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[email protected],. ‡ [email protected].uk. Abstract—Macrocells may suffer serious uplink interference introduced by the deployment of co-channel femtocells.
IEEE ICC 2012 - Wireless Communications Symposium

Interference-Aware Resource Allocation in Co-Channel Deployment of OFDMA Femtocells Haijun Zhang†‡ , Xiaoli Chu‡, Wei Zheng†, Xiangming Wen†

† Beijing

‡ Centre

University of Posts and Telecommunications, Beijing, China for Telecommunications Research, King’s College London, London, UK Email: † [email protected], ‡ [email protected]

Abstract—Macrocells may suffer serious uplink interference introduced by the deployment of co-channel femtocells. In this paper, an interference-aware pricing-based resource allocation algorithm for co-channel femtocells is proposed to alleviate their interference to macrocells without degrading the femtocell’s capacity. The subchannel and power allocation problem is modeled as a non-cooperative game. A suboptimal subchannel allocation algorithm and an optimal power allocation algorithm are proposed to implement the resource allocation game. Simulation results show that the proposed algorithm not only improves the capacity of the macrocell but also the total capacity of the two-tier network, as compared with the unpriced subchannel allocation and Modified Iterative Water Filling (MIWF) power allocation algorithm.

I. I NTRODUCTION Recently, more and more data services happen in indoor environment [1], where the coverage of macrocell may be not so good because of the wall penetration loss and long transmission distance. Thanks to femtocell, the shortcoming of macrocell can be overcome. Femtocells can operate on either the same or different frequency band with macrocells. The latter case, which is also known as dedicated channel deployment, may not be preferred by operators for the scarcity of spectrum and difficulty of implementation; while in the former case, i.e., co-channel deployment where femtocells and macrocells share the spectrum [2], cross-tier interference could be severe [3][4]. However, due to the fundamental role of macrocells in providing cellular coverage, their capacity and coverage should not be affected by femtocell deployment. Game theory has been considered to mitigate interference in two-tier networks with co-channel femtocells. In [5–7], the minimization of co-tier and cross-tier interference though power control based on game theory is investigated. In [8], game theory, learning theory and stochastic approximation are used to reduce the interference of femtocells to macrocells. In [9], a recursive core approach is proposed to minimize the number of collisions and maximize the femtocells’ spatial reuse based on a cooperative coalitional game. In [10], a decentralized femtocell access strategy based on non-cooperative game is proposed to manage the interference between nearby femtocells and from femtocells to macrocells. However, most of these works [5–10] are based on either power control or subchannel allocation. There are also some works consider the resource allocation in Orthogonal Frequency Divi-

978-1-4577-2053-6/12/$31.00 ©2012 IEEE

sion Multiple Access (OFDMA) femtocell networks, such as [11], but the cross-tier interference has not been paid much attention. In [12], a distributed resource allocation scheme based on non-cooperative game and convex optimization is proposed to maximize the system capacity while controlling the interference introduced and suffered by each user. In [13], a Lagrangian dual decomposition based resource allocation scheme is proposed, but subchannels are allocated randomly. In [14], a joint subchannel and power allocation algorithm is proposed to maximize the capacity of the femto-tier in dense deployments, but the interference from femtocells to macrocells is not considered. In this paper, we propose an interference-aware resource allocation algorithm for the uplink of co-channel femtocells. Our objective is to maximize the femtocells’ capacity while maintaining the macrocells’ capacity by allocating subchannels and power in femtocells properly. The power and subchannel allocation is modeled as non-cooperative game, and interference pricing is included to limit the interference caused by femto users to macrocells. The rest of this paper is organized as follows: section II provides the system model and the problem formulation. In section III, the interference-aware resource allocation algorithm is proposed. Performance of the proposed algorithm is evaluated by simulation in Section IV. Finally, Section V concludes the paper. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION A. System Model We consider a two-tier OFDMA network where K cochannel Femto Base Stations (FBS) overlaid by a macrocell, and focus on resource allocation in the uplink of femtocells, that is the subchannel allocation for femto users and the power allocation on each subchannel. Let M and F denote the number of active macro users camping on a macrocell and femto users camping on a femtocell, respectively. All femtocells are assumed to be closed access [15]. It is assumed that there are direct wire connections for the FBSs to coordinate with the central Macro BS (MBS) [3][7][16][17]. System bandwidth of the OFDMA system is B, which is divided into N subchannels. The channel fading of each subcarrier is assumed the same within a subchannel, but may vary cross different subchannels.

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th Let uF femtocell k,n ∈ {1, 2, ...F } denote the user in the k th M using the n subchannel. Let ui,n ∈ {1, 2, ..., M } denote the user in the ith (i = 1 in this paper) macrocell using the nth subchannel. We define gk,uFj,n , gk,uM and gi,uFk,n as the channel gain i,n F from the transmitting user uj,n to the receiving FBS k, uM i,n to the receiving FBS k and the transmitting user uF to the k,n receiving MBS i on subchannel n, respectively. Let puFk,n and puM denote the power of the femto user uF k,n and the i,n M macro user ui,n , respectively. Therefore, the received signal to interference and noise ratio (SINR) for the femto user occupying the nth subchannel in the k th femtocell is given by: puFk,n gk,uFk,n γuFk,n = (1) K  2 puFj,n gk,uFj,n + puM g M + σ i,n k,ui,n j=1,j=k

where

K  j=1,j=k

puFj,n gk,uFj,n is the interference caused by other

co-channel femtocells, puM g M is the interference caused i,n k,ui,n 2 by the macrocell, and σ is the additive white Gaussian noise power. th The SINR for the macro user uM subchannel i,n using the n is given by: = γuM i,n

puM g M i,n i,ui,n K  j=1

puFj,n gi,uFj,n +

CuFk,n =

B log2 (1 + γuFk,n ) N

(3)

CuM = i,n

B log2 (1 + γuM ) i,n N

(4)

B. Problem Formulation Let pnj denote the power on subchannel n of femto user j(j ∈ {1, 2, . . . , F }). Our target is to maximize the total capacity of the K femtocells, i.e., N K   k=1 n=1

CuFk,n

(5)

⎧ N  ⎪ ⎪ ⎪ pnj ≤ pmax , ∀j ∈ {1, 2, . . . , F } , ⎨ s.t.

max

K  k=1

CuFk,n , ∀n ∈ {1, 2, ..., N }

s.t. 0 ≤ puFk,n ≤ pmax , ∀n ∈ {1, 2, ..., N} , ∀k ∈ {1, 2, ..., K}

(8)

In this section, we first present a non-cooperative game theory [18] based power allocation assuming subchannel allocation is given, and then propose a subchannel allocation algorithm. Both algorithms protect macro users by pricing the femto users according to their cross-tier interference to the macrocell. A. A Game Theoretic Framework Based on the microeconomic theory [19], we model the femtocell resource allocation problem as a femtocell noncooperative resource allocation game (FNRAG). Femto users in each femtocell are considered as selfish, rational players. Each of them tries to maximize their utility without considering other users’ interest. The FNRAG can be denoted by,

G = S n , {An , P n }, μcn , F F where S n = {uF 1,n , u2,n , ..., uK,n }, ∀n ∈ {1, 2, ..., N} is the set of the femto users using the nth subchannel in the K femtocells; {An , P n } is the strategy space F F of the players, An = {aF 1,n , a2,n , ..., aK,n } and P n = {puF1,n , puF2,n , ..., puFK,n } are the subchannel allocation strategy space and power allocation strategy space, respectively, F F aF k,n ∈ {1, 2, ..., F }, e.g., ak,n = uk,n means the subchanF nel n is occupied by user uk,n in femtocell k. μcn = {μcuF , μcuF , ..., μcuF } is the set of net utility functions; 1,n

2,n

K,n

p−uFk,n = {puF1,n , ..., puFk−1,n , puFk+1,n , ..., puFK,n } and aF −k,n = F F F {aF , ..., a , a , ..., a } are the power vector of 1,n k−1,n k+1,n K,n co-channel femto users other than uF and the subchannel k,n allocation vector of subchannel n in all femtocells except for femtocell k, respectively. Definition 1 Player uF k,n ’s best response given the power allocation and subchannel allocations of all other co-channel femto users is expressed as, ˆF (ˆ puFk,n , a k,n ) = arg

max

puF

k,n

,aF k,n

μcuF (puFk,n , aF , aF k,n |p−uF −k,n ) k,n k,n

(9)

n=1

n if uF , else pnj = 0 ⎪ k,n = j, then pj = puF k,n ⎪ ⎪ ⎩ p F ≥ 0, ∀n ∈ {1, 2, ..., N} ; ∀k ∈ {1, 2, ..., K} uk,n

(7)

III. I NTERFERENCE -AWARE R ESOURCE A LLOCATION

(2) σ2

Based on Shannon’s capacity formula, the capacities (i.e., maximum achievable data rate) of the user who occupies the nth subchannel in the k th femtocell and in the macrocell are given respectively by:

max

power allocation are independent for each subchannel, then the maximization of the total capacity of femtocells is equivalent to the maximization of the total capacity of k femtocells on each subchannel, so the problem (5) under constraint (6) can be simplified as:

B. Interference-Aware Power Allocation

(6) As shown in (6), a femto user’s total transmit power is constrained by pmax , and the power allocated to each subchannel is nonnegative. If the subchannel allocation and

When μuFk,n = CuFk,n , a player will tend to maximizing its utility by using the maximum power, because CuFk,n monotonically increases with puFk,n for fixed p−uFk,n according to (1) and (3). This will lead to severe uplink interference to the

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macrocell, so this solution is far from Pareto-optimality [19]. In order to decrease the interference introduced by femto users, a price should be paid by femto users for causing interference to macrocell. The pricing function of femto user uF k,n can be modeled as: cuFk,n = αgi,uFk,n puFk,n

(10)

+

where α ∈ R (bps/W) is the price coefficient charged on femto user. Consequently, the net utility function can be expressed as: μcuF

k,n

= μuFk,n − cuFk,n

(11)

Nash Equilibrium (NE) is defined as the fixed points where no player can improve their utility by change its strategy unilaterally [19]. We want to find whether Nash Equilibrium exists for the power vector of femto users on an individual subchannel. For the proposed non-cooperative game, the Nash Equilibrium is defined as follows. puF1,n , pˆuF2,n , ..., pˆuFK,n } as the Definition 2 Denote Pˆ n = {ˆ optimal transmitting power vector of the K co-channel femto users under Nash Equilibrium, if the following equation is satisfied ∀uF k,n ∈ Sn , μcuF (ˆ puFk,n , pˆ−uFk,n ) ≥ μcuF (puFk,n , pˆ−uFk,n ), ∀puFk,n ∈ Pn . k,n k,n (12) ˆ −uF = {ˆ where p p F , ..., p ˆ F , p ˆ F , ..., p ˆ F } is u1,n uk−1,n uk+1,n uK,n k,n the optimal transmitting power vector of the K co-channel femto users under Nash Equilibrium except for uF k,n . Theorem 1: A Nash Equilibrium exists in the FNRAG: G = S n , {An , P n }, μcn . Proof: According to [19], the Nash Equilibrium exists if the following two conditions are satisfied: P n is non-empty, convex and compact in the finite Euclidean space RK . μcn is continuous and concave with P n .

1) 2)

Since the power allocated on each subchannel is constrained between zero and the maximum power pmax , with each femtocell condition 1) can be easily satisfied if the power vector is convex and compact. For condition 2), substituting (10) into (11), we have: μcuF (puFk,n |p−uFk,n ) k,n

=

B N log2 (1

+

puF

k,n

gk,uF

In,k

where In,k denoted the

k,n

) − αgi,uFk,n puFk,n

K  j=1,j=k

(13)

puFj,n gk,uFj,n + puM g M + i,n k,ui,n

σ 2 . It can be seen from (13) that μcn is continuous with P n . To prove the quasi-concave property of (13), to take the first order derivative of (13) with respect to puFk,n , ∂μcuF

k,n

∂puFk,n

=

Bgk,uFk,n

Taking the second order derivative of (13) with respect to pμFk,n yields: ∂ 2 μcuF

k,n

∂p2 uFk,n

2

=−

(15)

Therefore, ucuF is a quasi-concave function of puFk,n . Since k,n both conditions 1) and 2) hold, a Nash Equilibrium exists in the FNRAG. This completes the proof.  Lemma 1: The best power allocation response of the FNRAG in (9) is given by:

pmax 1 B In,k · − (16) pˆuFk,n = N ln 2 αgi,uFk,n gk,uFk,n 0

Proof: It is obtained by setting (14) to zero and solving the resulting equation for puFk,n . Notation [x]ba means min{max{a, x}, b}.  Since (16) should be nonnegative, and the price α is nonnegative too, we get gk,uFk,n B · (17) 0≤α≤ N ln 2 gi,uFk,n In,k Theorem 2: The FNRAG has a unique Nash Equilibrium. Proof: Due to limited space, the detailed proof is not presented here, which can be found in [5].  C. Interference-Aware Subchannel Allocation In this subsection, the subchannel allocation is studied based on the method in [18][20]. The difference between our work and [18][20] is that we protect macro users by pricing the femto users according to their interference to macro users in femtocell subchannel allocation. Given the power vector on subchannel n of femto users , the subchannel allocation probother than uF k,n , i.e., p−uF k,n lem can be written as: c F aF∗ ) k,n = arg max μuF (ak,n |p−uF k,n uF k,n

k,n

(18)

Substituting (13) into (18), (18) can be written as: puF gk,uFk,n B u ˆF ( log2 (1 + k,n ) − αgi,uFk,n puFk,n ) k,n = arg max N In,k uF k,n (19) Denote γˆ as the SINR when a femto user maximizes its utility, the corresponding transmit power of the femto user is γ ˆ In,k g F . Substituting the transmit power and the SINR( that k,u k,n

maximize the utility) into (18), we obtain

γ ˆ In,k B F uˆk,n = arg max N log2 (1 + γˆ ) − αgi,uFk,n g F uF k,n

gi,uF

= arg min g uF k,n

− αguM ,uF (14)  i,n k,n N ln 2 In,k + puFk,n gk,uFk,n

(gk,uFk,n ) B ≤0 N ln 2 (In,k + puF gk,uF )2 k,n k,n

k,n

k,uF k,n

k,u k,n

(20)

In,k

That is, to maximize the net utility for subchannel n, the FBS allocates it to a user according to (20).

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Since the optimal solution of the joint subchannel and power allocation is of a high complexity, we propose a suboptimal decomposition method to implement it, as shown in algorithm 1. Though the NE point is unique, it still needs an iterative algorithm to converge to it. The main idea of the suboptimal algorithm(Algorithm 1) is to decouple problem (5) into two subproblems, i.e., suboptimal subchannel allocation and optimal power allocation:

are simplified modeled as λd−4 and λd−3 respectively, where λ= 2 × 10−4 [5]. Besides, α is selected as 4 × 104 by try-anderror method in simulation. Femto user’s and macro user’s maximum transmit powers are assumed as 20dBm and 30 dBm, respectively. 9

12

Algorithm 1 Implementation Algorithm for FNRAG 1: Subchannel set: N = {1, 2, ..., N }, Femto User set: F = {1, 2, ...F }, FBS set: K = {1, 2, ...K} 2: Suboptimal Subchannel Allocation Algorithm 3: allocate the power equally to each subchannel; MF FF 4: calculate gi,k,u,n and gk,k,u,n , the channel gain on channel n from user u in femtocell k to MBS i and FBS k, respectively; 5: calculate Ik,u,n , the interference suffered by user u in femtocell k on channel n ; 6: for k = 1 to K do 7: for u = 1 to F do MF gi,k,u,n 8: a) find n∗ = arg min gFF Ik,u,n ; n∈N

11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23:

k,k,u,n

b) aF k,n∗ = u; c) N = N − n∗ ; end for while N = φ do a) find (u∗ , n∗ ) = arg min

Proposed FNRAG, K=20 USSA+MIWF, K=20 Proposed FNRAG, K=30 USSA+MIWF, K=30 Proposed FNRAG, K=50 USSA+MIWF, K=50

8 K=50

6 K=30

4 K=20

2

0 1

1.5

2

2.5 3 3.5 4 4.5 Number of Femto Users per Femtocell

5

5.5

6

Capacity of Femtocell versus F under M = 8

Fig. 1.

Fig.1 shows the total capacity of the femto-tier in both algorithms. As can be seen from the figure, the proposed FNRAG algorithm improve the total capacity of the femtotier over the USSA and MIWF Algorithm without Pricing by 5% ∼ 10% when the number of femto users per femtocell is larger than 3.

MF gi,k,u,n Ik,u,n ; FF g n∈N k,k,u,n

∗ b) aF k∗,n∗ = u ; c) N = N − n∗ ; end while end for Optimal Power Allocation Algorithm for k = 1 to K do for n = 1 to N do calculate (16); end for end for

7

5.5

x 10

5

4.5 Capacity of Macrocell(bps)

9: 10:

x 10

10 Total Capacity of Femtocell System(bps)

D. Suboptimal Algorithm

4

3.5

3

2.5

2

IV. S IMULATION R ESULTS AND D ISCUSSION

Proposed FNRAG, K=20 USSA+MIWF, K=20 Proposed FNRAG, K=30 USSA+MIWF, K=30 Proposed FNRAG, K=50 USSA+MIWF, K=50

1.5

Simulation results are given in this section, an Unpriced Suboptimal Subchannel Allocation(USSA) algorithm [21] and optimal power allocation based on the MIWF algorithm [22] without pricing the interference caused by femto users to macro-tier, are compared with the proposed interference-aware resource allocation algorithm. In the simulation, femtocells and macro users are randomly distributed in macrocell and share spectrum. The carrier frequency of 2GHz, B = 10M Hz, N = 50 and M = 50 are used in the simulation. The channel-fading is modeled as i.i.d Rayleigh random variables with mean variance of 1. The channel gain (including the pathloss, antenna gain except channel-fading) for indoor femto user and outdoor macro user

1 1

Fig. 2.

1.5

2

2.5 3 3.5 4 4.5 Number of Femto Users per Femtocell

5

5.5

6

Capacity of Macrocell versus F under M = 8

Fig.2 shows the macrocell’s capacity when the number of femto users per femtocell increases. It can be observed that the proposed FNRAG scheme outperforms the MIWF by up to 23%. We can see: the proposed FNRAG has strength in capacity compared to the USSA and MIWF Algorithm, especially for the improvement of the macrocell’s capacity, which alleviates the interference suffered by macro users.

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V. C ONCLUSION In this paper, an interference-aware resource allocation algorithm is proposed. The problem of subchannel and power allocation is modeled as a non-cooperative game. Moreover, a suboptimal subchannel allocation algorithm and optimal power allocation are proposed to implement the game. The proposed FNRAG algorithm has better performance in terms of capacity of the femtocells and the macrocell compared with MIWF algorithm. In the future, resource allocation in femtocells with limited feedback will be investigated [23, 24].

[10]

[11]

[12]

ACKNOWLEDGMENT The authors would like to thank Dr. David L´opez-P´erez for his helpful discussions. This work was supported by the Cobuilding Project of Beijing Municipal Education Commission “G-RAN based Experimental Platform for Future Mobile Communications”, the National Natural Science Foundation of China (61101109), and National Key Technology R&D Program of China (2010ZX03003-001-01, 2011ZX03003-00201).

[13]

[14]

[15]

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