EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS

Eur. Trans. Telecomms. (2010)

Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/ett.1434
Optimal soft frequency reuse and dynamic sub-carrier assignments
in cellular OFDMA networks

Mathias Bohge
1
, James Gross
2
and Adam Wolisz
1,3
1
Technische Universit at Berlin, TKN Group, Einsteinufer 25, 10587 Berlin, Germany
2
RWTH Aachen University, UMIC Research Centre, Mies-van-der-Rohe-Str. 15, 52074 Aachen, Germany
3
University of California, Berkeley, BWRC, 2108 Allston Way, Suite 200, Berkeley, CA 94704-1302, USA
SUMMARY
Soft frequency reuse (SFR) is a common technique for co-channel interference (CCI) mitigation in cellular
OFDMA networks. The performance of such networks signicantly depends on the conguration of the
power proles that implement the soft frequency reuse patterns. In this paper, we investigate the performance
of static soft frequency reuse by comparing it against the optimal case, in which a central entity optimally
distributes power among the users of the network. It is shown that there is a signicant performance gap
between both approaches, which needs to be lled by adaptive SFR mechanisms. Moreover, we show that
the achievable gain of static SFR is small in a system that is able to optimally decide on terminal/sub-carrier
assignments. Copyright 2010 John Wiley & Sons, Ltd.
1. INTRODUCTION
Orthogonal frequency division multiplexing (OFDM) to-
day is the dominant physical layer transmission scheme
in broadband wireless systems. Over the last decade, this
transmission scheme has been combined with multiple ac-
cess into a scheme known as orthogonal frequency divi-
sion multiple access (OFDMA). In OFDMA disjoint sets
of sub-carriers are assigned to different terminals for trans-
mission over a certain time period. As this can be combined
with channel-state dependent resource allocation, result-
ing system performance is high. Therefore, OFDMA is a
promising technique for use in various systems and scenar-
ios. While the application of OFDMAin single-cell settings
is well understood (see References [13]), a key open is-
sue with the application of orthogonal frequency division
multiple access in mobile cellular systems is the control of
co-channel interference. Especially terminals located at the
cell border largely suffer from the power radiated by the
* Correspondence to: Mathias Bohge, Technische Universit at Berlin, TKN Group, Einsteinufer 25, 10587 Berlin, Germany. E-mail: bohge@tkn.
tu-berlin.de

A previous version of this paper was presented in the 15th European Wireless Conference (EW 2009), Aalborg, Denmark.
base station of neighbouring cells in their communication
band.
During the last couple of years, soft frequency reuse
(SFR) [4] has been established as a standard technique to
control CCI in cellular OFDMAsystems. With SFR, a reuse
factor of one is applied between neighbouring cells, but for
the transmission on each sub-carrier the base stations are
restricted to a certain power bound. The amount of power
that is allowed to be radiated on a specic part of the spec-
trum is dened by cell-specic power proles (cf. Figures
2 and 5). Initially, the power proles have been assumed to
be of static nature and hence do not adapt to the current traf-
c situation [5]. Lately, in References [68], the possibility
is explored to dynamically adapt power proles as part of
self-organisation in a network (SON). These dynamic ap-
proaches show a performance gain compared to the static
approach. They, however, do not answer the question on
how much gain can be expected, if the power proles could
be optimally congured to mitigate CCI.
Received 1 December 2009
Copyright 2010 John Wiley & Sons, Ltd. Accepted 20 April 2010
M. BOHGE, J. GROSS AND A. WOLISZ
In this paper we give an answer to this question. Our cen-
tral contribution is the formulation of an according global
knowledge exploiting nonlinear optimisation problem. De-
spite the high problem complexity, several according prob-
leminstances are solvedina basic reference scenario. More-
over, we answer the related question concerning the benet
of using static power proles in a system with an optimal
dynamic terminal/sub-carrier assignment strategy.
The reminder of this paper is organised as follows. In the
following section, our system model is introduced. In the
section thereafter, the potential of adaptive soft frequency
reuse to mitigate CCI is explored by comparing the perfor-
mance results of a globally optimal working systemto those
of a system applying either no CCI mitigation mechanism,
a static soft frequency reuse approach, or a legacy hard fre-
quency reuse (HFR) scheme in a basic scenario. The benet
of using static power proles in a system with an optimal
dynamic terminal/sub-carrier assignment strategy is studied
in more detail in a more realistic scenario in the subsequent
section. Finally, we conclude our work and identify topics
for further study in the nal section.
2. SYSTEMMODEL
Throughout this paper, the downlink (DL) of an OFDMA
based cellular system with site-to-site distance d
s2s
is con-
sidered. Within each cell, a base station coordinates all data
transmissions. J terminals are uniformly distributed over
the considered area, each moving with speed v according
to the Manhattan grid mobility model.
2.1. Wireless channel model
In general, the impact of the wireless channel on the trans-
mitted data is expressed as one signal-to-noise and interfer-
ence ratio value
(t)
c,j,s
per cell c, terminal j, sub-carrier s
and time instance t:

(t)
c,j,s
=
h
(t)
c,j,s
p
(t)
c,s

c
i
=c
h
(t)
c
i
,j,s
p
(t)
c
i
,s
+
2
,s
(1)
Here, h
(t)
c,j,s
is the gain experienced by terminal j on sub-
carrier s at time t versus the base station of cell c, p
(t)
c,s
is the
power radiated by the base station of cell c on sub-carrier s
at time t, and
2
,s
is the noise power present on sub-carrier
s. Gain h
(t)
c,j,s
is commonly modelled by the composition
of three factors: path loss h
PL
, shadowing h
SH
, and fading
h
FA
. To model path loss, we use the following empirical
approach suggested for LTE macro-cell system simulations
by the 3GPP in Reference [9] (Table A.2.1.1-3):
h
PL
[dB] = 128.1 +37.6 log
10
(d) (2)
where d is measured in kilometers. Apenetration loss value
of 20 dB is added in accordance with simulation case 1 of
Table A.2.1.1-1 of Reference [9]. Also in accordance with
Reference [9] (Table A.2.1.1-3), shadowing is modelled as
a lognormal random variable with a standard deviation
sh
of 8 dB. Fading is modelled as Rayleigh fading according to
3GPPs spatial channel model Urban Macro with a median
root-mean square delay of 0.65 s. In the case of stationary
terminals, we assume fading to be present due to objects
moving within the system area at a speed of v = 3 m/s.
2.2. Link level performance model
The task of the link level performance model in simula-
tions is to translate the channel quality experienced by a
receiver into receiver performance in terms of, for example,
capacity, throughput or error values. In general, function F
denotes the mapping between channel quality (expressed
by the SNIR) and the achievable capacity or throughput. A
popular link level performance model is the Shannon ca-
pacity

shannon
[bps] = Blog
2
(1 +) (3)
It represents the an upper limit on the error-free throughput
than can be achieved over an AWGN channel for a given
SNR [10]. We assume that this applies also in scenarios
where interference is present and use the Shannon capac-
ity in the basic investigations of section Basic Multi-Cell
OFDMA Investigations.
For the more detailed investigations of section Extended
SCAand SFRExaminations, we use a more realistic model
suggested by the 3rd Generation Partnership Project (3GPP)
for LTE link level simulations [11]. It assumes that the
throughput of a modem with adaptive coding and modu-
lation can be approximated by an attenuated and truncated
form of the Shannon bound. The following equations ap-
proximate the throughput in bits-per-second (bps) over a
channel with a given SNIR , when using link adaptation:

tc
[bps] =
_

_
0 for <
min

tc
Blog
2
(1 +) for
min
< <
max

tc
B for >
max
(4)
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
OPTIMAL SFR AND SCA IN CELLULAR OFDMA NETWORKS
Table 1. Parameters describing baseline link level downlink performance for LTE simulations.
Parameter Symbol Value Notes
Attenuation factor
tc
0.6 Represents implementation losses
Maximum throughput in bps/Hz
tc
4.4 Based on 64QAM, code rate 4/5
Minimum SNIR in dB
min
10 Based on QPSK, code rate 1/8
where B is the channel bandwidth,
tc
is the attenuation
factor, representing implementation losses,
tc
maximum
throughput of the ACM codeset in bps/Hz, and
min
and

max
in dB are the minimum SNIR of the codeset, and the
SNIR at which maximum throughput is reached, respec-
tively. The parameterization of
tc
,
tc
and
min
is chosen
as suggested in [11] and is summarized in Table 1.
2.3. Physical layer model
The system under consideration uses orthogonal frequency
division multiplexing as transmission scheme for down-
link data transmission. It features a total bandwidth of B
at center frequency f
c
. The given bandwidth is split into
S sub-carriers, each featuring a bandwidth (also referred
to as sub-carrier frequency spacing) of f = B/S. The
maximum transmit power per cell p
max
is split among the
sub-carriers. Time is slotted into transmission time inter-
val (TTIs) of duration T
TTI
, where T
TTI
is assumed to be
smaller than the coherence time of the wireless channel
( i.e. in the order of milliseconds). Hence, the atomic re-
source unit has a size of one OFDMsymbol length T
s
in the
time domain and one sub-carrier bandwidth f in the fre-
quency domain, and is referred to as resource element (RE)
(see Figure 1). Prior to the transmission of the time domain
OFDMsymbol, a cyclic prexof lengthT
g
is addedas guard
interval.
2.4. Medium access layer model
Data multiplexing in the downlink is based on orthogo-
nal frequency division multiple access, where the smallest
allocatable resource unit is a resource block (RB) n (cf.
Figure 1). An RB consists of a number of adjacent REs in
Figure 1. Example resource blocks (RBs) consisting of 9REs.
the frequency domain (sub-carriers) N
subs
and spans all REs
available for user data transmission of a TTI [9].
The RB bandwidth (number of REs in the frequency
domain) is chosen, such that channel quality differences
among the sub-carriers belonging to a single resource block
are negligible (i.e. the RB is assumed to experience mostly
at fading). If N
subs
is the number of adjacent sub-carriers
(REs in the frequency domain) belonging to a single re-
source block n, the number of available RBs to transmit
data per TTI is N = S/N
subs
.
2.4.1. Scheduling decisions. At the beginning of each TTI,
a base station scheduler assigns RBs to the terminals in
each cell c. The distribution of the RBs among the termi-
nals has a signicant impact on the system performance. A
rather simple scheduler assigns the resource blocks stati-
cally (i.e. following a certain recurring pattern), as for ex-
ample, the round robin (RR) scheduler. Statically assigning
the resources yields the advantage that the resource allo-
cations do not need to be signaled more than once. More
sophisticated schedulers assign the resources following an
optimisation strategy [3]. In this paper, optimal scheduling
strategies are explored (as described in the next section),
whereas the simple RR scheduler serves as a benchmark. It
is also the schedulers task to distribute the maximumavail-
able transmission power p
max
among the RBs. Within each
RB n all sub-carriers s obtain the same power share.
3. BASIC MULTI-CELL OFDMA
INVESTIGATIONS
The investigations of this section aim at an comparison be-
tween the performance of systems employing standard hard
frequency reuse and soft frequency reuse CCI mitigation
techniques and the performance of a globally optimal dy-
namic power allocation and sub-carrier assignment based
system.
3.1. Global optimisation
A major assumption in the global optimisation case is that
the optimal resource scheduling decision at time t is made at
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
M. BOHGE, J. GROSS AND A. WOLISZ
a single point (referred to as central entity), at which unlim-
itedcomputational power andideal system-wide knowledge
is available. Particularly, the central entity is in charge of
determining the optimal real-valued power levels y
(t)
c,s
for
each sub-carrier in each cell c out of the set of active cells
C, as well as for nding the optimal binary terminal/sub
carrier assignments x
(t)
c,j,s
at time t, where
x
(t)
c,j,s
=
_
1, if in c sub-carrier s is assigned to j at t
0, if in c sub-carrier s is not assigned to j at t.
Integrating the power and sub-carrier assignment optimi-
sationvariables intoa single optimisationproblemthat max-
imises the system throughput yields the nonlinear global
OFDMA resource allocation formulation:
max
X
(t)
,Y
(t)
C

c=1
J
c

j=1
S

s=1
x
(t)
c,j,s
F
_
_
_
_
h
(t)
c,j,s
y
(t)
c,s

+

c= c
h
(t)
c,j,s
y
(t)
c,s
_
_
_
_
(5a)
s.t
S

s=1
y
(t)
c,s
p
max
c (5b)
J

j=1
x
(t)
c,j,s
1 c, s (5c)
where X
(t)
is the C J S matrix of terminal/sub-carrier
assignments and Y
(t)
is the C S matrix of power assign-
ment variables at time t, J
c
is the number of terminals in
cell c, and F(. . .) is the link level performance function that
determines the throughput depending on the instantaneous
SNIR. Note that there is a twofold nonlinearity property
in optimisation goal (5a): rstly, optimisation variable y
(t)
c,s
is present in the nominator, as well as in the denominator
of SNIR term, reecting that a better power distribution in
one cell might lead to a worse situation in another cell. Sec-
ondly, there is a nonlinearity due to the multiplication of
the terminal/sub-carrier optimisation variable x
(t)
c,j,s
and the
power allocation optimisation variable y
(t)
c,s
dependent F ()
term. Due to these nonlinearities and additional integer con-
straints global constrained max sumrate problem(5) is very
hard to solve. Furthermore, it requires all channel attenua-
tions to be known at the central entity for all sub-carriers,
terminals and base stations. Hence, this scheme serves pure
comparison purposes representing an upper bound.
In order to account for intra-cell fairness, required
throughput per terminal constraint (5d) is added to form
the complete global constrained max sum rate problem:
S

s=1
x
(t)
j,s
F
_
_
_
_
h
(t)
c,j,s
y
(t)
c,s

+

c= c
h
(t)
c,j,s
y
(t)
c,s
_
_
_
_

req,j
cj (5d)
Here, it is assumed that for each terminal j there is a required
throughput
req,j
, and that any throughput beyond
req,
is
useless. In other words, the overall optimisation goal is to
maximise the system throughput while assuring that none
of the users gets more than its required rate. This approach
corresponds to a simple piecewise linear utility function.
3.2. Local optimisation employing standard CCI
mitigation techniques
In the case of local optimisation, the base station schedulers
of each cell make individual scheduling decisions per cell,
i.e. no central entity is involved. Each scheduler relies on
local information only. All sub-carrier assignment decisions
in cell c are made by solving the according instance of the
local constrained max sum rate problem:
max
X
(t)
J
c

j=1
S

s=1
x
(t)
c,j,s
F
_

(t)
c,j,s
_
(6a)
s.t
J
c

j=1
x
(t)
c,j,s
1 s, (6b)

s
x
(t)
c,j,s
F
_

(t)
c,j,s
_

req,j
j J
c
(6c)
Since merely local information is available at each sched-
uler, there is no opportunity to optimise the power alloca-
tion per sub-carrier in order to mitigate CCI, as it is done
in the global optimisation approach. Instead, standard HFR
or SFR is used to suppress CCI. Recall that when applying
HFR or SFR power proles can be used to prescribes the
fraction of the maximum transmit power that the base sta-
tion may use depending on the part of the spectrum. In
the following, the power prole of cell c is denoted by

c,s
[0, 1]. It denotes the fraction of the total available
output power p
max
. On sub-carrier s, cell c thus transmits
with a power of p
max

c,s
. Considering power proles, the
SNIR experienced by terminal j on sub-carrier s in cell c
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
OPTIMAL SFR AND SCA IN CELLULAR OFDMA NETWORKS
Figure 2. Reference scenario for the basic investigations.
can be written as

(t)
c,j,s
=

c,s
p
max
h
(t)
c,j,s
C

c=1
c= c

c,s
p
max
h
(t)
c,j,s
+
2
,s
(7)
The above denominator sums up the CCI fromconcurrently
sending base stations c = c and the noise power
2
,s
.
3.3. Basic multi-cell reference scenario
The basic reference scenario is shown in Figure 2. It adopts
the system model described in section System Model.
Shannon capacity is assumed as link level performance
model in order to achieve the theoretical optimum and re-
frain from clipping effects that might appear when using
the truncated Shannon link level performance model (cf.
subsection Link Level Performance Model).
3.3.1. Parameterisation. The simulation parameterisation
largely follows the parameters for the LTE simulation
case 1 as presented in Tables A.2.1.1-1 and A.2.1.1-2
of Reference [9] with an inter-site distance of 500 m
and users dropped uniformly in each hexagonal cell. In
this basic reference scenario, however, two hexagonal
cells are considered only. The reason for this is that for
signicantly larger scenarios, the global constrained max
sum rate problem (5) is not solvable within reasonable
time bounds using regular hard- and software equipment.
Notwithstanding standard [9], which denes 25 resource
blocks for a 5 MHz system, the basic reference model
features 24 resource blocks with a resource block spacing
of 200 kHz. The reason for that is that 24 is divisible by
two, which allows fair resource sharing among the two
cells in the HFRand the SFRscenario. Each resource block
consists of 12 adjacent sub-carriers. Eight terminals, four
in each cell, are uniformly distributed over the cell area.
In the SFR case, the power proles are congured such
that the high power level is ten times the low power level.
Accordingly, each base station radiates 1/11 p
max
on one
half of spectrum and with 10/11 p
max
on the other half.
3.3.2. Methodology. The wireless channel as well as the
terminal mobility are simulated according to the system
model presented in section System Model. At the begin-
ning of each TTI a snapshot of the current CSI values per
terminal and base station is taken. These snapshot values are
used to create optimisation probleminstances following the
optimisation models presented in section Basic Multi-Cell
OFDMA Investigations. In the case of global optimisa-
tion, one global scheduling problem instance is created per
TTI and piped into LINDOs LINGO nonlinear optimisa-
tion problem solver [12]. If local optimisation is selected,
one local scheduling probleminstance per cell and TTI (i.e.
a total number of C problem instances) needs to be solved
per TTI. To solve the local probleminstances, they are piped
into ILOGs CPLEX linear problem solver [13].
After solving the individual instances, the solving soft-
ware pipes back the optimal scheduling decisions into
the simulator software that uses it for further process-
ing and throughput calculations. The simulator is based
on the free timed discrete event simulation library OM-
NeT++ [14]. Different required rate per terminal thresh-
old
req,j
scenarios have been explored ranging from 2 to
5 Mbps. In each scenario 100 different user distributions
have been simulated, resulting in a high level of condence
(as can be seen from the condence intervals in the result
gures).
3.4. Results
For each scenario, the mean cell throughput, the mean
throughput of the weakest (cell-edge) terminal of the sys-
tem, as well as the individual per terminal throughputs are
presented. For the rst two, error bars display condence
intervals with a condence level of 99 %.
The rst result that catches the eye when examining
the weakest terminal throughput performance comparison
in Figure 3a is fact that the global optimal weakest user
throughput grows linearly with the required rate per termi-
nal value. For a required throughput per terminal of
req,
=
5 Mbps the weakest terminals throughput is 5Mbps, i.e.
that all terminals achieve the required throughput. This fact
is also reected in Figure 4d that shows the individual mean
terminal throughput in the case of global optimisation. The
very narrow 99% condence intervals in Figure 3a indicate
that this is true for all simulation runs. Accordingly, the sys-
temthroughput performance achieves its maximumper cell
throughput of 20 Mbps.
Altogether, the application of global optimisation in the
basic reference scenario achieves signicant cell-edge ter-
minal throughput performance gains of up to 100% and
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
M. BOHGE, J. GROSS AND A. WOLISZ
2 2.5 3 3.5 4 4.5 5
x 10
6
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
x 10
6
required rate per terminal
req
/ bps
w
e
a
k
e
s
t

t
e
r
m
i
n
a
l

t
h
r
o
u
g
h
p
u
t

m
e
a
n

/

b
p
s
FR1
GLOBAL OPT
HFR
SFR
2 2.5 3 3.5 4 4.5 5
x 10
6
5
10
15
20
required rate per terminal
req
/ bps
m
e
a
n

c
e
l
l

t
h
r
o
u
g
h
p
u
t

/

b
p
s
FR1
GLOBAL OPT
HFR
SFR
x 10
6 (a) (b)
Figure 3. Basic reference model throughput performance results: (a) mean throughput (bps) of weakest terminal and (b) mean cell
throughput (bps).
system throughput gains of more than 10% compared to
the frequency reuse 1 scenario, in which no CCI mitigation
techniques are applied. Obviously, the application of sub-
optimal CCI mitigation mechanisms delivers less strong re-
sults. Comparing HFR to FR1, the graphs show that the
application of HFR hardly improves the cell edge terminal
performance, even though up to a required rate of 4 Mbps
HFR performs slightly better. The small advantage are due
to the fact that there is zero interference from the neighbour
cell, and, thus, the channel states of the cell edge terminals
are generally better than in the frequency reuse 1 case. Due
to the limited resources in the hard frequency reuse case,
however, the weakest terminals cannot take advantage of
the increasing required rate above that 4 Mbps threshold.
This is mainly because the cell edge terminals hardly get
any resources at all, if the terminals at the center are allowed
to consume resources for such high rates. Accordingly, their
mean throughput decreases with the increasing required rate
after that turning point.
Greater performance gains can be achieved, if SFR is
applied. Figure 3a shows a performance gain in cell edge
terminal throughput over FR1 of up to 30 %. This is an
immense gain, consideringthe fact that the gainsolelystems
frommasking the resource block power levels. Note that the
weakest terminals throughput gain is present in all chosen
required rate per terminal cases, and that it constantly grows
with an increasing required rate. In contrast to HFR, even
the overall system performance gains slightly, if SFR is
applied.
This result underlines the assumptionthat dynamic power
and sub-carrier assignment techniques bear a high poten-
tial to mitigate CCI in cellular OFDMA networks. Note,
however, that the gains have been achieved under idealistic
conditions.
2
4
6
8
2
3
4
5
0
2.5
5
x 10
6

req
/ Mbps
terminals
m
e
a
n

t
h
r
o
u
g
h
p
u
t

/

b
p
s
2
4
6
8
2
3
4
5
0
2.5
5
x 10
6

req
/ Mbps
terminals
m
e
a
n

t
h
r
o
u
g
h
p
u
t

/

b
p
s
2
4
6
8
2
3
4
5
0
5
2.5
x 10
6

req
/ Mbps
terminals
m
e
a
n

t
h
r
o
u
g
h
p
u
t

/

b
p
s
2
4
6
8
2
3
4
5
0
5
2.5
x 10
6

req
/ Mbps
terminals
m
e
a
n

t
h
r
o
u
g
h
p
u
t

/

b
p
s
(a) (b) (c) (d)
Figure 4. Individual mean terminal throughput results: (a) frequency reuse 1, (b) hard frequency reuse, (c) soft frequency reuse and
(d) global optimisation.
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
OPTIMAL SFR AND SCA IN CELLULAR OFDMA NETWORKS
4. EXTENDED SCA AND SFR EXAMINATIONS
In this section, the application of dynamic sub-carrier as-
signment and soft frequency reuse is studied under more
realistic conditions. Particularly, the network size and the
CSI availability are modelled closer to reality.
Increasingthe hexagonal networksize yields anincreased
impact of CCI in both, the FR1 case (where all neighbouring
cells use the same frequency band), as well as in the SFR
case (where power proles are reused in different cells).
In terms of CSI availability, in the previous section CSI
was assumed to be available at any point in time and the
scheduler was assumed to be able to adapt to it immedi-
ately. Obviously, in real systems these values are not in-
stantly available. The scheduler, thus, has to work with de-
layed channel measurements. Note that the advantage of a
highly accurate adaptation to the channel state in the opti-
mal case can turn into a disadvantage in reality. Therefore,
in this section the impact of CSI processing delay T
csi
on the performance of the dynamic sub-carrier allocation
and power proling combination in multi-cell scenarios is
studied. Different time spans between the measurement of
channel state information and its actual usage for channel
adaptation are considered. We assume the scheduler to use
the most recent SNIR value available from the terminals to
estimate the current capacity per terminal/sub-carrier pair.
4.1. Extended multi-cell reference scenario
The extended reference scenario is shown in Figure 5a.
It adopts the system model described in section System
Model. The truncated Shannon link level performance
model (cf. section Extended SCAand SFRExaminations)
is used.
4.1.1. Parameterisation. The extended reference system
and channel model parameterisation largely follows the pa-
Figure 5. Extended reference scenario with SFR power proling:
(a) hexagonal multi-cell layout and (b) cell conguration .
Table 2. Extended multi cell reference model parameters.
Parameter Symbol
Number of cells C 7
Number of terminals J 70
Terminal speed v {0; 10} m/s
Req. throughput per terminal
req,j
1 Mbps
RB freq. spacing f
n
200 kHz
Number of RBs N 25
Sub-carriers per RB N
subs
12
CSI processing delay T
csi
{0 . . . 5} TTIs
rameters for the LTE simulation case 1, as presented in
Tables A.2.1.1-1 and A.2.1.1-2 of Reference [5] with an
inter-site distance of 500 m and terminals dropped uni-
formlyover the systemarea. Additional parameters are sum-
marised in Table 2.
4.1.2. Power proles. In contrast to the basic reference sce-
nario, in this section SFR3 proling is assumed, i.e. each
power prole features three different power levels: high,
middle and low (as shown in Figure 5). Each cell uses one
third of the spectrum with each power level. Two different
standard SFR power prole types are considered:

SFR
[1;0.5;0.25]
: the low power level equals one forth and
the medium equals half of the high power level.

SFR
[1;0.1;0.01]
: the lowpower level equals one hundredth
and the medium level equals one tenth of the high power
level.
In order to stick to a consistent notation, we also assume
a power prole for the FR1 case, in which the power is uni-
formly distributed over the sub-carriers: the uniform power
prole, where
c,n
= p
max
/N for all n and c (where N is
the number of available resource blocks).
4.1.3. Methodology. The OFDMA system-level simula-
tion and the integration of the linear optimisation prob-
lem solver has been done as described for the basic ref-
erence scenario in section Basic Multi-Cell OFDMA In-
vestigations. Initially, the performance of plain dynamic
sub-carrier assignment (i.e. in the FR1 case) is compared to
a benchmark system that statically assigns the sub-carriers
among the terminals in a round robin fashion. The goal is
to determine its performance subject to large CCI and an
increasing CSI processing delay. Then, SFR is applied on
top of the dynamic SCA techniques.
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
M. BOHGE, J. GROSS AND A. WOLISZ
0 1 2 3 4 5
3
4
5
6
7
8
9
10
x 10
5
CSI processing delay in TTIs
w
e
a
k
e
s
t

t
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/

b
p
s
FR1
SFR
[1;0.5;0.25]
SFR
[1;0.1;0.01]
static
0 1 2 3 4 5
5
6
7
8
9
10
x 10
6
CSI processing delay in TTIs
m
e
a
n

c
e
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b
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FR1
SFR
[1;0.5;0.25]
SFR
[1;0.1;0.01]
static
0 2.5 5 7.5 10
x 10
5
0
0.25
0.5
0.75
1
x
F
(
x
)
FR1
SFR
[1;0.5;0.25]
SFR
[1;0.1;0.01]
static
0 2.5 5 7.5 10
x 10
5
0
0.25
0.5
0.75
1
x
F
(
x
)
0 2.5 5 7.5 10
x 10
5
0
0.25
0.5
0.75
1
x
F
(
x
)
(a) (b)
(c) (d) (e)
Figure 6. The gain of applying SFR on top of optimal SCA, stationary terminals: (a) mean throughput (bps) of weakest terminal,
(b) mean cell throughput (bps), (c) per terminal throughput cdf, 0 TTIs, (d) per terminal throughput cdf, 2 TTIs and (e) per terminal
throughput cdf, 5 TTIs.
4.2. Results
We start discussing the results by considering a scenario
with stationary terminals.

In Figure 6 the average through-

put of the weakest terminal as well as the mean cell through-
put are shown for different CSI processing delays. Let us
rst focus on the average throughput of the weakest ter-
minal. We observe a signicant throughput gain stemming
from dynamic sub-carrier assignments (in comparison to
the round robin scheduler). Due to the low time variability
of the channel, the impact of the CSI processing delay is
rather low. While the RR scheduler is not effected by the
processing delay, the dynamic schemes suffer slightly (at
most 10% throughput loss). Still, at the highest processing
delay the dynamic schemes outperform the RR scheme by
at least 30%. Among the dynamic schemes, for the weakest
terminal throughput the applied power prole is less impor-
tant. This is quite surprising in comparison to the results of

Note that we still assume some objects within the propagation environ-
ment to be mobile causing fading effects in frequency and time (see section
System Model).
section Basic Multi-Cell OFDMA Investigations as espe-
cially the FR1 scheme should perform worse than the SFR
schemes. Next, focus on the average cell throughput also
presented in Figure 6. Regarding this total throughput of
the cell, the advantage of dynamic (optimal) scheduling is
still present (compared to the RRscheme), however, the ap-
plication of power proles starts to become important. In
the case of SFR with a prole of [1; 0.1; 0.01] the mean cell
throughput is signicantly lower than for the other two dy-
namic schemes. This is due to too much power allocated in
the rst bandwidth partition and too less power assigned in
the other partitions. Altogether, this leads to a performance
loss of roughly 10% compared to the other SFR and the
FR1. Still, the loss due to delayed CSI information is rather
low and all dynamic system approaches outperform the RR
scheme. In addition to the average throughput plots, we also
provide in Figure 6 graphs showing the CDFs of the aver-
age throughput of the terminals within the considered cells.
Here, the main statements from above are conrmed. No-
tice in particular, that dynamic subcarrier assignments do
improve not only the situation of the absolute worst terminal
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
OPTIMAL SFR AND SCA IN CELLULAR OFDMA NETWORKS
0 1 2 3 4 5
3
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x 10
5
CSI processing delay in TTIs
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FR1
SFR
[1;0.5;0.25]
SFR
[1;0.1;0.01]
static
0 1 2 3 4 5
5
6
7
8
9
10
x 10
6
CSI processing delay in TTIs
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FR1
SFR
[1;0.5;0.25]
SFR
[1;0.1;0.01]
static
0 2.5 5 7.5 10
x 10
5
0
0.25
0.5
0.75
1
x
F
(
x
)
FR1
SFR
[1;0.5;0.25]
SFR
[1;0.1;0.01]
static
0 2.5 5 7.5 10
x 10
5
0
0.25
0.5
0.75
1
x
F
(
x
)
0 2.5 5 7.5 10
x 10
5
0
0.25
0.5
0.75
1
x
F
(
x
)
(a) (b)
(c) (d) (e)
Figure 7. The gain of applying SFR on top of optimal SCA, moving terminals, speed v = 10
m
s
: (a) mean throughput (bps) of weakest
terminal, (b) mean cell throughput (bps), (c) per terminal throughput cdf, 0 TTIs, (d) per terminal throughput cdf, 2 TTIs and (e) per
terminal throughput cdf, 5 TTIs.
but of about 75% of the terminals present in the cell. Espe-
cially for the lowest quartile, the average throughput gain
is quite signicant for all considered power proles (about
70% in case of no processing delay, which reduces to 50%
in case of the longest processing delay considered). In these
CDF plots we also observe the impact of choosing a strict
power prole, as is the case with SFR [1; 0.1; 0.01]. Com-
pared to the other SFRscheme, especially the throughput of
the strongest terminals is reduced due to the lower transmit
power setting (at no signicant throughput advantage for
the terminals in the lowest quartile).
This overall picture partially changes if the channel be-
comes more time variable. In Figure 7 we show the cor-
responding results for terminals moving with a speed of
v = 10 m/s. In general we observe that for the throughput
of the weakest terminal as well as for the total cell the pro-
cessing delay becomes important. For the largest considered
processing delay, the performance of all dynamic schemes
with optimal sub-carrier assignments drops below the per-
formance of the round robin scheduler. This is simply due to
outdated channel information which can not provide the re-
source allocation algorithm a valid decision base any more.
In fact, sub-carrier assignment could also be done random.
However, for the weakest terminal there is a oor that the
SFR scheme with power prole [1; 0.1; 0.01] reaches. This
is not due to dynamic sub-carrier assignments, instead it re-
sults from the strong suppression of interference at the cell
border which gives terminals positioned at the cell edge a
signicantly better SNIR than in all other cases. However,
as can be observed from the results regarding the overall
cell throughput, this advantage at the cell edges is paid for
by an overall lower total cell throughput. This is also re-
ected by the results regarding the CDFs of the average
terminal throughput of all terminals in all cells, shown also
in Figure 7. Here, the performance advantage of the dy-
namic schemes vanishes as the processing delay increases
(in fact, it vanishes for all terminals in the cell). This is
not true for the SFR scheme with a power prole setting
of [1; 0.1; 0.01], which can achieve some gain for cell edge
terminals but at the cost of reducing the performance for
terminals in the cell centers. Notice that this performance
difference solely stems from the used power prole and not
from the dynamic sub-carrier assignments.
Finally, for LTEsystems it is commonlyassumedthat CSI
will be delayed by at most 2 TTIs. Taking this into account,
it can be observed from the results that dynamic sub-carrier
Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett
M. BOHGE, J. GROSS AND A. WOLISZ
assignments provide a much better performance than static
RR assignments. Furthermore, there is no clear advantage
of SFRcompared to FR1 which is in contrast to our ndings
given imthe result of the section Basic Multi-Cell OFDMA
Investigations. However, take into consideration that de-
spite the mobility of terminals we have only taken static
power proles intoaccount incase of SFR, leadingtoless ef-
cient resource distributions throughout all considered cells
from time to time. We suspect the optimal system perfor-
mance to be much higher in this case due to mobility effects.
5. CONCLUSIONS
We have shown that optimally distributing power and sub-
carriers among the users of a cellular OFDMAnetwork sig-
nicantly improves the cell edge-user, as well as the over-
all system performance. Conventional static soft frequency
reuse approaches do not exploit this potential, even though
they show an advantage over legacy hard frequency reuse
and uncontrolled frequency reuse 1 systems. Furthermore,
the benet of applying static SFR in a system with an op-
timal dynamic terminal/sub-carrier assignment strategy is
rather small, which is due to the fact that already solely as-
signing the sub-carriers dynamically exhibits a high poten-
tial to combat co-channel interference in according systems,
even if the assignment decisions are based on signicantly
delayed channel state information.
The development of an SFR power prole adaptation
mechanismthat approaches the global optimumat lowcom-
putational costs remains as future work issue.
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Copyright 2010 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. (2010)
DOI: 10.1002/ett