IEEE TRANSACTIONS ON BROADCASTING, VOL. BC-25, NO. 3, SEPTEMBER 1979

COMPARISON OF MEASURED AND PREDICTED SIGNAL STRENGTHS OF NIGHTTIMEMEDIUM FREQUENCY SIGNALS IN THE U S A

Douglass D. CrombieInstitute for Telecommunication Sciences

National Telecommunication and Information AdministrationU. S. Department of Commerce

Boulder, Colorado 80303

This paper illustrates that the differencesbetween measurements and predictions of nighttimetransmission loss at medium frequencies (MF) in theU.S. during high solar activity show a statisticallysignificant dependence on the direction of propaga-tion. Transmission loss in the east to west directionis greater than predicted, and greater than for propa-gation in the opposite direction, for path lengthsranging from 300 to 2800 km. The differences amountto about 9 dB for the whole MF band and increase toabout 13 dB for frequencies .830 kHz. These differ-ences should be considered in any frequency assignmentprocess intended to make optimum use of the MF broad-casting band.

Transmission loss plays an important role inestimating the amount of interference which a radiotransmitter causes in distant regions. The magnitudeof estimated interference is used to determine thenecessary spatial separation between potentiallyinterfering transmitters. Because the spatial sepa-ration is an important factor in determining the num-ber of transmitters which can be assigned the sameoperating frequency, it is important that transmissionloss estimates be as accurate as possible, and thattheir uncertainties be minimized. By reducing uncer-tainties in estimation of transmission loss as much aspossible, the number of transmitters sharing the samefrequency can be maximized for a given set ofconstraints (power, antenna patterns, etc.).

The International Radio Consultative Committee(CCIR) has long been concerned with the problem ofestimating transmission loss at various frequencies.

The CCIR1 has published an improved model for esti-mating sky-wave transmission loss at medium frequen-cies (MF), which can be used in planning MF broad-casting services. For the North American continent,

this model takes the form2,

F = (10 log PKW + GH + GV) + (105.3 - 20 log p)+ GS - Lp - kR P x 10i3 dB above 1 VV/m) (1)

where

kR= 1. 9f°-15 + 0.24f°04(tan2 q-tan2370) + 4Rx1O2 (2)

andF = annual median field strength in dB above 1 V/mf = frequency in kHzGH = azimuthal pattern antenna gain (dB)

Gv = vertical pattern antenna gain (dB)

GS sea gain factor (dB) = 0 in this paper

kR = loss factor

L excess polarization loss factor = 0

PKW `

p =R =4 =

in this paperradiated power (kilowatts)slant propagation distance (km)twelve month smoothed sunspot numbermean geomagnetic latitude of transmitterand receiver.

Wang2 has evaluated this model for calculatingnighttime medium frequency signal strengths by apply-ing it to an extensive set of data collected in theUSA during periods of both low and high sunspotactivity. The measured data were collected at foursites, from 18 MF broadcasting stations in NorthAmerica, shown in Fig. 1. The measurements were madeon frequencies between 540 and 1630 kHz and over pathlengths between 165 and 3498 km oriented in variousdirections.

Wang2 found that the root mean square (RMS)differences between the predictions of the CCIR model1and their median measured data were smaller than thoseof other prediction models. The other models used forcomparison were developed by the Federal Communica-tions Commission (FCC), and the European BroadcastingUnion (EBU), respectively. As a result, it can beconcluded that the CCIR model is rather effective formaking MF nighttime predictions in the U.S.

This note describes a further comparison betweenthe predictions of the CCIR model and the FCC data.The comparison consisted of dividing the measured dataand the associated predictions from Ref. 2 into twosets. One set consisted of the measurements and pre-dictions for signals propagating within approximately±450of the west to east direction. The other setcomprised data for propagation in the oppositedirection.

The mean difference between the two sets ofdifferences was then compared. The philosophy behindthis test is that if the measured signal strengthsfavored a particular direction, then the difference A

A = (p - MWE) - (P - MEW)

would differ significantly from zero. Here, P rep-resents the prediction for each path, M the measure-ments, for the same paths and the subscripts, WE andEW, denote the direction of propagation. The barsdenote averages for each group of paths. Obviously,if the predictions differed from the measurements,then A would be significantly different from zero.

The data used (taken from Ref. 2) are shown inTable I for the high sunspot activity measurements andpredictions of the median signal strengths. Pathlengths of less than 200 km and greater than 3000 kmhave been excluded from this analysis in order toreduce the range of the distance variable and thusincrease the homogeneity of the data. It- is clearthat there is a significant difference amounting toabout 9 dB for the two propagation directions. Thisdifference, M, is significant because it is about 2.7times the Standard Error (SE). (If the two sets ofdata had been obtained from the same parent populationthe observed ratio, t, of the difference, M, to thestandard error, SE, would occur with a probability ofabout 2%.)

The difference between E to W and W to E propaga-tion shows a frequency dependence which can be seen byseparating the data into two further classes: (1) for

U.S. Government work not protected by U.S. copyright.

frequencies >830 kHz and (2) for frequencies <830 kHz.The higher frequency group shows a difference of12.7 dB with a standard error of 4.8 dB. This groupcontains 10 samples (and thus 8 degrees of freedom)and the difference is significant at about the 2%level. On the other hand, the differences between thetwo directions of propagation for the lower frequencygroup is not statistically significant.

The data in Ref. 2, shown in Fig. 1, containthree north to south paths (3-1, 17-1, 13-2) and threesouth to north paths (2-2, 5-3, 14-3). Treating thesedata in the same way shows there is no significantdifference between them.

Excluding the possibility that the calibration ofthe equipments, transmitters and antennas were system-atically in error, there is one other possibility forerror or confusion. The measurements in Ref. 2 relateto the period 2 hours after sunset at the center ofthe path. The CCIR predictions refer to a time of 6hours after sunset at the midpoint of paths less than2000 km. For longer paths, instead of the midpoint, apoint 750 km from the end where the sun sets last isused. Ref. 2 points out that the effect of thedifference between these times is less than 3 dB.Furthermore, inspection of Table I shows that deletionof paths over 2000 km long makes little difference.

An interpretation of the results obtained aboveis that the apparent difference arises because ofaccidental correlation between parameters such asfrequency, path length, geomagnetic latitude of thereflection point, and propagation direction. Suchcorrelation, if coupled with an inaccurate predictionformula, might account for the observed difference oftransmission loss in the two generally opposing groupsof directions.

In view of these factors, an analysis of thedependence of frequency, length, and geomagnetic lati-tudes of the paths on the direction of propagation isshown in Table II. The values of 4, the mean of thegeomagnetic latitudes of the transmitter and receiverfor each path, were taken from Ref. 2. Table IIshows, by inspection, that the path lengths and fre-quencies for the two groups of paths come from thesame populations because the ratio of the differencesto the standard errors of the differences are small.Thus the difference in the means is insignificant. Onthe other hand, it is clear that there is a more sig-nificant difference in the means of the geomagneticlatitudes, 4, for the two groups of paths. This dif-ference is 3.250, and 4 is larger for the EW than forthe WE paths.

The effect of a systematic difference in pathlatitudes can be investigated by reference to equa-tions (1) and (2) which show that the correspondingdifference between average signal strengths,SWE-SEW, should be given by

SWE-SEW = -(kRWE- kREW) p x 10-3 dB

= -p x 10-3 x .24f0 4[tan24)WE-tan24WJdB. (3)

The earlier analysis showed that the path lengths andfrequencies came from the same populations. Thus in(3) we can substitute the mean values of p(=1347 km)and f(=952 kHz) and put 4OE = 48.4°, O)EW = 51.650.The result is that

SWE - SEW = 1.7 dB.

In view of this result it seems unlikely that theobserved difference between predictions and measure-ments for the two groups of paths, 9 dB, could resultfrom their difference in the geomagnetic latitudes.Of course, this conclusion would be incorrect ifequation (2) were grossly in error.

One possibly interesting alternative explanationof the results obtained in this study is that at med-ium frequencies, transmission loss is non-reciprocalin directions perpendicular to the horizontal compo-nent of the geomagnetic field, as is the case at very

low frequencies3. This, however, must be investigatedfurther.

In conclusion, although it appears that the CCIRmodel for sky-wave medium frequency prediction may bebetter than other models for use in the U.S., it isnot capable of accounting for the apparently signif-icant differences in transmission loss of MF skywavesignals propagating in east to west or west to eastdirections during high sunspot activity in the U.S.This is because the model does not differentiatebetween propagation in opposite directions. Theapparent differences in transmission loss may beimportant in assigning frequencies so as to fostermaximum use of the spectrum for medium frequencybroadcasting.

References

1. International Radio Consultative Committee (CCIR),"Methods for predicting skywave field strengths atfrequencies between 150 kHz and 1600 kHz,"Report 575, Geneva, Switzerland, 1974.

2. John C. H. Wang, "A comparative study of mediumfrequency sky wave field strength predictionmethods," FCC Report FCC/OCE RS 75-07,December 1975.

3. D. D. Crombie, "Reflection from a sharply boundedionosphere for VLF propagation perpendicular tothe magnetic meridian," J. Res. NBS, 65D,p455-463, 1961.

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Table I

COMPARISON OF PREDICTED AND MEASURED SIGNAL STRENGTHS

Predicted - MeasuredFrequency Path Length Path Signal Strength

Path No. (kHz) (km) Direction W to E E to W

3-2- 700 647 W to E 11.9 dB

5-2 820 1957 W to E - 5.3 dB

9-2 880 322 E to W 16.9 dB

17-2 1530 676 W to E 3.6 dB

1-3 640 1895 W to E - 5.8 dB

3-3 700 1212 E to W 7.1 dBg6-3 830 629 E to W 8.5 dB

7-3 850 561 W to E - 2.6 dB

11-3 1040 432 E to W 6.8 dB

12-3 1160 1150 W to E - 11.5 dB

16-3 1500 632 E to W - 0.3 dB

5-4 820 2614 E to W - 1.0 dB

5-4 820 2614 E to W 5.5 dB

6-4 830 2280 E to W 13.4 dB

10-4 890 2821 E to W 9.3 dB

16-4 1500 2307 E to W 9.7 dB

18-4 540 1419 E to W 8.2 dB

Mean - 1.62 dB 7.64 dB

Std. Deviation 8.24 dB 5.20 dB

No. of Samples 6 11

Difference of Means M 9.3

Pooled Variance - (6 x 8.242) + (11 x 5.22) - 6.8526 + 11 - 2

Standard Error of Difference, S.E. _ 6.85 5/...,.-I- 3.47& 11

t 5 2.68 with 6 + 11- 2 15 Degrees of FreedomS.E.

Table II

DEPENDENCE OF PATH LENGTH, p, FREQUENCIES, f, AND MEAN GEOMAGNETICLATITUDES, *, ON PATH DIRECTION

W to Eoathg E to W paths

Path p(km) f(kHz) *(O) p(lkm) f(kHz) *(O)

3-2 647 700 50

5-3 1957 820 46

9-2 322 880 50.5

17-2 676 1530 50

1-3 1895 640 45.53-3 1212 700 50.5

6-3 629 830 53

7-3 561 850 49

11-3 432 1040 51

12-3 1150 1160 50

16-3 632 1500 53

5-4 2614 820 46.5

6-4 2280 830 53

10-4 2821 890 50.5

16-4 2307 1500 53

18-4 1419 540 55.5

Means 1148 950 48.4 1467 953 51.65

Std.Deviation 637 337 2.1 964 316 2.4

Difference of mean path lengths - 319 kin: Differd cE1Standard Error

Difference of mean frequencies = 3 kHz: l

Difference of mean * = 3.250 >2

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FIGUJRE 1: Map showing locations of paths (from Ref. 2)

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