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It is my first report for my final year at university
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ករសងអបរ យវជន នង រឡា
វទយាសថាន នបចករវទយាសថរពជា
េបា តពាង ាពោសលយអគគសន នង ថាពពល
គោងសញញា បកត វទយសកររ
កបធានបា : Refined evaluation of co-channel signal to interference power
ratio in wireless cellular systems
នសសត :
ឯរាស : ារគពនាគពន
កគាាលបនទជរ : បណឌ ត Monica Visintin
ឆន សរា : ២០០៩ - ២០១០
MINISTERE DE L'EDUCATION DE
LA JEUNESSE ET DES SPORTS
INSTITUT DE TECHNOLOGIE DU CAMBODGE
DEPARTEMENT DE GENIE ELECTRIQUE ET ENERGETIQUE
MEMOIRE DE FIN D'ETUDES
Titre : Refined evaluation of co-channel signal to interference power
ratio in wireless cellular systems
Etudiant : KHEANG Sokkhoung
Spécialité : Télécommunication
Maître de stage : Prof. Monica Visintin
Année Scolaire : 2009 - 2010
POLITECNICO DI TORINO
III Facoltà di Ingegneria
Bachelor of Science in Electronic and Computer Engineering
Refined evaluation of co-channel signal to interference
power ratio in wireless cellular systems
Supervisor:
Prof. Monica Visintin
Candidate:
KHEANG Sokkhoung
January 2011
ករសងអបរ យវជន នង រឡា
វទយាសថាន នបចករវទយាសថរពជា
េបា តពាង ាពោសលយអគគសន នង ថាពពល
គោងសញញា បកតវទយសកររ
របសនសសត ឃាង សខខង
ោលបរទយចេាោរពារារណា : រពភៈ ២០១១
អនញញា តអោយការពារគអោង
នាយរវទយាសថាន ន បណឌ ត អ ព រពយណ
ភនអេញ ថង ៃទ ខែ ឆន ២០១១
កបធានបា : Refined evaluation of co-channel signal to
interference power ratio in wireless cellular
systems
សហកាស : POLITECNICO DI TORINO
កបធានេបា តពាង : ោរ ជ ា រ
ាសតាា ចារយាាលបនទជ : Prof. Monica Visintin
ភនពញ ឆន ២០១១
MINISTERE DE L'EDUCATION,
DE LA JEUNESSE ET DES SPORTS
INSTITUT DE TECHNOLOGIE DU CAMBODGE
DEPARTEMENT GENIE ELECTRIQUE ET ENERGETIQUE
MEMOIRE DE FIN D'ETUDES INGENIEUR
DE M. KHEANG Sokkhoung
Date de soutenance: le février 2011
«Autorise la soutenance du mémoire»
Directeur de l'Institut : Dr. OM Romny
Phnom Penh, le…..………………2011
Titre : Refined evaluation of co-channel signal to
interference power ratio in wireless cellular systems
Etablissement du stage : POLITECNICO DI TORINO
Chef du département : M. CHY Cheapok
Professeur de responsable : Prof. Monica Visintin
PHNOM PENH 2011
i
ACKNOWLEDGEMENT
First of all, I would like to extremely thank to my family, especially,
my parents who always support me not only financial problem, but also
encourage, guide and give me with good advices since I was born up to now.
As a result, I can achieve my goal with final bachelor thesis in hands. If there
aren‟t supports from them I must not be able to have such a very great time
like today. Finally, I want to say you are my everything, Mom and Dad.
I am very grateful to my dear supervisor Prof. Monica Visintin, and
would like to thank her indeed for her supervision and encouragement.
Also I would like to show a deep thank to EM-EuroAsia project which
gave me a really priceless chance to get the exchange study and to realize my
final bachelor thesis.
Here, it is a great time for me to show my indeed thank to my host
university, Politecnico di Torino, coordinator providing facilities in my study
as well as my report.
I am thankful for the encouragement of Dr. OM Rommy, director of
Institute of Technology of Cambodia.
I send my sincere thank to, Mr. CHY Cheapok, head of Electrical and
Energy department for his recommendation and encouragement.
I would like to thank Mr. PHOL Norith, deputy of director and my
home institution EM-EuroAsia coordinator, who helps me a lot in the process
of my EM-ECW application access, visa process, and my travel arrangement.
Finally, I would like to thank to all lectures who teach , specially, in
department GEE and all my friends who always have good cooperation and
encourage me to study hard and I am very lucky to have them as my friends, I
really enjoyed studying with them.
ii
Table of contents
ACKNOWLEDGEMENT ---------------------------------------------------------------------------- I
TABLE OF CONTENTS ---------------------------------------------------------------------------- II
CHAPTER I : CELLULAR NETWORK ---------------------------------------------------------- 1
1.1 INTRODUCTION ------------------------------------------------------------------------------ 1
1.2 FREQUENCY REUSE ------------------------------------------------------------------------- 1
1.3 CLUSTER SIZE ------------------------------------------------------------------------------- 6
1.4 SIGNAL TO INTERFERENCE RATIO -------------------------------------------------------- 10
CHAPTER II: SIMULATION --------------------------------------------------------------------- 13
2.1 USER IN A RANDOM POSITION ------------------------------------------------------------- 13
2.2 POSITION OF CO-CHANNEL ---------------------------------------------------------------- 17
2.3 CALCULATION OF SIGNAL TO INTERFERENCE RATIO(S/I) ------------------------------ 20
2.4 RESULT OF THE SIMULATION ------------------------------------------------------------- 22
2.5 CONCLUSION ------------------------------------------------------------------------------- 29
CHAPTER III: CAPACITY AND INTERFERENCE IMPROVEMENT TECHNIQUE - 34
3.1 SECTORIZATION ---------------------------------------------------------------------------- 34
3.2 CELL SPLITTING ---------------------------------------------------------------------------- 37
3.3 INTERFERENCE PRECANCELLATION ------------------------------------------------------ 38
TABLE OF FIGURES ------------------------------------------------------------------------------ 39
REFERENCES --------------------------------------------------------------------------------------- 41
1
Chapter I : Cellular network
1.1 Introduction
The basic of cellular network is that a limited radio band is shared by a large
number of users by the reuse of the available frequencies. The total coverage area is
divided into cells and a mobile communicates with the base-station(s) close to it. Two
main problems that must be considered in cellular network are the co-channel interference
and adjacent channel interference. Sources of interference include another mobile in the
same cell, a call in progress in a neighboring cell, other base stations operating in the same
frequency band, or any non-cellular system which unintentionally leaks energy into the
cellular frequency band. Moreover, the interference on voice channels causes cross talk,
where the subscriber hears interference in the background due to an undesired
transmission. On control channels, interference leads to missed and blocked calls due to
errors in the digital signaling. Interference is more severe in urban areas, due to greater RF
noise floor and the large number of base stations and mobiles. Interference has been
recognized as a major bottleneck in increasing capacity and is often responsible for
dropped calls. Even though interfering signals are often generated within the cellular
system, they are difficult to control in practice (due to random propagation effects). Even
more difficult to control is interference due to out-of-band users, which arises without
warning due to front end overload of subscriber equipment of intermittent inter-modulation
products. In practice, the transmitters from competing cellular carriers are often a
significant source of out-of-band interference, since competitors often locate their base
stations in close proximity to one another in order to provide comparable coverage to
customers.
1.2 Frequency reuse
Frequency reuse refers to the use of radio channels on the same carrier frequency to
cover different areas which are separated from one another by sufficient distances so that
co-channel interference is not objectionable. Frequency reuse is employed not only in
present day mobile-telephone service but also in entertainment broadcasting and most
other radio services.
The idea of employing frequency reuse in mobile-telephone service on a shrunken
geographical scale hints at the cellular concept. Instead of covering an entire local area
from one land transmitter site with high power at a high elevation, the service provider can
distribute transmitters of moderate power throughout the coverage area. Each site then
primarily covers some nearby subarea, or zone, or “cell”. A cell thus signifies the area in
which a particular transmitter site is the site most likely to serve mobile-telephone calls.
Figure 1.1 illustrates the frequency reuse in cellular network. In principle, the spacing of
transmitter sites does not need to be regular, and the cells need not have any particular
2
shape. Cells labeled with different letters must be served by distinct sets of channel
frequencies to avoid interference problems.
Qi : ith
cell using channel set Q
: transmitter location
A cell therefore has the additional significance that it is the area in which a
particular channel set is the most likely set to be used for mobile-telephone calls. Cells
sufficiently far apart, such as those labeled A1 and A2, may use the same channel set.
Through frequency reuse, a cellular mobile-telephone system in one coverage area
can handle a number of simultaneous calls greatly exceeding the total number of allocated
channel frequencies. The multiplier by which the system capacity in simultaneous calls
exceeds the number of allocated channels depends on several factors, particularly on the
total number of cells.[1] [V.H. Mac Donald79 ].
Figure 1-0-1 Illustration of frequency reuse in cellular system
3
The frequency reuse plan is overlaid upon a map to indicate where different
frequency channel are used. The hexagonal cell shape shown in Figure 1.2 is conceptual
and is a simplistic model of the radio coverage for each base station, but it has been
universally adopted since the hexagon permits easy and manageable analysis of a cellular
system.
The actual radio coverage of a cell is known as the footprint and is determined from
field measurements or propagation prediction models. Although the real footprint is
amorphous in nature, a regular cell shape is needed for systematic system design and
adaptation for future growth. While it might seem natural to choose a circle to represent the
Figure 1-0-2 Illustration of the cellular frequency reuse concept. Cells with
the same letter use the same set of frequencies.
4
coverage area of a base station, adjacent circles cannot be overlaid upon a map without
leaving gaps or creating overlapping regions. Thus, when considering geometric shapes
which cover an entire region without overlap and with equal area, there are three sensible
choices: a square; an equilateral triangle; and a hexagon as shown in Figure 1.3. A cell
must be designed to serve the weakest mobiles within the footprint, and these are typically
located at the edge of the cell. For a given distance between the center of a polygon and its
farthest perimeter points, the hexagon has a largest area of the three.
Thus, by using the hexagon geometry, the fewest number of cells can cover a
geographic region, and the hexagon closely approximates a circular radiation pattern which
would occur for an omni-directional base station antenna and free space propagation. Of
course, the actual cellular footprint is determined by the contour in which a given
transmitter serves the mobiles successfully.
When using hexagons to model coverage areas, base station transmitters are
depicted as either being in the center of the cell (center-excited cells) or on three of six cell
vertices (edge-excited cells). Normally, omni-directional antennas are used in center-
excited cells and sectored directional antennas are used in corner-excited cells. Practical
considerations usually do not allow base stations to be placed exactly as they appear in the
hexagonal layout. Most system designs permit a base station to be positioned up to one-
fourth the cell radius away from the ideal location[3] [Rappaport].
To understand the frequency reuse concept, consider a cellular system which has a
total of S duplex channels available for use. If each cell is allocated a group of k channels
(k<S), and if the S channels are divided among N cells into unique and disjoint channel
groups which each have the same number of channels, the total number of available radio
channels can be expressed as
Figure 1-0-3 Possible choices of cell shape. For a given values of R, Ahex
provides the Max. Coverage -Area with fewest number of cells[2][google:
cellular-concept –design-fundamentals]
5
(1.1)
The N cells which collectively use the complete set of available frequencies is
called a cluster which will be detailed later on.
It is not too difficult to find the reuse cell. Due to the fact that the hexagonal
geometry of Figure 1.2 has exactly six equidistant neighbors and that lines joining the
centers of any cell and each of its neighbors are separated by multiples of 60 degrees, there
are only certain cluster size and cell layouts which are possible[4] [Rappaport]. Actually,
other 6 cells exist, which can be reached from A1 with a path of i cells in one direction and
j cells after a counterclockwise rotation of 60 degrees, as shown in Figure 1.4. In the
overall, A1 has 6 neighbor cells A2,…..,A7, which use the same set of frequencies, as
many as the sides of a hexagon (note that the number of neighbors does not depend on i or
j). The distance between the antennas of any of these neighbor cells and the antenna of A1
is always equal to D, the so-called reuse distance. [5][Monica‟s lecture]
Figure 1-0-4 Illustration of how to find co-channel cells.
6
Assume that the side of each hexagon is equal to R, while the apothem is L with:
(1.2)
Note that L is the radius of the inner circle, while R is the radius of the outer circle
of the hexagon. The antenna, placed at the center of the hexagon, should transmit a power
PT such that
i.e. the power received by a mobile phone at the vertex of the
hexagon (maximum distance from the antenna), is sufficient (higher than the phone
sensitivity).Parameter alpha ( ) depends on the antennas, transmitted signal frequency etc,
while n is the path loss exponent, which depends on the physical characteristics of the cell
and ranges between 2 and 4. Then, from the point of view of the antenna, the most
important parameter is R, which is often simply called the radius of the cell.
Then, in the coordinate system shown in Figure 1.4, the antenna of cell A1 is in
point
P1 = [0; 0], while the antenna of cell A2 is in point
(1.3)
In addition, the reuse distance between the main base station to each co-channel
cells can be expressed by:
(1.4)
1.3 Cluster size
The N cells which collectively use the complete set of available frequencies is
called a cluster. If a cluster is replicated M times within the system, the total number of
duplex channel, C, can be use as a measure of capacity and is given
(1.5)
7
As seen from equation (1.5), the capacity of a cellular system is directly
proportional to the number of times a cluster is replicated in a fixed service area. The factor
N is called the cluster size and is typically equal to 3,4,7,9, or 12. If the cluster size N is
reduced while the cell size is kept constant, more clusters are required to cover a given area
and hence more capacity (a larger value of C) is achieved. A large cluster size indicates
that the ratio between the cell radius and the distance between co-channel cells is large.
Conversely, a small cluster size indicates that co-channel cells are located much closer
together. The value of N depends on how much interference a mobile or base station can
tolerate while maintaining a sufficient quality of communication. From a design point of
view, the smallest possible value of N is desirable in order to maximize capacity(C) over a
given coverage area. The frequency reuse factor of a cellular system is given by 1/N, since
each cell within a cluster is only assigned 1/N of the total available channels in the system.
The area of the equivalent hexagon is
(1.6)
Where
While the area of the cluster is
(1.7)
With
The two areas must be equal, and therefore,
From equation 1.4 we can write
[6][Monica‟s lecture]
So the cluster size N can be evaluated by:
(1.8)
Where i and j are non-negative integers. As shown in Figure 1.2 the cluster size is
7.
8
From equation (1.8) we can get:
(1.9)
Then the co-channel reuse ratio is Q:
Where
D : reuse distance between base station A1 and its co-channel cells[Monica‟s
lecture].
N : cluster size
Note: A small value of Q provides larger capacity since the cluster size N is small,
whereas a larger value of Q improves the transmission quality, due to a smaller level of co-
channel interference.
With hexagonal cells, the center P(i,j)of any cell from the reference cell can be
specified by a pair of integers (i, j), where i and j are respectively the displacements, in
number of cells, along the U and V axes shown in the following diagram.
Note that the angular spacing between the 2 axes is 60o .
Figure 1-0-5 Show how to find the reuse distance
9
Table 1.1 lists some possible values for the cluster size N, figure 1.6 shows the
shape of some clusters, for N = 3, 4, 7, 9, 12.
i j N
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
1
3
7
13
21
4
7
12
19
28
9
13
19
27
37
Table 1.1 some possible values of cluster size N.
The number of cells per cluster, referred to as cluster size as well, is a parameter of
major interest, since in practice this number determines how many channel sets must be
formed out of the total allocated spectrum. If the total number of channels available to the
system is fixed, smaller cluster sizes provide more channels per cell and per cell site base
station. Therefore, each cell site can carry more traffic, thereby reducing the total number
of cell sites needed for a given total load.
10
1.4 Signal to interference ratio
The reuse of frequency implies that in a given coverage area there are several cells
that use the same set of frequencies. These cells are called co-channel cells, and the
interference between signals from these cells is called co-channel interference. Assume the
case of a mobile in cell A1 of figure 1.7: it receives the signal transmitted by the base
station A1 at a frequency f1, which belongs to the set of frequencies A, with a power PRu.
At the same time, the mobile receives also the signals transmitted by base stations A2; ….
;A7;… at frequency f1, respectively with powers PR1;…..; PR7 and the mobile user cannot
isolate the only useful signal coming from the base station A1.
Figure 1-0-6 Illustration of various cluster size which are typically used.
11
This phenomenon is called co-channel interference (CCI), since the interfering
signals are transmitted at the same frequency f1 of the useful signal. We define the co-
channel signal to interference ratio:
(1.10)
Where M is the number of interfering base stations, and the higher is this ratio, the
better it is (note that this ratio is typically given in dB).
The worst case is that in which the mobile is on the boundary of its cell, as shown
in figure 1.7. The number of interfering base stations is infinite in principle, but the main
part of co-channel interference is due to the first-layer of interfering cells, i.e. the nearest
ones. If the base station antenna is omni-directional, then M=6, as shown in figure 1.7 but
in some cases M can be smaller than 6. Assume that the power transmitted by each base
station is always equal to PT. Then the co-channel signal to interference ratio can be
approximated as:
Figure 1-0-7 Case of a mobile(red circle) at the boundary of cell A1 (useful
cell) for a cluster size of 7; the blue lines identify the distances between the
mobile and each of the first-layer co-channel base station
12
(1.11)
n is path loss exponent typically ranges between 2 to 4 in urban cellular system.
Note that
does not depend on the radius of the cell, large cells and small cells give
the same co-channel interference. On the contrary,
increases if the cluster size N is
increased and/ or the number M of interfering base stations is reduced. Moreover, if the
path loss exponent n is large, then
increases. In general, it is necessary to guarantee a
minimum value
of co-channel signal to interference ratio, in order to have the
desired quality of the received signal. Then the maximum value of cluster size is
found from
. For example, if
= 18dB, M=6 and n= 3, then
Which means that the smallest cluster size is N = 19. If n = 4, we have N 6.49,
which means N = 7.[Monica‟s lecture]
From the equation (1.10) we can also find the signal to interference for the user in a
random position. Then we can get:
Where The received power of the useful base station
The received power of the interference base station
Distance between the user and the interference base station
So the equation (1.10) becomes:
(1.12)
Where we can find the value of D depend on the position of the user and the
position of the co-channel base stations.[7][Monica‟s lecture]
13
Chapter II: Simulation
2.1 User in a random position
The algorithm below is the computation to find the user position in a random way.
The user position is one of the most important factor that should be taken into account in
order to find the signal to interference ratio. To find the user in a random position, firstly,
we need to set the area that the user should stay in and the area that the user should not. In
this case, there should be a program to plot the hexagon, then find the equations of the
lines of the hexagon. Having the equations we can set the condition on the user.
This program is to plot the useful hexagon with centre in (0,0) and radius equal to 1
and other hexagons around the useful one:
% Plot the hexagon
x_hexagon=[-1 -0.5 0.5 1 0.5 -0.5 -1];
y_hexagon=[0 -sqrt(3)/2 -sqrt(3)/2 0 sqrt(3)/2 sqrt(3)/2 0];
i=2;
j=1;
R = 1; % the outer radius of the hexagon
L = (R/2)*sqrt(3); % the inner radius of the hexagon
N = i^2+j^2+i*j; % cluster size
n = 5;
m = 5;
figure(1);
hold on
for nn=-5:n
for mm=-5:m
plot(x_hexagon+3*nn,y_hexagon+sqrt(3)*mm)
end
end
for nn=-5:n-1
for mm=-5:m-1
plot(x_hexagon+1.5+3*nn,y_hexagon+sqrt(3)/2+sqrt(3)*mm)
end
end
axis equal
grid on
xlabel('X km');
ylabel('Y km');
14
Figure 2-0-1 The plot of hexagon with (0,0) in km
Having plot the hexagon, let me randomize the position of the user. As the radius
of the cell is 1. The user position must be such that axis X is between -1 to 1 and as well as
axis Y. Then I will set the area that the user should stay. In this case, firstly I have to find
the equations of each line of the hexagon. Getting all the equations, I will compare the
coordinate of the user if the user is inside the useful cell the result is Pu, but if the user is
outside of the cell there will be a statement telling „that the user is out of the cell‟. Then I
have to run the program again until I can get the user position in the cell to calculate the
distance between the user and the six co-channels base stations.
%------------------------------------------------------------
% This program is to find the user position in a cell (random
position)
% In order to find a random position of user, first of all we
need to set
% random value of user's coordinate then we find the
equations of lines of
15
%the edge of the hexagon after that we compare the coordinate
that we have
% calculate with the random position of the user P
nruns=1000;
matH=zeros(nruns,5);
teoHdB=zeros(1,5);
for z=1:nruns;
px=(rand-0.5)*2; % axis x of user position
py=(rand-0.5)*2; % axis y of user position
if px>=-1&px<=-1/2
y = sqrt(3)*(px+1); % equation of line
elseif px>=-1/2&px<=1/2
y=sqrt(3)/2;
elseif px>=1/2&px<=1
y=sqrt(3)*(-px+1);
end
P=[px,py];
U=[px,y];
V=[px,-y];
if py<=y & py>=-y
prx=px;
pry=py;
Pu=P % user position in the useful cell
plot(prx,pry,'--rs','LineWidth',1,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','r',...
'MarkerSize',5)
In this case, if the user is outside the useful cell the program will random it again by
using a function bellow:
function [px,py]= checked(a)
px=(rand-0.5)*2; % axe x of user position
py=(rand-0.5)*2; % axe y of user position
if px>=-1 & px<=-1/2
y = sqrt(3)*(px+1); % equation of line
elseif px>=-1/2 & px<=1/2
y=sqrt(3)/2;
elseif px>=1/2 & px<=1
y=sqrt(3)*(-px+1);
end
P=[px,py];
16
U=[px,y];
V=[px,-y];
if py<=y && py>=-y
pux=px
puy=py
Pu=P % user position in the useful cell
else checked;
end
This function is used to random the user position in the case it is outside the useful
cell, yet it does not take into account in the calculation, it is just a suggestion of the
program which tell the user where she/he should stays in.
Figure 2-0-2 Show the user in the hexagon(cell). The red point is the mobile
user position.
17
2.2 Position of co-channel
In order to find the distance between the user and the co-channel base stations we
,firstly, have to find the position of each interfering base station.
Assume that the co-channels base stations are in the position P1(Px1,Py1), P2(Px2,Py2),
P3(Px3,Py3), P4(Px4,Py4), P5(Px5,Py5), P6(Px6,Py6) respectively .
Then we can find:
Where
The position of other five co-channels cells are also can be found using the same
set of equation as the first co-channel cell, but they have to shift by 60o respectively.
So P2 must in the position
Where k= 0o; 60
o;….;300
o
Let‟s consider the user is in the position A(a,b), so we can find the distance
between user and each co-channel base station :
18
The following algorithm is to find the six co-channels position and the distances
between the user and each co-channel base station.
%-----------------------------------------------------------
% This program is used to calculate the position of the co-
channel base station
% Let's set the coordinate of the antenna of cell A1 is in
point
% P1=[0,0] while the antenna of cell A2 is in point
P2=(Px2,Py2)
% R is the radius of the outer circle of the hexagon
% L is the radius of the inner circle of the hexagon
% D is the distance between the co-channel base station and
the main base station
hold on
px1 = 0;
py1 = 0;
deta=acos((i*sin(pi/3))/sqrt(i^2+j^2+j*i));
Di=zeros(6,1);
for k=0:5
nph=k*pi/3;
px2=2*L*sqrt(i^2+j^2+j*i)*(cos(nph+deta));
py2=2*L*sqrt(i^2+j^2+j*i)*sin(nph+deta);
plot(px2,py2,'--rs','LineWidth',1,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g',...
'MarkerSize',5)
P2 = [px2,py2] % co-ordonne of A2
plot(px1,py1,'--rs','LineWidth',1,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','b',...
'MarkerSize',5)
Dx = px2-prx;
Dy = py2-pry;
Di(k+1) = sqrt(Dx^2+Dy^2)% distance between user and co-
channel cell
end
title('Co-channel cell')
19
D = 2*L*sqrt(i^2+j^2+i*j) %Distance between each co-channel
cell and main base station
Du = sqrt(prx^2+pry^2)% Distance between user and useful base
station
hold off
Figure 2-0-3 Show the co-channel position for cluster size N=7. The green
point are the co-channel base station and the blue one is the useful base station. In
this case, the user is out of the useful cell.
20
Figure 2-0-4 The user is inside the useful cell.
2.3 Calculation of signal to interference ratio(S/I)
Having calculated all the distances we can find the signal to interference by using
the equation (1.12)
(1.13)
Where n is the path loss exponent and is between 1 to 3.
Note:
is typically in dB
21
%------------------------------------------------------------
%The signal to interference ratio is H = S/I
Pt = 1; % Transmitted power
%npath = Path loss exponent
k = 1;
figure(2);
newplot;
hold on
for nmo = 1:5;
npath=nmo*0.5+1.5;
H=(Pt*k/(Du^npath))/((Pt*k)*sum(1/(Di.^npath)));
matH(z,nmo)=H;
H1=(1/M)*(sqrt(3*N))^npath;
H2=10*log10(H1);
teoHdB(nmo)=H2;
end
else
checked; %disp('The user is out of the cell')
end
end
nmo=1:5;
npath=nmo*0.5+1.5;
mean(matH)
Hdb=10*log10(mean(matH))
hold on
teoHdB
plot(npath,Hdb,'--rs','linewidth',1,....
'MarkerEdgecolor','k',....
'MarkerFacecolor','g',....
'MarkerSize',3)
plot(npath,teoHdB,'--rs','LineWidth',1,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','y',...
'MarkerSize',5)
title('S/I vs npath')
h=legend('teoHdB_npath','mV_npath',2);
hold off
axis ([2 4 0 100])
grid on
xlabel('npath')
ylabel('H(dB)')
22
The value of S/I is not only depended on the distance of the user and the co-channel
base station, but also the path loss exponent. In figure 2.5 we can see that the S/I is
increased as the path loss exponent increased.
2.4 Result of the simulation
This section includes figures showing the result of the simulation of various
number of S/I for different cluster size with 1000 random positions of the users compared
with S/I of the theory in case the user is at the border of the cell. In particular, figure 2-0-6
shows the positions of the co-channel base station for a cluster size equal to 3 and figure 2-
0-7 compares the corresponding measured S/I with the theoretical worst case S/I as a
function of the path loss exponent n. Figures 2-0-8 and 2-0-9 refer to a cluster size N=7,
while figures 2-0-10 and 2-0-11 refer to N=9.
Figure 2-0-5 Shown the mean value and theoretical value of S/I in function with
npath. The greed point are the mean values of S/I and the yellow are theoretical
values
23
2.4.1 Cluster size N = 3 (i=1; j=1)
Figure 2-0-6 Illustrate the useful base station(blue), the six co-channel base stations
(green) and the user (red). In this case the cluster size is N = 3
24
2.4.2 Cluster size N = 7 (i=2;j=1)
Figure 2-0-7 Shown the mean value and theoretical value of S/I in function with
npath. The greed point are the mean values of S/I and the yellow are theoretical
values.
25
Figure 2-0-8 For cluster size N = 7
Figure 2-0-9 S/I for cluster size N = 7 and M = 6.
26
2.4.3 Cluster size N = 9 (i=3; j=0)
Figure 2-0-10 Useful channel and co-channel cell for cluster size N = 9
27
Figure 2-0-11 S/I for cluster size N = 9
Having plot the three cases, we can see that the S/I changes as the cluster size
changes. However, if we compare the theory and the program calculation we find that there
is a big difference.
Figure 2-0-12 compares the three cases of the signal to interference ratio for
N =3; N =7; N = 9 with number of interfering cells M equal to 6.
28
a) S/I for N = 3
b) S/I for N = 7
c) S/I for N = 9
Figure 2-0-12 Shown the three case of S/I
29
2.5 Conclusion
The result of the simulation has shown that there is a big difference between the
theory and the simulation if the user is in the worst case. From the theoretical point of
view, the larger the S/I is the better the signal. For the equation (1.10), we have
In this case the user is at the border of the cell. Now let us consider the user is at a
distance:
From its serving base station, being K a coefficient larger than 1.
Then
By replacing
We get
(1.14)
Let us now find the value of S/I in dB
Having the result from the plot above we can see that the differences between the
theory and the simulation in the three case (N = 3; 7; 9) are approximately the same. As the
above problem the user is in the worst case( user is at the border of the cell).
For n = 2 => 10*log10Kn = 15 then K = 5.6234 m
For n = 2.5 => 10*log10Kn = 18 then K = 5.2481 m
For n = 3 => 10*log10Kn = 23 then K = 5.8434 m
For n = 3.5 => 10*log10Kn = 29 then K = 6.7386 m
30
For n = 4 => 10*log10Kn = 35 then K = 7.4989 m
Calculate the average value of K
<K1> = 6.1905m
Finally, we can get a new value which the user is not at the border of the cell
(1.15)
From the equation (1.15) we can plot others new figures of S/I of the program and
S/I of the theory.
%The signal to interference ratio is H = S/I
Pt = 1; % Transmitted power
%npath = Pathloss exponent
k = 1;
figure(2);
newplot;
hold on
for nmo = 1:5;
npath=nmo*0.5+1.5;
H=(Pt*k/(Du^npath))/((Pt*k)*sum(1/(Di.^npath)));
matH(z,nmo)=H;
H1=((1/M)*(sqrt(3*N))^npath) ;
H2=10*log10(H1)+(10*log10(6.1905^npath));
teoHdB(nmo)=H2;
end
else
checked; %disp('The user is out of the cell')
end
31
end
nmo=1:5;
npath=nmo*0.5+1.5;
mean(matH);
Hdb=10*log10(mean(matH))
hold on
teoHdB
plot(npath,Hdb,'--rs','linewidth',1,....
'MarkerEdgecolor','k',....
'MarkerFacecolor','g',....
'MarkerSize',3)
plot(npath,teoHdB,'--rs','LineWidth',1,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','y',...
'MarkerSize',5)
title('S/I vs npath')
h=legend('mV_npath','teoHdB_npath',2);
hold off
axis ([2 4 0 100])
grid on
xlabel('npath')
ylabel('H(dB)')
Since the user is in a random position, so there must be a bit difference between the
theory and the simulation. To avoid too much interferences the user should be a bit far
away from the border where the user can receive almost all the signal from the
co-channel base stations. Moreover, when the user is at the boundary of the cell, it makes
the distance between the user and the co-channel base stations is shorter which is one of
the main factor that we should consider, as S/I depends on the distance and the path loss
exponent.
Below are some plot of the result after having made an improvement for N = 3; 7;
9 respectively.
Even if theory and simulation still do not match exactly, formula (1.15) gives a
good approximation of the measured S/I values, and has the advantage of being really very
simple.
32
a)
b)
33
c)
Figure 2-0-13 Comparison between the measured and the theoretic values of S/I
with the improved formula (1.15) : a) N=3, b) N=7, c) N=9.
34
Chapter III: Capacity and interference improvement technique
Most cellular systems suffer from interference problem (intra-cell, inter-cell). Thus,
the interference issue is a key factor in designing any cellular system. Many techniques
were developed and now used for mitigating the interference problem. These techniques
attempt to reduce the interference effects on the performance of cellular systems through
increasing SIR ( Signal to Interference Ratio) and user capacity. Some of these techniques
are: sectorization, cell splitting, interference precancellation.
3.1 Sectorization
The technique for decreasing co-channel interference and thus increasing system
capacity by using directional antenna is called sectoring. The factor by which the co-
channel interference is reduced depends on the amount of sectoring used. A cell is
normally partitioned into three 120o sectors or six 60
o sectors as shown in figure 3.1 (a)
and (b).
When sectoring is employed, the channels used in a particular cell are broken down
into sectored groups and are used only within a particular sector, as illustrated in figure 3.1
(a) and (b) [8][Rappaport]. Cell sectoring with directional antennas have been proposed
and used in wireless cellular systems to achieve better coverage of a small or populated
area with less power requirements. In addition to power conservation, cell sectoring allows
better frequency channel allocations, more flexible channel borrowing, less co channel
interference, and higher spectrum efficiency (i.e., networks capacity). One approach in cell
sectoring is to place directional transmitters at the corners of the hexagonal cell where
three adjacent cells meet. The sectoring technique increases the capacity via a different
strategy. In this method, a cell has the same coverage space but instead of using a single
omni‐directional antenna that transmits in all directions, either 3 or 6 directional antennas
are used such that each of these antennas provides coverage to a sector of the hexagon.
When 3 directional antennas are used, 120° sectoring is achieved (each antenna covers
120°), and when 6 directional antennas are used, 60° sectoring is achieved (each antenna
covers 60°). Dividing the cells into sectors actually reduces the network capacity because
the channels allocated to a cell are now divided among the different sectors. In fact,
handoff takes place when a cell phone moves from one sector to another in the same cell.
The gain in network capacity is achieved by reducing the number of interfering co‐channel
cells. If sectoring is done in a way that channels assigned to a particular sector are always
at the same direction in the different cells (i.e., group A of channels is assigned to the
sector to the left of the tower in all cells, and group B of channels is assigned to the
sector at the top of all cells, and so on), each sector causes interference to the cells that are
in its transmission angle only. Unlike the case of no sectoring where 6 interfering
co‐channel cells from the first‐tier co‐channels cells cause interference, with 120°
sectoring, 2 or 3 co‐channel cells cause interference and with 60° sectoring, 1 or 2
co‐channel cells cause interference. The number of co-channel interfering cells depends on
the cluster shape and size. By having less than 6 interfering first‐tier co‐channel cells
causing interference, the SIR is increased for the same cluster size. This allows us to
reduce the cluster size and achieve the same original SIR, which directly increases the
network capacity.[9][google. Lecture posted by Dr. Wajih A. Abu-Al-Saud]
35
Sectorization
The total number of available channels can be divided into sets (subgroups)
depending on the sectorization of the cell configuration: the 1200-sector system, the 600-
sector system, and the 450-sector system. A seven-cell system usually uses three 1200
sectors per cell, with the total number of channel sets being 21. In certain locations and
special situations, the sector angle can be reduced (narrowed) in order to assign more
channels in one sector without increasing neighboring-channel interference. Sectorization
serves the same purpose as the channel-borrowing scheme in delaying cell splitting. In
addition, channel co-ordination to avoid co-channel interference is much easier in
sectorization than in cell splitting. Given the same number of channels, trucking efficiency
decreases in sectorization.
Sectorized cells.
There are three basic types:
1. The 1200-sector cell is used for both transmitting and receiving sectorization.
Each sector has an assigned a number of frequencies. Changing sectors during a call
requires handoffs.
2. The 600-sector cell is used for both transmitting and receiving sectorization.
Changing sectors during a call requires handoffs. More handoffs are expected for a 60
sector than a 120 sector in areas close to cell sites (close-in areas).
3. The 120o or 60o sector cell is used for receiving sectorization only. In this case,
the transmitting antenna is omni directional. The number of channels in this cell is not
subdivided for each sect. Therefore, no handoffs are required when changing sectors. This
receiving sectorization-only configuration does not decrease interference or increase the
D/R ratio; it only allows for a more accurate decision regarding handing off the calls to
neighboring cells.[10][Google: AntennaSystemInCellularMobileCommunication]
a) 120o sectoring b) 60
o sectoring
Figure 3-0-1 Shown 3 sectoring cell and 6 sectoring cell.
36
Cell sectoring effectively reduces the co-channel signal to interference ratio at the
price of increased cost of the base station (three or six antennas instead of one), and
increased complexity, since a handover is needed if the mobile moves from one sector to
another sector of the same cell. This handover is called intra-cell handover and it is less
complex than an inter-cell handover (between two different cells), since the two involved
antennas are located in the same place and the base station can manage the procedure,
without the need of involving a higher-level structure.
Instead of locating the base station at the center of the cell, it is possible to locate it
at one vertex of the hexagon, using three antennas (each covering 120 degrees) with
radiation patterns such that each antenna covers an entire hexagon, as shown in figure 6.10.
In this case, the cluster size is 9 (i = 3; j = 0), but only 3 base stations are
needed.[11][Monica‟s lecture]
Figure 3-0-2 The black dots are the positions of the base stations for cluster size
N = 9.
37
3.2 Cell splitting
Why splitting?
The motivation behind implementing a cellular mobile system is to improve the
utilization of spectrum efficiency. The frequency reuse scheme is one concept, and cell
splitting is another concept. When traffic density starts to build up and the frequency
channels in each cell cannot provide enough mobile calls, the original cell can be split
into smaller cells. Usually the new radius is one-half the original radius cell site is not
used.
New cell radius = old cell radius/2
New cell area = old cell area/4
Let each new cell carry the same maximum traffic load of the old cell; then, in theory,
New traffic load / unit area = 4 Х traffic load/ Unit area
How splitting?
There are two kinds of cell-splitting techniques:
1. Permanent splitting. The installation of every new split cell has to be planned
ahead of time; the number of channels, the transmitted power, the assigned frequencies, the
choosing of the cell-site selection and the traffic load consideration should all be
considered. When ready, the actual service cutover should be set at the lowest traffic point,
usually at midnight on a weaken. Hopefully, only a few calls will be dropped because of
this cut-over, assuming that the downtime of the system is within 2 h
2. Dynamic splitting. This scheme is based on utilizing the allocated spectrum
efficiency in real time.
Effect of splitting:
When the cell splitting is occurring, in order to maintain the frequency-reuse
distance ratio q in a system, there are two considerations.
1. Cells splitting affects the neighboring cells, splitting cells causes an
unbalanced situation in power and frequency-reuse distance and makes it
necessary to split small cells in the neighboring cells. This phenomenon is the
same as a ripple effect.
2. Certain channels should be used as barriers. To the same extent, large and
small cells can be isolated by selecting a group of frequencies, which will be
used only in the cells located between the large cells on one side and the small
cells on the other side, in order to eliminate the interference being transmitted
from the large cells to the small cells.
3. Small Cells (Micro cells)
38
3.3 Interference precancellation
On the other hand, interference precancellation method is performed at the
transmitter. It is mainly used for the downlink case in cellular systems. It is based on that
the BS has the knowledge about the interference between users within its cell, and the
knowledge about the interference it causes for users in other cells. The BS has the ability to
presubtract the interference before it makes its transmission. This action has large effects
on system capacity, and it is implemented by using a transmission technique called "dirty-
paper coding" [10]. The improvement on system capacity achieved by using this technique
is affected by the number of antennas used at the BS. Note that the presubtraction process
of the interference requires the channel state information (CSI) to be known at the
transmitter. [12][Google:AntennaSystemInCellularMobileCommunication]
Figure 3-0-3 Cell splitting
39
Table of figures
Figure 1-0-1 Illustration of frequency reuse in cellular system ....................... 2
Figure 1-0-2 Illustration of the cellular frequency reuse concept. Cells with
the same letter use the same set of frequencies. ................................................ 3
Figure 1-0-3 Possible choices of cell shape. For a given values of R, Ahex
provides the Max. Coverage -Area with fewest number of cells[2][google:
cellular-concept –design-fundamentals] ........................................................... 4
Figure 1-0-4 Illustration of how to find co-channel cells. ................................ 5
Figure 1-0-5 Show how to find the reuse distance .......................................... 8
Figure 1-0-6 Illustration of various cluster size which are typically used. .... 10
Figure 1-0-7 Case of a mobile(red circle) at the boundary of cell A1 (useful
cell) for a cluster size of 7; the blue lines identify the distances between the
mobile and each of the first-layer co-channel base station ............................. 11
Figure 2-0-1 The plot of hexagon with (0,0) in km ........................................ 14
Figure 2-0-2 Show the user in the hexagon(cell). The red point is the mobile
user position. ................................................................................................... 16
Figure 2-0-3 Show the co-channel position for cluster size N=7. The green
point are the co-channel base station and the blue one is the useful base
station. In this case, the user is out of the useful cell. ..................................... 19
Figure 2-0-4 The user is inside the useful cell. ............................................... 20
40
Figure 2-0-5 Shown the mean value and theoretical value of S/I in function
with npath. The greed point are the mean values of S/I and the yellow are
theoretical values ............................................................................................. 22
Figure 2-0-6 Illustrate the useful base station(blue), the six co-channel base
stations (green) and the user (red). In this case the cluster size is N = 3 ........ 23
Figure 2-0-7 Shown the mean value and theoretical value of S/I in function
with npath. The greed point are the mean values of S/I and the yellow are
theoretical values. ............................................................................................ 24
Figure 2-0-11 S/I for cluster size N = 9 .......................................................... 27
Figure 2-0-12 Shown the three case of S/I ..................................................... 28
Figure 3-0-1 Shown 3 sectoring cell and 6 sectoring cell. ............................. 35
Figure 3-0-2 The black dots are the positions of the base stations for cluster
size N = 9. ........................................................................................................ 36
Figure 3-0-3 Cell splitting .............................................................................. 38
41
References
[1] : V.H. Mac Donald79 : Advanced Mobile Phone Service,
The cellular Concept(Manascript received July 17, 19978)
[2] : Google: Cellular-concept –design-fundamentals
[3] : Rappaport : Wireless_Communication 2nd
Edition, 1998, page 27.
[4] : Rappaport : Wireless_Communication 2nd
Edition, 1998, page 28.
[5] : Monica‟s lecture: Wireless networks “ Prof. Monica Visintin,
Politecnico di Torino, Italy”, page 143.
[6] : Monica‟s lecture, page 145.
[7] : Monica‟s lecture, pages 147-149.
[8] : Rappaport: Wireless_Communication 2nd
Edition, 1998, page 58.
[9] : Google: Lecture posted by Dr. Wajih A. Abu-Al-Saud.
[10] : Google: AntennaSystemInCellularMobileCommunication.
[11] : Monica‟s lecture, page 150.
