Abstract  —We propose an incremental frequency reuse (IFR)

scheme that reuses effectively the radio spectrum through sys-

tematic segment allocation over a cluster of adjoining cells. It

divides the entire frequency spectrum into several spectrum

segments. Based on the above segmentation, a set of cell- spe-

cific segment allocation sequences is designed for universal

frequency reuse. Here, each sequence defines its own base seg-

ment and allocation order. The designed sequences are then

assigned to respective cells over the cell cluster. In this scheme,

the base segments over the cell cluster are mutually

non-overlapped and collectively exhausted, and the added

segments are interfered with from surrounding cells, but only in

an incremental and coordinated manner. Hence, the proposed

scheme can provide better reuse efficiency over the conven-

tional ones such as the classical universal frequency reuse

scheme and the soft frequency reuse (SFR) scheme. In addition,

the simple and flexible IFR scheme can be easily configured as

most existing reuse schemes only by redefining the set of seg-

ment allocation sequences. A system-level simulator for an

orthogonal frequency division multiple access (OFDMA) cellu-

lar system covering surrounding cells up to 3rd-tier has been

implemented. Simulation results show that the IFR scheme

provides quite better reuse efficiency as compared to the clas-

sical universal reuse scheme and the SFR scheme, especially at

the cell-edge region.

 Keywords —Cellular System, Frequency Reuse, Incremental

Frequency Reuse, OFDMA

I.  INTRODUCTION

Over last two decades, there has been an upsurge of de-

mands for mobile and wireless communications from several

 points of view such as new services and the number of sub-

scribers [1]-[2]. In addition, next-generation mobile com-

munication systems should be able to meet high-quality ser-

vice requirements such as high-quality video and high-speed

Internet over wireless networks at the lowest possible price.

In particular, tremendous interests in multimedia services are

fueling the need for very high data rates in future wireless

networks [1]. However, a radio spectrum might be lacking for

supporting these demanding services unless an ep-

och-making improvement in spectrum utilization has been

done [1]-[2].

So far, several advanced mechanisms have been developed

for better use of a radio spectrum. They include adaptive

modulation and coding [3]-[4], hybrid automatic repeat re-

quest [5], fast channel-aware scheduling [6]-[7], and multi-

 ple-input multiple-output techniques [8]. Despite those ef-

forts, there are still a lot of limiting factors to the system

capacity in wireless cellular systems. In particular, inter-cell

interference (ICI) from neighboring cells is one of major

limiting factors to the achievable signal-to-interference-plus-

noise ratio (SINR) and the system capacity, especially at the

cell-edge region.

In classical cellular systems, frequency reuse mechanisms

have been adopted in order to avoid ICI from neighboring

cells [9]. Such mechanisms limit the utilization of the avail-

able frequency spectrum, of which amount is determined by

the frequency reuse factor (FRF) adopted. Hence, the FRF of

one or near one is getting one of most desirable features for

upcoming systems. However, the classical universal fre-

quency reuse scheme suffers from severe ICI from adjoining

cells [9]-[10] because of its tight frequency reuse.

Recently, some promising flexible spectrum reuse

schemes [10]-[13] have been proposed such as the SFR

scheme adopted in the 3GPP-LTE system [10], [12] and the

fractional frequency reuse (FFR) scheme [13]. Among them,

the SFR scheme achieving FRF-one can overcome severe ICI

from adjoining cells at a cell-edge region, by emphasizing a

 part (called as the primary band) of the available radio spec-

trum and allocating it preferentially for cell-edge users.

However, it still may incur even severer ICI to some of

cell-edge users, because the high-powered primary band can

accommodate only a pre-defined number of cell-edge users,

while the remaining cell-edge users may be allocated to lim-

itedly -powered secondary bands.

In this paper, we propose an IFR scheme that reuses ef-

fectively the radio spectrum by allocating systematically

spectrum segments over a cluster of adjoining cells. It divides

the entire frequency spectrum into several segments. A set of

cell-specific segment allocation sequences is designed for

universal frequency reuse. Here, each sequence defines its

 base segment and allocation order for additional segments.

The designed sequences are assigned to respective cells over

the cluster. In this scheme, all the base segments within the

cell cluster are mutually non-overlapping and collectively

exhausted, and the added segments are interfered with from

surrounding cells, but only in an incremental and coordinated

manner. In each cell, the base segment is occupied first, and

then the remainder of traffic channels is allocated over the

added segments. Hence, the IFR scheme can provide better

reuse efficiency over the conventional ones. To verify the

effectiveness of the proposed scheme, a system-level simu-

lator for an OFDMA cellular system covering surrounding

cells up to 3rd-tier is implemented. We use the outage prob-

ability, spectral efficiency, and overall cell capacity as per-

formance measures.

II.  SYSTEM MODEL

 A.  Spectrum Reuse and Inter-cell Interference

In this subsection, we deal with a spectrum reuse strategy

and an ICI model for a generic cellular system.

Fig. 1(a) and (b) show frequency assignments and inter-

fering cells or interfering sectors up to 3rd-tier in a cellular

system with FRF=3, for omni-cell and 3-sector cell, respec-

Ki Tae Kim O and Seong Keun Oh

School of Electrical and Computer Engineering

Ajou UniversitySan 5, Wonchon-Dong, Youngtong-Gu, Suwon, 443-749, KOREA

E-mails: {erene46O, oskn}@ajou.ac.kr

An Incremental Frequency Reuse Scheme for an OFDMA Cellular Sys-tem and Its Performance

978-1-4244-1645-5/08/$25.00 ©2008 IEEE   1504

 

 

tively. For a notation convenience, we would define the sets

of indices of interfering cells according to the loading factors

and sectorization types as follows:

{ }

{ }

 omni-cell and LF 1/3

  = 8,10,12,14,16,18,19,22, 25,28, 31,34

 omni-cell and LF > 1/3

  = 1, 2, 3, , 36

if 

 J 

if 

 J 

≤  

, (1)

{ }

{ }

 3-sector cell and LF 1/3,

  = 4,5,12,13,14,15,16,27, 28,29,30, 31,32

 3-sector cell and LF > 1/3,

  = 1, 2, 3, , 36

if 

 J 

if 

 J 

≤  

. (2)

γ  

 β 

 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

α γ  

 β 

 (a) (b)

Fig. 1. Frequency assignments and interfering cells or interfering

sectors up to 3rd

-tier, with FRF=3: a) Omni-cell; b) 3-sector cell.

For ICI modeling, we consider path losses, shadowing

factors and Rayleigh fading coefficients from 36 surroundingcells to the desired cell [9],[14]. The effective path loss in-

cluding the shadowing attenuation between the i -th center

user and the  j -th interfering base station (BS) is approxi-

mated to [9],[14]( , ) /10

( , ) ( , ) 10 i j

i j i j L d   ξ  ρ −

= ⋅ , (3)

where  ρ    denotes the path loss exponent but can also be

differentiated, and ( , )i jd   and ( , )i jξ  , respectively, denote the

 propagation distance and the shadowing factor between the

i -th center user and the  j -th interfering BS. The shadowing

factor ( , )i jξ    is modeled as a real Gaussian random variable

with zero mean and the standard deviation of  pσ   in dB [14].

In what follows, we would set the standard deviation  pσ   and

the path loss exponent  ρ   to 8 dB and 4, respectively [14].

From (1) or (2) and (3), the received signal at the i -th

center user can be expressed as

( )

( : ) ( ,0) ( ,0) ( ,0) ( ,0)

( , ) ( , ) ( , ) ( , )

 i j i i i i

i j i j i j i j i

 j J 

 R P S L H 

 P S L H N ∈

= ⋅ ⋅ ⋅

+ ⋅ ⋅ ⋅ +∑, (4)

where ( , )i j P  , ( , )i jS   and ( , )i j H  , respectively, denote the trans-

mit power, the transmitted signal, and the Rayleigh fading

coefficient from the  j -th interfering BS to the i -th center

user; ( , 0)i P  , ( , 0)i L , ( , 0)iS   and ( , 0)i H  , respectively, denote the

transmit power, the effective path loss, the transmitted signal,

and the Rayleigh fading coefficient from the center-cell BS to

the i -th center user; and i N   is an additive white Gaussian

noise at the receiver input of the i -th center user, with zero

mean and variance o N  . Assuming no downlink power con-

trol, we would set ( , )i j P  , 0,1, , 36 j  =    to a constant value.

 B.   Performance Metrics

 Now, we define three metrics to evaluate the system per-formance such as the SINR, the outage probability, and the

spectral efficiency.

First, we define the SINR of the i -th center user as

( )

2

( ,0) ( ,0) ( ,0) ( ,0)

( ) 2

( , ) ( , ) ( , ) ( , )

i i i i

i

i j i j i j i j i

 j J 

 P L S H SINR

 P L S H N ∈

⋅ ⋅ ⋅

=

⋅ ⋅ ⋅ +∑. (5)

From the SINR in (5), we define the outage probability as

( )[ ]out i P Pr SINR   η = < , (6)

where ( )[ ]

i Pr SINR   η <  denotes the probability that the

SINR value goes down below a service outage threshold η .

From using the SINR again, the spectral efficiency for the

i -th center user is defined as

( ) 2 ( )log (1 )i iC SINR= +  bps/Hz. (7)

To consider OFDMA systems, we would define sub-

channels each consisting of  N   OFDM-subcarriers. To

evaluate the performance of each user allocated to a sub-

channel in a frequency-selective fading channel, we use the

well-known exponential effective SINR mapping [15]-[16],

defined as

1

1ln

i N 

eff 

i

e N 

γ  

 β γ β −

=

= − ∑ . (8)

Here,  β   is dependent on a modulation and coding scheme

used and should be calibrated. For example,  β   has to be 2 in

a case of QPSK signaling [15]-[16].

III.  I NCREMENTAL FREQUENCY R EUSE SCHEME 

In this section, we present an IFR scheme that can reuse

effectively a given frequency resource in an OFDMA cellular

system and describe its operation principle in detail. Finally,

we give some design examples.

 A.  Concept of the IFR Scheme

The IFR scheme first divides the whole frequency spec-

trum into several segments each consisting of a

non-overlapping set of channels. The number of segments

might be larger or equal to the number of cells within a

cluster of adjoining cells. In addition, a set of segment allo-

cation sequences for a cluster of cells are designed according

to a segment allocation rule. Finally, the designed segment

allocation sequences are assigned to respective cells within a

cluster of adjoining cells again according to a segment allo-

cation rule. We define the first segment in each segment

allocation sequence as the base segment of the corresponding

cell. Each cell-specific sequence then determines the incre-

mental ordering for reusing additional segments beyond the

 base segment in the corresponding cell, when the amount of

traffic exceeds the capacity of its own base segment.

In this paper, we use the segment allocation rule as fol-

lows:

  The base segments among adjoining cells should not be

overlapped each other.

  If the number of users exceeds the capacity of the base

segment (called as simply the base capacity), additional

1505

 

 

segments assigned to a desired cell encroach partially or

fully base segments assigned to adjoining cells.

  At every incremental stage to define the set of sequences,

each segment is assigned only once, but at least once

over the whole sequences.

  A cluster consists of cells which use collectively the

complete set of segment allocation sequences.

 B.  Operation Principle

The details of operation principle are as follows:

1.  In each cell within the cluster, the proposed scheme can

allocate arbitrarily channels within its own base segment

if the amount of traffic does not exceed the base capac-

ity.

2.  Beyond the base capacity, it uses additional segments

according to the corresponding cell-specific segment

allocation sequence. It first completes channel alloca-

tion within its own base segment in the corresponding

cell and then allocates arbitrarily the remainder over the

newly added segments.

3.  This process will be continued until all the segments are

exhausted, as the amount of traffic increases.

Using this principle, we can avoid major ICIs from ad-

 joining cells when the amount of traffic is less than the base

capacity, while beyond the base capacity, ICI is averaged

over the newly added segments by arbitrary channel alloca-

tion. In addition, the IFR principle can be applied to both

omni-cell and 3-sector cell systems. The ICI control capa-

 bility of the IFR scheme could be maximized if the

cell-specific subchannel allocation sequences designed ac-

cording to the above segment allocation rule are used within

the cluster of cells.

C.   Design Examples

In our work, even if the IFR scheme can be widely applied

to cellular systems combined with various multiple access

technologies, we demonstrate its operation principle within

the viewpoint of an OFDMA cellular system, in which the

resource allocation is done on the basis of subchannel [17].

 Now, we give two design examples as follows:

  Scheme A for a cellular system based on FRF=3

Step 1.  The scheme first divides the whole frequency spec-

trum into three segments each containing one-third

set of total non-overlapping subchannels, such as A-,

B-, and C -segments as shown Fig. 2.

Step 2.  Below the loading factor of 1/3, the scheme allo-

cates arbitrarily subchannels only within only the

corresponding base segment for a desired cell to

demanding users.

Step 3.  If the loading factor is greater than 1/3 and smaller

than 2/3, the scheme first completes the subchannel

allocation within the corresponding base segment

for the desired cell, and then allocates arbitrarily the

remainder of requested subchannels within the 2nd 

segment (i.e., the 1st  incremental segment) to de-

manding users.

Step 4.  Finally, when the loading factor exceeds 2/3, the

scheme first completes the subchannel allocation

within the corresponding base segment and the 1st 

incremental segment for the desired cell, and then

allocates arbitrarily the remainder of requested sub-

channels within the 3rd segment (i.e., the 2nd incre-

mental segment) for the desired cell to demanding

users.

  Scheme B for a cellular system based on FRF=4

Step 1.  The scheme first divides the whole frequency spec-

trum into four segments each containing one-fourth

set of total non-overlapping subchannels, such as A-,

B-, C-, and D -segments as shown Fig. 3.

Step 2.  If the loading factor is greater than 1/4 and smaller

than 2/4, the scheme first completes the subchannel

allocation within the corresponding base segment

for the desired cell, and then allocates arbitrarily the

remainder of requested subchannels within the 2nd 

segment to demanding users.

Step 3.  This process will be continued until four segments

are exhausted.

0C 

1C 

2C 

 Power 

 Power 

 Power 

 Fig. 2. The concept of the proposed IFR scheme A in the omni-cell

environment for a cellular system based on FRF=3.

0C 

1C 

2C 

 Power 

 Power 

 Power 

3C 

 Power 

 Fig. 3. The concept of the proposed IFR scheme B in the omni-cell

environment for a cellular system based on FRF=4.

Here, we would summarize the two sets of segment allo-

cation sequences as follows:

  Using the scheme A

-  Sequence-C0 : A-seg.→B-seg.→C-seg.,

-  Sequence-C1 : B-seg.→C-seg.→A-seg.,

-  Sequence-C2 : C-seg.→A-seg.→B-seg.

  Using the scheme B

-  Sequence-C0: A-seg.→B-seg.→C-seg.→D-seg.,

-  Sequence-C1: B-seg.→C-seg.→D-seg.→A-seg.,

-  Sequence-C2: C-seg.→D-seg.→A-seg.→B-seg.,

-  Sequence-C3: D-seg.→A-seg.→B-seg.→C-seg.

IV.  SIMULATION R ESULTS AND DISCUSSIONS 

We performed computer simulations to demonstrate the

effectiveness of the proposed IFR scheme and also to com-

 pare the proposed scheme with both the classical universal

frequency reuse scheme with FRF=1 [9] and the SFR scheme

[10], [12]. We used three performance measures such as the

1506

 

 

outage performance, spectral efficiency, and overall cell

capacity. We considered an OFDMA downlink cellular sys-

tem in an omni-cell case for simulations.

We assumed a uniform loading factor over all the cells

considered for the purpose of simplicity. We assumed a uni-

form user distribution within a hexagonal cell region. For all

simulations, we used simulation parameters as shown in

Table I. The cell-edge performance has been evaluated by

averaging over all the users between the radius of 0.9 km and

1.0 km. The overall cell capacity has been obtained by cu-

mulating the respective capacities of all the users within a cell,

uniformly distributed within the hexagonal cell region. Sub-

channel construction has been done based on the partial usage

of subcarriers (PUSC) channelization of the IEEE 802.16

standard, each consisting of 24 data subcarriers [18]. We

assumed that only one subchannel is allocated to each user

and the exponential effective SINR mapping [15]-[16] was

used.TABLE I

SIMULATION PARAMETERS 

Parameter Value

 No. of total subcarriers 2048

 No. of data subcarriers 1680

 No. of subchannels 60 No. of data subcarriers per sub-

channel24

 No. of guard subcarriers Left(184), Right(183)

Path loss exponent 4Shadowing factor variance 8 dB

Spectral efficiency upper limit 4.5 bps/Hz

SINR outage threshold 3 dB

Maximum delay spread 81 n s

Cell radius 1 km (at a hexagonal vertex)

 No. of interfering cells 36 (up to 3rd tier)

Power amplification factor α   

(SFR scheme [10])1.5, 2

Figs. 4 and 5, respectively, show the outage probabilities

and spectral efficiencies of the IFR schemes and two con-

ventional schemes. From both figures, the proposed scheme

can reduce effectively the ICI, especially when the loading

factor is less than the base capacity (e.g., 1/3 and 1/4 for

cellular systems based on FRF=3 and FRF=4, respectively.).

The service outage performance of the IFR scheme A be-

comes approximately the same as that of the SFR scheme, but

outperforms that of the classical universal reuse scheme. This

improvement in the scheme A results from the following: At

the cell-edge region, center-cell users might be heavily in-

terfered with by signals from adjoining cells, since signals

transmitted from the center BS might be maximally attenu-

ated at cell-edge region; Below the base capacity, that is, the

loading factor of 1/3, the scheme A can avoid completely ICI

from adjoining cells, thus minimizing the ICI level. Beyond

the base capacity, both the incremental property and dis-

tributive property of the segment allocation sequences make

interfering cells evenly distributed and also the ICI level

gradually increased, thus keeping the ICI level lower.

Moreover, in the SFR scheme, cell-edge users might occupy

the power-emphasized primary band, thus cell-edge users

 being able to avoid severe ICI from adjoining cells. Therefore,

the SFR scheme performs slightly better than or comparable

to the IFR scheme, depending on the power amplification

factor value [10]. However, the ICI control mechanism of the

classical universal reuse scheme is to only average ICI over

the whole frequency spectrum. Hence, it is worst among three

reuse schemes. From Figs. 4 and 5, we conclude that the

scheme A based on FRF=3 performs better than the scheme B

 based on FRF=4 as the loading factor increases over 25%,

due to symmetric interference geometry. 

Fig. 6 shows the overall cell capacity of three reuseschemes considered here. From the results, we can see that

the proposed scheme can provide better overall cell capacity

than other two schemes. The improvement becomes moresignificant as the loading factor increases. With the full

loading factor, the overall cell capacity of the IFR scheme is

equal to that of the classical universal reuse scheme and isvery greater than that of the SFR scheme. This difference is

caused by the transmit power unbalance between the pri-

mary-band and secondary-band in the SFR scheme. In theSFR scheme, two-thirds of users allocated to the secon-

dary-band achieve relatively lower spectral efficiencies due

to the limited transmit power, while only one-third achievinghigher spectral efficiencies.

V.  CONCLUSIONS 

In this paper, we have proposed an IFR scheme that can

reuse effectively a given radio spectrum in an OFDMA cel-lular system, by defining a set of systematic segment alloca-

tion sequences over a cluster of adjoining cells. Below the base capacity, the scheme can avoid completely ICI from

adjoining cells, thus minimizing the ICI level. Beyond the

 base capacity, interfering cells are evenly distributed and also

the ICI level is gradually increased, thus keeping the ICI levellower. Hence, the proposed scheme provides better reuse

efficiency over the conventional schemes such as the classi-cal universal frequency reuse scheme and the SFR scheme. In

addition, we have verified the effectiveness of the proposed

scheme as compared with that of the classical universal reuse

scheme and the SFR scheme through extensive simulations.

From simulation results, we see that the IFR scheme per-

forms better over the classical universal reuse scheme does

and is comparable to the SFR scheme in terms of the averageoutage probability and spectral efficiency. The scheme A

 performs better than the scheme B when the loading factor isover 25%, due to symmetric interference geometry. The

 proposed scheme also can provide better overall cell capacity

than other two schemes. The improvement becomes more

significant as the loading factor increases. In addition, theIFR scheme can be easily configured as most existing reuse

schemes only by redefining the set of segment allocationsequences.

ACKNOWLEDGEMENT 

This research was supported by the MIC (Ministry of In-

formation and Communication), Korea, under the ITRC

(Information Technology Research Center) support programsupervised by the IITA (Institute of Information Technology

Advancement) (IITA-2008-(C1090-0801-0003))

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0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

 

  a  v  g .

  o  u

   t  a  g  e

  p  r  o

   b  a

   b   i   l   i   t  y

loading factor 

Cell-boundary (0.9-1km), SINRth=3dB

 Classical(FRF=1)

IFR scheme

 Scheme A(based on FRF=3)

 Scheme B(based on FRF=4)

SFR scheme

(Primary-band : Secondary-band)

 Power ratio 2:1 (α=1.5)

 Power ratio 4:1 (α=2)

 Fig. 4. Cell-edge average outage probability of three frequencyreuse schemes as a function of the loading factor, assuming uniform

loading factor over all the cells.

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

 

  a  v  g .

  s  p  e  c

   t  r  a   l  e

   f   f   i  c   i  e  n  c  y

   (   b  p  s

   /   H  z

   )

loading factor 

Cell-boundary (0.9-1km), SINRth=3dB

 Classical(FRF=1)

IFR scheme

 Scheme A(based on FRF=3)

 Scheme B(based on FRF=4)

SFR scheme

(Primary-band : Secondary-band)

 Power ratio 2:1 (α=1.5)

 Power ratio 4:1 (α=2)

 Fig. 5. Cell-edge average spectral efficiency as a function of theloading factor in the same environment as in Fig. 4

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

120

 

  o  v  e  r  a

   l   l  c  e

   l   l  c  a  p  a  c

   i   t  y   (   b  p  s

   /   H  z

   )

loading factor 

SINRth=3dB

  Classical(FRF=1)

IFR scheme

 Scheme A(based on FRF=3)

 Scheme B(based on FRF=4)

SFR scheme

(Primary-band : Secondary-band)

 Power ratio 2:1 (α=1.5)

 Power ratio 4:1 (α=2)

 Fig. 6. Overall cell capacity as a function of the loading factor in the

same environment as in Fig. 4

1508