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E

This is to certify that the

dissertation entitled ‘

POWER CONTROL AND INTERFERENCE MANAGEMENT IN A
SPREAD—SPECTRUM CELLULAR MOBILE RADIO SYSTEM

presented by

Hossein Alavi

has been accepted towards fulfillment
of the requirements for

Doctor of Philosophy degree in Electrical Engineering

/u/MM

Major professor

Date March 19, 1984

MSU is un Affirmative Action/Equal Opportunity Institution

0-12771

 

 

iV1ESI_] RETURNING MATERIALS:
Place in book drop to

LIBRARJES remove this checkout from

your record. FINES will

 

 

be charged if book is
returned after the date
stamped below.

POWER CONTROL AND INTERFERENCE MANAGEMENT IN A
SPREAD-SPECTRUM CELLULAR MOBILE RADIO SYSTEM

BY

Hossein Alavi

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering and Systems Science

1984

ABSTRACT

POWER CONTROL AND INTERFERENCE MANAGEMENT IN A
SPREAD-SPECTRUM CELLULAR MOBILE RADIO SYSTEM

BY

Hossein Alavi

Spread-spectrum multiple-access systems usually
require some form of power control when the terminals are
mobile, in order to prevent signals from nearby units from
swamping out more distant signals. Power control is even
more essential when the system is a cellular one, due to
the interference from cell to cell. Here we report on a
power control system that permits the
signal-to-interference ratio of every signal to be
equalized within each cell and, optionally, from cell to
cell throughout the system, for both upstream (mobile to
base station) and downstream (base station to mobile)
signals. The method is introduced mathematically and
results of a computer simulation are presented.
Downstream balancing eliminates the so-called "corner
effect", and upstream balancing eliminates the so-called
"near-far effect".

We conclude that in-cell balancing is essential for
the efficient operation of the system, and is
mathematically easy to accomplish. By comparison,

cell-to-cell balancing has a more marginal effect on the

system efficiency and is more difficult to perform; but
its use may still be advisable in systems where the
traffic load is distinctly nonuniform from cell to cell.
Results show that when practical implementations are
considered, the downstream balancing can easily be
accomplished with full dynamic range. Upstream balancing,
however, may be very hard to implement due to very high
values of dynamic range required of the mobile
transmitters, to battle the severe results of the near-far
effect. Truncation of the upstream dynamic range would
result in an "outage" phenomenon akin to the outage due to
shadow fading that occurs with narrowband systems. In the
spread-specrum case, however, outage is less probable due

to power control.

ACKNOWLEDGMENT

I wish to express my greatful appreciation to my
parents for their continued support and encouragement
throughout my studies. To my wife, Shakiba, I offer
sincere thanks for her continuous patience, help and
encouragement. To Dr. Ray W. Nettleton, my advisor, I
express my deep gratitude for his guidance throughout this
project. This work was supported by the National Science

Foundation under Grant no. ECS-81 00692.

ii

LIST OF

LIST OF

CHAPTER
1.1
1.2

CHAPTER
2.1

CHAPTER
4.1
4.2
4.3

4.4

CHAPTER

5.1

5.2

TABLE OF CONTENTS

TABLES . . . . . . . . . . . . . . . . .

FIGURES . . . . . . . . . . . . . . . . .

1: INTRODUCTION . . . . . . . . . . . .
Statement of Problem . . . . . . . . . .
Outline of Contents . . . . . . . . . . .

2: BACKGROUND . . . . . . .
Characteristics of the Channel . . . . .
2.1.1 Rayleigh Fading . . . . . . . . .
2.1.2 Shadow Fading . . . . .
Cellular Land—Mobile Radio Systems . . .
Narrow Band Systems . . . . . . . . . . .

3: DESCRIPTION OF THE SPREAD—SPECTRUM SYSTEM

Overview . . . . . . . . . . . . . .
Spread-Spectrum Performance Limitations .
Code Division Multiple Access . . . . . .
3.3.1 CDMA Limitations . . . . . . . .
Principle Features of a Spread-Spectrum
System . . . . . . . . . . . . . . . . .
3.4.1 Advantages . . . . . . . . . .
3.4.2 Disadvantages . . . . . . . . . .

4: POWER CONTROL . . . . . . . . . . . .
General Remarks . . . . . . . . . . . .

Assumptions . . . . . . . . . . .
Power Balancing Algorithms . . . . . . .
4.3.1 Upstream . . . . . . . . . . . . .
4. 3. 2 Downstream . . . . . . . . . .
Existence and Uniqueness of the Solution

5: SIMULATION . . . . . . . . . . . . .
Geometry . . . . . . . . . . . .
5.1.1 Base Station and Load Distribution
5.1.2 Fading . . . . . . . . . . . . .
Power Distribution and Interference . . .
5.2.1 No Power Balancing . . . . . . . .
5.2.2 In-Cell Balancing . . . . . . . .
5.2.3 Cell—to-Cell Balancing . . . . . .

Page

vi

iv

CHAPTER 6: RESULTS . . . . . . . . . . . . . . . . . 60

6.1 Load Distribution and Environmental Parameters 60
6.2 Upstream Results . . . . . . . . . . . . . . . 67
6.2.1 Denial Statistics . . . . . . . 67
6. 2. 2 Dynamic Ranges of Transmitted Powers . . 84
6.3 Downstream Results . . . . . . . . . . . . . . 93
6.3.1 Denial Statistics . . . . . . . 93

6. 3.2 Dynamic Ranges of Transmitted Powers . . 109
6.4 Signal- to—Interference Ratio . . . . . . . . . 118

CHAPTER 7: CONCLUDING REMARKS . . . . . . . . . . . . 122
7.1 Conclusions . . . . . . . . . . . . . . . . . 122

7. 2 Recommendations for Further Study . . . . . . . 123
7.2.1 Restricted Power Control . . . . . . . . 124

7. 2.2 Fading Model . . . . . . . . . . . . . 124

7.2. 3 Interference Modeling . . . . . . . . . 125

LIST OF REFERENCES . . . . . . . . . . . . . . . . . . 126

LI ST OF TABLES

page
Frequency allocations in "900 MHz" band ......... 2

Ratios of the load in different cells as a/a
varies ........ ...... ........................... 66
Power control dynamic ranges required at full

system capacity for the upstream link .......... 92

Power control dynamic ranges required at full
system capacity for the downstream link ....... ll6

Figure

2.1

LIST OF FIGURES

Page

Principle of the cellular land-mobile radio
system IIIIIII .....I'lht ........ ......0000000000

A cellular system in which cell sizes vary with
user density ........... ......... ...............

A narrowband/frequency-reuse system with L=4 ...
Spread-spectrum connecting system ..............
Interference geometry ..........................

Base station distribution in the 19 cell
simulated system ... ......... ......... ...... ....

Geometry used in simulating the shadow fading
Power Method for solving an eigenvalue problem .
Geometry for load distribution analysis ........

Pr{def> R} values versus the ratio d/R for
different a/a values .......... .......... .......

Denial statistics for the center cell, a = 3.0,
uniform traffic distribution, upstream .........

Denial statistics for the center cell, a = 3.5,
uniform traffic distribution, upstream .........

Denial statistics for the center cell, a = 4.0,
uniform traffic distribution, upstream .........

Denial statistics for the center cell, a = 3.0,
tapered traffic distribution, upstream .........

Denial statistics for the center cell, a = 3.5,
tapered traffic distribution, upstream .........

Denial statistics for the center cell, a = 4.0,
tapered traffic distribution, upstream .........

vi

12

l4
16
26
36

48
51
59
62

64

68

69

73

6.14

6.15

6.17

6.18

6.20

vii

Denial statistics for the total system,¢!= 3.0,
uniform traffic distribution, upétream .........

Denial statistics for the total system,¢!= 3.5,
uniform traffic distribution, upstream .... .....

Denial statistics for the total system,¢!= 4.0,
uniform traffic distribution, upstream .........

Denial statistics for the total system,¢!= 3.0,
tapered traffic distribution, upstream .........

Denial statistics for the total system,¢!= 3.5,
tapered traffic distribution, upstream .........

Denial statistics for the total system,¢!= 4.0,
tapered traffic distribution, upstream .... .....

Average power control dynamic ranges required
for upstream link balance, a =3.0, uniform
traffic ....... 0...... ...... ......OOOOOOOCOOOOO.

Average power control dynamic ranges required
for upstream link balance, a =3.5, uniform

traffic ............OOOOOOOOOCOOOOOOOO0.0.0.0...

Average power control dynamic ranges required
for upstream link balance, a =4.0, uniform

traffic ...O......OOOOOOOOOOOOOO.....OOOOOOOOOOO

Average power control dynamic ranges required
for upstream link balance, a =3.0, tapered

traffic 0.0.0.....OOOOOOOOOOOOOOOOOOOO00.0.00...

Average power control dynamic ranges required
for upstream link balance, a =3.5, tapered

traffic O.........OOOOOOOOOOOOOOOOOO00.0.0000...

Average power control dynamic ranges required
for upstream link balance, t1 =4.0, tapered

traffic ......O..0...0.0.00.0...00.00.000.000...

Denial statistics for the center cell, a==3.0,
uniform traffic distribution, downstream .......

Denial statistics for the center cell, a= 3.5,
uniform traffic distribution, downstream .......

Denial statistics for the center cell, a: 4.0,
uniform traffic distribution, downstream .......

74

75

76

77

78

79

85

86

87

88

89

90

94

95

96

viii

Denial statistics for the center cell, a= 3.0,
tapered traffic distribution, downstream ....... 97

Denial statistics for the center cell, a: 3.5,
tapered traffic distribution, downstream ....... 98

Denial statistics for the center cell, a: 4.0,
tapered traffic distribution, downstream ....... 99

Denial statistics for the total systenn a: 3.0,
uniform traffic distribution, downstream ...... 100

Denial statistics for the total systenn a: 3.5,
uniform traffic distribution, downstream ...... 101

Denial statistics for the total system, a= 4.0,
uniform traffic distribution, downstream ...... 102

Denial statistics for the total systenn a: 3.0,
tapered traffic distribution, downstream ...... 103

Denial statistics for the total system, a= 3.5,
tapered traffic distribution, downstream ...... 104

Denial statistics for the total system, a: 4.0,
tapered traffic distribution, downstream ...... 105

Average power control dynamic ranges required
for downstream link balance, a =3.0, uniform
traffic ............ ...... ..................... 110

Average power control dynamic ranges required
for downstream link balance, ¢!=3.5, uniform
traffic ..................... ...... ............ 111

Average power control dynamic ranges required
for downstream link balance, a=4.0, uniform
traffic .............. ....... .................. 112

Average power control dynamic ranges required
for downstream link balance, a=3.0, tapered
traffic ......0.0.000.........OCUOOIOOOOOOOOIDO113

Average power control dynamic ranges required
for 'downstream link balance, a=3.5, tapered
traffic 00.0.0... ..... 0....IOIOIOIOOOIOOOOOO...114

Average power control dynamic ranges required
for downstream link balance, a=4.0, tapered
traffic ....I.0.00.0.0.0...OOIOIOOIOOOICOOUOOIO115

6.39

6.40

6.41

ix
SIR versus average load per cell,¢x=3.0 .......
SIR versus average load per cell, a=3.5 .......

SIR versus average load per cell, a=4.0 .......

CHAPTER 1

INTRODUCTION

1.1 Statement of Problem

The increasing scarcity of the spectral resource in
recent years, together with increasing demand for that
resource, has led to much activity in the field of
spectrum management and conservation [H1].

In no other application has this problem been more
intensely 'felt than in the land mobile radio field.
Recent FCC allocations in the 900 MHz band include two
bands of width 20 MHz, intended for cellular land-mobile
radio use (Table 1.1) [53]. This allocation, coupled with
the introduction of the cellular frequency re-use concept,
promises to give temporary relief to this problem [Y1].
Cellular systems using this concept have been proposed and

a number of systems are under construction or have been

Table 1.1 Frequency allocations in the “900 MHz“

 

 

 

 

 

 

 

 

 

 

band.
Frequency, MHz Allocation
806-82] Conventional systems
mobile transmissions
82l-825 Held in reserve
825-8h5 Cellular systems
mobile transmissions
8b5-851 Held in reserve
851-866' Conventional systems
base stations
866-870 Held in reserve
870-890 Cellular systems
base stations
890-902 Held in reserve
902-928 |ndustrial,scientific
and medical equipment

 

 

 

 

constructed [$3,A2,Il]. The proposed schemes, however,
employ simple and traditional technologies, and the
systems are likely to be outstripped by demand for more
service, better quality, and diversified applications
before the end of the century.

The use of spread spectrum in cellular land-mobile
radio systems has been proposed and analyzed [C1,C2,N1].
Results to date have shown that spread spectrum techniques
provide better quality communications and a more efficient
use of the spectrum in the case of cellular systems.
However these techniques require some degree of power
control to reduce interference between users.
Particularly, systems employing direct-sequence modulation
become useless unless they use power control [T1].

The concept of power balancing to control
interference between co-users of the same spectral space
has been proposed and analyzed in the context of
multi-beam communication satellites [Al]. The principle
of power balancing may be readily extended to other
interference-limited systems however [P2], and the
spread-spectrum land mobile cellular radio scheme is a
prime candidate.

In the upstream links (mobile to base) a significant
difficulty is the so-called "near-far" effect, which
permits strong interferers in the immediate vicinity of

the base station to overwhelm weak signals from more

 

distant mobiles. This effect is considerably worse for
direct-sequence signalling than for frequency-hopping,
since in the latter case limiters can be placed in each
hopping channel to reduce the power imbalance. But in all
cases some improvement can be obtained by dynamically
controlling the transmitted power for every mobile
transmitter so that the base station receives more-or-less
the same power from each mobile. This is true whether or
not the system is cellular.

In the downstream (base to mobile) case, if the
system is not cellular, and if all signals are transmitted
with the same power then every receiver will suffer the
same signal-to-interference ratio regardless of distance,
and power control is not necessary. But if the system is
cellular, there is a distinct need for power control in
the downstream case. A mobile that is near its base
station will be almost unaware that there is any
interference from outside its cell. But in the cell
corners, a mobile will receive about three times the
amount of interference since it is roughly equidistant
from its own and two interfering base stations. Without
power control, some corner mobiles would be incapacitated
during periods of high communication traffic load.

This work describes schemes for balancing the signal
to interference ratio of the mobile downstream and

upstream links, for every mobile in a given cell and

(optionally) for all mobiles in the entire system.
Results are given at the receiver antenna so that they are
independent of the choice of spreading function,
modulation method or coding scheme. Results are also

compared for the upstream and downstream links.

1.2 Outline of Contents

Chapter 2 outlines the background material which
forms the basis of the work. Section 2.1 reviews the
general characteristics of the urban 900 MHz channel, and
a composite model, suitable for the analysis of the
proposed system, is presented. Section 2.2 outlines the
features of existing proposals for the solution of the
problems of the land-mobile radio service.

In Chapter 3, the spread-spectrum system is outlined
in general terms. The advantages and disadvantages of the
operation of the system are discussed, and some
comparisons with narrowband systems are drawn. The
general principles of the spread spectrum cellular
land-mobile radio scheme is described, without reference
to any specific signal design or modulation methods.

Chapter 4 presents the theoretical results of the
present work. The power balancing algorithms for both
upstream and downstream links are developed and analyzed,

and the existence and uniqueness of the solution to the

problem is discussed. The power balancing algorithms, for
both the upstream and downstream cases, permit the
signal-to interference ratio of every signal to be
equalized within each cell and, optionally, from cell to
cell throughout the system.

Chapter 5 discusses the considerations and
assumptions used in the computer simulation of a
hypothetical system. Geometrical and propagation
considerations based on an assumed service area of 19
equal size cells, arranged in three concentric rings, are
presented. We describe how the power control algorithms
were applied to the hypothetical system.

Chapter 6 presents the results of the computer
simulation of the 19 cell system. Results of the
interference, load capacity and dynamic ranges of
transmitted powers are presented for both upstream and
downstream cases, and are compared for different path loss
parameters. Results are also compared for cases where no
power control is applied; power control is applied only
inside each cell; and power control is applied
system-wide.

Chapter 7 summarizes the work and discusses

recommendations for further research in this field.

CHAPTER 2

BACKGROUND

2.1 Characteristics of the Channel

The new urban 900-MHz mobile radio channel has been
studied in great detail in the literature [J1]. We

summarize the pertinent features of the channel below.

2.1.1 Rayleigh Fading

The channel disperses the transmitted signal. in the
time domain. This results in a highly frequency-selective
fading. For example, a sine-wave continuous signal will
be received as the sum of a large number of sine waves
with different phases. The received signal amplitude will

have Rayleigh statistics that are different for different
7

 

 

 

—7—’ ' m;m_13.,_._ - i ,, _

frequencies [N1]. This fading occurs over distances of
about one half wavelength. Therefore, a mobile moving
through the field will experience up to hundreds of fades
a second at typical vehicular speeds.

The coherence bandwidth Bc of the channel is the
difference between two frequencies which have a
correlation coefficient of 0.5 or less. It can be shown
that Bc is inversely proportional to the rms time spread
of the channel impulse response [Kl]. Typically, the
coherence bandwidth ranges from 30 KHz to 1 MHz. Thus the
frequency-selective property Of the channel causes a
spread-spectrum transmission to suffer different fades at
different portions of its spectrum. This results in a
form of frequency diversity which reduces the effects of

fading [Kl].

2.1.2 Shadow Fading

When a mobile moves around the service area, the mean
strength of the signal changes slowly. This is shadow
fading due to buildings and terrain. This imposes a
non-frequency selective, slowly changing median upon the
Rayleigh field statistics. This fading has a lognormal
characteristic (i.e., normal if measured in dB) with
standard deviation, sometimes called the dB spread,

varying between 7 and 12 dB.

The mean of the overall fading distribution is a
deterministic function of distance from the transmitter
ranging from an inverse cubic law to an inverse
fourth-power law [J1].

Consequently we may define an instantaneous

attenuation factor:

ainst = s(t)r(t) (2-1)

where r(t) is due to the Rayleigh fading and has a mean of

unity; and s(t) is due to the combined effect of shadow

fading and attenuation with distance. Thus, if
{(t) = 10 loglo(s(t)) (2-2)

then the random variable 5 is Gaussian with probability

density function:

1 2 2
£_(§) =——exp( -(6- m) /20' ) (2-3)
= \iZw 0
where a varies between 7 and 12 dB depending on the
severity of the shadow fading. The mean value m reflects
the median attenuation in signal strength in the mobile

environment and is given by:
C!
m=10 loglo (1/d ) (2-4)

where d is the distance between the mobile and the base

station. The path loss exponent or propagation parameter,

10

a, .varies between 3 and 4 ( ‘1: 2 represents the free
space situation.)

The rapid Rayleigh fading envelope, however, causes
the instantaneous attenuation to fluctuate rapidly. For
example, with a velocity of 30 miles/hr, a vehicle would
have traveled 44 ft (about 44 wavelengths at 900 MHz) in
one second and experienced that many Rayleigh fading
cycles. This rapid fluctuation is averaged due to the
filtering effect of the human hearing response. This time
averaging is equivalent to ensemble averaging, for ergodic

signals, thus we set the average attenuation factor;

a = E {a- } = s(t) (2-5)

1nst

This is a more meaningful indicator of the attenuation for
a mobile environment and is independent of the Rayleigh

fading.

2.2 Cellular Land-Mobile Radio Systems

Existing mobile telephone systems can serve a limited
number of users due to spectral overcrowding. One radio
frequency can only be used by one user at a time in the
service area in which the mobile user is allowed to
operate. But a new technology called Cellular Land-Mobile
Radio (CLMR) is about to change the present situation.

This technology now offers better service to several

ll

hundred thousand users than was previously offered to a
few hundred users [C3].

While most of the literature concerning CLMR systems
have addressed the narrow band/frequency-reuse schemes
[Ml,Sl,SZ], recent publications calling for the use of
spread spectrum as a more efficient technique for CLMR
systems, have attracted much attention [C1,C4,N1,C3].
Despite the differences in the modulation techniques, all
cellular systems have many characteristics in common which
are summarized below with reference to Figure 2.1.

The geographic area is divided into small "cells" the
sizes of which reflect the expected traffic load in the
area. Each cell has its own base station antenna,
typically located in the middle of the cell. Although the
shape of the cells are typically represented as hexagons,
the actual shapes are determined by the terrain, and
density and locations of hills and buildings, in the
service area. Thus the region served by each base station
(or its cell), is the area in which the signal strength
from that base station is stronger than from all other
stations. However, the use of "hexagonal" cell
representation has become common practice in the technical
literature and will be used in the sequel with no further
apologies. Each mobile communicates only with the base
station serving the cell in which the mobile unit is

located, and a central controller interconnects different

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/ / Mobile unit
0
Cell
Base station
\ . /
\\ ’ /
\‘\ CENTRAL
fl Land CONTROLLER
lines

 

 

 

Figure 2.1 Principle of the cellular land-mobile radio system.

"b

13

base stations, via a non-broadcast link, thus making
communication from cell to cell possible. Therefore there
is no mobile-to-mobile communication and every link is via
one or two base stations, depending on whether the mobiles
are located in the same or different cells. The
transmitted power to and from the mobile units is limited
to the amount required to communicate with satisfactory
quality within the cell and at the same time to minimize
the interference to neighboring cells.

The central controller also keeps track of the
location of each mobile unit. When a mobile passes the
boundary of a cell and enters another cell, the controller
re-routes the call to the appropriate base station without
any noticeable interrupt in the communications. This
operation is referred to as "handoff".

Interference between simultaneous users increases as
the number of users in the service area increases. System
performance is then limited by interference, rather than
background noise [C7]. The amount of interference is
mostly a function of the number of users inside each cell,
and thus the expansion of the system in order to serve
more users can be accomplished by reducing the size of the
cells rather than by expanding the spectral space [52].
Figure 2.2 shows a cellular system in which the cell-size
distribution reflects the non-uniform distribution of user

density.

)\

 

 

/ j

Figure 2.2 A cellular system in which cell sizes vary
with user density.

 

———— ' ' " "-._......¢~.~;-.~_-:_~ Mu. _ «4: . ._ -. '

15

Besides the above characteristics that are common
between all systems, there are some additional features
characterizing the narrow band/frequency-reuse scheme and
the spread-spectrum scheme. We summarize some of the
characteristics of the narrow band systems here, and
Chapter 3 is devoted to the characteristics of the

spread-spectrum system.

2.3 Narrow Band Systems

In the narrow band/frequency-reuse systems the
available spectrum is divided into narrow band channels.
The channel set is divided into L disjoint subsets, and
each subset is assigned to one cell of a cluster of L
cells. This is to minimize the cochannel interference
that may result from the use of the same channel in the
neighboring cells. The number of subsets of channels is
equal to the number of cells in a cluster. The cluster is
formed such that it can tesselate the plane. Figure 2.3
shows a system with a cluster size of 4 [M1]. The channel
assignment, then, is repeated in the same configuration in
all clusters.

In addition, each subset of channels is divided into
two portions; one for base station transmissions and one
for mobile unit transmissions.

When handoff occurs, in addition to re-routing the

16

Figure 2.3 A narrowband/frequency-reuse system
with L = 4.

17

call, the central controller must find an idle channel
pair to assign to the mobile to use in the new cell. In
the case where there are no channels available, the call
is terminated or "blocked".

When a mobile moves around the service area, it may
pass through areas in which signal-to-interference ratio
is unacceptable. This is caused by shadowing due to
buildings and terrain. This phenomenon is referred to as
"outage".

Despite the advantage of being simple in concept and
design and the availability of fully-developed technology,
the narrow band/frequency-reuse scheme has many
disadvantages, particularly in the case of the present FM
schemes. These disadvantages include the high cost of
analog circuitry and the poor quality of reception in a
fading environment [P1]. In an environment where the
signal strength attenuates only as the inverse cube of the
distance and the standard deviation of the signal
variation is as large as 10 dB, 30-40 channel sets are
required to provide good service probability (on the order
of 99 percent) [C8]. In addition, waste of spectrum
resulting from allowing only a portion of the spectrum to
be used in any given location, and the lack of privacy due
to the use of simple modulation methods are among many
other disadvantages that can be named. As such, it is

felt that the narrow band/frequency-reuse scheme provides

 

18

a useful but necessarily temporary solution to the problem

of the land-mobile radio service [N1].

CHAPTER 3

DESCRIPTION OF THE SPREAD-SPECTRUM SYSTEM

3.1 Overview

Spread-spectrum is an alternative to the narrow band
schemes in multiple access systems. In systems employing
spread-spectrum, different users are distinguished by
different signature sequences. This technique is referred
to as code division multiple access (CDMA). In such a
system the base band signal is embedded into a spreading
signal that has a bandwidth much greater than the data
rate. This is the reason this technique is called
spread-spectrum. The analysis in this chapter is more
appropriate to the transmission of binary data using
direct-sequence spectral spreading [Wl,P3]. More careful

analysis however, is needed for frequency hopped schemes.

l9

 

20

3.2 Spread-Spectrum Performance Limitations

Generally, in any digital communication, the
probability of bit error Pb must not exceed some value PO.
This restriction is satisfied if the ratio of energy per
bit Eb' to the one-sided spectral density of the noise NO,

exceeds some threshold value T;

Pb 5 PO iff Eb/NO > T (3—1)

Particularly, if ideal matched filters are used, Pb for a

BPSK scheme is given by
p = Q[(ZE /N )1/2] (3—2)
b b O '

where Q(x) is the Gaussian integral function defined by

Q(x) =f(2x)’1/2exp(-u2/2)du. (3-3)
X

Typically, PO is required to be in the range 10.3 - 10

-6
This can usually be achieved with T in the range 5 to 15
dB.

Suppose the received spread-spectrum signal has the

average one-sided power spectral density of S in the band

of width B. That is, if the transmitted spectrum is S(f),
on
p = SB =fs(f)df (3-4)
0

where P is the power of the constant envelope signal, and

is equal to the product of the energy-per-bit and the bit

21
rate R. Then (3-1) becomes
Eb/NO = P/NOR = (S/N0)<B/R) 3 T
thus, we have
5 Z NOT/(B/R) (3_5)

Note that (3-4) and (3-5) are true for any type of
spreading function. The factor B/R is often called the
processing gain of the spread-spectrum system.

The inequality in (3-5) suggests that for a given T,
the power spectral density S of the desired signal may be
less than the noise spectral density, provided that the
processing gain is large enough. It is thus possible for
a spread-spectrum receiver to operate even when the input
signal is buried in noise. This suggests the use of a
technique known as spread-spectrum multiple access (SSMA),

also called code division multiple access (CDMA).
3.3 Code Division Multiple Access

Multiple access can be achieved by spread-spectrum
code division using direct-sequence, frequency hopping,
time hopping, or a combination of these techniques. All
of these schemes use spreading signals that are minimally
correlated with each other as well as with the

time-shifted versions of themselves. This is to

22

facilitate easy recognition of the desired signal and easy
synchronization of the receiver to the signal. The
following discusses some analysis and performance
limitations of CDMA systems that use the direct-sequence
technique [W1]. Perfect synchronization of the matched

filter in the receiver for the desired signal is assumed.

3.3.1 CDMA Limitations

The analysis in 3.2 also applies if the noise
spectral density is replaced by a spectrum composed of
thermal noise and a number of noise-like interferers. In
direct-sequence techniques that use pseudonoise functions
as their spreading signal, the ensemble of interferers
behave like independent sources of white, Gaussian noise
[P3]. Suppose that there are K interferers and the ith
interferer is received with power spectral density aiS
Watt/Hz, where S is the power spectral density of the
desired signal. Thus the total noise-plus-interference

power spectral density over the transmitted bandwidth

becomes
N = N + S 2 a.. (3-6)

Thus at the input of the receiver, the

signal-to-interference ratio (SIR) is given by

23
SIR = S/N = (Eb/N)(R/B). (3-7)

But B is much greater than R, so Eb/N can be in an
acceptable range (about 10) even when SIR is very small.
For example, for a processing gain of 30 dB, and Eb/N of
10 dB, SIR is as small as 0.01. Therefore if the effect
of the thermal noise is neglected and all signals are
received with equal powers, 100 interferers can be present
in the same band, and the performance of the receiver will
still stay within the acceptable range.

Combining (3-5) and (3-6) we have

S 3 N0 k , (3-8)

(B/R)/T - finai

It is clear that in order to have equal reception quality
for all users in the system, the received power must be
the same for every signal. Thus the value of the
coefficient "a" must be unity for all i. (In order to
achieve equal received power from users with different
path lengths, some sort of power control is required.
This is discussed further in the next chapter.) This will
also maximize the traffic capacity of the system. In that

C686

and (3-8) becomes

 

24

No
S 3 . (3-10)
(B/R)/T - K
Note that if K 3 (B/R)/T there is no value of S that will
lead to the required probability of error P0. This leads

to the fundamental limit for the traffic capacity of a

CDMA channel with equal power interferers;

K 5 (B/R)/T (3—11)

However, the capacity bound for a TDMA or FDMA scheme
using binary antipodal signaling is" K 5 B/R. Thus in
general, the fundamental bound on the capacity of a system
employing CDMA is less than the bound on both TDMA and
FDMA by the factor T, provided that they have the same
amount of available bandwidth. This, however, is not true
in the case of the cellular land-mobile radio systems. In
order to combat interference, in narrow band
frequency/re-use systems, the available channel set is
divided into many subsets, each of which is assigned to
one cell in a cluster. Then, if the cluster size is L,
the available bandwidth in each cell is reduced to B/L and
the capacity bound is reduced by a factor of L. Thus we

have

x 5 (B/R)/L (3-12)

25

In cellular systems using CDMA, however, no
clustering is required and all of the available band can
be assigned to every cell. Thus for the cases where
T < L, a CDMA scheme can have larger capacity than TDMA or
FDMA schemes. This condition is expected to be true in
many cases, since for good service probabilities in the
frequency/re-use systems cluster size must be as large as

30-40 [ca].

3.4 Principle Features of a Spread-Spectrum System

The spread-spectrum cellular land-mobile radio system
has been described in detail in the literature [C1,C2]. A
suggested layout for the connecting system of such a
system is shown in Figure 3.1. The overall features of

this system are summarized below:

1. The available spectrum is divided into two
segments, one for upstream and one for
downstream. All mobiles and all base stations
use the appropriate segment in its entirety for
communication. The bandwidth of the signals

might be in the tens of megahertz.

2. Interference between users is controlled by

26

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27

signal design, using the large processing gain
which results from transmitting a narrowband
message embedded into a broadband signal [D2].
The set of signals is large enough to assign one
signal uniquely to every mobile unit. No attempt

is made to synchronize the mobile transmitters.

The "local" cell of a mobile is the cell of the
base station which receives the most power from
the mobile. This definition changes as the
mobile moves, and "handoff" occurs when the
mobile crosses a boundary from one cell to

another.

The quality of the message is degraded by
increasing interference levels, i.e. as the
traffic load in the vicinity builds up. The
switching network may fail to connect a call for
one of two reasons: first, if there is no
communication path through the system (due to
hardware limitation), the call is "blocked" in
the classic sense of the telephone traffic
literature [Bl]. Second, if the system senses
that the addition of another call will result in
excessive degradation of quality for all local

calls, the connection will be refused by the

28

system. The latter failure will be referred to
in the sequel as "Denial" to distinguish it from

blocking.

3.4.1 Advantages

In addition to increased user-density that is
possible in a small-cell system employing CDMA, many more
advantages result from the use of spread-spectrum in such
systems, some of which are summarized below:

The use of bandwidths that are much greater than the
coherence bandwidth of the channel in such systems results
in a form of frequency diversity which reduces the effects
of frequency selective rapid fading significantly.

Every user is assigned a unique signal that is not
used by any other user (at least locally.) This results
in several advantages. First, any user can access the
system at any time without having to wait for a free
channel. Thus, there are no "blocked" calls in the usual
sense, other than those caused by hardware limitation.
The second advantage is message privacy with respect to
the casual listener. Of course, this does not refer to
message interception by a properly equipped receiver.
Finally, the third advantage of this is that there is no

channel switching or address change when the user moves

29

from one cell to another. Therefore, there is no
"forced termination", which occurs in the narrow band
systems due to unavailability of channels.

When the number of simultaneous users in the service
area increases, the result is degradation in the quality
of the communication for 'all users, due to increased
interference. This is usually referred to as "graceful
degradation". Therefore, there is no hard limit on the
number of users that can be active simultaneously.
However, the switching network may fail to connect a call,
if the system senses that the addition of another call
will result in excessive degradation of quality for all
local calls (denial).

Other advantages that can be named are; identical
user hardware; easy accommodation of priority messages by
increasing the power level or the time-bandwidth product
of the priority signal; and finally the possibility of
co-existence with other narrow band systems in the same

frequency band without excessive mutual interference.

3.4.2 Disadvantages

Despite all of the significant advantages mentioned,
the spread-spectrum approach has some disadvantages also,
some of which are summarized below:

In the first place, the cost to start up such a

Ilb

30

system is higher than that of the narrow band system.
This is due to the more complex technology, as well as the
fact that the base stations must have the initial
capability for handling any of the possible sequences. In
other words, the base station design must start with a
mature system rather than grow as demand builds.

A second disadvantage is the need for an effective
power control, to achieve the greatest system capacity.
It may also be desirable to balance power among cells with
different user densities. A set of solutions to this
problem are reported and analyzed in the following
chapters.

Another disadvantage is the requirement of a mobile
locator technique, to determine the base station with
which each mobile must communicate. This is also needed
for the power control, to combat the near-far effect.
However, such facility is required by all proposed small

cell schemes whether narrowband or spread-spectrum.

CHAPTER 4
POWER CONTROL
4.1 General Remarks

Power control is essential for the efficient
operation of the proposed spread-spectrum cellular system.
In the upstream link, every mobile located in each cell
must adjust its transmitter power, such that the base
station of that cell receives the signal from each mobile
with equal strength. This is to overcome the significant
difficulty in the upstream link called the "near-far"
effect. In the downstream link, the signal power to each
mobile must be adjusted such that the
signal-to-interference ratio (SIR) at every mobile
receiver is the same. This is to overcome the difficulty
that occurs for mobiles located at or near the cell

corners.

31

32

The "near-far" effect permits strong interferers in
the immediate vicinity of the base station to overwhelm
weak signals from more distant mobiles. This problem is
common to most spread-spectrum systems. In
frequency-hopping systems, however, limiters can be placed
in each hopping channel to reduce the power imbalance.
This can eliminate much of the interference between users
[C6]. But in the cases where direct-sequence signalling
is used, the near-far effect is considerably worse. In
all cases, however, some improvement can be obtained by
dynamically controlling the transmitted power for every
mobile, whether or not the system is cellular.

In the downstream case, the near-far effect is not a
problem. For a non-cellular system, where all of the
signals are transmitted with the same power, every
receiver suffers the same signal-to-interference ratio
regardless of distance. But if the system is cellular,
some degree of power control may become necessary. A
mobile that is near its base station will be almost
unaware that there is any interference from outside the
cell. But a mobile located in the cell corner is roughly
equidistant from its own and two interfering base stations
and thus, it receives three times the amount of
interference. So if there is no power control in a
heavily loaded system, some corner mobiles may receive too

much interference and become incapacitated.

33

Also, in both upstream and downstream cases, when the
load is not uniform from cell to cell, the amount of
interference inside a heavily loaded cell can be reduced
by controlling the interference from the neighboring
cells. In other words, a lightly loaded cell can take
more interference from outside, while a heavily loaded one
is able to tolerate little outside interference.

This chapter presents schemes for balancing the SIR
of both upstream and downstream links, for every mobile in
a given cell and (optionally) for all mobiles in the
entire system. Results are given at the receiver antenna
so that they are independent of the choice of spreading

function, modulation method or coding scheme.

4 .2 Assumpt ions

1. The service area consists of N cells, whose
boundaries coincide with the most probable
location for cell-to-cell handoff. Although
cells are shown as hexagons (as is usual), real
cells are likely to be somewhat amorphous and may
not even be simply-connected. Our analysis does

not depend on cell shapes or sizes.

2. The load of the i-th cell is Li Erlangs.

34

Although the general traffic model permits
variations about this mean from time to time, we
will use the simplifying assumption that
precisely Li users are linked to the i-th base

station at a given time.

The i-th base station receives Pg Watts of power
from any one mobile in the i-th cell. The power
transmitted by the k-th mobile in the i-th cell

is ng, k=l,2,...,L. (the superscript U denotes

1

upstream.)

Base station i transmits a total of Qi Watts
which we divide up two ways as follows: The
average power per mobile, P5; and the actual
power to the k-th mobile, pfk, k=l,2,...,Li. (The
superscript D denotes downstream.) Thus

L- D
Q. = {fipik = L. Pi. (4-1)

Knowledge of the propagation loss between each
base station and each mobile is necessary for two
distinct purposes: First for deciding which cell
each mobile is located in; and second, for

controlling the transmitted power to and from

 

35

each mobile. This knowledge can be acquired by
direct measurement of signal strengths using a
pilot signal with fixed power radiated from each
station. Some caution must be exercized here,
however. In a multipath environment, the
reciprocity theorem is true only at a single
frequency; if the upstream and downstream
channels are separated by more than the coherence
bandwidth, their respective path losses will be
uncorrelated. However, the means of the Rayleigh
fading channels will be the same for any
frequency separation. Hence since the Rayleigh
fading behavior is averaged out (as discussed in
chapter 2) then "reciprocity in the mean" may be
used in the system [N1]. The attenuation factor
between the k-th mobile in the i-th cell and the
base station of the j-th cell is denoted by
aikj (see Figure 4.1.) Thus assuming the pilot
signal is transmitted from the j-th station with

the power Z3 and is received by the k-th mobile

in the i-th cell having the power zgkj, the
attenuation factor is given by
a Zi/Zr . (4-2)

ikj = j ikj
Hence, the total power received by mobile k in

cell i is given by:

36

 

Figure 4.1 Interference geometry

 

 

 

37

o N o
Rik '- 12:1Ljpjaikj' (4-3)
we also have:

U _ u _

And the total power received by the base station

in cell i is given by:

R 2" p” 2" p” L' / (4 5)
‘ ,--.-. jkajki i=1 affirm ajkj

Since the signal from every mobile must be

received with the same power.

6. The system is assigned a signal-to-interference
lower limit S, determined from message-quality
and service-grade requirements. This number is
considerably less than unity because of the
spread-spectrum processing gain. Denial occurs
when the admission Of a mobile requesting service

would result in an SIR below the limit S.

4.3 Power Balancing Algorithms

The strengths Of the transmitted signals can be
adjusted such that the SIR becomes the same for all
mobiles within a given cell or Optionally for all mobiles

in the entire system. Such a balance may be achieved for

 

 

38

both upstream and downstream links, by means of similar

algorithms.
4.3.1 Upstream

The total power received -by the base station
expressed in (4-5) contains the desired signal with power
P? and the interference from the other mobiles. Thus the
interference from signals received by the base station of

the i-th cell can be expressed as

U _ N u Li _ u _
Ii — i1pj§=1[ajki/ajkj] Pi, (4 6)

the signal from every mobile in the i-th cell thus suffers

the signal-to-interference ratio

U U U
si = Pi/Ii. (4-7)
Hence
U
1 + s. L.
1 u N u I
P. = P. . . . - . (4'8
s? 1 i=1 3 3.. [am/am] )

Here, it is assumed that the received signal power from a
mobile by its base station is the same for all mobiles in
each cell.

This assumption results in a balance in the SIR
values for each mobile in each cell. We refer to this

operation as "in-cell balancing" since equalization is

39

done only within each cell, and different cells will in
general have different SIR values. This equalization is
easily accomplished using the set of estimated attenuation
values by solving equation (4-4) for every mobile.

To equalize the value of SIR for all cells, we let

U U U
pU = [p1,p2,...,pN]T;
U _ u
B [Bij], where
a” - H [ / 1- d (4-9)
in" L ajki ajkj ' 3“
SE= SU for all cells.

Then we have

1 + sU
—-——U—p =Bp. (4-10)

S
This is a classic eigenvalue problem, where pU is the
eigenvector and the factor (1+SU)/SU is the eigenvalue.
Solving this problem together with (4-4) leads to the

required upstream signal strengths ng that will lead to

the uniform SU for all mobile signals.
4.3.2 Downstream

The total received power expressed in (4-3) has three

components; the power of the desired signal, the

40

interference from the user's own cell, and the

interference from outside. The first term is given by;

D
= P.

Pdes 1kaiki'

(4-11)

Subtracting (4-11) from (4-3) we get an expression for the
interference encountered by the mobile k in cell i,

D N
I 21? °

— D — —
ik ‘ 1:,ijaikj Pikaiki° (4 12’

Thus this mobile suffers the signal-to-interference ratio,

PD a
_ ik iki _
ik

Combining (4-12) and (4-13) and solving for the

transmitted power we have:

 

sD 1

D ° N D

Pik = lko . — 2_1Pijaikj. (4-14)
1 + 51k aiki "

To balance the SIR values for each mobile in cell i, we

set

U)
M:-

H
2

(4-15)

F

U
H- a

II
i—M

D
—_ — P.L.a. ..
1 D k=1 '=1 3 J 1k]

1 + Si aiki

Solving for 8:, we get an expression in terms of the set

41

 

D
of Pi'
L PD
5? = 1 1 , (4-16)
Li N D o
1.1/aim f3, Pijaikj ' Lipi

and observing that (4-14) must be true for each k in i,

0
9° - -—S—1—- ——l—— N PDL a (4—17)
ik ' o ' ._ j j ikj'
l + Si aiki l-1
Equations (4-16) and (4—17) are simply solved

algebraically for transmitted powers, thereby balancing
the downstream SIR values for all mobiles in a given cell.
As in the upstream case, in general these values will be
different from cell to cell, and within a given cell the
SIR values will be different for the upstream and
downstream links.

To balance the values of S? for all cells, we
construct an eigenvalue equation similar to (4-10).

. D . .
Setting all the Si in (4-17) to SD, and u51ng (4-1), we

have,
D N '-i
S a. .
Q, = ...—.2 92 —SL-1k . (4-18)
1 1 + SD 3
1:1 k=1 aiki

We now define:

ll

42

q = [Q1.Q2..-..QN]T;

D _ o o _ . _
B — [Bij1' where Bij —1§£ [aikj/aiki1' (4 l9)
k=1
The eigenvalue problem then becomes
1+sD D
'__—TT_- q = B q (4-20)

Where q is the eigenvector and the factor (1+SD)/SD is the
eigenvalue.

Solving the eigenvalue problem and using the
Qi values in (4-1) and (4-17) lead to proper values for
the signal strengths ng that will result in a uniform

D

signal-to-interference ratio S throughout the service

area.
Comparison of the defining equations (4-9) and (4-19)

reveals that

U

B = [BD1T.

(4-21)

so that the eigenvalue solution to (4-10) and (4-20) and

SU and SD are identical [G1]. Therefore if

hence
system-wide balancing is performed, the quality of
transmission will be the same for all mobiles in both the
upstream and the downstream links. Therefore denials will

occur in both links at the same time.

43
4.4 Existence and Uniqueness of the Solution
The following theorem on the property of

(i.e., the eigenvalues and eigenvectors)

matrices is due to Perron [G1].

Theorem: A positive matrix H =[hik]?

real and positive eigenvalue r which

the spectra

of positive

always has a

is a simple

root of the characteristic equation and exceeds

the moduli of all other characteristic values.

To this "maximal" eigenvalue r there corresponds

an eigenvector e = (el,e2,...,en)

of H with

positive coordinates ei>0, (i=l,2,...,n.)

The following two properties about r and

shown to be true [G1]:

1. A positive matrix H can not have

independent positive eigenvectors e.

e are also

two linearly

2. If we define w. as the sum of the elements in the

1
i-th row of H;

n

wi = :E hik; (1=l,2,...,n),
k=1

and

(4-22)

w = min wi, W = max wi; l g i 5 n (4-23)

Then for the positive matrix ,we have
w E r E W, (4-24)
and the equality sign holds when w = W.

Here, since r is a simple eigenvalue, the eigenvector
e corresponding to it is determined uniquely within a

BD and BU are always

scalar factor. Now the matrices

positive matrices since if a cell is not occupied, the

size of the matrix can be reduced instead of having a zero

row and column. Then there exists one and only one all

positive eigenvector (within a scalar factor), the

elements of which are the required transmitted powers
U

u .
Pi for the upstream matrix B , or Qi for the downstream

matrix BD. This eigenvector corresponds to the maximal

eigenvalue of the matrix BU or BD, which is equal to

(1+sU)/sU or (1+sD)/sD.
Here, we note that the solution is acceptable only if
the maximal eigenvalue r is larger than unity, since for

any SIR such that O < (SU,SD) < m,
(1 + sU)/sU > 1 and (1 + SD)/SD > 1. (4-25)

This can be shown to be true using the second property

mentioned above. Let w? and w? be defined as

45

N

w1 = %;f13 and
N

wo = .2 BD

1:11J
Then from (4—9) and (4-19), it is obvious that ij > 1 and
ij > 1 for all i and j, and thus using (4-24), maximal

eigenvalues for both upstream and downstream cases are

B

larger than unity. Therefore the solution to the problem
always exists and is unique.

Many computer methods are available for solving an
eigenvalue problem, one of which is used in the solution
of a simulated hypothetical system discussed in the next

chapters.

CHAPTER 5

SIMULATION

To evaluate the proposed scheme, a hypothetical
system has been simulated by computer. Since the system
is interference limited, it is important to understand how
interference varies with traffic load and mobile location.
The effect of Rayleigh and shadow fading on the
interference levels need to be investigated also. The
probability of denial, which is an interference-dependent
mechanism, its dependence on traffic levels and
environmental parameters, and the effect of power control
on the interference and denial mechanism also need to be
investigated. A small scale computer simulation Of the
proposed scheme is thus undertaken to investigate the
system under different load distributions and

environmental parameters.

46

47

5.1 Geometry

In order to simulate the system a hypothetical
geometry is used, which determines the location of the
base stations, the environmental parameters, and the
distribution of the users in the area. Attempts have been
made to simulate a geometry which resembles a relatively

realistic situation.

5.1.1 Base Station and Load Distribution

The base station distribution in an actual service
area must be determined considering many factors such as
the topology of the service area, the distribution of
blocking objects such as tall buildings, and statistics of
mobile user quantity and distribution throughout the
system. Then, as mentioned in chapter 2, the cell
associated with each base station is the area in which the
received signal from that station is the strongest (i.e.
the attenuation from that station is smallest.) However,
in our simplified model, the base stations are distributed
as if the service area consisted of nineteen hexagonal
cells, each of equal size, arranged in three concentric
rings (See Figure 5.1.) The purpose Of the hexagonal
shape assumption is only to determine the location of the

base stations. The actual shape of a cell varies and its

48

.. Base station

Figure 5.1 Base station distribution in the
19 cell simulated system.

49

parts may not even be connected.

TO simulate the random positions of the mobile units,
two spatial distributions were used. In the first, the
mobiles were distributed randomly with "uniform"
distributions so that the mean number of units in each
cell was the same. In the second case, a bivariate
Gaussian distribution was used, with mode at the center of
the system and the variance adjusted to give the mean
number of units per cell in the ratios: 7.5 for the center
cell; 4 for the intermediate ring of cells; and l for
outer ring. In the sequel this will be referred to as the

"tapered" traffic distribution.
5.1.2 Fading

In section 2.1 we mentioned that in a mobile
environment the received signal fluctuates very rapidly
due to the rapid Rayleigh fading. We also mentioned that
these fluctuations are averaged by the filtering effect of
the human hearing response. Neglecting the effects that
these fluctuations may have on the performance of the
receiver, we have considered the attenuation to be
independent of Rayleigh fading.

To simulate the distance-plus-shadowing composite
attenuation factor for each mobile to each base station,

the service area was divided into small squares Of sides

50

1/5 the radius of a cell (i.e. 1/10 the distance between
two base stations), each square representing, for example,
a city block in a suitably scaled cell (See Figure 5.2.)
Each square was then assigned a normally distributed
random number as its shadow fading coefficient to each
base station. Thus, each square was assigned 19
independent values corresponding to the path loss from
that square to each base station. These values are
denoted by Phi; where m denotes the square and i, the
corresponding base station. Thus for an'initiating mobile
(IM) located in the m-th square, the attenuation factor to

the j-th base station b3? is given by;

IM _ IM a _
10 loglo(bj ) - ”ikj + 10 log10(l/dj ) (5 l)

where 0'€[7,12],
a 5 [3,4]. and
dgfl= The distance from the initiating mobile
to the j-th base station.

(Note: The attenuation factor is log-normal with variance
0 and mean 10 loglo(l/df!.)

The mobile "belongs" to the cell i for which the
attenuation factor is smallest. Thus, if there are k-l

mobiles in the cell i prior to the arrival of the new

mobile, we have:

_ 'M °_ _
aikj - bj' j—l,...,l9 (5 2)

R th
mobile
in
cell i

 

/
/
\
\ CELL j
\
\
\
\ p -
\\ aikj m3
/
/
\/ )‘l l
/ /
\h \ /
.\/ /
4
x I \ \
>\

 

/ \s(\~ / \~
/ Vx / \
/ ‘2‘» ‘~‘~ I
\ / /\
/ 2x /
CELL i ’ ,‘\
/
/
/

Figure 5.2 Geometry used in simulating the

shadow fading.

m th
square

52

aiki = min(b?‘), j=1,...,l9 (5-3)

The purpose of dividing the service area into small
squares was to simulate a realistic urban situation in
which, although the overall shadow fading has a lognormal
characteristic, the mobiles located within an immediate
geographic area (e.g. a city block) of each other
experience the same amount of shadowing. The total amount
of fading, however, is still a function of their distance

(~ d“), and different for mobiles at different locations.
5.2 Power Distribution and Interference

Results were generated for each set of mobile
locations with no power balancing, for in-cell balancing
only, and for in-cell plus cell-to-cell balancing. The
value of SIR criterion S used in the simulation was
-20 dB, which corresponds to a signalling system with a
processing gain of 30-35 dB with typical coding schemes.
The capacity of a power-balanced single-cell system with

this SIR criterion would be l/S=100 users.
5.2.1 No Power Balancing

To generate the results with no power control, it was

assumed that the power transmitted to and from every

 

53

mobile was the same. Thus if we let ng = PU and
o . .
Pik = PD for all (k=l,...,Li) and (1=l,...,N), then u51ng

(4-4) and (4-5), we have:

u _ U
Pj - P aikj'
N L]
U _ U
h’zzpfim
i=1 k=1

and thus (4-7) becomes;

N L
U _ U
2:138 ' Paiki
k:

i=1

Thus we have:

 

Sik= . (5—4)

Also, using (4-1), we have:

L] D P0
2:P Li Pi'
k=1

D

I

D
= P. = PD,

80 P- 1k

and then (4-3) becomes;

N
o _ D
R k - :5 LjP aik
i=1

Therefore, (4-13) becomes

54

D
a. .P
SD _ 1k1

ik’ N
D _
Ea Ljaiij aikip
i=1

thus we have:

D

D
Sik—_ N

j:

l

 

(5-5)

(5-4) and (5-5) were used to generate the SIR's for
all mobiles where no power control was applied. Some
denial statistics then were produced using the SIR

threshold of -20 dB.
5.2.2 In-Cell Balancing

In-cell balancing was simulated by balancing the
powers within every cell, without any attempt to balance
SIR's system-wide. In general these values will be
different for different cells and also for the upstream
and downstream links. For the upstream case, it was
assumed that ng is adjusted according to (4-4) to lead to

the same P? for every mobile in a given cell. In

addition, P3 was assumed to be the same for every cell.

Thus we have:

93 = p” for (j=l,...,N),

55

and (4-7) becomes

U PU
S. =
1 N - °

H
u _ U
:2 P 2;_[ajki/ajkj1 P

i=1

 

So we have:

 

S. = N ‘ . (5'6)
:5 [ajki/ajkj1 ‘ 1

For the downstream case, it is assumed that the
. D .
average transmitted power Pi 15 the same for all cells.

Thus we have:
D .
P. = P for all (1=1,...,N),

and (4-16) becomes

0 Lip!)

S o = . o

1 L,"
ZZPDLj1aikj/aiki1 ' Li’DD

k=1j=1

 

So, we have:

 

s. = L . (5—7>

Then (4-17) was used to compute ng for individual signal

—-

M:

i

ii

strengths.

56

(5-6) and (5-7) were used to generate the SIR's for
every cell, where power control was performed to equalize
the SIR for the mobiles inside each cell. Again in this
case, denial statistics were produced using the SIR

threshold Of -20 dB.
5.2.3 Cell-To-Cell Balancing

Cell-to-cell balancing was performed on the simulated
system, by solving the eigenvalue problems expressed by
(4-10), for the upstream case and (4-20), for the
downstream case. Then the dominant eigenvalue and its
corresponding eigenvector are the accepted solutions to
the problems. Many numerical techniques exist for
evaluating eigenvalues and eigenvectors of various types
of matrices [D1]. Here we use an iterative method called
the Power Method. This method is used for determining the
eigenvalue with the largest absolute value (dominant
eigenvalue) and a corresponding eigenvector. The Power

Method is based on the following theorem [W2].

Theorem: Let A be an nxn matrix having n linearly
independent eigenvectors and a dominant
eigenvalue. Let x0 be an arbitrary chosen
initial vector such that Axo exists. The

sequence of vectors

57
xl=Ax0, x2=Axl,..., xk=Axk_l,...,

as k becomes larger, will approach an eigenvector
for Al, the dominant eigenvalue, if x0 has a
nonzero component in the direction of an

eigenvector for A1.

In the cases where N is large (19 in our simulation)
the probability of matrices BU or BD, having linearly
dependent rows (ranks less than N) is very small and they
almost always have N linearly independent eigenvectors.
Also, the chances of the arbitrary chosen initial vector
x0 being perpendicular to the eigenvector is very remote.
SO this method, almost always, will lead to the correct
results.

It remains to find the dominant eigenvalue. If A is

an eigenvalue of A and if x is its corresponding

eigenvector, then
(x.Ax)/(x.x) = (x.Ax)/(x.x) = A.

Thus the expression (xi.Axi)/(xi.xi) is computed with

each approximation xi to the eigenvector. The method is
continued until successive approximations to every
component of the eigenvector and the eigenvalue are within
the required accuracy.

The components of the vectors x1, x2,... may become

58

very large, leading to significant round- off errors.
This problem is overcome by dividing each component of

xi by the largest component and using this vector, which

is in the same direction as x.

1, in the following

iteration.

This method is very accurate since any error in
computation only means that a new arbitrary vector has
been introduced at that stage. Therefore, the only
round-off errors that occur are those arising from the
matrix multipication carried out during the last

iteration. A flow chart for the Power Method is shown in

Figure 5.3.

'lb

59

/READX1, 8,A Ax

= x1 1A):1
xi'xi

 

 

NO

 

 

Axi

 

 

Figure 5.3 Power Method for solving an eigenvalue
problem.

 

 

CHAPTER 6

RESULTS

In this chapter we present some results generated by
our simulation of the system. Based on these results, we
discuss the effects of power control on SIR, denial
statistics and capacity of the system for both upstream
and downstream links. The effects of the environmental
parameters (a,a) on the performance of the system as well
as the feasibility of different degrees of power control,
based on the dynamic ranges of transmitted powers are also

discussed.

6.1 Load Distribution and Environmental Parameters

Distribution of load in the service area varies as
the environmental parameters change. Shadow fading may

cause a given mObile to receive the strongest signal from
60

61

a base station that is not closest to it. The severity of
this effect varies as a and a change, since they change
the mean and variance of the log-normal distribution of
fading. To formulate the dependence of load distribution
on a and a; consider a mobile at distance d from a base
station (See Figure 6.1.) For clarity of analysis in this
section, we will refer to the geographic area closest to a
base station as a "hexagon" as opposed to a "cell", which
is the area receiving with the least attenuation from a
base station. Hexagon would have been the shape' of the
cell if there was no shadow fading. Suppose that the base
station is located at the center of a hexagon of radius R
(R is the radius of a circle with the same area as the
hexagon.) If there was no shadow fading then for d < R,
this mobile would communicate with the base station in the
same hexagon. The effect of shadow fading may be
considered to be changing the effective distance between
the transmitter and the receiver.

ef

Let d be the effective distance between the base

station and the mobile due to shadowing. This means that

the attenuation would have been the same if we had a

ef

mobile at distance d from the base station and there was

no shadowing. Thus we have

a = 1/(def>“, (s-1)

ef>

where "a" is the attenuation factor. Now if d R, the

62

A possible cell
perimeter

    

\
l
I
I
mobile \
d R I
l
\
l

A hexagon
perimeter

\\‘_

 

Figure 6.1 Geometry for load distribution
analysis.

63

mobile appears to be located outside the hexagon. The
rate at which this occurs represents how load distribution
may vary with shadowing. The attenuation factor a, and
thus l/(def)a have log-normal distributions with variance

0; and mean 10 loglOl/d"(See section 2.1.) So,

Pr{def > R}

Pr{lO log l/(def)a < 10 log l/Ra}
10 10

no
10 Iog1o1/

a
-(t - 10 loglol/d )
:§--- ldt

 

exp[

1
_G‘V2n'a' 2¢r

@[(10 loglol/Ra - 10 loglOl/dal/O'].

Thus

Pr{def > R} o[ 10 a/a' loglOd/R 1, (6-2)

where<D(x) is the normal probability distribution function
of x, which is tabulated in the literature [C5]
( 0(x)=l-Q(x), where Q(x) was defined in 3-3.)

Figure 6.2 shows Pr{def> R} values versus the ratio
d/R for different combinations of a' and a'(different
values of a/au) We observe that load distribution varies
as a function of the ratiO¢z/au As this ratio decreases,
more mobiles appear to be located outside the hexagon.
Thus a smaller (z/a' causes more mobiles to link up with
base stations not closest to them. As the load in a

hexagon grows, the number of such mobiles also grows.

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64

 

 

m}. H

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a? 2..
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65

This results in a balancing effect between cells when the
load is not uniform from cell to cell.

The balancing effect can be observed very clearly in
our simulation results. Table 6.1 shows the ratios of the
load in the center cell, cells in the intermediate ring,
and cells in the outer ring. Results are shown for
different load distributions (tapered and uniform), and
different a/a ratios (a: 3 or 4, 0': 7 or 12.) For the
uniform load distribution, there is little change as a/a
changes. This is because with uniform load as a/a
decreases, the number of mobiles that link up to base
stations of neighboring hexagons ‘ increases by
approximately the same number in every hexagon. This
results in about the same number of users in every cell.
In the tapered load distribution case, however, variations
of tr/a' causes a marked change in the load distribution.
It is obvious in this case that as a/a'decreases, the load
distribution becomes more uniform. Table 6.1 shows that a
physical load distribution of ratios 7.5, 4, and l in the
center hexagon, hexagons in the middle ring and hexagons
in the outer ring changes into a distribution of ratios 5,
2.7, and l as a/a gets as small as 1/4 (¢1= 3, 0': 12.)
It will be shown in the next sections that this effect
reduces the necessity for cell-to-cell balancing, which is

fortunate since it is not an easy task to perform.

 

66

Table 6.l Ratios of the load in different cells as a/o varies.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LOAD FADING -070- CENTER INTERMED. OUTER
DISTRIBUTION CELL CELL CELL
N0 FADING _-:-- 1 1 1
';;i:3§;§" 'Z}}' 1 1 1.15
0N11001 '£;3:I§;}" '3}}_ 1 1 1.06
';;i:16;12' '173' 1 1.06 1.02
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1101000 'J;§:1§;1" '3}}' 6.8 3.7 1
’QLLilJLIS' ‘1}S' 6.5 3.1 1
‘6;3:7§;15' '1761' 5.0 2.7 1

 

 

 

 

 

 

 

 

 

67

6.2 Upstream Results

Results were generated for the upstream case using
(5-4), (5-6), and solving the eigenvalue problem in
(4-10). Here we present and discuss the results for
denial rates for the three cases of no balancing, in-cell
balancing, and cell-to-cell balancing. Results are also
discussed for dynamic ranges of the required transmitted
powers for in-cell balancing, and cell-to-cell balancing.
Effects of the environmental parameters on these results

are also discussed.
6.2.1 Denial Statistics

Figures 6.3 to 6.8 show the denial probability values
of the upstream case, versus load per cell for the center
cell of the system; and Figures 6.9 to 6.14 show these
values versus average load per cell throughout the system.
Results are given for both the uniform, and the tapered
load distributions. Typically acceptable values of
blocking in a radiotelephone system are in the 1% to 2%
range, so that probability of denial in the no-balancing
cases are quite unacceptable except at trivially low
traffic loads. The problem is very severe for the
upstream case because the near-far effect is significant

whenever two or more users are accessing the system.

 

68

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80

We note also that when no balancing is used, the
capacity of the system reduces as a increases from 3 to 4.
This can be explained by the following: Suppose there are
only two users (a and b) in a cell, transmitting the same
amount of power P (i.e. no power control.) Also suppose
that they are located at the effective distances of

if and dif from the base station. Neglecting the effects

d
of the neighboring cells, the SIR experienced by the base

station for the signal from a is

p/(dif)“ (dfif)“
SIR = = .
a P/(dfif)“ + P/(dff)“ (djf)“ + (dif)a

 

 

(6-3)

Now, to illustrate the effect of on the near-far effect

let dif << dif. Thus (6-3) reduces to
~ ef ef a _
SIRa~ (dID /da ) . (6 4)

(6-4) shows that a more rapid attenuation law (larger (1)
results in a worse SIR and thus a lower capacity for the
system in the upstream link.

We also note that with no power control, capacity of
the system increases as 0 decreases from 12 to 7. This is
also due to the near-far effect. A larger 0’ means a
larger spread in the value of the effective distances of
the mobiles (i.e. The ratio of the maximum effective
distance to the minimum effective distance is likely to be

larger.) This results in a more severe near-far effect.

81

Considering the balanced case results, for the
uniform traffic distribution, the two types of balancing
are barely distinguishable at all levels of denial, so
that in the uniform traffic distribution case there
appears to be little advantage, in terms of system
capacity, in implementing the cell-to-cell balancing
algorithm. This is due to the fact that with uniform
load, there already exists some degree of balance from
cell to cell, without the application of the cell-to-cell
balancing algorithm. However, with in-cell balancing the
increase in system capacity over the non-balanced case is
very significant, though difficult to quantify at low
traffic levels due to the low levels of statistical
significance attached to our non-balanced results at these
levels. The improvement ratios we encountered were more
than 1000% for the upstream case.

For the tapered traffic distribution, our results
show that in-cell balancing improves the capacity of the
upstream link by about the same amount as for the uniform
case. Further improvement of about 15% is obtained when
cell-to-cell balancing is applied. This improvement is at
all levels of denial rate for the center cell. In the
total system, however, the improvement is only at the low
levels of denial rate (1% to 2%). This improvement for
the total system is due to the "matching" effect of the

cell-to-cell balancing upon the individual cell

 

82

capacities; where the capacity of each cell is adjusted
such that the ratio of the capacities match the ratio of
the loads for all cells. With in-cell balancing the outer
cells use only a small portion of their actual capacity.
This extra capacity is sacrificed in the cell-to-cell
balancing algorithm in order to increase the capacity of
the heavily-loaded cells (center cell, in the tapered load
distribution.) However, the effect of the capacity
sacrifice of one cell on another is not very large and as
the load grows throughout the system, the cells around the
center cell have to give up much of their capacity to
compensate for the high load in the center cell. Although
the load in the outer individual cells is much smaller
than the center cell, the total load in these cells gets
large as the load in the system grows. Thus the denial
rate of the total system in the cell-to-cell balancing
case climbs above the in-cell balancing case at higher
loads. This, however, occurs at denial levels that are
unacceptable and a system at such levels of denial needs
to be expanded (Sizes of the cells must be reduced
resulting in lighter load per cell.)

Comparing the uniform and tapered load distributions,
it is obvious that the capacity of the system, when
balanced, is much higher for the uniform load than for the
tapered one if the total system is considered (about 50%.)

This higher capacity is due to the "matching" effect in

 

83

the cell-to-cell balancing case. In the in-cell balanced
case, however, no such sacrifice of capacity exists
between cells, and the denial rates do not increase as
rapidly for the tapered case. So at higher loads, the
in-cell balancing denial rate for the tapered load gets
much closer to that of the uniform load case.

It can also be seen in each of these figures that
upstream link capacity grows as ardecreases from 4 to 3.
However, the difference is very small and not more than
15% depending on the mobile distribution and traffic load.
Comparing the balanced results for 0': 7 and 0': 12, the
lack of sensitivity to the shadow fading dB spread is
striking. The variation in capacity as a varies from 7 to
12 is not more than 20% and contrary to the corresponding
results for a narrow band frequency re-use system, these
results are better for (7: 12 than for (r: 7. This can be
explained by the balancing effect due to the decrease of
the ratio a/a- explained in section 6.1. This effect is
more obvious in the in-cell balanced results for the
tapered load distribution (Figures 6.11 to 6.13) where the
denial rate decreases as a/a' decreases. The effect is
stronger in this case because the physical load
distribution is not uniform and no attempt has been made

to balance the system from cell to cell.

 

84

6.2.2 Dynamic Ranges of Transmitted Power-s

Figures 6.15 to 6.20 show the average dynamic range
of powers (DRPU) required of the mobiles to transmit in
order to achieve balance in the upstream link. For the
upstream link these ranges are the same for the cases
where only in-cell balancing is used, and cases where
cell-to-cell balancing is also applied. It can be seen
that these ranges are rather high and possibly impractible
for some parameters, particularly at heavy loads. The
high values of these ranges are results of the severity of
the near-far effect. As we mentioned in section 5.2, for
the upstream case in-cell balancing is accomplished by
adjusting the individual transmission powers ng according
to (4-4) such that the signal power PU received by all

mobiles is the same. Thus for cell i we have

 

 

 

u U .
max (P. ) P /m1n(a- .)
DRPg = '—.-__l]jk—- = U lkl I (k=lr0oorLi)
min (pik) P /max(aiki)
Thus
max(a. .) max d?'. a
DRPg= . lkl =[ . ifl ]. (k=l,...,Li.) (6-5)
m1n(aiki) min diki

This ratio can take on arbitrary large values, and there

is no limit that can be imposed on it. It is obvious from

U

(6-5) and the results that DRP grows very rapidly as a

 

85

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89

 

 

 

 

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91

gets larger. Results show that as a goes from 3 to 4, the
average DRPU increases by more than 10 dB at full traffic
capacity (onset of denial.) We also note that the dynamic
ranges grow as 0 gets larger. As 0 goes from 7 to 12 the
average DRPU increases by more than 7 dB at full traffic
capacity. Table 6.2 shows these values at full traffic
capacity. This increase is due to the fact that larger (7
causes a more severe near-far effect, by causing a larger
spread in the values of the effective distances.

If a more restricted range is employed for the
upstream link (i.e. if there is a fixed upper and lower
limit to transmitted power) the resultant near-far effect
will have some effect on system capacity and performance.
Such a truncation will result in an "outage" phenomenon
similar to the outage that occurs with narrowband systems
due to shadowing. The degree of degradation will depend
strongly on the type of modulation and its susceptability
to near-far effect. Direct-Sequence (Pseudo-Noise)
Signals are well known to be strongly sensitive to
near-far effect, whereas frequency-hopping systems are far
less sensitive. The latter is particularly true if
limiters are used in each hop-frequency channel [C6].
This strongly indicates in favor of using FH rather than

DS modulation for spread-spectrum cellular mobile radio.

 

 

92

Power control dynamic ranges required at full

system capacity for the upstream link.

Table 6.2

. _ . . _

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93

6.3. Downstream Results

Results were generated for the downstream link using
(5-5), (5-7) and solving the eigenvalue problem in (4-20).
Here we examine the results of denial rates for different
degrees of power control, and the dynamic ranges of the
required transmitted powers for the balanced cases. These
results are also compared for different environmental

parameters.
6.3.1 Denial StatiStics

Figures 6.21 to 6.26 show the values of the denial
rates for the downstream case versus load per cell for the
center cell of the system, and Figures 6.27 to 6.32 show
the denial rates versus average load per cell throughout
the system. Results are given for both the uniform and
the tapered load distributions. Here, although the denial
rates for the unbalanced case are not as bad as the
upstream case, the capacity of the system is still very
low (about 15 at 1% to 2% denial rates.) The problem is
less severe for the downstream case because the "corner
effect" is less severe than the "near-far" effect, and
requires relatively high traffic levels to become
noticeable.

Also in the downstream case with no balancing,

 

94

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106

contrary to the upstream case, the capacity of the system
goes up as the value of a grows. This is because a more
rapid attenuation law shrinks the size of the region near
cell corners where the corner effect is manifested. This
can be shown as follows: The "corner region" is the area
in which a mobile receives about the same amount of power
from several base stations (3 in the model with hexagonal
cells.) Now if we consider a simplified model where there
are only two cells in the system, a mobile located in the
corner region receives about the same amount of power from
the two base stations. Suppose a mobile is located at an
effective distances of d?f from one station and dfif from
the other. Also suppose that both of the base stations

transmit an equal amount of power P. Then the corner

region can be defined as an area in which

 

p/(d?f)“
P/(def)a - 1 g 6, (6-6)
2

where e is small. Thus we have
<1-e>1/“ 5 d?f/dff 5 (1+eI1/“. (5-7)

Now as grows, (l i ()1/a gets closer to l; which means
ef

I

that for a larger a, d and dff must be closer to each
other so that the mobile can be considered to be located
in the corner region. In other words, a larger shrinks

the size of the corner regions.

   

107

Comparing the uniform case and the tapered case, when
there is no balancing applied, the capacity of the system
is higher for the uniform load case. It is also obvious
that the tapered unbalanced case is more sensitive to
variations in 0 than the uniform case. When the total
system is considered, the capacity for cases with (T: 12
is higher than cases with 0': 7 by up to 20%. This can be
explained by the balancing effect due to an increase in 0
explained in section 6.1. This effect causes the tapered
case to resemble the uniform case more closely, when
distribution of load in different cells is the
determinning factor.

Considering the balanced case, results are identical
for the upstream and downstream cases, when in-cell and
cell-to-cell balancing are both applied. This is because,
as was shown in chapter 4, the SIR's and thus the denial
rates are the same for upstream and downstream cases when
the system is fully balanced. For the uniform traffic
distribution, the results of the two types of balancing
are almost identical, as we found in the upstream case.
Therefore in the uniform case there is almost no advantage
in applying the cell-to-cell balancing algorithm for both
upstream and downstream links. The improvement achieved
by in-cell balancing, however, is considerable. We
encountered improvements of 30% to more than 100% for the

downstream case.

 

 

108

For the tapered traffic distribution, the upstream
and downstream results are different with in-cell
balancing only. Our results show improvement ratios over
the non-balanced case of over 100% with in-cell balancing
and a further 15% when cell-to-cell balancing is added.
This latter improvement is at all levels of denial
probability for the center cell, and at low levels of
denial rate for the total system. Also comparing the
uniform load and the tapered load cases, when full power
control is applied, the capacity of the system is much
higher for the uniform load than for a tapered one if the
total system is considered. In the tapered case, when
only in-cell balancing is applied, this higher denial rate
does not increase as rapidly as the case with cell-to-cell
balancing; and as load goes up, it gets closer to the
denial rates of the uniform case. This effect which was
also observed in the upstream case, is caused by the
"matching effect" of the cell-to-cell balancing and the
capacity sacrifice that it causes for the cells with lower
loads.

In the balanced system, the effect of variations of a
on the denial rates of the downstream link is very similar
to the upstream case. IAs a decreases from 4 to 3 the
difference is very small and not more than 15%. The
absence of sensitivity to the variations of U is

noticeable in the downstream, balanced case also.

109

Improvements of up to 20% are observed as 0'varies from 7
to 12. This is due to the balancing effect of the
increase in a/o ratio on the load distribution, as

previously discussed.

6.3.2 Dynamic Ranges of Transmitted Powers

Figures 6.33 to 6.38 show the average dynamic range
of powers (DRPD) required for the transmitted signals to
the mobiles, in order to achieve balance in the downstream
case. Contrary to the upstream case, these ranges are
different for the cases where only in-cell balancing is
applied, and cases where cell-to-cell balancing is also
applied. Results show that the downstream ranges are
quite reasonable in terms of hardware realizability. This
is because the corner effect is not a very severe effect
and can easily be compensated by transmitting a few dB
more power to the mobiles at the corners. For example a
mobile that is located near the corner of three cells and
receiving the same amount of power from 3 base stations,
suffers three times as much interference as a mobile near
one of the base stations. Therefore the strength of the
signal transmitted to this mobile must be larger by a
factor of 3 (about 5 dB.) Table 6.3 shows the required

D

DRP values at full system capacity.

The results for the case where only in-cell balancing

110

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Table 6.3 Power control dynamic ranges required at full

system capacity for the downstream link.

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117

was applied are very close to 5 dB. The reason they go
slightly above this value at higher loads is due to the
fact that loads are not perfectly uniform from cell to
cell and many corner mobiles may suffer more interference
than the corner mobile in the above example, especially in
the tapered traffic distributions. This non-uniformity
becomes more noticeable when cell-to-cell balancing is
applied also. In that case, the base stations in cells
with heavier loads, transmit even more power per user and
thus make the system less uniform as far as power
transmissions are concerned. Thus a mobile located in a
corner of a lightly loaded cell, neighboring one or two
heavily loaded cells, needs a signal strength of much more
than 5 dB higher than a mobile near the base station.
This is the reason we see higher dynamic ranges when
cell-to-cell balancing is applied.

Comparing the results for different values of a, the
ranges go down slightly as a grows, when only in-cell
balancing is applied. This is because the corner regions
shrink as t! gets larger. When cell-to-cell balancing is
applied, however, the system becomes less sensitive to
variations in a, Results also show very little
sensitivity to variations in the value of a, for the

dynamic ranges.

 

 

118

6.4. Signal-to-Interference Ratio

Figures 6.39 to 6.41 show the decline of SIR in the
cell-to-cell balanced system as the system average traffic
load per cell grows. Results are given for both uniform
and tapered distributions. The SIR values are of course
the same for both the upstream and downstream cases, when
cell-to-cell balancing is applied. These curves
illustrate the principle of "graceful degradation" with
increasing load, for which spread-spectrum systems are
famous. We note that variations in the values of a and <7
make very little difference to these results. Load
distribution, however, has a significant effect on these
values. A uniform load throughout the system results in
higher SIR values than the tapered load. A difference of

about 3 dB is observed for the two load distributions.

 

 

 

 

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CHAPTER 7
CONCLUDING REMARKS
7.1 Conclusions

This work has presented analysis and simulation
results of a power control system for spread-spectrum
cellular mobile radio. We conclude that in-cell balancing
is essential for satisfactory operation, and that
cell-to-cell balancing may be desirable in cases where the
traffic distribution is not uniform. Downstream balancing
eliminates the so-called "corner-effect" and can easily be
implemented with full dynamic range. Upstream balancing
eliminates the so-called "near-far" effect, but probably
can not be fully implemented. In our simulation the
required dynamic range of transmitted powers by the
mobiles took on values of more than 50 dB. This may be a

difficult requirement to impose on a mobile transmitter.

122

123

This practical restriction provides a strong argument for
the use of frequency-hopping modulation in such a system.
Frequency-hopping is less sensitive to the near-far effect
and thus when it is used, a power control scheme with a
restricted dynamic range should operate nearly as well as
one with full range. In frequency-hopping modulation,
hard limiters may also be employed to compensate a
restricted dynamic range.

We observed that the capacity of the systems shows a
remarkably small sensitiVity to environmental parameters
such as rate of attenuation with distance (a) and
shadow-fading standard deviation (0). The dynamic range,
however, is effected by these parameters. Results show
that a higher a'or 0 require a considerably higher dynamic
range.

The ratio a/a was shown to have much significance in
the operation of the system. A smaller a/o results in a
higher uniformity in the traffic distribution from cell to
cell. This results in a higher capacity for the system
and lessens the need for application of the cell-to-cell

balancing algorithm.

7.2 Recommendations for Further Study

The research reported here has answered some

questions regarding the interference management of the

124

system, while raising more questions. We conclude by
discussing briefly some of the most pressing questions

that need to be answered.

7.2.1 Restricted Power Control

Results presented in chapter 6 suggested that it may
be difficult to apply power control with full dynamic
range in the upstream link. Further study of the system
using a restricted dynamic range is required to examine
its effectiveness and practicality. Data on the resultant
"outage" probability should be generated. It is also
desirable to compare different modulation techniques, when
such a restriction is imposed. The best alternative seems
to be a frequency hopped scheme employing hard limiters

together with power control with a restricted range.

7.2.2 Fading Mbdei

The interference analysis presented here relies on
the assumption that the median attenuation in a mobile
environment may be assumed to be independent of Rayleigh
rapid fading. This assumption is only based on the
filtering effect of the human hearing response on the
rapid' fluctuations of this fading. It is important

however, to investigate the effects of rapid fading on the

 

 

125

performance of the receiver. At typical data rates, each
deep fade may cause hundreds of bits to be lost. This may
cause a disruption in the proper performance of the
receiver, such as loss of synchronization. The degree of
such disturbances may vary depending upon the structure of
the receiver, and on the presence of burst-error
Vcorrection coding. Thus any such investigation would have

to be on particular receiver design.

7.2.3 Interference Modeling

It is assumed in our analysis that interference
between users may be modeled as white noise. This
assumption is a more valid one when direct-sequence
signaling is used. More careful analysis however, is

needed for frequency-hopped schemes.

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V. E. Benes.

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Academic Press, 1965.

George R. Cooper, Ray W. Nettleton and David
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l P