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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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Verdu, S., “Minimum Probability of Error for Asynchronou s Gaussian

Multiple-Access Channels”, IEEE Trans. Inform. Theory, vol.

IT-32,

no.1, Jan. 1986.

Hagerman,

B.,

“Single-User Receivers for Partly Known Co-Channel

Interference”, Liceniiute Thesis, TRITA-IT R

94:11

Royal Inst. of

Technology, 1994.

Hagerman,

B.,

“On the Detection

of Antipodal

ayleigh Fading Signals

in Severe Co-Channel Interference”,

IEEE

Vehicular Technologj

Conference, Stockholm, Sweden,

June, 1994.

Jakes, W. C., Microwave

Mobile

Communication, New York: Wiley,

1974.

Gudmundson,

M.,

“Cell Planning in Manhattan Environm ents”, IEEE

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