NAT'L INST. OF STAND & TECH

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**»eAU °* *./ NBS TECHNICAL NOTE 1077

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

-QC

100

.115753

No. 1077

1985
TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

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MD, unless otherwise noted; mailing address
Cr WSS

lNFORMATlZ,

QCkDO

Transparent Metrology of Signal to Nois^S^

Ratios of Noisy Band-Limited

Digital Signals

Donald Halford

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued June 1985
National Bureau of Standards Technical Note 1077

Natl. Bur. Stand. (U.S.), Tech Note 1077, 32 pages (June 1985)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1985

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
CONTENTS

Page

1 . Introduction 1 2. Transparent Metrology and Correct Measurement Procedures 3 3. Measurands for Digital Signal Power to Additive Noise Power Ratio 4 3.1. Varieties of Digital SNR 4 3.2. SNR and Its Generic Relatives 8 4. The Template Method for SNR 9 4.1. Statement of the Problem 9 4.2. Measurements Using a Template 1(1 4.3. Data Analysis for SNR 12 4.4. Comments on the Measurements 16

5. Remarks 17 5.1

Significance 17 5.2. Applications 17 5.3

Comments 18 5.4. Further Work 18

6 . Summa ry 19 6.1. Template Method for SNR 19

6 .2

Revi ew 20

7. Acknowledgments 20

8. References 20

Appendix A: Confidence of Measured SNR 23

Appendix 8: Glossary 24

Transparent Metrology of Signal to Noise Ratios

of Noisy Band-Limited Digital Signals*

Donald Halford

Center for Electronics and Electrical Engineering

National Bureau of Standards

Boulder, Colorado 80303

I propose the use of a template method for quantitative, correct, and transparent

measurement of signal power to additive noise power ratios (SNR) of digital signals

and systems under full operating conditions. Outer guard chips of digital templates

hold intersymbol interference fixed on inner target chips in realizations of the

respective template patterns in traffic. The proposed template method needs to be

developed and proven as a potentially valuable metrology capability; it can be

especially important for real time online performance assessment and monitoring of

digital communication systems.

A covvect measurement procedure by definition actually measures a specified

parameter of a specified signal, channel, device, or system. A transparent

measurement procedure by definition measures the specified parameter without

degradation of the usable channel capacity and without modification to or interference

with the functioning of the measured system.

I discuss the significance of transparent metrology, the measurement of various

SNR's by the template method, and the general applicability of the template method for

measurements on any noisy digital signal. The template method can provide transparent

metrology procedures for other basic measurands, e.g., intersymbol interference,

multiplicative noises, and synchronization.

Key words: communications; correct measurement procedure; digital signals; energy per

bit to noise density; monitoring; noise; online measurements; performance assessment;

real time; signal to noise ratio measurement; template method; transparent metrology.

1. Introduction

Noise and distortion affect the quality of performance of advanced digital communication

systems and place upper limits on the information carrying capacity of digital channels. Some

relevant basic quality parameters [l]-[7] for noise and distortion of digital signals are signal

*A talk on this topic was presented at the XXth General Assembly of the International Union of

Radio Science (URSI), Washington, D. C, 10-19 August 1981 [8].
power to additive noise power ratios (SNR), intersymbol interference (ISI), dispersion,

multiplicative noises, and synchronization. See table 1.

Table 1. Some basic noise and distortion measurands for digital signals,

channels, devices, and systems

1. ADDITIVE EFFECTS (RANDOM AND DETERMINISTIC):

1.1. Digital signal power to additive noise power ratios (SNR, CNR, C/N

Q

, C/kT, E

b /N

Q

,

E chip/ N 0)

Note: Additive noise power, as operationally defined here, includes power from any

additive interference which is uncorrelated with the signal.

2. DISPERSION:

2.1. Intersymbol interference (ISI)

2.2. Group delay dispersion (GDD)

2.3. Amplitude response dispersion (ARD)

Note: Dispersion, as defined from a measurements point of view, includes effects which

arise from the presence of any time invariant, additive interference which is correlated

with the signal .

3. MULTIPLICATIVE EFFECTS (RANDOM AND DETERMINISTIC):

3.1. Incidental amplitude modulation (IAM)

3.2. Incidental phase modulation (IPM)

3.3. Synchronization offset and jitter

Note: Incidental modulation, as defined from a measurements point of view, includes

effects which arise from the presence of any time varying, additive interference which

is correlated with the signal.

Definitive measurements of these quality parameters are needed for design and redesign of

digital communication systems, operational monitoring of performance, impairment detection,

technical control of systems (e.g., channel power allocation, impairment isolation), and for proof

of performance for contractual purposes. Standards of performance for specifying quality of

digital equipment and signals should be based in part upon measurements of these quality

parameters

.
It is important that it be possible to measure such parameters by practical procedures which

are quantitative, correct, and transparent. For discussion, see section 5.

In this paper I propose the use of a template method for explicit measurement of digital

signal power to additive noise power ratios of noisy, dispersed (e.g., band-limited) digital

signals. For a concise description of the template method, see section 6.1. The measurements can

be quantitative, correct, and transparent. They can be made in real time on working systems in

full operation and carrying any digital traffic. I propose these concepts as an advance in the

state of the art of the science of metrology [8].

In related work, Grabowski and Davis have described the use of digital patterns (templates)

at baseband for a novel adaptive equalization technique [9], Jankauskas and co-workers have

developed the Adaptive Channel Equalizer which estimates signal to noise ratio and other

parameters of an in-service digital communication system [10]-[12], Milstein has discussed the

importance of correct measurement procedures [13].

The concepts of transparent metrology and correct measurement procedures are presented,

defined, and discussed in section 2. The existence of and relationships among various measurands

for digital signal power to additive noise power ratio are presented in section 3. The template

method as applied to the transparent measurement of digital signal power to additive noise power

ratios is introduced and described in detail in section 4. The significance of these concepts is

discussed in section 5, together with indicated applications of the template method for

transparent and correct metrology of SNR. I also comment on further work to be done on these

metrology concepts and methods. Section 6 summarizes the proposed template method and gives a summary review of the paper.

2. Transparent Metrology and Correct Measurement Procedures

A correct measurement procedure by definition actually measures a specified parameter (rather

than a proxy for the parameter) of a specified signal, channel, device, or system (rather than of

a proxy for the signal, channel, device, or system).

A transparent measurement procedure by definition measures the specified parameter without

alteration of its value; without modification to or interference with the functioning of the

measured signal, channel, device, or system; and without degradation of the usable channel

capacity.

The availability of metrology methods which are transparent and correct would mean that one could measure the desired quantities in the specified system under full operating conditions.
Proxies for parameters, signals, channels, or devices are not required . The system can be

carrying any digital traffic. Such non-disruptive in-service measurements can be online and yield

results in real time. All channels are fully in service; the measurements do not require any down

time. Such measurement results are especially valuable because they are valid for the actual

signal in the actual system under the actual operating conditions at the actual time of interest.

Generally speaking, many existing and proposed measurement and estimation methods for digital

signals are transparent. Some examples include signal to noise ratio [4]-[5], [11]-[12], [16],

out-of-band noise [3], [6], [14], received signal level, eye pattern [3], [6]-[7], [17], pseudoerror [3], [6], [11], [18]-[21], channel tap gains [10], [12], timing jitter [l]-[3], [6]-[7], and

partial response format violation [3], [6], [21]-[22].

The concept of correct measurement procedures, defined at the beginning of this section, is useful in discussions of transparent metrology procedures [8], [13], The terminology is adapted

from computer science, which uses the concept of a correct algorithm [23]-[26] . For illustration,

the eye pattern measurement procedure [3], [6]-[7], [17], properly implemented, is a correct

procedure for measuring eye pattern. Furthermore, eye pattern measurement is a transparent

metrology procedure. Although it is practical and very useful, and it is affected by many basic

parameters, eye pattern does not separate SNR, ISI, and other basic parameters from each other.

Eye pattern is not a correct procedure for measuring SNR, nor for ISI, nor for incidental

amplitude modulation, nor for any of the other definitive basic measurands shown in table 1.

I note that while many useful measurement procedures in common use in digital communication

systems are indeed transparent and practical, their object measurands often are not basic ones.

They often are not correct procedures for specific definitive basic measurands of primary interest

such as those of table 1.

3. Measurands for Digital Signal Power to Additive Noise Power Ratio

3.1. Varieties of Digital SNR

There are several varieties of signal to noise ratio (SNR) measurands which are relevant to digital signals [l]-[2], [4], [6], [12], [16]. Some appropriate and useful examples are described

in this section.

The choice of the most appropriate varieties of SNR measurands for any particular digital

signal or system depends upon how the signal is used and what aspects of the digital signal are to

be characterized. For example, in some receivers the decision device samples only the center of a

Proxies are often used in measurements when it is difficult or impossible to measure the desired

entity directly. One common method [14] used for determination of ratio of carrier power to noise

power density (C/Nq) of a specified channel is to measure directly two quantities: (a) the level

in the specified channel of the carrier together with the noise and (b) some other noise level in

a frequency band adjacent to the specified channel. The latter then is used as a proxy for the

noise level in the channel in the algorithm for determining C/Nq for the specified channel. In a correct measurement procedure for C/Nq of a specified channel, the noise in the channel per se is what would be determined. For other methods using proxies, see [5] and [15].
chip . See figure 1(a). In such a case, an appropriately defined point SNR at the center of the

chip is a useful quantity to measure and specify. For an integrate and dump (I/D) decision device

[1], an SNR of the integrated chip signal developed by the"\I/D decision device is appropriate.

See figure 1(b). For general use, e.g., in charts of bit error rate (BER) versus ratio of energy

per bit to noise power density (E

b /Ng), an appropriate E

b /Ng [1], [5], [16] is one defined over

the entire composite signal. Additional varieties of SNR can be defined and used as needed.

In the following discussion of possible measurands for digital signal power to additive noise

power ratio, I assume the composite signal to be measured is a dispersed digital signal corrupted

with additive random white noise. For simplicity, I assume that the undispensed digital signal

contains sequences of chips which are binary and bipolar and that there are no other corruptions

of the composite signal.

3.1.1. SNR of a Point in an Environment (POINT SNR LOCAL)

Consider the specified chip state sequence, <A B C T X Y Z >, for any specified chip states,

A,B,C,T,X,Y,Z. Consider the SNR at a specified point in the target chip T. POINT SNR LOCAL is a local measurand; that is, it depends upon the target chip T and upon the chip environment,

< A B C - X Y Z >, of the target chip.

POINT SNR LOCAL =

square of:

digital signal amplitude

at specified point

mean square fluctuations of:

composite signal amplitude

at specified point

1)

The target point is any specified point in the target chip T. The target chip T has any specified

chip state. The chip environment of the target chip is any specified sequence of chip states.

3.1.2. SNR of a Chip in an Environment (CHIP SNR LOCAL)

Consider the specified chip state sequence, <ABCTXYZ>, for any specified chip states,

A,B,C,T,X,Y,Z. Consider the SNR of the specified target chip T. CHIP SNR LOCAL is a local

measurand, that is, it depends upon the chip environment, <ABC-XYZ>,of the target chip T.

CHIP SNR LOCAL =±

square of:

digital signal amplitude

averaged over target chip

mean square fluctuations of:

composite signal amplitude

averaged over target chip

All, or a specified portion, e.g., the middle 70 per cent, of the specified target chip T is used

for defining the amplitude of the composite signal for that chip. The target chip T has any

A chip [1], [27]-[28] is the smallest signaling segment, or time interval, in a digital signal.

Chip is defined such that baud is a unit of measure for chip rate.
(a)

INTEGRATION

INTERVAL

(b)

Figure 1. Two commonly used modes of sampling a chip. In curve (a) the sample is taken at a point in the center of each chip. In curve (b) the sample is an average over a significant

fraction of each chip. These modes use only a portion of the entire digital signal waveform.
specified chip state. The chip environment of the target chip is any specified sequence of chip

states.

3.1.3. SNR of a Chip State (CHIP STATE SNR GLOBAL)

For the composite digital signal being measured, consider the set of all chip sequences

<abcTxyz> in the digital signal, for any specified chip state T and all occurring chip

states a,b,c,x,y,z. CHIP STATE SNR GLOBAL is a global measurand; that is, it does not depend

upon chip environment.

For a specified target chip state, for example, "0" or "1", this measurand is the ratio of

(1) the weighted average, over all possible chip environments of the target chip, of the signal

power in the target chip, to (2) the weighted average, over all possible chip environments of the

target chip, of the noise power in the target chip. The weighting is proportional to the

probability of occurrence of each chip environment in the entire composite signal.

weighted average of: square of:

CHIP STATE SNR GLOBAL s -^

[square of:

/digital signal amplitude \

I averaged over target chip J

weighted average of:

[mean square fluctuations of: /composite signal ampl

(averaged over target

itude\

chi p J

(3)

All, or a specified portion, e.g., the middle 70 per cent, of the specified target chip T is used

for defining the average amplitude of the digital signal and of the additive noise. The target

chip T has a specified chip state, for example, "0" or "1".

3.1.4. SNR of a Symbol State (SYMBOL STATE SNR GLOBAL)

SYMBOL STATE SNR GLOBAL is a global measurand for a specified target symbol state. It is

similar to CHIP STATE SNR GLOBAL, except it is defined for a symbol rather than for a chip. A symbol is a specified sequence of one or more chips.

3.1.5. SNR of a Word (WORD SNR GLOBAL)

WORD SNR GLOBAL is a global measurand for a specified target word. It is similar to SYMBOL

STATE SNR GLOBAL and to CHIP STATE SNR GLOBAL, except it is defined for a word rather than for a symbol or a chip. A word is a specified sequence of one or more symbols.

3.1.6. SNR of the Entire Composite Signal (SIGNAL SNR)

SIGNAL SNR is a global measurand. It is similar to CHIP STATE SNR GLOBAL, except the

weighted averaging also is carried out over all target chip states. SIGNAL SNR corresponds

closely to the usual concept of SNR of an analog signal in an analog channel.
3.2. SNR and Its Generic Relatives

3.2.1. SNR

As usually defined, SNR refers to the ratio of signal power of the entire channel and entire

signal waveform to additive noise power coincident with the entire channel and entire signal

waveform. The previous subsection discussed several related varieties of digital SNR

measurands. The differences have to do with including specified portions of the channel and

digital signal waveform while excluding other portions.

SNR e CNR

[total signal power in channel]

[coincident additive noise power in channel]

(4)

SNR also usefully can be defined to be a point function of Fourier frequency, such that it is the

ratio of spectral density of signal power to spectral density of additive noise power. CNR is an abbreviation for carrier power to noise power ratio.

In addition to SNR per se, there are closely related types of measurands which generically

also are ratios of signal power to additive noise power.

3.2.2. C/Ng and C/kT

One such related type is called ratio of carrier power to noise power density [1], [5],

[14]. It often is denoted by C/Nq, or equivalently by C/kT, where by definition T (temperature)

is such that kT is equal to Ng, where k is Boltzmann's constant. Conceptually, Nq is the additive

noise power per unit bandwidth (e.g., one hertz). Often, Ng is used as the total additive noise

power in the channel normalized by the bandwidth of the channel. The carrier power, C, is the

signal power in the entire channel.

C/Ng = C/kT,

C/Nn

[signal power in channel]

[additive noise power /

in channel /

C/Ng E [channel bandwidth] x [SNR].

channel bandwiidthT

(5)

(6)

(7)

Sometimes Ng is used in its purer sense as a point function of frequency, i.e., as spectral

density of additive noise power.
3.2.3. E

b /N and Echip /NQ

Another type of basic digital signal measurand which is^a ratio of signal power to additive

noise power is called ratio of energy per bit to noise power density, usually denoted by E^/Nq

[1], [3], [16]. The energy per bit is the digital signal power in the channel normalized by the

bit rate. For the exactly analogous ratio of energy per chip to noise power density (E

c hip/Ng),

the energy per chip is the digital signal power in the channel normalized by the chip rate.

E

b /N

[digital signal energy in channel per bit]

, (8)

[additive noise power in channel per unit bandwidth]

[channel bandwidth] x [SNR]

E b /N

Q

= — , (9)

[bit rate]

[C/Np]

E b /N

o

= rh . t —•< 10 > [bit ratej

I have discussed three closely related types of measurands, SNR, C/Ng, and E^/Ng. Bandwidth, bit

rate, chip rate, symbol rate, and word rate are auxiliary parameters of a digital system which

usually are well determined, or can be. Insofar as these auxiliary parameters are well

determined, in many situations a measurement of one variety of a measurand belonging to any one of

the above three types is adequate to determine the corresponding measurands belonging to each of the other two types.

4. The Template Method for SNR

4.1. Statement of the Problem

The template method is presented as a solution to a problem. The problem is to measure, transparently and correctly, for composite digital signals, the ratio of the power of the

dispersed digital signal to the power of the additive noise. This is to be accomplished, to better than some specified precision and accuracy (see Appendix A), in the presence of the

intersymbol interference ( IS I ) [1], [17], [27] engendered by the dispersion of the digital signal.

In practice, there are many ways to implement the template method for transparently measuring

SNR and other quantities. I present the basic concept here. The essential function of the

template is to fix the ISI in the target chips of a large set of realizations corresponding to that template and to provide a means of distinguishing additive noise from the dispersed digital

signal .

The template method may be used under a wide variety of conditions. In the following

example, the assumed constraints are not necessary; they are used only for simplicity and clarity

of presentation.
As a specific example, I assume the composite signal to be measured is a dispersed digital

signal corrupted with additive random white gaussian noise. I assume the undispensed digital

signal is a continuous sequence of chips which are binary and bipolar. The chip state sequence,

the relative amount of additive noise, and the amounts and spectral shapes of the amplitude

response dispersion and group delay dispersion are unknown a priori.

I further assume there are no other corruptions of the composite signal, for example,

multiplicative noises (incidental amplitude modulation, IAM, and incidental phase modulation, IPM)

and imperfect synchronization. I assume the statistical parameters of interest of the composite

signal are stable over the measurement interval.

4.2. Measurements Using a Template

The test set uses a digital template, a specified pattern of N chips. In the following

example, I arbitrarily consider a single template of five chips with the pattern "1-1-0-1-0". See

figure 2(d). The test set transparently and continually looks for realizations of that particular

digital pattern to come along in the native digital traffic of the composite signal. I assume the

test set has available to it the following three specific signals , shown in figure 2(a-c):

a) Baseband analog signal before input to decision device, representing the composite

signal ,

b) Digital output of decision device, representing the digital aspect of the composite

signal, and

c) Digital clock signal, representing the clock rate of the composite signal.

A measuring device, e.g., an analog to digital converter, in the test set is repetitively

measuring the baseband analog signal. For the current example, the measuring device is triggered

by the digital clock signal, figure 2(c), to perform three uniformly spaced measurements on every

chip as it occurs in the baseband analog signal, figure 2(a). These measurements provide the raw data for the template method. Concurrently, a sequence comparator is comparing the digital

pattern of the five-chip template, figure 2(d), to the most recent five digital chip values of the

output of the decision device, figure 2(b).

Each raw datum from the measurements of the baseband analog signal is put immediately into a buffer, which, for the example of a template with five chips and three data points per chip, need

be only fifteen elements long. This raw data buffer is used as a queue to temporarily and

sequentially hold the raw measurements. As each new raw datum is pushed into the front end of the

queue, the oldest raw datum is discarded from the other end.

J The front end of the test set itself can generate the three specific signals from the composite

signal sampled at any desired place of measurement, e.g., at carrier band. It must generate the

signals precisely and accurately.

10
(a)

1 1 1 1 F

(b)

_r

(c)

fT~r \u

(d)

Figure 2. The test set uses three specific signals derived from the composite digital signal

under test: (a) noisy dispersed baseband analog signal before input to decision device,

representing the composite signal, (b) digital output of decision device, and (c) digital clock

signal. Curve (d) shows a digital template with the pattern "1-1-0-1-0". Raw data samples for

the example of three points per chip are shown on curve (a).

11
At any particular moment, the raw data buffer contains the most recent fifteen data points;

they represent the baseband analog signal for the most recent five chips. When the sequence

comparator decides that the most recent five chips are a realization of the chosen digital

template, the contents of the raw data buffer are frozen, and those fifteen data points then are transferred into the first row of an initially empty array in long term memory.

The test set continues looking for another realization. When another realization occurs, its

ordered set of fifteen data points (which are different in value from the earlier set of fifteen)

is transferred from the raw data buffer into the second row of the array of realizations in

memory

The embedded digital pattern (in effect, a sporadically recurring known digital sequence) is the same for both the first and second realizations. The embedded dispersed digital signal, i.e.,

the digital signal with its ISI, has the pattern of the template, "1-1-0-1-0" in the example. The

additive noise contribution is different for each realization, figure 3(a-d). The ISI in the

outermost chips is somewhat different for each realization, figure 3(a-d).

The test set continues to find realizations until there is a statistically useful number of

realizations, e.g., one thousand, stored in the array of realizations (see Appendix A). The array

has fifteen columns and one thousand rows. For a stream of random chip states, there are about

one thousand realizations of a specified five-chip template in a thirty-two thousand chip

interval. For a one-megachip per second signal, this occurs within about 32 milliseconds.

4.3. Data Analysts for SNR

The central chip, a "0" in the example, is used as a target chip; the two leading chips and

the two trailing chips are used as guard chips, as in figure 4(b). In general, there can be any

number of target chips and any number of leading and trailing guard chips, depending on the size

of the template. See figure 4(a-c).

There is ISI in the target chips engendered by the neighboring chips. To the extent that any

ISI from chips which are three or more chips away may be neglected, the ISI in the target chips is an invariant. That is, over those one thousand target chips in the array of realizations, there

is negligible variance engendered by ISI, because the adjacent symbol environment for the target

chips is the same for each of the realizations. If the ISI from more distant chips were not negligible, then one would use a longer digital template in order to have more guard chips around

the target chip(s)

For the target chip points, the average of the measured realizations represents the dispersed

digital signal which is embedded in the composite signal, while the variations from each other of

the different realizations represent the additive random noise (figure 5). For averages of one thousand realizations with noise, the random noise of the averages is about 30 decibels lower than

the random noise of the numbers being averaged.

12
REALIZATIONS

Figure 3. Four differe

stored as ordered s amplitude of a comp

device.

>nt realizations of the five-chip digital template "1-1-0-1-0". They are

sets of fifteen points in an array of realizations. Each curve is the

•osite noisy dispersed baseband analog signal before input to the decision

13
TEMPLATES

3 CHIPS: 8 Possible Templates

LG T TG

(a)

5 CHIPS: 32 Possible Templates

LG LG T TG TG

(b)

8 CHIPS: 256 Possible Templates

LG LG LG LG T T TG TG

(c)

Figure 4. Some practical template structures. LG is leading guard chip. T is target chip.

TG is trailing guard chip. Template (b) corresponds to the choice of target versus guard chips

in the example discussed in the text.

14
FOR TARGET CHIPS

EMBEDDED DISPERSED DIGITAL SIGNAL

Corresponds to

Average Realization

ADDITIVE NOISE

Corresponds to

Variation about Average Realization

Figure 5. The embedded dispersed digital signal, additive noise, and SNR can be obtained for the

target chips of a template. The embedded digital signal with its ISI is the same for each

realization. The additive noise varies from realization to realization. SNR is the ratio of

the square of the average of the realizations to their variance.

15
The square of the average realization for the target chip points represents the power

(subject to a normalizing scalar which need not be determined) of the dispersed digital signal at those points, while the variance of each realization from the average realization represents the

power of the additive noise at those points.

Hence, the ratio of the dispersed digital signal power to additive noise power at each point

is the ratio of the squared average to the variance at that point (figure 5). This is the POINT

SNR LOCAL described in section 3.1.1. In general, the POINT SNR LOCAL is different at each point

in the template, and is template dependent as well.

The SNR of the entire composite digital signal (SIGNAL SNR) can be obtained by averaging the

target chip SNR values (CHIP SNR LOCAL) for all possible digital templates of the chosen length,

with appropriate weighting given to each template based upon its relative probability of occurrence in the entire composite signal. See section 3.1.

Consider an integrate and dump (I/D) type of digital detection [1]. The I/D receiver's

decision device samples each chip. It averages the composite baseband analog signal over all or nearly all of the chip, as shown in figure 1(b). Instead of obtaining three raw data points for

each chip, the template method measuring device can digitize the I/D chip sample, or an equivalent

sample, to yield one raw datum. The SNR's obtained from such raw data are SNR's of the I/D

samples; for many applications these are appropriate SNR's to specify and measure for an I/D

system. This corresponds to the CHIP SNR's described in sections 3.1.2. and 3.1.3.

4.4. Comments on the Measurements

The measured values are valid at the place of measurement in the system under test. They are

not necessarily good estimates for a different place in the system.

Depending upon the nature of the digital channel, the additive noise power may tend to be the same for all points in the template. The dispersed digital signal power depends upon the point

where it is sampled inside the digital template, and it may depend slightly upon the choice of

structure of the template.

There are advantages in using a set of several, or all, templates of length N, rather than

using only a single template. More information can be obtained per unit of measurement time; the

signal can be sampled in a more representative manner; and additional statistical information on the validity of the results can be obtained. Note that any and ewery sequence of five chips is a realization of one member of the set of thirty-two possible five-chip templates. If only one of

the set of possible templates of length N is to be used, I expect that most choices will work

well, and that a few template structures, e.g., all "l"'s or all "0"'s, will be relatively

ineffecti ve.

The effect of statistical sampling scatter on the precision of determination of SNR is discussed in Appendix A.

16
5. Remarks

5.1. Significance

Practical, economic, and administrative advantages accrue when digital communication systems

can be measured transparently. The transparent measurement procedures can measure meaningful

quantities of interest on a communication system at the appropriate time under the actual

operating conditions with the system totally in service. Users of the communication system are in no way inconvenienced by transparent measurements. System revenues and system availability are

not impaired. Instead, they are enhanced by the system improvements which occur with the better

knowledge of the technical status of the operating communication system made possible by

transparent metrology.

The ability to perform transparent measurements of basic performance parameters, using

correct procedures, on digital traffic directly, without taking the system offline, and without

using proxies, is expected to lead to more meaningful measurement data and ultimately to reductions in the cost of obtaining information on the true performance of systems.

The template method is expected to be a powerful method for correct and transparent

measurements of definitive fundamental parameters of digital signals, channels, devices, and

systems. The template method has no adverse impact on the capacity of the channel being

measured. All of the channel capacity can be used for other system functions, e.g., traffic and

protocols .

The template method can be applied without exception to any and all types of digital data.

Any kind of source coding, channel coding, and channel design can be accommodated. From the

standpoint of metrology, there is no need for redundancy. The digital symbol stream can represent

completely encrypted information; code groups; plain text; framing, stuffing, and idling symbols;

or any combination of any type. This is an important aspect of the transparency feature of the

template method.

5.2. Applications

Transparent metrology methods, e.g., the proposed template method, can measure directly and

correctly most of the definitive basic measurands, including digital signal power to additive

noise power ratios (SNR, C/Ng, E^/Nq), intersymbol interference, multiplicative noises (random

noise modulation of amplitude and of phase), and synchronization parameters (jitter and offset).

Transparent metrology methods will support efforts to establish definitive performance standards

which are technically relevant and valid, highly useful, unquestionably objective, and potentially

widely acceptable. Such performance standards are needed to specify quality and acceptability of

equipment, systems, and service.

These new methods of correct and transparent measurement of basic performance parameters are relevant to the technical quality of operational systems. They will influence hardware design,

system validation, technical performance objectives, performance standards, system monitoring, and

17
technical control. They may lead to more powerful language and terminology for the specification

of system design and operation.

Correct and transparent procedures give increased confidence that the measurements being made

are indeed appropriate and adequate. They permit less overdesign (e.g., less fixed margin in the

design) of digital communication systems, because the measurements are more informative and allow

more intelligent control of operating conditions.

The transparency of the template method allows it to be used by a system manager to measure

or monitor SNR on customers' leased channels with no knowledge, either a priori or a posteriori,

of the information content of the traffic. There is no need to violate in any way the

confidentiality and security of customers' traffic.

The template method can be the basis for test sets for transparent measurements. In the

future, if it proves to be sufficiently useful, the template method can be built into

communication equipment as part of its original design. Generally speaking, the template method

can be applied to any digital system. The details of optimum implementations for each system are expected to be strongly system dependent.

5.3. Comments

I note that bit error rate (BER), per se, can not be measured transparently. However, via

transparent measurement of SNR, ISI, multiplicative noises, and synchronization parameters,

together with knowledge of a reasonable model of the system, one expects to be able transparently

and accurately to estimate BER and other related overall performance parameters of in-service

digital systems.

The template method concept is similar to techniques used in some automatic adaptive

equalizers for digital channels [l]-[2], [9], [27]. In this paper, I am concerned with improved

fundamental methods of measurement. Prior art from adaptive equalization will assist greatly the

development of the template method for transparent metrology [4], [9]-[12], [16].

5.4. Further Work

The proposed template method is expected to be especially important for digital communication

systems, especially for those systems with stringent design constraints on transmitted signal

power and system bandwidth, i.e., for systems with critical amounts of additive noise and

intersymbol interference. The template method for SNR measurement should be studied, developed,

and evaluated, and then further tested and proven by being applied to synthesized channels and to

actual traffic on actual channels.

In the development of the template method one should look at various factors involving

template design: which templates, how many different templates, length of template, numbers of

target chips and guard chips, and points per chip. In the design of analysis algorithms, the

factors to be studied include choice of SNR measurands (point, chip, symbol, word, or signal;

18
local or global), Fourier transform methods versus non-Fourier transform methods, and measurement

speed. Accuracy and precision must be studied as functions of the number of realizations, leading

and trailing guard chips, and target chips. The effects of ISI from distant chips, incidental AM

and PM, and synchronization jitter and offset can be controlled; they must be studied.

Development of the template method should be extended to the transparent metrology of other

basic measurands. The raw data (analog values stored in the array of realizations) that are used

for SNR analysis also can be used for analyses of ISI, multiplicative noises, and synchronization

parameters. Transparent measurements of these additional measurands by the template method need

not require any hardware beyond what is used in measurement of SNR. Data processing for these

additional measurands will be much more complicated than for SNR and will require much more time

for computation.

The extension of the template method from the measurement of SNR to the other measurements

represents a sophisticated software challenge, with critical trade-offs anticipated among speed,

precision, accuracy, and memory requirements. Optimum algorithm design and efficient code will be

important factors in the extension to the additional measurands. The extension to these

additional measurands will be the topic of another paper.

6. Summary

6.1. Template Method for SNR

In the template method, measurements of raw data are performed continually on an analog

baseband value of the composite noisy, dispersed digital signal under test. Concurrently, the

digital signal's chip stream is monitored for occurrences of a digital pattern corresponding to a designated and arbitrary N-chip-long digital template.

The template has leading and trailing guard chip(s), with target chip(s) located between

them. The function of the template is both to fix the intersymbol interference in the target

chips by using a sufficiently large number of guard chips and to distinguish the digital signal

from additive noise. The length of the template is arbitrary and can be chosen to be short, e.g.,

five chips. The test instrumentation determines a posteriori when the pattern of the template has

occurred in the signal under test.

Each time the designated N-chip pattern is found, the analog values for these N most recent

chips are saved and put aside for analysis; the earlier intervening analog data points need not be

retained. That is, an array of sets of analog data points is created in memory; each set corresponds to a realization (occurrence) of the template's pattern. The target chips portion of

the array of sets of analog values then is analyzed for a) its average dispersed digital signal

component and b) its noise variation about the average signal. Additional computation using a correct algorithm yields the desired SNR measurands.

In a complete measurement protocol, a variety of templates is used, possibly concurrently, to improve the accuracy of the measurement and to obtain confidence measures for the results. For

19
some applications, it is possible to use every template of length N; as an example, for binary

signals and N of four chips, there are only sixteen distinct templates to process.

The measurement of SNR by the template method is quantitative, correct, and transparent. A correct measurement procedure actually measures the specified parameter of the specified signal,

channel, device, or system. A transparent measurement procedure measures the specified parameter

without degradation of the usable channel capacity and without modification to or interference

with the functioning of the measured signal, channel, device, or system.

6.2. Review

I presented the concept of the template method for transparent measurement of digital signal

power to additive noise power ratios (e.g., SNR, C/Mq, E^/Ng). The template method needs to be

developed; it has widespread applicability to important useful measurements in digital

communication systems.

I discussed the existence of various useful measurands for digital SNR, the concept of

transparent metrology for digital systems, and the concept of correct measurement procedures. I pointed out that the template method is generally applicable to transparent measurements of

several important measurands other than SNR (i.e., intersymbol interference, incidental amplitude

and phase modulations, and synchronization jitter and offset) on any noisy, dispersed digital

signal .

7. Acknowledgments

With pleasure, I acknowledge colleagues John Wakefield, Andres Gonzalez, and William L. Gans

for extensive discussions and assistance. Many people within DoD, FAA, NASA, and TRW provide

information, comments, criticism, and motivation; their help and encouragement is much

appreciated. I am stimulated by discussions with Robert C. Davis of Harris Corporation; his

insights are cogent and valuable. John Gadoury of GTE kindly provided information on the Adaptive

Channel Equalizer. I thank C.K.S. Miller for originally placing this interesting metrology

problem at my attention and gratefully acknowledge continued support from him and Drs . David F. Wait, Ramon C. Baird, and Robert A. Lawton of the NBS Electromagnetic Fields Division.

8. References

[1] J. J. Spilker, Jr., Digital communications by satellite. Englewood Cliffs, New Jersey:

Prentice-Hall, 1977.

[2] R. L. Freeman, Telecommunication system engineering, analog and digital network design. New

York: Wiley & Sons, 1980. Chapter 10, "Digital transmission on an analog channel," pp. 319-

327.

[3] J. L. Hammond, D. J. Schaefer, and B. J. Leon, "Methods of monitoring and fault isolation for

digital communication links," in 1976 Nat. Telecommun. Conf. Rec. , Dallas, Texas, Nov. -Dec.

1976, pp. 22.3-1 to 22.3-5.

[4] R. M. Gagliardi and C. M. Thomas, "PCM data reliability monitoring through estimation of

signal-to-noise ratio," IEEE Trans. Commun., Vol. COM-16, no. 3, pp. 479-486, June 1968.

20
[5] C. Burwell and S. Gover, "Hardware simulation facility for 120-Mbit/s QPSK/TDMA system,"

Comsat Technical Review, Vol. 12, no. 2, pp. 335-369, Fall 1982. Appendix A, "Determination

of energy to noise ratio E b /NQ," pp. 365-368.

[6] E. A. Newcombe and S. Pasupathy, "Error rate monitoring for digital communications," Proc.

IEEE, Vol. 70, no. 8, pp. 805-828, August 1982.

[7] K. Feher, Digital communications: microwave applications. Englewood Cliffs, New Jersey:

Prentice-Hall, 1981. Chapter 11, "Measurement techniques," pp. 230-249.

[8] D. Halford and A. Gonzalez, "Transparent metrology of signal-to-noise ratio of noisy digital

signals," in Book of Abstracts, International Union of Radio Science (URSI), XXth General

Assembly, Washington DC, U.S.A., 10-19 August 1981, p. 24.

[9] J. Grabowski and R. C. Davis, "An experimental M-QAM modem using amplifier linearization and

baseband equalization techniques," in 1982 Nat. Telesyst. Conf. Rec, Galveston, Texas, Nov. 1982, pp. E3.2.1 to E3.2.6.

[10] L. E. Jankauskas , "Adaptive estimation of discrete nonlinear channels for performance

assessment," in IEEE 1976 Canadian Commun. and Power Conf. Digest, Montreal, Quebec, Canada,

Oct. 1976, pp. 60-62.

[11] H. A. Sunkenberg and L. E. Jankauskas, "Performance assessment of high-speed digital

transmission systems," in 1976 Nat. Telecommun. Conf. Rec, Dallas, Texas, Nov. -Dec. 1976,

pp. 51.5-1 to 51.5-5.

[12] L. E. Jankauskas, M. M. Landesberg, D. Spector, and C. Meyer, "Technical control of the

digital transmission facilities of the Defense Communications System," IEEE Trans. Commun.,

Vol. COM-28, no. 9, pp. 1516-1523, Sept. 1980.

[13] L. B. Milstein, "Performance monitoring of digital communication systems using extreme-value

theory," IEEE Trans. Commun., Vol. C0M-29, no. 9, pp. 1032-1036, Sept. 1976.

[14] E. E. Steinbrecher and L. F. Gray, "A computer-controlled satellite signal monitoring

system," Comsat Technical Review, Vol. 1, no. 1, pp. 79-116, Fall 1971.

[15] I. Dostis, C. Mahle, V. Riginos, and I. Atohoun, "In-orbit testing of communications

satellites," Comsat Technical Review, Vol. 7, no. 1, pp. 197-226, Spring 1977.

[16] R. B. Kerr, "On signal and noise level estimation in a coherent PCM channel," IEEE Trans.

Aeros. Electron. Syst., Vol. AES-2, no. 4, pp. 450-454, July 1966.

[17] P. Bylanski and D. G. W. Ingram, Digital transmission systems. Stevenage, England: Peter

Peregrinus, 1976. Chapter 9, "Regeneration and waveform transmission," pp. 207-243.

[18] D. J. Gooding, "Performance monitor techniques for digital receivers based on extrapolation

of error rate," IEEE Trans. Commun. Techn., Vol. C0M-16, no. 3, pp. 380-387, June 1968.

[19] B. Leon, J. L. Hammond, P. A. Vena, W. E. Sears, and R. T. Kitahara, "A bit error rate monitor for digital PSK links," IEEE Trans. Commun., Vol. C0M-23, no. 5, pp. 518-525, May

1975.

[20] D. J. Schaefer, "Techniques for TDMA system monitoring," Comsat Technical Review, Vol. 9, no. 2A, pp. 387-412, Fall 1979.

[21] D. R. Smith, "A performance monitoring technique for partial response transmission systems,"

in 1973 IEEE Int. Conf. on Commun. Rec, Vol. II, Seattle, Wash., June 1973, pp. 40-14 to 40-

19.

[22] J. F. Gunn and J. L. Lombardi , "Error detection for partial -response systems," IEEE Trans. Commun. Techn., Vol. C0M-17, no. 6, pp. 734-737, Dec. 1969.

[23] S. Alagic and M. A. Arbib, The design of well- structured and correct programs. New York:

Springer-Verlag, 1978.

[24] 0.-J. Dahl, E. W. Dijkstra, and C. A. R. Hoare, Structured programming. New York: Academic

Press, 1972, pp. 4-16 and 166.

21
[25] S. E. Goodman and S. T. Hedetniemi, Introduction to the design and analysis of algorithms.

New York: McGraw-Hill, 1977.

[26] D. Gries, "On believing programs to be correct," Commun. of the ACM, Vol. 20, no. 1, pp. 50- 51, Jan. 1977.

[27] J. G. Proakis, Digital communications. New York: McGraw-Hill, 1983.

[28] M. P. Ristenbatt, "Alternatives in digital communications," Proa. IEEE, Vol. 61, no. 6, pp , 703-721, June 1973.

[29] K. A. Brownlee, Statistical theory and methodology in seience and engineering. New York:

Wiley & Sons, 1965, second edition, p. 84.

22
Appendix A: Confidence of Measured SNR

I expect the template method to provide measurement precision and accuracy for SNR which is adequate for many if not all practical applications. A complete error budget for SNR measurement

accuracy capability would contain several factors. A detailed analysis of all of these factors is

dependent upon the specific system implementation and is beyond the scope of this concepts paper.

For many practical situations, the accuracy capability is expected to be limited by sampling

scatter. Insofar as sampling scatter is dominant, precision and accuracy can be improved by

increasing the number of realizations used in the determination. Another factor is the number of

target chips in the template, which, for measurement efficiency, should be only one or two. For POINT SNR LOCAL, in the example with one target chip, for M realizations, the sampling scatter

gives rise to a fractional precision [29]

[standard deviation]

of POINT SNR LOCALl

= /T7M . (Al)

[measured POINT SNR LOCAL]

For M equal to one thousand realizations, sampling scatter limits the fractional accuracy

capability to be not better than + 4.5 per cent (one sigma). For M of only fifty, sampling

scatter amounts to + 20 per cent (one sigma), which is sufficiently small for many useful system

appl ications

.

23
Appendix B: Glossary

ARD

BER

CC/kT

C/NQ

chip

CNR

correct

"VNo

Echip/ N GDD

global measurand

guard chips

I/D

IAM

IPM

ISI

klocal measurand

M

N

Nproxy

realization

SNR

Ttarget chip(s)

template

transparent

amplitude response dispersion

bit error rate carrier power (same as signal power)

ratio of carrier power to noise power density

ratio of carrier power to noise power density

smallest signaling element, or time interval, in a digital signal

carrier power to noise power ratio

see definition in section 2 ratio of energy per bit to noise power density

ratio of energy per chip to noise power density

group delay dispersion

value is averaged over all local environments

leading and trailing chips in a template

integrate and dump

incidental amplitude modulation

incidental phase modulation

intersymbol interference

Boltzmann's constant

value is averaged only over specified environments

number of realizations in a measurement set number of chips in a template

noise power per unit bandwidth

surrogate or substitute used in place of a specified parameter or signal

an occurrence of the pattern of the template

signal power to additive noise power ratio

equivalent noise temperature

central chip(s) in a template

a finite length, specified search pattern of chips

see definition in section 2

24
NBS-114A (REV, 2-BC) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN-1077

2. Performing Organ. Report No. 3. Publication Date

June 1985

4. TITLE AND SUBTITLE

Transparent Metrology of Signal to Noise Ratios of Noisy Band-Limited

Digital Signals

5. AUTHOR(S)

Donald Hal ford

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Same as #6

10. SUPPLEMENTARY NOTES

|] Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT f A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

I propose the use of a template method for quantitative, correct, and transparent

measurement of signal power to additive noise power ratios (SNR) of digital signals

and systems under full operating conditions. Outer guard chips of digital templates

hold intersymbol interference fixed on inner target chips in realizations of the

respective template patterns in traffic. The proposed template method needs to be

developed and proven as a potentially valuable metrology capability; it can be

especially important for real time online performance assessment and monitoring of

digital communication systems.

A correct measurement procedure by definition actually measures a specified parameter

of a specified signal, channel, device, or system. A transparent measurement procedure

by definition measures the specified parameter without degradation of the usable

channel capacity and without modification to or interference with the functioning of

the measured system.

I discuss the significance of transparent metrology, the measurement of various SNR's

by the template method, and the general applicability of the template method for

measurements on any noisy digital signal. The template method can provide transparent

metrology procedures for other basic measurands, e.g., intersymbol interference,

multiplicative noises, and synchronization.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

communications; correct measurement procedure; digital signals; energy per bit to

noise density; monitoring; noise; online measurements; performance assessment; real

time: signal to noise ratio measurprnpnt.: t. pmplar.p mpt.hnd; fransparpnt mptrnlncm- 13. AVAILABILITY

Q\j Unlimited

3 For Official Distribution. Do Not Release to NTIS

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~^\ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

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