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8005821

NETILETO~,

RA YMO:\,D WILLIAM

SPECTRAL EFFICIENCY IN CELLULAR LAND-MOBILE COMMUNICATIONS: A SPREAD-SPECTRUM APPROACH

Purdue University

University Microfilms Inte rnat ion aI 3OO~. Zeeb Road, Ann Arbor, MI 48106

PH.D.

1978

18 Bedford Row, London WeIR 4EJ, England


SPECTRAL EFFICIENCY IN CELLULAR LAND-MOBILE COMMUNICATIONS:

A SPREAD-SPECTRUM APPROACH

A Thesis Submitted to the Faculty of Purdue University by

Raymond William Nettleton

In Partial

Fulfillm~r.t

of the

Requirements for the Degree of Doctor of Philosophy

December 1978


Grad. School Form No.9 Kevisea

PURDUE UNIVERSITY Graduate School This is to certify that the thesis prepared

By ____________~R~ay~mo~n~d~W~i~l~l~ia~m~N~e~t~t~le~t=o=n~_____________________________

E nti tl ed _______-=S.l:.p.::.ec.::.t.:..:r:....::a:....:l~E:..:..f..:..f..:..ic:..!..:ie:::.n:.=c~Y--=-i:..:..".....:C::..:e:....:l~l-=u..:..l::,.a:...,r...,:L:.,:a:..:.":.,::d:--.:...:.Mo::::,;b:::...·:...,:I1:....::e=---_____________

Communications:

a

Spread-Spectrum Approach

Complies with the University regulations and that it meets the accepted standards of the Graduate School with respect to originality and quality For the degree of: Doctor of Philosophy

Signed by the final examining committee:

--~~--="-"~="":--7IF-"'G=-.....:I'''''''~~~''---'-----' chairman M~~

Approved by the head of school or department:

A

/q

To the librarian:

19?K

~

~~ to be regarded as confidential

This thesis .

Profe~n charge of the thesis


-ii-

To my loved ones

(

{'


-iii-

( ACKNOWLEDGMENTS

To Professor George R. Cooper, for tance, patience, Jnd humor:

his

guidance,

assis-

To Dr. Harrison Rowe of Bell Laboratories and Dr. John P. Costas of General Electric, for their vigorous but goodhumored criticism of my work: To my good friends Dave Grybos and Jim Bucklew for helpful suggestions: To Mellanie Boes, typist and UNIX operator extraordinary:

(

And to my dear wife, Jenny, source of my fountain of love:

inspiration

and

My most sincere and heartfelt thanks.

(


-iv-

(-

TABLE OF CONTENTS Page LIST OF TABLES LIST OF FIGURES • • LIST OF SYMBOLS AND ABBREVIATIONS

........... .. ·.. ..... ·..

ABSTRACT CHAPTER 1.1 1.2 1.3

(

n

. . . . . .. . . . . . .

1: INTRODUCTION Statement of Problem Outline of Contents. Background Material. 1.3.1 Channel Models 1.3.2 Cellular Land-Mobile Systems. 1.3.3 Foundations of the Present Work 1.4 Original Contributions of This Research.

•

•

·.. .... .... ..

CHAPTER 2: PROPOSED SPREAD-SPECTRUM SYSTEM • • • • 2.1 Overview • • • • • • • • • • • • • • • • • • • • • • 2.2 Principal Features of a Spread-Spectrum System ••• 2.2.1 Advantageous Features • • • • • • • • • • • • 2.2.2 Disadvantageous Features. • • • • • ••• •••••••• 2.3 Principle of Operation 2.4 Signal Set Design • • • • • • • ••••• 2.5 Modulation and Receiver Model •••••••••• CHAPTER 3: CHANNEL MODELS • • • • • • • • • 3.1 General...... • ••• 3.1.1 Spatial Dispersion and Coherence Distance •• 3.1.2 Time Dispersion and Coherence Bandwidth ••• 3.1.3 Frequency Dispersion and Coherence Time 3.2 Na r rowband Mode l • • • • • • • • • 3.2.1 Rayleigh Fading • • • • • • • • • • • • • • • 3.2.2 Shadow Fading ••••••••• 3.3 Broadband Model •••••••• 3.4 Composite Model • • • • • • • • • • • • • •

.. ·..


vi i viii xii xxi 1 1 4 7 8 9 16

17

20 20 22 22 26

27 32 40

44 44

47 47 50

52 52 53 54 55

-v-

(

(

· · · · · ·· · ·· ·· · ·· · · ···· · ····· · · · · · · · · · · · · · · ·· · · · · · · · ·· ·· · · · ·· · · · · · ·· ······ ·· ·· ·· ·· ·· ···· · · · · · · · · · · · ·· · · · ·· ·· ·· ·· ·· ······ · · · · · · .······· · · ·· ·· · ·

CHAPTER 4: RECEIVER PERFORMANCE 4.1 Assumptions and Definitions 4.2 Error Probability. 4.2.1 Conditional Probability of Error 4.2.2 Noise Statistics 4.2.3 Error in Nonfading Channel 4.2.4 Error in "Ideal" Fading Channel 4.3 Effect of Coherence Bandwidth 4.3.1 Wide Coherence Bandwidth 4.3.2 Narrow Coherence Bandwidth 4.3.3 Composite Performance Loss 4.4 Error in Rician Channel 4.5 Some Possible Improvements 4.5.1 Space Diversity 4.5.2 Mismatched Filters 4.6 Threshold Errors 4.6.1 False Alarm Probability 4.6.2 Miss Probability • 4.6.3 Results

61 61 67 67 72 76 80 81 81 87 93 95 99 99 103 105 107 108 109

CHAPTER 5.1 5.2 5.3 5.4

112 112 114 115 122 123 124 130

5: POWER CONTROL AND MOBILE LOCATION General Comments A Proposed System Mobile Location Errors Power Control Errors 5.4.1 Case 1; Mobile Unit Stationary 5.4.2 Case 2; Mobile Unit in Motion A Sample Design

···· ·········· ······· ········

·· ·· ·· ·· · · · · · .. · · 5.5 .·· ···· CHAPTER 6: INTERFERENCE MODELING · · · · · · · ·· ·· ·· ·· 6.1 Upstream Interference • · 6.2 Downstream Interference ····· · · ·· ·· · · 6.3 Directional Base-Station ·Antennas. 6.4 Equivalent Interference Bandwidth 6.5 A Simplified Interference Model ·· ·· ·· ·· ·· "

(

CHAPTER 7: SPECTRAL EFFICIENCY AND SYSTEM PERFORMANCE 7. 'j' Measures of System Performance 7.1.1 Spectral Efficiency 7.1.2 Service Grade 7.1.3 Subjective Evaluation 7.2 Spread-Spectrum System Performance 7.2.1 Spectral Efficiency v 7.2.2 Factors Affecting Service Grade 7,,2.3 Factors Affecting Subjec~ive Evaluation 7.2.4 Potential for Improvement .. 7.3 Narrowband System Performance .. .. .. 7.3.1 Systems Under Development 7.3.2 Performance of Narrowband/FrequencyReuse Systems .. 7.3.3 Potential for Improvement 7.4 Spread-Spectrum and Narrowband Systems Compared

···· ····· ······ ···· ·· · ···· ····· · · · · · ·········· ·········· ·· ·············· ········


132 132 139 144 145 151 153 153 153 155 156 158 158 160 162 164 167 167 168 169 170

-viCHAPTER 8: CONCLUDING REMARKS 8.1 Conclusions • • • • • • • • • • • • 8.2 Recommendations for Further Study • •••• 8.2.1 Interference Modeling 8.2.2 .Construction of a Prototype 8.2.3 Subjective Testing and Comparison •••• 8.2.4 Control and Systems Aspects 8.2.5 Receiver Robustness and Adaptation • 8.2.6 Effect of Nonlinearity in Receivers 8.2.7 Compatibility with Existing Systems 8.2.8 Alternative Spectrum-Efficient Techniques 8.3 Final Remarks • • • • • • • •••

173 173 174 174 174 175 176 177 177 177 178 179

LIST OF REFERENCES

181

APPENDIX A1:

MONTE CARLO TECHNIQUES

190

A2: IMPLEMENTATION OF RECEIVER Delay-Filter Receivers. Filter-Delay Receivers. Receiver Stability

196 197 199 199

APPENDIX A2.1 A2.2 A2.3 VITA

...........

(


204

-vii-

LIST OF TABLES

Table 3.1 Typical Channel Time-Dispersion Parameters. • • • • • •

Page 49

4.1

Typical Values of t1 • • • • • • • • • • • • • • • • • •

S.1

Ratio of Mean-to-Standard Deviation of PM Due to Noise • • • • • • • • • • • • • • • • • • • •

....

126

Ku as a Function of Cell Radius and Attenuation Law for a SO km Service Area • • • • • • • • •

....

139

6.1

7.1

l 7.2

91

Narrowband/Frequency-Reuse Parameters for Commercial Developmental Systems • • • • • • • • • • • • • •

168

U/B Per Cell Compared

171

.. .................

,I


-viii-

LIST OF FIGURES

Figure 1.1 Frequency allocations in the "900 MHz" (806-947) band • • • • • • • • • • • • • • • • • • • Principle of the cellular land-mobile radio system

10

1.3

Evolution of a cellular system with increasing load

13

1.4

A narrowband/frequency-reuse system with L = 4

15

2.2 2.3 2.4 2.5 2.6

(

2

1.2

2.1

(

Page

··..·.········ Simplified mobile unit block diagram ···· · Principle 0f operation . . ···..·.··· Typical signal from the undivided signal set ······ Number of potential users of the subdivided signal set . . . . . . . . · · · · · .. · Receiver demodulator model ········ ··· System overview

~

23 24 31 34 39 42

3.1

A simple scattering channel

45

3.2

Envelope of channel impulse response

48

3.3

Doppler spectrum geometry

51

4.1

Vector-matrix model of source, channel and receiver

64

4.2

Probability density function of nongaussian component of noise in observation space (solid) compared with Gaussian curve (dashed). Linear ordinate: n = 32 •

75

Same curve as 4.2 but with logarithmic ordinate

75

4.3


4.4

Complementary distribution function 1 - '(a~ (solid) compared with Q(a) (dashed): n = 32 • • • • •

77

4.5

Probability of bit error, nonfading channel

78

4.6

Probability of bit prror, nonfading channel, n = 32; comparison of results using '(a), Q(a) and Viterbi's upper bound •• • • • • • • • • • • • • • • • • • •

"

D

79

4.10

···· Probability of bit error; fading and nonfading compared . ·· ··········· ·· Probabi l ity of bit error; wide coherence bandwidth ··• Simplified channel-receiver model · . . . . . . .

4.11

Distortion of waveform x,(t) due to multipath fading

90

4.12

Locus of matched filter performance in signal loss• ••••• timing error pLane • • • • • • • •

92

Composite performance loss for n = 32, 8 = 20 MHz, Rb = 30 kb/s • • • • • • •••••••••

94

4.7 4.8 4.9

4.13

(

·. ·.....

Probabi l ity of bit error; "idea.l" fading channel

~

,

4.14 Probability of bit error for "ideal" Rician channel 4.15.

Probability of bit error for Rician channel: O~4 • • • •••••••

4.16 4.17 4.18

Effect of dual diversity on b',!1 ~ error probability: Be'8 = 0.1

··..···········..······ Effect of duaL diversity on bit error probability: 8 c 18 = 0.4 ··..···········..··· Effect on bit error probability of utilizing two resolvable signal paths; "ideal" fading channel

5.1

( .~

86 87

98

101 102

·...

106

·....

110

Threshold error for optimum threshold levels; Bc/a = 0.2 • • • • • • • • • • • • • • ~ • • • • • • • •

111

Spectral block interleaving for upstream and downstream bands • • • • • • • • • • • •

114

4.19 Threshold error for optimum threshold levels; "ideal" fading channel • • • • • • • • • • • • 4.20

83

97

·..

Be/S =

82

·.....

.....


-x-

c·

5.2 5.3

a) Mobile locator/power control system model b) Block diagram of one demodulator in model Contours of constant error probability for mobile locator

5.4

........••....

~

120

• . . .

Fuzzy boundary defined by hysteresis in mobile locator

•••••••••••.

121

• • • • •

Powe:- control error stCltistics: unit

stationary mobile

5.6

Power control error statistics:

moving mobile unit

5.7

Po~er

control error statistics: error levels

versus H for fixed

5.5

6.1

(

116

.·............• ......

125 128

........... ........

129

~

A typical energy distribution for one signal waveform in the time-frequency plane • • • • • •

~33

6.2

Geometry for upstream interference calculation.

136

6.3

Normalized downstream

SIR

142

6.4

Probability distribution function of normalized downstream SIR • • • • • • • • • • • • • • • • •

143

Expected energy in filter response to pulse with uniformly distributed center frequency • • • • •

149

Logarithmic mean of SNRO versus Eb/NO for 6-bit uniform PCM ••• ~ ~ • • • • • • • •••

165

6.5

7.1 7.2

A1.1

for various cell locations

Normalized logarithmic variance of SNRO versus SNRO for 6-bit uniform PCM

D

•

•

•

Monte-Carlo algorithm for probability of message error • • • c • • • • • • • • • • • • • • • • •

•

•

••

166

•

•

•

193

•

A1.2 Monte-Carlo algorithm for probability of threshold error -

194

A1.3: Monte-Carlo algorithm for probability of mobile locator error • • • • • • • • • • • • • • • • •

195

·.............. .. ...... ~

.. .l.


-xi-

( ~

A2.1

Typical delay-filter receiver

A2.2

Typical fil. ter-del ay receiver

A2~3

Complex envelope filter-delay receiver •

1QB

....


200 202

-xii-

(-

LIST OF SYMBOLS AND ABBREVIATIONS

(

A

Area of a cell; km 2

AM

Amplitude modulation

a

Rayleigh parameter

a~1

The ith integer of the kth cod in the one-coincidence code set; the ith element of gR

B

Total available one-way bandwidth

Bc

Channel coherence bandwidth

Bd

Channel doppler-spectrum bandwidth

b

The smallest priffiitive root of the integer p

bls

Bit:; per second

C

Any constant of proportionality

c

Velocity of light; 3 x 108 mls Reflection constant of kth scatt~rer; proportional to the square root of its scattering cross-section Differential signal (+1) corresponding to jth time chip of kth mobile unit

D ••

Distance between center of Cj,iJth cell and

Ds

Safety radius in mobile locator system

D(f)

Doppler power spectrum

d

Mean excess delay.

11

('

mobil~

unit

First moment of channel impulse response.


-xiiid(x.,x.) , J

Distance in observation space between the ith and jth elements of the signal vector ~(t)

Eb

Energy per message bit

E{x}

Expectation or mean value of x.

E (AW) y

Energy in the response of a filter to a pulse with the same complex envelope as its impulse response but with center frequency separated by Aw.

Also denoted by

x.

Expectation of above if Aw ;s uniform on [-11'8,11'8]

(

x

exp(x)

e

F

Vector of fading coefficients, generally exponentially di stributed

F

I !, where! is the identity

FCC

Federal Communications Commission

matri~

Frequency modulation Fourier transform of x A nominal carrier frequency Minimum frequency shift; incremental frequency step of the signal set

f~

,

Frequency assigned to the ith time chip of the kth waveform of the signal set Maximum doppler shift; 2V!A Gain (generally angle e

co~plex)

of an antenna at azimuthal

g

Portion of received signal power due to specular component

H

Number of pilot signals averaged in power control system The nth order Hadamard matrix [h ij ]


-xivhbiCt)

Impulse response of ith bandpass filter in receiver

hcCt)

Channel impulse response

~cCt)

Composite channel model matrix impulse response

I...

The identity matrix

i id

Independent and identically distributed

J

Number of pilot signals averaged in mobile locator system

j

K

Number of signals in a K-ary orthogonal signal set Modified Bessel function of the second kind, of order q and argument x

(

Ratio of speech time to total time in a typical telephone conversation Ratio of upstream interference power from outside cell to total upstream power from inside the cell, when mobiles are uniformly distributed in the service area

L

Number of cells in the repetitive pattern of cells, or cluster, in a narrowband/frequency-reuse system Number of time chips in pilot signal

(

M

Number of signals in the subdivided signal set

MNB

Multiple-narrowband (channel model)

m

Number of time chips in member of undivided signal set

One-sided noise Cor interference) spectral density


c.

-xvNumber of time chips in member of subdivided signal set

n

Power received at base station Signal controlling mobile transmitted power Pilot signal transmitted power Pulse code modulation PM

Phase modulation Probability of message bit error Probability of waveform error Probability of event x A prime integer

rex)

Probability density function of x

Q.

Number of times the ith pilot code is used ;n a service area

Q

... n

An nxn orthogonal matrix [q 1) .. ]

Q(a)

Complement of the normal distribution function

( 1

Q(a)

= (21T) -1/2 Sco

2

exp(-x 12)dx

a

q

Number of quantizing levels in speech digitizer

Message bit rate, bls IIRadius

ll

of cell; distance along one side of hexagon

Waveform repetition rate for pilot signal Radius of circle with area equal to hexagon of IIradius Rc ll

Waveform repetition rate for message signal

(

( r

Radial distance variable


-xviret)

Received signaL-pLus-noise vector at output of receiver bandpass fiLters

S

Rece~ved

Si (x)

x Sine-integral of x, Si(x) = S t- 1sin t dt

SIR

SignaL-to-interference ratio

SNR

SignaL-to-noise ratio

S5

Spread-spectrum

SSB

Single-sideband

gk

The kth code of the one-coincidence code set

s

Delay spread of channeL impulse response; square root of its second centraL moment

sk(t)

Vector containing the n time-chip pulse signals of the kth mobile unit

T

nt 1 , duration of signal in divided signal set

T'

mt 1 ' duration of signal in undivided signal set

T

Channel coherence time

signaL power

o

(

c

t1

Duration of one time chip in signal set

u

Average number of simultaneous users, or traffic load; ErLang

u(x)

Heaviside function; 1 if x > 0, 0 if x < 0 kth eLement of averaged and sampled pilot signal vector Real part of complex envelope of w'(t)

u(t)

(

ReaL part of complex envelope of wet)

kth element of demoduLated piLot signal vector


-xvi i-

(-

v

Vehicular velocity, mls

v' (t)

Imaginary part of complex envelope of w' (t)

vet)

Imaginary part of complex envelope of wet)

W(r)

Transmission intensity (watt/m 2) from a unit cell area. A function of distance from the transmitter

WGN

White, Gaussian noise

w'

Vector of n narrowband noise elements; WGN, iid from element to element and sample to sample

(t)

* ~(t),

wet)

w'(t)

{X}

The set of n elementary message vectors; x. ;s the ith row of the identity matrix -1

n

i.e.,

~'(t)

after bandpass filtering

x(t)

Received, demodulated and co-ordinate rotated message vector. Signal in observation space.

y

1/~

.li

A channel message corresponding to -1 x.; .L.1 v. = x. Q -1'"

.l(t)

Received and demodulated message vector

1.' (t)

.l(t) before low pass filtering

~

Square matrix in which every element is unity

z

Threshold level normalized to signal received power

a

Path-loss-law exponent; e.g. a = 2 implies an inverse-square law of path loss with distance from the transmitter

aCt)

Envelope of the response of a receiver bandpass filter to its corresponding time-chip pulse

(

times amplitude of received signal


-xvi i i-

rev)

Gamma function.

rev)

=j

o

t v- 1 e- t dt

Lognormal coefficient of kth scatterer in composite channel model y

Ratio of specular to scattered signal power in dB Rayleigh coefficient of kth scatterer in lth subchannel of composite channel model Complex envelope of x(t)

Doppler shift, Hz Angular Doppler shift of kth scatterer in channel model Kronecker delta; 1 if i Dirac delta function;

= j;

f

0 otherwise

x('r)o(t-T)dT

= x(t)

-CD

of

Frequency spacing between adjacent channels

€(t)

Envelope of each pulse in transmitted signal

~

Normalized variable

~(t)

N~n-gaussian

n

Trunking efficienc/: ~gtio of offered load to maximum number of channels in a closed system

e

Equivalent uniform beamwidth of an antenna e = IG(6 )1- 2 S~ IG(e)1 2de 0

~t1

component of the noise signal in the receiver observation space

-~

(

ek

Phase shift associated with kth scatterer

ACf)

Covariance function of channel


-xix-

(

Covariance matrix of MNB channel Wavelength, meters Poisson parameter

Inverse of the time constant in exponential decay factor in composite channel model

Dummy noise variable; zero mean, unit variance

v

Threshold level Random phase variable

n

(

Product operator Permutation operator associated with the prime p

Correlation coefficient

p

Summation operator a

x

Standard deviation of x.

Square root of variance

~k

Time delay associated with kth scatterer

~

Normalized variable

~

Dummy variable

T

Number of different pilot signals in power control mobile locator system

,

t/t~

(


-xx-

x

Sum of squares of Rayleigh coefficients

~

Vector of co-ordinate rotated fading coefficients

~(t)

Multiple - narrowband channel matrix; diagonal

~i

(i,i)th

~(x)

~lement

of !; Rayleigh distributed

Noise probability distribution function x '!'Cx)

=f

pCv) dv

-00

Round-trip error fdctor in power control system

w

Angular frequency; 2nf, radians/second

Other Notation [x]

The largest integer

-x

The mean of x: also E{x}

X

An imperfect (e.g., noisy) observation of x

x

A vector x

x... xT

A matrix x

x!y Y

~

x

The transpose of x x given y; or, x conditioned on y For all values of •••


-xxi-

l ABSTRACT

Nettleton, Raymond William. Ph.D., Purdue University, December 1978. Spectral Efficiency in Cellular Land-Mobile Communications: A SpreadSpectrum Approach. Major Professor: George R. Cooper.

Severe spectral congestion in the land-mobile phasizes the need for a new system design.

radio

services

em-

The recent allocation by the

FCC of the 900 MHz band presents a unique opportunity for

the

applica-

tion of modern technology and co-ordinated planning toward a satisfacto-

(

ry solution to this problem. basis

for

such

a

Cellular communications systems offer

solution, but cellular schemes currently under con-

struction use conventional narrowband modulation techniques, notoriously

unsuited

the

to

which

are

the available channel and which are unable to

adapt to future system applications. A spread-spectrum system design is presented here which is

capable

of offering a high-quality, lasting and spectrally efficient solution to the problems of land-mobile radio. In the

prop~sed

system the available spectrum is divided

into

two

portions, one for mobile transmission and one for base station transmission. izes /

(

No further subdivision of the spectrum is used; every user the

appropriate portion in its entirety.

util-

An automatic power con-

trol system is used to minimize interference between users.


-xxiiEach mobile unit is assigned a unique which

is used

for

translated form). correlation necessary.

both

transmission

The signal set used has

properties,

so

time-frequen~y

and

reception

favorable

coded waveform (in frequency-

aperiodic

cross-

that no synchronization of mobile units is

The signal set is very large, permitting unique

assignments

to be made to each member of a large user population. An analysis of a differentially-coherent receiver is presented it

is

shown

and

that the degradation of performance due to fading is very

small, due to the high order of

frequency

diversity

inherent

in

its

design. A preliminary analysis of an open-loop power control and mobile locator system indicates the feasibility of the open-loop approach.

(

An analysis of the spectral efficiency of the proposed system indicates that it offers a substantial improvement over existing techniques, by a factor of at least five even when relatively inefficient speech digitization methods are used. Although much of the work is written explicitly in the context,

land-mobile

the suitability of the technique for other multiple-access ap-

plications will be obvious to the informed reader.

(


- 1 -

(-

CHAPTER 1: 1.1

Statement of ProbLem

It is wideLy recognized that beLeaguered

resource,

INTRODUCTION

and

Land-mobiLe radio services.

the eLectromagnetic

nowhere

is

this

spectrum

is

a

more evident than in the

Modern society demands that people on

the

move be able to communicate by radio, but the spectraL allocations made for this function have traditionaLly beer meagre have been

(

(

fully

and

new aLlocations

subscribed almost as soon as they have been assigned.

As a result, huge backlogs of potential users with no

spectral

aLLoca-

tion have buiLt up in many locations. The allocation by the FCC of the so-called "900 MHz band" two bands

of

width 20 MHz which are intended for ceLlular land-mobile

radio use, as shown in Figure 1.1 unique

incLudes

opportunity

for

the

[S1].

This

allocation presents

a

appLication of modern technology and co-

ordinated planning to produce a comprehensive and

Lasting

soLution

to

the problem of spectral efficiency in the land-mobile services. CelluLar Land-mobiLe radio systems are wideLy recognized to provide a potentiaL

soLution to this probLem by permitting muLtipLe use of the

same spectrum in a given serv1ce area. tionaL

using

conven-

narrowband anaLog moduLation techniques have been proposed and a

number of deveLopmental (These

CelluLar systems

schemes

are

systems

are

under

construction

[A1,I1,S1].

described in Section 1.3.2.> The proposed schemes,



)

Size of allocation, MHz I

I

80_ 806

.... .,c .."

I'D

~

•

~

c::

C

en

I'D Q..

'C

.,....0 .... 0

::J

en

., I»

I'D

cr

.... I'D

:l

(Q

::r

I'D

c-.." Q..ll

n

'< I» ,..

,..

0 n

::J

en

....

.c c:

N 0

I

N

V'1 ~

I

Convent!onal systems mobile transmissions

-

Cellular systems mobile transmissions

(1)

::J

(")

-

:J: N

:l

Cellular systems base stations

)

I'D

.0

I'D

3

:J:

I'D

N:

Thus the narrowband/frequency-reuse scheme is a straightforward extension of

existing

technology

in which

the available channels are

trunked (i.e., accessible to a large number of users

on a

first-come,

first-served basis) and in which geographical separation is used to control interference between users. are

that

all

the

The principle advantages of the method

technology needed has been available for years, and

that the system is simple in concept particularly

and design.

The disadvantages,

in the case of the present F.M. schemes, include the high

cost of Jnalog circuitry, the poor quality of reception in a fading

en-

vironment [P1J, the unsuitability of the technique for new applications, the spectrum waste inherent in permitting only a portion of the spectrum

(

to be

used

in

any given

location,

the unsuitability

telephony-oriented systems for many user communities such services, techniques. scheme

and

the

as

emergency

lack of privacy due to the use of simple modulation

In short, it is felt

provides

of trunked,

that

the

narrowband/frequency-reuse

a useful, but also ad-hoc, piecemeal and necessarily

temporary solution to the problems of the land-mobile radio service.

1.1.1 sequel

is

Foundations of the Present Work. part

University on the multiple-access

of

The work reported

in

the

an ongoing sequence of research projects at Purdue

subject

of

communications

time-frequency systems.

coded

signal

sets

and

The principal projects which

form the basis of the present work are described briefly below. The time-frequency coded signal

set

was

reported

in the

Ph.D.

thesis of Yates [Y2J, who described the theory of generating signal sets

(


- 17 -

c

with prescribed coincidence properties.

The one-coincidence signal

set

of that thesis is identical with the undivided signal set described here in Section 2.4. these

signal

It is interesting to note that at the sets

tire~

(1966)

that

were described, generating and receiving them would

have required prohibitively complex, bulky and expensive hardware.

That

is no longer the case, as will be seen in Appendix A2. The signal sets lend themselves well to the implementation of unsynchronized

random-access, discrete-address (RADA) communications sys-

tems, and research was done on the suitability of the multiple-access satellite communications systems.

signal

sets for

Weinrich EW1J modeled

inter-user interference as white, Gaussian noise, and in a more detailed study

(

Schleuter

[55] investigated, among other things, the validity of

Weinrich's

interference model.

difference

in performance

Schleuter's

when using

work

indicated

little

the more accurate interference

model, and that result forms part of the justification

for

the simple

interference model proposed in Chapter 6 of the present work. The possibility of using a divided version of the signal set cellular

land-mobile

system was reported in the Ph.D.

in a

thesis of Finch

[F3J, who also analyzed a number of other possible modulation schemes in the

same

context.

Finch concluded that a 3pread-spectrum system could

provide a significantly more efficient method of utilizing the available spectrum than other methods. 1.4 ---

------ - --------

Original Contributions of This Research

The present work is a collection of results in various validity.

f:

states of

Some of the following contents are as close to being defini-

tive results as the available techniques for solution will permit; oth-


- 18 -

(

ers represent preliminary investigations or feasibility require

further

which

refinement; and some are topics raised for the purpose

of discussion or informed conjecture. here

studies,

Not all of the material presented

is original, and where appropriate the source of the material has

been identified.

Section 8.2 identifies those results given here which

require extension or

refinement, as well as suggesting new avenues of

research. The following identifies the broad areas of the field to

which

it

is believed that an original contribution, either in concept or in substance, has been made. 1.

It is established that system

a cellular

land-mobile

communication

can be constructed in which all of the available spec-

trum can be used in each cell

by every user;

and that

the

result is a more efficient use of the spectrum.

( 2.

A spread-spectrum communication system design is which differentially -

coherent

presented

matched filters are used to

dete'ct the signal, rather than the correlation techniques in conventional

spread-spectrum

in

CD1J.

sche~es

used

This permits

low-duty-cycle users to randomly access the system without

the

need for lengthy pauses for synchronization. 3.

An analysis of the proposed scheme shows that the receiver performance

is degraded by fading by only 2-3 dB, compared to the

20-30 dB' loss encountered in conventionaL CP1,J1J •

This advantage

narrowband

is gained by the

quency diversity inherent in the method,

and

hig~

schemes

order of fre-

estabLishes

suitabiLity for use in a highly - dispersive channeL.

(


its

- 19 -

(

4.

A preliminary control

feasib~lity

study demonstrates that the power

system required for satisfactory operation of the pro-

posed scheme can be constructed without the need for

elaborate

closed-loop control systems. It is not uncommon for the early work in a new field

to

generate

more questions than are answered, and the present work is no exception to this principle.

Nevertheless, it is felt that the material presented

in the sequel represents a significant first step in the long-term solution of the problems of land-mobile communications.

("

~-


- 20 -

l

CHAPTER 2:

PROPOSED SPREAD-SPECTRUM SYSTEM

2.1

Overview

The mobile communication system considered here is a cellular tem

~f

the type illustrated in Figure 1.2.

sys-

The base station antenna may

be omnidirectional in the horizontal plane, thus illuminating the entire cell;

or

it

may have sectoral beam patterns, illuminating three rhom-

boidal subcells or six triangular ones with 1200 and 600 respectively.

other

patterns

The available frequency spectrum is divided such that one

portion is used for mobile-to-base station (upstream) the

beam

for

base

transmission

and

station-to-mobile unit (downstream) transmission.

All mobile transmitters are assumed to have automatic power control that maintains the average received signal level at the base station constant regardless of the location of the mobile unit within the cell. Each mobile unit iR also assigned a unique coded

waveforms

that

are

used

for

set

of

time-frequency

both transmission and reception.

These waveforms have large time-bandwidth products such that interfering signals

can be

well-suppressed, and which provide a very large set of

signals so that a large number of potential users can each be assigned a unique set of waveforms.

Message modulation is accomplished by digitiz-

ing the speech and encoding the resulting binary sequences into the of

waveforms available to each user.

set

The encoding into binary form may

(


(-

- 21 -

be conventional PCM, differential PCM, delta modulation,

or

any

other

digital encoding procedure which provides acceptable results. The system to be described Hence,

whatever.

requires

no

waveform

synchronization

considerable versatility is permitted; each user ca-

tegory might choose to encode its speech (or other data) in a different way

and

at

a different

bit

rate.

methods might then be employed (such as

More exotic speech communication vocoder

speech)

user-density demands and the application permits. in efficiency

m~y

result

from

transmitting

no

as

and

when

Further improvements energy during

speech

pauses, thus reducing inter-user interference. The presence of multipath results in a loss of phase

(

the

received

signals.

each

a differentially

received

waveform.

waveform

in

Thus, time correlation or matched filter detec-

tion of the signal is net possible. employing

coherence

are

This difficulty is circumvented by

coherent compared

procedure in which the phases of with

those

of the

This is possible because the coherence time* of

preceding

the

channel

is greater than the duration of one waveform. Power control in the mobile transmitters is used to compensate changes

in signal level at the base station due to path loss variations

and slow fading.

No attempt is made to have the

the rapid fading due to multipatha

power

control

under

the

derived

from

the

sta-

assumption that reciprocity holds in the mean, (i.e.,

once the rapid-fading variations have been averaged

(

follow

The control signal is derived from a

pilot signal, transmitted from and uniquely identifying each base tion,

for

pilot

out).

Information

signal is also used to determine the most ap-

*channe( parameters such as coherence time are defined in Chapter 3.·


- 22 propriate signal path for the communication link tion

will

receive

which base

sta-

the. highest level of signal from the mobile).

This

(i~~.,

function is referred to as the mobile locator function, and is used

in

call initiation and cell-to-cell handoff operations. System control messages used for call initiation, handoff and mination and

user identification are also carried on "dedicated" chan-

nels, which may be identical with the pilot signal used for These

trol.

ter-

power

con-

channels are required in both the downstream and upstream

directions. Figure 2.1 shows a general overview of the system, illustrating the four

basic

signals

required

for

each mobile.

waveforms are unique to each mobile unit, but the shared by all mobiles in a given cell.

(

The message signal control

signals

are

The downstream control signal is

the pilot signal. Figure 2.2 illustrates in simplified form a typical receiver block diagram for use with this system.

The functions of some blocks (such as

amplifiers) are conventional and will not be discussed further.

Most of

the more novel functional blocks are the subject of detailed examination in the sequel. 2.2 Principal Features

£.£.1 same

~~

Advantageous Features.

Spread-Spectrum System

The use of signals all occupying the

frequency band at the same time results in a number of operational

characteristics that can be very advantageous in a mobile system.

(

communication

In addition to the increased user-density that is possible in a

small-cell system, these advantages may be summarized as follows:


- 23 -

(

Central

-

controller

,

~

,,.

...

,

base station

JIIl

,~

"

CU

MU

,

To other base stations

Local

.~

To nonmob i Je services

-

-

Signal Designations MU : Upstream message

(

CU : Upstream control

II

MD : Downstream message CD : Downstream control and pi lot

Mobfle unit

Figure 2.1

System overview

(


-~--.,.


.r-

Ga i n-contro 11 II ed R.F. amplifier Upstream

Upstream signals signa I s

I-

\t::: L..J • j

r

Upstream control modulator(s}

~

lrcuI ator ~

..... -r-""

-

.....-----,1-

~

8

Data source, e.g. digitized speech

L...--./): "

/

~

.-----; .-----1

Upstream message modulator

Power Initiation/ control & handoffl f---*I mobil e r---- term ina t ion locator contron er

Power control signal Downstream control demodul ator (s)

Downstream signals

R.F. amplifier

LJ

r--

Downstream message demodulator

N

.1

~

Data sink, e.g. D-to-A convertor

Figure 2.2 Simplified mobile unit block diagram

~

- 25 -

1)

The use of a large number of frequencies results

in a form

waveform

of frequency diversity that significantly

reduces the degradation in performance that from rapid fading.

in each

normally arises

This aspect is discussed further in Section

2.3 and in Chapters 3 and 4. 2)

Any user can access the system at any time without waiting a free channel.

for

Thus, there are no blocked calls in the usual

sense, although of course traffic will be ultimately limited by the available plant and its associated software. 3)

There is no hard limit on the number of active users be

handled simultaneously by the system.

that

can

When the number of

active users exceeds the design value, the result is a degradation of performance for all users rather than denial of access.

(

This is usually referred to as "graceful degradation." 4)

Since each potential user of the system is assigned signal

set, message

a unique

privacy is achieved as a fringe benefit.

This, of course, refers to privacy with respect to

the

casual

listener and does not preclude message interception by a properly equipped third party. 5)

Because each user retains his unique there

is no channel

moves from cell to cell. characteristic

of

FM

signal

set

permanently,

switching or address change as the user Hence the particularly objectionable systems known as "forced termination,"

which occurs when a mobile crosses a boundary into a cell which no channel is available, will not occur in this system.

(


in

- 26 6) . Since all users occupy the same band, all identical signal set. these gy. 7)

except

for

the

user hardware

is

filters associated with the unique

(A recent feasibility study [C9]

has

shown that

receivers can be fabricated using existing CCD technolo· Receiver implementation is discussed in Appendix A2.)

Priority messages (e.g., public safety vehicles) can be accommodated in the system, even in the presence of system overload, without assigning dedicated channels or denying other users access

to the system.

This can be done either by

inc~easing

the

power level, on an emergency basis, or by increasing the timebandwidth product of the priority signal. 8)

Under circumstances in which the full capacity of the system is not required, a spread-spectrum system may co-exist in the same frequency band as conventional narrowband systems without cessive mutual

interference.

This

ex-

suggests the possibility

that a spread-spectrum system could be phased into operation in a given geographical area without immediately obsoleting existing equipment operating in the same band.

It is even possible

that spread-spectrum and narrowband schemes could co-exist permanently, using the same band twice [C1,C13]. 2.2.2 noted

Disadvantageo~s

Features.

The desirable

above cannot be achieved without cost.

characteristics

Some of the disadvantages

of the spread-spectrum approach are summarized below: 1)

Effective power control is required in order to prevent near

(

the base

users

station from overpowering more distant users.

The preliminary study reported in Chapter 5 indicates that


a

- 27 -

c:

satisfactory power control system is realizable, however. 2)

Message encoding and decoding is full

advantage of

inherently more complex

if

the available frequency diversity is to be

achieved. 3)

A mobile locatcr technique, having modest accuracy, is required on order to adequately monitor the mobile unit as it moves from cell to cell.

However, some such facility is required of all

the small-cell schemes that have been proposed; also it is anticipated that locator and

power

control

circuitry will

be

essentially common in the receiver, as shown in Fig. 2.2. 4)

Fully coherent detection 0 as

=

1 -1,; n-1 (n-1+r)! I;n-1-r n ~o r!(n-1-r)! 2r 2 (n-1)! e

(4.30>

The expression (4.30) is readily integrated to reveal the distribution V(a), for a > 0, as


- 75 -

c ~

~

~

c

~

~

~

~

~

m 0.5

~

0

~

~

~

> ~

m ~

0

~

0

2

4

3 v

Figure 4.2

( ~

Probability density function of nongaussian component of noise in observation space (solid) compared with Gaussian curve (dashed). Linear ordinate: n = 32

0

~ ~

c

~

~

~

~

-3

~

m

~

0

~

~

~

>

-6

~

m ~

~

0 ~

~

0

-9

~

0

Figure 4.3

2

3

4

Same curve as 4.2 but with logarithmic ordinate


- 76 -

'l' (a)

=1

-a n-1 n-1-r (n-1+r).1 n-1-r-j e ~ E "::'T"l~iI-=~.,. "::'T":~li-::~..,.. ..;;;.a_ __ n ~ r! (n-1-r-)! r 2 (n-1)! r=O j=O 2

-

(4.31)

The function 1 - 'l'Ca) above is compared to the more familiar tion

Q(a), the complementary Gaussian distribution function (defined in

the list of symbols), in Figure 4.4 for n is

func-

logarithmic.)

= 32.

(Note that the ordinate

The difference can be seen to be quite small, so that

it is felt that the use of (4.31) rather than the true mixture distribution

is

justified.

A

further

justification is contained in Section

4.2.3, where the probability of error is calculated

using

both

(4.31)

and Q(a) and the difference is seen to be less than 1 dB. 4.2.3 matrix

(

nal

~

Error in Nonfading Channel.

for the fading matrix

probab~lity

substi tut i ng

the

identity

the integral (4.27) becomes the margi-

of error for a nonfading channel;

L 00

~

~,

By

= 1 .-

n ~(v) j~2 'l'{\1 + d(x 1,x j I.!

= I)}dv

(4.32)

The above result may be readily evaluated by digital computer using numerical

integration.

The results are shown for n

= 8,

16, 32, and 64

in Figure 4.5. It is instructive to use this simple case in order to gain an of

the

idea

error involved in using (4.31) instead of the true mixture dis-

tribution.

Figure 4.6 shows the result of using either the form

or 1 - Q(a) as 'l'(a) to compute (4.32).

(4.31)

The difference between these two

extremes is less than 1 dB in the abcissa for the region of greatest interest, and the result using the mixture will of course fall between the

('

two.

Thus the simplification afforded by (4.31) seems well justified.


- 77 -

c.

o~--------------------------------------------------------------, o---------------------------------------------------------------~

-1

-2

, ~ ~

-3

'\

'\ \

\

\

,...

......

(

o .... C.!3

o

-'

\ \

-

\

\ \ \

-6

\ \ \

\

-7

\ \ -8~

________________________

~

______________

~

__

\

~~

-8~---------_r---------_r-------_r-------,_------,_--~~

o

2

3

it

6

5 a

Figure 4.4

Complementary distribution function 1 compared with Q(a) (dashed): n = 32

~(a)


(solid)

- 78 -

(

0 ·5--------------, O·51-r---------------,

(

10--5~____~~~~~~~~~~~~ 10-~5~~~~~~~~~~~~~_.~

o (

Figure 4.5

5 Probability of bit error, nonfading channel


15

- 79 -

(

0·5-,.-----------------,

upper bound: coherent, Gausslan. Differentially coherent: Gaussian noise. Differentially coherent; Nongaussian noise.

(

\

, , 10--5+-~~~~~~+-+-~~~~~~ o 10 5 15 \

\

Eb/No' dB

Figure 4.6

Probability of bit error, nonfading channel, n = 32; comparison of results using ~(a), Q(a) and Viterbi's upper bound


- 80 -

~

Figure 4.6 also shows the familiar upper bound on error due to terbi

Vi-

[V3J which demonstrates that whilst the receiver design is 5UDOP-

timal, the sacrifice made is quite small. It should be noted that Figures 4.5 and 4.6, and all bil ity of error nate.

other

proba-

graphs, show probabil ity of bit error CPb on the ordi-

This is for consistency with the abcissa quantity which

involves

mean energy per bit, and uses the familiar substitution [V3J CPb =

~

,i.£.,i Error means

•

2(~-1)

i.!l

(4.33)

"Ideal:' Fading Channel.

The "ideal" fading channel

the MNB channel of (3.12) in which the inequality (3.7) is satis-

fied; i.e., the frequency - slots used in the waveform of

(

so

far

apart that they fade independently.

interest

are

Then the elements of Fare

independent and the joint probability density function may be written as n = n 1'(41 i=1

i)

(4.34)

The marginal probability of error for such a channel is obtained by integrating (4.27) over all possible values of

,i.

Thus

(4.35)

Since the expression (4.35) is an n-fold multiple integral, where n

»

1, it is clear that systematic evaluation by digital computer is en-

tirely impossible.

(

Fortunately, it is precisely in

the

evaluation

of

probabilistic expressions of high dimensionality such as (4.35) that the


- 81 -

(

well-known Monte-Carlo technique comes into its own nique

was

used

extensively

in

the

[S7J.

This

tech-

evaluation of almost all results

derived in the sequel, and a brief explanation of the technique and algorithms

used

is

contained

in Appendix A1.

the

In the case of (4.35),

some 600 to 800 random vectors F were generated with

each

element

ex-

ponentially distributed, and the expression (4.27) evaluated for each F and for a range of values of SNR. samples

of

averaged

(

all

error

The resultant estimates of probabili-

are ploted in Figure 4.7, for n

= 8,

16, 32, and 64.

benefits of diversity inheient in a choice of large n are this

over

so that the solution was the sample mean from a "typical" popu-

lation in the space defined by!. ty

The results were

obvious

The from

graph, and it appears that n > 32 is necessary for a good level of

perfoimance. Fading and nonfading performance are compared for n = 32 in 4.8.

It

can be seen that loss due to fading is less than 2 dB for the

error-probability range of interest. the

20 dB

Figure

This compares very favorably

with

or so loss that is encountered in digital transmission over

narrowband fading channels with no diversity [A3,P2J. 4.3.

Effect of Coherence Bandwidth

This section considers the effects upon

probability of

error

of

failure of the inequalities (3.7), first separately and then in combinationa

Section 4.4 considers some possible remedies for the losses dis-

cussed ht!rein.

i.l.l

Wide Coherence Bandwidth.

If the

inequality Bc«

not satisfied by the channel, the random elements be independent.

,?, in -F will

BIn

is

no longer

In that case, the integration of (4.27) over all possi-


- 82 -

0 ··5 ,-- --. 0 5--------------------

(

10--5+-__ ~~____~~____~~~~~~ 10--5+-~~~~~~~~~~~~~~

o (

Figure 4.7

5 Probability of bit error; "ideal" fading channel


15

- 83 -

0·5----------------,

( Nonfading

Fading

',0 --5+-_r_-r-_r_~-r-_r_~T'__r__,.__,_L_.___.---,r__I --5+-_r__-r-_r__~-r-_r__~+_r__r__,_L_r___r___r__I o 0 5 15 ftJ/Ha. dB 1

(:

Figure 4.8 Probability of bit error; fading and nonfading compared


- 84 -

ble values of ,~1 takes on the more general form moo

CPe

2

00

2

= 1 - f S ••• f 1'(, l' '2' ... , o0

(4.36)

0

Fortunately, random-number generating routines are available generate

vectors

which

of numbers with a specified covariance matrix, and so

the evaluation of (4.36) by Monte-Carlo methods becomes as simple as the tasks of the previous section.

The exact form of the covariance matrix

to be specified, however, must depend

upon

the

form

of

the

channel

model, and for this reason reference must be made to the broadband model of (3.11). The covariance function of the channel is the magnitude squared of the

(-

Fourier transform of the channel impulse response or, equivalently,

the Fourier transform of the autocorrelation the

channel

impulse response [C10].

function

associated

with

The latter definition is more ap-

propriate in the case of a random channel; thus A(f) =~[E{h (t)h (t+T)}] c

For a stationary channel the expectation is a variable variable. over

L,

and

the

(4.37>

c

Fourier

function

of

the

transform is taken with respect to that

(The channel may, of course, only be considered

a small

single

"stationary"

interval in space, as discussed in Chapter 3 and Section

4.1.> For the "exponentially decaying" channel

model

of

(3.11), A(f)

will have the familiar form of a first-order Butterworth response


- 85 -

(4.38)

A (f)

where unimportant constants arising from channel absorbed

into

the

constant

C.

parameters

In translating this function into the

form of a correlation matrix, the simplifying assumption the. frequency

slots

are

have been

uniformly

is made

spaced over the available band B.

(Some ad hoc experiments with the Monte-Carlo algorithm in which of

that

a

few

the entries of the correlation matrix were perturbed revealed a dis-

tinct lack of sensitivity of the results to these perturbations, so that the

simplifying

assumption seems justified.) In that case the transla-

tion of (4.38) into the matrix is,

and SNR are all as previously defined.

Once again the result may only be estimated by Monte Carlo methods, and

a simple modification of the previously used algorithm was used to

produce the results given in the next section. i.~.l

Results.

The results

of

the

previous

two

sections

are

parameterized on z, n, Bc' and Eb/NO so that a complete presentation for all values of parameters would require as much space as all the rest this

chapter

combined.

of

Hence the presentation here will be restricted

to the following set of conditions; 1.

n = 32.

2.

z=

z,

In condition (2), the

system

selected dynamically so that ~m

z might

design

it

= ~f'

Y Bc' Eb/NO.

be considered an optimum threshold level if in is decided that the miss and false alarm events

have "equal cost" in terms of performance degradation. Figures 4.19 and 4.20 show

the

probabil ity of

threshold

error

t =~m =::Pf for an "ideal" channel and for BclB = 0.2 respectively. Other values of BclB were tried and the results are consistent with

~

those presented; namely, that in the range of bit error probabilities of "'" < 10-2 , say) the threshold errors are at least an order interest (-'b

magnitude

less than the maximum-likelihood message errors.

This satis-

fies the criterion which permits the "no threshold error" assumption

(

be used.


of

to

- 110 -

0·5

C

....

,,

,,

,

,, \ \

Probability of bit error

\

.'

\ \

CJ?

'. \

\

, \ \

\

\ \

\

\

\

\

\

\

\ \

\

\

(

\

Opt imum threshold error

\ \

\ \ \

\

\

\

\

\

\

10- 5 0 Fi gure 4.19

(~

5

~JNo' dB

10

Threshold error for optimum threshold levels; "ideal" fading channel


15

- 111 -

0 ·5--,.----------------. 0·5--,.-----------------. .....

" . . . . Probabi 1 ity of bit error

",

""

" , ,

,,

"" ,

,,

Optimum threshold error

\

,,

,,

,,

( \ \

,,

,,

,

,

\

10--5T-.-.-r-r_~r_~~~~ 10--5r-.-.-r-r_~r_~~~ ________ ~____~

o Figure 4.20

5

10

15

Threshold error for optimum threshold levels; Bc is = 0.2


- 112 -

(. ,'

,

CHAPTER 5:

5.1 Every

mobile

transmitter

power

POWER CONTROL

General Comments

transmitting

in

a

given

cell

must

adjust

its

in such a way that the base station of that cell re-

ceives every signal with equal signal strength.

If this

is

not

done,

mobiles close to the base station will swamp the signals of those further away.

(This is the "near-far" problem common to most spread spectrum

systems.) Two distinct steps are necessary in the power control problem;

(

1.

A decision transmitting

must in

be made

periodically,

for

every mobile

the service area, as to which cell the mobile

is in. 2.

The propagation loss (in relative terms) and

its

assigned

base

between each

mobile

station must be periodically (or con-

stantly) monitored to determine the level of mobile transmitter power required. Probably the most appropriate criterion for (1), the mobile tion

problem,

is that the mobile is assigned to the base station which

receives the greatest signal strength from it. but

it

must

This may appear obvious,

be realized that the resulting assignment will not always

have geographic meaning; that is, the hexagonal boundaries drawn

(

map

will

loca-

on

a

undoubtedly not represent lines of equal signal strength in a


- 113 real city.

Hence it is quite possible for a mobile actually in

cell

A

to be assigned to cell B because of a more favorable propagation pattern in that direction.

It is a reasonable contention, however, that service

quality is more important than the accuracy of geographical location information, at least in the present context. A principle that is of considerable utility in an implementation of power

control

is the reciprocity theorem, which in the present context

says that mean path loss from base station-to-mobile loss

from mobile-to-base station.

however. at

all

equals mean

Some caution must be exercised here,

In a multipath environment the reciprocity statement points

in

time

and

(

is

true

space only at a single frequency; if the

upstream and downstream channels are separated by more than ence

path

the

coher-

bandwidth, their respective path losses will be uncorrelated.

The

respective means of the Rayleigh fading channels will be essentially the same,

however,

for

any

frequency

separation; hence if the Rayleigh-

fading behavior may be "averaged out" then reciprocity may be

used

in

might

be

the system. As a means of enhancing desirable

the

reciprocity

principle

it

to break up the upstream and downstream bands into blocks and

interleave them, as shown in Figure 5.1.

This would have the added

ad-

vantage of further separating frequency slots in a given signal and thus reducing correlation between them; in fact of course, there is not a

requirement

that

even

the blocks be contiguous, and if they are not the

latter advantage would be further enhanced.

(-


·

,

- 114 -

-

.....

~

U

~

U

0

U

0

-' co

C(

LLI

~

c..

.,Jo

;:)

-' co

V)

~

U

0

-' CQ

-' co

LIJ

~

~ LLI

e:: ....

....

ex:

tV)

0..

~

c..

:3

c::

tV)

z:

Z

::>

0

::>

ex:

UJ

V)

V)

0

~

~

U

0

---

--.

lH lH

~~tQlJf:NCy

Figure 6.1

A typical energy distribution for one signal waveform in the time-frequency plane

- 134 1.

Superimposed on the desired signal will be signals

from

mobile

units

in

virtue

All will have of

the

power

system described in Chapter 5) regardless of their lo-

cation in the cell. tion

interference

the same cell.

equal power with the desired signal (by control

(U-1)

The Rayteigh fading and multipath

distor-

of each, however, will be independent, and their relative

disposition in time will be random and time-varying

by

virtue

of mobile unit motion and local-clock-frequency drifting. 2.

In addition to the signals described in (1) above, every mobile in

every

other cell will contribute an increment of interfer-

ence power to the received signals. tipath

The Rayleigh fading,

distortion and relative disposition in time will all be

random, time-varying and independent, as in (1).

(

mul-

however,

the

In

addition

average power from each outside mobile unit will

be random because the power control system of each will be compensating

for

the

losses

in a signal path leading to a dif-

ferent base station. 3.

If the mobile location system in each mobile uses strength"

the

"signal

criterion discussed in Chapter 5, then the lognormal

distribution of interference power from each

mobile

which

is

implied by (2) above wiLL be truncated at or near a Level equal to the received

power

from

the

desired

mobile.

Thus

the

overall outside interference power is the sum of a large number of severely truncated lognormal random variates. The exact form of the distribution of due

to

shadow

fading

out~ide

and control-switching

interference

truncatio~

power

is an unsolved

(


- 135 problem at this time. for

Indeed, no analytic solution has

been

developed

the sum of lognormal random variables, truncated or otherwise [M4J.

However, it does appear that the decibel standard deviation of such sums diminishes rapidly with increasing number of summands; for example, in a Monte Carlo simulation by Nasell [N3J, the variates

with

less than 1 aBe side

standard

deviation

sum

of

256

iid

lognormal

of 8 dB had a standard deviation of

It seems reasonable, therefore, to assume that the out-

interference power will have a standard deviation which is consid-

erably smaller than its mean. Mean upstream signal-to-interference power, below.

SNR

AU

'

is

calculated

The subscript A means "measured at the antenna terminals", i.e.,

over the entire system bandwidth B; the subscript

U means

"upstream".

The analysis is adapted from Finch [F3J, and assumes the following. (

1.

All cells are hexagonal and of equal radius.

2.

The service areas is a plane disc of 50 km radius. cides

This

coin-

approximately with the radio horizon for typical antenna

heights [R1J. 3.

Mean path loss is uniform over the service area and follows "inverse-a-power"

law.

an

Shadow fading is ignored, for the rea-

sons outlined above. 4.

Each hexagonal cell is approximated by a disc (A

5.

equal

of

area.

hexagon inscribed in a circle of radius R is equal in area c

to a circle of radius R = 0.9094R c·) s The location of each mobile unit is independent distributed

in the service area.

and

uniformly

The number of units per cell

using the system is U for every cell, where U »1. (


This

per-

- 136 -

mits the discrete summation of signal power to be

approximated

by an integral. The model used for upstream interference analysis is shown in

Fig-

ure 6.2.

,

Figure 6.2

Geometry for upstream interference calculation

Consider the ith cell with respect to the cell of interference source is modeled as an element of area. ure 6.2, each element of area dA = rdrd9 transmits with 2 watt/m ,

contributing

a

interest.

Each

Referring to Figintensity

W(r)

transmitted power W(r) dA watts to the total.

From each element dA, base station Y receives an element of i of


power

dPe

- 137 -

dP

B

= Wet) a

dA,

(6.1 )

r

where multiplicative constants due to antenna gains have been Power

control

maintains

ignored.

each contributing dPa constant, which implies

the relationship (6.2)

where C is defined by the total received power PB, also a constant. P is given by the integral B

f

P = B A

~

(

C

W(r) dA = C 1T R2 ra

(6.3)

s

_ PB - 1T R2

and

But

W(r)

(6.4)

s

The base station X receives each element of power as given by

(6.5)

,

Thus, the total contribution from cell Y. is P B

=

1T

2n

R

R2 { { s

a+1

s

2

(D., + r

2

r 12 dr de - 2 Di. r cos·e) a

Dividing by PB and summing the contributions from all interfering yields the upstream interference ratio K given by u

(


(6.6)

cells

- 138 -

K

1

A

u-

11'

N 211' RS

R;

l: i f

i=2

a a

(l+1

,

,

where N is the total number of cells in the service area. base

station

area

as a whole.

(6.7)

2 2 r 12 dr de (D. + r - 2D.r cos e)(l That

is,

if

(1) receives Ps watts of signal power from the mobiles in cell (1), it receives Ps(K u + 1) watts from the mobiles in the service Then if each cell contains U » 1 users, the ratio of

mean signal power for one mobile to total mean interference power is 1 nR"AU = (0-1) + 1 CK 0) :: ,.,O"7'l(K.,...;...,+->r'..... ) u u

,

U » 1.

(6.8)

Analytic solutions for (6.7) are available only when (l/2 is a positive

integer.

Numerical solutions are necessary for other values of (l.

Note that the interference ratios are independent of cell size

2,

say.

In practice a typical value of t1B would be 100. Finally the normalizing factor (6.14) may be removed, yielding result -' Ey (t 1B)

+

1/t1 for large argument.

the

This factor may be interpret-

ed as the "equivalent interference bandwidth"

of

the

filter,

and

is

identical in value to its equivalent noise bandwidth. The "test" implicit in this analysis is too far removed from a fully structured interference model to draw final conclusions, but since it considers the effect of a single, fully-synchronized, non-fading intuition suggests that it

~epresents

an upper limit on the departure of

fading, multi-pulse noise from the white-noise reasonable

to

suppose

that

pulse,

model.

Thus

it

seems

the effect of interference in the spread-

spectrum system will greatly not exceed that of white, Gaussian noise.


- 151 ~.1

~

Simplified Interference Model

At the time of writing no rigorous modeL has the

interference

are

compeLling

which

been

constructed

occurs in the proposed syttem.

heuristic

arguments,

certain

of

However, there

preliminary

analytical

results, and some items of empiricaL evidence which tend to point toward the acceptability of the "white, Gaussian noise" (WGN)

model

suggested

previousLy. Heuristically, for be

composed

of

e~ample,

in the upstream case interference

will

Literally hundreds of enargy distributions of the type

shown in Figure 6.1; each different, each unsynchronized and each "peak" of

which fades independentLy.

components of t1

(-

= 5~s

width

and n

= 32,

(between

SpectraLly, each distribution contains n first

nulls)

20

MHz,

For

example,

If the avaiLabLe bandwidth

it wiLL obviously require onLy a few such distributions to

fill the band with a more-or-less uniform spectral density. domain,

the

if

the total space taken up by the main lobes of each

distribution is 12.8 MHz, ignoring overlaps. is

2/t • 1

receiver

In the time

samples each interference pulse at a random time

(because the mobiLes are

~ot

synchronized), and each puLse

dependently random amplitude with zero mean.

has

an

in-

The WGN interference modeL

therefore has strong intuitive appeal. Analytically, the result of Section 6.4 appears to suggest that any error due to the WGN model is unlikely to be very Large.

Earlier inves-

tigations of systems such as that proposed, in which the number terferers

was

quite

smaLL,

of

in-

synchronization was used and there was no

fading [S5J, tend to corroborate this conjecture.

co


- 152 Finally a limited amount of direct simulation has been again

with

small

numbers

of

undertaken,

interferers and no fading [C12J, and no

results have been obtained which tend to contradict the WGN assumption. In the downstream case, interference is more factors

structured, but

two

tend to suggest that the situation will actually be better than

in the upstream case given that SIR Firstly,

the

signals

are

is the same in both directions. A synchronized in blocks, which means that at

least some pairs will be orthogonal; and secondly, a portion of the terfering

signals

will

fade

in step with the wanted signal.

seems reasonable to assume that over most of the service area,

in-

Thus it upstream

interference will be the system performance - limiting factor. For the purposes of Chapter 7, then, interference will

be

modeled

as white, Gaussian noise with noise spectral density proportional to the

(

load density U/B.

(


- 153 -

SPECTRAL EFFICIENCY AND SYSTEM PERFORMANCE

CHAPTER 7:

This chapter contains some preliminary predictions of

the

way

in

which the proposed spread-spectrum system will perform in the urban cellular mobile radio context. performance, analysis. proposed

and

the

The results of Chapters 4 and 5 on receiver

assumptions

of

Section 6.5,

Some comparisons are drawn between the scheme

and

that

of

presently under development.

the

are used in this

performance

of

the

narrowband/frequency-reuse systems

The potential impact of

developing

tech-

nology on both schemes is discussed. The chapter begins with a discussion of the measures of system performance which are pertinent to the present application. 7.1

I.l.l the

Spectral Efficiency.

electromagnetic

spectrum

beleaguered resource. panding

Measures £i System Performance It is widely recognized that space for

the

purpose

either turally. jor

of communication is a

Legitimate applications abound, and many are

rapidly (or would, if spectral space were available).

tion, the spectrum contains unwanted energy

in

distributions

ex-

In addi-

which

exist

as a result of human activity (such as machine emissions) or naThe problem of spectrum management has therefore become a ma-

international

concern [C13), and, although it does not necessarily


- 154 -

impinge upon the user's perception of performance,

the

spectral

effi-

ciency of a communications system is rapidly becoming its most important parameter. In telephone engineering the basic unit of telephone (0~,1· :;:~te

load

correctly, "offered load") is the Erlang, which is the product

of subscriber call-attempt rate and call-holding time. which

traffic

is

occupied

at

all

Thus one channel

times carries one Erlang of load [S2].

In

two-way, or duplex, systems such as domestic telephones, it is of course immaterial

whether

this measurement. only

one counts one link direction or both directions in For the purposes of this discussion the one-way

link

will be counted, with the understanding that two bands of frequen-

cies of the given width will be needed for duplex applications

such

as

telephony. Perhaps the most obvious measure of spectral efficiency is load per

(

unit spectrum, or Erlang per MHz.

It is clearly a valid figure of merit

in most communications contexts, but it fails to take into geographic

density

aspect of the land-mobile problem.

two cities of different sizes, if their respective terns

carry

account

the

For example, in

communications

sys-

the same total load per unit spectrum, it is clear that the

smaller city has the more efficient system since

mobile

larger

city must be more spread out geographically.

~eaning

for land-mobile applications [H1].

units

in

the

The composite unit "load per unit spectrum per unit area", Erlang/(MHz km 2) say, has more

A degree of normalization may be lar

schemes

the amount of load

~

used~

however, since in all cellu-

cell that can be handled in a given

bandwidth and for a particular geometry remains essentially constant re-


- 155 -

gardless of cell size.

Hence the unit "load per unit spectrum per cell"

conveys exactly the same information as "load per unit spectrum per unit area" if the cell area is known, but has the additional it

advantage

that

has essentially the same value for any size cell and has more intui-

tive meaning to the engineer.

In the sequel, the

unit

Erlang/MHz per

cell will be used as the basic unit of spectral efficiency. Composite units which involve capital and operating costs have also been proposed [L2J.

Whilst these considerations are important, however,

they will not be considered here since for the proposed system (and to a lesser degree even for the current developmental systems) they valve speculation and be subject to radical change with the time

~ould

in-

passage of

(as, for example, has been the case recently in the digital calcu-

lator market).

(

1.1.£ sociated

Service Grade.

parameters,

All measures of spectral efficiency have as-

and none is more important than the service grade

of the system, a term once again borrowed [J1 J.

Service

grade

is

from

telephone

engineering

directly observable to a regular user of the

system in that it determines how responsive the system is to the demand for service.

The measures associated with service grade are pro-

bability of blocking and average waiting time, both system "busy hour".

user's

measured

during

a

The first is the probability that a subscriber ini-

tiating a call will be denied service because all channels are occupied.

".

The second is the average time which elapses between the initiation of a blocked call and the availability of a free channel. quoted.

In

One or both may be

the sequel, blocking probability during the busy hour will

be assumed to be a fixed system parameter.

Average waiting time will be

(~

.,,- -


- 156 -

ignored, since if probability of blocking is "sufficiently small", waiting time is of no real significance.

Currently developing systems have

a design probability of blocking, ~CB), of around two or

three

percent

CI1 ,J1J.

Offered load in a telephone system is a monotone tion of

~CB).

~(B)

= 0.2,

func-

In a closed system (i.e., a system with a fixed number of

available channels) the load is equal to the when .:pCB) = 1.

increasing

For

acceptable

values

number

of

channels

only

of .:p(B) in a typical system,

say, the load per cell is around 60% to 80% of the number of

channels available in each cell [AS].

L.l.l link

can

Subjective Evaluation.

when

a digital

data

easily be quantified by such objective measures as the proba-

bility of bit error.

(

The performance of

digital

In the case of telephony, however, and

especially

transmission and a fading channel form parts of the link,

quality of performance is less easily judged. In the reproduction of sound for

entertainment

purposes,

certain

objective measures are commonly used in the evaluation of the equipment; e.g., frequency response, signal-to-noise ratio, etc.

The

engineer

distortion

will no doubt be familiar with all these, but will

probably be less aware of the way in which they subjective

percentage

satisfaction

with

what

he

hears.

affect In

the

listener's

the case of high-

fidelity engineering, the constraints are few and the solutions The

simple.

requirement may be to maximize bandwidth, power and signal-to-noise

ratio, and minimize distortion, all constrained by cost. telephony,

the

But

in

radio

constraints are more restrictive and the solutions more

difficult (and in many cases, unsolved at the time of writing). (. \.


- 157 -

In telephony applications it is the subjective satisfaction of subscriber

which,

in

the light of the cost of the service, determines

the acceptability (and, indirectly, the commercial success) of the tem.

Primarily,

the

sys-

the requirements are that the system respond promptly

and without error to the initiation of

the

call

(i.e.,

"getting

the

right number"); that the verbal communication of the call take place intelligibly and without undue strain on either talker that the call be uninterrupted.

listener;

and

Secondary considerations include suffi-

dent "fidelity" in the link for the voice of recognizable;

or

a

known

speaker to

be

privacy of the message; and provision for additional ser-

vices such as paging and data transmission. The primary requirements are, of course, essential, and familiar to every

(.

home and office telephone subscriber.

The secondary requirements

are obviously highly desirable, but the additional

constraints of

the

mobile radio service may render one or more of them difficult to achieve and perhaps even dispensible in the light of cost. The

fact

separately

that

intelligibility and

fidelity

have

been

listed

above reflects the somewhat non-intuitive fact that they are

quite separable characteristics of a speech communication

system.

For

example, it is possible to analyze speech signals into such characteristics as pitch and amplitude, voiced and unvoiced sounds, and to transmit parameters

~hese

to

a

synthesizer which reconstructs the speech pat-

terns.

falls below

a

specified

value due to shadow fading be less than some small value during the busy hour.

(

In

This might require that its mean be some

that

case

number

say.

the value of (7.4) is fixed by the message bit rate, the

system performance criterion and the value of the

normalized

parameter

(USIR A) discussed in Chapter 6. The values of transmissions

and

(USIRA)

given

in

Chapter

6 were

for

omnidirectional base station antennas.

continuous If transmis-

sion of power occurs only during periods of nonzero message energy (say, in a telephony application) then (USIR A) must be divided by a constant Ks which represents that proportion of overall during

speech

transmission

sounds

time

when nonzero transmission power occurs.

In the case

of a normal telephone conversation, K will presumably be approximately s 0.5. Further, if U per cell is held constant and antennas with an equivalent uniform beamwidth of a radians are used at the

base

sites, then (US!RA) must also be multiplied by the factor 2w/a.


station

- 160 -

c

rel~tion

Combining the above with (7.4) and substituting the

(6.8)

into the result yields • 1

-K

s

• 21T

(7.5)

9'

where the implied assumption is that upstream interference is the system performallce-limiting factor, as discussed in Section 6.5. Specific values of U/B depend on the parameters chosen. is

given

below;

the

choices

of

An example

parameters are discussed in Section

7.4.1. Let Rb = 30 000 bit/s and Ks = 0.5 (i.e., a typical plication).

* (Eb/NO)

(

e is

Let

=8

in

K

u

= 1'

a

representative

telephony

ap-

value from Table 6.1; and

dB, as discussed in Section 5.4.2.

Then U/B

= 33.2/9

where

radians, or 5.3 Erlang/MHz where omnidirectional base-station

antennas are used. Factors Affecting Service Grade.

l.~.~

phone

systems

similar and

way~

and

narrowband

radio

telephone systems behave in very

in terms of their response to

termination during the busy hour.

Conventional trunked tele-

subscriber

call

initiation

In both cases a finite number of

"lines" is accessed by a much greater number of subscribers, each with a low call duty factor and with independent initiation times. number of calls permitted at one available

lines (or channels).

to as closed.

time

is

identically

The maximum

the

number

of

Such a system has already been referred

The traffic theory of closed telephone

systems

is well

developed for both trunked and cellular land-mobile systems [ASJ. In contrast to these well-established and readily analyzed systems, the

proposed spread-spectrum scheme has features which appear to demand


I

! \

- 161 -

\

I

an entirely revised traffic theory. is

In the radio-frequency sense

there

really only one "channel" which every subscriber shares; in terms of

addressing, the number of "channels" and the number

of

subscribers

is

identical (at least in the sense that every new subscriber "creates" his own channel). however,

For every call to be completed with

acceptable

quality,

requires that only a tiny subset of all subscribers operate in

a given cell, so that the maximum number of calls permitted in cell is far smaller than the number of available channels.

a given

In fact, for

the purposes of analysis the number of channels might well be considered infinite, forming a system which will be referred to as open. A traffic theory of open systems is called for in order stand

the

busy-hour

behavior

of the proposed scheme.

aspects

of

the

problem

under-

At the time of

writing this task remains a recommendation for further study; tain

to

but

cer-

are sufficiently obvious to permit some

preliminary observations to be made. 1.

The limit on system load per cell is less well defined in

open

systems

sub-

than

in

closed systems.

stantial overload beyond the tolerated

Hardware permitting,

nominal

limit

could

~

easily be

by the system, with a resulting gradual, uniform de-

gradation in message quality for every user (at least locally). Overload

levels of perhaps 100% might be permitted before ser-

vice is denied; in the meantime, each subscriber audible

clue

that

the

behavior

given

an

system is heavily loaded, i.e., lower

than normal message quality. blocking"

is

This

implies

a kind

of "soft

in which, possibly, subscribers with unim-

port ant messages might react to the poor channel by hanging


up

- 162 and calling again later. 2.

Since all base stations are identically equipped,

a potential

exists

For example,

for

dynamically adaptable cell geometry.

sectoral illumination might be adaptive, switching from 360 0 to 120 0

t~

60 0

as the cell's load builds up.

Cell radius could

also be adaptive, since it is simply a function of pilot-signal power.

Thus a pair of adjacent cells with unevenly distributed

loads could react by increasing the pilot-signal power lesser-loaded

cell and vice-versa.

use of interstitial base stations the

the

Another possibility is the physically

located between

constantly-operating stations, but which operate only dur-

ing the busy hour. 3.

of

No doubt many other possibilities exist.

A built-in message priority system could be installed simply by permitting

(

different

mobile units to be received at different

powers by the same base station (i.e., by

assigning different

values of C in (5.8) to different units).

The obvious benefi-

ciaries of such priority assignments are emergency service

mobile

and

public

units, which will then be guaranteed a channel

even when the system is overloaded. l.~.l

subjective

Factors Affecting Subjective

Evaluation.

The

problem of

evaluation rests in presenting "typical" results to a cross-

section of subscribers and measuring their responses to the system. ther

Q

working model of the system (full-scale or smaller) or a realis-

tic simulation is required for such an exercise. model

Ei-

nor

a

realistic

Neither

an operating

simulator of the proposed system has been con-

structed at the time of writing, however, so that results in

(


this

area

- 163 -

do not exist at present. tion

lies

in

the

Probably the most obvious area for

investiga-

transitions from analog to digital signals and vice

versa. The choice of coding scheme and of speech digitization method are of critical importance in balancing the conflicting requirements of message quality and spectral efficiency. tized

Subjective evaluation of

digi-

speech is highly multidimensional (G2,J3J and the additional fac-

tors of fading and environmental noise (in vehicles, for example) render the problem still more difficult.

This area is clearly of the first im-

portance in any follow-on effort to the research reported here. As a preliminary observation, it r~sults

of

is

interesting

to

examine the

a Monte-Carlo simulation which was performed in conjunction

with the probability of error analysis described in Chapter 4.

(

In this

case the well-known results relating to Pulse Code Modulation with uniform quantization steps (C14] were used to translate the probabil ity of error

for

each

sample

in

channel space into a baseband The decibel values of SNRO and SNR 02 were the

fading

signal-to-noise ratio, SNR O• accumulated and used to estimate the mean and variance (in decibels) of SNR O•

(The choice of a logarithmic scale corresponds more

closely to

the subjective effect on the human ear.) SNRO is given by (7.6)

where SNR q is the signal-to-noise ratio that would result from quantization

only

and SNR d is the signal-to-noise ratio that would result from detection errors only. These are defined to be (F3]


- 164 -

( and

SNR q

= 4q

(7.7>

SNR d

q-1 4 = (4q-1):'P. b

(7.8)

where q is the number of quantizing levels (i.e., there are sage bits

per

l092q mes-

sample) and :Pb is the probability of bit error.

In the

simulation 6 bits per sample were used. Figure 7.1 shows the mean, SNR O' versus Eb/NO for various values of 2 =2 . and Figure 7.2 shows the normalized variance 0SNR /SNRO of the

o

output signal-to-noise ratio versus SNR O• It can be seen that for acceptable values of SNRO (say, 20 dB) the corresponding variance is quite small, indicating that the subjective quality should be perceived by

(

subscriber to be very consistent in spite of It is probable that PCM will for

a practical

~

available

fad~ng.

be the digitization method

chosen

implementation of the proposed scheme, but it is felt

that since non-companded PCM probably choices

a

for

represents

one

of

the

poorest

the application, the above results are most en-

couraging. l.~.i

possible

Examination of (7.5) reveals two

opportunities for a substantial improvement in system spectral

efficiency. typical

Potential for Improvement.

The value of Ks depends on

the "sound/silence"

ratio of

conversations, which is not open to adjustment by the engineer;

but the exact definition of "silence" is likely to be a critical factor. The

threshold of

sound level below which transmission is cut off, and

the time delays involved in switching the transmission on and off, both have

an

important

effect on Ks; and also on the subjective quality of


- 165 -

c 30 -r------------------------~~~r_--~ -r--------------------------~--~----~

25 'h

J; 'f

20 CD "'C

...

0

I~

(

15

10

5

o 2

Figure 7.1

6

8

10

12

Logarithmic mean of SNRO versus Eb/NO for 6-bit uniform PCM

c: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

- 166 -

'""0

(

I~

10- 1

0

"0

""z

."

'""0

o

10

Figure 7.2

20

30

Normalized logarithmic variance of SNRO versus SNR O for 6-bit uniform PCM

.[

' ..


- 167 -

r~

the speech.

The parameters chosen will reflect the need for

compromise

between Ks and speech quality. Advanced methods for low-bit-rate digitization of speech have been a major

topic of research for some time.

Intelligible speech has been

reported using digitization at bit rates as low as 4.8 kbits/s [C2] using

vocoding

techniques at even lower rates.

and

Since U/B is inversely

proportional to Rb, there is a strong motivation for investigating the applicability of such techniques to the proposed system. It might be conservatively estimated that spectral efficiency could be improved tenfold

over

the

five

or

so

Erlangs/MHz mentioned in Section 7.2.2 by

bringing the appropriate technology to bear, at the expense

of

message

fidelity.

I.I

( I.I.!

Narrowband System Performance

Systems Under Development.

At the time of writing, 900

MHz

cellular mobile communications systems are under development by Bell Laboratories every sample

is taken at regularly-spaced intervals throughout the space. routine

Carlo

(

differs from the systematic method only in the manner in

which the sampling operation is performed. and

net

A Monte-

Instead

of

constructing

a

summing the integrands in some deterministic order, the Monte-

Carlo method samples the space randomly in a manner probability

density

function

of the integrand.

determined

by

the

The idea is to sample

the more "typical" points from the space, thus hastening the convergence of

the

integral approximation.

Experience shows that the rate of con-

vergence in typical cases can be increased by orders of pared

to

systematic

magnitude

com-

methods, particularly in the case of integrals of

high dimensionality [57]. The error in the Monte-Carlo estimate of an integral is, generally, difficult

to

estimate.

In

the

present

work no attempt was made to

evaluate bounds on the error; instead, the sample points themselves were monitored in order to judge their degree of conformity with the required


- 192 -

c[

probability density function. variance

Specifically, the running sample mean and

of the random ~~ were monitored for convergence to the correct 1

value (equal to n) and the algorithm was stopped

when

the

below 1% for the mean and 2% for the standard deviation. occurred after some 600 to 800 vectors F had been vector for n

required

= 32,

the

error

fell

Generally this

generated,

and

generation of 2n Gaussiatl random variates.

each Hence

approximately 40 000 variates were used in the generation of

each data point presented in Chapters 4 and 5. Figure A1.1 shews the basic algorithm used to generate all the probability of message error results given in Chapter 4. the algorithm used to estimate alarm

the

miss

All

probability

(4.56).

(False

probability did not require a Monte-Carlo algorithm.) Figure A1.3

shows the algorithm used to estimate the

(

Figure A1.2 shows

algorithms

were

written

mobile

locator

error

(5.6).

in FORTRAN IV and executed on the tandem

pair of CDC 6500 computers of the Purdue University

Dual-Mace

system.


computer

- 193 -

Read parameters z, Bc/B, p Generate A ...

Generate random ... us ing ...A Demodulate and rotate input

Accumulate samples of F

Eb/NO = 0 dB Ca 1cu 1ate error probability

Add 1 dB

Accumulate samples of cP e

to Eb/No { \

Calculate SNRO for 6-b it PCM

Accumulate sampl es of SNRO

No

No

Calculate & output sample mean & variance ofF, cp, SNRO -

Figure A1.1 /-

t.

e

Monte-Carlo algorithm for probability of message error


- 194 -

Read parameters n, 8 /8 c

Generate

~

Generate random

~

Demodulate and rotate input

z

Accumulate samp 1e~; of F

= 0.2

Calculate miss error probability

Accumulate samples of cPmIz

.,,--

(......

Add 0.1 to z

No

Calculate & output sample mean & variance of F,CP ... m z

Figure A1.2

Monte-Carlo algorithm for probability of threshold error


- 195 -

Read a~ hyesteresis factor, cartesian map of base station locations

(~

Pos i t i on mobi1 e

Re-position mobil e

Generate random pilot signals

Calculate SIR Calculate mobile locator error

Accumulate samples of SIR

Accumulate samples of locator error

( No

No

Calculate & output sa~ple SrR, means & variances of SIR, locator & power control errors

No

Figure A1.3

Monte-Carlo algorithm for probability of mobile locator error


- 196 -

( APPENDIX A2:

IMPLEMENTATION OF

REr~IVER

The principal obstacle to the construction of the proposed spectrum

system is the various delay operations which must be performed Figure

on the signals in the receiver. which,

spread-

though

2.6

shows

a

receiver

model

convenient for analysis, is both wasteful of delay lines

and probably non-implementable with currently available technology (C9]. The problem here is one of time-bandwidth product; broadly speaking, delay lines with wide bandwidth are of short duration, and those with long duration

tend

to

be

narrowband

devices.

The

combination of broad

bandwidth and long duration is a difficult goal to

achieve

technologi-

cally. Fortunately, in a linear system signal operations are so

that

such operations as delaying and filtering (and even, with cer-

tain caveats, frequency translation) can This

commutative,

implies

be

performed

in

any

order.

that many possible implementations of the receiver struc-

ture must exist; hopefully some subset of them will be capable of implementation

using

current

technology.

Much of the following is adapted

from an implementation feasibility study by Cooper and Grybos [C9J. Possible implementations fall into two main categories, which be

termed

operations.

c

operation.

delay-filter

and

will

filter-delay to indicate the order of the

Both may include frequency

translation

They are discussed separately below.

as

an

additional

During the discussion,


- 197 -

c

expressions for certain quantities are followed in curly brackets { } by a numerical Rb

= 30

example

using

the

parameters

n = 32, B = 20 MHz, and

kb/s. A2.1

Delay-Filter Receivers

A typical member of this category is shown in Figure A2.1.

Such an

implementation appears to be very attractive because it uses only a single, tapped delay line.

However,

this

delay

line

requires

a time-

bandwidth

product of (2n-1)Bt 1 , {or 6 562}, since all time-chips of all frequencies must be handled by the device. Probably the only class of delay line

bandwidth

products

currently

are

the

able

to

offer

surface-acoustic

such

wave devices

(SAWs), of which several types are currently available [G4].

(

bandwidth

product

suggested

here,

though,

is

right

perhaps

300

~s

are

on

be

avail-

Signal

strength

loss

is likely to be in the tens of dB, requiring large

driving power and compensatory amplification. cities

time-

In any case, there are addition-

al problems with attenuation and physical S1ze. over

The

at the edge of

state-of-the-art experimental components, and is unlikely to able in production form for some time.

time-

Typical propagation velo-

the order of 3 km/s, so that the physical length of the

wave path would be on the order of 1m.

Although "folding" is

practiced

in delay-line technology, its is unlikely that the required SAW could be made small enough to be practicable. Hence implementation of delay-filter receivers does not be a promising avenue at the present time.


appear

to


:'~

(*~

,.~,

Signal in Tapped tl fn

I

~

-- - - I

I I f n-l n- 1 I

Delay Delay

(n-1)ttl ~ (n-l) 1

nt 1

Bandpass

-- - ...

Line (2n-l) tl

Fil ters

I

fl f1

I I

fn

....-0 00

.. - -

--

Product detectors

To lowpass filtering and other functions as in Figure 2.5

Figure A2.1

Typical delay-filter receiver

- 199 Filter-Delay Receivers

A2.2 A typical this

Although

member

of

this

category

of

shown

in

Figure

A2.2.

implementation appears to be clumsy because of the large

number of delay lines involved, it is terms

is

current

technology.

nevertheless

more

practical

in

This is because each delay line handles

only one time-chip pulse of bandwidth (say)

2/t1~

so

that

the maximum

is now only (nt 1 )(2/t ) = 2n {or 64}, 1 which is readily available from a variety of delay devices, including required

time-bandwidth

product

coupled devices (COOs).

charge

circuits [S9], so that using every

reason

to

The latter are fabricated as integrated

large-scale

integration

(LSI)

there

is

suppose that all (2n-1) delay lines could be combined

into a single chip and manufactured at a reasonable cost. COOs are, however, inherently low-pass devices, so

(

that

frequency

translation to either zero or a very low carrier frequency would have to be employed.

There is, in any case, a pressing reason

to

employ

low-

frequency delay lines for the present application, and this is discussed in the next section. A2.3

Receiver Stability

A mobile unit is likely to changes,

particularly

be

subjected

to

if it is vehicle-mounted.

drastic

temperature

The temperature range

for vehicular mcdels might conservatively be estimated at +50 0 C from its median

value.

Hence

stability with respect to temperature ;s a major

concern in mobile unit design. The differential phase modulation feature of implies

that

there

be

between set) and s(t+T).

a

fixed

number

the

proposed

scheme

of cycles of burst frequency

This means, specifically, that the delay T em-


- 200 -

Signal in

f

Bilndpass f i 1tl'rs n

r1

Delays

T

T

-

Delays

-

Product detectors

To lowpass filtering and other functions as in Figure 2.5

Figure A2.2

Typical filter-delay receiver

(-


T

- 201 ployed in the receiver' should not change by more than a few burst

degrees of

signal.

At 900 MHz, a single cycle lasts approximately 1.1ns; if stability of, say, +1n o is considered adequate, then T must be accurate

to +0.031ns {or 0.1833 parts per million}.

SAW devices have temperature

coefficients ranging from 1 to 100 ppm/oC, which implies that they would have

to

operate

in a temperature - controlled environment, or in con-

junction with extremely elaborate temperature - compensation systems, if the device was to operate

at-~arrier

frequencies.

Translation to a lower frequency would help only to a In order

tent.

to

retain

phase

occur;

and

in any

SAW devices operate best in the 10 MHz - 1 GHz range CG4J.

the SAW again appears to be a very poor choice for the present

(

ex-

information, the carrier frequency

should not fall below, say, 1ft1 or aliasing would case,

limited

Hence

applica-

tion. CCDs, however, have delay lengths which are dependent only upon the clock

frequency

and

the

number

of

"bins" in the device.

Since the

latter is a fixed integer, the stability problem is then transferred

to

the problem of clock oscillator stability, which is far more easily controlled.

(Indeed, if necessary a control loop could be used,

utilizing

some signal derived from the base station.> The problem could be helped by translating the signal frequency.

to

a

In fact, if a "complex envelope" procedure were used, trans-

lation to baseband (zero frequency) would essentially eliminate the lay

line

stability problem.

plex envelope receiver. performed

lower

de-

Figure A2.3 shows what is meant by a com-

Frequency translation of each frequency slot is

simultaneously by two quadrature versions of the same local-


- 202 -

Signal in

--------4t------- - - -- --

O--... 0 - -....- - - - - -...... - - - - - - - - -

f

Bandpass filters

f n- 1

n

sin 2nf n- lt~~~ lto-~~

---'"" .. --(~ cos 2nf 1 t nLPF

Quadrature branch

LPF

Lowpass f 11 ters

In-phase branch

tl

(

Mixers

T

Delays

Delays

T

Product detectors

Adders To co-ordinate rotation and other functions as in Figure 2.5

Figure A2.3

Complex envelope filter-delay receiver


- 203 oscillator signal, so that the. resultant lowpass functions represent the real

and imaginary parts of the complex envelope of the incoming signal

with respect to the local oscillator frequency [FSJ.

The two components

are then delayed and multiplied separately and the resulting signals added and delivered to the linear combiner.

(It is left to the interested

reader to demonstrate that this procedure is mathematically identical in result to the procedure in Chapter 4.) The fact that the receiver of Figure number

(4n-2)

{or

A2.3

requires

a

prodigious

126} of delay lines is passed over for the present

with the comment that surprisingly complicated devices

have

been

con-

structed in recent years using LSI techniques. The only remaining question with respect to the complex-envelope

(

stability. problem

receiver

relates

stability of

to the question of local oscillator

This matter is essentially the same

alluded to in Chapters 3 and 4.

as

the

the

criterion

of

coherence-time

Specifically, the phase of the

local oscillator must not drift outside certain limits

If

within

time T.

+10 0 stability is invoked, this implies that the

frequency error of the local oscillator must not exceed +1/36T Hz, +167 Hz}.

the

{or

{At 900 MHz this represents a stability of +0.2 ppm.} Clearly

this requirement may be met with careful design, even if it is necessary to

employ a control loop locked to some transmitted reference to accom-

plish the objective.


(

VITA

('........


- 204 -

VITA

Raymond W. Nettleton was born in London, England on He

entered

the

~arch

22, 1945.

United States in August, 1972 and graduated Magna cum

Laude from the University of Dayton in May, 1974.

He

was

awarded the

degree of Master of Science in Electrical Engineering by Purdue University in May, 1976. the

His professional activities have

biomechanics of

heart

muscle;

blood

included

cations.

communi-

He is a member of IEEE and Eta Kappa Nu.

Mr. Nettleton has been married to the former since

on

flow measurement using ul-

trasound; optical radar; array processing; and spread spectrum

(

work

December,

1971.

Jenny M.

Winstanley

Their interests include music and gourmet cook-

ing.

c Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.