1

Performance Analysis of Flexible Reuse in

Cellular Networks

Subbarao Boddu,Student Member, IEEE, Suvra Sekhar Das,Member, IEEE

and R. V. Rajakumar,Member, IEEE

Abstract

Flexible frequency reuse schemes namely Fractional Frequency Reuse (FFR) and Soft Frequency

Reuse (SFR) are suggested in literature to improve cell edgethroughput over unity frequency reuse in

Orthogonal Frequency Division Multiple Access (OFDMA) networks. In this paper we focus on Real

Time (RT) traffic for which blocking probability and Erlang load are the important performance metrics.

Both FFR and SFR have Signal to Interference plus Noise Ratio(SINR) threshold and power ratio as

important design parameters, while FFR has bandwidth partitioning ratio as an additional parameter. We

investigate cell capacity and cell edge performance in terms of Erlang load with blocking probability

constraint brought about by suitable choice of these parameters. We also analyze the fairness aspect

which is a critical indicator of user satisfaction. Resultson the influence of these parameters on Best

Effort (BE) traffic are also considered. We give a complete comparison between FFR and SFR for

cell edge as well as total cell for both RT and BE traffic. For RTtraffic, with proper choice of SINR

threshold and power ratio parameters, the cell edge and total cell performance in FFR and SFR is

improved by a notable gain over the reference scheme. It is observed that FFR and SFR provide a

noticeable enhancement in percentage satisfied coverage area over the reference scheme. For BE traffic,

the cell edge performance of FFR is improved by a factor of nine and four when compared against

reuse one and reuse three respectively, whereas in SFR it is improved by a factor of nine and three.

Index Terms

LTE, WiMAX, Fractional frequency reuse, Soft frequency reuse, SINR threshold, Power ratio,

Bandwidth partitioning ratio, Real time traffic, Best effort traffic, VoIP.

I. I NTRODUCTION

Broadband wireless networks use OFDMA [1], [2] as the transmission scheme. Frequency

reuse of unity is usually considered for such networks. Due to heavy co-channel interference,

2

cell edge users suffer from high outage probability. Flexible frequency reuse methods namely

Fractional Frequency Reuse (FFR) [3] and Soft Frequency Reuse (SFR) [4] are suggested to

improve the situation. In FFR and SFR the total available bandwidth is divided into Center Band

(CB) and Edge Band (EB). The CB is used at reuse factor of unity and EBis used at reuse

factor greater than one in FFR. In SFR, EB uses higher power thanCB.

FFR and SFR deployments require three important design parameters. The first is SINR

threshold‘γth’, which is used to categorize an user as cell center band. If the average SINR of

a user is greater than the SINR threshold it is alloted to CB otherwise to the EB. Power ratio

‘ρp’ is the second parameter which is used to distribute the total transmit power between cell

center and cell edge bands. The power ratio influences the SINR experienced by the user in both

the bands. The third parameter is bandwidth partitioning ratio ‘α’. It is used to divide the total

frequency resource into center and edge bands. This is applicable to FFR primarily. Bandwidth

may be partitioned in a cell according to four methods in FFR [5]. However, in this work we

use Grade of Service (GoS) fair method of bandwidth partitioning as it has the best performance

amongst the four.

SINR threshold‘γth’ which is used to classify users is affected by power ratio‘ρp’. Since

‘α’ identifies the amount of bandwidth resource available in a band, a combination of these

parameters thus influences the performance of such networks. The aim of this work is to set

up a performance evaluation framework, and find the influenceof these parameters on the

gains brought by FFR and SFR schemes in Real Time (RT) and Best Effort (BE) traffic over

conventional reuse one and reuse three OFDMA networks.

The authors in [3], [6], [7] present FFR and show the potential of FFR to improve cell edge

performance. FFR is studied by using frequency reuse three in EB while2/3rd of the bandwidth

is reserved for CB. FFR scheme has been analyzed [8] through Radio Resource Allocation (RRA)

algorithm which presents dynamic power and bandwidth allocation and focus on interference

avoidance as the main outcome. The work in [9] analyzed FFR and discussed the impact of

scheduling strategies by considering distance as the parameter for BE traffic. They have shown

that cell throughput increases and the distance threshold decreases with the number of users.

They have compared fixed power ratio and presented only sum cell throughput. FFR and SFR

schemes are compared in [10] and [11]. They show that SFR provides better capacity than FFR

with an appropriate resource allocation algorithm. They consider1/3rd of users in cell edge,

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but leaves user grouping as an open problem. Performance evaluation of the frequency planning

schemes is analyzed in [12]. It presents a collision model for elastic traffic. However, it is limited

in analyzing the influence of key design parameters of FFR. FFRand SFR schemes are compared

in [13] and shown that SFR performs better than FFR, but they did not analyze the cell edge

performance. The authors examined the expected performance gains of SFR with irregular cell

patterns in [14] with subband allocation algorithm. However, while separating the users into cell

center and cell edge band users, these works consider fixed thresholds in terms of distance and

SINR. Authors in [15] analyzed FFR and SFR and presented interference avoidance algorithm.

The analytical performance of FFR and SFR for BE traffic is presented in [16], where the base

station distribution following Poisson point process is considered. The authors show that the sum

capacity in SFR is greater than FFR, and edge capacity in FFR isbetter than SFR. Although

it is a comprehensive work, it is restricted to BE and methods are usable for a certain pathloss

exponent only. SFR scheme is analyzed in [17], [18] with power allocation algorithm applicable

to BE traffic. Authors assume a fixed SINR metric to separate theusers into cell center and edge

regions.

It can be seen from above that one set of works focus on RRA algorithms for a given method

of FFR or SFR. There are some investigations which look into the individual effects of the

different parameters. Some of the works compare FFR and SFR, but only comment on the sum

cell capacity. Most of these works focus on BE traffic and provide the throughput performance.

It is mentioned in [19], [20] that RT traffic would occupy a large fraction of the total traffic

carried over Long Term Evolution (LTE)/Worldwide interoperability for Microwave Access

(WiMAX) networks. Performance of SFR is analyzed in [21] in view of call admission control

by assuming the users associated to a single cell. They have studied SFR, but not influencing on

design parameters. They consider call blocking probability and outage probability as performance

measures. However, no interference is considered from neighboring cells. For RT traffic, Erlang

load and GoS or blocking probability are important Key Performance Indicators (KPI). Direct

inference about the performance of such traffic cannot be derived from results obtained using

BE traffic assumptions as will be evident from the results. Accordingly, in this paper we focus

on the performance analysis of flexible reuse schemes for RT traffic. We look into the influence

of γth, ρp andα on the performance enhancement at both cell edge and total cell for RT as well

as BE traffic. In our earlier work [5], [22], such evaluation ispresented, however the analysis is

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limited to FFR with equal power.

The main contributions of this paper are as follows. We present a comprehensive analysis to

relate the important design parameters namely, SINR threshold γth, power ratioρp and bandwidth

partitioning ratioα for FFR and SFR for both RT and BE traffic. We analyze RT traffic inFFR

using Kaufman Roberts Algorithm (KRA) which helps in analyzing detailed variation of Grade

of Service (GoS). We analyze RT traffic in SFR using KRA which helps in analyzing detailed

variation of GoS. We implement KRA and evaluated cell capacity in terms of Erlang. We analyze

the effect of power variation over CB and EB of FFR as well as SFR.We analyze the effect

of γth over CB and EB of FFR as well as SFR. We analyze the effect ofα for FFR as well as

SFR which influences cell capacity. We have studied the effect of variation of weighted average

GoS over CB and EB for FFR as well as SFR. We evaluate classwise blocking probability and

percentage coverage area aspects of the schemes, which influence cell capacity and shown that

percentage coverage area in FFR is improved by 12% when compared against SFR and reference

scheme. We analyze the fairness aspect, which is a critical indicator of user satisfaction, in terms

of GoS in CB and EB and shown that FFR provides better user satisfaction at 117 Erlangs while

SFR has satisfactory GoS values for CB and EB users at 144 Erlangs. We analyze the effect of

the design parameters on the performance at cell edge and total cell for BE traffic for FFR as

well as SFR, and shown that the mean and edge SE of FFR is improved by 20% and 11% over

SFR respectively at different values of design parameters.

The rest of the paper is organized as follows: section II presents system model of FFR

and SFR for RT traffic. This section describes the number of channels available at different

SINR thresholds and power ratios. Section III presents the implementation of Kaufman Roberts

Algorithm (KRA) in FFR, SFR and reference schemes for RT trafficand describes the method of

evaluation of GoS and supported capacity in the schemes. This section also addresses the fairness

issues of cell center and edge users, and presents the subcarrier classwise blocking probability

and percentage useful/satisfied coverage area in the schemes. Section IV presents the system

model and results obtained for BE traffic, while the last section concludes paper.

II. SYSTEM MODEL

We consider FFR and SFR OFDMA based downlink cellular networks as in Fig. 1. The band

division in FFR is described through Fig. 1a. The available bandwidth is divided logically into

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(a) FFR scheme cellular layout (b) SFR scheme cellular layout

Fig. 1: FFR and SFR scheme cellular layout.

cell center and cell edge bands, where cell center users use the frequency bandf1 while cell

edge users are allocated with one1/3rd of the rest of the available bandwidth. Thef2, f3 and

f4 indicate frequencies used in those geographic regions. As shown in Fig. 1b, in SFR, the

frequency bandsf1, f2; f2, f3 andf1, f3 are used as center bands while the bandsf3, f1 andf2

are used as edge bands in cell 1, cell 2 and cell 3 respectively. As shown in Fig. 1, in FFR and

SFR, when the bandwidth is partitioned between center and edge regions in the ratio of‘α’,

then the number of subcarriers used for center and edge bandsis Nsc,c andNsc,e respectively.

Total number of subcarriers isNsc. The center band is labeled asBc and edge band asBe.

We have assumed uniform distribution of users over the surface of the cell. The location of

a user ‘u’ is given by (r, θ) with respect to the center of the cell(0, 0), where0 ≤ r ≤ R and

0 < θ < 2π. The cell radius is R. SINR experienced by the user is given by

γu,b(r, θ) =Pr0(r, θ)

PIs(b) + PN

, (1)

wherePN is the noise power,PIs(b) is the total interference power inbth band, the indexs ǫ

{FFR, SFR}, PIs(b) =∑

i∈Is(b) Pri andPri(r, θ) is the power received from theith base station,

which is given by

Pri(r, θ) = PTi.L.d

−np

u,i .χu,i.|hu,i|2. (2)

The suffix b ǫ {c, e} where ‘c’ indicates center band and ‘e’ indicates edge band.The value

of i=0 indicates the signal from the desired base station. The set {I(b)} is the index of base

stations which cause interference inbth band.

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The interference term in the denominator of (1) includes thetotal interference power received

from center and edge frequency bands from all the base stations. Therefore, the total interference

power in bth band for a user is given as

PIs(b) =∑

i∈Isc

PTc.L.d

−np

u,i .χu,i.|hu,i|2+

ρp∑

i∈Ise

PTe.L.d

−np

u,i .χu,i.|hu,i|2, (3)

whereIsc consists of all interfering base stations transmitting in the CB with powerPTc. Similarly

Ise consists of all interfering base stations transmitting in EB with powerPTe. χu,i is the shadowing

component which is log normal distributed, ‘h’ is due to small scale fading,np is the pathloss

exponent,ρp is power ratio andL includes fixed loss. The distance fromith base station to a

user ‘u’ is du,i. From (3), it is assumed that the transmission power and shadowing component

is assumed to be identical for all the base stations. The transmit power fromith base station is

PTi. From (1), the received signal power from the desired base station has a meanµshpr0

(r, θ) =

ln(PT0) − np.ln(du,0) and varianceσ2

shpr0

= ζ2σ2u,0 [23], where ζ = 0.1 × ln 10 is a scaling

constant,σ2u,0 is the variance of received signal power from desired base station, anddu,0 is the

distance form the desired base station to a user. The received interference signal power from the

ith base station has a meanµshpri(r, θ) = ln(PTi

)−np.ln(du,i) and varianceσ2shpri

= ζ2σ2u,i, where

σ2u,i is the variance of received interference signal power from the ith base station. The received

interference from all the base stations is approximated as asum of log-normal random variables.

It is assumed that the sum of log-normal random variables follows a log-normal [24]. From the

above, the SINR of user equipment is the ratio of two log-normal random variables, which also

follows a log-normal distribution [25]. The channel powersfrom the desired and interfering base

stations are modeled as log-normal random variables havingmeanµRaypr0(r, θ) = ζ(µshpr0

(r, θ)−2.5) and varianceσ2

Raypri(r, θ) = ζ2(σ2

shpri

+ 5.572). Since we consider the Rayleigh distribution

for fast fadingh, the power of fast fading|h|2 follows Gamma distribution with unity mean.

However, it is to be noted thatPTcandPTe

in (3) are different for FFR and SFR schemes.

1) Power configuration in FFR: Let the total bandwidthB be divided between the center

and edge band based on the ratio,α. The bandwidth alloted to cell center region isBc = αB

and the amount of bandwidth alloted to cell edge region isBe = (1−α3)B as shown in Fig. 1a.

Let the total transmit power from the downlink transmittingantenna bePT . We defineρpc to be

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the power per Hz in center region andρpe to be the power per Hz in edge region. Therefore, the

power ratioρp is defined as the power spectral density of cell center regionto power spectral

density of cell edge region, that is,ρp =ρpcρpe

. Therefore, in FFR we write

PT = ρpc .(αB) + ρpe .(1− α

3)B, (4)

the total transmit power for center and edge band region isPTc= ρpc .(αB) andPTe

= ρpe .(1−α3)B

such thatPTc+PTe

= PT . The power spectral density over the center and edge bands isexpressed

as

ρpc =3PTρp

1 + α(3ρp − 1)B, and (5)

ρpe =3PT

1 + α(3ρp − 1)B. (6)

Hence, by using these relations, the total transmit power for center band is derived as

PTc=

3PTρpα

1 + α(3ρp − 1)(7)

and total transmit power for edge band as

PTe=

PT (1− α)

1 + α(3ρp − 1). (8)

2) Power configuration in SFR: Let the total bandwidth available beB. The total bandwidth

B is divided between the center and edge band in the ratio such that (23)rd of total bandwidth is

alloted to cell center region and(13)rd of total bandwidth is alloted to cell edge region. As shown

in Fig. 1b, the bandwidth allocated to center band region isBc =2.B3

, bandwidth allocated to

edge band region isBe = B

3. Bandwidth partitioning ratioα = Bc

B. That is, in SFRα is fixed

which is equal to 2/3. The power ratioρp is defined in SFR like in FFR. Therefore, in SFR we

write

PT = ρpcB2

3+ ρpeB

1

3(9)

Using the ratioρp, the power spectral density over the center and edge bands are given as

ρpc =3PTρp

(1 + 2ρp)B, and (10)

ρpe =3PT

(1 + 2ρp)B. (11)

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Hence, the total transmit power for center band regionPTcis derived asPTc

= 2.ρp.PT

1+2.ρpand total

transmit power for edge bandPTe= PT

1+2.ρprespectively such thatPTc

+PTe= PT . The transmit

powers over the cell center and edge bands at differentρp are given in Fig. 2. The transmitted

powersPTcandPTe

are calculated atPT = 41 dBm. Fig. 2 shows transmit power assignments

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

40

45

Power ratio ( ρp)

Tra

nsm

it po

wer

s fo

r ce

ll ce

nter

and

edge

ban

ds in

FF

R a

nd S

FR

(dB

m)

FFR center powerFFR edge powerSFR center powerSFR edge power

Fig. 2: Transmit powers for cell center and cell edge bands atdifferent ρp in FFR and SFR.

over center and edge bands fromρp = 0.0001 to 1. It is seen that whenρp decreases the total

transmit power to cell edge band increases and vice versa. Itis observed from figure thatPTc

andPTeare different for FFR and SFR schemes. It is to be noted thatρp is a design parameter

influencing the system performance in FFR and SFR.

3) Number of subcarriers required to make a call: A user is allocated to bandb =‘c’ (CB)

if γu,c(r, θ) ≥ γth, otherwise a user is allocated to bandb =‘e’(EB), whereγu,c(r, θ) is the mean

SINR of a user at a location when in center band,γth is the SINR threshold and is another design

parameter in FFR and SFR. The effective bandwidth required toguarantee delivery of a real

time service with an equivalent rate requirement ofRu is given as considering semi persistent

scheduling of RT traffic,

Bru(r, θ) =

Ru

βlog2(1 +γu,b(r,θ)

η), (12)

where β accounts for bandwidth efficiency loss andη captures the SNR loss due to system

implementation [26]. System parametersβ is in between0 < β < 1, while η > 1. Here

β = 0.83 andη = 4 dB are used for all traffic classes in accordance with LTE. Further,Bru(r, θ)

is the required bandwidth to supportRu b/s at location(r, θ) which experiences SINRγu,b(r, θ).

Incoming bursty traffic such as Voice over Internet Protocol(VoIP) can be modeled with an

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effective bit rate value [27], [28]. That means, we can assign an average bit rate to the incoming

bursty traffic which would encompass the variation of packetsize as well as inter arrival packet

delay. VoIP capacity [19] in 4G networks is usually given in terms of number of simultaneous

VoIP users with satisfied Quality of Service (QoS). This can be mapped to number of circuits

(channels) available for simultaneous calls. It can also bemodeled as a single connection with a

capacity expressed in b/s, equal to the number of users supported times the bit rate of the service.

In traditional telecommunication cellular networks, dimensioning of the network for RT traffic is

done using the Erlang formula [20], [29]. The Erlang formulagives the blocking probability as

a function of number of channels available (which is equal tothe Erlang capacity of the system)

and input traffic intensity given in Erlangs.

The analysis may be done with different models and differentset of assumptions. However,

here the method described in [29] is used. In that paper the cell dimensioning for variable bit

rate traffic for OFDMA cellular networks is presented. The model is well established. Further,

in OFDMA systems, subcarriers (Physical Resource Blocks (PRBs)) are allocated to users. The

allocation strategy depends upon the scheduling algorithmused [30]. It is shown in [30] that

the average number of subcarriers required to support a VoIPcall in a OFDMA network can be

found. This is a function of wide band SINR of user. This number indicates the average number

of subcarriers occupied by a user in the duration of a call forQoS condition to be satisfied

successfully. The granularity of a time-frequency resources in a OFDMA network allows a logical

connection of the subcarrier to channels. Taking all of thisinto account, we have considered

a model where we abstract the physical layer and the scheduling process such that a certain

number of subcarriers which is dependent upon the average SINR of user can be calculated, so

that the users’ VoIP QoS is satisfied.

In a real time service, packet delay is an important QoS measure of performance. Here we

consider that issues related to packet delay during a call are addressed by the Packet Scheduling

(PS)-RRA unit in the base station as in [19], [28], [30]. Usually a certain amount of resource

needs to be available for user QoS to be met satisfactorily [31]. A call is admitted provided

that a sufficient amount of resource available in the system.It is assumed in this work that the

amount of resource allocated to the user for a call request issufficient to maintain the call.

Let the total number of subcarriers available beNsc. Subcarrier bandwidth∆fsc = B

Nsc.fs,

where fs is the oversampling factor [2]. The number of carriers required is given asNb =

10

⌈Bru(γk)∆fsc

⌉, where ⌈.⌉ indicates ceiling function to the next higher nearest integer. Clearly for

γk ≤ γu,b(r, θ) < γk+1, Nb = Nk,b; that is for a range of SINR values[γk, γk+1), Nb will remain

constant due to the⌈.⌉ operator. Thus all locations and users whereγu,b(r, θ) lies in that range

require the same number of carriers (Nk,b) to make a call with effective rate requirement ofRu.

This set of users (range of SINRs) whereNk,b number of carriers are required to make a call is

called a class and indexed by ‘k’ in band b, andKb is number of classes in band ‘b’. In other

words, it is to be noted that due to variation of SINR over a cell we get different user classes

where each user class is associated with a certain number of carriers required to make a call. As

described earlier, the bandwidth allocated by scheduling and RRA algorithm for RT traffic [30],

[32] is usually done based on average SINR. We find the average number of carriers required

to make a call as a function of area averaged SINR to finally calculate cell capacity (in later

section) as given by

N savg,b(γ) =

Kb∑

k=1

Nk,b

∫ γk+1

γk

p(γ)dγ, (13)

wherep(γ) is the probability density function (PDF) of area averaged SINR. The average number

of subcarriers required to make a call is seen from Fig. 3. Thefigure shows that when SINR

increases the number of carriers required to make a call decreases and vice versa. As users at cell

−6 −4 −2 0 2 4 6 81

2

3

4

5

6

7

8

9

10

11

Average SINR in dB

Num

ber

of s

ubca

rrei

rs

re

quire

d to

mak

e a

call

(Nav

g,b

s)

SFRFFR

Fig. 3: Number of subcarriers required to make a call.

edge experience low SINR, they will require more number of carriers to make a call compared

to cell center users. This behavior is same at anyρp.

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4) Probability of selecting center and edge bands: Let Nu be the total number of users

deployed in the cell. Number of users in a band isNu,b = Nu.PAb, wherePAb

is the area

averaged probability of selecting bandb. The probability of a user ‘u’ at a location(r, θ), being

in CB is given by [33]

Pbc(γu,c(r, θ) > γth) =1

2− 1

2erf

(γth − γu,c(r, θ)

σγ

√2

)

, (14)

whereγu,c(r, θ) andσγ are the mean and standard deviation of the SINR,γu,c(r, θ) is the center

band user SINR at the location(r, θ). The probability of a user to be in cell center or edge region

is found based on their SINR condition using (1). Therefore,the area averaged probability of

selecting center bandPAcis given by

PAc=

∫

r

∫

θ

[1

2− 1

2erf

(γth − γu,c(r, θ)

σγ(r,θ)

√2

)]

pu(r, θ)rdrdθ, (15)

wherepu(r, θ) =r/(π.R2) for uniform user distribution. Area averaged probability of selecting

the edge band is given byPAe= 1−PAc

. The probability of selecting center and edge bands as

given by (15) whenγth andρp change can be seen from Fig. 4. Asγth increases, the probability

−10 −5 0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR threshold ( γth

) in dB

Pro

babi

lity

of s

elec

ting

cent

er a

nd e

dge

band

s (

PA

c, P

Ae)

FFR ρp=0.5 center

FFR ρp=0.5 edge

SFR ρp=0.1 center

SFR ρp= 0.1 edge

SFR ρp=0.5 center

SFR ρp=0.5 edge

SFR ρp=0.7 center

SFR ρp=0.7 edge

Fig. 4: Probability of selecting center and edge bands for different ρp andγth in FFR and SFR.

of selecting edge band is high and vice versa. It means that when γth increases the percentage

of users to be in edge band is more and vice versa.

5) Effective number of channels: In FFR, the number of available carriers for center and

edge band users is given asNFFRsc,c = ⌈ α.B

∆fsc⌉ and NFFR

sc,e = ⌈1−α3.B. 1

∆fsc⌉ respectively. The

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supported number of channels (simultaneous calls) for a given effective rate requirement,Ru in

a band ‘b’ is

NFFRch,b = ⌊

NFFRsc,b

NFFRavg,b

⌋, (16)

In SFR, the number of available carriers for center and edge band users is given as2Nsc/3

andNsc/3 respectively. Therefore, the number of channels supportedin center and edge band

is NSFRch,c = ⌊2Nsc/3

NSFRavg,c

⌋ andNSFRch,e = ⌊ Nsc/3

NSFRavg,e

⌋. Therefore the total number of channels is

N sch = N s

ch,c +N sch,e. (17)

Fig. 5 shows the number of channels available vs.γth in a cell. It is evaluated by using (17).

For FFR, it is seen that whenγth is from 0 to 8 dB, the number of channels in FFR are more

than that of the reuse one scheme which is taken as reference scheme. We have found in [22]

thatα is function ofγth. As γth increasesα decreases. This implies that the numerator of (16) is

affected byγth. Further, asγth increases the range of SINRγ in edge band is more. This leads

to more percentage of situations with larger number of carriers required to make a call. This

affects the denominator of (16). Together it yields a regionof γth where number of channels is

greater than the reference.

In case of SFR, in addition to the above, number of channels is also affected byρp. It is

seen that asρp decreases the number of channels increase and it is also noticed that whenρp

decreases, the number of channels suddenly drops to zero after certainγth. This is because as

ρp decreases, the power transmitted to edge user band is more, hence it receives high amount

of interference from its adjacent neighboring base stations as well.

It is observed from the figure that, atγth = 6 dB there is a sudden rise in number of channels

in a cell. This is because at this threshold, the number of carriers required to make a call is

minimum which gives rise to a sudden increase in number of channels. This is as per the number

of channels in center and edge bandsNSFRch,c andNSFR

ch,e in SFR. From these relations, we say

that asρp increases, the number of channels in center band increases and number of channels

in edge band decreases and vice versa. In SFR asρp decreases, orγth increases the probability

of selecting center bandPAcdecreases and vice versa. However, proper selection ofγth andρp

is required in order to study the behavior of RT traffic since these values influence the traffic

capacity, and the traffic capacity is a function ofγth andρp.

13

−10 −5 0 5 10 15 20 25 3050

100

150

200

250

SINR threshold ( γth

) in dB

Num

ber

of c

hann

els

in a

cel

l (N

ch)

RefFFR ρ

p = 0.5

SFR ρp = 0.001

SFR ρp = 0.01

SFR ρp = 0.5

SFR ρp = 0.7

Fig. 5: Number of channels in a cell in FFR and SFR.

6) Capacity of FFR and SFR for RT traffic: Since we have considered that the bandwidth

to be allocated is such that the bit rate requirement is to be guaranteed to a user as given by

(12), capacity is evaluated in terms of Erlang. Further, GoS(Blocking probabilityPb) is another

parameter whose detailed analysis is also considered. Therefore the objective of our work can

be stated as to find the values of design parametersγth, ρp andα so that the Erlang loadρs is

maximized and GoS fairness between cell center and cell edgeband users is achieved for RT

traffic. This can be expressed as

(

γ+th, α

+, ρ+p)

= arg maxγth,α,ρp

[ρs], (18)

subject to the following constraints:

1) 0 ≤ γth ≤ γmax

2) 0 ≤ ρp ≤ 1

3) 0 ≤ α ≤ 1

4) Pb ≤ Pbth

The parametersγth, ρp andα are chosen such that the GoS of center and edge band users is

less than the allowed GoS thresholdPbth. To quantify the user satisfaction in both bands, the

GoS fairness criteria is given byPb(c) <= Pbth andPb(e) <= Pbth, wherePb(c) andPb(e) are

the average blocking probabilities of center and edge bandsrespectively.

Blocking probability Pb is usually evaluated using Erlang B formula [33]. But, ErlangB

14

formula does not give classwise or regionwisePb. Instead, it gives the cell averagePb. That is,

with Erlang B analysis, only an aggregate view of GoS is available. It is shown in [31], [34]

that calculating classwisePb gives a detailed picture of user satisfaction and yields more useful

results on estimating capacity. Therefore instead to directly find Pb, for the cell, we findPb of

each classPb(k) in each band (CB and EB) using Kaufman Roberts Algorithm (KRA) [35],

[36], which is explained below.

III. I MPLEMENTATION OF KAUFMAN ROBERTSALGORITHM

Let there beK classes of users with subcarrier requirementN1sc, N

2sc, N

ksc . . . , N

Ksc . Let the

rate of Poisson call arrivals beλ and average call duration beH. The service time for all classes

of calls is exponentially distributed with mean1µ

whereµ = 1H

. Let there be a proportion of

arriving calls (hence users) that are from subcarrier classk, denoted byζk, wherek ∈ [1, 2, ..., K].

The rate of classk call arrivals isλζk. Thus the offered load for classk is τsk = ρsζk where

ρs =λµ. A state indicates the number of users of a particular class.Nu = (N1

u , N2u , N

ku . . . , N

Ku )

defines the system state, whereNku is number of users belonging to classk. Letting N

k

sc=

N1sc, N

2sc, N

ksc . . . , N

Ksc we may alternatively say that for a valid stateNu.N

k

sc≤ Nsc, where

Nsc is total number of subcarriers. On the other hand, for a validsystem state we must have∑K

k=1 NkscN

ku ≤ Nsc.

The total amount of resource utilized by all classes in the system is

Nk

sc.Nu =

K∑

k=1

NkscN

ku (19)

An arriving incoming call of class-k is blocked in a system havingNsc number of subcarriers,

if N lsc > Nsc −

∑Kk=1N

kscN

ku .

Let S = {Nu ∈ IK : Nk

sc.Nu < Nsc} be the state space, whereI is the set of non-negative

integers. In order to address the steady state of the system,for Nu ∈ S we denoteπ(Nu) as the

probability that the system in stateNu is in equilibrium. Therefore, the steady state probability

is π(Nu). The steady state probability of the stateNu ∈ S is given by

π(Nu) =1

G

K∏

k=1

τNk

usk

Nku !, Nu ∈ S, (20)

where, the normalizing factorG =∑

Nu∈S

∏Kk=1

τNku

sk

Nku !

. Let Sk be the subset of states in which

the system admits the incoming call of classk, Sk = {Nu ∈ S : Nk

sc.Nu ≤ Nsc − Nk

sc} The

15

sum of steady state probabilities of this subset is equal to the blocking probability of classk.

For Poisson arrivals the probability of blocking a classk is Pb(k) = 1 −∑

Nu∈Skπ(Nu). This

equality along with eq. (20) gives an explicit expression for blocking probability

Pb(k) = 1−∑

Nu∈Sk

∏Kk=1

τNku

sk

Nku !

∑

Nu∈S

∏Kk=1

τNku

sk

Nku !

, (21)

However, it is typically impractical to brute force sum the terms in numerator and denominator

because the discrete state spacesS andSk are prohibitively large even for moderate values of

Nsc andK. Hence we use KRA [35], [36] to find thePb(k) recursively. The KRA is an efficient

recursive algorithm for computingPb(k)∀k ∈ [1, 2, ..., K] which does not involve the brute force

summation.

Let S(n) = {Nu ∈ S : Nk

sc.Nu = n} andop(n) =

∑

Nu∈S(n)π(Nu). SinceNk

sc.Nu represents

the number of subcarriers, we denote this quantity asnoccsc . Then the occupancy probabilities

op(noccsc ), n

occsc = 1, . . . , Nsc satisfies the following recursive relation

noccsc op(n

occsc ) =

K∑

k=1

Nkscτskop(n

occsc −Nk

sc), (22)

wherenoccsc = 0,. . . ,Nsc. After computingop(nocc

sc ), the classwise blocking probabilityPb(k) is

given by

Pb(k) =1−Nsc−Nk

sc∑

noccsc =0

op(noccsc )

=Nsc∑

noccsc =Nsc−Nk

sc+1

op(noccsc )∀k ∈ [1, 2, ..., K]. (23)

Classwise blocking probabilityPb(k) is used to calculate cell averagePb. The cell averagePb,

Pb =∑K

k=1 ζkPb(k). We need the following input parameters to implement KRA: (a)total number

of subcarriers availableNsc (b) traffic intensity for each classτsk , (c) number of subcarriers

required for each user classNksc and (d) number of subcarriers occupied for classk, nocc

sc .

A. Evaluation of GoS and Supported Traffic Intensity

The procedure to evaluate the subcarrier classwise GoS and cell average GoS in case of

reference, FFR and SFR schemes is as per the following steps:

16

a) Reference scheme:

1) The probability of a user to be within the SINR range is found such that the same number

of subcarriers are required for making a call.

2) Traffic intensity of each of the classes of traffic is calculated by multiplying the total traffic

in the cell by the probability of the user to be in that class.

3) GoS for each of the classes is calculated using KRA algorithm as per (23).

4) The weighted average of the GoS of all the classes are takento find out the mean GoS

throughout the cell.

The weighted average GoS factor is given as

wGoS =

∑

k∈K Nku .Pb(k)

∑

k∈K Nku

, (24)

Denominator term gives the total number of users in a cell.

b) FFR and SFR:

1) The probability of an user to be in a band ‘b’ is calculated, thereby the traffic intensity in

each of the bands is calculated.

2) The probability of an user to be within a SINR range is foundas mentioned in step 1 of

reference scheme.

3) Traffic intensity of each of the classes of traffic is calculated by multiplying the traffic in

each of the bands by the probability of the user to be in that class.

4) Now we calculate GoS of center and edge classes using KRA. Weevaluate the weighted

average GoS of all the classes in center and edge bands to get the mean GoS in the bands.

The weighted average GoS in center band is expressed as

wcGoS =

∑

k∈K Nku,c.P

cb (k)

∑

k∈K Nku

, (25)

and the weighted average GoS in edge band is expressed as

weGoS =

∑

k∈K Nku,e.P

eb (k)

∑

k∈K Nku

, (26)

whereNku,c andNk

u,e are the number of users belonging to center and edge classes and,P cb (k)

andP eb (k) are the blocking probabilities of the center and edge band classes respectively.

5) The weighted average of the GoS in each of the bands are taken to evaluate the mean GoS

throughout the cell, and it is expressed as

wsGoS =

∑

k∈K Nku,c.P

cb (k) +

∑

k∈K Nku,e.P

eb (k)

∑

k∈K Nku

, (27)

17

TABLE I: System Parameters

Parameter Value

Cellular layout (omni) Hexagonal Grid with 19 Sites

Scenario Urban Micro

Inter-site distance 200 m

Carrier frequency 2.5 GHz

System bandwidth 5 MHz

Number of Subcarriers 512

Number of Useful Subcarriers 300

Subcarrier Spacing 15 KHz

Shadow Fading 6 dB

Number of classes 15

eNB transmit power 41 dBm

UE Noise Figure 7 dB

Minimum UE distance from eNB 10 m

BS Antenna height 10 m

power ratios 0.0001 to 4

Scheduling Round Robin

Thermal Noise Level −174 dBm/Hz

Rate Used 12.2 Kbps

Peak GoS supported 2%

SINR Thresholds -10 to 30 dB

IV. RESULTS AND DISCUSSIONS FORRT TRAFFIC

We compare the performance of the FFR and SFR schemes againstreuse one system which

is taken as the reference. We assumed that the rate requirement of users is equal to 12.2 Kbps

(VoIP traffic). Evaluation parameters are as given in table I.

In this work, we evaluate the following: supported traffic intensity with a GoS constraint of

2% in a cell, weighted average GoS in a cell, weighted averageGoS in center and edge bands,

subcarrier classwise blocking probabilityPb(k) and percentage useful/satisfied service area for

FFR, SFR and Reference (reuse one) schemes. In the figures, Reference scheme is marked as

‘Ref’.

18

A. Supported Traffic Intensity

Traffic intensity supported while satisfying a GoS of 2% in a cell at different γth and ρp

is shown in Fig. 6. It is seen that atγth=2 dB, the capacity of FFR is more than that of the

reference scheme. We evaluated the performance of FFR at differentρp, ranging from 0.0001 to

1. The maximum capacity is obtained whenρp = 0.5. Hence we show the performance of FFR

at γth = 2 dB andρp = 0.5.

−10 −5 0 5 10 15 20 250

50

100

150

200

250

300

SINR threshold ( γth

) in dB

Tra

ffic

inte

nsity

(E

rlang

s) s

uppo

rted

with

GoS

less

than

0.0

2

RefFFR ρ

p=0.5

SFR ρp = 0.0001

SFR ρp = 0.01

SFR ρp = 0.3

SFR ρp=0.5

SFR ρp = 0.7

SFR ρp = 4

Fig. 6: Traffic intensity supported with a GoS less than 2% fordifferent γth andρp in FFR and

SFR.

It is seen from the figure that reference scheme provides 109 Erlangs of traffic. In FFR, when

γth is less than -7 dB, the performance of FFR is equal to referencescheme. Asγth increases

the capacity goes down afterγth = 5 dB. It is noticed that atγth=2 dB (whenρp=0.5), FFR

provides the peak traffic intensity of 117 Erlangs. Now we look into the effect ofρp in FFR. The

performance of FFR at differentρp is shown in Fig. 7. It shows the traffic intensity supported

with Pb less than 2% at differentρp whenγth = 2 dB. It is seen that at allρp, the traffic intensity

supported in FFR is more than the reference scheme. Whenρp = 0.5, the Erlang capacity is

highest and the improvement is almost 7% over the reference scheme.

From Fig. 6, in case of SFR, it is seen that on increasingγth, the supported traffic intensity

(Erlangs) is more for lower values ofρp. This is because whenγth increases, the average

bandwidth required by the user decreases [5]. Further, while increasingγth, more and more

19

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 150

60

70

80

90

100

110

120

Power ratio ( ρp)

Tra

ffic

inte

nsity

(E

rlang

s) s

uppo

rted

with

Pb

less

than

0.0

2 at

γ th

= 2

dB

RefFFR

Fig. 7: Erlang capacity withPb less than 0.02 with respect toρp whenγth = 2 dB in FFR

center users switch to edge band. That is, the percentage of users to be in edge band is more.

When ρp is low, the amount of power transmitted to edge band is more. Consequently, the

received power for cell edge users being satisfied and hence their SINR is better. Therefore, the

effective bandwidth requirement reduces, and, hence, the supportable traffic in a cell increases.

Whenρp is high, the total power transmitted to cell center users is high compared to cell edge

users. This may lead to low SINR for edge region. Thus there ismore percent of situation with

high bandwidth requirement, which results in lower overallcell capacity. At value ofρp < 0.01,

γth appears to influence the performance. Forγth < 10 dB, ρp < 0.01 has high capacity but for

γth > 10 dB capacity drops to zero. At highγth the number of users in EB is more which results

heavy traffic demand for edge band. In addition to this there is high interference for neighboring

cells. It is seen that withρp = 0.01 SFR provides highest capacity. At thisρp, the power for

edge band is more than center region. It can, thus, be inferred from the figure that the supported

capacity is strongly dependent on the parametersρp andγth.

In order to maintain GoS fairness in both bands, we need to choose the operating point ofρp

andγth in FFR and SFR. Therefore, we evaluated the performance of FFRand SFR at different

ρp (from 0.0001 to 1) andγth. We choose the values of the parameters which provide a better

GoS fairness. The power ratioρp = 0.5 andγth = 2 dB in case of FFR, andρp = 0.3 andγth =

15 dB in case of SFR are chosen. Atρp = 0.3, the SFR scheme surpasses the reuse one.

We evaluate the Erlang capacity supported in FFR, SFR and reference while satisfying the

20

Pb of 2% in a cell and show the results in Fig. 8. It shows blockingprobabilities vs. traffic

intensity for each scheme. It is noticed that in FFR the difference in GoS of edge and center

0 50 100 150 200 2500

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Traffic intensity (Erlangs)

wG

oS

RefFFR centerFFR edgeFFR throughout a cellSFR center SFR edge SFR throughout a cell

FFR throughout a cell

FFR edge

FFR centerSFR throughout a cell

SFR edge

SFR center

Fig. 8: Weighted GoS in center band, edge band and throughoutthe cell with traffic intensity at

[γth, ρp]=[2 dB, 0.5] in FFR and [γth, ρp]=[15 dB, 0.3] in SFR.

bands is very small. In FFR scheme, the curves of center band,edge band and throughout the

cell are overlapped. So, we used different markers and indicated the curves with arrows in order

to distinguish the curves. Table II also shows the weighted GoS of center, edge and total cell

at the maximum supported traffic intensity. From the resultswe say that FFR provides a better

GoS fairness to both center and edge bands. From Fig. 8, in case of SFR, it is seen that the

difference in weighted average GoS values is larger at higher traffic intensities. For example, at

160 Erlangs of traffic, the center users’ GoS is low whereas edge users are not satisfied since

their GoS is more than permissible limit. Hence, we can say that cell average GoS is not a good

metric. Therefore, we have chosen the traffic supported in a cell where the GoS of each center

and edge bands satisfyPb ≤ 2%. The traffic supported in a cell in SFR with their corresponding

weighted average GoS is shown in table II as well. At the supported traffic of 144 Erlangs in

SFR, the center users and edge users have satisfactory GoS values. It is observed that the mean

and edge capacity in SFR is improved by 22% and 20% while the supported traffic in a cell is

144 Erlangs, whereas, in FFR mean and edge capacities are improved by 7% while the supported

traffic in a cell is 117 Erlangs when compared against reference scheme.

21

TABLE II: Traffic supported (Erlangs) in SFR and reference scheme with their weightedPb

Method ρs GoS(cell) GoS(center) GoS(edge)

Ref 109 0.0171 - -

FFR 117 0.019 0.0149 0.0197

SFR 144 0.0196 1.35x10−5 0.0199

SFR 109 6.13x10−5 2.67x10−8 7.10x10−5

B. Classwise Blocking Probability

Now we look into the classwise blocking probabilityPb(k) of users and it is evaluated by

considering the peak traffic intensity of a particular method as a reference. ThePb(k) is evaluated

using (23). Fig. 9 shows thePb vs. different subcarrier classes for FFR, SFR and reference.In

FFR, Pb(k) of edge users is lower than that of reference scheme for most of the subcarrier

classes which indicates the effectiveness of SFR and FFR schemes. As the subcarrier class ‘k’

0 5 10 150

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Subcarrier class (k)

Pb

RefFFR center FFR edge SFR center SFR edge

SFR edge

ReferenceFFR edge

FFR center

SFR center

Fig. 9: Subcarrier classwise blocking probability at [γth, ρp]=[2 dB, 0.5] in FFR and [γth, ρp]=[15

dB, 0.3] in SFR at 109 Erlang.

increases thePb(k) increases slowly. This is natural as a higherk indicates lower SINR region

(move towards cell edge) user class. It can be seen that the reference scheme has the highest

22

number of user classes whosePb > Pbth(2%). It is followed by FFR while SFR has the lower

number. Thus it can be said that SFR provides highest user satisfaction followed by FFR which

the reference scheme is the worst, when evaluated at the lower traffic intensity (capacity of

reference scheme).

C. Percentage Useful Coverage Area

We analyze the percentage useful/satisfied coverage area orpercentage useful service areaFu

in FFR and SFR and compared it with reference scheme in this section. Drawing the concept

of useful service area from [31], [34], the useful/satisfiedservice area is obtained as follows:

Let there bek = 1, 2, 3, ...K classes in a cell, number of subcarriers required to make a call

beNksc per classk and probability of a user belonging to classk bePb(k). As mentioned before,

the GoS threshold isPbth = 0.02. It is evaluated as follows:

(i) Initially the Pb(k) of all the classes of users are evaluated.

(ii) If all the classes of users are satisfied then it is said that 100% useful service area is attained.

(iii) If any of the classes have aPb(k) exceedsPbth, then that particular class is not getting served.

Therefore, that percentage of users is not getting served.

Mathematically the useful/satisfied service area is given by

Fu(Pbth) = Pr(Pb(k) < Pbth |Pb = Pbth) ∀k, (28)

whereFu is the measure of proportion of satisfied users which is also ameasure of fairness since

fairness is maximized if all users are satisfied. Percentageuser satisfaction vs. traffic intensity

for reference, FFR and SFR is shown in Fig. 10. ThePb at 98% service area and the cell average

Pb satisfy the 2% constraint are marked in the figure with solid and dashed arrow respectively.

Important values are captured in table III as well. It is seenthat FFR provides 77% coverage and

SFR provides 53% coverage, whereas reference scheme provides 65% at their respective peak

supported traffic intensities. The percentage coverage area in FFR is improved by 12% when

compared against reference.

From the results above, it can be said that SFR gives more traffic support than FFR and

reference scheme with lowerPb, but its fairness is lower at peak supported traffic.

23

0 20 40 60 80 100 120 140 1600

10

20

30

40

50

60

70

80

90

100

Traffic intensity (Erlangs)

Per

cent

age

Use

ful A

rea

0.020273

0.00543190.0055181

0.020561

RefFFR SFR

0.0149

0.019P

b at 98 percentage traffic

Cell average Pb ( < 2%)

Fig. 10: Percentage useful service area in FFR and SFR and reference.

TABLE III: Traffic supported at 2% cell averagePb and 98% useful service area with% coverage

area

Method Traffic at 2%

cell average

Pb (Erlangs)

Traffic

at 98%

service area

(Erlangs)

%Coverage

area(at

2% Pb)

Ref 109 106 65%

FFR 117 110 77%

SFR 144 130 53%

V. SYSTEM DESCRIPTION FORBEST EFFORTTRAFFIC

The Key Performance Indicator (KPI) in case of BE traffic is Spectral Efficiency (SE) measured

in b/s/Hz. While mean SE gives the cell capacity, the 10% is an indicator of cell edge perfor-

mance. The users in the region are divided into two sets whereone belongs to the center band

and other belongs to edge band. Center and edge band users are served using two independent

parallel RR allocations and their SE is evaluated. We comparethe performance of FFR and SFR

against reuse one and reuse three schemes.

24

The aim is to find the values of the design parametersγth, α andρp for which the cell edge

performance of BE traffic is improved while the sum cell throughput does not suffer significantly

with respect to that of reuse one. It is expressed as

(

γ∗

th, α∗, ρ∗p

)

= arg maxγth,α,ρp

{SE : p = Prob(s ≤ SE)|p}, (29)

subject to the following constraints:

1) 0 ≤ γth ≤ γmax

2) 0 ≤ α ≤ 1

3) 0 ≤ ρp ≤ 1

4) s ≥ (1− q)sref ,

From above,γ∗

th, α∗ and ρ∗p are the optimum values ofγth, α and ρp, ‘s’ is the value of the

received metric (received user SE) and ‘SE’ is the threshold value of the received metric (SE

threshold point),p=0.1 for 10%-ile probability,sref is the reference mean cell (area) capacity

for frequency reuse one andq is the allowed % reduction in aggregate throughput. The free

variables in the objective function areγth, α andρp. However,α is obtained as per probability

method in case of FFR [5], whereas it is fixed to 2/3 in case of SFR. Therefore, the mean SE

of FFR is given as

SE = SEc + SEe,where (30)

SEc = αβ

∫ γmax,c

γth

log2(1 +γcη)P (γc|γc > γth)dγc, and (31)

SEe =(1− α)

3β

∫ γmax,e

0

log2(1 +γeη)P (γe|γc ≤ γth)dγe. (32)

However, asα = 2/3 in SFR, the mean SE of SFR in center and edge bands is similar to (31)

and (32), but the termsαβ and (1−α)3

β in the equations become23β and 1

3β. The conditional

PDFs in (31) and (32) are obtained numerically. The probability of user to be in any band is

obtained using (15).

A. Results and Discussions for BE traffic

This section presents the performance evaluation of SFR andFFR schemes. The simulation

parameters used for performance evaluation are as in table I. Fig. 11 shows the comparison of

mean SE of FFR and SFR against that of reuse one (R-1) and reuse three (R-3) at different

values ofγth and atρp = 0.2 in FFR andρp = 0.35 in SFR.

25

−5 0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

SINR threshold ( γth

) in dB

Mea

n an

d ed

ge c

apac

ity (

b/s/

Hz)

Reuse 1 Mean Reuse 3 Mean Reuse 1 edge Reuse 3 edge FFR mean (ρ

p=0.2)

FFR edge (ρp=0.2)

SFR mean (ρp=0.35)

SFR edge (ρp=0.35)

SFR mean (ρp=0.5)

SFR edge (ρp=0.5)

Fig. 11: Mean and edge capacities at differentγth andρp in SFR and FFR

Whenγth is very low (-6 dB as shown in figure) mean SE of SFR is almost equal to reuse

one and it is almost equal to reuse three at higher values ofγth (40 dB as shown in figure). It is

important to note that the cell edge performance is best atγth=12 dB. At this threshold, the cell

edge performance is improved by a factor of three and nine when compared against reuse three

and reuse one respectively. The mean SE of SFR is maximized atγth=12 dB. At this threshold,

the gain over the mean SE of reuse three is 32.5%. However, themean SE of SFR is 2.8%

lesser than the mean SE of reuse one. For a fair comparison of SFR with FFR and reference,

the curves of SFR atρp=0.5 are provided in Fig. 11. It is seen that atρp =0.5 andγth =12 dB,

the mean and edge SE of SFR are 1.374 b/s/Hz and 0.84 b/s/Hz respectively, however the mean

SE of SFR is 6% lesser than that of reuse one.

The percentage gains in SFR over reuse one and reuse three aresummarized in table IV. The

mean and edge spectral efficiencies obtained with parameters (α, γth and ρp) are given in the

table.

The performance of FFR is evaluated with different power levels over the cell center and

cell edge bands, andρp is found which gives highest SE in both cell edge and total cell when

compared against reuse one and reuse three schemes. From Fig. 11, it can be seen that the mean

SE of FFR is more, in the range ofγth values from -4 dB to 15 dB, than reuse one and reuse

three. Further, it is seen that the cell edge SE of FFR is more than reuse one and reuse three

26

TABLE IV: Mean and edge SE comparison in SFR and FFR

SFR(mean SE (b/s/Hz)) R-1 R-3 % gain/loss

(α = 0.67, γth = 12 dB,ρp= 0.35) (b/s/Hz) (b/s/Hz)

1.42 1.46 1.07 2.8% less than R-1

32.5% over R-3

SFR(edge SE (b/s/Hz)) R-1 R-3 % gain

(α = 0.67, γth = 12 dB,ρp= 0.35) (b/s/Hz) (b/s/Hz)

0.888 0.1 0.232 9 times over R-1

3 times over R-3

FFR(mean SE (b/s/Hz)) R-1 R-3 % gain

(α = 0.207, γth = 6 dB, ρp= 0.2) (b/s/Hz) (b/s/Hz)

1.716 1.46 1.07 17% over R-1

56% over R-3

FFR(edge SE (b/s/Hz)) R-1 R-3 % gain

(α = 0.207, γth = 14 dB,ρp= 0.2) (b/s/Hz) (b/s/Hz)

0.987 0.1 0.232 9 times over R-1

4 times over R-3

for lowestγth range, and it is maximized atγth = 14 dB. For unequal power allocation case, it

is found that atρp= 0.2, FFR scheme provides highest mean SE and it is maximizedat γth = 6

dB. The percentage gains in FFR over reuse one and reuse three are summarized in table IV.

It is noticed that with power configuration in FFR, the cell edge performance is improved by

a factor of four and nine when compared against reuse 3 and reuse 1 respectively atγth of 14

dB. The mean SE is maximized atγth = 6 dB where the gain over mean SE of reuse one and

reuse three are 17% and 56% respectively.

From the above results, the mean and edge SE in FFR and SFR are maximized at different

values of the design parameters. The mean SE of FFR is improved by 20% over SFR and the

edge SE of FFR is improved by 11% over SFR.

However, it is seen from the work that the performance gains are attained only by selecting

proper values of the key design parameters. It is seen from Fig. 11 that the cell edge performance

is more in the range of SINR threshold values, i. e., from -4 dBto 30 dB, and the total cell

performance is more in the range of -4 dB to 18 dB. However, based on the design requirement,

one has to select the threshold value. If the objective is to improve both the cell edge and total

27

cell performance, we must choose the value which improves both. For example, at the threshold

of 6 dB, FFR provides gain of 17% for total cell over reuse one and 56% over reuse three. At

this threshold, the cell edge performance is improved by 8 times over reuse one and 3 times over

reuse three. If the objective is to improve cell edge performance while providing minimum loss

to reuse one, then we choose the threshold point accordingly. For example, at 20 dB threshold

the mean cell capacity of FFR is less than reuse one, but, at this threshold point the cell edge

performance of FFR is better than reuse one and reuse three schemes, because of the scenario

that there are more number of users in cell edge band when SINRthreshold increases. In this

scenario, we choose the threshold point 18 dB. Similar procedure is followed in SFR. Hence,

by meeting the design requirement, one can select the designparameters. In practice, the choice

of selecting the parameters will be left to the system designer based on his/her requirements.

VI. CONCLUSION

Flexible frequency reuse schemes namely, FFR and SFR schemes have been analyzed and a

framework for analysis of RT and BE traffic in OFDMA networks ispresented in this paper. For

RT traffic, with proper choice of SINR thresholdγth and power ratioρp parameters, the mean

Erlang capacity in FFR and SFR is improved by 7% and 22% over the the reference scheme. It

is found that the SFR and FFR provide better user satisfaction, when measured in terms of GoS

fairness across the cell, over reference scheme. This is seen in terms of average GoS in center

band and edge band as well as classwisePb. The percentage useful area in FFR is greater than

SFR and reference.

For BE traffic, with proper choice of the design parameters (γth andρp) in SFR, it is possible

to improve cell edge SE by a factor of nine and three when compared against reuse one and

reuse three respectively. Cell edge and mean cell performance is best at SINR threshold of 12

dB. At this threshold, gain over mean SE of reuse three is 32.5%, and mean SE of SFR is 2.8%

lesser than mean SE of reuse one. However, with appropriate power configuration in FFR the

cell edge performance is improved by a factor of nine and fourwhen compared against reuse

one and reuse three respectively. The mean SE of FFR is maximized and the gain over mean

SE of reuse one and reuse three are 17% and 56% respectively.

However, it is seen from the work that it is very important to configure the design parameters

in order to obtain the appropriate gains. It is also true thatwhile none of the techniques are

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uniformly applicable for different traffic types, their operating parameter values are also found

to be different. Therefore it can be said that improvement incell edge performance as well as

overall cell capacity for real time as well as best effort traffic can be achieved by both FFR and

SFR techniques over frequency reuse one in OFDMA cellular networks, but it must be noted

that the gains can be attained only by selecting proper values of the important design parameters

namely SNR threshold, power ratio and bandwidth partition ratio for each scenario.

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