1 performance analysis of flexible reuse in cellular...
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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,
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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
28
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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