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Downlink R elative Co Chan nel Interference Powers in C ellular Radio
Systems
Bo Hagerman
Radio Communication Systems Laboratory
Dept. of Teleinformatics, Royal Institute of Technology
ELECTRUM 204, S- 164 40 KISTA,
SWEDEN
Email: bosseh@ it.kth.se
Abstract
One method to achieve high capacity in cellular
radio systems involves interference cancellation techniques at the
receivers.
To
design and evaluate the performance of such
interference cancellation receivers,
i t
is essential to use realistic
models of the co-channel interference. In the paper we study the
ordered statistic of the relative co-channel interferepce, i.e. the
ratio between the power level of i:th strongest interferer and the
total co-channel interference power. Results from Monte-Carlo
simulations show that
for
base stations on a symmetric grid,
hexagonal cells or half-square Manhattan like street cells, the
probability density functions pdf) of the interference ratios are
almost independent of the cluster size and
of
the base station
activities. The results demonstrate the dominance of the
strongest interferer and show that this dominance is even more
pronounced in those situations when the signal to interference
ratio is low. The presented results provide a base for more
realistic models for performance evaluation in cellular systems
than the commonly used Gaussian interference model.
I . INTRODUCTION
In cellular radio systems, the limited available bandwidth is
one of the principal design constrain ts. For future high
subscriber density systems, frequency reuse is one of the
fundamental approaches for efficiency spectrum usage and for
achievin g the demand s of required capacity. The possibility to
reuse the sam e channels, the frequency bandwidth, in different
cells is limited by the amount of co-channel interference
between the cells. The minimum allowable distance between
nearby co-cha nnel cells or the maxim um system capacity)
is
based on the maximum tolerable co-channel interference
at
the receivers in the system. Receivers resistant to co-channel
interference allow a dense geographical reuse of the spectrum
and thus a high system capacity. This can be achieved by
using interference cancellation techniques that take advantage
of the structure of the co-channel interference [l-31. Fully
centralized detection algorithms may be feasible in a base
station receiver since the active users signaling waveforms
can be distr ibuted via a backbone network. Even though the
task requires a high degree of implementation complexity,
these type of algorithms may be acceptable in a base station
which demodulates information from a subset of all mobile
stations. However, the m obile station is the destination of
information from only one base station in the downlink case.
The implementation costs of central ized algori thms may be
unacceptably high for this case. In the downlink there may
also
exist restrictions
on
the amoun t of information that can be
distributed about the active users. O ne approach
to
alleviate
this problem is to consider only the strongest active co-
channel users at the receiver. Other active users may be
neglected and regarded as background noise.
To
design and
evaluate the performance of receivers with the approach
describe d for the down link abo ve, it is essential to use realistic
models of the co-channel interference levels in the cellular
radio environment. In this paper, we investigate the ordered
statistic of the relative co-channel interference, i.e. the ratio
between the power level
of
i:th strongest interferer and the
total C O-cha nnel interference power.
We
consider radio
systems consist ing of a cluster of cells, each with a base
stat ion which communicates at a fixed power level with a
subset of all mo bile stations in the system . In Section I1 the
used symmetrical cell patterns are described. Hexagonal cells
models macrocellular systems and microcellular systems are
modelled with street covering cells in a so called Manhattan
environment, i .e.
in a
regular network of streets. The
propagation models for the different systems are presented in
Section 111. Further, in Section IV we define the ordered
stat istic of the co-channel interference. Results from M onte-
Carlo simulations are shown in Section
V.
Finally, in Section
VI som e conclusions are drawn.
11. C ELLU LAR ODELS
In planning a cellular system, the whole service area is
divided into non overlapping cells that cover the area without
gaps
[4].
he cells are grouped into clusters, wherein the
available channels are not al lowed to be reused. The cluster
size C,
defined
as
the number of cells per cluster, determines
how many channel sets the available spectrum must form.
Smaller cluster sizes provide more channels per cell and
thereby offering more capacity per cell. Therefore, with fixed
cell size the system capacity is increased for a decreased
cluster size.
A.
Hexagonal Cell
Coverage
Model
In macrocellular systems, where base stat ion antennas are
placed at high locations, cel ls are large and of almost circular
shape. When designing such systems, cells are modelled as
hexagons and the cluster size is determined by
[4],
1)
2 .. .2 . .
Since and j are integers, the cluster size can only take certain
c = l J J
,
l , J > O .
0-7803-2742-XI95 4.00
995 IEEE
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Fig
1
A hexagonal cell pattem example The reused coverage of one channel
group for cluster size 7 is shown
realizable values,
{
1, 3,4,7,B, 12, .. } . The normalized
channel reuse distance,
R H ,
and1 the cluster size required to
cover a fixed assignment plan is related
as
[4],
R H = ,J
2)
An example of channel reuse in a hexagonal layout is shown
in Figure
1.
B. Half-Square Manhattan Co wr age Model
A
street microcellular system is defined in this paper as a
system with outdoor cells, each with the base station antenna
mounted at a height low compared to the heights of
surrounding buildings. The en \ ironment used , the so called
Manhattan mode l, is based on
a
ideal city modelled
as a
large
“chessboard” where each square corresponds to one block
with a regular network of streets between the blocks. We place
a
base station antenna
at
every street crossing and the cell size
is assumed to be half a block in all directions. The cluster size
for this so called half-square cells, can only take the values [ : ]
3)
to cover the whole service area in a symmetric cell plan. As
seen, the cluster size can take on only certain realizable
values,
{ 1, 2 ,4 ,
5,
8, 9, . } .
An example
of
channel reuse in
a
half-square Manhattan layout is shown in Figure 2. T he
distance to the nearest geornetric co-channel neighbors,
normalized to the cellblock side length is given by
[S
2
c = + j 2 , i , j > O ,
R S G
= i
.
(4)
An important distance in this kind of env ironm ent is the
distance to the nearest LOS Line Of-Sight) co-channel
neighbor. Normalized to the ci:ll/block length, we can write
the nearest line of sight co-channel neighbor distance as
[5]
(
5
where gcd i ,j) denotes the grealest common divider
of
i and j .
C
R S L =
jjzm
Fig.
2. A half-square Manhattan cell pattern example. The reused co verage of
one channe l group for cluster size 2is shown.
C. TrafJic Mode l
We will in this paper assume that the studied cellular
systems are uniformly loaded, i.e. all base stations carry on
the averag e the same a moun t of traffic. The channel al location
within
a
cell is assumed to be done at random and independent
of the channel allocation in all other cells. Thus,
a
specific
channel within a cell is used with probability P. P will be
called the base station activity factor.
111.
PROPAGATIONODELS
A. Macrocellular Propagation Model
The propagation attenuation for base station antennas
placed at high locations is generally modelled as the product
of the -a: th power
of
distance and with
a
log-normal
compo nent representing shadow ing losses [4]. Thus, for a user
at a distance r from a base station, link gain is proportional to
where y is the dB attenuation due to shad owing, with zero
mean and standard deviation (J. In this paper, we use the
standard deviation J
=
8 dB and
a
= 4 for the power law.
B. Microcellular Propagation Model
In a street environme nt for
a
system operating at
870
MH z,
the at tenuation has been measured and modelled in [6]. The
presented empirical propagation mode l shows that along
a
street with LOS propagation to the base station, the
attenuation basically corre spon ds to free-space loss in the
vicinity of the transmitter. At
a
distance of
100 - 400
meter
from the ba se stat ion a breakpoint can be observed whereafter
the attenuation increases faster than in free-space. Let
m ,
and
m2 represent the power law before an d after the breakpoint
xL
respectively. Thus ,
the distance link
gain along the
LOS
street
is modelled
as,
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-20
-30
9 -
-
m
Activity 50
Cluster sizes
11.3,
4
7. 9. 121
l \ I
, An\
-40 -
S -50-
-70
-80 -
0 50 100
150
200
250
300
350 400
Distance
[m]
-100
Fig
3
environm ent Distance between street crossings is assumed to
be
100 m
The lin k g i n
as
function of distance in the Manhattan street
where the smooth ness of the transit ion is de termined by q .
A
street corner was found to have the same impact on the
received power along a crossing NLOS Non Line Of-Sight)
street, as a hypothetical transmitter at the corner transmitting
with the sam e power level as the received power at the corner.
The l ink gain along the NLOS street is equal to
which mathematically is identical with 7 ) . yo in 8 ) may be
interpreted as the distance from the corner to the hypothetical
transmitter and 8) is not valid
for y
<
yo.
The
NLOS
expression is always used in combination with the LOS
expression which form the aggregate NLOS distance gain as
G xc,Y = GL O S p N L 0 S O : ) ’
9)
In (9)
xc
s the distance from the base stat ion to the corner and
y is the distance along the NLOS street . The results in
[ ]
suggest the following choices to represent a typical ci ty
envi ronment : inl = 2 , m, = 5, xo = 1 m, xL = 200 m , nl = 2, n2
= 6 o = 3.5 m , y L = 250 m and q
= 4.
In Figure 3. the distance
attenuation given in 7) and 9) with the above parameter
values is presented.
A
signal from a base stat ion can reach a
NLOS receiver through many paths. Since a corner implies a
strong attenuation, we will only regard co-channel
interference that has passed maximum one corner. The
shadow fading was found in
[6]
to be well modelled as log-
normal fading with a suggested standard deviation os=
3.5
dB. The total aggregate at tenuation is then modelled as the
product of the distance at tenuation and the log-normal
component .
IV.
CO-CHANNEL
NTERFERENCE
In interference l imited systems, the receiver performa nce is
a function of the signal to interference ratio SIR) [2-31, which
is defined as
where
S
denotes the desired signal pow er level at the receiver
and the compound co-channel interference power level is
denoted by
1.
Without loss of generali ty i t is assumed that the
individual co-chann el interferers are ordered numb ered) such
that their power levels satisfy
I , ,
2 . 2
I,,,
. T he commonl y
used interference model for perform ance evaluations is based
on the central l imit theorem by which
I
= X I , is
approxim ated by a Gaussian rando m variable. Ho wever, when
studying co-chan nel interference cancellat ion receivers which
only consider the strongest subset of the active co-channel
users. the question arises how well I
=
can be
approximated by
I
(II
+
I , ) ,
...
in the cellular environm ents.
For this purpo se w e are interested in th e stat istic propert ies
of
the relat ive co -channel interference comp onen ts, i .e. , I , / [ , the
ratio between the power level of the i : th strongest interferer
and the total co-channel interference power. This is done by
studying the pdf, the mean and standard deviation values of
the ordered relat ive co-ch annel interference.
V. NUMERICAL ESULTS
The results presented in this paper were obtained by m eans
of Monte-Carlo simulations of the two system environment
cases studied, macro- and micro-cellular systems. The
simulated systems are set up such that a large amo unt of cells
of prospective co-channe l interferers are placed arou nd
a
cell
with the used wanted channel. To mitigate border effects in
the simulations we have, indep endent of the cluster size, used
7 2 and 68 prospective co-channel interferer cells for the
hexagonal and the half-square Manhattan cell patterns,
respectively. For all results presented, the mobile position is
uniformly distributed within the used cell coverage. For each
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Base Act ivi ty [ /I
[17.
33. 50,
67,
83, 1001
\
h
6
i
hird strongest interferer
5
4
3
econd strongest interferer
2
1
.I
0 0.1 0.2 0.3 0.4
0.5
0.6 0.7 0.8 0.9 1
Ix
5.
Examples of the p df s for the three strongest interference ratios in
;a
hexagonal environment
9 Cluster sizes
8
[I
2 . 4 , 5.
8
91
7
6
10
d strongest interferer
4
3
2
nd strongest inlerferer
1
'0
0.1
0.2 0.3 0.4 11.5 0.6
0.7
0.8 0 9
1
l < l
Fig.
6 .
Examples of the p dfs
for
the
three
strongest interference ratios in
a
Manhattan street environment.
set of parameters, data was collected from
10,000
mobi le
posit ions where we have assumed the shadow fading to be
independent between different runs. For eac h mob ile posit ion,
we also assumed that signals from different base stations are
exposed to independent fading. In Figures 4 and
5 ,
w e show
results for a macro-cellular system with a hexagonal cell
pattern with a cell radius of 1 kmThe pdf:s for the three
strongest co-channel interference ratios are shown. In Figure 4
the base station activity factor is 0.5 and a set of pdf:s are
presented fo r each of the different cluster sizes in
[ l
3 , 4 , 7 , 9 ,
121.
As seen in Figure 4, the
p d t s
of the interference ratios are
almost independent of the cluster size. The absolute values of
the amount of co-channel interference powers are
of
course
decreasing with increasing cluster size, e.g. increasing reuse
distance. The dominanc e of the strongest co-channel interferer
in the hexagonal cell pattern is demonstrated in the results
shown in Figures
4
and 5 If all relative CO-chaninel
interference are of the same order of magnitude, the pdifs
10
9
8
7
hird strongest interferer
-
,5
4
3 d strongest interferer
2
1
0
0
0.1
0.2 0.3 0.4 0.5
0.6 0.7 0.8
0.9
1
X
/
Fig. 7. Examples of the pdf:s for the three strongest interference ratios in a
Manhattan street environment.
0.8,
0 6 1 P=0.17
Cluster size
3
Base Activity [%]
17,
33,
50,
67,
83,
1001
1 2 3
4
5 6 7
8
9 10
x [ Interference strength nu mber]
Fig.
8.
Examples of the mean and the standard deviation for the ten strongest
interference ratios in a hexagonal environment.
would be concentrated in the leftmost part of the figures. In
Figure 5 we can see that the strongest co-channel interferer is
more dominant for a small traffic load on the system.
However, the differences depending on the base station
activity factor is small and the basic shape of the pd fs remain
for the whole set of activity factors shown. Results are shown
in Figures
6
to 8 for a micro-cellular system using a half-
square cell pattern in an ideal Manhattan ci ty environment
with a cellblock length of 100 m .
As
seen from the presented
results, this case follows the previous. However, the
domina nce of the strongest co-channel interferer is even more
pronuunced . Th e variations for different cluster sizes Fig.
6)
and base station activity factors Fig.
7)
is larger here then in
the former case. Th is since in the street environm ent, the co-
channel neighbors at LOS distance wil l cause more
interference than the nearest geometric neighbors. In Figure 8
and 9,
we
prescnt the mean
and
the
standard
deviation for the
ten strongest co-channel interference ratios in the hexagonal
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0.8
[
9 -
8
7-
6 -
Base Activity [“
(17. 33, 50 .
67 83,
001
9-
8 -
7
0.2
Std(lx I
0.1
n
“1
3 4
5 6
7 8 9 10
x [Interference strength number]
Fig. 9. Examples of the mean and the standard deviation
for
the ten strongest
interfer ence ratios in a Manhattan street environme nt.
and the half-square Manhattan street environments,
respectively.
A
set of curves are presented for each of the
different base station activity factors in
[116 113
112,
213, 516,
9,
11 when the cluster size is
3
Fig. 8) and 2 Fig. 9),
respectively. The dominance of the strongest co-channel
interferer can be seen and if
a
receiver can take into account a
subset of the strongest interferers, the amount of co-channel
interference will be greatly reduced. In Figures
10
and 11, we
s t udy t he pdf s of the two strongest interferer ratios
conditioned on that the received SIR is less then a signal to
interference value threshold, i.e. SIR
< T . As
seen
for
both the
hexagona l Fig. 10) and the Manha ttan street Fig. 11)
environm ents, for decreasing signal to interference threshold
the dom inance of the strongest interferer is more em phasized.
VI. DISCUSSION
In this paper we have studied downlink co-channel
interference powers in symmetrical macro- and micro-cellular
systems. The results demonstrate the dominance of the
strongest co-channel interferer.
A
conclusion would be that
the central limit theorem Gaussian assum ption ) is a poor
approximation in the studied environments.
The
presented
results may provide a base for more realistic models of the
co-
channel interference for performance evaluations
of
cellular
systems than the commonly
used
Gaussian interference
model .
As
show n, the basic shape of the pdf:s of the ordered
relative co-channel interference are almost independent of the
cluster size and the base station activity factor. It is shown by
utilizing receivers that take into account a subset of the
strongest co-channel interferers, that the amount of co-
channel interference can be greatly reduced. With interference
cancellation
of
or 2 of the strongest co-channel users, we
may reduce the mean value of the co-channel interference
with approximately 60 to 90 . The results indicate that the
improvement by using interference cancellation receivers may
Activity 50%
Cluster size
3
SIR Threshold T
[dB]
[Int..
15,
9,
31
4~ T=lnf.
3
2
1
0
0
0.1
0.2 0.3 0.4 0.5
0.6 0.7 0.8
0.9 I
1x11
10.
Examples of the pdf:s for the two strongest interference ratios in a
hexagonal e nvironment
Activity
50
Cluster size 2
SIR Threshold T [dB1
[Inf.. 15.
9. 31
’ Second strongest interferer
Stronqest interferer
Fig. 11. Examples of t he p d f s for the’.two strongest interference ratios in a
Manhattan street environment.
be even greater in those situations when the signal to
interference ratio is low.
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94:11
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B.,
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ayleigh Fading Signals
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