MSc rjfg V1

Instituto Tecnol´gico y de Estudios Superiores de
o
Monterrey
Campus Monterrey

Divisiń de Electrńica, Computaciń, Informaciń, y
o o o o
Comunicaciones
Programa de Graduados

Interference and Capacity Analysis of CDMA multi-service
linear Ad Hoc Networks

THESIS

Presented as a partial fulfillment of the requeriments for the degree of
Master of Science in Electronic Engineering
Major in Telecommunications

Rodolfo Javier Fuentes Gonz´lez
a

Monterrey, N.L. October 2003

c Rodolfo Javier Fuentes Gonz´lez, 2003
a

Instituto Tecnol´gico y de Estudios Superiores de
o
Monterrey
Campus Monterrey

Divisiń de Electrńica, Computaciń, Informaciń, y
o o o o
Comunicaciones
Programa de Graduados

The members of the thesis committee recommended the acceptance of the thesis of
Rodolfo Javier Fuentes Gonz´lez as a partial fulfillment of the requeriments for the degree
a
of Master of Science in:
Electronic Engineering
Major in Telecommunications

THESIS COMMITTEE

David Muõz Rodr´
n ıguez, Ph.D.
Advisor

C´sar Vargas Rosales, Ph.D.
e Jos´ Ramń Rodr´
e o ıguez Cruz, Ph.D.
Synodal Synodal

Approved

David Garza Salazar, Ph.D.
Director of the Graduate Program

October 2003



Rodolfo Javier Fuentes Gonz´lez, M.Sc.
a
Instituto Tecnol´gico y de Estudios Superiores de Monterrey, 2003
o

Abstract

Wireless systems have been under an evolutionary process along the time, in order
to satisfy the demanding user needs of these types of systems. Those needs and inquiries
of wireless markets have grown considerably in a short time. This fast market growth
has pushed companies to employ state of the art technology in order to use and share
trustworthy databases in an instantaneous and imperceptible way for the final user.
Ad Hoc mobile networks are being developed and implemented in order to solve and
satisfy the needs and problems of mobile users. This technology can be an actual solution
in which users demands good quality of service (QoS) in their personal communications
and internet devises, according to the current and future market needs.
Code Division Multiple Access (CDMA) seems to be the future wireless interface and,
because of its characteristics, it could play an important role in future communications
systems. Operational characteristics allow CDMA to be considered an adequate access
method for conventional and Ad Hoc networking systems. As a mentioned above, this work
will base its access method on CDMA, where the main limiting factor is the interference,
so here we will characterize the interference and the outage probability for an ad hoc linear
network for different scenarios and different physical conditions.



Rodolfo Javier Fuentes Gonz´lez, M.Sc.
a
Instituto Tecnol´gico y de Estudios Superiores de Monterrey, 2003
o

Resumen

Los sistemas de comunicaciń inalambrica han venido evolucionando a lo largo del
o
tiempo para tratar de cubrir las demandantes necesidades de los usuarios de este tipo de
sistemas. Estas necesidades e inquietudes del mercado crecen rapidamente por lo que se
requiere contar con sistemas que sean el estado del arte en cuanto a tecnolog´ que cuenten
ıa,
y puedan accesar confiablemente a fuentes y bases de datos de manera instantanea y de
manera inperceptible para el usuario final.
Las redes m´viles Ad Hoc estń siendo diseãdas e implementadas para tratar de
o a n
resolver y satisfacer las necesidades y problemas de este tipo de usuarios, esta tecnolog´
ıa
pueden ser una soluciń a acorde a la problem´tica actual, en donde se requiere contar con
o a
una buena disponibilidad de servcicios de comunicaciń personal e internet acorde a las
o
demandas de los mercados actuales y de un futuro pr´ximo.
o
CDMA parece ser la interface inal´mbrica de sistemas futuros, debido a sus car-
a
acter´ısticas es que podr´ jugar un papel importante en los sistemas de comunicaciones
ıa
inal´mbricos que vienen. Las caracter´
a ısticas operacionales de CDMA le permiten ser
cosiderado como un modo de acceso adecuado a la redes convencioneles y del tipo Ad
Hoc. Por todo lo anterior es que este trabajo aborda, el problema de la caracterizaciń de
o
la interferencia, limitante primordial de sistemas CDMA, as´ como una caracterizaciń de
ı o
la capacidad y de la probabilidad de outage en un sistema ad hoc lineal, bajo diferentes
escenarios y con diferentes variantes f´
ısicas.

Contents

List of Figures iii

List of Tables v

Chapter 1 Introduction 1
1.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Justiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Chapter 2 Basic Concepts of Wireless Ad-hoc Networks 3
2.1 Ad-hoc Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Ad Hoc Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Link Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Application Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Multi-Hop Wireless Link Systems . . . . . . . . . . . . . . . . . . . . . . . 8
2.4.1 Single Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.2 Funnel Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.3 Double Branch Funnel Networks . . . . . . . . . . . . . . . . . . . . 10
2.5 Propagation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Medium Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6.1 Interference Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6.2 CDMA Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 Outage Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapter 3 Model Description 19
3.1 Linear Ad Hoc CDMA Modeling . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Proposed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Point Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 Path Loss Exponent Inﬂuence . . . . . . . . . . . . . . . . . . . . . . . . . 23

i

ii CONTENTS

3.5 Variable Activity Factors for Multi-Service CDMA Wireless Systems . . . . 24
3.6 Working With Funnel Networks . . . . . . . . . . . . . . . . . . . . . . . . 26
3.7 Outage Quantiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Chapter 4 Numerical Results 29
4.1 Interference Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.1 Empirical CDF of Interference . . . . . . . . . . . . . . . . . . . . . 33
4.2 Capacity and Outage Probability . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Multiservice Traﬃc Results . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.1 Stochastic vs deterministic network behavior . . . . . . . . . . . . . 44
4.4 Double Branch Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . 45

Chapter 5 Conclusions and Future Work 49
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Bibliography 53

Vita 55

List of Figures

2.1 (a) heterogeneous ad-hoc devises (b) homogeneous ad-hoc networks . . . . 4
2.2 (a) Link of adjacent individuals, and (b) link of no adjacent individuals . . 7
2.3 Single Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Funnel Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Double Branch Funnel Network . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 r(x) along x-axis in the space . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.7 Description of a mobile radio environment . . . . . . . . . . . . . . . . . . 12
2.8 Multipath fading region . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.9 CDMA Spreading Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 Planar to linear scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Linear generated scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Analized scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Point Process in one and two dimensions . . . . . . . . . . . . . . . . . . . 22
3.5 AF considerations on linear ad hoc networks . . . . . . . . . . . . . . . . . 25
3.6 Algorithm diagram of a CDMA linear ad hoc network . . . . . . . . . . . 28

4.1 Comparative interference density for 64 users . . . . . . . . . . . . . . . . . 30
4.4 Comparative interference density for different λ and γ = 2 . . . . . . . . . 33
4.5 Comparison of interference density for different λ and γ = 4 . . . . . . . . 34
4.6 Empirical CDF of interference for a funnel network with γ = 2 . . . . . . . 35
4.7 Empirical CDF of interference for funnel network with γ = 4 . . . . . . . . 35
4.8 Outage probability single network, γ = 4 . . . . . . . . . . . . . . . . . . . 36
4.9 Outage probability single network, γ = 2 . . . . . . . . . . . . . . . . . . . 37
4.10 Outage probability of a funnel network with different PLE . . . . . . . . . 37
4.11 Outage probability funnel network γ = 4 . . . . . . . . . . . . . . . . . . . 38
4.12 Outage probability funnel network γ = 6 . . . . . . . . . . . . . . . . . . . 39
4.13 Outage probability funnel network γ = 2, BW 30MHz . . . . . . . . . . . . 39

iii

iv LIST OF FIGURES

4.14 Outage probability funnel network γ = 4, BW 30MHz . . . . . . . . . . . . 40
4.15 Capacity comparison single VS funnel networks . . . . . . . . . . . . . . . 41
4.16 Outage probability funnel multiservice network, γ = 4 . . . . . . . . . . . . 41
4.19 Outage probability funnel multiservice network λ = .005 . . . . . . . . . . 43
4.20 Capacity of a multiservice network . . . . . . . . . . . . . . . . . . . . . . 44
4.21 Stochastic vs deterministic network, users distance 500m . . . . . . . . . . 45
4.22 Stochastic vs deterministic network, users distance 1000m . . . . . . . . . . 46
4.23 Outage probability funnel multiservice, double branch γ = 4 . . . . . . . . 46
4.24 Outage probability funnel multiservice, double branch γ = 6 . . . . . . . . 47

List of Tables

3.1 Path Loss Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Diﬀerent rates with diﬀerent AF´s . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Reached capacity with parallel codes . . . . . . . . . . . . . . . . . . . . . 26

4.1 Characteristics of the simulated scenarios . . . . . . . . . . . . . . . . . . . 29
4.2 Interference statistics single network: 64, 32, and 8 users. . . . . . . . . . 32
4.3 Interference statistics funnel network: 64, 32, and 8 users. . . . . . . . . . 32
4.4 Characteristics of the simulated scenarios . . . . . . . . . . . . . . . . . . . 32
4.5 Parameters of current CDMA systems . . . . . . . . . . . . . . . . . . . . 36
4.6 Experimental parameters in funnel CDMA systems . . . . . . . . . . . . . 38
4.7 Multiservice parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.8 Parameters of compared scenarios . . . . . . . . . . . . . . . . . . . . . . . 44
4.9 Multiservice parameters for double branch networks . . . . . . . . . . . . . 47

v

Chapter 1
Introduction

Advances in wireless technology and portable computing along with demands for greater
user mobility and bandwidth have provided a major impetus toward development of an
emerging class of self-organizing, rapidly deployable network architectures referred to as
ad-hoc wireless networks [18]. Ad-hoc wireless networks are systems of mobile nodes with-
out a fixed infrastructure. In such networks, users can communicate with each other by
using intermediate nodes as relays. Several advantages can be seen by using ad hoc wire-
less networks. Alternatively, an area can be served with fewer base stations, and faraway
terminals can connect via a neighboring node. Due to the benefits and the unique versatil-
ity that ad hoc networks provide in certain environments and applications is that ad hoc
networks will be implemented. Their properties are turning relay stations into an attrac-
tive feature for operators of conventional cellular networks. New services, such as email,
internet, ftp and video-service, are offered by companies, implying that the user bandwidth
requirement will grow considerably. The equipment supplier or network operator must be
able to guarantee a definite Quality of Service (QoS) to their customers at all time.

1.1 Objective

The objective of this thesis is to evaluate the performance of a network by simulating the
interference and its behavior when we work on funnel and single-network schemes, using
CDMA as a Medium Access Control (MAC) in a linear ad hoc network. This work also
analyzes the outage probability for both schemes when we have different physical conditions
such as user separation, path loss exponent (PLE) and size of the network. Finally, we will
present results for the case of multi-traffic schemes and for one branch and double branch
communications system networks.

1

2 CHAPTER 1. INTRODUCTION

1.2 Justification
Due to rapid advances in technology along with the change of platform to wireless and de-
mands of new services and mobility, the installation of new infrastructure and renovation
could be unprofitable to the operator. For this reason, the development of self-organizing
network architectures that are capable of managing a nonhomogeneous collection of sub-
scribers is of great importance for the health of the market. On the other hand, the most
important aspect that all network operators must guarantee in order to be commercially
successful is the QoS. As result, an analysis that enables us to determine the way to ensure
a good QoS for these kinds of networks needs to be conducted.

1.3 Organization
This thesis is organized as follows: Chapter two gives a brief description of an ad-hoc wire-
less network. Chapter three presents thoroughly expounds on the problem characteristics
and describes the methodology used to obtain the interference and outage probabilities.
Chapter four presents the results obtained under different scenarios as well as in this work.
Finally, Chapter five presents both the conclusions of this analysis and the opportunities
for further research.

Chapter 2
Basic Concepts of Wireless Ad-hoc Networks

Today we see a great expansion in the production of technology to support mobile com-
puting. Not only are computers themselves becoming more and more capable, but many
applications are being developed in order to interact with other devices. The purpose of
this chapter is to present the fundamental aspects of multi-hop, ad-hoc wireless networks,
such as their main characteristics and configuration.

2.1 Ad-hoc Wireless Networks
An ad-hoc wireless network is a collection of two or more devices equipped with wireless
communications and networking capability. Such devices can communicate with another
node that is immediately within their radio range or one that is outside their radio range.
For the latter scenario, an intermediate node is used to relay or forward the packet from
the source toward its destination,[1].

An ad-hoc wireless network is self -organized and adaptive. This means that a formed
network can be de-formed on the fly without the need of any system administration. The
term “ad-hoc” implyes that it can take different forms, and it can be mobile, standalone,
or networked. Since ad-hoc wireless devices can take different forms (laptop, palmtop, in-
ternet mobile phone, etc.) the computation, storage, and communications capabilities of
such devices can vary tremendously. Ad-hoc devices should not only detect the presence of
connectivity with neighboring devices/nodes, but also identify what type the devices are
as well as their corresponding attributes.

In general, cellular networks consist of a number of centralized entities, such as BS
(Base Station), MSC (Mobile Switching Center), HLR (Home Location Registry), and so
on. These centralized entities perform the function of coordination. But an ad-hoc wireless

3

4 CHAPTER 2. BASIC CONCEPTS OF WIRELESS AD-HOC NETWORKS

Figure 2.1: (a) heterogeneous ad-hoc devises (b) homogeneous ad-hoc networks

network is characterized by the lack of a wired backbone or centralized entities. However,
due to the presence of mobility, routing information will have to change to reflect changes
in link connectivity [1]. The diversity of ad-hoc mobile devices also implies that the battery
capacity of such devices will also vary. In Figure 2.1 we see two different networks: the first
is made by one type of device and the second network is made by different devices. Since
ad-hoc networks rely on forwarding data packets sent by other nodes, power consumption
becomes a critical issue.
In flat-routed networks, all nodes are “equal” and the packet routing is done based
on peer-to-peer connections, restricted only by the propagation conditions, and we sim-
ply note that flat-routed networks are more suitable for a highly versatile communications
environment, [11]. Figure 2.1(b) shows two different forms of ad hoc devices. There are
great differences among these devises, and this heterogeneity can affect communications
performance and the design of communications protocols. It is evident that each device
has different computational power, memory and battery capacity. The ability of an ad
hoc device to act as a server or service provider will depend on its computation, memory
storage and battery life capacity. The presence of heterogeneity implies that some devices
are more powerful than others. Some can also be servers while others can only be clients,
in addition relay communications from other users can result in a device expelling its own
energy [11].

2.1.1 Ad Hoc Characteristics
A few salient characteristics of the ad hoc networks are the following, [11]:

5
2.1. AD-HOC WIRELESS NETWORKS

• Network size
Usually refers to the number of network nodes, but it can also refer to geographical
area covered by the network. Both are critical parameters coordinating network
actions with distributed control mechanisms. Taking together the number of nodes
over a given geographical space defines the network density.

• Connectivity
This refers to a number of neighbors to which each node can link directly. This
may or may not be directional links because of, for example, interference conditions.
Connectivity also refers to the link capacity between two nodes. Also related to
connectivity are specialized military operating modes, such as emission-controlled
operation. During this (EMCOM) nodes do not transmit to prevent detection by the
enemy, and they must be still able to receive critical messages.

• Network topology
User mobility can directly affect the speed of the node connectivity and, hence, the
network topology changes. Thus, it influences how and when the network protocol
must adapt to changes.

• User traffic
The characteristics and types of user generated traffic heavily influence the design of
an ad hoc network. How is the users traffic; Does it consist of short, busrty packets
that are without strict delay bound but intolerant of loss, does it consist of longer
packets that are generated periodically with strict delay bound but tolerant to loss?
Such knowledge is obviously important to the design of the medium access control
layer, because efficient access to the spectrum can be a bottleneck in a mobile ad hoc
network.

• Operational environment
Operational environment refers to the terrain (urban, rural, maritime, etc) that may
prevent line of sight (LOS) operation. It also refers to potential sources of interference
in the radio channel, which is especially relevant in the military environments where
the potential for intentional enemy interference necessitates that the design of the
physical MAC and network layers resist such attacks.

• Energy
Unlike a commercial cellular communications system. There are few or no fixed base
stations in a mobile ad hoc network (MANET). All nodes have roughly equal status,
so the energy burden cannot be transferred to energy advantaged nodes such as fixed
base stations, although nodes that are in Platt forms do have an energy advantage


over those that are battery operated. Specifically, battery-operated store-and-forward
nodes present a significant challenge in developing low-energy networking approaches.
Often overlooked in the design of MANET is the impact on energy consumption of
layers above the physical layer.

• Regulatory
A MANET must adhere to existing regulations for emitted power, for both legal and
public health reasons.

• Performance metrics
After determining the basic framework of a MANET, the designer must choose the
important performance metrics to satisfy user needs. Typically throughput and delay
along with their associated mean, variance, and distribution, are used as performance
metrics for user data.

• Cost
Ultimately cost-versus-performance trades must be made if the MANET design is
to be implemented. The designer must determine how cost affects the most critical
aspects of the design, specially the performance perceived by the users.

2.2 Link Establishment
Mobile users in ad hoc networks can communicate with their immediate peers, this is a peer-
to-peer single radio hop. Each individual has an influence area defined by its transmitting
power and its sensitivity threshold. Two individual are said to be adjacent if they are within
the intersection of their influence areas. Therefore, they can establish a direct connection
by a single link. Nonadjacent individuals are connected via a relaying individual lying in
the intersection of the influence areas of individuals A and B. Both sceneries are shown in
Figure 2.2.

2.3 Application Scenario
Since the ad hoc wireless networks have a network architecture that can be rapidly deployed,
without the pre-existence of almost any fixed infrastructure, they have a number of special
characteristics that are listed below, [11]:

• No central control and no hierarchical structure

7
2.3. APPLICATION SCENARIO

Figure 2.2: (a) Link of adjacent individuals, and (b) link of no adjacent individuals

• Large network coverage; Large network radius

• Large number of network nodes

• Terminals are distributed stochastically

Examples of the scenarios where ad-hoc wireless networks are being used are described
below:

• Military communication
For fast establishment of communication infrastructure during deployment of forces
in hostile terrain.

• Rescue missions
For communication in areas without adequate wireless coverage.

• Security
For communication when the existing communication infrastructure is non-operational
due to a natural disaster.

• Commercial use
For setting up communications in exhibitions, conferences, or sales presentations.

• Education
For operation of virtual classrooms.

• Sensor networks
Mounted on mobile platforms.

Although all the applications mentioned represent the most eﬃcient, secure and cheap-
est way to solve the speciﬁc problem. the application that is changing the way of concep-
tualizing future communications systems is the addition of ad-hoc wireless networks to the


existent cellular systems in order to get crowded heterogeneous networks with very high
data rates and bandwidth. This kind of networks will appear gradually in the next years
and are expected to be the network architecture of 4G. Its main advantages will be the
deployment of adaptive applications and partial coverage in places with a reduced density
of users. This will be possible because users will be those who deploy the network. Finally,
due to the multiple kinds of hosts, an analysis to determine the QoS in such networks is
an important research issue. A sketch of this scenery can be seen in Figure 2.3.

2.4 Multi-Hop Wireless Link Systems
The IMT-2000 mobile communications system, which supports global roaming services, is
to be introduced, as expected for broadband mobile multimedia services. Based on new
generation, mobile communications should offer at least 20 Mb/s data communications
channels. They also indicate that the network for these systems will utilize IP based tech-
nologies and transfer traffic 10 times bigger than current traffic, since broader bandwidth
mobile multimedia services will be offered so that not only people but also things will be
connected [1].
Because there will be the need to transport an enormous amount of traffic in a more
efficient manner by increasing the spectrum efficiency, the coverage of a base station will be
shorter than present systems. The radio frequency signal bandwidth will be broadened to
provide broadband communications, and because the propagation loss increases according
to the radio frequency increase, the cell radius is also supposed to be shorter. Therefore, a
new system will require more base stations to cover a wide area.
In order to utilize wireless links in future communications systems, these links must
have greater traffic capacity and economic performance. The radio frequency band of the
wireless link will become higher (such as the millimeter-wave band) to support a much
broader link bandwidth. Thus, the range of each radio link is assumed to be shorter
because of its broader link bandwidth and higher radio frequency band requirements. To
compensate for this problem, we could increase the output power and use high directivity
antennas. However, this is not desirable from the point of view of equipment cost.
To address the above mentioned problems, [3] proposes to apply a multi-hop wireless
link system. The multi-hop wireless link employs a set of short distance links instead of a
long-distance links. The required link bandwidth will increase since the links include not
only the traffic generated by the relevant user (native traffic) but also the traffic carried from
other users. In ad hoc multi-hop wireless networks, we can see two particular cases of these
networks. Single wireless networks and other network configuration that we have call funnel
wireless networks in the next sections, we will explain and see their main characteristics

9
2.4. MULTI-HOP WIRELESS LINK SYSTEMS

Figure 2.3: Single Network

Figure 2.4: Funnel Network

and how do they work.

2.4.1 Single Networks
We have seen in the previous section that a multi-hop network can transport not only native
traffic but also other users traffic. This means that the radio link between mobile users
must be ready to handle highrate information. Figure 2.3 shows a multi-hop radio network
in which information departs from an access point and travels along the communication
path until it reaches its destination node.
In a single network scheme we see how information hops from user to user by using
one key per hop link. Every code key is orthogonal from each other. In later sections of
this work we will explain and define CDMA as the access method employed, which means
that the used key will be a CDMA code taken from the code pool of the system, [3].

2.4.2 Funnel Networks
On the other hand, we define a funnel network as a network array in which information
could appear to be in an imaginary funnel where the wider part is at the starting part
and as it goes ahead it becomes narrow as information is delivered to each element of the
network.
Considering this network configuration, we will refer to it as a funnel network which


Figure 2.5: Double Branch Funnel Network

works in the following way: each element of the network demands a certain fixed quantity
of information. This information must flow from an access point. We have to take into
account that each user demands a certain amount of information, a key multiple keys of
information that will be carried along the network. The main repercussion of this is that
the information will be carried in a cumulative way from its starting point, meaning that
the first link will carry all information belonging to the n elements of the network. Carried
information will be delivered user by user. Each user will take its information part and will
forward the rest of the information to the next user until information reaches the last user.
The main advantage of this type of ad hoc configuration is that the network can carry the
whole block of information and deliver to each user its requested information. Figure 2.4
shows an example of a funnel network.

2.4.3 Double Branch Funnel Networks
A double branch scheme could be possible when two communications branch are held by
the same access point. This is seen in Figure 2.5. This scenario is formed by two funnel
networks, one running in the opposite sense of the other. The double branch system will
work like the funnel network that we have described in previous part. Of course, we need
to analyze and see the repercussions that the use of this network configuration could have
for the system´s behavior and, in general, how the network performance is.

2.5 Propagation Model
The propagation model chosen for the system design is closely affected by the wavelengths
of the propagation frequencies and also by the distance between Tx and Rx. But when

11
2.5. PROPAGATION MODEL

Figure 2.6: r(x) along x-axis in the space

designing a mobile radio system in certain environments several factors need to be account.
Such factors are listed as follows:

• Free Space Loss

• Antenna height of mobile units

• Multi-path fading

• Scattering

The field strength of a signal can be represented as a function of distance in the space
(space domain) or as a function of time (time domain). We can see that if a Tx antenna
is fixed, then the field strength varies, as is seen in Figure 2.6. The field strength at every
point is measured along the distance, and it is measured by the receptor. In Figure 2.6, we
see how a signal behaves along the distance.
The received field strength along the distance shows severe fluctuation when the mo-
bile is located far away from the base station. The average signal level of a fading signal
r(x ) o r(t) decreases as the mobile unit moves away from the transmitter unit which, for
example in a cellular environment, is the radio base station. This average signal level drop-
ping is the propagation path loss.


Figure 2.7: Description of a mobile radio environment

In the real environment instead of just having one direct signal from an antenna of
a mobile, we have another, or several other paths that are produced when the waves are
reflected in buildings or in the terrain. Figure 2.7 shows this effect [5].

In addition to the losses that the signal suffers when travels in space there are other
considerations such the condition of the terrain, which can be represented by a random
variable that follows a Log-Normal distribution this is called slow fading. Another type of
fading is caused by multipath when the signal is reflected by buildings or big objects, and
this effect is called fast fading.

Dispersion in a communication link is caused by the time in which different copies of
a signal arrive, and the frequency dispersion is called the Doppler effect, we can see this
effect in Figure 2.8.

Finally it is important to observe the next two points:

• Classical propagation models predict the mean signal strength over distances at many
hundreds of meters. It is important in predicting likely received power levels (cov-
erage and interference) in cells of mobile networks. Large-scale path losses may be

13
2.5. PROPAGATION MODEL

Figure 2.8: Multipath fading region


compensated by adaptive antennas and/or power control.

• Fading (small-scale) is a much more rapid fluctuation of received signals, caused by
constructive and destructive interference between two or more versions of the same
signal. This may be corrected by adaptive equalizers or by robust modulation and
error correction.

2.6 Medium Access
Unlike in cellular networks, there is a lack of centralized control and global synchronization
in ad hoc wireless networks. Hence, time division multiple access (TDMA) and frequency di-
vision multiple access (FDMA) schemes are not suitable. In addition many MAC protocols
do not deal with host mobility. As such, the scheduling of frames for timely transmission
to support QoS is difficult.
In ad hoc wireless networks, since the media are shared by multiple mobile ad hoc
nodes, access to the common channel must be made in a distributed fashion, through the
presence of a MAC protocol. Given the fact that there are no static nodes they cannot rely
on a centralized coordinator. The MAC protocol must contend for access to the channel
while at the same time avoiding possible collision with neighboring nodes.

2.6.1 Interference Factor
Interference is the main limiting factor in wireless communications. As a result of this, it is
vital to use the radio spectrum efficiently and to the limited resource among multiple users.
The channel assignment strategies minimize interference between users in different cells
in conventional cellular environments. Interference is caused by transmitted signals that
extend outside the intended coverage area into neighboring cells. The choice of multiple-
access technique directly affects subscriber capacity, which is a measure of the number of
users that can be supported in a predefined bandwidth at any time. Because of this is the
importance of characterize and study the interference.

2.6.2 CDMA Principles
CDMA is a multiple access concept based on the use of wideband spread-spectrum tech-
nique that enables the separation of signals that coincide in time and frequency, and all
signals share the same spectrum (signals are interferent each other). The energy of each
mobile station’s signal is spread over the entire bandwidth and coded to appear as broad-
band noise to every other mobile. Identification and demodulation of individual signals

15
2.6. MEDIUM ACCESS

1 chip period
1 bit period

Data signal

PN Code

Coded Signal

Figure 2.9: CDMA Spreading Process

occur at the receiver by applying a replica of the sequence (code) used for spreading each
signal. This process enhances the interested signal while dismissing all others as broadband
interference.In Figure 2.9, we show how the expansion processes is done by a sequence which
is a unique code for each user. The period of the code is shorter than the information, so
the band width is bigger, because when signals are multiplied, the bandwidth is wider.
The CDMA concept can be contrasted with other multiple access techniques. In
(FMDA), each mobile station has full usage of the spectral allocation. In TDMA, breaks
down the allocation into a number of time slots. Each mobile cofinites its signal energy
within a time slot. In CDMA, the base station has full-time use of the entire spectral
allocation and spreads its signal energy over the entire bandwidth. Base stations and mobile
station use a unique code to sign each signal and to distinguish those signals coincident in
time and frequency.
There are two types of CDMA Direct Sequence (DS-CDMA) or Frequency Hop (FH-
CDMA). In the direct sequence all users share the same frequency at the same time with
a special and unique code. Before a signal transmission, user signals are multiplied by a
sequence which is different for each user [15].
Capacity considerations are fundamental to CDMA planning and operation, by ca-
pacity we mean simply the number of users that can be simultaneously supported by the
system. Power control minimizes the impact of interference by adjusting each signal level
to the minimum necessary to achieve desired call or service quality.
The relation between both bandwidths information and sequence, is known as the
Processing Gain and is defined by

Bss
PG = , (2.1)
B
where Bss is the bandwidth of the sequence used and B is the bandwidth of the information.


E
In digital communications there is an important metric denoted Nb , or bit energy to
0
noise power density ratio, this quantity can be related to the conventional signal-to-noise
ratio (SNR) by recognizing that energy per bit equates to the average modulation signal
power allocated to each bit duration, that is

Eb = ST, (2.2)
where S is the average modulating signal power and T is the time duration of each bit.
Notice that (2.2) is consistent with dimensional analysis, which states that energy is equiv-
alent to power multiplied by time. We can further manipulate (2.2), by substituting the
bit rate R, which is the inverse of the bit duration:

S
Eb = , (2.3)
R
Eb
is thus
N0

Eb S
= , (2.4)
N 0 RN0
We further substitute the noise power density N0 , which is the total noise power N
divided by the bandwidth W , which is,

N
N0 = , (2.5)
W
substituting (2.4) into (2.5) yields

Eb SW
= , (2.6)
N0 NR
E
which relates Nb to two factors: the S/N of the link, and the ratio of transmitted bandwidth
0
W to bit rate R. The ratio W/R is also known as the processing gain of the system, which
is the same as that in [15], and it handles and commands the performance of a CDMA
system.
Here we consider the reverse-link capacity since in CDMA this is often the limit-
ing link in terms of capacity. Assuming that the system possesses perfect power control,
which means that the transmitted power from all mobile users are equal. Based on this
assumption, the SN R of one user can be written as

S 1
= , (2.7)
N M −1

17
2.7. OUTAGE PROBABILITY

where M is the total number of users present in the band. This is so because the total
interference power in the band is equal to the sum of the powers from individual users. We
proceed to substitute (2.7) into (2.6), and the result is

Eb 1W
= , (2.8)
N0 M −1 R
Solving for (M − 1) yields
W
R
M −1= , (2.9)
Eb
N0

Note that if M is large, then
W
R
M= . (2.10)
Eb
N0

2.7 Outage Probability
The Outage probability is deﬁned as the probability that the output signal to interference
(SIR) falls below a prescribed level. This is given by:
γb
C0
P OU T = P ≤
I PG
C0
γb W
=P ,
≤
I R

where γb is the required SIR for the system in order to ﬁll the BER requirements. W is the
system´s bandwidth and R is the rate of data transmission.

Chapter 3
Model Description

In order to analyze the network performance from the point of view of its capacity and
interference in this chapter we have made a simulation to model and analyze the behavior
of a wireless CDMA multi-service lineal ad hoc network. In the following sections we will
explain the characteristics considered to model and simulate a linear ad hoc network when
single and funnel schemes are used, both under one type of traﬃc and for the case of
multi-traﬃc scheme.

3.1 Linear Ad Hoc CDMA Modeling
For the analysis proposed in this work, we have considered the following points:

• In this work, we analyze an ad hoc network that uses CDMA as the access method,
which is deployed on a straight line, so the analysis will be considered in such scenario.

• We have chosen a point for the interference analysis. We will address this point as
the Analysis Point (AP) a point at which the interference conditions will have bigger
or crucial repercussions.

• Omnidirectional antennas are considered.

• The transmission power is considered in the sense that this power is the lowest possible
and is about -80dBm, which is the minimum receiver signal level [13].

• Power control is considered in order to reach the closest mobile, and the signal level
received is the minimum, and the same, for all users.

• User position follow a Poisson distribution, and mobiles are distributed independently
of each other.

19

20 CHAPTER 3. MODEL DESCRIPTION

Figure 3.1: Planar to linear scenario

Figure 3.2: Linear generated scenario

• In this work all interference measures will be done before considering the cross-
correlation factor of each code.

• Mobiles use the closest neighbors to communicate.

• It is important to say that our system do not consider signal processing algorithms
such as, blind deconvolution and adaptive ﬁlter theory. Signal processing is proposed
as part of future work.

3.2 Proposed Model
The interference analysis made here was done by using simulations of a linear ad hoc net-
work. It is important to say that a planar model can be reduced to a linear scenario. In
Figure 3.1 we see a planar ad hoc network. Distance between points is represented by δi ,
and the distance which will be refereing as the linear distance is represented by Di . Every
Di , will be formed by the sum of the previous radio Di−1 , starting on the reference point.
For example D3 is formed by the sum of D2 and the projection of δ3 . Every time a node is
added the total distance DT otal also grows as it is seen in Figure 3.2.

21
3.2. PROPOSED MODEL

Figure 3.3: Analized scenario

The simulated scenario is shown in Figure 3.3 and has the following configuration.
Our linear ad hoc network starts with an access point. The first element in the network is
placed at the first network’s position. After this point, we find user or node one, and then
successively the rest of the users; All network elements are generated with a Point Process
on the line. Based on this process we generate the mobile positions, which will compound
our complete scenario. Each event in the point process represents the mobile position along
the network.

3.2.1 Point Process
In order to model the mobile positions we use the Poisson Point Process on the line, with λ
as the parameter of occurrence, where λ is the average number of mobile stations per unit
length. The Poisson Point Process arises in many situations where the arrival or events
need to be counted and modelled. Our case events, produced by the point process are
considered as mobile positions on the working space that, for this work, will be on a line.
All our analysis will start here with the point process, so it is vital for the rest of the work to
have trustable point process. Figure 3.4 shows a point process in one and two dimensions.
Assuming that the points are distributed in a line according to a Poisson distribution
with intensity λ, the probability to have n points on the working space is given by

(λx)n e−λx
Pn = , n = 0, 1, 2...,
n!
where λ is the average number of event occurrences, and X is the random variable for
the number of mobiles n=0,1,2,... Our mobile scenario was based on a point process on a


Figure 3.4: Point Process in one and two dimensions

limited line (working space WS), where the occurrence of an event represents a point which
is considered a mobile user in a particular scenario.
The exponential random variable arises in situations where the time of event occur-
rences and time modeling need to be modeled. In this work we use the exponential density
to generate the distances between the mobile positions, this density used is

f (x) = λe−λx , x ≥ 0, (3.1)

where the parameter λ is the rate at which events occur. So the probability of an event
occurring by the time x increases as the rate λ also increases.

3.3 Power Control
In CDMA, the system capacity is maximized if each mobile transmitter power level is
controlled so that the signal arrives at the mobile receptor with the minimum required
signal-to-interference ratio [17].

In order to have the minimum interference and to work with minimum interference
levels in the network, all signals must be transmitted at the minimum possible level, but
the minimum threshold level must be achieved at the receiver in order to ﬁll the quality
requirement levels, most equipment suppliers have settle this level at -80dBm, [13] so for
this work our mobile receptors will be receiving that signal level.

Figure 3.3 shows the mobile positions and how the signals are transmitted to the next
consequent user. Mobile users know the position of the mobile to which they must trans-
mit, which is the next closest user. Also in Figure 3.3, we use In to refer to the interference
from the nth interferent (hitting our analysis point), while the line in the upper part of the
link in the picture represents a wireless link.

23
3.4. PATH LOSS EXPONENT INFLUENCE

We have proposed an analysis point in which all interference has critical repercussions,
so the applied power for each link will depend on the distance between users. In this way
we come to the following. The power of the transmitted signal, [10] is given by

P Tx = P0 [1 + d]γ , (3.2)
where P Tx is the transmitted power, P0 is the threshold reception level, γ is the loss
exponent, and d is the distance between transmitter and receiver. The power at the receiver
is given by the following

P Rx = P Tx [1 + d]−γ (3.3)

= P0 [1 + d]γ [1 + D]−γ . (3.4)

3.4 Path Loss Exponent Influence
Path loss exponent is an important factor that must be consider when a communications
system is designed. Loss factor is related to the signal attenuation of the transmission
media. In free space, the causes of propagation path loss are merely frequency f and
distance d. In the next equation, we see how all of these this factors behave and we see, if
one changes how it affects the entire behavior of signal and interference

Por 1
= 2
Pt 4πdf
c
1
= 2, (3.5)
d
4π λ

where c is the speed of light, λ is the wavelength, PTx is the transmitting power, and PRx
is the received power in free space. The next equation defines the difference between two
received signals. The difference between two received signals in free space and the different
distances is given by

PR2
∆P = 10 log10
PR1
d1
= 20log10 (dB) , (3.6)
d2
and if d2 is twice distance d1 , then the difference in the two received powers is


∆P =20log10 (.5) = −6dB,

so the free space propagation path loss is 6 dB/oct (octave), or 20 dB/dec (decade). And
an octave means doubling in distance, and a decade means a period of 10. Twenty dB/dec
means a propagation path loss of 20 dB and will be observed in distances between 3 to
3 km, in the case in which we would be working with signals in dB at the receiver we
must work also the path loss exponent (PLE) in dB units. A PLE changes depending on
the environment characteristics. In Table 3.1, we show diﬀerent values of γ for diﬀerent
environments [8].

Table 3.1: Path Loss Exponents

Environment Path Loss Exponent
Free space 2
Ideal specular relfection 4
Urban cells 2.7-3.5
Urban cells, shadowed 3-5
In building, line-of-sight 1.6-1.8
In building, obstructed path 4-6
In factory, obstructed path 2-3

3.5 Variable Activity Factors for Multi-Service CDMA
Wireless Systems
Voice activity factor (VAF) can enhance the network performance in a very convenient way
but also can be used to solve the management problem of multi-service in CDMA wireless
networks. For example in a conventional voice link, the user´s voice is active about half
the time, and if transmitters vary output power with voice activity, the total interference
power from a large number of users will be reduced about a factor of two. This reduction
in interference translates naturally into a direct increase in system capacity. The use of
voice activity is possible because all subscribers reuse the same channel [8].

If we are working with a channel which has a rate of R=14.4Kbps (as in today´s
conventional cellular systems) and if we consider a VAF of 0.4, we really would be trans-
mitting 5760 bps, because the transmitter would be transmitting 0.4 of a second. This way

3.5. VARIABLE ACTIVITY FACTORS FOR MULTI-SERVICE CDMA WIRELESS SYSTEMS25

Figure 3.5: AF considerations on linear ad hoc networks

of thinking will allow us to work with channels of higher rates, for example 1Mbps with
the possibility of choosing different VAF’s and multiple parallel codes of this capacity, in
order to adapt our channel to the changing and demanding user information request we
see an example in Figure 3.5. we see that each link has its own VAF which depends on the
amount of information that is being carried.

Table 3.2 gives us the real rates that we could reach when three different transmission
capabilities are used, combined with different activity factors. If we have a channel of 1
Mbps and we need to transmit at 500Kbps, we employ a VAF of 0.5, which will allow us to
reach that transmission rate. In the case in which we need to transmit 1.5Mb, the system
would be using one full code. Another code would be used, at half of its capacity in order
to reach the required capacity.

Table 3.3 refers to the data rates that we are able to reach if we transmit parallel
codes with different data rates. In this scheme, the system splits into N parallel channels,
the entire block of information that we would need to transmit until the desired data rate
is reached with several parallel codes [7].


Table 3.2: Different rates with different AF´s
Total Capacity
AF 512 Kbps 1 Mbps 2 Mbps
0.1 51.2 Kbps 100 Kbps 200 Kbps
0.2 102.4 Kbps 200 Kbps 400 Kbps
0.3 153.6 Kbps 300 Kbps 600 Kbps
0.4 204.8 Kbps 400 Kbps 800 Kbps
0.5 256 Kbps 500 Kbps 1.0 Mbps
0.6 307.2 Kbps 600 Kbps 1.2 Mbps
0.7 358.4 Kbps 700 Kbps 1.4 Mbps
0.8 409.6 Kbps 800 Kbps 1.6 Mbps
0.9 460.8 Kbps 900 Kbps 1.8 Mbps
1.0 512 Kbps 1000 Kbps 2.0 Mbps

Table 3.3: Reached capacity with parallel codes

Total Capacity
Parallel Codes 256 Kbps 512 Kbps 1 Mbps 2 Mbps
1 256 Kbps 512 Kbps 1 Mbps 2 Mbps

3.6 Working With Funnel Networks

As we saw in Section 2.4.2, funnel networks could be useful to transport information from an
access point to a desired user, when there is not deployed infrastructure. The versatility of
this networks consist in the fact that they are used as relay stations, carrying not only their
own traffic but also other users traffic. Every time a user is going to transmit, transmitter
must calculate an Activity Factor. Each transmitter-link has its own activity factor which
is useful in order to calculate the number of parallel or percentage of codes that it will use
to fulfil data transmission requirements.

27
3.7. OUTAGE QUANTIFICATION

3.7 Outage Quantiﬁcation
Outage probability is a very important parameter related to the QoS of a network. In
general outage values must be under 2-4%. Values beyond this threshold means poor´s
network Quality. Equipment suppliers must warranty this level. For this work Outage
statistics will be taken from the number of users that a network can accept successfully.
This means that all interference generated by the network in out reference point must be
less than a ﬁxed value γtarget .

Finally in Figure 3.6 we see the employed algorithm for this work.


Figure 3.6: Algorithm diagram of a CDMA linear ad hoc network

Chapter 4
Numerical Results

In this chapter, we present results obtained for those schemes proposed in chapter two.
The first scenario analyzed is single networks, in which users transmit one key per link
as current conventional cellular systems. On the other hand we have funnel networks,
which are formed when the user´s traffic is cumulative then is transmitted to relay nodes,
until information reaches its destiny. In both scenarios CDMA is used as the MAC. We
make a comparative analysis of the interference measures. We continue analyzing the
outage probability, where we can see the behavior of the capacity for different scenarios,
and changing different physical parameters, such as loss exponent, transmission rate, node
density, finally we make some appreciations.

4.1 Interference Analysis
In this part we will analyze the interference behavior for both scenarios carried out here
in Figure 4.1, we see the interference distribution comparison for a CDMA ad hoc network
carrying one type of service. Parameters used in this simulation are seen in Table 4.1.

Table 4.1: Characteristics of the simulated scenarios
Loss Exponent γ 2
Sensibility -80dBm
λ .01
1/λ 100 m
Working Space 10 Km

In Table 4.1, loss exponent is explained in Section 3.4, sensibility is refereed to the
minimum signal threshold needed to set a successful communication. λ is refereed to the
user occurrence, and 1/λ is refereed to the separation distance between users.

29

30 CHAPTER 4. NUMERICAL RESULTS

0.2
Funnel Network
Single Network
0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0
−85 −80 −75 −70 −65 −60 −55
Interference (dBm)

Figure 4.1: Comparative interference density for 64 users

In Figure 4.2, we are comparing a single network vs a funnel network in their inter-
ference level using the same parameter values showed in table 4.1, because the nodes in a
funnel network work as relay stations, not only carrying their own traffic but also carrying
other user traffic. Funnel networks produce higher interference levels. On the other hand
we can see that single networks produce fewer interference levels because these networks
carry links of a single code, compared with the funnel networks which carries multiple codes
under the same physical conditions. Interference levels were reduced when the number of
users were also reduced, as we see in this case in which we have 32 users in the network
under the same physical conditions. Also in this scenario, the network which was carrying
funnel traffic was seen with the highest interference levels, but the highest interference
levels are seen for the 64-user scenario, as is shown in Figure 4.1.

In Figure 4.3, we are considering 8 users, also using the same parameters as shown
in table 4.1. We can see that interference levels are close similar in its level so there is a
tendency to reach the same level but, it will not be the same because of the funnel effect on
the traffic. The closest interference level between both schemes (single and funnel) would
be when we have two interfering users.

In Table 4.2, we see the main statistical parameters for a single network with three
different users number. For the case of funnel networks we have Table 4.3, for the same
users number. In the table std refers to the standar deviation, minimum refers to the lower

31
4.1. INTERFERENCE ANALYSIS

0.2
Funnel Network
Single Network
0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0
−90 −85 −80 −75 −70 −65 −60
Interference (dBm)


0
10
Funnel Network
Single Network

−1
10

−2
10

−3
10

−110 −105 −100 −95 −90 −85 −80 −75 −70 −65
Interference (dBm)



level. The maximum refers to the highest interference level, and the mean which is the
expected value.

Table 4.2: Interference statistics single network: 64, 32, and 8 users.

Single network
Statistic values (dBm) 64 users 32 users 8 users
minimum -87.28 -89 -99.96
maximun -75.95 -75.84 -76.72
mean -79.57 -79.75 -81.69
std 3.3284 3.78 6.121

Table 4.3: Interference statistics funnel network: 64, 32, and 8 users.

Funnel network
Statistic values (dBm) 64 users 32 users 8 users
minimum -71.34 -73.75 -92.35
maximun -58.21 -62.07 -69.46
mean -62.13 -65.76 -74.41
std 3.773 3.415 6.041

Table 4.4: Characteristics of the simulated scenarios
Loss Exponent γ=2, γ=4
Sensibility -80dBm
Rate of user occurrence λ1 = .04, λ2 = .02, λ3 = .01
Working Space 3.5 Km

In Figure 4.4, we have a comparison of interference density using parameters from
table 4.4. We choose diﬀerent user density. For the ﬁrst λ1 , users would be separated
about 25m, In the second case λ2 , user´s separation would be about 50m. Finally in the
third case λ3 , distance would be around 100m. The highest interference levels are seen in
the case in which distance between users is bigger.

In the last scenario we considered a working space of 3.5Km, this means, that all of
users would be inside of this space. So depending on the distance between users is the

33
4.1. INTERFERENCE ANALYSIS

f(I) Probability
0.5
λ=.04
λ=.02
0.45 λ=.01

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0
−66 −65 −64 −63 −62 −61 −60 −59 −58 −57 −56 −55
Interference (w)

Figure 4.4: Comparative interference density for diﬀerent λ and γ = 2

number of users that we will have in our proposed scenario. The same working space is
used in Figure 4.5, in which also we vary the occurrence rate of users. Table 4.4 show the
values used to simulate the scenario in which we have diﬀerent values of node occurrence.

Figure 4.5 shows a comparison of interference distribution levels using a loss exponent
of γ = 4. When we use this value instead of using γ = 2, we have lower interference levels
because the attenuation is higher, producing lower interference levels for the rest of the
users, in this simulation we used values of Table 4.4.

4.1.1 Empirical CDF of Interference
In this part, we will analyze the empirical Cumulative Distribution Function (CDF) of
interference for the proposed scenarios in Figure 4.6, we show the empirical cumulative
distribution function of the interference. We see that for the same working space under
funnel scenario we have higher interference probabilities, when we have a bigger separation
between mobile users, meaning that if the distance between mobiles is lower nodes, would
need less power to communicate each other, and if distance between them is bigger, they
would need more power in order to reach the minimum receiver signal, in order to excite
the receptor but increasing the signal level that will produce higher interference levels for
the rest of the users in the network.


0.25
λ=.04
λ=.02
λ=.01

0.2

0.15
f(I) Probability

0.1

0.05

0
−68 −66 −64 −62 −60 −58 −56
Interference (dBm)

Figure 4.5: Comparison of interference density for diﬀerent λ and γ = 4

Empirical CDF graphs are generated from statistics that are taken in the reference
point. These statistics consists of multiple values of interference of our generated scenarios.
Once we have repeated the experiment a good number of times, we have a data collection
of interference. The whole block of statistics is ordered, starting from minimum values
to the maximum values. At this point we can get the data range which is the maximum
value less the minimum level. This data range we divide it into several intervals. Those
sub segments represent the data density (With this information it is possible to plot the
interference density). The empirical CDF is done adding each of the sub segment density
values, until the plot reach the maximum value of 1.

Finally Figure 4.7, shows the empirical CDF graphic for the same scenario, using a
loss exponent of γ = 4, also employing values of Table 4.4.

4.2 Capacity and Outage Probability
In this part of the chapter we will present obtained results for CDMA linear ah hoc net-
works that use the same parameters as current cellular systems, Table 4.5. We see the
network behavior in Figure 4.8, using γ = 4, as the loss exponent, and a working space of
18Km. Figure 4.9 we see the outage behavior for a funnel network using parameters as in
Table 4.5, but for this case we are using a loss exponent of γ = 2, we see that the outage


0
10

Outage Probability

−1
10

λ=.003
λ=.002
λ=.001

−2
10
10 20 30 40 50 60 70
Interferents

Figure 4.8: Outage probability single network, γ = 4

behavior is also under 0.04 percent which guaranties good QoS.

Table 4.5: Parameters of current CDMA systems

Bandwidth 1.25MHz
Tx Rate 14.4Kbps
Eb/No 7 dB
VAF .4
Loss exponent γ = 2, γ = 4

In Figure 4.10, make a comparison of the outage probability between three loss ex-
ponents. In this case, we are working with a funnel network. We have use a occurrence
rate λ = .0111, which implies a user separation of about 90 meters. In this case the outage
probability is also under levels of 0.04 percent of outage which is also appropriate to guar-
anty good QoS.

Figure 4.11 shows the outage probability results for the case of a funnel network, using
the same parameters as current cellular systems, those parameters are listed in Table 4.5.
We can see that the number of users present in the funnel network is fewer that those levels
observed in the single network, for this case we are using a loss exponent of γ = 4. In
Figure 4.12 we see the behavior when we change the loss exponent to γ = 6. Here we see

37
4.2. CAPACITY AND OUTAGE PROBABILITY

0
10

Outage Probability

−1
10

λ=.003
λ=.002
λ=.001
−2
10
10 20 30 40 50 60 70
Interferents

Figure 4.9: Outage probability single network, γ = 2

0
10
Outage Probability

−1
10

γ=2
γ=4
γ=6

5 10 15 20 25 30 35 40 45 50 55 60
Interferents

Figure 4.10: Outage probability of a funnel network with diﬀerent PLE


0
10

−1
10
Outage Probability

−2
10

λ=.003
λ=.002
λ=.001

−3
10
0 5 10 15 20 25 30 35 40 45 50
Interferents

Figure 4.11: Outage probability funnel network γ = 4

lower outage probability levels, because signals suffer high attenuation.

Finally before going to the multiservice section we will make an experiment in which we
propose to use different values of system´s characteristics. We will use a bigger bandwidth
and a bigger transmission rate. Table 4.6, show these experimental parameters.

Table 4.6: Experimental parameters in funnel CDMA systems

Bandwidth 30MHz
Tx Rate 128Kbps
Eb/No 7 dB
VAF .4

Employing a bandwidth of 30 MHz and a rate of R=128Kbps with a γ = 2, we see
the outage probability behavior in Figure 4.13. For the same scenario, but using now a loss
exponent of γ = 4, we see the outage probability behavior in Figure 4.14. Both simulations
are on a working space of 10Km.

In Figure 4.15, we see the capacity behavior. In this graph we have users number
versus user separation. We have set two outage values to analyze the capacity, the first is

39
4.2. CAPACITY AND OUTAGE PROBABILITY

0
10

−1
10
Outage Probability

−2
10

λ=.003
λ=.002
λ=.001

−3
10
5 10 15 20 25 30 35 40 45 50
Interferents

Figure 4.12: Outage probability funnel network γ = 6

0
10
Outage Probability

−1
10

λ=.003
λ=.002
λ=.001

−2
10
10 20 30 40 50 60 70
Interferents

Figure 4.13: Outage probability funnel network γ = 2, BW 30MHz


0
10

Outage Probability

−1
10

λ=.003
λ=.002
λ=.001
−2
10
10 20 30 40 50 60 70
Interferents

Figure 4.14: Outage probability funnel network γ = 4, BW 30MHz

0.04% and a second value for outage 0.08%. We can compare both schemes, single net-
works, and funnel networks. The figure shows bigger user capacity for the case of single
users. For the case of the fixed outage, if we decrease the outage requirement, the number
of users grow. Refer to Table 4.5, to see the utilized parameters to simulate both schemes
single and funnel CDMA networks.

4.3 Multiservice Traffic Results
In this section, we present results obtained when different transmission rates are used in the
ad hoc network. The procedure used here to use different activity factor (AF) is the same
as in section 3.6. For this work we consider that the network will be offering three types of
services with the same probability of occurrence in each node of the network. Parameters
used for the present scenarios are shown in Table 4.7.

Figure 4.16, shows the network behavior for a funnel network using a bandwidth of
20Mhz as well as the three proposed services with the same probability of the user demand.

In Figure 4.17, we see the network behavior with different values in lambda and the
same services, in this case we used λ1 = .001, λ2 = .002 and λ3 = .003. For this case, we
have a γ = 4.

41
4.3. MULTISERVICE TRAFFIC RESULTS

70
Outage Single @ .04%
Outage Single @ .08%
Outage Funnel @ .04%
Outage Funnel @ .08%
60

50
Users Number

40

30

20

10

0
300 400 500 600 700 800 900 1000 1100
User separation 1/lambda (m)

Figure 4.15: Capacity comparison single VS funnel networks

0
10
Outage Probability

−1
10

Service types

S1= 64Kbps
S2=128Kbps
S =384Kbps
3

λ=.001
λ=.002
λ=.003

−2
10
5 10 15 20 25 30 35 40 45 50 55 60
Interferents

Figure 4.16: Outage probability funnel multiservice network, γ = 4


Table 4.7: Multiservice parameters

Bandwidth 20MHz
Tx Rate 512Kbps
Eb/No 7 dB
VAF variable

0
10
Outage Probability

−1
10

Service types

S1= 64Kbps
S =128Kbps
2
S =384Kbps
3

λ=.001
λ=.002
λ=.003

−2
10
5 10 15 20 25 30 35 40 45 50 55 60
Interferents


We can see the same scenario, but now using a path loss exponent of γ = 2 and
offering the same services, in Figure 4.17. To see the effect that the loss exponent plays in
the network behavior, we have Figure 4.18. In this figure, we are using a γ = 6. Under
these physical conditions, in which we expected to observe the best results. Finally, Figure
4.19 directly compares three different values of γ1 = 2, γ2 = 4, γ3 = 6. Expecting to have
the best results when the path loss exponent is biggest.

From the capacity point of view we present Figure 4.20, in which we see the capacity
behavior for a network that works under multiservice scheme. Also for this scenario we
have taken into account two values of outage to see the capacity behavior. The first is
outage @ 0.04% and the other is @ 0.08%. In this case we see that the outage at 0.08%
accept more users than the other outage number 0.04%. On Table 4.7, we see the utilized
parameters to simulate these scenario.

43
4.3. MULTISERVICE TRAFFIC RESULTS

0
10

−1
10
Outage Probability

Service type

S1= 64Kbps
−2
10
S =128Kbps
2
S =384Kbps
3

λ=.001
λ=.002
λ=.003
−3
10
5 10 15 20 25 30 35 40 45 50 55 60
Interferents


0
10
γ=2
γ=4
γ=6

Service types

S1= 64Kbps
S2=128Kbps
Outage Probability

S3=384Kbps

−1
10

−2
10
10 20 30 40 50 60 70
Interferents

Figure 4.19: Outage probability funnel multiservice network λ = .005

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