An Inter-cell Interference Coordination Algorithmfor OFDMA Forward Link

Dandan Wang, Bo Wei, Mazin Al-Shalash

Huawei Technologies USA

1700 Alma Dr., Plano, TX 75075

Email: {dwang, wbo, mshalash}@huawei.com

Abstract—In OFDMA systems, reducing the inter-cell interfer-ence among adjacent cells is a very important issue especially forthe cell-edge users. In this paper, we propose a distributed algo-rithm that maximizing the system total throughput consideringproportional fairness. In our proposed algorithm, the frequencyresources in each cell is divided into high and low power regions.The bandwidth allocations within a cell is adapted on a large-time scale, while the transmission power is adapted on a small-time scale, so as to be practical for dynamic scheduling. Theproposed algorithm only needs limited inter-cell coordination,and guarantees the fairness among different users and cells.Simulation results show that our proposed algorithm convergesquickly and achieves good throughput compared with otheralgorithms.

I. INTRODUCTION

Orthogonal Frequency Division Multiplexing (OFDM) has

been adopted in various standards. Due to the orthogonality

among different sub-carriers, there is ideally no intra-cell inter-

ference among different users inside a single cell. However,

in multi-cell scenarios, inter-cell interference from adjacent

cells may become the performance limiting factor, especially

for users at the cell edge. In this paper, our focus is on

forward link inter-cell interference coordination (ICIC). Two

approaches have been used to address the problem of ICIC in

the literature. The first approach is to formulate this problem as

a resource allocation problem in a multi-cell system, and then

solve this optimization problem to obtain the instantaneous

sub-carrier and power allocations. Some suboptimum semi-

distributed scheme has been proposed in [1][2] to reduce

the calculation complexity of the non-convex optimization

problem. However, these semi-distributed scheme involves the

exchange of a potentially huge amount of information among

BSs, such as the path loss of each user from each of the

adjacent BSs. The second approach is to reuse the frequency

band among adjacent cells, such as soft frequency reuse (SFR),

partial frequency reuse (PFR) and fractional power reuse

(FPR) [3][4][5]. However, they did not give the distributed

algorithm to adapt the power and bandwidth according to

different load conditions. The distributed algorithm in [6], [7]

shows good convergence, but they combine the scheduling

problem with the ICIC together. In this paper, different from

the other algorithms proposed in the literature, we view ICIC

as a large time scale operation. We aim to gain some insights

into this inter-cell interference coordination problem. After

obtaining the power and bandwidth allocation from the ICIC

algorithm, different scheduling algorithms can be applied.

In this paper, we also consider the fairness among different

users and cells in our ICIC scheme design. We proposed a

distributed algorithm which needs very limited information

exchange among cells and also shows good performance with

fast convergence compared with other algorithms.

The remainder of this paper is organized as follows: In

Section II, the system model and problem formulation are

presented. In Section III, a two-cell model is given as an

exmaple to gain some insight and several classical approaches

in the literature are presented. Our proposed algorithm is

presented in Section IV. Simulation results are given in Section

V. Finally, Section VI concludes the paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION

In this paper, we consider a OFDMA system with multiple

cells and the carriers are groups into resource block (RB) in

each cell. There is no inter-carrier interference among different

RBs in the same cell while simultaneous communications in

the same RB in different cells introduce inter-cell interference.

Further, we assume the inter-cell interference is with Gaussian

distribution and the associated spectrum efficiency for a par-

ticular user is given as

C = Blog2(1 +PG

N0 + I), (1)

where B is the allocated bandwidth for this user, P is the

transmission power density, and G is the channel gain between

this user and its serving cell and I denotes the interference

received from the other cells. We assume the system is a fully

loaded system, in which each cell is serving multiple users

randomly distributed in the cell. Similar to the approached

used in [4], all the users in each cell are partitioned into two

groups: cell-center (noise- limited) and cell-edge (interference-

limited) groups. For cell-center group, the interference-and-

noise term in (1) is dominated by the noise. For cell-edge

group, the inter-cell interference dominates over the thermal

noise. For tractability, in the following analysis, we abstract all

the users into two users: a cell-center user and a cell-edge user.

978-1-4244-2515-0/09/$25.00 ©2009 IEEE

After we obtain the power and bandwidth allocation from the

two-user model, different scheduling algorithm can be utilized.Fairness is one of the key issues for any interference

coordination schemes. In this paper, we aim to achieve theproportional fairness. Let N denote the number of cells andCn,i(n = 1, 2, ...N) denote the throughput associated with thei(i = 1, 2)th group in the nth cell. Thus, our objective of theoptimization becomes:

maxP n

i ,Bni

{∑

n,i

log10(Cn,i)}

subject∑

i

P ni Bn

i ≤ Ptot, ∀n

∑

i

Bni ≤ Btot, ∀n,

(2)

where Btot and Ptot are the total bandwidth and total

transmission power, respectively. Pni and Bn

i denote the trans-

mission power and bandwidth associated with the ith group

in the nth cell.

III. TWO CELL MODEL AND ICIC ALGORITHMS

In this section, we model a simplified system with two-cell-

four-users to get some insights. Let us assume user 1 and user

2 are in cell 1 while user 3 and user 4 are in cell 2, respectively

(see Fig. 1). In addition, one of them is assumed to be closer

to the base station (BS) and considered to be a cell-center user

(i.e. user 1 and 3) while the other is closer to the cell edge (i.e.,

user 2 and 4). Note that for simplicity, the notations in this

section are different from the above section. Let Gi,j denote

the link gain between ith BS and jth MS, which represents

the large scale pathloss and the antenna gain. Let B denote the

total number of RBs in the system. Let Bi,0 and Bi,1 denote

the number of RBs allocated to user i with and without the

co-channel interference from another cell, respectively. Let Pi

denote the transmission power density associated with the ithMS.

Cell 1 Cell 2

P1G11

P2G12

P4G24P3G23

MS1

MS2

MS4

MS3

G14

G13

G22

G21

Fig. 1. Two-cell-four-user scenario

In the following, four ICIC algorithms are presented.

A. Scheme A: Reuse factor=1 with constant average power

In this approach, the constant power level Pavg is given on

all the RBs. The frequency reuse factor is “1”, which means

that both cells use up all the bandwidths. Note that in the

forward link, it is the transmission power of the adjacent cells

on each RB that determines the interference. To which user

the RB is allocated does not have impact on the interference to

other cells. In this scenario, since all RBs receives interference

from another cell, Bi,0 = 0 for i = 1, 2, 3, 4.

C1 = B1,1log2(1 +PavgG11

N0 + PavgG21) (3)

C2 = B2,1log2(1 +PavgG12

N0 + PavgG22) (4)

C3 = B3,1log2(1 +PavgG23

N0 + PavgG13) (5)

C4 = B4,1log2(1 +PavgG24

N0 + PavgG14) (6)

where B2,1 = B − B1,1 and B4,1 = B − B3,1. This scheme

is try to find the optimum allocation of B1,1 and B3,1. In this

case, the optimization problem simplifies into

max{log10B1,1 + log10(B − B1,1)} (7)

and

max{log10B3,1 + log10(B − B3,1)} (8)

Thus, the optimum allocation of the bandwidth is B1,1 = B2

and B3,1 = B2 .

B. Scheme B: Reuse factor=1 with different power levels

In forward link, increasing the transmission power should

increase the throughput of the target cell while also causing

more interference into adjacent cells. Thus, to reduce the

interference to other cells, each base station should transmit

as low power as possible. For the cell-edge users, high trans-

mission power is necessary to guarantee their throughput due

to the large path loss. While for cell-center users, reducing the

transmission power could effectively reduce interference to the

other cells without significant impact to their own throughput

(since they are already in high signal-to-noise region). Thus,

it is reasonable to assume the frequency resources of each

cell can be divided into two power regions, a high power

region used mostly for allocations to cell edge users, and a low

power region for cell center users. By mutually avoiding the

high power regions from other cells, some level of frequency

reuse is achieved. In scheme B, all the cells use up all the

frequency resource but different bands are allocated to differ-

ent transmission power to reduce the interference and improve

the throughput. Similar to scheme A, since all RBs receives

interference from another cell, Bi,0 = 0 for i = 1, 2, 3, 4. Two

scenarios based on the overlap of the high-power region of

two cells are illustrated in Fig. 2.

1) Scenario (a):

C1 = B1,1log2(1 +P1G11

N0 + P4G21) (9)

C2 = (B4,1−B1,1)log2(1+P2G12

N0 + P4G22)+B3,1log2(1+

P2G12

N0 + P3G22)

(10)

C3 = B3,1log2(1 +P3G23

N0 + P2G13) (11)

Fig. 2. Reuse factor=1 with different power levels

C4 = B1,1log2(1 +P4G24

N0 + P1G14)

+ (B4,1 − B1,1)log2(1 +P4G24

N0 + P2G14)

(12)

and

Pavg ∗B = P1∗B1,1+P2∗B2,1 = P3∗B3,1+P4∗B4,1 (13)

2) Scenario (b):

C1 = B4,1log2(1 +P1G11

N0 + P4G21)

+ (B1,1 − B4,1)log2(1 +P1G11

N0 + P3G21)

(14)

C2 = B2,1log2(1 +P2G12

N0 + P3G22) (15)

C3 = B2,1log2(1 +P3G23

N0 + P2G13)

+ (B1,1 − B4,1)log2(1 +P3G23

N0 + P1G13)

(16)

C4 = B4,1log2(1 +P4G24

N0 + P1G14) (17)

and

Pavg ∗B = P1∗B1,1+P2∗B2,1 = P3∗B3,1+P4∗B4,1 (18)

C. Scheme C: Reuse factor=2

In this scheme, the reuse factor is 2, which means the

frequency used by the two cells do not overlap. Two power

levels are also applied in this scheme. Since there is no

interference on the RBs allocated to each cell, Bi,1 = 0.

Fig. 3. Reuse factor=2 with different power levels

C1 = B1,0log2(1 +P1G11

N0) (19)

C2 = B2,0log2(1 +P2G12

N0) (20)

C3 = B3,0log2(1 +P3G23

N0) (21)

C4 = B4,0log2(1 +P4G24

N0) (22)

and the constraints are

Pavg ∗B = P1∗B1,0+P2∗B2,0 = P3∗B3,0+P4∗B4,0 (23)

and

B1,0 + B2,0 + B3,0 + B4,0 = B. (24)

D. Scheme D: Soft Reuse

In this scheme, some RBs are shared by both cells while

the other parts do not overlap with each other. Let B0 denote

Fig. 4. Soft Reuse with constant power allocation

the bandwidth shared by both cells. Since users transmitting

on the shared bandwidth will receive the interference from

adjacent cells, it is reasonable to allocate the shared bandwidth

to the cell-center users. Thus, B0 = B1,1 = B3,1. Then, the

capacities of different users can be calculated as

C1 = B0log2(1+P1G11

N0 + P3G21)+B1,0log2(1+

P1G11

N0) (25)

C2 = B2,0log2(1 +P2G12

N0) (26)

C3 = B0log2(1+P3G23

N0 + P1G13)+B3,0log2(1+

P3G23

N0) (27)

C4 = B4,0log2(1 +P4G24

N0) (28)

and

Pavg∗B = P1∗(B0+B1,0)+P2∗B2,0 = P3∗(B0+B3,0)+P4∗B4,0.(29)

In this paper, we only consider the constant power allocation

in the soft reuse scheme.

IV. PROPOSED ALGORITHM

In this section, similar to scheme B, we adopt the idea of

fractional power reuse and assume the frequency resources of

each cell can be divided into two power regions, a high power

region used mostly for allocations to cell edge users, and a low

power region for cell center users. we assume that there exist

inter-cell coordination messages that carry bandwidth alloca-

tion information such as the location of the high-power region

and low-power region and also the corresponding high-power

and low-power. After each cell receives this information, it

will try to avoid the high power region by allocating the low

power on this region (which means to allocate this part of

bandwidth to cell-center users). If a cell can not find enough

bandwidth to allocate its high power region, it will overlap

part of the high power region of the cells with the lowest high

transmission power. Because of the dynamic characteristic of

the user distribution, these high/low power regions should be

TABLE IMODULATION AND CHANNEL CODING SCHEMES

Cellular layout 2 cells, 1 sector/cellDistance to cell 1 [0.2 0.9 1.6 1.2]kmDistance to cell 2 [1.8 1.1 0.4 0.8]kmNo. of subcarriers 600BS transmit power 43 dBmBS antenna gain 17 dBMS antenna gain 0 dBother loss 12 dBSubcarrier noise figure 10 dBThermal noise density -174.0 dBm/Hz

adaptive in nature. Any fast fading related small scale power

boosting or reduction can be taken care of by the scheduler

by moving the resource back and forth into different region.

In the following, we propose a distributed algorithm by

joint adaptation of the power and bandwidth. The algorithm

is performed in the nth cell as follows:

Initially set Bn,1 = Bn,2 = Btot

2 .

First for a given setting of Sm = (Bn,1, Bn,2), adaptively

adjust the power for each cell as follows:

Initial setting Pn,1 = Pn,2 = Pavg = Ptot

Btot.

At kth iteration, calculate C(Sm, k) = log10(Cn,1) +log10(Cn,2) based on the current Bn,i, n = 1, 2, ...N, i = 1, 2.if C(Sm, k) > C(Sm, k − 1)Pn,1 = max(Pn,1 − Δ, 0), where Δ is the power adjuststepsize, and update Pn,2 accordingly.;elsePn,1 = Pn,1 + Δ;end.The algorithm runs until it reaches a convergence point,(Let

Cmax(Sm) denote the achieved throughput) and begin to

adjust the bandwidth allocation as the follows:

if Cmax(Sm) > Cmax(Sm−1),Sm+1 = Sm + 1,elseSm+1 = Sm − 1,endNote that the operation Sm + 1 means that the current

bandwidth of Bn,1 is increased by 1 while Sm − 1 means

that the current bandwidth of Bn,1 is decreased by 1. For

multiple users in the system, according to the cell-center/cell-

edge group, detailed scheduling algorithms can be applied as

defined in [8].

V. SIMULATION RESULTS

A. Simulation settings

The simulation settings is given in table I.

B. Simulation Results

In this section, simulation results are provided to illustrate

the performance of the proposed algorithm.

The maximum spectrum efficiency of scheme A is 2.0168

bps/Hz as shown in Fig.5. The maximum spectrum efficiency

of scheme B is 2.7177 bps/Hz as shown in Fig.6. The

bandwidth allocated to user 1 is 35, user 2 is 15, user 3

010

2030

4050

010

2030

4050

0

0.5

1

1.5

2

2.5

B11

B31

Spectr

um

effie

ncy (

bps/H

z)

Fig. 5. Spectrum efficiency of scheme A

01

23

45

01

23

450

0.5

1

1.5

2

2.5

3

P1/PavgP

3/Pavg

Sp

ectr

um

eff

ien

cy (

bp

s/H

z)

Fig. 6. Spectrum efficiency of scheme B

is 33, user 4 is 17. The relative power compared with the

average power, which is the ratio of the allocated power to

the average power, allocated to user 1 is 0.1, user 2 is 3.1,

user 3 is 0.2, user 4 is 2.55. From Fig. 6, we can see that

the eNB tends to allocate more power to the cell-edge users

and smaller bandwidth. The maximum spectrum efficiency of

scheme C (Fig.7) is 2.3553 bps/Hz. The maximum spectrum

efficiency is achieved when the bandwidth allocated to user

1 is 13, to user 2 is 12, to user 3 is 13, and to user 4 is

12. The relative power allocated to user 1 is 1.3, to user 2

is 2.7583, to user 3 is 1.6, to user 4 is 2.43. The maximum

01

23

45

0

1

2

3

4

50

0.5

1

1.5

2

2.5

P1/PavgP

3/Pavg

Sp

ectr

um

eff

ien

cy (

bp

s/H

z)

Fig. 7. Spectrum efficiency of scheme C

010

2030

4050

0

10

20

30

40

500

0.5

1

1.5

2

2.5

3

B1,0

+B2,0

B1,0

+B2,0

+B3,0

+B4,0

Spectr

um

effic

iency (

bps/H

z)

Fig. 8. Spectrum efficiency of scheme D

spectrum efficiency of scheme D (Fig.8) is 2.6431 bps/Hz. The

maximum spectrum efficiency is achieved when the shared

bandwidth is 24, the non-overlapping bandwidth allocated to

user 1 is 1, allocated to user 2 is 12, to user 3 is 1, to user 4

is 12. In table II, the comparison of the maximum spectrum

efficiency achieved under different schemes are given where

scheme E is our proposed scheme. Note that the main different

between scheme B and E is scheme B is the centralized

upper bound solution of scheme E. From table II, we can

see that scheme B with the power adjustment can achieve

the best performance, which is consistent with the observation

made in [4]. Our proposed distributed algorithm only loss a

little spectrum efficiency (from 2.71 to 2.68) compared with

TABLE IICOMPARISON OF DIFFERENT SCHEMES

Schemes A C D B EThroughput 2.0168 2.3553 2.6431 2.7177 2.6805

the centralized scheme B. The convergence of the proposed

algorithm is shown in Fig. 9.

0 5 10 15 20 25 30 35 40 45 502

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Iteration

Spec

trum

effici

ency

(bps

/Hz)

Fig. 9. Spectrum efficiency of the proposed algorithm

VI. CONCLUSION

In this paper, we investigate the ICIC problem in OFDMA

systems. Using the simplified two-cell-four-user model as an

example, we look into some classical solution for the ICIC

problem and gain some insights of this problem. Furthermore,

we propose a distributed algorithm that maximizing the system

total throughput considering proportional fairness. The pro-

posed distributed algorithm divide all the frequency resources

into two regions: high power and low power region. The

bandwidth allocations within a cell is adapted on a large-time

scale, while the transmission power is adapted on a small-

time scale. The proposed algorithm only needs limited inter-

cell coordination, and guarantees the fairness among different

users and cells. Simulation results show that our proposed

algorithm converges quickly and achieves good throughput

compared with other algorithms. Investigation on the impact

of the distance between cells and the location of the users is

our future work.

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[2] C. Koutsimanis, “Inter-cell interference coordination techniques for multi-cell ofdma networks supporting narrow band and elastic services,” M.S.thesis, Royal Institute ofTechnology, 2007.

[3] 3GPP, R1-051059, ”Inter-Cell Interference Mitigation for EUTRA”,TI.[4] X. Wu, A. Das, J. Li, and R. Laroia, “Fractional power reuse in cellular

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