because SM , SF , gˆk, ¯ in (3) is hard to be m ¯ and g k acquired by the FBS of femtocell k, the interference to its neighboring victims is difficult to be known the FBS of femtocell k in practice; 2) (3) is an NP-complete combinatorial problem [11], which cannot be solved in polynomial time. Therefore, the PHO based power and subchannel adaptation scheme is proposed and introduced in Section III. III. P SEUDO -H ANDOVER BASED P OWER AND S UBCHANNEL A DAPTATION S CHEME

n∈Nc

n where gˆk, m ¯ is the path gain from the FBS of femtocell k to n MUE m ¯ (m ¯ ∈ SM ) on subchannel n, and gˆk, m ¯ is set to zero if m ¯ ∈ / SM ; N0 is the noise spectrum density; Pkn is the transmit power of the FBS of femtocell k on subchannel n. Similarly, SF is defined as the set of co-channel FUEs interfered by the FBS of femtocell k. Then, the interference power received by any FUE in set SF can be represented as    n ¯ n = ¯ Pkn gˆk, (2) ζco k, ¯ , ∀k ∈ SF , k n∈Nc

n where gˆk, ¯ is the path gain from the FBS of femtocell k to k n ¯ the FUE k (k¯ ∈ SF ) on subchannel n, and gˆk, ¯ is set to zero k ¯ if k ∈ / SF . Therefore, considering minimizing the interference to neighboring co-channel UEs (including MUEs and FUEs) and satisfying the camped FUEs’ data rate requirements, i.e., Ri , i ∈ Nku , the minimizing radiating interference problem of femtocell k can be formulated as   ¯ n , ∀m ¯ ∈ SM , ∀k¯ ∈ SF ¯ n) + ζco k, min  ζcr (m, u s.t. (3) n∈Nic B log (1 + ϑ (k, n)) ≥ Ri , ∀i ∈ Nk . n Pk ≥ 0

As for (3), ϑ (k, n) is the Signal to Interference plus Noise Ratio (SINR) of the FUE using the subchannel n in femtocell k, which is represented as ϑ (k, n) =

Pkn gkn , + BN0

Ikn

(4)

where gkn is the path gain from the FBS of femtocell k to the FUE using subchannel n; Ikn is the interference power received by the FUE using subchannel n in femtocell k, which contains the interference from MBSs and the interference from FBSs in its neighboring femtocells. Then, Ikn can be represented as   n n n Ikn = P g + Pfn gf,k , (5) m m,k ˆ ˆ m∈SM

f ∈SF

A. Pseudo-Handover based Scheduling Information Exchange As shown in Fig.1, FUE (2,2) and MUE 1, which are non-CSG (Closed Service Group) users of femtocell 1, lie in the coverage of FBS1. If FBS1 allocates subchannels occupied by FUE (2,2) or MUE1, collision interference can jam the communication of them. In order to avoid the collision interference, FBS1 should find out occupied subchannels of the non-camping UEs in its coverage at first. Therefore, we propose the Pseudo-Handover based scheduling-message exchanging method.

Fig. 1.

Collision interference scenario.

Fig.2 shows an applicable femtocell architecture compatible with the LTE-Advanced system, where an intermediate entity called Femto gateway (GW) is located between FBSs and the mobile Core Network (CN). It connects the FBSs and CN through wired way. The interfaces between FBSs and Femto GW, and the interface between Femto GW and MME/SGW [12] are all S1 interface [12]. In one MBS coverage area, X2 interface [12] exists between Femto GW, which can be seen as a ”virtual” MBS, and the MBS. Seen from the femtocell architecture, the Pseudo-Handover is executed in the Radio Access Network (RAN), not referring to Mobility

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Management Entity (MME), which is de facto a significantly reduced version of the regular handover procedure. 00(6*: 6

6 )HPWR*: 6 6

; 0%6

Fig. 2.

)%6

)%6

6

5HJXODU +DQGRYHU 3VHXGR +DQGRYHU

)%6

An applicable femtocell architecture.

As same as the regular handover procedure [13], UEs start searching for femtocells when they are in their vicinity. However, because femtocells only provide services to their CSG users, performing a handover in the two-tier femtocell networks is not always a possible option. This feature can be utilized to execute a control plane handover for co-tier and cross-tier scheduling information exchanges. As shown in Fig.3, the cross-tier Pseudo-Handover procedure is presented. When any MUE or FUE steps into the coverage of its non-camping femtocell, i.e., the Received Signal Strength (RSS) of a neighboring cell pilot plus a given threshold stronger than the RSS of the serving cell pilot, the UE judges whether it is in the CSG according to the received Physical Cell Identity (PCI) and Cell Global Indicator (CGI) from the FBS [13]. If it is a CSG user, the regular handover is triggered; or else, the pseudo-handover is triggered as shown in Fig.3. In the procedure of pseudo-handover, every FBS sets up and maintains the table containing the IDs of non-CSG interferers (hereafter, we call them pseudo-handover users) and their scheduling messages, which are obtained in the process of Pseudo-Handover. Seen from Fig.3, FBSs do not provide data services for pseudo-handover user, but complete handover initialization procedure plus scheduling information exchanges in the control plane. As indicated by Fig.3, the procedure of the pseudohandover ends in the Femto GW, and does not refer to the MME/S-WG to minimize the cost of overhead. Furthermore, the only difference between the cross-tier Pseudo-Handover and co-tier Pseudo-Handover is that information transmission between FBS and Femto GW is through S1 interface, whereas information transmission between MBS and Femto GW is through X2 interface. B. Subchannel and Power Adaptation Scheme

Fig. 3.

Procedure of cross-tier pseudo-handover.

radiated by FBSs depends on their transmit power allocated to each subchannel. According to above analysis, we ignore n n gˆk, ˆk, ¯ in (3), and reconstruct (3) as a minimum m ¯ and g k transmit power problem as (6), which is also an NP-complete combinatorial problem. To solve the problem, we propose a two-phase iterative subchannel and power allocation scheme. According to (3), when the transmit power of every subchannel is given, the subchannel allocation depends on the FUEs’ data rate requirements (i.e., Ri ), and every FUE’s SINR of every subchannel, which in turn influences the strength of the FBS’s radiating interference of each subchannel. Therefore, in the subchannel allocation phase, a modified proportional fair scheme is proposed, which takes into account Ri and FUEs’s SINR. In the power control phase, utilizing the subchannel allocation result from the first phase, a modified water-filling algorithm is proposed to minimize each FBS’s total transmit power. The main procedure of the iterative subchannel and power allocation scheme is as: 1) Initialize the power allocation of one FBS by distributing the total power randomly among the different subchannels in ˆc ; N 2) For the given power allocation, the subchannel allocation is optimized by the scheme in Subsection C; 3) For the given subchannel assignment, the power allocation is optimized by solving the problem in Subsection D; 4) Iterate steps2) and 3) until the resource allocation n n convergence, i.e., ˆ c |Pk (t) − Pk (t − 1)| ≤ ε, where ε n∈N i

Having received the scheduling message, the FBS can find out subchannels which are being used by pseudo-handover users, and delete these subchannels from its candidate subchannel set Nc to construct a new candidate subchannel set ˆc . So the collision interference to UEs in the coverage of N femtocells is avoided, which means the main interference to MUEs in SM and FUEs in SF is eliminated. Long distance or bad link qualities between the remainder UEs in SM or SF n n and their interferers, i.e., gˆk, ˆk, ¯ , makes the interference m ¯ and g k between them relatively small. So the strength of interference

i∈Nku

is the convergence threshold and t is iteration index, which is omitted for analysis convenience. C. Subchannel Allocation Phase In this phase, the interference power received by different FUEs on different subchannels is taken into consideration, n n and Ii,k as which is reported to FBSs by FUEs. Define gi,k the link quality of FUE i and the interference power received by FUE i using subchannel n in femtocell k, respectively. The subchannel allocation scheme is provided in Table I.

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TABLE I S UBCHANNEL A LLOCATION S CHEME

TABLE II P OWER ALLOCATION ALGORITHM

ˆc and N ˆ c = φ, i ∈ N u , where n is the Initialize: Set n = 0, n ∈ N i k c ˆ ˆ index of subchannels in Nc ; Ni is the FUE i’s subchannel set and  ˆ ˆc u N = Nc is satisfied after the subchannel allocation is

Initialize: Define the power allocation set for FUE i in femtocell k as

 ˆ c ; set a = 0. P n = P n |n ∈ N

completed; Nku is the active FUE set of femtocell k. The transmit

Pkn = −aB − Ikn + BN0

i∈Nk

i,k

i

k

n as (1) Calculate the transmit power for all items in Pi,k

i



(2) If any item (i.e.,

(1) Given transmit power Pkn , FBS k calculates the service rate gains

(3) According to current

∇An i =

B log2 Ri



1+

n Pkn gi,k In i,k



as

, ∀i ∈ Nku ;



(4) If

ˆc n∈N i



gkn ; n in Pi,k is less than zero, set Pkn n , current FUE i’s data rate is Pi,k

Pkn )

power is randomly allocated for the first iteration. for for all FUE i (in Nku ) on subchannel n:



= 0; calculated

B log (1 + ϑ (k, n)).

ˆc n∈N i

B log (1 + ϑ (k, n)) < Ri , decrease a the predefined

(2) FBS k calculates the sum of the current service rate gain of for all

step size and return to Step (1). Or else, the power allocation of FUE i

FUEs (in Nku ) on subchannel n:

is completed.

Si =



B ˆ c Ri log2 m∈N i



1+

m Pkm gi,k

I m +BN0 i,k



, ∀i ∈

Nku

;

transmission power is allocated to the subchannel, (i.e., the subchannel is turned off), which experiences heavy interference caused by cross-tier or co-tier interference from MBSs or neighboring FBSs.

(3) Assign subchannel n to the FUE according to the rule: i∗

= arg min

i∈N u k

max

u j∈Nk

|(Si + ∇Ai ) − Sj |;

j=i

ˆ c∗ = N ˆ c∗ ∪ n; (4) Update the FUE i∗ ’s subchannel set as N i i ˆc = N ˆc − n; ˆc as N (5) Exclude subchannel n from N ˆc , i.e., n = n + 1, and go back (6) Consider the next sub-channel in N ˆ to Step (1) until Nc is empty.

IV. P ERFORMANCE E VALUATION In this section, system level simulations are performed to evaluate the performance of the proposed scheme, comparing with three other schemes.

D. Power Control Phase In the power control phase, the FBS minimizes the transmit power of the allocated subchannels according to FUEs’ data rate requirements. Since each FUE’s subchannel set in femtoˆ c ) is determined in the subchannel allocation cell k (i.e., N i phase, this phase solves the following power-minimization problem for every FUE with inequality constraints:  min n∈Nˆ c Pkn , ∀i ∈ Nku  i u s.t. (6) ˆ c Blog2 (1 + ϑ (k, n)) ≥ Ri , ∀i ∈ Nk . n∈N i n c ˆ P ≥ 0 , ∀n ∈ N i

k

FBS k solves this problem by each FUE i independently. a and bn are referred to as Lagrange multipliers. Deriving the Lagrange function of (6) and substituting ϑ (k, n) by (4), we have  L(Pkn , a, bn ) = n∈Nˆ c Pkn    i n n gk Pk n +a ˆ c B log 1 + I n +BN0 −Ri − ˆ c bn Pk . n∈N n∈N i i k (7) Then, the necessary and sufficient conditions for optimality are given by the Karush-Kuhn-Tucker (KKT) conditions: Pkn =

I n + BN0 a B− k n , bn − 1 gk

ˆ c. bn Pkn = 0, ∀n ∈ N i

(8)

A. Simulation Environment and Assumptions An OFDMA cellular system with 7 macrocell, i.e., one ring case, is considered. MUEs and houses which have an area of 20 × 20 m2 are randomly dropped within each macrocell. Moreover, every house owns only one FBS which randomly dropped in the house and serves 4 FUEs. Taken their home FBS as the circle center, FUEs are randomly dropped in a circle with the radius of 10 meters. FBSs are connected to one Femto GW in every macrocell. In the macrocell tier, all the available subchannels are transmitted with equivalent power according to [14] and the scheduler for the MBS is proportional fair resource allocation. The main simulation parameters are listed in Table III, which are obtained from [14] [15]. According to [15], the path loss model covers the following 5 links: 1) MBS to outdoor MUE: P L = 15.3 + 37.6log10 R,

2) MBS to indoor UE (including the MUE and the FUE): P L = 15.3 + 37.6log10 R + Low ,

(11)

3) FBS to indoor UE (including the MUE and the FUE): P L = 38.46 + 20log10 R + 0.7dindoor ,

(9)

Equation (8) denotes a water-filling system when all bn are zero. Assuming bn are non-zero, a modified water-filling algorithm for FUE i in femtocell k is performed in Table II and power allocation for other FUEs can follow the same way. It is noticed from the power allocation algorithm that more transmission power is assigned to the subchannel which experiences less interference or better link gain, while no

(10)

(12)

4) FBS to outdoor MUE: P L = max(15.3 + 37.6log10 R, 38.46 + 20log10 R) +0.7dindoor + Low ,

(13)

5) FBS to FUE inside a different house:

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P L = max(15.3 + 37.6log10 R, 38.46 + 20log10 R) +0.7dindoor + 2 × Low ,

(14)

where R is the distance between the BS and the UE; dindoor is the shortest indoor distance from BS to UE; Low is the penetration loss of outdoor wall for the house. Obviously, R equals dindoor in (12).

1 0.9 0.8 0.7

TABLE III S YSTEM S IMULATION PARAMETERS Parameter Value

C.D.F

0.5 0.4

500m 43dBm 1

0.3 The proposed scheme The proposed scheme without PHO Random allocatoin scheme Scheme based on Reuse 3

0.2 0.1 0 −30

8dB 50m SCME 2000MHz 10MH 15KHz 1024 50 12 Full buffer

B. Comparison Schemes Comparison scheme 1-the proposed scheme without PHO: The proposed scheme does not operate the PHO based collision interference avoidance. Comparison scheme 2-the random allocation scheme [9]: Each femtocell randomly selects a subset of subchannel for transmission. The fraction of radio resources per transmission interval accessible by each femtocell is set as 60%. Comparison scheme 3-the scheme based on reuse 3: The system frequency reuse factor is 3, and the femtocell tier can only use 2/3 frequency spectrum that is not allocated to its local macrocell. The transmit power of each femtocell is controlled according to its FUEs’ data rate requirements.

−20

−10

0

10 SINR[dB]

20

30

Fig. 4.

CDF of MUEs’ SINR.

40

50

Fig.5 shows the CDF of FBSs’ transmit power. Because the proposed scheme minimizes every FBS’s radiating interference, the signal transmit power to meet the given SINR requirement (i.e., the data rate requirement) is reduced. Therefore, the FBS’s transmit power of the proposed scheme is 1.1dB and 0.84dB less than that of the random allocation scheme and that of the proposed scheme without PHO on average. Compared with random allocation scheme, the proposed scheme without PHO brings 0.35dB gain, which demonstrates the effectiveness of the resource allocation scheme of the proposed scheme. In addition, since the scheme based on reuse 3 avoids the cross-tier interference at the cost of low spectrum efficiency, the transmit power of it is 0.6dB less than that of the proposed scheme. 1 0.9 0.8 0.7 0.6 C.D.F

Cell Parameters Cell Radius Total MBS transmit power Frequency reuse factor Channel Model Shadowing standard deviation Auto-correlation distance of shadowing Fast fading OFDMA Parameters Carrier frequency Bandwidth Subcarrier spacing FFT size Number of subchannels Number of subcarriers per subchannel Traffic Model

0.6

C. Simulation Results

0.5 0.4

The simulation results in Fig.4, 5 and 6 are obtained as there are 50 femtocells randomly distributed in every macrocell and the data rate requirements of all FUEs are randomly assigned within the value set {100kbps, 150kbps, . . . , 10Mbps}. Fig.4 shows the Cumulative Distribution Function (CDF) of MUEs’ SINRs. Since the collision interference to MUEs is avoided by the PHO method, the proposed scheme remarkably improves the MUEs’ SINR performance, where MUEs’ SINRs increase 3.8dB and 11.85dB on average compared with the proposed scheme without PHO and the random allocation scheme, respectively. Although there is no cross-tier interference in the scheme based on reuse 3 due to orthogonal subchannels allocation to the femtocell tier and the macrocell tier, MUEs’ SINR of the proposed scheme is only 2.3dB lower on average. This is mainly due to the effectiveness of the subchannel allocation and power control algorithm in the proposed scheme.

The proposed scheme

0.3

The proposed scheme without PHO

0.2

the scheme based on reuse 3 Random allocation scheme

0.1 0 −5

0

5 10 15 20 Transmit Power per FBS [dBm]

Fig. 5.

CDF of FBSs’ Transmit Power.

25

30

Fig.6 shows the CDF of the reciprocal of co-tier interference power received by FUEs. Compared to the random allocation scheme, the proposed scheme without PHO and the scheme based on reuse 3, the proposed scheme decreases the FUE’s co-tier interference by 9.92dB, 10.68dB and 17.58dB on average, respectively. In addition, it can be seen from the figure that the scheme based on reuse 3 suffers the greatest co-tier interference, which is mainly due to the fact that it has only 2/3 available subchannels set, which can be reused among

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femtocells in one macrocell.

4.5 The proposed scheme The proposed scheme without PHO Random allocation scheme Scheme based on reuse 3

4

1

0.8

3.5

The proposed scheme The proposed scheme without PHO Random allocation scheme Scheme based on reuse 3

Average throughput [b/s/Hz]

0.9

0.7 C.D.F

0.6 0.5

3 2.5 2 1.5

0.4

1

0.3

0.5

0.2

0

0.1 0 −20

0

20

40

60 80 100 The number of Femtocells

120

140

160

Fig. 7. Average throughput per FUE varying with the number of femtocells.

0 20 40 60 80 100 Reciprocal of co−tier intereference power received by FUE [dBm]

Fig. 6. CDF of the reciprocal of co-tier interference power received by FUEs.

Fig.7 depicts the average throughput per FUE varying with the number of femtocells. The simulation method to obtain the result is that all FUEs’ data rate requirements are equally increased until the average throughput cannot be improved any more. Seen from the figure, with the number of femtocells increasing, the average throughput per FUE decreases for all the four schemes due to the growth of interference. However, the proposed scheme is more robust to the growth of interference than the other schemes. As the number of femtocell is less than 30, the average throughput of the proposed algorithm without PHO can reach throughput performance of the proposed scheme. However, with the number of femtocells increasing, more collision interference deteriorates its performance. As for the scheme based on reuse 3, when the number of femtocells is below 40, orthogonal subchannel allocation between two tiers has its advantage. However, since its available subchannel set is limited, the average throughput per FUE falls sharply when the number of femtocells exceeds 80. As for the random allocation scheme, only 60% of the system frequency resource can be used by each femtocell makes its average throughput lowest when the number of femtocell is less than 60. However, when the number of femtocells exceeds 60, its average throughput declines more slowly due to the frequency hopping characteristic of this scheme. In addition, the convergence speed is irrelative to the number of femtocells, and the iteration is within 8 to 13 as the proposed iterative scheme converges in 95% femtocells. Due to the limited number of FUEs in one CSG femtocell, the iterative calculation burden of the proposed scheme is released. Hence, the proposed algorithm is suitable for the femtocell context. V. C ONCLUSION In this paper, we have constructed a problem of minimizing the co-tier and the cross-tier interference, the essence of which is a problem of joint resource allocation. The PHO based subchannel and power adaptation scheme is proposed to solve the problem. Performance evaluation results show that minimizing the interference radiated by each FBS is in turn

beneficial to reduce every FBS’s own required transmit power and improve its FUEs’ throughput. With comparison with three other schemes, the proposed scheme is better in reducing interference and the FBS’s transmit power, and improving the spectrum efficiency. The optimality of the constructed problem and the performance evaluation of the PHO scheme will be completed in our future work. ACKNOWLEDGMENT Key Project of Beijing Municipal Science & Technology Commission (No. D08080100620802), International Cooperation and Exchanges Project (No. S2010GR0902) and NSFC Project (No. 60872048, No. 60772112). R EFERENCES [1] 3GPP TR 25.967, ”Home NodeB Radio Frequency (RF) Requirements (FDD)”, v9.0.0. [2] 3GPP TR 36.922, ”LTE TDD Home eNodeB RF Requirements”, v1.3.0. [3] V. Chandrasekhar and J. G. Andrews. ”Spectrum Allocation in Tiered Cellular Networks”. IEEE Trans. Commun., Vol. 57, No. 10, pp. 30593068 ,Oct. 2009. [4] H.C. Lee and D.C. Oh, ”Mitigation of Inter-Femtocell Interference with Adaptive Fractional Frequency Reuse”, in proc. ICC, pp. 1-5, 2010. [5] I. Guvenc and M.R. Jeong, ”A Hybrid Frequency Assignment for Femtocells and Coverage Area Analysis for Co-Channel Operation”, IEEE Commun. Letters, Vol. 12, Issue 12, pp. 880-882, Dec. 2008. [6] V. Chandrasekhar, J. Andrews and A. Gatherer, ”Femtocell Networks: A Survey” IEEE Commun. Mag., Vol. 46, Issue 9, pp. 59-67, Sep. 2008. [7] V. Chandrasekhar and J.G. Andrews, ”Uplink Capacity and Interference Avoidance for Two-Tier Femtocell Networks”, IEEE Trans. Wireless Commun., Vol. 8, Issue 7, pp. 3498-3509, Jul. 2009. [8] D. Lopez-Perez, G. de la Roche, et al. ”Interference Avoidance and Dynamic Frequency Planning for WiMax Femtocells Networks”, in proc. ICCS 2008, pp. 1579-1584, Nov. 2008. [9] X. Chu, Y. Wu, L. Benmesbah, et al. ”Resource Allocation in Hybrid Macro/Femto Networks”, in proc. WCNC workshops, Sydney, Australia, pp 1-5, Apr. 2010. [10] 3GPP TR 36.921, ”LTE FDD Home eNodeB RF Requirements”, v2.0.0. [11] B. Korte, J. Vygen, Combinatorial optimization: theory and algorithms. Berlin: Springer, 2006. [12] 3GPP TS 25.913, ”Requirements for Evolved UTRA (E-UTRA) and Evolved UTRAN (E-UTRAN)”, v9.0.0. [13] A. Golaup, M. Mustapha, et al., ”Femtocell access control strategy in UMTS and LTE”, IEEE Commun. Mag., pp. 117-123, Sep. 2009. [14] 3GPP TR 36.814, ”Further advancements for E-UTRA physical layer aspects”, v9.0.0. [15] R4-092042, ”Simulation assumption and parameters for FDD HeNB RF requirements”, Alcatel-Lucent, picoChip Designs and Vodafone, 2009.

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