Network Simulator Definition - DTIC

0 downloads 0 Views 757KB Size Report
Oct 13, 1989 - COSATI CODES. 18. ... of discrete conditonal probability density functions (pdf's) for a phase state variable shall be ... order to produce a phase reference or estimate, S(n). Here. the ..... used for sifting or masking some of the.
t; 71

,

" ",

1

I,4CT...1,8-7

Fir aI Technical Report 00,66w 10W

NETWORK SIMULATOR DEFINITION cV) (0 0q

1 frmacise University

Dr. Pramod K. Varshney

APPROVED FOR PUBLIC RELEASE; DISTRIBUT ION UNUMITED

.. EA..T1 E E

OCT 13 1989

ROME AiR DEVELOPMEN1 CENTER

Air Foc c. Systems Cummand Grifflss Air Force Base, NY 13441-5700

89 10 18 048

This report has been reviewed by the RADC Public Affairs Division (PA, and is releasable to the National Technical Information Service (NTS). At NTIS it will be releasable to the &eneral public, including foreign natiorvs. RADC-TR-89-167 has been reviewed and is approved for publication.

APPROVED:

/U1

~

JOHN B. EVANOWSKY, Ph.D. Project Engineer

APPROVED: JOHN A. GRANIERO Technical Director Directorate of Coumunications //

FOR THE COMMANDER:

M1 JAMES W. HYDE III Directorate of Plans & Programs

If your address has changed or if you wish, to be removed from the RADC or if the addressee is no longer employed by your organization, mailing list, This will assist us please notify RADC (DCLD ) Griffiss AFB NY 13441-5700. in maintaining a current mailing list. Do not return copies of this report unless contractual obligations or notices on a specific document require that it be returned.

UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE

Forwm Alllr

REPORT DOCUMENTATION PAGE

419N.

q

0701

lb. RESTRICTIVE MARKINGS

Ia. REPORT SECURITY CLASSIFICATION

N/A

UNCLASSIFIED

3. DISTRIBUTION/AVAILABIUTY OF REPORT

Za. SECURITY CLASSIFICATION AUTHORITY

N/A

Approved for public release;

2b.DICLASSIWICATIONI DOWNGRADING SCHEDULE N/A

distribution

4. PERFORMING ORGANIZATION REPORT NUMBER(S)

unlimited.

S. MONITORING ORGANIZATION REPORT NUMBER(S)

N/A

RADC-TR-89-167

6a. NAME OF PIERFORMING ORGANIZATION

Sb. OFFICE SYMBOL 6

W.I

Syracuse University G. ADDRESS (Cl, Stato, and ZIP Code)

7&. NAME OF MONITORING ORGANIZATION

Rome Air Development Center (DCLD) 7b. ADDRESS (City, State, and ZIP Code)

Griffiss AFB NY 13441-5700 Syracuse NY 13244 8 b. OFFICE SYMBOL

0& NAME OF FUNDING/SPONSORING

ORGANIZATION

9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER

(f appa(k)

DCLD

Rome Air Development Center

F30602-81-C-0169

C AOORESS(Cy, Stan,and ZIP Code)

10. SOURCE OF FUNDING NUMBERS

Griffiss AnE NY 13441-5700

PROGRAM

ELEMENT NO.

NO.

63789F 11.TiTLE (NIC,,'

WORK UNIT

TASK

PROJECT

ACCESSION NO.

NO

2747

1A

02

P8

Secu,,y aaaf, am)

NETWORK SMIMUATOR DEFINITION 12. PERSONAL AUTHOR(S)

Pramod K. Varshney 114. DATE OF REPORT (Year, AotEh, Day)

13b. TIME COVERED

13a. TYPE OF REPORT

IS. PAGE COUNT

To Sep,87

36 October 1989 IS SUPPLEAENTARY NOTATION Figures are out of sequence because they are part of a more comprehensive report which will entail a stressed tactical communication network being designed for PC's Netwok Dsin Laboratory FROMOCt 86

Final

17.

COSATI CODES FIELD

GROUP

SU-ROUP..-

0

25

18. SUBJECT TERMS (Com ome on revere ,f nhctry and edeef by,bfck number) Networks))

-- C99.JIqCjao1

-Ciest and Evaluation

~~SimulationIaIKz

02 19. ABSTRACT (Contbiue an rtvers if ihEmC6wy and, oden fyby 11-c, numbr)

A white paper was delivered to RADC which provided a detailed analysis of a technique utilizing state transition probability matrices that provided a reali~tir-model-of a digital coounlcations channel. As such, the technique offers a computationally viable method for implementing a large number of realistic channel models. This work

will feed or transition to efforts eventually implementing this technique to perform network survivability analyses. The results will be incorporated in more comprehensive reports resulting from this work and in the actual implementation of these techniques in RADC s Network Design Laboratory. 7- h

20, DISTRIOUTION/AVAILBILUTY OF ABSTRACT M UNCLASSIFIEDAINUMITEO 03 SAME AS RPT

22a. NAMI OF RESPONSIBLE INDIVIDUAL

Dr. John B. Evanowsky DOrfa, 14ji.

JU14 &6

21. ABSTRACT SECURITY CLASSIFICATION

C

OTIC USERS

UNCLASSIFIED 22b.TELEPHONE (/oIduo Ae# Cock)

(315) 330-7751 PVreW@a11omwe 0611101

22c. OFFICE SYMBOL

AX (DCLD SECURITY CLASSIFICATION OF THIS PAGE

UNCLASSIFIED

UNCLASSIFIED

UNCLASSIFIED

A DECISION DIRECTED PHASE ESTIMATOR MODEL

INTRODUCTION The objective of this effort was to develop techniques for modeling digital errors which occur in a communication system.

The model was to be

computationally efficient for applications which require a large number of replications of the model such as a communication network analysis. In this effort, an important component of a digital communication system, namely a digital phase-locked loop was analyzed.

The analysis produced a stochastic

model of the digital error producing process associated with the system.

A

state transition probability matrix formulation was used which allowed the calculation of a variety of digital error performance measures. In this leport, an analysis will be performed of a digital phaselocked loop.

Using standard analytical procedures and assumptions, a set

of discrete conditonal probability density functions (pdf's) for a phase state variable shall be developed.

This will then form the basis for a

state transition matrix formulation which will be used to calculate vari>Lprobability of error statistics. The standard cross-correlation demodulator described in the literature implies that a carrier with proper phase is present at the receiver. In practice, the correct phase must be determined at the receiver.

One

popular technique for performing this function is the decision directed phase estimate.

It finds its place in this report because of the "memory"

it imparts to the error producing process.

'

-1-

.....i''" a ro e

i ,, " -

t

I

tI

'

Ci n I

are

There be

might

ind

assumed

an

to

be

the

before,

considering received

SYSTEM

A

at

gnsumed spectral used

to

of

presentation,

demodulator

the

shall

of

which

decision will

requires

a

phase

That

iS,

is

system

transformation

phase

by

analysis

receiver.

only

the

the

This

the

assumed.

be

demodulators

phase

of

as

reduced

being

technique

for

vector.

implementation shown

introduced with

input to

clarity

For

dimensionality

signal

is

along

the

a demodulator

MODEL

estimator

s(t),

at

be

of

multiple

to

will

performed

demodulator

generated

typical

notation

be

additive

of

noise

phase

Drevions.Lv.

any

for

useful

of

preser':e

transformation

described

as

reference

the

keyed

appropriate

boundaries

by

will loop.

shift

the

only

that

noise

phase

of

causes

source

applicable

is

analysis

prove

the

analysis

an

phase

binary

using

as

noise

a phase-locked

employing

The

Here,

hypothesized.

white Gaussian

a

underlying

many

be

the to

generate

of an

Figure

a decision 6.

earlier, additive the

white

density

in

of

noise

noise

A reference

in-phase

-2-

and

with

transmitted

waveform,

The

with

phase

Consistent

waveform,

demodulator.

Gaussian N 0.

the

directed

a

z(t),

additive two

sinusoidal

quadrature

is

the

shown

noise

sided

power

waveform

signal,

is

each

is of

0

ldU4 E-4~

411w

410 0.j

*

OE-4e "ID

U-3

C

S

O

I

E

T

D

q

S

SIUA

J

v,

which

signal

vectors.

time

is

n

The

given

in

dissertation,

should

equal

In

the to

equal

is

received converge

phases.

is

to

order

to

the

first-order

the

decision

process.

by

a voltage

received

previous

at

vector

signal

received

this

for

voltage

the

of

vector,

signal

generated

control

received number

phase more

vector.

the

vector

Thus,

as

-reference,

An

one

an

shown

-4-

of

of

or

the

used

should

phase,

or

i(n),

technique

Figure

,

the

This,

of used

signal

loop

phases,

modeled 7.

is

received

estimate,

be

for

measurement

digital

received

shall in

the

analog

reference

filter

phase

averaging

value

sequence

phase

loop

network

signal

2aE.

than

Typically

a

being

viewpoint

the

to

due

expected

process

produce

Here.

on

signal

vector used

the

based

to

is

required

zero.

general,

demodulator

the real

the

ideally

these

]/Re[v(n) ])

that

before,

from

ideally

of

by

Recall, this

the

the

of

phase

tan 1'(Im[v(n)

(n)-

in

phases

the

using

generated

is

VCO

received

The

(VCO).

os,!illator

controlled

the

reference

phased

properly

This

used

be

ultimately

will

of

phase

correct

the

assure

to

phase

is

estimate

phase

accurate

An

waveforms.

reference

each

of

argument

the

in

used

is

$,

estimate,

A

integrator.

cross-correlation

a

in

used

is

which

filter

4(n),

in

S(n).

as of

a digital course,

FII~ST ORDER

LOOP

-5-

FITER,

computes

values

for

the c

a(nT)-

The

transfer

been

derived

first-order

in

for

textbooks

the

system

such

equation:

0(nT)

(nT-T)+

function

difference

as

Gold

shown

in

Figure

and

[1969]

is

7 has given

by jwT H(e

-1/2 )=(i

c-2c

-I

coswT)

exp[jwT-jtan

(sinwT/(coswT-c))!, (4-1)

This

function

in

terms

T.

Note

that

one-half

the

the

of

loop

the

wT(n),

is

random

expressed

phase

model

of

the

filter

discussion

)f

coefficient

c0

c

c

(n)

loop

The

expected (n).

An

the

(n).

filter

which

correct

phase

value

of

the

implementation

random

sequence.

the a

filter,

generic

(4-3)

h(n-1) l

controls

pass

is

recursive

using

the

variables,

reference. the

of

as



lw

random

phases

0

coefficient

of

to

input loop

4(n)-

The

implementation

first-order

equal

sequence

the

digital

the as

first

normalization

-10-

roll-off indicated order factor

frequency

for

the

in

the

filter.

The

earlier

digital which

assures

that

each phase

estimate

;s

a~sc

defined

relationship

satisfies in

the

some

very

coefficients

are

it

is

that

for

the

known low

pass

case,

respectively,

that

if

as

zero, the

the

Co.1,

and

digital

approaches

1,

filter

approaches

zero.

c l1

and

0(n-l)= (n)-

phase

initial

for

phase

previous

From

c1

i.e.,

then

demodulation

limiting

the

c 0=0,

properties filtering roll-off

the

theory,

frequency

Therefore,

Equations

of

4-3

in

this

and

4-2,

yield

the

the

correct

following

the

(4-4)

considered.

(n)-

is,

],

' (n)

1

interesting

O(n)-

That

(-rv

Since

-T.

-

0

limiting

region


i}

3

composed

of

five

probability

of

falling

given

by

Equation

segments in

}

as

any

is

defined is of

in

noted Equation

a result the

of

random

S(n-l).

(In

given

a

the

is

fact

chat

variable,

of

an

4-10.

the

4-12

Example

probability Equation

that

$(n-l). this

error

is the

previous

P(error(n)I$(n-l)=$

>

is than

4-15

equal

to

c 0 N/4

previously provide

the

states the

states

the

computed

probabitity

of

error

probability.

This

step state

-21-

is

a

function

particular

value

of

calculated

using

of

a

error

as

follows:

number

estimate

-

>

c

a

$3)

symbol

the

(4-15)

N/4)

of

transition that

was

0

probability

Recall

single

symbol

probability

of

Example

a

(n)

probability away.

a

.

that

a

of

value

1.

Equation

these

particular

phase

P(

of

probability

For

4.1,

Express

particular

conditional this

of

in

4-10.

probability

a

shown

one

End

It

(4-14)

3

the

transition

a symbol to

a state

components matrix,

transitions.

error more

of

F1

However.

the

(7 i the

computation single more

in

step than

Squation transition

c 0 N/4

representation the

set

S

of

j for

l,..,N;

the

that

modulo

these

integers

uses

matrix

states,

of

(j,

(i)-

4-15

produce N.

elements, each

such

i

that

elements

For

define

such

a

of

this

transition a

of

convenient

the

set

Sj.i)

as

that

>

ji-jl

c

j

N/4.

modulo

N)

0 ( 4- 16)

Now

Equation

components

of

4-15 the

can

single

be step

expressed

in

tran-ition

matrix

terms

}=

P(error(n)j$(n-l)= i

f

the

(4-17) S

(i)

j

J

The

average

arbitrary

Pu e

time

n

probability is

given

of

a

symbol

vector,

P(inf]-

previous 4-17,

the

into

phase

components (Pi(inf)},

estimate

Equation

4-18

Pe, e'

at

an

by

N Z P(error(n)I$(n-l)-O > P(O(n-l) =il i

Substituting

error,

of for

0(n-1), yields

-22-

the

steady

the and

(4-18) i

state

probability

distribution the

results

in

of

the

Equation

N P

p

=

e

This to

equation

the

sum

state

relates

of

than of

relationship

S

that

the

C 0 N/4

being in

in

a

(i)

transition

units

state

matrix

j

probability

of

(4-19)

1

(inf)[ i

probabilities

more

probability

i1

i.

of from

away, In

form,

error

is

state

weighted

order define

equal

i to by

to

express

the

matrix,

a the

this S,

as

fol lows

S-

} where

(s ij

Thus, the

ij

for

those

values

corresponding

Example

I for all li-jl < ( 0 otherwise

s

4.1

The

i and

element

of

the

j

for

c N/4 0

which

matrix

is

(4-20)

an

error

equal

matrix

S

for

1 1 1 1

this

1 1

I 1 0 0 0 1 1 1 o 0 11110001 1 0

1 0

example

is

given

order

product

to one.

by

1 1 1 1 1

1 1 0 0 1 1 1 0

; N

8,

c

=.5, 0

c

N/4=

to

use

operation,

the

I

0

0 0

(4-21) End

In

occurs,

Continued

00111110 0 0 0 1 10001111 S=

of

>

matrix,

referred

S, to

-23-

a as

relatively

of

Example

unorthodox

congruent

matrix

multiplication rules used

of for

matrix. matrices,

is

used.

standard

matrix

sifting

or

It

term

is

A

a

and

C=

B,

A*B

This

defined

c

;

J

The

can

be

the

NxL

average

now

of

is

the of

not

follow

simply

a device

components two

the

of

identical

a

order

; i,j-

l,..,N

(4-22)

ij

vector of

with error

in matrix

Ptinf ] (-l*S)

-

It

product

b ij

probability

P

does

by:

a

column

be expressed

some

term

ij

Let

algebra.

masking by

operation

all

elements

derived

in

equal

to

Equation

1.

4-19

form as

J

(4-23)

e

As

alluded

dissertation certainly chapter.

error

time.

the An

resulting bit

is

from given

given

earlier, error for

an

measure

an

the

is

error

probability

major with

phase-locked

this memory that

the

models

the

excellent

This

n

on case

Equaticn 4-18, time

to

of

the

the

be

probability of an

error

at

the

previous

-24-

of

memory. loop

This

model

error

this

in

is this

dependence

average probability of

occurred

will

focus

in

the

calculated error at time

n-1

previous

next. an is

a

bit

As

in

arbitrary given

by

P

! error(n-l)>

P(error(n) ele

N

Z

> P($(n-l)= $

P(error(n)J$(n-l)=

i~1

i

error(n-l)> i

(4-24)

The

last

expression

is

the

result

version of

the Chapman-Kolmogorov

process.

That

dependent only probability second

estimate

ends,

occurs.

This

which

to

rather

process present

at

problem.

these

developed.

In

used

for

corresponding

in

is

Before

is

more

inverse of

the

last

given

past

known.

is

problem

this

development,

each of

the phase

times:

-25-

when

the

is

the

phase

an

error

problem scived the

transition

current

to

of

problem, the

given

that

is the

inference

be evaluated,

transitions

The

in each state of

calculated

This

first

the probability

the

system was

Equation 4-24 can phase

and

compute In

n is

It

that $.

to

The

development.

at

used

time

Equation 4-17.

begins,

the

the

by

probability

was

Markov-l

estimate.

given

phase state.

that

concerning

be

the

was

next

state

phase

the

state

matrix

a time

at

than

just

probability

probability of error

requires

phase

the

a

4-24

is

equation

the discrete

for

previous

this

is

a

probability

the

the

probability that

jumping

on

the

in Equation

observed

in

is,

of applying

the

following

estimates 4 at

some

its

theory

past must indices the

be

shall

following

.

, 4(n)

(n-1)=O

,

4(n-2)=4

......

k

(4-25)

.....

j

i

Let

Then, p (n-2) iT (n-2,n-1) ki k (n-l,n-2) -.-------------------p (n-1) ik

(4-26)

i

As

forward and that 3-19

the

is

substituted

chat

assume

Equation

steady

state

so

limiting

state

probabilities

in the the

and

applies

single-step Also,

probabilities.

backward transition

process

the

for

dropped

is

argument

the

usual,

are

yielding

in Equation 4-26,

p (inf) k ik

Now the

--

-

p

(int)

return

i

(4-27) ki

4-24.

to Equation

second conditional

discrete

Using Bayes

theorem on

probability distribution:

error(n-1))-

P(Vn-)*$ i

(4-28) P(error(n-L))

Considering

each of

the

terms

on

-26-

the

right

hand side:

P>=(n-l)

p (inf)

i That of

is,

this

the phase

is the

P{error(n-l))}

Finally,

the

last

N E k 1

)

an

error results

conditioned

value "from"

This

probability

probability first in

Equation

the steady

in the

p (inf) k

steady

S

state:

z (k)

(4-30) ki

i

term:

i

is,

state probability distribution

Also,

P = e

P(error(n-l)J$(n-l)=$

That

.i

steady

estimates.

(4-29)

uses

the

discussed 4-26,

=

2 S (i) k

if

the

p

(n-l,n-2)

phase

a phase estimate inverse earlier.

then Equation

state:

-27-

(4-31)

ik

jumped

cON/4 units

single

step

Therefore, 4-27

"to"

into

the away.

cransitio.n substituting

Equation

4-31.

p (n-2) k

-k p (n-1) i

P(error(n-l)j$ n-1.-4 S (i) k

(n-2,n-l)

I

ki

p (inf) k

(4-32)

---

S (i) k

Now,

p (inf) i

4-32

and

substituting Equations 4-17

ki

into

Equation 4-24

IT

p (inf)

yields:

p

(inf) k

N

-

---

S (i)

i-1

j e

N Z k-I

e

p

i

z S (k)

(inf) k

ki

(inf)

p

S (i) k

ij

ki

i N Z

[

(inf ) -r

p

T

j

ki

k

S (i)

ij

S (i)

i--

k --------------------------------------P

(4-33)

e

Thus, the

the

previous

probability dependent

bit matrix

errors

can

has

been

given

an error

calculated

using

a transition

formulation. be

computed

-28-

in

an error

probability of

average

Other

in a similar

measures fashion.

for

MISSION of Rome Air Development Center RADC plans and executes research, development, test and S selected acquisition programs in support of Command, Control, Communications and Inteligence (C1) actities. Technical and S engineering support within areas of competence is provided to ESD Program Offices (POs) and other ESD elements to perform effective acquisition of C! systems. The areas of technical competence include communications, command and control, battle management information processing, surveillance sensors, intelligence data collection and handling, solid state sciences, electromagnetics, and propagation, and electronic reLiabdity/maihtainabilityand compatibility.

a?