Document 2488635

I
MORPHOLOGY OF IONOSPHERIC SCINTILLATION*
.I
'N
R. K. C r a n e
Lincoln Laboratory, Massachusetts Institute of Technology
Lexington, Mas sachus e t t s
Abstract
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S m a l l s c a l e ionospheric i r r e g u l a r i t i e s in the
F - r e g i o n can c a u s e fluctuations in the amplitude,
phase, and angle of a r r i v a l of VHF. UHF, and
SHF signals t r a v e r s i n g the ionosphere. Under
s o m e conditions , t h e power level fluctuations o r
scintillations a t VHF and UHF m a y become s e v e r e
with 12 dB signal level i n c r e a s e s and fades in
e x c e s s of 30 dB being observed. C u r r e n t information about the probabilities of o c c u r r e n c e of
s e v e r e fades is derived f r o m a number of experiments using e i t h e r radio s t a r o r satellite borne
sources. The m e a s u r e m e n t s a r e generally of signal level only and have been used to calculate
scintillation indices to c h a r a c t e r i z e scintillation
intensity. An examination of t h e global d i s t r i b u tion of scintillation indices show that scintillations
a r e of importance to communication s y s t e m p e r formance p r i m a r i l y in the a u r o r a l and pola
regions and at night n e a r t h e geomagnetic equator.
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I.
Introduction
E a r l y radioastronomical observations of
s o u r c e s of s m a l l angular extent exhibited significant intensity fluctuations. Spaced r e c e i v e r m e a s u r e m nts made at the J o d r e l l Bank Experiment
f
Station at 81.5 MHz showed that the intensity
fluctuations originated in t h e F - r e g i o n of the ionos p h e r e , w e r e c o r r e l a t e d with the o c c u r r e n c e of
s p r e a d - F , and formed a random intensity pattern
on the ground with a c o r r e l a t i o n distance of approximately 4 km.
This paper i s d i r e c t e d toward providing information to communication s y s t e m s d e s i g n e r s f i r s t
about scintillation a s observed in a single e x p e r i ment, second about t h e adequacy of the existing
models used t o i n t e r p r e t scintillation data, and
finally about the variation of scintillation with
geophysical p a r a m e t e r s . Scintillation due to elect r o n density fluctuations h a s been observed on
line-of-sight paths through the ionosphere at f r e q uencies ranging f r o m 20 MHs to 6 GHz. F r e q uencies between 100 and 400 MHz a r e emphasized
in this paper because of their immediate concern
in s y s t e m design. An exhaustive literature exists
on the subject of ionospheric scintillation. _ T h e
r e f e r e n c e s cited in this paper a r e not complete
and a r e only intended t o be illustrative. When
possible the r e f e r e n c e s will be to m e a s u r e m e n t s
made at frequencies in t h e LOO to 400 MHz range.
Prediction of fading statistics for the design of
communication s y s t e m s r e q u i r e s m o r e than a cataloging of data f r o m available observations. Most
of the experimental data a r e f r o m observations of
limited duration f o r path g e o m e t r i e s , frequencies,
*This work has been sponsored by the Dept. of t h e Navy.
1
and locations d i f f e r e n t f r o m the s y s t e m to be d e signed. To obtain fading statistics f o r s y s t e m
design, e i t h e r additional experiments m u s t be made
using p r e c i s e l y the frequency and path geometry of
the proposed s y s t e m o r one of the diffraction o r
scintillation models m u s t be used to i n t e r p r e t available data. The recent discovery of scintillation at
4 and 6 GHz in the equatorial region' was a s u r p r i s e b e c a u s e it was not predicted using available
data and the thin phase s c r e e n , Gaussian c o r r e l a tion function model.
C u r r e n t knowledge of received signal fluctuations o r scintillation caused by the ionosphere h a s
been derived f r o m a l a r g e number of observations
of amplitude fluctuations made at m e t e r , decim e t e r and c e n t i m e t e r wavelepgths. The o b s e r v a tions have been made o v e r the past two decades at
a n u m b e r of locations using radio s t a r s o r s a t e l l i t e borne sources. The data have generally been
r e c o r d e d on s t r i p charts. Various scintillation
indices have been used t o c h a r a c t e r i z e the a p p e a r ance of t h e recorded data on the charts. The scintillation indices w e r e often subjectively e s t i m a t e d
o r , in r e c e n t y e a r s , calculated using the e x t r e m e
values observed on s h o r t sections of the r e c o r d ing.
Information about the dependence of s c i n tillation on geophysical p a r a m e t e r s such a s i n v a r iant latitude, magnetic activity index, and sunspot
number h a s been published f r o m s u m m a r i e s of
t h e behavior of the qualitative scintillation index
values compiled f r o m available experimental
data?-9
B o o k e r e t l " proposed that diffraction by
fluctuations of electron density in the ionosphere
could c a u s e the observed scintillation and that the
effect of the e l e c t r o n density fluctuation could be
modeled by a thin phase changing diffraction
s c r e e n . Currently, scintillation phenomena a r e
usually modeled a s being caused by a thin s c r e e n
using the refinements to the original analysis made
by M e r c i e r l l and Briggs and Parkin. l2 The r e finements included the introduction of a Gaussian
spatial c o r r e l a t i o n function to d e s c r i b e the anisot r o p i c fluctuations in electron density at and above
the s c r e e n , Measurements of the spatial and
t e m p o r a l c o r r e l a t i o n p r o p e r t i e s of the fluctuations
observed a t t h e ground a r e often c h a r a c t e r i z e d by
t h e s c a l e s i z e o r c o r r e l a t i o n distance f o r the
ionospheric diffraction s c r e e n using the Gaussian
c o r r e l a t i o n function assumption. 13, 14
Recent observations have shown that the region
of the ionos h e r e causing the fluctuations is often
quite thick1' and the thin s c r e e n model may not
be adequate. The effects of random fluctuations
of r e f r a c t i v e index ( o r e l e c t r o n content) in a thick
region m a y be analyzed using the Born (single
scattering) approximation to the wave equation16
o r the Rytov method (method of smooth p e r t u r b a t i o n ~ when
) ~ ~ the scintillation index is not too
large. In the limit of weak scintillation, a l l t h r e e
approximate methods a r e identical. F o r strong
scintillation, multiple s c a t t e r i n g m u s t be taken
into account and none of t h e models are adequate.
11.
Millstone Observations
Experiment Description
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Observations of scintillation at 150 and
400 MHz w e r e m a d e during the period January1971
t o M a r c h 1973 using U. S. Navy Navigation System
satellites and r e c e i v e r s at the Millstone Hill
R a d a r Facility. l8 T h e satellites t r a n s m i t t e d "
phase coherent signals which w e r e simultaneously
recorded a t the r e c e i v e r site. T h e UHF (400 MHzj
r e c e i v e r s y s t e m included t h e 84-foot Millstone
Hill antenna equipped f o r elevation and azimuth
tracking and simultaneous observations using
right and left hand c i r c u l a r polarization; a phase
lock tracking r e c e i v e r ; and analog t o digital conversion of t h e principal polarization channel AGC
voltage, e r r o r channel signals, and the in-phase
and q u a d r a t u r e orthogonal polarization channel
voltages ( r e f e r e n c e d t o t h e principal polarization
signal). T h e data w e r e s a m p l e s at 15 t i m e s p e r
second together with time, antenna pointing angle,
and the VHF data and recorded on digital magnetic tape f o r post m e a s u r e m e n t analysis. T h e VHF
r e c e i v e r s y s t e m provided in-phase and quadrat u r e voltages f o r the 150 MHz signal referenced to
the phase of the UHF signal divided down by the
ratio of the frequencies. The VHF antenna was an
eleven-element yagi mounted on one of the feed
s t r u t s of the Millstone antenna.
T h e s a t e l l i t e s w e r e in circumpolar o r b i t a t an
approximate altitude of 1000 k m and w e r e tracked
f r o m horizon-to-horizon. F o r each p a s s the
average signal levels a t each frequency v a r i e d by
about 10 dB. The VHF r e c e i v e r s y s t e m had a
predetection bandwidth of approximately 250 Hz.
The UHF predetection bandwidth was approximately 10 KHz and the AGC s y s t e m had an effective bandwidth (closed loop) of 250 Hz. T h e s i g nal to noise r a t i o f o r optimum observing conditions was approximately 35 dB a t UHF and 25 dB
a t VHF. The r e c e i v e r s y s t e m was calibrated
p r i o r to each satellite pass.
Amplitude Fluctuations
Sample observations of received signal level
a t both frequencies a r e shown in Fig. 1. T h e data
a r e f o r a p a s s during the m o s t s e v e r e magnetic
disturbance that o c c u r r e d during the experiment
(the planetary t h r e e hour magnetic activity index,
Kp, equaled'8 a t the t i m e of the pass). T h e
quiet conditions w e r e observed to the south, the
disturbed conditions through the a u r o r a l region
to t h e north. E a c h 1/15 s e c s a m p l e i s displayed.
Under quiet conditions, s o m e fluctuations a r e
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QUIET CONDITIONS
RELATIVE TlYEfuel
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DISTURBED CONDITIONS
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observed a t each frequency. Some of the v a r i a - ;
tion at 150 MHz is a l s o due to r e c e i v e r noise. . .
F a r a d a y fading of the linearly polarized VHF s i g n a l is a l s o evident a s noted i n the figure. Under
disturbed conditions, peak-to-peak level changes
of 45 dB at 400 MHz and 4 0 dB at 150 MHz a r e
evident-.
'
T h e data displayed in Fig. 1 a r e f o r roughly the
same elevation angles, the mid-point elevation
angle f o r the one minute quiet period was 7. 6";
the mid-point elevation f o r the disturbed period
was 8. I". F o r lines-of-sight to the satellite a t
t h e s e elevation angles, the undisturbed signal
levels should b e identical f o r observations t o the
north and to t h e south of the r e c e i v e r site. T h e
detailed F a r a d a y null s t r u c t u r e of the 150 MHz
signal will change, however, due to differences i n
the m e a n p r o p e r t i e s of the ionosphere. T h e
sampled data w e r e analyzed in overlapping 8. 5
~.
second intervals. The mean and l i n e a r l e a s t
s q u a r e fit line f o r the logarithm of the signal a m p litude a r e displayed between the v e r t i c a l lines f o r
a l t e r n a t e analysis intervals. The s h o r t analysis
intervals w e r e chosen to b e s t provide straight line
fits to the variation in signal levels caused by the
satellite, r e c e i v e r geometry and F a r a d a y fading
a t 150 MHz. The rms variation of the observed
values about the l e a s t s q u a r e lines w e r e computed
t o c h a r a c t e r i z e the intensity of the fluctuations.
F o r each analysis interval and frequency, the
rms variation of received power about a l e a s t
s q u a r e straight line fit to the observed power
values was a l s o calculated. The l a t t e r rms value,
when normalized by the m e a n value of received
power f o r the analysis interval is the S4 index
proposed by Briggs and Parkin. l2
The values of S4 f o r each analysis interval
(with midpoints spaced by 4. 3 s e c ) a r e displayed
in Fig. 2 f o r the s a m e satellite p a s s a s for F i g . 1.
T h e satellite r o s e in the south and the relatively
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quiet conditions a r e evident f o r t h e first five minutes of the pass. Data f o r elevation angles below
2' a r e contaminated by t r o p o s p h e r i c s c i n t i l e i o n
and s u r f a c e multipath and a r e not displayed. The
analysis of Briggs and P a r k i n indicates that S = 1
4
is a limiting value f o r s t r o n g scintillations
although values a s high a s 1.5 a r e possible f o r the
right combination of s c a l e s i z e and distance f r o m
the thin s c r e e n . Although s t r o n g scintillation
r e q u i r e s a consideration of multiple s c a t t e r i n g , no
analytical multiple s c a t t e r i n g model is available.
E x p e r i m e n t a l data both f o r ionospheric scintillation and t r o p o s p h e r i c scintillation a t optical f r e q uenciesl9 show that f o r s t r o n g scintillation o r
multiple s c a t t e r i n g a limiting value i s reached.
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.. . .
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LEVEL RELATIVE TO MEAN LOG RECEIVED POWER (dB)
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QUIET CONDITIONS
F i g u r e 4a
A n obvious limiting value is shown in Fig. 3.
This figure i s a plot of the r m s variation of t h e
-I
logarithm of the received signal,
, vs t i m e f o r
the s a m e pass. In Fig. 3, the 95 o confidence
limits f o r the e s t i m a t e d e r r o r in calculating u
a r e a l s o depicted. The confidence l i m i t s a r e
based upon t h e number of t i m e s different electron
density i r r e g u l a r i t i e s a r e observed within the
f i r s t F r e s n e l zone due to satellite motion. The
data show that u r e a c h e s a limiting value of
X
approximately 5.
6 dB a t each frequency. The
limiting values depicted in F i g s . 2 and 3 a r e calculated values f o r a Rayleigh received signal
amplitude distribution. The s p r e a d of S4 values
about the limiting value of 1 a t 150 MHz in Fig. 2
m a y be due e i t h e r t o sampling e r r o r o r to a different signal amplitude distribution.
7
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. ,. . .
--- 150 MHZ
Ux=5.5dB
LEVEL RELATIVE TO MEAN LOG RECEIVED POWER ( d e )
DISTURBED CONDITIONS
The e m p i r i c a l signal amplitude distributions
for the two minutes depicted in Fig. 1 a r e shown
in Fig. 4. The data show n e a r l y identical d i s tributions f o r the two frequencies and disturbed
conditions. The U H F e m p i r i c a l distribution function a p p e a r s to be l o g - n o r m a l f o r quiet conditions
Tropospheric scintillation a t optical frequencies
a l s o appear to have a l o g - n o r m a l distribution in
the limit of s t r o n g scintillation. 2o The d i s t r i b u -
F i g u r e 4b.
tion functions a r e , however, definitely not logn o r m a l for ionospheric scintillation u n d e r - d i s turbed conditions. Bischoff and Chytil" proposed
t h e u s e of the Nakagami-m distribution a s an
approximation to the e m p i r i c a l distributions with
3
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.
m = 11.5 2. Although the Nakagami-m distribution
4
i s not theoretically c o r r e c t f o r the thin s c r e e n
diffraction problem, 2 2 it m a y provide a reasonable approximate distribution and h a s been used
f o r the construction of long t e r m amplitude distribution functions. 23 The Nakagami-m distribution
reduces to the Rayleigh distribution f o r S4 = 1 and
approaches the log-normal-distribution f o r u l e s s
than 1 dB. 24 The e m p i r i c a l distribution funcjions
depicted in Fig. 4 w e r e test8d'ag&hit both the logn o r m a l and Nakagami-m distributipns for the caldistribuculated ax values. Using the P e a r s o n
tion t e s t and a 0 . 0 5 significance level, the d i s t r i butions depicted i n Fig. 4 w e r e neither log-normal
n o r Nakagami-m. The VHF diatribution for d i s turbed conditions had an m - p a r a m e t e r of 1.0 and
t e s t e d to b e Nakagami-m (Rayleigh) a t a 0.01 significance level. The VHF distribution function
for the minute preceding t h e disturbed minute
(between 11 and 12 in Fig. 3) a l s o t e s t e d as being
Rayleigh with a 0 . 0 5 significance level. The UHF
distribution f o r disturbed condition had an m-value
of 0.92 and t e s t e d to be different f r o m a Nakagami
m distribution at reasonable significance levels.
It was a l s o observed that the in-phase and quadrat u r e signals w e r e c o r r e l a t e d when m was not equal
to one and w e r e uncorrelated when m = 1.0.
9
imately relating t h e various signal v a r i a n c e values
proposed by Briggs and P a r k i n and for relating the
e x t r e m e value indices to o t h e r m e a s u r e s of s c i n tillation is documented by Bischoff and Chytil.
The V H F amplitude fluctuations depicted in
Fig. 1 appear t o be m o r e rapid f o r disturbed than
for quiet conditions. The t e m p o r a l behavior of
scintillation can be quantitatively depicted by c o m puting distributions of the t i m e durations the signal
i s below o r above p r e s e n t thresholds. E m p i r i c a l
distribution ftirictions of duration below and above a
l e v e l 3 dB below the mean log received power f o r
each of the analysis intervals in the two minutes of
data shown in Fig. 1 a r e presented in Fig. 6. The
--- 150MHz, ux = 2.6dB
Threshold
The Nakagami-m distribution, although not
identical to t h e observed distributions, does p r o vide a useful approximation for relating t h e various
f o r m s of scintillation index used i n the reduction
of experimental data. Calculated values of S4 and
u f o r the satellite pass depicted in Figs. 2 and 3
X
a r e shown in Fig. 5. The relationship between
S and u calculated using both the Nakagami-m
4
X
1
2
3
TIME DURATION (set)
TIME DURATION (sac)
QUIET CONDITIONS
$
2.0
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- 400MHz, ux
--- 150MH2, ux
E
= 5.9dB
= 5.5d0
1.5
=4
1.0
0.5
Distribution
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ex (dB1
2
Figure 5
0
1
2
3 . 0
1
2
3 .
TIME DURATION ( s e d
TIME DURATION (sec)
DISTURBED CONDITIONS
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Figure 6
and log-normal distributions together with a weak
s c a t t e r approximation a r e a l s o shown. Of the distribution functions shown, t h e Nakagami-m p r o vides the b e s t e s t i m a t e of t h e S -9( relationship
f o r t h e e n t i r e range of observe%values. T h e usefulness of t h e Nakagami-m distribution f o r a p p r a -
data show that the duration distribution functions
a r e approximately exponential with different slopes
for t i m e s above and below the - 3 dB threshold.
The a v e r a g e f a d e duration i s given by t h e value of
t i m e duration required to reduce the number of
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o6servations by l/e. F o r t h e -3 dB threshold and
disturbed conditions, the a v e r a g e fade'duration
Was 0.08 s e c at 400 MHz and 0.05 s e c a t 150 h4Hz.
The fade r a t e i s t h e r e c i p r o c a l of the a v e r a g e fade
duration f o r a 0 dB threshold. F o r t h e quiet conditions depicted in Figs. 1 and 4, the fade r a t e s
w e r e 3.8 Hz a t UHF-and 6.2 Hz a t VHF. F o r d i s turbed conditions, t5k fade r a t e s w e r e higher being
7.2 Hz a t UHF and 9,Z,&Lz at VHF,
s p e c t r a approximates a power law f o r frequencies
g r e a t e r than 1 Hz. Power law power s p e c t r a have
been reported by Rufenach" and the power law
f o r m is eviden in t h e data reported by Elkin and
Papagiaxmis.
A line with a slope of - 3 i s drawn
on t h e f i g u r e but t h e b e s t f i t slope f o r the power
s p e c t r a - m a y lie between - 2 and -3. The fluctuations of_the power s p e c t r a with frequency a r e due
to &he l i m i t e d s t a t i s t i c a l a c c u r a c y of the 'reported
values. h e - m i n u t e s a m p l e s i z e s w e r e chosen
b e c a u s e t h e p r o c e s s i s obviously not s t a t i o n a r y
o v e r longer t i m e i n t e r v a l s (except perhaps when
the s t r o n g scintillation l i m i t is reached a s shown
in Fig. 3) and m a y well not be stationary even o v e r
a minute. S h o r t e r s a m p l e lengths w e r e not chosen
b e c a u s e the s t a t i s t i c a l e r r o r would become signi-
"
The tempbra1 b e h a v i o r - o f Btintillation m a y a l s o
be c h a r a c t e r i z e d by e m p i r i c a I c o r r e l a t i o n functbns
o r power spectra. Power s p e c t r a f o r selected
t i m e periods f r o m the p a s s depicted in Fig. 3 a r e
displayed in Figs. 7 and 8. The power s p e c t r a
w e r e calculated using detrended log received
power data f r o m each analysis interval. T h e data
for each i n t e r v a l w e r e parabolically weighted p r i o r
to calculating the F o u r i e r t r a n s f o r m and t h e resultant power s p e c t r a w e r e averaged o v e r 13 analysis
i n t e r v a l s within a minute. T h e Esultant confidence
limits f o r the power s p e c t r a e s t i m a t e s a r e shown
in the figures. The s p e c t r a r e p r e s e n t signal plus
noise. T h e r e c e i v e r noise levels a r e a l s o depicted
on each figure. The r e c e i v e r bandwidths p r i o r to
sampling a r e approximately 250 Hz and witsampling r a t e of only 15 p e r second (Nyquist f r e q uency of 7. 5 Hz) considerable aliasing i s possible
in t h e reported s p e c t r a .
.
.
ficantly l a r g e r .
> ' -
Loq (Received Power1 150MHz
95% Confidence
Limits
.-.
I-
tii . . 4 L - . d ' -
0 06-Hz Bondwidth
lo=,
N
Log (Received Power) 400 MHz
95% Confidencs
Limits
0.06-HZ Bondwidth
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7-0 and
12-I4rnm
The s p e c t r a f o r disturbed o r s t r o n g scintillation l i m i t fluctuations a r e r e p r e s e n t e d by solid
lines. T h e s e data show little change of l e v e l with
frequency implying that s e v e r e aliasing i s p r e s e n t
in the d a t a and the sampling r a t e was not high
enough to adequately r e p r e s e n t the strong s c a t t e r ing case. The data w e r e obtained a s a p a r t of a
g e n e r a l propagation study and higher sampling
r a t e s would have compromised the other e l e m e n t s
of the program. What i s evident i n the data is r e l atively little change i n the low frequency v a r i a n c e
energy and significant i n c r e a s e s a t higher frequencies. The c o r r e l a t i o n t i m e t h e r e f o r e d e c r e a s e s
and t h e s p e c t r u m s p r e a d s (fade r a t e i n c r e a s e s ) a s
the s t r o n g scintillation limit is reached. This
r e s u l t h a s been predicted h e u r i s t i c a l l y by many
w o r k e r s , l2
FREOUENCY (Hz)
Figure 7
The UHF s p e c t r a f o r the quiet and disturbed
t i m e s a r e identified on the figure. T h e dashed
s p e c t r a a r e for minute i n t e r v a l s between 2 and
5 minutes as shown in Fig. 3. The horizontal
lines with u values i n Fig. 3 r e p r e s e n t the d u r a tion spanne3by the s p e c t r a displayed in Fig. 7.
The dashed lines a r e f o r quiet o r weak scintillation conditions. The quiet data a r e b a r e l y above
r e c e i v e r noise and a r e not useful in describing
scintillation phenomena. T h e dot-dashed s p e c t r u m , f o r minute 9-10, is f o r a period when the
s t r o n g scintillation limit was not reached. The
The VHF spectra. f o r the disturbed period a r e
a l s o flat spectra. F o r quiet conditions, the 9(
value i s approximately the s a m e a s f o r the dotdashed c u r v e in Fig. 7. As in Fig. 7, the s p e c t r a
at lower frequencies have a l m o s t the, s a m e levels
a s f o r t h e s t r o n g scintillation limit. F o r quiet
conditions and frequencies above 1 Hz, t h e signal
5
c
v a r i a n c e to noise v a r i a n c e ratios a r e not l a r g e
enough to provide an adequate m e a s u r e of t h e
shape of each spectrum.
conditions m a y be due to actual changes in total
e l e c t r o n content o r to random inclusions of.2n
radian phase ambiguities.
P h a s e Fluctuations
The r m s variation in differential doppler and
phase a r e depicted in Fig. 10 for the e n t i r e pass.
The differential doppler values a p p e a r to show a
s t r o n g scintillation limit a t 4. 3 Hz cor.responding
to the n/d3 r m s value for phase change between
s u c c e s s i v e obs'erv-ations of a Rayleigh.process.
The..r.ms variations in differential phase show
m o r e uqc.ertainty f o r s t r o n g scintillation due.-ta
possible phase ambiguities.
-
The phase of t h e signals f r o m the satellite
fluctuates when scintillation occurs. The differential phase path length was m e a s u r e d using the
VHF in-phase and q u a d r a t u r e voltage values. The
p h a s e ' r e f e r e n c e f o r t h e VHF signal was the phase
o{ the. UHF signal divided down b y t h e ratio of the
We.frequencies. The differential phase path
length values, reported in t e r m s of phase change
at 150 MHz r e f e r e n c e the initially reported phase
value, a r e shown i n Fig. 9. T h e differential
phase value a t a s a m p l e instant i s computed f r o m
the r e p o r t e d in-phase and q u a d r a t u r e voltage
values and can only be determined modulo 2n. In
processing t h e data, t h e assumption i s made that
the phase cannot change by m o r e than r radians
between s u c c e s s i v e samples. This assumption i s
adequate only i f the d a t a a r e s a m p l e s at a sufficiently high rate. The in-phase and q u a d r a t u r e
channel bandwidths w e r e 250 Hz p r i o r to sampling
and it i s possible that phase shifts g r e a t e r than
2n can o c c u r between sampling times.
Power s p e c t r a for the differential phase fluctuation observations a r e shown in Fig. 11. The
dashed c u r v e s correspond to weak scintillation and
a sampling r a t e adequate to unambiguously m e a s u r e differential phase. These power s p e c t r a show
a region of generally l i n e a r (power law) d e c r e a s e
until the data a r e contaminated by r e c e i v e r noise..
F o r frequencies below 3 Hz the s p e c t r a a r e
increasing with d e c r e a s i n g frequency though at a ' _
lower r a t e than f o r frequencies f r o m . 3-. 6 Hz. ..The data a t the low frequencies a r e , however, .
contaminated by the c u r v e fitting, detrending p r o c e d u r e used to p r e p a r e t h e data f o r t r a n s f o r m
.
analysis. P h a s e difference power s p e c t r a o b s e r vations reported by P o r c e l l o and HughesZ8 show
reasonably convincing power law power s p e c t r a
o v e r a range f r o m . 1 to 10 Hz f o r satellites in
orbits s i m i l a r to those used f o r the Millstone
measurements. The slopes of t h e power s p e c t r a
observed by P o r c e l l o and Hughes ranged f r o m
-2. 8 to -3. 0. The s t r o n g scintillation data a l s o
show a power law behavior caused by t h e low
frequency fluctuations evident in Fig. 9. This
behavior however may be due to phase ambiguities
and a higher sampling rate is r e q u i r e d to adequately d e s c r i b e strong scintillation effects.
.
100
-2
1
RCLATIVL TlYL Ir)
M U A M TIM (rrl
W E T COIQlTlONS
MSTURBEO C M I T I O N S
*
Figure 9
The differential doppler values for quite conditions ( s a m e observation t i m e s as f o r Fig. 1) show
a relatively n a r r o w s p r e a d of values-about-the o r i gin suggesting that no phase ambiguity problems
occurred. The differential phase values showed a
smoothly changing t r e n d caused by the change in
integrated electron content along t h e path ( s e e
G a r r i o t t etal,
1970). The data show an i n c r e a s e in
phase flucutations at the F a r a d a y null cuased by a
d e c r e a s e in signal to noise ratio. The differential
doppler data for disturbed conditions show a nearly
uniform distribution of points between 27. 5 Hz kn
change between s u c c e s s i v e samples). F o r this data,
occasional phase ambiguities a r e quite likely which
introduce e r r o r s into the differential phase values.
The low frequency differential p h a s e f l u c t u a t i o n s a p p a r e n t i n Fig. 9 f o r disturbed
6
-
j 100
-
-
-
w
-
-
- e-
w
0
z
w
K
LL
1'
-
k
0
In
In
Differential Doppler
Differential Phase
1
-
11
0.1
0
'
I
I
I
I
I
I
I
2
4
6
8
10
12
14
TIME (min)
F i g u r e 10
-0.1
16
H
,.I
-
.
!
with the scintillation in the principal polarization
channel. T h e data t h e r e f o r e show no uncorrelated
fluctuations.
Phose Path Length
Difference 150-400 MHz
I
1.0,
., .
.+. .
.
5 OBw
E
06-
I
LL
LL
.
8 04-
...
:.. ....
.. .
. ...
. . .
. . .
.
i
. I
F i g u r e 11
F
Depolarization
-0.4'
0
Simultaneous observations w e r e made on both
left and right hand c i r c u l a r polarizations at UHF.
T h e t r a n s m i s s i o n s w e r e nominally right hand c i r c u l a r but in p r a c t i c e w e r e elliptically polarized.
The polarization s t a t e changed slpwly with changes
in satellite, r e c e i v e r station geometry. The o r t h ogonal polarization r e c e i v e r was gain controlled
by the p r i m a r y polarization AGC signal. The AGC
control s y s t e m was effective i n removing fluctuations of limited dynamic range that o c c u r r e d simultaneously on both channels a t frequencies up to
250 Hz. F o r strong fluctuations with peak-to-peak
s p r e a d s of m o r e than 20 dB. the AGC s y s t e m did
not remove a l l of the simultaneous fluctuations
f r o m t h e orthogonal channel output and the residual fluctuations w e r e detected. F o r weak s c i n tillation, only fluctuations on t h e orthogonal channel that w e r e not c o r r e l a t e d with the principal
polarization fluctuations would b e detected. F o r
strong scintillation, the residual fluctuations had
t o be c o r r e l a t e d with t h e principal polarization
fluctuations t o detect the p r e s e n c e o r absence of
uncorrelated fluctuations i n the orthogonal polarization channel. T h e signal to noise ratio f o r
uncorrelated fluctuations was i n e x c e s s of 20 dB
'
'
'
2
4
6
'
8
'
'
'
'
I
IO
12
14
16
18
TIME (min)
F i g u r e 12
',,
T h e s e observations show that the fluctuations
on both polarizations a r e c o r r e l a t e d and polarization diversity s y s t e m s will not be useful in combating ionospheric scintillation a t UHF. If significant uncorrelated orthogonal polarization fluctuations w e r e p r e s e n t they would have a u value n e a r
those in Fig. 3 which obviously w e r e
not o b s e w ed in t h e data presented i n Fig. 12 even for the
s t r o n g e s t scintillation levels. S i m i l a r conclusions
have been drawn by Whitney and Ring29 f r o m
observations made a t 137 MHz f o r scintillation
levels below the strong scintillation limit and by
Koster3O f o r s t r o n g scintillation at 137 MHz i n the
equatorial region.
Observations a t frequencies lower than 54 MHz
show that orthogonal c i r c u l a r polarization channels
m a y fade independently3' and diversity is possible.
At frequencies below about 50 MHz, the ordinary
and extraordinary r a y s may b e s e p a r a t e d by m o r e
than the radius of the f i r s t F x e s n e l zone and the
electron density fluctuations causing scintillation
will not b e c o r r e l a t e d f o r two orthegonal polarizations. 32 Sufficient separation between o r d i n a r y
and e x t r a o r d i n a r y r a y paths- for-the.f luctuations t o
become independent is not possible a t frequencies
above 100 MHz.
f o r typical satellite, r e c e i v e r geometries. T h e rms variation of the log of the orthogonal
channel amplitude and the correlation coefficient
between the log of the orthogonal channel output
and the log of the principal channel output is shown
in Fig. 12 f o r the e n t i r e p a s s ( s e e Fig. 3 f o r principal polarization variation). F o r weak scintillation, the output is n e a r r e c e i v e r noise and no
correlation is evident. After seven minutes, the
scintillation is much s t r o n g e r and a low level v a r iation is evident in the orthogonal channel data.
This residual output is however highly correlated
7
!
5
111.
C a r r i e r Frequency Dependence of the
UHF, VHF Observations
Frequency Dependence of the Scintillation Index
The data presented above a r e provided to illust r a t e the c h a r a c t e r i s t i c s of scintillation a s
observed a t UHF and VHF. These data cna be
used to provide information about scintillation at
other locations, frequencies, and path geometries
only if a model i s available f o r t h e i r interpretation.
In t h e limit of weak scintillation, the available
models d i s c u s s e d above a l l r e l a t e the power spect r u m of amplitude (or log amplitude) a s observed
on the ground to the power s p e c t r u m of the e l e c t r o n density fluctuations modified by the effects of
t h e s c a t t e r i n g p r o c e s s ( F r e s n e l filtering). The
power s p e c t r u m of t e m p o r a l changes observed on
a line-of-sight path to a low orbiting satellite may
be related to the power s p e c t r u m of spatial fluctuations of e l e c t r o n density by assuming that the
e l e c t r o n density fluctuations do not change during
t h e t i m e the line-of-sight sweeps through the d i s turbed region of the ionosphere.
E a r l y models of scintillation a s s u m e d that the
spatial c o r r e l a t i o n function f o r e l e c t r o n density
fluctuations was approximately Gaussian with diff e r e n t s c a l e s i z e s along and perpendicular to the
magnetic field lines.
The Gaussian model i m plies a Gaussian power s p e c t r u m with power spectral densities d e c r e a s i n g rapidly f o r spatial f r e q uencies above o r below t h e r e c i p r o c a l of the s c a l e
size. In .the l i m i t of high frequencies corresponding to spatial frequencies l a r g e r than the r e c i p r o c a l of the F r e s n e l zone size, the s p e c t r u m
observed on the ground should be identical to the
two dimensional s p e c t r u m of electron density fluctuations observed i n a plane n o r m a l to the direction
of the propagation path. F o r a Gaussian model,
the high frequency limit should have a parabolic
shape with increasing negative slopes f o r i n c r e a s ing frequency when observed f o r weak scintillation. The dot-dashed c u r v e in Fig. 7 has sufficient signal variation to noise variance ratio to
show the slopes of the s p e c t r u m to be n e a r l y
l i n e a r shape f o r high frequencies is indicative of
a power-law power s p e c t r u m r a t h e r than a
Gaussian power spectrum. 25
Power s p e c t r a at both UHF and VHF with a
reasonably high signal v a r i a n c e to noise variance
ratio and f o r weak scintillation a r e shown in
Fig. 13. These s p e c t r a a r e f o r the s a m e one minute observation periods and f o r a t i m e period
wh?n the individual r m s log amplitude values f o r
e-b analysis i n t e r v a l changed little a t both f r e q uencies (the p r o c e s s was n e a r l y stationary).
Both s p e c t r a show power-law high f r e q u t n c y
regions.. T h e scintillation models predict that.
the power s p e c t r a l density values should i q c r e a s e
by the s q u a r e of the ratio of the c a r r i e r wavelength. The b e s t fit s t r a i g h t lines to both observed
s p e c t r a having a wavelength s q u a r e d s e p a r a t i o n
a r e shown on the figure. The slope of t h e s e lines
8
is approximately -3. This c o r r e s p o n d s to a power
law dependence f o r the t h r e e dimensional spatial
power s p e c t r u m of e l e c t r o n density fluctuations
with an index of 4 (Scuk-P, S = power s p e c t r a l density, k = wavenumber, p = index) and a one dimensional s p e c t r u m with an index of 2 . The data
presented i n Fig. 13 a r e f o r observations to the
northwest at an elevation angle of 18". F o r the
satellite, r e c e i v e r station geometry, the F r e s n e l
zone s i z e at a height of 300 k m was 0. 7 k m at
400 MHz and 1.1 k m a t 150 MHz. The r a y moved
a t approximately 1. 0 k m / s e c through the ionos p h e r e (velocity perpendicular to the line-of-sight
at 300 km). The frequency at which each of the
s p e c t r a flatten (1. 5 Hz at 400 MHz: 0. 9 Hz at
150 MHz) i s approximately the ratio of the ray
motion to F r e s n e l zone s i z e and higher f r e q uencies c o r r e s p o n d t o s c a l e s i z e s s m a l l e r than
the F r e s n e l zone size.
102
Log(Received Power)
I
0.1
I
I
I
I
,,Ill
95% Confidence
Limits
0.06 Hz Bandwidlh
I
1
I
I
1
1
1
1
1
1.0
FREQUENCY (Hz)
F i g u r e 13
The weak scintillation theory f o r a power-law
s p e c t r u m predicts a scintillation index (S o r u )
frequency dependence given by33
4
x
where A i s wavelength, the s u b s c r i p t s r e f e r to the
c a r r i e r frequencies, and T\ is the s p e c t r a l index.
F o r a t h r e e dimensional power-law index of 4,
the s p e c t r a l index is 1. 5. Using this s p e c t r a l
index, S( at 150 MHz should be 4. 4 t i m e s
at
400 M H z . F o r the data displayed in Fig. 7 3 , u
a t 400 MHz was 0. 5 dB, 0 at 150 MHz was 2.4%
2 . 4 dB, and the predicted Xvalue using = 1. 5 i s
2. 3 dB, well within the measurem'ent- e r r o r of the
observed value. The relationship between (5 a t
ea150 MHz and % a t 400 MHz for a pass with r X
sonably high signal variance to noise v a r i a n c e
ratios i s shown on Fig. 14. T h e w e a k s c i n -
. .3
-,
I
tillation limit c u r v e corresponding to a s p e c t r a l
K
index of 1. 5 is shown together with the s t r o n g
scintillation limit. T h e data appear to lie along
the weak scintillation e s t i m a t e c u r v e until the
s t r o n g scintillatio'n l i m i t is reached, then u
X
r e m a i n s a t the l a t t e r value.
,I , /-.-
eL,
,
I
I
,
I
,
I I I
i
,
,
I
I I
I I I
I
I
I
1
I
4
I
'4
1
Weak Scinlillolin
-
%"
4
c
Aarons et38
and ~ l l e n 3 9argue, for o b s e r v a tions made above 63 MHz f r o m the S a g a m o r e Hill
Radio Observatory, t h a t a s p e c t r a l index of 2. 0
b e s t fits t h e i r data in the l i m i t of weak s c a t t e r
curve
although the plots of scintillation index vs
have a median value of 1. 6 as long as the scintillation index a t 113 MHz is between 5 and 25% (S
4 at
63 MHz l e s s than 0. 6 and m e a s u r a b l e scintillation
a t 113 MHz). Recently reported observations f r o m
the s a m e o b s e r v a t o r y at frequencies of 137 and
show, f o r s i m i l a r weak
412 MHz by Whitney et29
but m e a s u r a b l e scintillation conditions, a d i s t r i bution of 'ilvalues between 1. 2 and 1. 8 with a m e a n
value of 1. 49 f 0. 05.
cX (dB) AT 400MHZ
F i g u r e 14
t o r y , l e s s than 100 k m i r o m Millstone. Aarons 36
reported observations a t frequencies between 22
and 39 MHz f r o m Arecibo, P u e r t o Rico under weak
scintillation conditions and found a median s p e c t r a l
index of 1. 6. Amplitude scintillations observed by
Lawrence et5
at 53 and 108 MHz show, f o r S
values at 53 MHz below 0. 01 (-S = 0. 7). a me&an
s p e c t r a l index value of 1. 5. E a A y observations
r e p o r t e d by C h i ~ e r m
s a~d e~ at J o d r e l l Band Experimental Station a t s e v e r a l frequencies between 36
and 408 MHz using radio stars had m e a n s p e c t r a l
indices ranging f r o m 1. 9 to 2.1. Observations a l s o
m a d e at J o d r e l l Bank at 79 and 1390 MHz and
r e p o r t e d by Chivers and D a ~ i e showed
s ~ ~ in the
limit of weak s c a t t e r a t 79MHz and just detectable
fluctuations at 1390 MHz, a value of q n e a r 1. 5.
.
T h e frequency dependence of ionospheric
scintillation has received considerably attention in
the literature. The thin phase s c r e e n , Gaussian
correlation function model predicted a s p e c t r a l
index of two when the scale s i z e w a s l a r g e r than
the first F r e s n e l zone radius ( n e a r field limit)
and of one when the s c a l e s i z e was s m a l l e r (far
field limit)!' T h e power-law power s p e c t r a model
predicts a single value f o r all c a s e s (provided the
power law holds o v e r all s c a l e sizes). Experimental verification of the frequency dependence
predictions is difficult because the scintillation
index m u s t be l e s s than the saturation limit value
at both the high and low frequency. F o r strong
scintillation at both frequencies, the empirically
determined s p e c t r a l index would be zero. F o r a
random selection of observations, the e m p i r i c a l
s p e c t r a l index should lie between 0 and 1. 5. Sign a l to noise and m e a s u r e m e n t dynamic range
problems inherent in many of the e a r l y m e a s u r e ments could f u r t h e r d e g r a d e t h e estimates of spect r a l index. F r o m Fig. 3 f o r the period between
two and five minutes the r a t i o of u values is
X
approximately 10 implying a s p e c t r a l index of 2. 3.
As shown i n Fig. 8, the lower frequency was contaminated by r e c e i v e r noise causing a fictitiously
high s p e c t r a l index estimate.
Only a limited number of s p e c t r a l index e s t i - .
mations have been m a d e f o r equatorial regions.
,
Blank and Golden40 r e p o r t I)- 0. 2 to 0. 3 f o r f r e q uencies between 137 and 400 MHz. They comment
that the r e s u l t s pertain, in p a r t , to s t r o n g s c a t t e r .
T a u r 4 l reported a value of I)- 2 f o r equatorial
m e a s u r e m e n t s at 4 and 6 GHz. T h e l a t t e r o b s e r vations w e r e f o r weak scintillation and m a y indic a t e e i t h e r the existance of an inner s c a l e where
the power law region ends and a different power
s p e c t r u m shape o c c u r s or the problems of detecting s m a l l fluctuations i n noise.
C o r r e l a t i o n of Amplitude Fluctuations a t T w o Freeuencies
The r m s amplitude fluctuations d e c r e a s e with
i n c r e a s i n g frequency f o r weak scatter. They a r e
a l s o c o r r e l a t e d o v e r a wide frequency range. Calculations of the expected c o r r e l a t i o n coefficient
f o r power-law indices ranging f r o m 3 to 4 a r e
shown in Fig, 15. S i m i l a r calculations f o r Gaussian s p e c t r a have been made by Budden4'.
Since
the available power s p e c t r a and frequency dependence data support the power law model, the Gaussian model predictions will not be presented. Meas u r e d c o r r e l a t i o n coefficients f o r the Millstone
data and f r o m available p a p e r s a r e a l s o presented.
T h e p = 4 c u r v e provides the b e s t e s t i m a t e based
upon the above analysis and should r e p r e s e n t t h e
upper bound f o r m e a s u r e m e n t s f o r each A f value.
T h e lower frequencies used i n the two frequency
observations a r e listed in the figure. F o r strong
Simultaneous observations of radio s t a r scinshowed a spectillation reported b y Basu
t r a l index value of approximately I. 5 f o r frequenc i e s at 112 and 224 MHz and a lower value for the
63, 112 M H z frequency pair. The lower value f o r
t h e lower frequency presumably is caused by
s t r o n g scintillation data. T h e s e observations
w e r e made at t h e S a g a m o r e Hill Radio Observa-
et34
9
I
scintillation, the c o r r e l a t i o n coefficient should be
upon the elevation angle of the line-of-sight t o the
lower than the calculated values. F o r low f r e q satellite, t i m e of day, s e a s o n of the y e a r , the
uency observations, the f i r s t F r e s n e l zones a t
degree of magnetic disturbance. and sunspot numeach frequency m a y not overlap due to different
ber. In m o s t of the observations, the exact n a t u r e
ionospheric refraction at each frequency. F o r an
of t h e dependance could not be determined due t o
elevation angle of 10". r a y s at 150 and 400 MHz
the limited duration of the observations and possia r e s e p a r a t e d by m o r e than 30 k m at a height of
ble correlations between s o m e of the geophysical
300 km. The Millstone observations depicted i n
and geographical p a r a m e t e r s . F o r observations of
Fig. 1 show no correlation between the two f r e q a radio s t a r , the elevation angle and t i m e of day
uencies. Since t h e elevation angles a r e less than
a r e c o r r e l a t e d f o r each s e a s o n and the diurnal,
10" f o r the data depicted in Fig. 1 and the f i r s t
.elevation angle dependances cannot be separated.
F r e s n e l zone r a d i i a r e l e s s than I. 3 km. no c o r F o r observations of satellites in low circumpolar
relation was expected.
orbits, the effects of elevation angle and geo-magnetic latitude cannot be s e p a r a t e d without making
simultaneous observations f r o m a number of locations. 43
.
Scintillations m a y be caused by electron density
fluctuations anywhere in the ionosphere. E a r l y
studies showed strong correlation with the occurrence of s p r e a d - F and v e r y weak c o r r e l a t i o n with
sporadic E and s p r e a d E. This implies that the
majority of scintillation o c c u r r e n c e s a r e caused
by F region i r r e g u l a r i t i e s . Studies of the heights
of regions causing scintillation deduced f r o m t h e
r a t e s of change of fluctuations observed using low
orbiting satellites or f r o m simultaneous observations at m o r e than one station on t h e ground show
that the electron density i r r e g u l a r i t i e s m a y o c c u r
o v e r a wide range of heights, 200-600 k m both
in the a u r o r a l and equatorial regions. 47,48,49
-
The r a d a r data of Pomalaza e l 5show that the
i r r e g u l a r i t y region is usually s e v e r a l hundred
kilometers thick.
The data displayed on Fig. 15 show reasonable
agreement with the 'calculations. The data reported by Taur41 are the only data f o r weak scintillation only. T h e s e data with a lower frequency a t
1550 MHz f o r a n equatorial station shows b e t t e r
agreement f o r p between 3 and 3. 5 than a t 4.
This again m a y indicate a change in the power
s p e c t r u m of electron density fluctuations a t s m a l l
s c a l e s i z e s i n the equatorial region. The o b s e r vations reported above f o r a u r o r a l and mid-latitude s i t e s a r e a l l in reasonable agreement with a
power-law power s p e c t r u m model with an index of
4 f o r the t h r e e dimensional fluctuations of elect r o n density. T h e situation f o r equatorial regions
is not as convincing and m o r e data a r e required.
It is, however, evident that the correlation coeffients a r e reasonably high over a wide frequency
range. This implies that extremely wide frequency separations (-10 to I) are required to provide
adequate frequency diversity operation and f r e q uency diversity is not useful in combating the
effects of scintillation.
Using the Rytov method t o analyze weak scinthe
tillation due to a thick i r r e g u l a r i t
variance of the log amplitude ((5
T~g~~~60rtional
to the integral of the product of the variance of the
electron density fluctuations (intensity) and d i s tance f r o m the i r r e g u l a r i t i e s to the r e c e i v e r over
the thickness of the i r r e g u l a r i t y region f o r plane
waves incident on the ionosphere and a t h r e e
dimensional power law power s p e c t r u m with a n
index p = 4. T h e scintillation i n d e x , t h e r e f o r e ,
depends both upon the s q u a r e root of thc extent of
3-of-sight path
the i r r e g u l a r i t y region along the
and to t h e s q u a r e root of the dista..de f r o m the
r e c e i v e r to the i r r e g u l a r i t y region. Both the d i s tance to the i r r e g u l a r i t y region and the extent of
the region along the r a y v a r y with elevatir angle.
If the s i z e intensity and location of the i r r - g u l a r i t y
region a r e known, the scintillation index m a y be
computed f r o m the model f o r any combination of
frequency and path geometry f o r u < 2 - 3 dB (weak
X
scintillation). It i s difficult however to deduce the
intensity of the i r r e g u l a r i t i e s f r o m observations
using low orbiting satellites because the scintillation index value changes m a y be due to a change i n
s i z e , a change of intensity, or a change i n elevation angle.
,I)
IV Dependence of Scintillation on
Geo phy s ic a1 P a r a m e t e r s
Morphological studies of the dependence of
scintillation on geophysical p a r a m e t e r s have
shown that scintillation is m o s t s e v e r e and prevelent in and north of the ariroral zone and n e a r the
geomagnetic equator (equatorial region within
t 15" to 2 0 " of the geomagnetic equator). T h e s e
studies of available scintillation observations
show that the s e v e r i t y of scintillation a l s o depends
T h e Millstone data f o r the satellite p a s s
r e p o r t e d i n Figs. 3 and 10 w e r e replotted vs the
invariant latitude of the line-of-sight to the
to
.,
I
satellite at a height of 300 k m and a e presented
in Fig. 16. T h e s e d a t a show a relatipely rapid
change f r o m weak t o s t r o n g scintillation a s t h e
variant latitude, A, changes f r o m 56 to 59". This
sudden change m a y be d e s c r i b e d a s a scintillation
boundary in analogy with the boundary observed
by Aarons
T h e scintillation boundary cons i d e r e d by Aarons & is defined a s the latitude
where their. e x t r e m e value scintillation index, SI,
exceeds 50% a t 40 MHz. This t r a n s l a t e s to a n S4
value of 0.02 (a = 0. 08 dB) a t 400 IhHz using 1
s p e c t i a l index
1. 5 and t h e relationship between
SI and S4 reported by Bischoff and Chytil. 21 The
400 MHz observations made a t Millstone do not
have sufficient sensitivity to o b s e r v e t h e boundary
defined at 40 M H z although an apparent boundary
is sometimes evident in the data. The abrupt
changes in a and the apparent differences in ax
X
values to the north and south of Millstone ( A = 56")
shown i n Fig. 16 indicate changes in e i t h e r t h e intensity o r extent of e l e c t r o n density fluctuations
with invariant latitude, the elevation angles being
approximately the s a m e f o r latitudes equispaced
above and below 57" f o r the p a s s depicted in the
figure. The data reported i n Figs. 1 and 9 c o r r e s pond to 51" and 64' f o r quiet and disturbe&onditions to the n o r t h and south of t h e boundary,
respectively.
et?
03
-
-
0.1!5
55
I
50
I
60
I
65
I
70
I
7
INVARIANT LATITUDE (deg)
,:
..
F i g u r e 16
-.>
i
.
A u r o r a l and mid-latitude scintillation regions
a r e s e p a r a t e d by the scintillation boundary. The
position of the boundary changes with t i m e of day.
magnetic activity, and possibly sunspot number.
Aarons5'reported that t h e position of t h e bounchry
defined using the m e a n SI values f o r a number of
observations ranged f r o m 54" to 76" depending
upon t i m e of day and magnetic activity. The
d i u r n a l variation of S4 at 400 MHz tabulated f r o m
Millstone data f o r detrended three-second o b s e r vation periods51 a r e shown in Fig. 17 Two invariant latitude bands w e r e analyzed, 44 to 46"
corresponding to positions always within the midlatitude region (south of the boundary) and 64 to
66" corresponding to locations within the night
t i m e a u r o r a l region. Data f r o m a total of 2471
p a s s e s w e r e analyzed. F o r t h e two-invariant
latitude bands used, t h e elevation angles ranged
f r o m 3" to 14". The elevation angle values f o r
each p a s s however w e r e generally different in
each band. Over the range of elevation angles,
t h e S4 or aX value m a y change by a f a c t o r of 2.
The elevation angles should have n e a r l y the s a m e
o c c u r r e n c e distribution f o r each band and no elevation angle bias i s expected.
..
-
LQY RE I*)
F i g u r e 17
The o c c u r r e n c e percentages of S i values
above 0. 2, 0.4, 0. 6 and 0. 8 (a values of 0. 9, 1. 4
X
2. 8 and 4. 2 dB, respectively) w e r e c h o s e n t o
c h a r a c t e r i z e t h e observations. F o r S4 > 0.8, the
64-66' data show a morning minimum and an afternoon maximum. Data reported by Aarons5' f o r
N a r s s a r s s u a q having an invariant latitude of 63"
and an elevation angle of 18" show, at 136 MHz, a
morning minimum i n mean SI and a nighttime
maximum o c c u r r i n g between 2100 and 0500 hours.
It
T h e Millstone afternoon maximum is not evident in
reported occurthe 136 MHz data. Aarons et4
r e n c e percentages f o r SI > 60% at 136 MHz (equivalent t o S4 > 0.15 at 400 MHz) that displayed a
morning minimum and a nighttime maximum.
Although the N a r s s a r s s u a q data a r e f o r n e a r l y t h e
s a m e invariant latitude a s t h e Millstone d a t a - a n d
t h e elevation angles d i f f e r slightly, the l a t t e r data
show an afternoon maximum not p r e s e n t i n the
f o r m e r . The Millstone data a r e f o r observations to
the north, t h e N a r s s a r s s u a q data f o r observations
toward t h e south and differences i n propagation
d i r e c t i o n relative t o t h e field lines mi ht be impoltant. 113 M H z d a t a reported by AaronsS O f o r radio
s t a r observations toward the North at an invariant
latitude of 66' at t h e s a m e elevation angles a s f o r
Millstone show relatively higher m e a n SI values in
t h e afternoon than i n the morning displaying t h e
s a m e g e n e r a l t r e n d a s t h e Millstone data. T h e
113 MHz data a l s o showed a lower m e a n SI value
averaged o v e r all t i m e s of day than the 136 M H z
data. The lower SI values a r e presumably due t o
d i f f e r e n c e s in sunspot number, the 113 M H z d a t a
w e r e taken at the minimum of the sunspot c y c l e ;
the 136 MHz and Millstone data n e a r t h e maximum.
The shape of the d i u r n a l variation curvek. m a y b e
affected by differences in t h e intensity and extent of
t h e i r r e g u l a r i t i e s along and n o r m a l t o the field
lines.
have only shown that scintillation tends t o be both .'
m o r e prevalent and m o r e intense on a v e r a g e
during y e a r s of high sunspot n*.mber.
T h e mid-latitude region observations show significantly s m a l l e r percentages of o c c u r r e n c e f o r
each of t h e t h r e e hour intervals. The number of
satellite p a s s e s associate& with t h e observed
o c c u r r e n c e s with S4 .> 0.2 range between 0 and 2
for all i n t e r v a l s except 2100-2400 h o u r s implying
that insufficient data w e r e available to deduce a
diurnal trend. Mid-latitude ~ b e r v a t i g n sby
Aarons et52
a t 54 MHz show mean SI values to
have relative maxima at noon and midnight.
Equatorial region observations show scintillation
to b e a nighttime phenomena with Occurrences
r a r e ' between s u n r i s e and sunset? Observations
reported by Aarons et4
f o r Huancayo, P e r u
(equatorial) show that a t 136 M H z t h e scintillations
w e r e m o s t prevelent at 2200 h. l o c a l time with a
60% o c c u r r e n c e f o r SI > 60. This t r a n s l a t e s to a
60% o c c u r r e n c e of S4 > 0.15 at 400 MHz. The
data in Fig. 17 show l e s s than 10% o c c u r r e n c e f o r
S4 P 0. 2 indicating that equatorial scintillations
tend to be m o r e prevalent than a u r o r a l zone s c i n tillations.
.L
I
MONTH
F i g u r e 18
I
64' < A < 6 6 O
(Auroral)
The s e a s o n a l dependence of scintillation is
shown for the Millstone mid-latitude and a u r o r a l
region observations in Fig. 18. T h e s e data show
a s p r i n g minimum and a fall maximum for the
a u r o r a l data a t S4 > 0. 2. The August peak is
caused by a t h r e e day i n t e r v a l associated with the
highest magnetic activity indices observed during
the January 1971 to March 1973 t i m e period. The
August event b i a s e s the observations. The s e a sonal variation of m e a n SI at 54 MHz reported by
Aarons et52
show a minimum i n the number of
o c c u r r e n c e s i n Winter a s compared to other s e a sons f o r a l l observations to the north and south
of the Sagamore Hill Observatory. The 54 M H z
data a r e however for the minimum of the sunspot
cycle. The data,therefore, show little r e a l seasonal variation. Equatorial region observations tend
to show relatively higher percentage o c c u r r e n c e s
at the t i m e s of the equinoxes and a minimum at
the n o r t h e r n solstice.
s4
0-1' 2-3+ >4-
Observations of scintillation in the a u r o r a l
region generally show a c o r r e l a t i o n between mean
SI values and magnetic activity, Kp. F i g u r e 19
shows t h e i n c r e a s e i n t h e o c c u r r e n c e of scintillation with increasing Kp f o r t h e a u r o r a l region.
Little change in percentage o c c u r r e n c e s of S a.2
i s noted f o r the mid-latitude region.
noted that the position of the scintillation boundary
is c o r r e l a t e d with Kp, moving south a s Kp
i n c r e a s e s . In'contrast to the apparent dependence
of scintillation on magnetic activity in the a u r o r a l
region, Koster9 notes that scintillation in the
equatorial region is s u p p r e s s e d during periods of
enhanced magnetic activity. These r e s u l t s m a y
v a r y with t h e sunspot cycle but insufficient data
a r e available to t e s t dependences on sunspot numbers. Available long t e r m observations of s c i n tillation over a significant p a r t of the sunspot cycle
..
KP
Figure. 19
12
0-1' 2-3'
KP
>4-
.
.
I
V.
Conclusions
/M.
The s t a t i s t i c a l s u m m a r y of the Millstone data
show a c l e a r dependence upon-magnetic activity
although diurnal and seasonal variations a r e not
well defined. The data a r s h o w e v e r . f o r a r e l a tively s h o r t t i m e period when compared with the
.sunspot cycle and are,therefore,not complete
enough t o provide an empirical mudel-for t h e p r e 'diction of scintillation s t a t i s t i c s f o r use in communication s y s t e m design. To provi'de the
iequired statistics, data f r o m a l a r g e number of
observations s p r e a d over a t l e a s t half a sunspot
cycle a r e required. Other available observations
have generally been made a t frequencies below
137 MHz and a r e only useful f o r the prediction of
scintillation at lower frequencies due to the limiting effect of strong scintillation.
*
The a u r o r a l region obs ervations c l e a r l y show
that scintillation will affect s y s t e m design at f r e q uencies up t o at l e a s t 400 MHz. The equatorial
region observations of Taur' show frequencies up
t o 6 GHz a r e affected. Since scintillation is a
fact of life a t UHF and VHF what methods can be
used to mitigate its effects ? While the d m a r e
somewhat inadequate, s o m e recommendations can
be made. F i r s t , s o m e negative recommendations:
The two frequency correlation function analysis
showed that scintillation i s a wideband phenomena
and frequency diversity is not practical,- The
c r o s s polarization observations showed that scintillations on the principal and orthogonal c i r c u l a r
polarizations w e r e c o r r e l a t e d implying that
polarization diversity will not work a t UHF.
While t h e s e analyses and m e a s u r e m e n t s w e r e p e r formed f o r a u r o r a l region observations, we
believe the r e s u l t s a160 apply i n t h e equatorial
region. F o r the a u r o r a l region, the weak scintillation data showed power law power s p e c t r a f o r
electron density i r r e g u l a r i t i e s
Preliminary
analysis of 254 MHz data reported f o r the equat o r i a l region4' a l s o show power law s p e c t r a
(with a three-dimensional index p = 4). This
suggests that although the mechanisms causing
equatorial region i r r e g u l a r i t i e s may be different
f r o m those active in the a u r o r a l region, the
resultant effects of the i r r e g u l a r i t i e s on propagation a r e the s a m e and the r e s u l t s obtained f r o m
the Millstone data apply in the equatorial region.
.
One possible solution is space diversity: The
Millstone observations w e r e taken using a low
orbiting satellite. The t e m p o r a l variation of the
signal level is caused by the motion of the lineof-sight throughthe irregularities. The satellite
motion is known,hence the t e m p o r a l variations
may be interpreted in t e r m s of the spatial v a r i a tion of electron density. The frequency s c a l e on
Fig. 13 may be interpreted a s a wavenumber
s c a l e with, f o r the satellite, r e c e i v e r geometry
pertinent to Fig. 13, the 1 Hz value equivalent to
2rr km-' (scale s i z e of 1 km). Since the width of
each power s p e c t r u m i s approximately the reciprocal of the correlation distance, the correlation
13
distance is approximately 0.5 k m a t UHF and 0. 8 k m
at VHF. This implies that the scintillation o b s e r v e d
a t r e c e i v e r s spaced by m o r e than the correlation
distance (- F r g s n e l zone eize) should be uncorrelated and could be combined to get diversity. F o r
strong scin+illai+oh, the power s p e c t r u m broadened
implying that s m a l l e r -diversity distances m a y be
useful in that limit.
Another possjble solution i s t i m e diversity: The
fade duration s t a t i s t i c s reported above reflect the
motion of the line-of-sight through the medium and, *
f o r weak scintillation the duration values should be
inversely proportional to the translation velocity of
the r a y a t the height of the i r r e g u l a r i t i e s . F o r
geostationary satellites, the line-of-sight i s fixed
and the i r r e g u l a r i t i e s drift by. The fade duration
values then should be inversely proportional to the
drift rate. Using a 100 m / s e c drift r a t e a s typical4
the fade durations should be an o r d e r of magnitude
l a r g e r than those shown in Fig. 6.. F o r strong
scintillation, the fade durations should be s h o r t e r
than f o r weak scintillation a s shown in the discussion of Fig. 6 The power s p e c t r a shown in
Fig. 13 imply a correlation time the o r d e r of
0.5 s e c at UHF and 0. 8 s e c a t VHF. As with the
fade duration values, the correlation t i m e is
dependent upon the velocity of the i r r e g u l a r i t i e s
perpendicular to the line-of-sight. Since the signal becomes uncorrelated in time, t i m e diversity
i s a l s o possible. F o r geostationary satellites,
correlation t i m e depends both on t'he F r e s n e l zone
s i z e and the d r i f t velocity of the i r r e g u l a r i t i e s .
The l a t t e r i s a random variable that has to be
observed a t many locations over a long period of
t i m e t o provide an adequate s t a t i s t i c a l description.
Since the fade rate o r correlation t i m e is different
f o r strong scintillation, observations m u s t be made
in the weak scintillation regime to define drift
velocities.
VI.
Recommendations
The only solutions we have recommended a r e
the use of space of time diversity. Some guidelines f o r t h e i r application may be obtained f r o m
Millstone and other available data. However, to
optimize s y s t e m deisgn, m o r e information i s
required, We recommend:
1. Additional available weak scintillation data
should be p r o c e s s e d t o determine the s t r u c t u r e of
the power s p e c t r u m to establish if the power law
f o r m r e p r e s e n t s a l l observations.
2. Available weak scintillation data f r o m geostationary satellite observations should be analyzed t o d e t e r m i n e d r i f t r a t e statistics.
3. N,ew observations using both low-orbiting and
geostationary satellites with s e v e r a l cbherently
related c a r r i e r frequencies widely s p r e a d in the
U H F , SHF band at and above the frequencies of
i n t e r e s t should be made.to provide adequate statist i c s of amplitude, phase, and drift velocity, The
-
I
-,
I
frequencies should be chosen such that weak s c i n tillation is always observed a t one of t h e f r e q uencies.
.
.
.
.
.
.
.
.
.....
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1.
.
L
I
. .;'
..''.-.:
... . . . ., =
.
.I.j
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_. i \
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!
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.
The author acknowledges t h e help and support
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'
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'.
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._
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%
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.
**
\
d
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-
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14
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27. 0. K. Garriott. A. V. daRosa, "Electron
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15
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*)
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Fig. 12
R m s variation in the output f r o m the
orthogonally polarized channel and c o r relation coefficients between t h e princip a l and orthogonal channel outputs f o r
p a s s of Object #3133 rising a t 0411 GMT
on 4 August 1972 (Kp = .
)'8
.
Fig. 13
P o w e r s p e c t r a f o r log received power
fluctuations a t both UHF and VHF f o r the
s a m e one minute observation period of
the p a s s of Object #3133, 5 August 1972
at 0334 GMT (Kp = 8').
Fig. 14
R m s variation of log received power a t
VHF vs simultaneously observed value
a t UHF f r o m p a s s of Object #3133 rising a t 2342 GMT on 4 August 1972
)'8
(Kp = .
Fig. 1 UHF and VHF amplitude m e a s u r e m e n t s
obtained f r o m a p a s s of Object #3133 on
4 August 1972.
Fig. 15
Two frequency c o r r e l a t i o n functions f o r
amplitude fluctuations.
Fig. 2. S4 $8 t i m e f o r p a s s of Object #3133 ris' - ing a t 0411 GMT on 4 August 1972 (Kp = 8').
Fig. 16
Latitude dependence of scintillation f o r
p a s s of Object #3133 rising a t 0411 GMT
4 August 1972 (Kp = 8').
Fig. 17
Diurnal variation of scintillation a t
400 MHz f o r a u r o r a l and mid-latitudes
f o r 2471 s a t e l l i t e p a s s e s observed
between January 1971 and M a r c h 1973.
Fig. 18
Seasonal variation of scintillation a t
400 MHz f o r a u r o r a l and mid-latitudes
f o r 2471 satellite p a s s e s observed
between J a n u a r y 1971 and M a r c h 1973.
Fig. 19
Magnetic activity dependence of scintillation a t 400 M H z f o r a u r o r a l and midlatitude f o r 2471 satellite p a s s e s o b s e r v ed between J a n u a r y 1971 and March 1973.
-
.
J. V. Evans, ed., IIMillstone R a d a r P r o p a -
51.
.
gation Study: Scientific Results ,Ig Technical
Report 509, Lincoln Laboratory, MIT (In
p r e s s , 1973).
52. J. A. Aarons, J. Mullan, a n d S . Basu,
''The S t a t i s t i c s of Satellite Scintillations a t
a S u b a u r o r a l Latitude, J. Geophys. Res.
. .
69 1785-1794 (1964).-.
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lust rations
.
.,
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.
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e.,
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Fig. 3 % v s t i m e f o r p a s s of Object #3133 rising a t 0411 GMT on 4 August 1972 (Kp= 8').
Fig. 4 E m p i r i c a l amplitude distribution functions f o r data shown in Fig. 1.
- _ - Fig. 5 S4 vs u f o r p a s s of Object #3133 rising a t $411 GMT on 4 August 1972 ( K p = 8').
Fig. 6 E m p i r i c a l distribution functions f o r d u r a tions below and above a - 3 dB threshold
relative t o the mean log received power
f o r the data shown in Fig. 1.
Fig. 7 UHF log amplitude power s p e c t r a f o r
selected minutes f r o m the p a s s of
Object #3133 rising a t 0411 GMT on
4 August 1972 (Kp = 8').
Fig. 8 VHF log amplitude power s p e c t r a f o r
selected minutes f r o m the p a s s of
Object #3133 rising at 0411 GMT on
4 August 1972 (Kp = .)'8
Fig. 9 Differential phase and differential dopp l e r m e a s u r e m e n t s obtained f r o m a
p a s s of Object #3133 on 4 Aug. 1972.
Fig. 10
Rms variations in differential phase
and differential doppler f o r p a s s of
Object #3233 rising a t 0411 GMT on
4 August 1972 (Kp = .
)'8
Fig. 11
Differential phase power s p e c t r a
f o r s e l e c t e d minutes f r o m the p a s s
of Object #3133 rising at 0411 GMT on
4 August 1972 (Kp = 8').
16
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