A FURTHER ANALYSIS OF TASO PANEL 6 DATA ONSIGNAL TO INTERFERENCE RATIOS AND THEIRAPPLICATION TO DESCRIPTION OF TELEVISION

SERVICE

Harry FineFederal Communications Commission

Office of the Chief EngineerTechnical Research Division

Washington 25, D. C.

Introduction

Panel 6 of TASO performed a monu-mental and very creditable task in organ-izing and accumulating data on the signalto interference ratios required for tele-vision service, as presented in its re-port. Because the Panel was uncertain asto the uses to which the F.C.C. mighteventually put the.data, the presenta-tions were left in a relatively unfinish-ed form. It is the purpose of this reportto develop the data further into a formmore useful for certain purposes and todevelop the formulae for the applicationof these signal to interference ratios tothe description of television service.As a by-product of this analysis it ishoped that the reader will have a betterunderstanding of the basic concepts ofquality and service. The report will bedivided into two parts. In Part I, theTASO data will be reanalyzed and develop-ed into the new form, and in Part IIthese results will be applied to thedescription of television service.

PART I: FURTHER ANALYSIS OF TASO DATA

TASO AnalysisBasically the data was taken by

Panel 6 using a six point rating system.Thus, a picture was displayed with agiven signal to interference ratio, R,and each viewer rated the picture as fall-ing into one of six quality classes -Excellent, Fine, Passable, Marginal,Inferior, or Unusable. This procedurewas followed for a number of discrete Rratios for each displayed picture and typeof interference. Great care was taken toensure that no bias was introduced intothe results by careful viewer and pictureselection. After each test the voteswere added and the data could then beput into the form of a vote density table,such as Table I. Each box in the tablerepresents the percentage of votes castfor the pertinent quality class with thegiven sional to interference ratio R, aslisted in the first column and first row,respectively.

The data in the tables were thenanalyzed, interpreted and displayed in

two methods, each giving different signalto interference ratios required for thevarious classes of service. In Method I,cumulative distributions for each R ratiowere computed of the percentage of view-ers voting that the displayed picture wasof a given quality class or better. Thesedata were plotted on linear-normal prob-ability paper with the R ratio in deci-bels as the ordinate and the above cum-ulative percentages as the abscissa.Then a smooth curve was drawn throughthe percentages pertaining to a givenclass of service (see Fig. 1).

In Method II, a quality grade numberfrom 1 through 6 was assigned to each ofthe above discrete classes of quality, as.shown in Fig. 2A. The mean grade, m, wascomputed for each ratio R from densitytables, similar to Table I, by taking theweighted arithmetic average of all theratings for that ratio. Thus, the meanquality grade m is equal to thie sum ofthe cross products of grade number anddensity percentage divided by the sum ofthe density percentage for a given signalto interference ratio R. These meangrade ratings were then plotted versusthe signal to interference ratio R togive a sigmoid type of curve for eachexperiment.

As recognized by TASO, both MethodsI and II give different answers fortypical observer reaction, if they areliterally interpreted. In this writer'sopinion, neither type of presentation istoo useful, except that the Method Idistributions supply the basic data fromwhich a more accurate and useful inter-pretation can be developed.

Interpretation of TASO Results

In order to develop a better under-standing of the concept of quality andas to what information is desired fromthe TASO experiments, imagine severalhypothetical experiments carried out witha very large group of viewers. The firstexperiment would be one in which the sig-nal to interference ratio R is variedover a very wide range in small incre-mental steps. At every step each viewerrates whether the ratio R is too large,

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too small, or just right for a givenquality class of picture. When as manyof the viewers say that the ratio R is toolarge as say that it is too small, thenthe pertinent R ratio is that required forthe given quality class by the median ortypical observer. This type of test isrun for the middle four classes - Fine,Passable, Marginal and Inferior - and theR ratios required for the median observerare the typical levels for quality Grades2, 3, 4 and 5, respectively. Grades 1 and6 would be the conditions of no interfer-ence and no desired signal, respectively.It will be shown in a later section thatthe above interpretation of Grades 1 and6 fits the statistical structure of thedata, in addition to which similar workin the field of psychometrics 2.3,4/ alsofits this type of interpretation for theextremal grades of quality.

Now imagine a similar experiment inwhich the signal to interference ratio Ris again varied in incremental steps butthe observer rates the quality of thepictures using the six point class systemof Fig. 2. Then, at the R ratio for whichhalf of the observers rate the pictureExcellent and the other half rate it asFine or worse, the quality must be half-way between Grades 1 and 2 or Grade 1.5.Similarly, when half of the observersrate the picture as Fine or better andthe other half rate it as Passable orworse, the pertinent R ratio correspondsto Grade 2.5. Thus, from this type ofexperiment the R ratios for Grades 1.5;2.5; 3.5; 4.5; and 5.5 could be estab-lished for the median or typical observer.These grade numbers are recognized asthose which separate the adjacent qualityclasses.

From the above hypothetical experi-ments it could be established that qualityincreases continuously as the R ratio isincreased, as evidenced by the fact thatthe percentage of viewers voting for abetter grade increases continuously. Now,returning to the individual viewer, it isobvious that each of the six classes ofquality which he uses for voting (Excel-lent, Fine, Passable, etc.) must cover arange of R ratios, which ranges are con-tiguous for adjacent classes of qualityand usually not the same for differentviwers. Therefore, each class embraces arange of quality, which the viewer may ormay not recognize individually. Thus, inthe range from just barely Passable tovery Passable but not quite Fine, theviewer will vote Passable. In other words,the Passable class includes the range ofquality from Grade 3.5 to Grade 2.5. Bysimilar reasoning the grade number rangesfor each of the classes may be derived.With respect to the extremal Excellent

and Unusable clapses these are limited bythe highest and lowest grade numbers. Inother words, the Excellent class includesthe range of quality from Grade 1.5 toGrade 1 and the Unusable class extendsfrom Grade 6 to Grade 5.5. The gradenumber ranges covered by the six classesare shown in Fig. 2B.

Returning to the TASO Method I formof presentation, as illustrated in Fig. 1,it becomes evident that these are not dis-tributions of quality reaction by themedian viewer for the average qualit-y ofeach class. Thus, in computing the per-centage of viewers rating a picture asPassable or better, all the votes forPassable were naturally counted, includingthose from viewers who thought that thequality of the picture was just barelyPassable. In other words, this Passabledistribution represents more precisely thepercentage of viewers voting for Grade 3.5or better and not Grade 3 or better. Ittherefore becomes apparent that the cumu-lative distribution for each class of qual-ity represents the distribution of observ(.er ratings above the highest grade number(or lowest quality) for the class. Thus,the Excellent, Fine, Passable, Marginaland Inferior distributions of Method I areactually distributions of viewers ratingthe picture quality as of Grades 1.5; 2.5;3.5; 4.5; and 5.5 or better, respectively.Any signal to interference ratio R obtain-ed from the Method I curves would, there-fore, not represent the median viewer re-action for the average quality of thepertinent class but rather the reaction ofthe median views for the lowest quality ofthe class.

The TASO Method II form of analysissuffers from two defects. First, as rec-ognized in the TASO Report, it assumesthat the various grades are equally spacedin quality, which assumption is not ap-propriate except in a limited region, aswill be evident later. Secondly, itassumes that Excellent extends upward toa Grade 0.5 and Unusable downward to aGrade 6.5. It will be shown later thatthe statistical structure of the observerreaction best fits the concept that Grades1 and 6 are the extremities. Since theabove two assumptions are not valid exceptpossibly in a limited range,.the Method IIaverage grades, m, are not quite correct,the discrepancies increasing as theaverages approach the extremities for highor low R ratios.

Further Analysis

Since the concept of a continuouslyvariable quality must be accepted, it isnecessary to find an analytical parameterfor the quality which fits the statistical

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structure of the data. Furthermore, sincethe original distributions of votes wereobtained by fixing the R ratio and usingquality as a variable, any regular dis-tribution and pattern should be developedwith quality as the variable.

On the basis of analogous work car-ried out in psychometrics, a plot of themean grade, m, of Method II versus the Rratio in decibels is expected to give asigmoid type of curve, as it does, char-acteristic of a logistic function. 2.3e4/It has been found that a transformationfrom m to

(1) Mo = log M - 1

converts the sigmoid curve into a straightline. The dependent variable M may berecognized as the logarithm of the ratioof the probability of a favorable rating(Passable, Fine or Excellent) to theprobability of an unfavorable rating(Marginal, Inferior or Unusable) for thesix point rating system.

It was then decided to try a similartransformation to a parameter of the typein (1). Accordingly, each grade numberof Fig. 2A was transformed into an equiv-alent quality index M by:

6-q(2) M = log qq-1where q is the quality grade number (notthe mean grade m). Fig. 3 shows a set ofcumulative distributions of the M factorsfor the various R ratios for Table I. Itis noted that the distributions are ap-proximately normal and parallel, the var-iations from normal being what might beexpected for limited finite samples. Indrawing these distributions, the data wereplotted at Grades 1.5, 2.5, 3.5, 4.5 and5.5, corresponding to the classes Excel-lent, Fine, Passable, Marginal and Infer-ior, respectively. These distributionsare all combined in Fig. 4 to get anaverage normal distribution by plottingthe deviations from the medians of thecurves of Fig. 3. The best fit linethrough the data is drawn in Fig. 4 andthis line determines the standard devia-tion. The medians of the individualdistributions of Fig. 3 were then plottedversus the pertinent signal to interfer-ence ratios R in Fig. 5 to provide a nicelinear relationship. This latter curvemay be expected to depart somewhat fromlinearity at the extremities, since inthese areas some of the observers maytend to rate the quality of the pictureon factors other than interference-- i.e.,picture content. At any rate, thereappears to be no doubt as to the appro-priateness of the normal distribution forthe quality index M, nor as to the linear-

ity of the median M versus the signal tointerference ratio R in the useful range.A somewhat better fit might-have beenachieved in Figs. 4 and 5 had the mean, M,been used in place of the median, but thecomputation of a mean M would have beenlaborious without yielding much betterresults.

Similar plots were made, but are notshown here, under the assumption that thegrade numbers of Fig. 2B extended from 0.5to 6.5 and from 0 to 7. Neither of theseapproaches gave anywhere near as coherentor linear results. Since the normal orGuassian distribution is probably the mostbasic in statistics, it is reasonable topresume that the M index of (2) is thebasic quality parameter and that Grades1 and 6 are the extremal values.

To complete the proof, table II wascomputed from the mean normal distributionof Fig. 4 and the linear relationship ofFig. 5. The technique for the computa-tions is outlined in the next section ofthis report. It is observed that theagreement between the observer reactiondensity Tables I and II is quite goodconsidering that the number of observersinvolved constitues a relatively smallsample, statistically.

Analytic Form

It is now possible to put the resultsin an analytic form so that a singleequation is sufficient for the predictionof quality in the presence of a giventype of interference.

It has been shown that for a giveninterference the viewer response may bedescribed by a simple normal distribution.The normal distribution is, of course,given by:

(3) Q(c'c) ='

where co is the standard normal variableand Q(ccoco.) is the probability that c'is greater than or equal to the value w .For convenience, QvscJis plotted in Fig.30.

From the plots of Figs. 3 and 4, ithas been shown that the quality index Mis normally distributed with a mean M andstandard deviation O; and may be put intothe standardized normal form as:

(4) 'A9= AYzM

M = log 6-c-where q-l

q = the quality grade rating number,as shown in Fig. 2B

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(5)

M _ the quality index

6v = the standard deviation of viewerreaction in quality rating thepictures for the given type ofinterference

M the mean value of M for a givensignal to interference ratio R

R _ the signal to interference ratioin decibels

It has been shown that the median oraverage (both are equal for the normaldistribution) quality index M is linearlyproportional to R, so that

,6) M (R - RO)

where Ro is the value of R for M equalzero (q = 3.5). In other words, at thislevel half of the observers would be ex-pected to vote for a favorable rating(Passable or better) and the other halffor an unfavorable rating (Marginal orworse). Eq. (4) and (6) may be combinedto give

(7) cWV)= M - + (R4Ro) = R.(Rn+bM)TIv- ~bO-V

=log ) - + (R - RO)

Eq. (7) shows that not only is the viewerquality index M normally distributed fora given ratio R but so should be theviewer response to the signal to inter-ference ratio R deemed necessary for agiven grade of service. Eq. (7) alsoshows that

(8) Q(W'>Wv) = Q(M'>M) =

Q(q'4 q) = Q(R'4 R)where q is the quality grade numbercorresponding to M. In other words, thepercent of viewers who rate the pictureas of a given grade or better for a givenR ratio is equal to the percent of viewerswho think that the pertinent R ratio orsmaller is needed for the given grade ofpicture quality q. The latter statementbecomes obvious with a little thought.

The question arises then as to whysome of the TASO Method I plots do notshow up as more linear, as they should beon the basis of (7). This lack of linear-ity probably occurs for the followingreasons.

First, from the plots of M versus Rthere sometimes appears to be other

factors wnich affect the viewer qualityrating at the high and low signal tointerference levels. Thus, for high Rratios the quality may not increase asrapidly as in the middle R ranges, andfor low R ratios the quality may seem toincrease faster than normal, most likely,the result of the viewers rating the pic-ture on the content, rather than interfer-ence. These departures are indicated onthe M versus R type plots by the dashedlines. The apparent linearity of thesedepartures indicates that these extremaltrends also have a similar statisticalstructure. At any rate, these departuresfrom normal tend to bow the R distributions.A second reason for the lack of linearityin some of the R distributions may lie inthe sample size and the method of sampling.In other words, the data were taken underconditions for which the R ratio was heldconstant and the quality ratings were var-iable. The departures from a normal dis-tribution to be expected for a relativelysmall sample of observers would then bein quality grading observations M ratherthan R. The distribution identified by(6) is one in which the ratio R is variedcontinuously for a given observer and heselects the average level at which hethinks that a given grade of qualityoccurs. Thus, each observer should reallyvote only once per quality grade,

Fortunately, the distribution in R isrelatively unimportant. The distributionof quality and the linearity of M versus Rin the range of quality grades 2 through 4are the important trends which are usedfor TV service description, as discussedin Part II.

On the basis of the above argumentsit appears that at least the midranges ofthe ratio R should be normally distributedfor a given quality grade. For thisreason, the median R values from plots ofthe TASO Method I type were also used in theM vs R plots (see Fig. 5) to give moredata in determining the best fit line forthese trends.

Returning to (7) again, this equationmay be used in conjunction with (3) forcomputing the ratio R required to providea given grade of quality or better to agiven percentage of the viewers for agiven type of interference. Thus, thequality grade and the percentage of view-ers would determine M and I), respectively,and knowing b, RoH and co the value of Rmay be computed from (7). Conversely,given a value of R, the distribution ofviewer rating may be calculated from (7).Table II, which has been mentioned pre-viously, was derived in this fashion.Each of the discrete class ratings wasconsidered to contain the sum of the view-

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er ratings (or more precisely, viewerprobabilities) between the limits of theclass in grade numbers as shown on Fig.2B. Thus, if Vql is the percentage ofviewers rating the picture as of Gradeor better, and V 2 is the percentage ofviewers rating tie same picture as ofGrade q2 or better, then IVql.- Vq2lisnaturally the percentage of viewers vot-ing in the quality range between q1 andq2. In computing Table II the quaIitygrade ranges of Table III were used.

For more details as to the applica-tion of (3) and (7) to the description ofTV service, where the signal to interfer-ence ratio R varies both with locationand time, the reader is referred to PartII of this report. It will be shown thatthe simple linear results developed hereblend very well with the analytic rela-tionships already established for thevariation of signal strength with timeand location.

Another advantage to the simplelinear relationships developed accruesfrom the fact that in the future a smallernumber of measurements will be requiredin measuring observer responses to inter-ference of the same or other types, sinceit is much easier to fit a straight lineto data than an unknown curve.

Cochannel Interference

Rather than draw individual M dis-tributions and curves for all the individ-ual tests compiled for the TASO report,it was decided to combine the densitytables into the desired output combina-tions where possible, and then evaluatethe pertinent trends. Table III liststhe various cochannel offset frequenciesand the nearest odd or even multiple ofthe frame rate frequency. For those notfamiliar with the F.C.C. standards, thestandard frame rate is 1/525 of the hori-zontal scanning frequency, or 29.97 cps,but for monochrome transmissions a nominalframe rate of 30 cps is permitted.

It is noted from Table III that the9985 cps offsets for both frame rates maybe combined, since this frequency is only5 cps away from the worst offset condition(odd number of frame rates) in both cases.The 19,995 cps offset for 29.97 cps isexactly at the worst condition, whereas.for a 30 cps frame rate it is only halfway between the worst and best (evennumber of frame rates) conditions. There-fore it was decided not to combine thedata for the 19,995 cps offset, 30 cpsframe rate, with the 19,995 cps offset,29.97 cps frame rate, or with the 9985 cpsoffsets, since these latter combinations

represent the worst conditions only. In asimilar fashion, it was decided to use onlythe 10,010 and 20,020 cps offsets with the29.97 cps frame rate as representative ofthe best offset conditions. With the 30cps frame rate, the 10,010 and 20,020 cpsoffsets were 10 and 20 cps, respectively,away from the optimum condition, too farto be really optimum.

Density tables, similar to Table I,were derived for all the pertinent offsetcombinations from the cumulative distribu-tions of the Method I displays in the TASOPanel 6 Report. Then, when possible, thetables were combined by averaging thepercentage densities for each box to ob-tain density tables for the desired com-binations.

The results for the 9985 cps offset,both scenes and frame rates pooled, havealready been described in Figs. 4 and 5.The corresponding curves for 19,995 cpsoffset, 29.97 cps frame rate with scenespooled, are shown in Figs. 6 and 7. Thesetwo sets of figures represent the worstoffset conditions for the nominal 10 kcand 20 kc offsets respectively. The twosets of data were then combined on anequal weighting basis in Figs. 8 and 9 toobtain the overall combined results forthe worst offset conditions. The variance--r -_ of Fig. 8 was derived by averag-ing the variance of Figs. 4 and 6, whereasthe line of Fig. 9 was obtained by averag-ing the constants b and Ro of Figs. 5 and7. Both the 9985 cps and 19,995 cps off-set data are displayed along with thecurves to show the fit of the data. Thebasic density tables for the 9985 cps and19,995 cps offsets could not be averagedbecause the R ratios for the two sets ofdata were not generally the same. It isapparent that the cochannel interferencewith a 19,995 cps offset is a bit moresevere than with the 9985 cps offset.

The results for the best offset con-ditions 10,010 cps, 29.97. cps frame rate,and 20,020 cps, 29.97 cps frame rate, areshown in Figs. 10, 11, 12, and 13. It isapparent from the range of the dashedlines that at the lower signal to inter-ference ratios other factors were influ-encing the quality rating more than forthe upper R ranges.

The density tables for the above twooffsets were averaged to give Figs. 14 and15. The individual data for the 10,010cps and 20,020 cps offsets are alsoplotted on Figs. 14 and 15.

Figs. 16 and 17 show the viewerresponses to the best "on-frequency"operation, normally called "very precise

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offset," for an offset frequency of 360cps. Fig. 17 seems to indicate that theviewer response as reflected in M changedquite rapidly up tox'a quality of aboutGrade 2, after which some other factorcaused the viewer response to change muchmore slowly as the R ratio increased stillfurther. It is this influence whichcaused the relatively poor fit of thedata to a normal distribution in Fig. 16.That something unusual was happening isalso apparent from the original Fig. 46of the TASO Panel 6 Report, which indi-cated very little change in the qualityrating for signal to interference ratiosbetween 27 and 57 db. This type of inter-ference is not expected ,- occur fre-quently and when it does occur it willusually be secondary to the cochannel"precise offset" type of interference.

Probably the worst cochannel inter-ference occurs with an offset of 604 cps.Figs. 18 and 19 show the results for thisoffset condition. This condition hasbeen assumed by the Commission for com-puting the interference between stationsoperating "on frequency" with no veryprecise frequency control.

Adjacent Channel Interference

The same M parameter works equallywell for adjacent channel interference.Figs. 20 and 21 show the Upper AdjacentChannel interference. The Lower AdjacentChannel interference is shown in Figs. 22and 23 for the presently normal conditionof the sound power down 3 db below thevideo peak power. Figs. 24 and 25 showthe interference for the conditions inwhich the (present) sound power is furtherreduced by 7 db so that it is 10 db belowthe video peak power. It is noted thatthe mean curves of M vs R in Figs. 23 and25 for the two levels of sound power areapproximately parallel and separated byabout 5.5 db.

The average of the interferencecurves for the upper adjacent channel andthe normal (sound power 3 db down) loweradjacent channel interference is shownin Figs. 26 and 27. These lines were alsoobtained by averaging the o-2 v b, and RO.Noise

The interference from random noiseis shown in Figs. 28 and 29. Only thedata from the Miss TASO scene (see orig-inal TASO Fig. 38) was used since thistest represented the largest number ofviewers. Actually, the distribution ofratings for Fig. 39 of the Panel 6 Reportwith seyen scenes pooled but with a muchsmaller number of viewers is close tothat of TASO Fig. 38 so that had the re-

sults of these two figures been combinedthe resulting curves would have been sub-stantially the same.

PART II

Descri2tion of Television Service

The theory will be developed herewhereby the simple quality formulae,developed in Part I, may be applied to thedescription of television service for thepractical case where both the desired sig-nal and interference may be varying inamplitude both with time and from locationto location.

The instantaneous field strength froma station may be described analytically by:

(9) F = [F - FT (50 + T (50)- F(50,503

= Xi + Yi + F(50,50) dbu

where

FT(50) the average field strengthat a given location indecibels above one micro-volt per meter (dbu) overa long period of time.

F (50, 50) =

(10)The average field strengthin dbu, both in time andfrom location to locationfor a given distance,antenna height, power,frequency, etc.

Xi = [F - FT(501 represents thevariation with time at agiven location.

Yi -[FT(50) - F(50,509 representsthe variation of timeaverage field from loca-tion to location.

Because it is not practical to pre-dict the individual variations for everylocation and instant of time, it is nec-essary to treat these amplitude variationson a statistical basis. Thus, a statis-tical field strength variable is intro-duced:

(11) F(L,T) = xi + yi + F(50,50) dbu

where F(L,T) is the field strength levelexceeded for T percent of the time at Lpercent of the locations or better. An-other way of considering F(L,T) is todefine a T percent field, F(T), as thefield- strength exceeded for T percent ofthe time at a given location, then F(L,T)becomes the field strength level exceeded

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by T percent fields at L percent of thelocations.

It is known from measurements thatthe time variable xi is approximatelynormally distributed 5.6,9/ with zeromean and standard deviation, cTTip whichvaries with distance, frequency and an-tenna height. Likewise for reasonablesized areas the variation with locationYi is also approximately normal with zeromean and standard deviation, Ofl, whichvaries with at least frequency. The usualassumption is that OrL is independentof distance or antenna ?ieight. The sta-tistical variables xi and yi may be rep-resented as

xi(= C4i T,iYi = OLLi

where, of course, CCi andcJLi are stand-ard normal variables related by (3) orFig. 30 to the probabilities that xi andYi, respectively, are exceeded.

The receiver input power in decibelsabove one watt is related to the fieldstrength at the receiving antenna by:

(13) P = F+G-20 log fmc -Pe-105.1 dbuG the receiving antenna power

gain for the pertinent direc-tion in decibels above that fora half wave dipole.

fmc - the frequency in megacycles persecond

(14)Pe - the receiving installation

transmission line loss indecibels

F _ the field strength in decibelsabove 1 microvolt per meter(dbu)

Substituting (11) and (12) into (13) thestatistical power input variable is ob-tained.

(15) P(L,T) = xi + yi + F(50,50) +

G - Pe- 20 log ImC-105.1= CTi C'1Ti + '7Li C--Li

+ F(50,50) + G - Pe- 20 log fmc - 105.ldbu

Here P(L,T) is the level of power input tothe receiver exceed for T percent of thetime at L percent of the locations orbetter -- corresponding to F(L,T). In the

case of noise power generated at the re-ceiver input.(16) Pn = 10 log ktB + NF

= 10 log B + NF - 204.0 dbu

where

B - the bandwidth of the receiver incycles per second

(17)NF - the receiver noise figure in

cycles per second

t.- the temperature in degrees Kelvin

k - Boltzman's constant (1.38 x 10-23)The numerical value assumed2or k t atroom temperature is 4 x 10-2 . In comput-ing TV service, noise is generally assumedto have negligible time fading or varia-tion from location to location, so that Pnis assumed to be constant for a givenfrequency and type of. service.

The ratio R in decibels of a desiredsignal to interference at the receiver in-put then becomes

(18) R = Pd - Pu = (xd-xu)+ (yd-Yu)+ Fd(50,50) - FU(50,50) + Gd

- Gu - 20 log fmcdY;;E

Roo + x + y db

where

x xd - xu

(19) y = -

Roo = Fd(50,50) - Fu(50,50) + Gd - Gu

- 20 log fmcdfmCu

In the above, the d and u subscriptsrefer to the desired and undesired signals,respectively. R is also recognized as astatistical variable or level which couldhave been labelled as R(L,T). x representsthe variation with time of the ratio ofthe desired signal to interference and ythe variation of this ratio from locationto location.

It is known from the theory ofstatistics that the sum or difference oftwo normal variates is also normallydistributed. Thus.

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(12)

(20)C)T = Xd *As

X

C-' C-1And with a 90% time criterion forthe adjacent channel interferenceare usually solved by determiningR from Fd(50,90) - Fu(50,50).

CAJ Yd YuL

y

L

TacrTd -Tu -2< tw

a:2rLJ CLv OfXJ CrLwhere, again, 0T andC are standardnormal variates, related by Fig. 30, tothe percentages T and L for which theservice variables x and y, respectively,are exceeded. Measurements 9,10.11/ haveshown that for most practical cases Xhecorrelation coefficients P0T and i Lare negligible and may be assumed as zero.

Substituting (20) into (18),

(21) R = R + CTJ cAl + QL CL

For the special cases where the timefa.ding of one of the signals is at leastseveral times greater than that of theother, some simplifying approximationsmay be applied, Thus

(22) Fu(50,50) + GtC1 -Fu(50,l00-T)

R + -TWCT)TFd(50,50)F (50,100-T) + Gd Gu

mcd

20 log ------

fmcuThe Commission makes use of this approxi-mation by specifying that the service atany location is not acceptable unless itexists for 90% of the time or better(T = 90%). Under this definition of ser-vice, most cochannel interference prob-lems resolve themselves into determiningR from the ratio Fd(50,50) - FU(50,l0)

Similarly, for adjacent channelinterference in which the time fading ofthe undesired signal is usually muchsmaller than that of the desired signal

Fd(50,50) + Oc9'' Fd(50,T)

(23) 00+ d-%F ,T)-

~~~~~mcdu Gd - GU 20 logmc117 mcu

Td >>tTu

When receiver noise is the interferepce

X = d =rT=-Td(24) Y =YdL-d

R + COT - = Fd(50,T) Gd -

Pe 20 log f - 10 log Be mcdlo

NF + 98.9

(25) R = Pd - Pm = Roo + X + Y

= Roo + cF-T,)T + C-L e= Fd(50,T) + Gd - Pe

20 log fmcd - 10 log B -

NF + C-LWL+ 98.9 db

And for the 90% service time requirementthe computation of service in the presenceof receiver noise becomes one of determin-ing R from Fd(50,90).

It has also been shown in Part I thatthe quality index M is normally distribut-ed with a standard deviation 0v' about themean R as given by (6), so that

R = Ro + bM - bO-v v

(26) = Ro + bM - Z

Z = brv CWk

Since CAkv is the standard normal variateand b C,, is constant, Z must be normalwith zero mean and standard deviation bOv.The observer or televiewer response to TVsignals may then be derived by equating(26) with (18) or (25) to give

(27) bM= (Roo0-Ro) + x + y + z

= (Roo - RO) + cTTCA + a-LCL +

b C>, csOv

In (27) there are four normal varia-bles -- x, y, and M. X describes thefluctuations of the signal to interferenceratio R with time, y the variation of Rfrom location to location, z the variationin viewer response with R, and M the vari-ation in picture quality. Only three ofthe above variables can be considered asindependent, the fourth being related tothe other three by (27). It is obviousthat an infinite number of combinations ofT, L, q and V (percent of time, percent oflocations, quality grade number and percentof viewers) will describe the same signal

29

service,problemsthe ratiO

to interference ratios. In practice, itis customary to standardize three of thevariables - usually M, x and z; i.e., T,q and V, - so that only the percent oflocations L varies for a given type ofservice. In defininc distance contourlimitations of service all four of thevariables are preset.. Standard receivinginstallations are normally assumed whichmay be different for different types ofservice.

In any practical situation for. whichTV service is to be estimated the ob-servers or viewers are randomly located,so that it is usually desirable to com-bine the variation in viewer response withthe variation in R from location to location,Thus,

(28) bM = (Roo - Ro) + X + u

where u =Y + Z(29) 2V +- b2+ 2

In the above, u describes the-viewer re-sponse when the viewers are randomly dis-tributed at different locations. Now,there are only three normal variables -x, u and M - of which only two are inde-pendent. In practice, it is likely thatx and M - i.e., T and q - will be presetto describe a given type of service.

In order to show the actual procedurefor the computation of service, severalnumerical examples will be carried throughand the procedural steps tabulated.

Example I

Consider the problem of computing thepercentage of rural viewers getting aGrade 3 picture or better 90% or more ofthe time in the presence of receiver noiseat a distance of 40 miles from a Channel4 TV station radiating 100 kw from a 1000foot transmitting antenna. The receivingantenna is assumed to be a height of 30foot with a gain of 3 db above that for ahalf wave dipole. Further, it is assumedthat the average receiver noise f'igure is7 db and that the transmission line lossis 2 db. From these given values and theavailable field strength curves the pro-cedure in computing the desired servic,eresults .may be tabulated.

Factor Value Reference

Fd(50,90) 64 dbu Ref. No. 6

C-L = crLd 8.28 db Ref. No. 7

10 log B 66 db B = 4,000,000

(Continued)

Factor

Gd

Pi

Value Reference

3 db Given

2 db Given

20 log fmc 36.5 db

NF

brvb

Ro

M

fmc= 67.25 mc/s7 db Given

0.356 Fig. 28

12.3 db Fig. 29

27.8 dbu Fig. 29

9.37 db (29)

0.176 (4)

Roo+ jT WT 54.4 db (24)

WVL -2.60 (28)V (Percent 99.5%

of viewers)Fig. 30

Example 2

As another typical example, it is de-sired to compute the service range on aline between stations of the above TVstation, as limited by a similar cochannelstation at a separation of 170 miles andemploying a 10,101 cps offset with a 29.97cps frame rate. Further, the service underconsideration is to be for Grade 2 pictureor better for 90% of the time or more toat least 70% of the viewers. The receiv-ing antenna is assumed to have a 5 dbfront to back ratio. No other sources ofinterference are assumed to exist. Formultiple interference considerations thereader is referred to Vol. II of the AdHoc Report. This problem may be solved byusing the approximation (A14) and computingthe required value of Fd(50,50) - FU(50,10).Then this ratio of median desired to 10%undesired fields is found for several dis-tances from the available propagationcurves and the required distance to thespecified service contour is interpolated.The computation procedure may be tabulatedas follows:

Factor Value Reference

ULd= riu(YLGd -Gu

fmod2)l0g ---

cu

8.28 db Ref . N. 12

11.71 db (20)

5 db Given

0 db Given

30

(Continued)

Factor Value Reference

16.0 db Fig. 11

15.7 db Fig. 11

.481

GVL

CA>T

M

Fd (50,50)-Fu(50,10)required

Fig. 10

14.01 db (29)

-1.28 Fig.30(T=90%)

-.525 Fig.30(V=70%)

.602

32.7 db

27.7 db

Fd(50,50)at 40 miles 66.5 dbu

Fu(50,10) 37 dbuat 130 miles

Fd(50,503- 29.5dbuFu(50,10)

Fd 2(50,50)at 45 miles

(4)

(28)

(22)

Ref. No. 6

Ref. No. 6

Ref. No. 6

62.5 dbu Ref. No. 6

Fut(50,10) 37.5 dbu Ref. No. 6at 125 miles

Fd (50 50- 25.0 db-Fu2.(50, 10)

By interpolating between 40 and 45 miles,the required service contour is found tobe 42 miles.

Conclusion

In Part I of this report a moreprecise interpretation of the TASO Panel 6signal to interference ratio data isdeveloped. By transformation to a newquality index M, the viewer reaction toany given type of interference can bedescribed as a continuous variable havinga basic normal distribution. Further,a simple linear relationship has beendeveloped between the average qualityindex M and the signal to interferenceratio R.

The above relationships are combinedin Part II with the known variability ofTV signals, both with time and from loca-tion to location, to proxide usefulanalytic relationships which permit afairly complete prediction of TV service.

BIBLIOGRAPHY

1. Report of Panel 6 "Levels of PictureQuality" Television AllocationsStudy Organization, Jan. 1959

2. "Subjective Impairment of TelevisionPictures" by L. E. Weaver, Electronicand Radio Engineer, May 1959

3. "Psychometric Methods" by J. P. Gulfoid,McGraw Hill, 2nd Edition, 1954

4. "Probit Analysis" by D. J. Finne,Cambridge Univ. Press, 2nd Edition

5. "summary of Tropospheric PropagationMeasurements and the Development ofEmpirical VHF Propagation Charts" byE. W. Allen, W. C. Boese and HarryFine, F.C.C. Report TRR 2.4.6,Reference D to the Report of theAd Hoc Committee

6. "Propagation Data and Service Calcula-tion Procedures Used for the Rescind-ed Appendix "A" of Report and Order(Docket 11532) Released June 26,1956" by H. Fine and J. Taff, F.C.C.Report TRR 2.4.16

7. "Ground Wave Propagation Over Irregu-lar Terrain at Frequencies Above50 Mc" by K. A. Norton, M. Schulkinand R. S. Kirby, Reference C to theReport of the Ad Hoc Committee,June 6, 1949

8. "UHF Propagation Within Line ofSight" by H. Fine, F.C.C. ReportTRR 2.4.12

9. "East Coast Tropospheric and SporadicE Field Intensity Measurements on47.1, 106.5 and 700 Mc" by G. V.Waldo, F.C.C. Report TRR 2.4.4(Revised), June 3, 1949

10. "VHF Propagation Measurements in theRocky Mountain Region" by R. S.Kirby et al, NBS Report 3564, Jan.1956

11. "Correlation in VHF Propagation OverIrregular Terrain" by R. S. Kirbyand F. Capps - I.R.E. - P.G.A.P.,Jan. 1956

12. "Report of the Ad Hoc Committee forthe Evaluation of the Radio Propaga-tion Factors Concerning the TV andFM Broadcasting Services Between50 and 250 Mc" - May 31, 1949, sub-mitted to the F.C.C. for DocketsNos. 8736, 8975 and 9175.

31

b

TABLE I

Cochannel Interference, 9985 cps Offset, Frames a(TASO Figs. 46, 48, 50, 52)

Measured Percent of Viewers Voting for Various C

Class R in db 10 14 18 22 26

Excellent 0.75 3.25 10.5

Fine 0.75 7.25 19.25 38.75

Passable 2.25 8.0 27.5 37.75 31.0

Marginal 9.0 28.0 35.0 28.5 13.5

Inferior 40.25 39.5 20.0 11.0 5.25

Unusable 48.5 23.75 9.5 0.25 1.0

TABLE II

Cochannel Interference, 9985 cps Offset, Frames i

Computed Distribution of Viewer Votes from I

Class R in db 10 14 18 22 26

Excellent 0.1 0.6 2.8 9.3

Fine 0.9 3.7 10.7 24.0 39.4

Passable 5.1 12.6 23.3 30.7 29.4

Marginal 16.8 26.8 31.4 26.6 16.2

Inferior 47.8 43.5 29.5 14.8 5.5

Unusable 29.4 13.3 4.5 1.1 0.2

and Scenes Pooled

2uality Classes

30 34 3E

21.75 36.75 6'

45.0 45.75 2(

18.5 12.0

9.75 4.75

4.75 0.75

0.25

and Scenes Pooled

Figs. 4 and 5

30 34 31

23.2 44.1 6'

47.8 43.1 21

20.3 10.2

7.2 2.3

1.5 .-_

3

3.0

6.5

7.25

3.0

0.25

7.0

38.8

3.7

0.52

TABLE III

Quality ClassUpper Limit

Grade qlLower LimitGrade q2

Percentage VotingFor Class

V1.5 - V1

V2.5 - V1 5

V3.5 - V265V4.5 - V3.5V5 5 - V4 5

V6 - V5 5

Excellent

Fine

Passable

Marginal

Inferior

Unusable

1

1.5

2.5

3.5

4.5

5.5

1.5

2.5

3.5

4.5

5.5

6

32

__

TABLE IV

Cochannel Offset Frequencies as Related to Frame Rates

Nearest Multiple of Frame Nearest Multiple of FrameOffset Freq. Rate 29.97 cps Rate 30 cps

(cps)Frequency Multiple Frequency Multiple

360

604

9,985

10,010

19,995

20,020

359.64

599.4

9,980

10,010

19,995

20,020

12

20

333

334

667

668

360

600

9,990

10,020

20,010

20, 010

12

30

333

334

667

667

Type of InterferenceCochannel

'I

'1

*1

it

it

Upper Adjacent Ch.

Lower Adjacent Ch.

Adjacent Channel

Lower Adjacent Ch.

Random Noise

TABLE V

SUMMARY OF NUMERICAL CONSTANTS

Frame Inter-Offset Rate ference _(cps) (cps) Condition 7v

9985 29.97,30 Worst .465

19,995 29.97 Worst .398

Average of above two .433

10,010 29.97 Best .481

20,020 29.97 Best .487

Average of above two .484

360 29.97 Best .493

604 29.97, 30 Worst .438

--- .617

(Sound down 3 db) .448

Average of above two .538

(Sound down 10 db) .360

--_ __ --- .356

20.7

25.9

23.3

15.7

17.5

16.5

23.0

41.2

-26.8

-26.5

-26.6

-32.1

27.8

33

b

15.0

19.1

17.0

16.0

14.6

15.3

7.3

23.0

9.7

13.6

11.6

13.5

12.3

Grade2

29.6

37.5

33.6

25.4

26.4

25.9

29.1

55

-20.9

-18.4

-19.7

-24.1

35.2

Grade3

23.3

29.3

26.3

18.5

20.2

19.3

24.4

45.2

-25. 1

-24.1

-24.6

-29.8

30.0

Grade4

18.0

22.6

20.3

14.7

15

14.9

21.7

37.2

-28.6

-28.9

-28.7

-34.5

25.6

IRo

Fig. 2ATASO METHOD II FOR NUMERICAL GRADINGOF PICTURE OUALITY CLASSES

Grade Number

1ice7 e PASSASE SARICNAL INFEIROO UNUSiALEOualily

Fig. 2BGRADE NUMBER RANGES FOR VARIOUS QUALITY CLASSES

Grade Number

Quality Class

_i= .2

:~~~~~~~~~~~~~~~~~~~~~'o~~.T5 I Z 5 10a I0 444 so is 00.~~~~~5

Pered of V_les ting PLclure s QudtyGraft q or low

*L5

2.1

2O 15220 25 30 35 4 6

.5 3R.I n~~~~~~~Medianis of Mdistr4njons

adlans of RBdstrhatn se

t. 1~~~~~~~~~~~~~~~~~..5

.3~ ~~

599N5cps0ftseL FrameesAFPitures Fooled1TAS0 Figs. 46.46.50.52).1 -~~~~~~~~~~~~~~~~~~~5.5

00 05 70 25 30 35 40 45

Signalto interference Ratio (ROin Decibels

.,v-

,,

* leg29B.D.4gCAwalmrRFEE£

3-

lo29 0.9430

00 0025125 1-73dFaonoymr ugFcued eulyGaeqo 41

7~~~~~~~~~~~~~~~~160Figs. 610C'6 ____ COC=NNEL INWERfERE ]

1. T- --- - !- X

Legend.10.2 0.5 l12 5 0 2399

7-1-9 b i

Percent of Viewers Rating Picture As ot Ouality Grade q or Better

34

IsB9

2.

5

+ *

99

.5?IIa

.51

IL5

Z ahII (bI[t-5a9] iZ' Z

Fl 7COCHAW IWIEISIIC

19.I cps M. 29.97cFPictres Pae

ffASO Figs. 701

25 30 35 4D 4Signal b InteferAeln b IRU in DEscbs

20 25 30 35Signal lo Inttrfmence Ratio IR) in Decibels

2.5 Z.2

2

_ 1.5

A.os1

a

-3.51

.3.25.2

.15

Fig. ICDCOCHANEL INERFENCE

Combined 9U cps OfS 129.97 & 30 cps Free)And 19.9S9 cps Olltd 09.9cps Frem

_Fig. 4 & 6 PooledI

0.01 0.102 0.5 1 2 5 10 20 30 0 50 60 70 8D 90 ff °09 99.5 99.9 99.99Peed ofl Yiw s Rking Picture Amof Quaity GrW qor Salr

A1.2.1 5I

.6

.5

.3.2512

.15Ou01 0.102 0.5 1 2 5 10 20 30 D 50400X0D 0 9 o9 999.5 99. 9 9.9

Pnmun do Virs king Plotura Asof udNSy Crafs q or Sr a

A

1.

:1i.IL

6

.25

.21

.157

0.01 Q1 0.2 0.5 1 2 5 10 2003 a50o d 70 D 90 9f 9o 9.5 9.9 w.wPecdofVkwws kting Plcure As of Qualty Gre 4 or a

a

35

Aj

.25

.2

.15

laZr,6

a

II

1 I.- -...I - I 11

;I

5s

2.5< / < - a <2

,+ medle offtdistrlkltbnseoMedlianseodistrhateons SI

.9~~~~~~~~~~~~~~~~~~~~~~i*-, i iI-K -V-I <4

25 5lt 4COCHANN INOERFEENCEM , Ofio 29.97 cps Frame.15 ~~~~~~~~~Picttores Pooled

ITASO Figs. 76,781

10 IS 20 25 30 35 4 45+ Signal bD Interforencu Rrio IR) in Docibs

F-I-T-0S I[Iol1 X 4/>*JI 1- 1 t 12 1 1 ~~~~~~~1.5i

v-l_

*1.v--+ Cld MSAU '---t--

0010 cps ,4x 20.O -1pA Coelnad AR eeins

0CHANNE0L Wtusit 1 1.05 S-) lOO0q2t01tUpesPLI cps sls4. 29.97 cps Freme

lOgs. 11,2k 3

0 a152 25 0 so atS igqoel nterferenc Roeo(SI in Decelbs

M.o lL\ oi ,

.'

21 / -t;2.535A[~ ~_ a1'/'-i* 1

2i 30 35 4D 45 50 55

Signal Interherene Ratio JR) in Detibels

I

is

vI*1'

7 Fl ~~~~~~~~~~~~~~~~14

C5 _ _ _ __-_ 10, 010 cps & 21i10.M cp Oft1,Z@lK2.97 cpis Fro

:'~~~~~~~~~~~~~~~~~~~Fp 10 12) .._P= g3ol-l0s.igi,u4114 Q ii req rll roq

0 ITASO~~~~~~Fig.16

t:|6 t: | 1 CDCHANNEL lNmER cE11C

1-il010.20502 50 203 002 3609055Of 9999.529.97pFr 99

Percentofloooro Raing Picture Asof Ouelity Crad q or Siftr

LegendSena

.3 e 1oIAo4i Fi -

25 n R*l2d -\ 1- O l8E E

.2I

R - 1

':- .2!g 4df

0 R4:471b

is5 .3 52574ld

0.01 0.1 02 0.5 1 2 5 10 20 30d050 D0 90D 95 99. . 99.

Poen of ViNr... n itr s fOs ranqo o

slinol bf Intefreg ReoAlb in Pawts

36

-

Ar.

-1- - + MediansofMdistributions.7 A - -jW ----- -- ----;-* --Modionsof R distributons

-

.4~~~~~~~~~~91

.Z5=- - f. 17d*|IOKHAM" I"ERFER 5.

.544---r-1_~~~~~ K.97cpsFrPe| ! t~~~~~TASOFig. 411

.,. s I I . 1-~~~~~~~~~5.5

ziil . b, (t I [ 17.44L 14.6a 51 I/I

; / r-!

:',- r

A- --I5- i

I

.

i ]Eg

II .f43

N_ ed oMsoMdistrbiions 35- edans of R distrbtisons

_ + - -~~~~~~~~~~~~~~~~~4.5

.25 g ' i.i.5

,/~~~CCHNEE IWTERFERENCE.15 l < 104 cps ORs Stns & Frms PeoWs

.1 t*/ ¢ s ITASO Fig )2-

20 25 30 35 40 a6 so 55Sipn le Interferene Raio (Ri In Dscies

t; ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/ i

+ MedinsoRdMdistributins -MRedieotd R irstrlinions 1 -.-- ---i .

Fig. 20UPRAAEWCANLIWOERFERENCE

Scone &FrosooPOsIaiTASO Figs. 26.27

/

r 1.5

1- 1

.,,M; .7__.6

II.3

.25.2

.151

1M 1,!

A AI.6

3D

w

4 1

4.5 .07

.1

15.5.1 1 *8-45 AD .35 -30 -25 -10 -15 -104 Signl to Iinteference Roats (i in DeciDes

I.. IT +2c5]

!- VI ..

:2I:- ,,,,1-.>/+ Modies MdistrbjfiossMedlmndoItdiotnibutibns

.6 _ . J _ _ _ __. _

.5

3 1!.5 i 1 .5

.4.81'r

_ 6

.5

.0.IS

Cs

0.1 02 0.5 1 2 5 10 20 3 4a 509t70 s07& '9 99"I 99.5 9.9 9.99Percetof Vimers Rating Plcture Asof quaity artt or aeIr

- F 1: -,---r'

0.01 0.1 0.0.51 2 5 10 2&M05, S 6D06 9lbff °O9i99O 99.9PwCnOatdVi99 Raing Pioure As of Qualqy rat oOr Mie

0.03 0,1 0uJ )I. 5 13R (JOi 0U W 99 r 09 p 9w.5 w.V n.wPmnnt d Views bRng P9UorgA; so QuatRyoGor q or dWr +

;Zt/ ,t1 < EECI. ,

I /+ LOWER APA(CENTCRAM9EL IN0ERRESJ3*2/5- + + Sound Power Down 3Rs Scnes & Frem Peeed

I 1/ AOPig.F530

.9 .9 .5 .,3 '3 -:5 '''-o5.''jS- . -a35-3A -ai (R -In-i0I Signal to Iriterf rt Ratio IR) in Decibls

37

At90

.1

.5

.4

.25.255

A-

F4. 22LOWER ADJACENT CHANEL IRVERPERENCESound Power Down 3 Db, Scenes & Froi Poold

(TASO Fg. Xe

Vb 04LOWER ADJACENT CHANML INTER0ERENCESoundrPower n 10 Pk, Doms * Frones Peolid

iTASO FPl. 31i

2

I' 'I --A11 1.5

.1

.1

s76

4

,1

I1

-11 .1

a - wo j-.Q[.-..2] ) 2

4s *l. ^[tmzt

I - I-*-tIt.3 _ aifm!r i_ I_ -5

LO ADAO CHNE 1MFRN.1a e SsW Fw kw110 DWA Sct & From bll

ffASO FI 31)A 1. I -30 5.5

.1- _-35 -30 I 25 In -15

SWwiL Inbkrwr Rb1bIRin Dbsil s

LI

hi1

LS

-10

_

Ir1-1-

I, 2

M 1..

*1- :9

_; I

3I

!II

1A

LW

.-r- 7NAMi oO IM Il

I ,I /41

.4

.3

.25

.2

.31

.102 0. 1 2 5 10 20 303 0 60 IU 90 95 909"9.5 9.9 9.9

Percento Vimn RHing Pirtun Asof Quly Grak q or Better

Prii9y In PFnc NdEKadad

3 " 90 soD0 so a 3 |0 01

32 THE NDIAAL DISTRIIUTION |.4

2. 12

4-

1. -20

1.2 -2.4

*= = =- _ _

0.01 0.1 1 10 0 30 SO 60 9099.9g.99

I~~aI3i

L

23~~~~~~~~~~~~2.2 t | IIIIF FRMlRA9 NISE

Scu0 2U 3 TASO

(TA00 FU 361

0 30 35 40

Acknowledgement

The drafting in this Report was doneby Mr. Braxton Peele of the FederalCommunications Commission.

38

1.S

.1Z..-8

rr_mat in reev Trst OrdWih IsEAS

-t.M -

I

S*Wa lo Intlerem Mibi IRO in DoiNcirs