JOURNAL OF RESEARCH of the National Bureau of Standards-D. Radio Propagation Vol. 66D, No.2, March- April 1962

Fading Characteristics Observed on a High-Frequency Auroral Radio Path

J. W. Koehl a n d H. E. Petrie Contribution from Central Radio Prop a gation Laboratory, National Burea u of Sta ndards, Boulder, Colo .

(R eceived Jun e 22, H)61 ; rcy iscd September 14, 1961)

Obsen·ations of f,.d ing chamcLeri sLics of h igh-frequency sig na,ls have been carried ou t on a long path (4,470 ki lometer,) pass i ll '~ Llnoug h the a uroral zone. SLaListics were obLain ed on fad ing rate, shor t-Lern1. carrier amp liLud e flu ctuaLio ns, and fad e duraLio ns. Fad in~ raLes higher than 20 c:vcles per seco nd were observed for a s mall percenLage of Lhe time at eac h of the t hree carrier frequencies u sed , >Lnd show only a minor d itlrnalLrend, wiLh lhe maxi­mum usually occu rring during t he early morning h ours. Rayleigh di sLribuLions of carrier envelope ampli Lude were obtain ed for man y of the obse rvaL ions; however , fading d epLh was normally reduced durin g periods of rap id fad ing.

1. Introduction

Th e ch aracteristics of carr ier envelope ampliLude flucLuations, or fading, musL be co nsidered in at­lempting to predict Lhe perrormance of radio systems. Fa.dillg on high-Jrequency io nospheric links may be caused by changes in absorpLion of Lhe waves, by interference between two or more componen L of the waves arriving by different paLh or by changes in polarization of t he downcoming waves. Absorption fading is usually much slower than Li lC oLher types. Movement oJ ionosp heric Jayers and irreg ularities in the ionosphere cause changes in phase path lengths and in the state of polariza tion of the mulLi­path components, accounting for the more rapid amplitude fluctuations. A very rapid fading, some­times referred to as "fl uLler" facli ng, has been ob­served lor m any years on Jligh-frequency paths passing through or ncar the auroral zone.

~everal investigaLors [Rice, 1944, 1945, 1948, 1958 ; .\1cKicol, 1949 ; Norton, Vogler, Mansfield, and S bort, 1955; Norton, Rice, J anes , and Bar·sis , 1955] have made theoretical analyses of carrier fading, considering the problem on the basis of envelope behavior for narrow-band Gaussian noise models, with or withou t steady components. Ob­servations of certain short-term high-frequency prop­agaLion characteristics h ave been performed by many workers in the field, for example, Grisdale, :Morris, and Palmer [1957], Aggarwal [1959], and Yeh and Vill ard [1960] . The purpose of the obser­vations reported in this paper is to provide some ad­ditional s tatis tical information on short-term fading cbaracteristics for signals propagated on a long pa.th thro ug h auroral regions. Resul ts of the observ8 tions are presented in several different forms; the intent is to give as clear a picture as possible of the observed statistical beh8vior of carrier envelope fading on the path.

1 Present address: Ball Brothers Research Corp., BOUlder, Colo.

2. Experimental Facilities

Observations were carried out over a paLh from Barro \ , Alaska, to Boulder, Colo ., during 1959 and 1960, at frequencies of 9.9475 M c/s, 14.688 M c/s, and 19.247 M c/s. The great circle d istance is 4,470 km. Figme 1 shows the geographic location of the path relaLive to the ul1cli Lmbed auroral zone.

- APPROXIMATE ZONE OF MAXIMUM AURORAL ACTIVITY

III

140' 130'

120' 11 0'

FI G lIRE 1. Geographic location of transmitter and receiver stations.

G 19483-62--3 159

2.1. Transmitting and Receiving Stations

The transmitting station was set up at the camp of the Arctic Research Laboratory, Barrow, Alaska, with three 3 kw transmitters. All transmitters had precise carrier frequency control, with stability of better than one part in 108 per day. The trans­mitters were operated with unmodulated steady carrier for these observations.

The receiving station was set up at the National Bureau of Standards Table Mesa field site near Boulder, Colo. Receiving equipment consisted of high quality communication type receivers with external heterodyne oscillators. The oscillator sta­bility was within one part in 108 per day. Modifi­cations were made in the receivers to provide a 1-msec time constant in the automatic gain control (AGO) circuits. An external envelope detector with a 2-msec time constant was used to provide the AGe voltage for each receiver and to supply an envelope voltage for recording purposes. An .intermediate frequency tra~slated down frOl~l the car!'ler freque~cy was also avaIlable for operatmg contmuous fadll1g rate recording equipment. A twelve-second time constant was used in the AGC circuit when the receivers were used for continuous fading rate record­ing. The receiving anten.nas at th.e Table Mesa .site were half-wavelength hOl'lzontal dIpoles at a hmght of one wavelength above the ground.

2 .2 . Data Recording and Analysis Equipment

a . Fading Ra te Recorder

Each receiver had an associated fading rate recorder which operated continuously except for short periods when recordings were being made for other fading analysis. The fading rate instruments [Koch, Harding, and Ja,nsen, 1960] record on paper charts the average number of times per second the instantaneous carrier envelope voltage crosses the six-second average canier envelope level with a positive slope. Fading rates recorded by this inst!·u­ment may differ by a very small amount from fadmg rates as defined by Norton, Rice, Janes, and Barsis [1955], i. e., the number of tim es per second ~he instantaneous envelope voltage crosses the median level with a positive slope.

h. Instantane ous Carrier Envelope Voltage Recording a nd Analysis Equipment

Instantaneous carrier envelope voltages at the outputs of the receiver enve~ope detectors were recorded on magnetic tape for later analysis. The FM recording technique was employed, wherein the detector output voltages modulate FM sub carriers in the tape recording equipment.

An amplitude distribution analyzer and fade dura­tion analyzer were used with the tape reproducif!.g equipment to obtain ~tatis.tics on the fine ~ram fluctuations of the fadmg sIgnals. The amplItude distribu tion analyzer samples the carrier envelope voltage 1,000 times per second with 50 p.sec pulses,

and displays on decade counters the percentage of time the carrier envelope voltage exceeds threshold levels set at 5 db intervals. The fade duration analyzer displays on decade counters the percentage of time the carrier envelope fades to and remains below preset levels for various minimum durations of fades. Fade duration s from 2.5 to 500 msec were analyzed in this manner. Fading rates at different carrier levels relative to tbe median and for different durations of fades are also obtained with this equipment.

3 . Carrier Envelope Fading Characteristics

3.1. Theoretical Curves

It is of interest to examine the behavior of fading signals based on assumed theoretical model of the propagating medium. The theoretical curves pre­sented here have been derived by reference to the considerable amount of work by S. O. Rice [1958]. He has assumed that the envelope voltage of the received radio wave varies in the same manner as the envelope of narrow-band Gaussian noise (Ray­leigh distributed) having a normal-law power spec­trum centered on the transmitter frequency .

The probability that the duration of a fade equals or exceeds a time T seconds in length for a given crossing level has been developed by Rice [1958]. The following expression has been applied to his results to obtain a family of curves, figure 2, showing the distribution of carrier envelope amplitudes for various minimum durations of fades:

0.0 I

0.02

~ ~ 0.05 ~ i=<n o c ~ 0. 1

:i~a :; ~ 0.2

~ ~~ O.S

<t ~ 1.0

~~5 ;z I- i5 2.0

~~~ f5 S 3 5.0

~ ~~ ~ ~ ~ 10.0

~ =e i= ~ ~ 20.0

~~: 4 0.0

~~~ ~ ;.: ~ 60.0

~ ~ 0 80.0

~ a) 95.0

99.0 99.9 99.9 9

P (D r, R)= P (DrIR) P (R )

1 "- \ 1\ \\ k---- TN m=500

\ \ \\\ 1\ 300

200

""-\ 1\ \ \ \ 100 \ \ \

'TI~ \ \ \ \ " t- RAYLEIGH

l-\ \ \ .\ \ 25

DISTI!IBUTION

~\\ 1\ \ \ ~ \\\

~\ \\\ ~\~

~'\

- 30 -20 -10 +10

db RELATIVE TO CARRIER ENVELOPE WEDIAN LEVE L

FIGURE 2. Theoretical distributions of carrier envelope amplitude for various minimum fade durations.

T is minimum duration of fades in milliseconds. N m is average number of time~ per second carrier en velope voltage passes downward across median ]ovel; narrow·band Gaussian ranclom noise model with normal-law power spectrum.

160

where

j (Il) = probability that instantaneoLls carrier envelope voltage is equal to 01' less tban R for a Rayleigh fading signal;

P (D T / H) = condi tional probability that a fade has a duration equal to or exceeding T, given that the crossing level is R;

P (D~I" H) = probability that the carrier envelope volt­age fades to and r emains below the level R for a time duration equal to or exceed­ing T.

W'h en th e mll1unum fade duration is such that all fades are included, the distribu tion becomes Rayleigh.

Figure 3 is a plo t of thcoretical average fading rates versus crossing levels relative to the median carrier envelope level, using th e expr ession [Rice, 1958] :

where

Nn = aver age fading raLe (all fad es) at level R ; N m= average fading rate (all Jades) at m edian level; En = carri er envelope voltage at level R; E m=m.edia n carrier envelope voltage.

Figure 4 shows theoretical Jading rales versus minimum. fade durations for various crossing levels, based 011 the assumption that,

where N TR = P (D1' /R)Nn

Nz·n= a\Terage fading rate for minimuill fade du­ration T at crossing level R.

~ ~ « ~

C> z 0

~ C> ;}. « ~ ~

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> > « ~ ~

~ 0 z 0 «

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./

/

- 15

= ./ -"

./ --" ./ \

l \

- 10 -5 +5 + 10

CROSSI NG LEVEL IN db RELATIVE TO CARRIER ENVELOPE MEOIAN LEVEL

FIG eRE 3. Theoretical fading rate versus crossing level for na1Tow-band Gaussian noise model.

L -7.4db

+ 4.5db b -13.5db ......... '\

\ - 19.4 db ~ \

\

~ ~ o~~

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500 X rJ-m

2.5 10 25 50

FADE DURATION. m sec

100 250

FIGURE 4. Theoretical Jading rale versus minimum Jade dW'ation Jar indicated cctlTiel' levels relative to median carrier envelope level.

]\'". is average number of l.imcs per second carri er CI1\'c lopc \Toltagc passes down. ward across median level; narrow-band Gaussian random noise mod el.

3 .2. O bserved Fading Rates

Average fading raLe observations have been car­ried ou t during t he period from Augus t 1959 tln'ough January 1960 on Lhe Barrow Lo Boulder paLh. The recordings have been scaled for hourly maximum and 10-l11in fading rates.

Figures 5 and 6 are plots of diurnal variations of fading rates for the monLhs of October 1959 and

20

19247 kc/s 15

10%

10

50%

90% 0

00 02 04 06 16 20 22 24 LOCAL TIME AT RECEIVER (105·WI

20

-;; 14688 kc/s 15

w ~ 10 .., '" '"

10% z <5

50% ~ 90%

08 10 12 14 16 18 20 22 24 LOCAL TIME AT RECEIVER 1105· wi

20

15

10%

10

50%

90%

02 04 06 08 10 12 14 16 18 20 22 24 LOCAL TIME AT RECEIVER 1105· WI

FJG URE 5. Diurnal variations of houdy maximum fading rates, October 1959.

Hourly maximum fad ing rates are exceeded for percentage of time indicated by cur ve parameters.

161

25

1924 7 kc/s 20

10% 15

50% 10

~ 90%

0 00 02 04 06 08 10 12 14 16 18 20 22 24

LOCAL TIME AT RECt:IVER (lOSo wI

25

20 10% u

15

10 50%

02 04 06 08 10 12 14 16 18 20 22 24 LOCAL TI ME AT RECE IVER (105° w )

20

10% 15

10 50%

'--_ 90%

02 04 06 08 10 12 14 16 18 20 22 24 LOC AL TIME AT RECEIVER (105 0 w )

FIGURE 6. Diurnal variations oj houdy maximwn Jad'ing rates, January 1960.

]Tonrly maximUlll fading rates arc exceeded for percentage of time indicated by curve parameters.

January 1960, and show the 10,50, and 90 percentile values of hourly maximum fading- rates. It appears that there is a tendency for the high er fading rates to occur during the early morning hours . Figures 7 and 8 are distributions of houdy maxim.um. Jading rates for the months of October 1959 and Januan' 1960. Distributions of 10-min median fading' rates for the sam.e months are shown on figures 9 and 10. From th e data obtained, i t was found that fading rates gradually incr eased from October to J anuary, with the lowcst fading rates being observed in October, and the highest fading rates being observed in J anuary.

An attempt was made to determine if there were any characteristic changes in fading rates immedi­ately preceding or following major magnetic fluc­tuations. The results of the analysis did not show an:)' significan t factor in this regard; however, fading rates were generally high er on disturbed days t han on quiet days , as shown by comparing figures 11 and 12 .

The received median signal strengths fLre usually lowered in value by 10 to 20 db when a period of fast fading occurs, although this is not always the case. Fading rates often change from 1 to 2 cis to

0

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~, ' 'tI-19247.0 kc/s .,

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-....... , , .

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I~ I\.' -S 12

~." \"" ~9947. 5kC/s I

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14688,0 kcl5 ~ , .,

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t-= t---==: o

OD! 0.05 0.1 0.2 0.5 I 2 5 10 20 40 60 80 90 95 98 99 99.5 99.9 99.99 PERCENTJ\GE llF TI ME HOURLY MAX IMUM FADING RATES EXCEED ORD INATE

FIGURE 7. D'istriblltions of hourly maximum fading rates, October 1959.

9.9475 ~Vl c/s-420 I1l' 14.688 M c/s-497 h l' 19.247 1\1c/s-318 hl'

25

. ....... , ~

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~~ -

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146BB_Okc/s ~

20

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'5 15

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l- T -I-

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I- k::k -I- -~ o

001 0.05 0_1 02 0.5 I 2 5 10 20 40 60 80 90 95 98 99 99.5 99.9 99.99

PERCENTAGE OF TIME HOU RLY MAXIMUM FA DING RATES EXCEED ORDI NAT E

FIG uRE 8. Distributions oj hOlldy maximum fading Tates, Janlla1'y 1960. 9.947.\ :l1c/s- 649 hl' 14.688 .\1c/s-586 hr 19.247 NIe/s-307 hl'

values in the order of 6 to 15 cis within a fow minutes time. Change from the fast fading rates to slow fading rates occurs just as rapidly.

3.3. Carrier Envelope Amplitude Distributions

Typical ampli tude distribution curves for the received carrier envelope vol tages are plotted on figures 13 and 14. It will b e noted that several of the curves approach a Rayleigh distribution for t he fading carrier envelope. vVhen a R ayleigh distribu­tion is obtained, the average fading rate is usually fairly low, although there are exceptions. During fast fading conditions, associated with auroral activity, t he depth of fading is normally somewhat

162

I~

20

1- .,~. 19241 0kcls~

1 16

-

'5 I

i' \ '\ 2 '\0 1\ \'\ ., '\, .,

\ 8

1'. , '-'I r,

• .1 r, o~ 9941.5 kc/s 1 4688.0 kC/s~ 4

r"-. 1'-. ~ ::,.. '-... f""'::: ~ ~, r-r- .

• 0 0.01 0.050.10.2 0.5 I 2 5 10 20 40 60 80 90 95 98 99 995 999 99.99

PE RCENTAGE Of TI ME 10- MINUTE MEDIAN FADING RATES EXCEED ORDI NATf

FIGURE 9. Distrib1,/1:ons of 10-min median fading mtes, Dctobel' 1959.

9.9475 M 0/s-2538 to- min sam pies :14.688 1\l c/s-2203 IO- min sa mples 19.247 1\1 c/S-1,\22 Ie- min samples

00.01 0.050102 0.5 I 2 5 10 20 40 60 eo 90 95 98 99995 99.9 PERCENTAGE Of TIME 10 - MINUTE MEDIAN fADI NG RATES EXCEED ORDINATE

----

----. 9999

FIGUR E 10 . Distl'ibutions of lO-min median fad'ing rates, Januw'Y 1960.

9.9475 M r/s- 3935 JO- mjn sa mples 14.688 Mc/s-3435 lO- min samples 19.247 MC/S-1836 lO- min samples

redu ced ' til is effect is indicated by the curvature at tbe low~r level portions of some of the distribution curves. A statistical model of a constant vector plus a Rayleigh distributed vector as described by Norton, Vogler , Mansfield, a,nd Short [195~], will produce shallow fading when the power ll1 tbe co nstant vector is several ti.mes greater t han the power in t he Rayleigh distributed component.

3.4. Di stributions of Envelope Amplitudes for Various Minimum Durations of Fades

The distributions of canicl' envelope amplitudes for various minimum fade dura,tions, figures 15 through 19 reflect the stfttis tics of the depth of fading for ce;'tRin minimum fade lengths. This type of infonna-

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LOCAL TIME AT RECEIVER (lOS· wi

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- 160 ~\ ,~, '\ '"-

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--~ --...... -180

00 04 08 12 16 20 24 LOCAL TIME AT RECEIVER 1105· wi

-110

-120 14688 kc/s

a - 140 w > W u w

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- 180 L-L--'-_l....--L....:...c._l....--'---'-_l....-:.L---'-_

-160

~ 00 04 08 12 16 20 24 ~ LOCAL TIME AT RECEIVER (105 0 w) :t:

- 120 '-'---'--'--'--'-'---'--'-OJI,,-'-,

19247 kc /s

- 140

-1 60

" '"---_/ -

30

20

10

0

30

20

10

0

30

20

10

- 180 L-,---,_-,---'.---':::L....--'---'---'--L--'---'---'24 0 00 04 08 12 16 20

LOCAL TI ME AT RECEIVER (105 · wi

~ <..)

w f-<t cr

'" Z

0 ~ Z <t 0 w

'" ~ cr :::> 0 :r:

FIGL;RE 11 . Diurnal vW'iatio ns of signal strength, fading rates. and Barrow, Alaska, magnetic activ'ity index for quwt day,

December 10, ]959

tion has been found to be quite useful as an aid in predicting performance. of c~rtain co~mun~cation systems. As noted prevlOusly 111 co nnectlOn wlth the am plitude distribution curves, when t h? c.b aracter­istic auroral- type fast fading occurs, the £admg depth is normally reduced, especially for the ~bort f.ade durations, from that obtained with R ayleIgh fadll1g. However, one sample was obtained, figure 16 , which had the fairly fast fading rate of 6 cis and maintained a nearly Raylei.gh distribu tion for the very short mi.nimum fade durations.

3.5. Observed Fading Rates at Various Crossing Levels Versus Minimum Duration of Fades

Some of the fade duration data obtained has been plotted so as to show the observed fading rates as a

163

>< : ~ : : : : : ':: ' I ; : ~ w co z

()() 04 08 '2 'S 20 24 LOCAL TIME AT RECE'VER ( 'OS OWI

- '20 30

- '40 ~ 20

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, -'-; " or - '80 >- 0 ~ <.0 ()() 04 08 '2 'S 20

~ z 24 u w

~ LOCAL TIME AT RECE'VER ( 'OSO WI .... >-

--' -' 30 25 : ~

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~ ~ > r ...

§ --" \ z 'v"",- ..

- ISO 10 i;j '" '- '" ...." \ I '" z '4S88 kc/s .. " ~ 0

w

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or

~ 00 04 08 '2 'S 20 24 => LOCAL T'ME AT RECE'VER ('OSO WI co or

- '40 20

- 'SO '0

'9247 kc/s

- '80 0 00 04 08 '2 IS 20 24

LOCAL TIME AT RECE'VER ('OSO WI

FIGURE] 2 . D'iu1'nal vaTiations oJ signal sl1'ength, fading m tes, and Ban'ow, Alaska magnetic actwtty mdex fOT distuTbed day.

December 14, 195!J

fun ction of crossing levels and minimum duration of fades; figures 20 and 21 ar e examples of this informa­t ion, It is interesting to no te t hat the maximum crossing rate occurs near the median carrier level in all cases for shor t duration fades. At levels a few decibels above the median tbe crossing rate curves are fairly fl at, indicating that only r elatively long duration fades occur at these levels, while at the lower levels most of the fades are of short duration.

4 . Summary

Statistical information has been ob tained on certain experimentally observed fading characteristics of high-frequency con tinuous wave signals propa­gated over a long path t hrough auroral regions. Fadi.ng rates in the order of 20 cis have been observed for short periods at all of the obser ving frequencies. I n most instances t he received median canier envelope level drop 10 to 20 db when a period of fast fading set.s in. Fading n,tes were generally higher on magnetically disturbed days than on qui et days. It was found for these observations that

99,9

99.9

; 99,9

99.9

99.8

99,S

...J 99 .0

::' ~ 98.0

95.0

~ 90.0

::IE 80.0

" ~ 60.0

j ::: _ 5.0

1.0 0.1 0.0 I

9

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150

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140 130 - 120 -11 0 -100 -90 RECEIVED CARRI ER ENVELOPE LEVEL , db w

FIGU RE 13, Amplitude distTibutions of can 'ier envelope-9.9475 Mc/s.

Sampling period 200 sec Low pass bandwidth of system 312 cis (-6 db ) Ray lei ~h distribution is straight li ne w ith slope or m in'J s onc, A- Sept. 23, 1959;0353 LTR (105° W ) 8 cis average fa ding ratc B- Oct. 2, 1959; 2021 L T R (105° W) 1..1 cis average facling rate O- Oct. 2, 1959; 1933 LTR (' 05° W) 1 cis average facl in g rate D - Oct. 2, 19.59; 2217 L'l'R (105° W ) 6 cis average fading ratc E-Sept. 23, 1959; 0443 LTR(l 05° W ) 12 cis average fad ing ratc

99.99

99,98

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~ 99.95

99.9

99.8

99.5

oJ 99.0

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95.0

~ 90.0

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40.0 z

20.0

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0.0 ·150 -1 40 -1 30 -1 20 - 11 0

RECEIVED CA RRI ER ENVELOPE l EVEl 1 dbw

"' -100 - 90

FIGURE 14. Amplitude distributions of carrier envelope-19.247 Mc/s .

Samplin g pcriod 200 sec Loss pass band wiclth of system 312 cis (-6 db) Hayleigb distribut ion is s traight line with slope of mi nus one. A-Sept. 15, J959; 1337 LTR (105° \1' ) 1 cis avcrage fad ing rate B-Scpt. 15. 1959; 0936 L'1' R (105° W ) 6 cis average facling rate O- -Sept. 15, 1959; 1142 L 'I'R (10.10 \1' ) 10 cis average fad ing rate D- Oct, 2, 1959; 1933 L'1'1< (1050 W ) 1 cis avcrage fading rate E- Nov. 20, 19,19; 1544 L '1' R (1050 \1' ) 2 cis average fad ing rate

fading rates generally increased from October 1959 to J anuary 1960. However, the au tumnal equin octial period in 1959 was unusually quiet from an auroral­disturbance standpoint and should not be co nsidered typical.

164

0.0 I \ \ \ , ~l \ \ \

\ \ \ ~ '" OINI.U. OURATION " \ \ \ -100 FADES, msec _

002

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0. 1

0.2

0.'

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' .0

tO,O

~ ~ 20.0 :o~

40.0 ~~ ... ~ 60.0

~ ~ 80.0

95.0 99.0

99.9 99.99

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0

,,'-

-30 ~ 20 -to 0 t 10

db RElAriVE TO CARRIER ENVELOPE MEDIAN LEVEL

FIG UR E 15. Dtstrib1dions oj carrier envelope amplitude .for various minimum Jade dumtions.

Sampling period 200 sec Low pass bandwidth of system 312 cis (-6 db) Med ian carrier to noise ra tio 38.0 db A vcrage fading ra te 1.5 cis 9.94751!.,[c/s, Octoberl.j 1959. 1933 L'l'R (105° w )

0.0 I \ \ \ I \ I \

I 0.02 : L OOj 25 I \ \ I' 250 MINIMUM DUR ATION OF

\ \ _ IO -------.l\ I ' 100 fADES, m sec

~ ~ 3 5.0 ~5~ ~ ~ ~ 10.0

: ~ g 200

.... ~ ~ 400

~:~60.0 ~ ;3 c 80.0 ~CD

95.0

99.0

99.9

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~\ \ \ -~l\ .~

~. \ ~~ ~\\ -~ .

~. ~

-30 -20 · 10 '10 db RELATIVE TO CARRIER ENVELOPE MEDIAN LEVEL

FIGURE 16. Distributions of carrier envelope amplitude for vanous mininmm fade dumtions .

Sampling period 200 sec Low pass ban dwidth of system 312 cis (-6 db) M ed ian c,uTier-to-noise ratio 32 db A I'crage fading mte 6 cis 9.9475 Mcls, October 2, 1959; 2217 L'l'R (105° W)

Fading r ates exceeded for small percentages of the time were highest at the higher of the three carri er frequencies observed ; however, for fading rates exceeded for large percentages of the time , the lowest carrier frequency exhibited the highest fading rate.

The depth of carrier envelope Jading, as deduced from the ampli tude distribution measurements for all fades and for fades exceedin g various minimum

0.0 I

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5:~ nJ. \ ,

, 25 \ 1 : :S250 _\~\~ \ -~~~roo MIN IMUM DURATION Of 10 __ 'I \ I I

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-9

-30 -20 -10 0 '10 db RELATIVE TO CARRIER ENVELOPE MEDIAN LEVEL

FIG URE 17. Distributions oj can'iel' envelope amplitude for vaTious minimwn fade dumtions.

Sam pling period 200 sec Low pass bandwidth of systcm3J2 cis (-6 db) Median carrier-to-noise ratio 27.5 db Average fading rate 12 cis 14.688 Mcls, December 23. 1959: 1435 L'T' ll (105° \\' )

0.0 I \ , , , \

\ 002

\ I I \ \

\ \ ~ - '" } "-f! . .. ~ 250 MINl totUM DURATION Of -

99.0 99,9 99.99

-"

"--........ 100 FADES, msec

,,- ~~;-'" \

~j\ '. \ .~\ '\ ~ ~\\

.~,

'\~

'"

- 20 -10 '10 db RELATIVE TO CARRIER ENVELOPE MEDIAN LEVEl

FIGURE 18. DistTibutions of can'ieT envelope ampWude for various minimum fade dt,rations.

Sampling period 200 sec Low pass bandwidth of system 312 cis (-6 db) Median carricr-to-noisc ratio 32.0 db A verage fading ratc 1 cis 19.247 Mcls, Octo ber 2, 1959 ; 1933 LTR (1050 W )

time durations, is normally somewhat Ie s for the auroral-type fast fading than for slow fading. This would seem to indicate Lhe presence of a relatively sLeady component and a weaker fast-fluctuating componen t when fast fading conditions exist.

A Rayleigh distribution of carrier envelope ampli­tude was observed for a few of the periods, usually when the fading rates were fairly low. Most of the time, however , the carrier envelope amplitudes depar ted considerably from a Rayleigh distribution.

165

0.0 I \ I I , ,

0.0 , I SOD · l~~ \ I :.-1--"0 , MI NIMUM DURATION OF 25--: ~ ~V

100

I-- FADES, msec IO~ 1\ \ , 25~O 1\ , I .\ \

99.0 99.9 99,99

-3D

\ I I \\ ,, \ ' \ \1\ ~ .\ \ \ II \ ~\\ \ \ .: \

\ \\ \ 1\\ \:\\ \ \\

'\'

-20 -10

db RELATIVE TO CARRIER ENVELOPE: MEDIAN LEVEL

tlO

FIGURE 19. Distributions of carrier envelope amplitude f01' various minimum fade durations.

Sampling period 200 sec Low pass bandwid th of system 312 cis (-6 db) M edian carrier-to-noise ratio 28.0 db Average fading rate 7 cis 19.247 Me/s September 15, 1959; 1936 LTR (105° W )

20.0 -1.5 db

-y-+3 .5db

~.5db \ \

\ \ ~;~ I~ \

- 11.5 db

'\. \ '\ \

\ \

0.1 \ \

'\. '\.

\

- ,\

\ \ \

2.5 10 25 50 100

FADE DU RATI ON, m sec

\ \

\ 250 500

FIGURE 20. Fadmg rate versus minimum fade durations for va1-ious carrier levels Telative to median caTTier envelope level.

Sampling period 200 sec Low pass bandwidth of system 312 cis (-6db) Median carrier-to-noise ratio 34 db 9.9475 Mc/s, September 23, 1959; 0443 LTR (105° W )

The experimental study reported herein was sponsored by the U.S. Ail' Force Wrigh t Air Develop­m ent Division, Wrigh t-Patterson Air Force B ase, Ohio_ T he assistance of the Arctic Research Laboratory , Office of Naval Research, Point Barrow, Alaska is gratefully acknowledged; Max Brewer, Director, and other personnel of that laboratory have provided logistics and housing for equipment installation and operation at Barrow. Other NBS p ersonnel who have contributed substantially to the

lU.U

""- 10.0 z: :;j

I---1

f-- ~~b '" '-' 1;'; 5.0

'" "'", '" 0. 0 '" > '" "'''' ~~~a 2.0 ""-'''' I.£..<e O Z

=>",0 "-O u 0'" '" 1.0 ~~~~ ", 0 u

+ 2.5 d b

"" ·1......:.. "- 1, T 7. 5 d b r, ,

" I \ 1\ 1\ ~d.b

::E ~ ~o => """"z: 0.5 ZCJ:: (I) -

=> '" +7.5 d b - '\ ~

w°<=> '" '" "" '" '" '" z: "" '" :; > 0.2 "" "" '"

I \ \ \. 1 '\ '\ 1\ '\

r~dl b \ \ \ A 0. 1

I 2.5 10 25 50 100 250 500 FADE DURATION. msec

FIGURE 21. Fading rate versus mmimurn fade duratwns f or various can-ieT levels relative to median carrieT envelope level.

Sampling pcriod 200 sec Low pass bandwidth of system 312 cis (-6 db) M ed ian carrier-to-noise ratio 40 db 11.68S Me/s, September 15, 1959; 0910 I !l'R (1 0.5° W )

project include: W. B. Harding, C. H. Johnson, G. E. Wa.sson, and J. L. Workman (Barrow, Alaslc1). The au thors also thank Miss Freda L'Manian for her assistance in preparing the manuscript.

5 . References

Aggar w3.l , Ie. K ., Statistical analysis of fading on short-wave transmissions, J. Inst. Tel. E ngl's. (New Delhi) 5, No.4, 230- 237 (Sept. 1959).

Grisdale, G. L., J . G. Morris, and D. S. Palmer, Fading of long-distance rad io signals and a comparison of space and polorization-d iversity recep tion in t he 6- 18 Mc/s range, Proc . Inst . E lec. Engrs. 1MB, No. 13, 39- 51 (J a n. 1957).

Koch , J. ' V., YV. B. I-larding, and R. J . Jansen, Fading rate reco rder for p ropagation r esear ch, E lectronics 32, No. 51, 78- 80 (Dec. ] 8, 1960).

McNicol, R. YV. E., The fading of radio waves of medium and high frequencies, Pl'Oc. lust. E lec. Engrs. pt. III 96, No. 44, 517- 524 (Nov. 1949).

Norton, K . A., P . L. Rice, H. B. Janes, and A. P. Ba rsis, The rate of fading in prop agation through a turbulent atmosphere, Pl'Oc. I.R.E. 43, No . 10, 1341- 1353 (Oct. 1955).

Norton, K . A., L. E . Vogler, W. V. Mansfield , and P. J. Short, The probability distribution of the amplitude of a constant vector p lus a Rayleigh-distributed vector, Proc . I.R.E. 43, No. 10, 1354- 1361 (Oct. 1955) .

Rice, S. 0., Mathematica l analysis of random noise, pts. I & II, Bell System T ec h. J . 23, No.3, 282- 332 (July 1944).

Rice, S. 0. , Mathematical analysis of random noise, pts. III & IV, Bell System Tech. J . 24, No.1, 46- 156 (Jan . 1945) .

R ice, S. 0 ., Statistical properties of a sine wave plus random noise, Bell System T ech. J. 27, No.1, 109- 157 (Jan. 1948).

Rice, S. 0., Distribution of the duration of fades in radio transmission: Gaussian noise model, Bell System Tech. J. 37, No.3, 581- 635 (May 1958).

Yeh, K . C., and O. G. Vill ard, Jr ., Fading and attenuation of high-frequency radio waves propagated over long p ath s crossing the auroral, temperate, and equatorial zones, J. Atmospheric and T errest. Phys . 17,255- 270 (1960) _

(Paper 66D2- 183)

166

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