National u^i t^au Qf StanfisrdS

NBS

NATL INST, OF STAND & TECH

A11107 ^D7^^b

100-A

Loading Factors and FDM-FM System

Performance Calculations

Supplement to Appendix C of the National

Bureau of Standards Technical Note 100

entitled Required Signal -to- Noise Ratios,

RF Signal Power, and Bandwidth for Multichannel Radio Communication Systems

£

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

#^

*i>^:?v
THE NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE

Alexander B. Trowbridge, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 100-A

ISSUED SEPTEMBER 1967

LOADING FACTORS AND FDM-FM SYSTEM

PERFORMANCE CALCULATIONS

Supplement to Appendix C of the National Bureau of Standards Technical Note 100

entitled Required Signal-to-Noise Ratios, RF Signal

Power, and Bandwidth for Multichannel

Radio Communication Systems

E. F. FLORMAN

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

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

Price 20 cents.

SUPPLEMENT TO APPENDIX C

OF

THE NATIONAL BUREAU OF STANDARDS

TECHNICAL NOTE 100

E. F. FLORMAN

INTRODUCTION

This supplement was written for the purpose of extending the scope

of the original paper, by providing a more complete set of system-performance design equations, which apply to the Frequency Division Multiplex—Frequency Modulation type of multichannel telecommunication

systems; these equations may be used for various types, and combinations

of types, of message signals.

The page numbers of this paper correspond to the pages in "The

National Bureau of Standards Technical Note 100", on the topic of FDMFM systems-performance calculations, based primarily on the FM radio receiver transfer function.

The referenced page numbers and equation numbers in this paper refer,

of course, to NBS Technical Note 100.
173a

Factors Which Affect Frequency Deviation

of the RF Signal in FDM-FM Systems

For military-service communications, the multichannel system and the

FDM-FM equipment should be designed and operated so as to fully utilize

the RF spectrum bandwidth, B , employing a composite baseband noisetype modulating signal having an average power level P__,. The output

message-channel ° signal-to-noise ° ratio, S /N , should be calculated for

oc oc

a composite baseband modulating-signal total average power level P ;

and a message-channel modulating-signal average power level (p ) » in

the baseband signal spectrum.

Equation (C.5), p. 169, NBS Technical Note 100, applies only to the

case of sinusoidal modulating signals. For multichannel systems, we are

required to calculate the message (voice) channel output signal-to-noise

ratio, S /N „ , for the case where the composite baseband modulating

signal (closely) resembles a noise-type signal; and the message-channel

signal may be either a sinusoidal signal or a noise-type signal. Hence,

the factors to be substituted in (C.15), p. 172, are obtained from a

modified form of (C.5), p. 169.

The general form of (C.5) is based on the following four basic concepts and assumptions:

a. The message-signal output average power, S , is proportional

to (AF )^^ as indicated by (C.3), p. 168.

c s ,n "' ' ^

b. (AF ) is dependent upon both the average power level of

c s ,n the modulating message-signal power (p ) and the "peak factor," /2
173b

of the rms voltage associated with (p ) 2— m s,n

c. The maximum bandwidth of the generated RF signal spectrum

is a function of the peak frequency deviation , (AF) as shown by (C.9) ' ^^———————— S • li and (C.IO), p. 171. And,

d. (aF) is dependent upon the average power level of the coms,n

posite total baseband modulating signal, (Pin)s n> and the "peak factor", (P^'k^s n'

of the voltage associated with (P-,)- ^'

The general form for (C.5) is:

(AF )2 - 2 (p ) c s,n '^m s,n

(AF)^ ^ (PF^) (P ) s,n b s,n m s^n

2 ,

' ^Pm^s,n

or, (AF )^ = (AF)"^ x x (C.5a)

c s,n s,n

(PF^) (P ) b s ,n m s ,n

where, (AF ) = Root mean square (rms) deviation of the RF signal

due to the message-signal power, (p^i^g n* ^^ ^^®

modulating baseband signal; for sinusoidal or noisetype modulating signals, as indicated by the subscript letter.

(AF) = Peak RF-signal frequency deviation due to the composite baseband modulating signal, for sinusoidal

or noise-type modulating signals, as indicated by

the subscript letters.
173c

(PF ) = Peak factor of the composite baseband signal (see

b s,n

p. 17) either sinusoidal or noise-type signals,

as indicated by the subscript letters; at the

modulator input terminals.

(p ) = Average power level of the message signal, in the m s ,n message-signal-channel bandwidth, at the modulator

input terminals; for sinusoidal or for noise-type

signals, as indicated by the subscript letters.

(P ) = Average power level of the composite baseband signal, at the modulator input terminals; for sinusoidal or for noise-type signals, as indicated by

the subscript letters.

The peak factor, PF , is defined as: The ratio of the signal voltage

peak amplitude which is exceeded for only (approximately ) 1/10 percent

of the time-to-the rms voltage of the composite signal. For a discussion of the effects of noise-type modulating signals see pp. 11-22, inclusive. For noise-type signals, the voltage-ratio peak factor is /2^

or, 13 db in terms of a power ratio. For sinusoidal signals the voltageratio peak factor is /2. Composite baseband modulating-signal voltage

peaks determine the peak RF deviations and thereby determine the (effective

or operating) maximum bandwidth of the RF-signal spectrum.

Hence, equation (C.5) assumes the following forms, depending upon

the type of message-channel signal, the type of baseband signal loading,

and the peak factor of "ftie (modulating) composite baseband signal:
173d

Conditions Form of Equation

Voice-channel tone

modulating signal. <^^'s

=

2 X p*^ms

and baseband tone- UT)l 2 X Pms signal loading

Pms

Pms

or. <^^c>s

r (AF)2 X

s

Voice-channel white2

noise modulating sig- (a^^^„ en 2 x pmn

'" c'n n lOPmn

(AF^)J 2 X p

ms

Ur)l 20 X Pmn

2

(AF ) = c s

2

: (AF) X

n

p^ms

lOP

(C.5b)

(aF)^ 20 X P n mn

2 2 TMn , ^ (aF^)^ = (aF)^ X (C.5c)

nal and baseband

white-noise signal

loading

or.

Voice -channel tone

modulating signal,

and baseband whitenoise signal loading.

or. (AF )" = (AF)" x ^^^— (C.5d)

mn

Equations (C.5b), (C.5c), or (C.5d) are used to derive equations

(C.20) to (C.22a), inclusive, see pp. 173j to 1731, inclusive.

Baseband-Signal Loading Factors

The three "loading factors", P /p , P /p , and P /p , used in ms ms mn mn mn ms equations (C.5b), (C.5c), and (C.5d), respectively, are considered
173e

separately in the following discussion.

The loading factor Pms'^Pms "'PPli^s only to the case where the baseband modulating signals are sinusoidal and are limited to only two or

three separate signals, with a total power of P ; hence this factor does

not apply and may not be used for frequency division multiplex multichannel

systems. Note also that P is much greater than p . ms ^ '^ms The loading factor P /p applies to the "operating" case where

both the composite baseband signal power, P , and the voice-channel

mn message-signal power, p , are composed of noise-type signals. Note that

the voice-channel signal may also be composed of a number of randomlyphased sinusoidal signals, such as independent teletype signals; however,

in this particular case, the voice-channel signal cannot be a single

sinusoidal signal. For the operating case, where the message signals

are of various types, such as voice, teletype, digital data, etc., and

the message-signal power levels, p ., are unequal, the "operating

loading factor" is derived as follows:

P =N,p ,+N_p -+... mn al ^mnl a2 *^mn2

where, N . is the number of "active" channels each of which transmit a

particular type of message signal and a particular message-channel signal

power, Pj^j^i* therefore.

Operating Loading Factor = ^mn I al ^mnl a2 Pmn2

(C.5e)

P

J P op *^mni

Hence, the "operating loading factor" is defined as the ratio of the

composite modulating (noise type) baseband signal power, P , to a

particular message-signal power level, P^^ni* i^i the baseband-signal spectrum.
173f

The number of active channels, N ., associated with each particular

type of message signal, depends upon the "activity factor" which in turn

depends upon the characteristics of the message signal. For voice signals,

the activity factor is approximately 0.25, that is, if N' channels are

allocated for voice messages, then N = 0.25 N'. For data or noiseav

type signals (in the voice channel) the activity factor may be assumed

to be 1.0, and if N" channels are allocated for data messages, then

N , = N". This difference between the activity factor for voice signals

and for data signals is the basic reason for the comparatively "heavy"

loading effects of data signals. The total number of active channels is:

\ = ^al + ^2 +

• •

• (C.5f)

In (C.5f), N is the maximum number of simultaneously active channels,

of the N available channels, for " peak message load" conditions ; where

the peak-message load is exceeded for less than (approximately) one

percent of the time.

When all channels are noise loaded at the same power level, p , the

loading factor, Pnin'^Pmn' ^® equal to the total number of available

channels, N. The standard method of conducting "noise-power-ratio" (NPR)

measurements requires that all channels , except one, be noise loaded;

therefore, the "NPR loading factor" is given as:

'P NPR Loading Factor = mn

.Pmn

= N (C.5g)

npr

The loading factor P /p applies to the case where the composite ° mn '^ms baseband signal, having an average power level of P , is composed of a
173g

large number of randomly-phased sinusoidal signals and/or white-noise type

signals; and the voice-channel signal, having an average power level, Pj^g

is a single test-tone sinusoidal signal. The channel test-tone signal

is used as a convenient means of properly adjusting the equipment, this

test-tone signal is also used as a standard reference power level, and

may be set approximately 10 db higher than the allowable power level of

the channel noise-type signals, p^^j- Hence the "test-tone or standard

loading" factor", P /p , will differ from the loading factor P /p ,

' mn '^ms

^ mn ^mn'

given by (C.5e) or (C.5g), and will be inversely proportional to the

power level p and directly proportional to the power level p ., therefore

Test-Tone

or Standard Loading ** Factor

mn

ms

mnmm

mm

p op '^ms

mn

mn

mn

X

npr ms

te (C.5h)

^al Pmnl N.9 "a2 Prt'mn2 + + .

N p mn

ms ms ms

It is evident from (C.5f) and (C.5h) that if any two of the three

parameters: (1) the "standard loading factor", Pjnn/PiTi<? ' ^^^ ^^^ channel

message-signal "loading ratio", p . /p ; anc (3) the number of "active"

channels, N ; are specified, the third parameter is determined.

The "standard loading factor", (A + B Log N), is defined by the CCIR

Recommendation 29U (IXth Plenary Assembly, Los Angeles, 1959) as the average

power level of the composite modulating baseband signal, P_,„» referred

to the average power level of the voice-channel test-tone signal, Pj^s

therefore

,

Standard Loading Factor = 10 Log

10 jm = (A -^ B Logj^QN), db (C.5i)

ms
173h

where, A and B have particular assigned values, depending upon the total

number of available message-signal or voice channels, N, and the types

of messages^ for example: for N = 12 to 240 channels, A =-ldb and B =4;

for N 240 channels, A = -15db and B = 10.

Note that the CCIR definition of the Loading Factor is simply the

ratio of the composite modulating (noise type) baseband signal power,

^mn' *° ^^® test-tone signal power, P^„\ both signal powers are measured

at the same point in the composite baseband-signal channel.

The standard loading factor, P /p ; may be specified and/or

determined either in terms of the "maximum" number of simultaneously

active channels, N , (not exceeded for approximately one percent of the

3. time) and the ratio of the message-signal power, p^^,,- , to the test-tone

signal power, p^^g, in the message-signal channels, see, (C.5f) and (C.5h);

or , the Loading Factor P^^/Pms ^^y ^^ specified in terms of the standard

type, A + B Log,QN, see (C.5i).

The system output signal-to-noise ratio depenas upon the relative

power levels of the individual message signals, as is evident from the

above loading factors. However, in order to avoid signal distortion

within the equipment, the absolute power levels of the individual message

signals, (p )_ _, and also the composite baseband-signa] power, P , m 5 , n

,

mn must be adjusted so that the voltage peaks of these signals do not

overload the circuts in the equipment.

If the maximum bandwidth of the RF-signal spectrum, B , is fixed,

an increase in the value of the Standard Loading Factor, A + B Log^pN,

or an equivalent increase in the number of "active" channels, N , will

increase the Operating Loading Factor, ^mr/^mnl* ^"^ cause a reduction of
173i

the output signal-to-noise ratio, S /N , and consequently, will degrade

the system performance

In summary, the above types of loading factors are used in equations

(C.20) to (C.22a), (p. 173j to p. 1731) inclusive, to calculate the output message-signal and test-tone signal-to-noise ratio, and the output

noise-power-ratio. Detailed instructions regarding the correct loading

factor to be used with each of the above equations are given on pp. 173

j

to 1731.

The Loading Factor (A + B Log N) is usually in terms of the "hybrid"

unit, dbmO. This unit is confusing because of the fact that the powerratio term, 10 Log,^* (P /p ), is by definition, in db units, and not

lu mn ms —

in dbm units ; also, the factor is often interpreted to mean that the

test-tone signal power level, P^jg , is dbm--in general, this interpretation is not correct.

Composite Baseband-Signal Power, P , m and RF-Signal Spectrum Bandwidth, B^

In order to modify (C.15), p. 172, to apply to the cases where either

sinusoidal or noise-type modulating signals are considered, we note that

equal values of baseband modulating signal powers P and P , do not

generate the same effective RF spectrum bandwidths , (B ) and (B-^) »

respectively. This fact implies that (AF)s is not equal to (AF) , for

the same (particular) value of the generated RF spectrum bandwidth. By,*

The relationship between (aF) and (aF) , for particular values of

B^/f may be obtained from Figure 3-1, p. 12.

The power level of the baseband sinusoidal modulating signal, P^^^
173 j

which is required to generate a particular RF signal spectrum having a

bandwidth B , depends upon the characteristics of the Modulator and

the pre-emphasis circuit; the same 'Effective" RF signal bandwidth would

be genecated by a noise-type modulating signal having a power level P ,

which is somewhat lower than the power ^ level P . The ratio, P /P „« ms ' mn ms

of the noise-type baseband (modulating) signal power, P^m* "^o "^^^ sinusoidal baseband (modulating) signal power, P , each of which will generate

the same effective RF signal spectrum, B , may be obtained from Figure

3-U, p. 20, NBS Technical Note 100.

System-Performance Design Equations

Equation (C.15) applies only to the case of sinusoidal modulating

signals. The following work covers the cases where noise-type modulating

signals and white-noise signal loading techniques are used. The formats

of the following equations, derived from (C.15) are of the following two

types

(1) The antenna noise-power temperature is assumed to be approximately equal to the "standard" temperature, T ; under this condition, the

radio receiver "noise figure", F , may be used instead 'of the term

r

"T + T "; however, this form of equation would not be accurate for lowA er noise antenna systems. Also, this (type of) equation differs in format

from (C.15)

(2) The second type of equation, also derived from (C.15), has

the same form as (C.15), includes the term "T. + T '' , is accurate for

the case of low-noise antenna systems, and can be used directly with the

design curves in this report.
173 k

To obtain a general form of the system-performance design equation,

we substitulfe (C.5a), (C.6d), (C.IO), and (C.14) in (C.U) and obtain:

(S ) B (PF. ) (P ) /(AF) Y P oc s,n c D s,n m s,n s,n| r

X — X = I ^ X (C.lSa)

(N ) f 2(p ) \ f / 2K (T. + T ) fn, oc s,n m *^m s,n \ c^ A er ">

The receiver- input effective noise-power temperature, T , is:

T = (F -1) T (C.16) er r o where, F = the receiver noise figure, as a ratio

and, T = "standard" temperature in degrees Kelvin, (* 290 deg. K)

Under conditions where T = T = 290 deg K, we have:

A o

^A ^ "^er =

"^A ^ Vr "

"^o = Vr ^C.17)

Also, f cm= f (C.18)

and, B ^ = B.^ (C.19)

rf if

Substituting (C.5b), (C.17), (C.18), and (C.19) in (C.15a), and rearranging terms, we obtain:

(S ) P B.. AAF)\" p oc s r 1^ / SI "^ms

(N ) kT B.^F B \ f / 2P oc s o If r c \ m / ms ^

^if h^^A Pms

(C.20)

^ (T. + T„^) B.^ B \ f / 2P„^

A er' if c \ m/ ms

Equation (C.20) may also be written with the same terms and in the

same form as (C.lSa), and is.
1731

oc s

(N ) oc s

2P

ms

m ms

k (T. + T ) f

A er m

(C.20a)

Note that (C.20) and (C.20a) apply to the case where both the baseband modulating signals and the channel modulating signals are sinusoidal

and are limited to not more than two or three separate signals; also,

p << P . Hence this form of equation may not be used for frequency

division multiplex systems, employing composite noise-type baseband signals,

Proper values for (AF) /f in (C.20) and (C.20a) may be obtained from

s m

Figure 3-1, p. 12, for particular given or assumed values of B.^/f . The

ratio, p /P , may be calculated from measured or assumed values of p ms ms ms and Pms

If both the composite (baseband) modulating signal and the messagechannel signal are noise-type signals, we have, using (C.5c):

(S ) oc n

(N ) oc n

B.if

kT B.^F

o if r

B

or. k (T^ + T ) B.^

A er if

y(C.21)

mn

2 OPmnJ

Equation (C.21) may also be written in the same form as (C.lSa), and

is:

(S ) oc n

(N ) oc n

20P

mn

m mn

k (T + T ) f

A er m

(C.21a)
173m

The ratio, p /P , may be calculated from (C.5e), p. 173e, or (C.Sh),

mn mn ' '^ '

p. 173f. These equations are used to calculate the operating loading factor (P /p .) , which is then substituted in (C.21) or (C.21a) to calcumn mni op

late the baseband output message signal-to-noise ratio, (S )j^/(Nq^,)j^.

Equations (C.21) and (C.21a) yield the output baseband-signal "Noise-Power

Ratio," NPR, provided ^ that the ratio p /P is obtained from (C.5g), or is ^mn mn made equal to 1/N. The NPR in the output baseband signal is defined and

may be measured by the same methods used for the output voice-channel

measurements; except that the latter measurements include the noise contributed by the (receive) multiplex equipment.

Again, the factor (AD/f^^^, in (C.21), and (C.21a), may be obtained from

Figure 3-1, p. 12, for given or assumed values for B._/f .

If the composite (baseband) modulating signal is a white-noise type signal, and the message-channel signal is sinusoidal, we have, using (C.5d);

oc s

(N )^ oc n

^if I^^^K\

kT B.^F

o if r

ms "A

VfJ 20P

or.

k (T. + T ) B.^

A er If

^if

B

th ' mn

2 /(AF).

>> (C.22)

n ms V

X

20P

c m mn _y

Equation (C.22) may also be written in the same form as (C.15a), and is:

v2 (S ) oc s

(N ) oc n

B

c X — X

fm

20Pmn

^(AF)

ms m

k (T. + T ) f

A er m

(C.22a)

Proper values for (AF) /f , in (C.22) and (C.22a), may be obtained from

n m ' -^ Figure 3-1, p. 12, for particular given or assumed values of B. /f . The

ratio p /P may be calculated from(C.5h), p. 173f, or(C.5i),, p. 173g.

*^ms mn -^ ' f > ^. t- e,
173n

It is very important to note that equation (4.19), (p. 69, NBS Technical Note 100) differs from the above equations (C.21a) and (C.22a), by a

factor of 10 ; due to the difference between the peak factor of 3 db for

a sinusoidal (modulating) signal, and the peak factor of 13 db for a

noise type (modulating) signal. The net result, when using the systemdesign^ curves of NBS Technical Note 100, is that the factor, P /f (T, + T ), ' r m A er

must be increased by 10 db (in absolute value) above the value which is obtained from these design curve charts.

Note that in the above derivations , no allowance was made for pre-emphasis of the modulating signal—proper allowance for the effect of this

technique can be made by using a multiplying factor; however, the value

of this pre-emphasis factor depends upon the baseband-signal frequency,

being a maximum for the highest frequency, f , in the baseband signal.

The primary purpose of pre-emphasis (plus de-emphasis) is to equalize the

S N ratio, and the NPR across the output baseband-signal spectrum.

Also, the mess age -channel output noise power, N , is assumed to be

ti II flat weighted, FlA weighting reduces the noise power, and increases the

output test-tone signal-power to noise-power ratio, S /N , by 3 db. "C"

weighting increases the output test-tone S /N by 1.5 db. Noise-powerratio measurements are not affected by weighting techniques, because the

weighting affects both the signal and the noise equally.

Proper ^ allowances are made for diversity-^ effects on the S^„N ratio,

oc oc '

in the system-performance design equations and curves in NBS Technical

Note 100
173o

Application of Equations (C.20) to (C.22a), Inclusive

In conclusion, the output signal-to-noise ratio, S /N , has been

considered for the following three cases

(a) Sinusoidal modulating signals only ; use (C.20) or (C.20a); with

the explicit understanding that P >> '^ p , and that these equations are ° ms '^ms not to be used for FDM-FM systems employing noise-type signals in the

composite baseband signal.

(b) For noise type signals in the active or operating channels, calculate

(P /p .) from (C.5e) or (C.5h), and substitute in (C.21) or (C.21a) to

mn mm op

calculate the output message signal-to-noise ratio, ^S^ )j^/(N )^. For

noise-type signal loading in all channels except for "slots"; use (C.21) or

(C.21a), and (P /p .) = N, to calculate the NPR. mn *^mni npr '

(c) For test-tone signal in a voice channel and noise-type signal loading

of some, or all, of the remaining channels; obtain P^in^Pms ^^°"' (C.5h) or

(C.5i) and insert in (C.22) or (C.22a), to calculate the channel output testtone S^^N^^ ratio.

The above system-performance equations apply primarily to the transfer

function of the FM radio receiver, in terms of the receiver thermal noise and

the power level of the receiver-input RF signal; path-intermodulation noise

and intermodulation distortion effects in the RF Modulator, the frequencydivision Multiplex, and other (extraneous) equipment-noise effects are not

included^ The system-performance design equations, (C.20) to (C.22a), can

be used interchangeably with (U.19), p. 69, provided that the proper forms are

used for the factors: (P )_ „/(p„)„ ^, (AF)^ ^/f ; and the correct peak factor. m s ,n ^m s ,n ' s ,n m

2 or 20 is used with the term Pmn

*To optimize equipment performance, thermal noise may be assumed to be

equal to the equipment-intermodulation distortion. Path intermodulation noise

has the effect of limiting the bandwidth, B^^, which can be transmitted over

a tropospheric radio path without serious distortion effects.
173 p

Discussion and Conclusions

A great deal of confusion would be avoided in the interpretation of

telecommunication system performance by the use of the following guidelines:

(A) The "message"-channel signal power, (p ) , and the composite baseband signal power, P , should be adjusted to their proper

mn operating levels in the Multiplex equipment ; for the maximum number of

simultaneously-active channels during peak load conditions, (pp. 173e,

173f) . This procedure *^ establishes the Loading Factors P /p and P /p ^ mn *^mn mn *^ms (B) The proper Loading Factors P /p and P /p should be ^ ^

^ mn *^mn mn *^ms used in the system-performance design equations, (C.20) to (C.22a), inclusive, and these loading factors should be specified and measured at

the input terminals of the RF Modulator .

(C) The absolute power level of the composite baseband modulating

signal, P__> should be adjusted, at^ the input terminals of the Modulator,

so as to produce an RF-signal spectrum bandwidth, B , equal to the effective IF-signal bandwidth, B , of the radio receiver. Note that this

required modulating-signal power level, P-,n» is independent of the "normal"

operating power level of the composite baseband signal of the Multiplex

equipment, and hence either an attenuator or an amplifier is required to

adjust the modulating-signal power at the input terminals of the Modulator.

The "optimum" value of P may be obtained from NPR measurements, made

with the (entire) equipment arranged in a back-to-back configuration, including operating values of pre-emphasis and de-emphasis.
173

(D) The system-performance criterion should be the ratio:

message-channel output average message-signal power ^ ^oc

message-channel output average noise power ' moc

this ratio should be specified and measured at the system output terminals,

More specifically, the time-varying statistical characteristics of this

output signal-to-noise ratio is an accurate measure of the system-performance, and may be combined with the performance characteristics of the

message-signal decoding units, to obtain an estimate of the message error

rate.

The output message-channel average noise power level cannot be used

as a system-performance criterion, without a corresponding measurement

of the message-signal or the test-tone signal average power. In other

words, system performance can not be specified or measured simply in

terms of an absolute output noise-power level ; the system must be specified and measured in terms of the output signal- to-noise ratio .

Equations (C.20) to (C.22a), inclusive, were derived for multichannel

FDM-FM systems, and apply to the mess age -channel output signal-to-noise

ratio in the output baseband- signal spectrum ; however, proper allowances

must be made for the "acceptance bandwidth" of the instrument used to

measure the message-signal power and the noise-signal power, in the baseband signal spectrum; this bandwidth must be somewhat less than the message-signal spectrum bandwidth. These equations may also be used to

calculate and to define the measurement of the signal-to-noise ratio in

the output message channel, provided that proper allowance is made for
173 r

the degradation of the signal-to-noise ratio due to the multiplexing

equipment

The following list of factors and terms, used in this paper, is

provided for convenient reference

S = Average message-signal power level, per message channel.

oc

oc

at the radio receiver output, in watts.

N = Radio receiver output average noise power level, per

message -signal spectrum bandwidth, in watts.

B = Message-signal spectrum bandwidth, in Hz.

cf = Maximum or highest frequency in the baseband modulating

in • . Signal.

(p ) = (See p. 173c) m s,n

(P ) = (See p. 173c) m s,n

(aF) = (See p. 173b)

s,n

(aF^)^ „

- (See p. 173b)

P = Total available carrier-signal power at the input terminals of the FM radio receiver, in watts.

k = Boltzman's constant = 1.380'+xl0~^^ Joules per degree

Kelvin

T = Receiving antenna system output noise temperature, degrees Kelvin, see Appendix A, NBS TN 100.

T = Radio receiver effective input noise temperature (IRE

Comm. on Noise, 1960), degrees Kelvin, see (C.16), p. 173j

T = Standard temperature (290 degrees, Kelvin)

o

AF

-p— = Deviation ratio, or (frequency) modulation index. m

(PF. ) = (See p. 173c).

b s,n

kT = 4.00316xl0"^-'- Joules = -201 dbw x sec = -17U dbm x sec

o F^ = Radio receiver noise figure, see p. 173j

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