Although it is common knowledge that temporal radio sig- nals are usually degraded after propagating through the iono- sphere under the scintillation environment, there are very few precise data sets against which the theoretical predictions can be checked. However, there are a number of simulation studies carried out on computers which attempt t o check the theory, t o enhance our physical understanding of the problem, or to elucidate the phenomenon. As described in the previous two sections, both amplitude and phase of a sinusoidal wave will experience fluctuations when there exists scattering from ionospheric irregularities. For propagation of temporal signals, the important point is how the amplitude and phase vary across the signal bandwidth. Let A (0) be the amplitude func- tion and $(a) be the phase function. Then it can be shown that the time delay in the arrival of the pulse is related to the slope of the phase function at the carrier frequency, the pulse spreading is related to the curvature of the amplitude function at the carrier frequency, and the skewness is related to the third derivative of the phase function at the carrier frequency [ 1961, [ 1971. For a particular realization of the turbulent ionosphere corresponding t o an equatorial bubble, A ( w ) and
#(a) may have the behavior shown in Fig. 30 which is obtained numerically [ 1971. Substantial distortions in A and $ can be seen across the frequency band above the 500-MHz carrier frequency. These distortions in A and # are responsible for the instantaneous deviations in time delay, pulsewidth, and skewness. As the-irregularities drift such as in a frozen flow, the time delay, the pulsewidth, and the skewness will fluc- tuate with time. The mean values of these quantities should agree with those derived earlier by using the temporal mo- ments ((5.22) for mean arrival time and (5.27) for mean- square pulsewidth). Such simulation studies have been made and good agreement with the theory has been found [ 1981.
For spread spectrum systems using a direct sequence PN scheme the received degraded signal plus noise is correlated with an approximately delayed PN modulation waveform.
The correlator output under three scintillation levels may
l29
1.6
i
I .4
. 6
.4
0 .
.2676 .3376 .3676 -4376 4876 .5376 .5676 .6376 .6876
.3126 ,3626 . 4 1 M .4626 . 5 1 2 6 . 5 6 2 6 . 6 1 2 6 . 6 6 2 6
1
q.
t
5 '-h
E 6 .
I .
t
0 . 1 . . . : . . : : : : : : . : . .
.2876 .3376 .3876 .4378 .4876 .6576 . S O 7 8 .6378 . E 0 7 6 .3 176
.
3676 .4 126 .4628 a 6 128 .6826 .6 128 .E626FREOUENCY IN GI42 (b)
Fig. 30 The amplitude (a) and the phase (b) of the transfer function aaoss the frequency band centered at a 500-MHz carrier frequency.
The ionosphere is simulated from the in-situ data corresponding to an equatorial bubble. (After Tucker (1971 .)
behave in a manner shown in Fig. 3 1. When the coherence bandwidth is comparable to or greater than the signal band- width (top frame of Fig. 31), the shape of the correlator output suffers little distortion even though the peak value fades up and down with time. With the increased scintillation level, the coherence bandwidth s h r i n k s t o one-fourth (middle frame of Fig. 31) or one-tenth (bottom frame of Fig. 31) of the signal bandwidth; severe distortions in the correlator out- put are possible [ 1991. Such distortions may pose difficult problems t o receiver designers t o assure proper locking and consequently proper decoding. This problem is especially acute in spread spectrum communications because of the wide bandwidth needed t o achieve the desired process gain
12001.
The loss of coherence bandwidth with the increased scintilla- tion activity has been experimentally documented by the Wideband Satellite data [ 201. A comb of seven equally spaced frequencies (413.02 5 11.47n MHz, where n = 0, 1,2, 3) were used t o obtain the discrete two-frequency one-position mutual coherence functions under various scintillation levels. The
YEH AND LIU:
(a)
RADIO WAVE SCINTILLATIONS IN THE IONOSPHE :RE 3 5 5
[207] show that these sharp gradients can indeed be the sources of large amplitude fluctuations beyond those that can be predicted by using the stochastic theory. Large fluctua- tions in amplitude are apparently caused by scattering and diffraction near the sharp gradients and are especially apparent at gigahertz frequencies. The deterministic approach to the problem is new, and further investigations in this area are desirable.
Section I1 reviews structures of ionospheric irregularities.
Exuerimental evidence for their existence is abundant. How-
r - T T - - T 7
-e
- --.T -&- ever, the quantitative characterization of these irregularitiesTI.iIE D E L A 1’ (CHIPC)
Fig. 31. The correlator output in a direct sequency spread spectrum re- (a) The coherence bandwidth o f the ionospheric propagation channel ceiver as a function o f time for three levels o f scintillation activities.
is comparable t o the PN spread spectrum signal bandwidth. (b) The (c) The coherence bandwidth is about one-tenth of the signal band- coherence bandwidth is about one-fourth o f the signal bandwidth.
width. (After Bognsch er al. [ 1991.)
results show good agreement with the theory [ 2011. Using these experimentally obtained discrete mutual coherence func- tions, the approximate waveform of a synthesized pulse is obtained, from which the mean time delay can be computed and checked against the theory. Again good agreement has been obtained.
V I . CONCLUSION
We have reviewed in this paper both theories and experiments of radio wave scintillations after transversing the ionosphere.
This review attempts to update the information previously reviewed using radio star observations [38] and satellite trans- missions [ 391, [ 2021, [ 2031. This review opens with a discus- sion of the motivation for stochastic formulation, on which the scintillation theory is based. Even though the scintillation theory agrees in a large measure with the experimental results, there are areas in which the stochastic approach may not be fruitful. Irregularities inside the equatorial bubbles show wedgelike structures with steep gradients [ 2041, [ 2051. These steep gradients show high coherence and do not appear to be statistically homogeneous. Crain er ai. [206] note that these sharp gradients can provide a refractive scattering mechanism whereby gigahertz scintillation can be explained. By numeri- cally solving the parabolic equation in a deterministic ion*
sphere model constructed from the in-situ data, W e d et ai.
is improving. For applications in which the frozen flow as- sumption is adequate, the three-dimensional spectrum is known to be of the form @ N ( K ) Q K - ~ with p = 4 1 [421,
[ 1571. There is some evidence t o indicate the dependence of the spectral index p on the strength of fluctuations or the local time in the equatorial region. The outer scale, if it exists, is not known, although tens of kilometers have been used in many computations. It is possible that other prevailing iono- spheric perburbations of different origins, such as traveling ionospheric disturbances, may have prevented the true outer scale from experimental disclosure. On the other hand, radar measurements [ 541, [ 551 strongly suggest the existence of an inner scak-and a possible change of spectral law far yery small irregularities. Very liffle is known a b u t the nonfrtJzen flow nature of the ionospheric irregularities. Radar returns show a Doppler shift, indicative of the ionospheric drift, and a Doppler broadening, indicative of turbulent motion. The review of Section I1 stresses irregularity characterization, but it does not touch the production mechanisms for these irregularities. It is generally believed that some plasma instability mechanism is responsible for initiating irregularities. This subject matter is covered in several reviews [48], [208], [ 2091.
Section 111 is concerned with the scintillation theories.
Ionospheric scintillations differ from the usual discussion of random medium propagation in at least two aspects. The first difference is that the background medium is highly dispersive, so that severity of scintillation is frequency dependent. The second difference is the propagation geometry. Since the ionospheric irregularities can be anisotropic, the propagation path can make an arbitrary angle relative t o the irregularities.
Also the existence of free space below the ionosphere allows diffraction effects to take place after the wave has traversed the irregular region. The theories under weak-scatter regime seem to be well at hand. The S4 scintillation index, the mutual coherence functions, and the spectra can be computed using the phase screen or Rytov approximations as long as the scin- tillation is weak. When the scintillation is strong, some of the moment equations are difficult to solve. Some numerical solutions do exist and they have been helpful in indicating the nature of behavior in the strong scatter regime. Work is still needed to develop a comprehensive theory which would indi- cate regorously the probability distribution of the scintillating signal. Several heuristic arguments have been used in support of some probability distribution models. Chi-square tests of these models have been devised using experimental data. The results as reviewed in Section IV indicate the preference of a bivariate distribution that would reduce to the product of a Nakagami-m distribution for the intensity and a normal dis- tribution for the phase in the limit of zero correlation between the two variates [ 1671.
In addition to reviewing the signal statistics in Section IV, other experimental results have also been summarized. Experi-
356
mentally measured or deduced irregularity structures are sum- marized first. The structure information includes not only irregularity spectra but also the dimensions of irregularity patches and the propagation geometry. In the weak scintilla tion limit, a frequency law of the form S4 a f - ” , n = ( p
+
2)/4, has been confirmed. For any level of scintillation a universal solution can be constructed by adopting the Rytov scintilla- tion index S40 as an ordering parameter [ 11 51. In this way the true scintillation index S4 can be scaled from the universal curve if the Rytov scintillation index S40 is known.Because of the saturation of scintillation due to multiple scattering, the spectral index n for the frequency dependence of the scintillation index becomes frequency dependent itself.
Experimental results are shown to agree with theoretical pre- dictions. Phase fluctuations seem to follow the geometric optics result which predicts the l/f behavior for rms fluctua- tions of the phase. The data show that except for intense scin- tillation cases, the departure from l/f dependence is not appreciable. This is the consequence of the dominance of phase fluctuations in ionospheric scintillations by large-scale irregularities.
The correlation distance (or coherence time) of the intensity fluctuations is controlled by two competing factors: Fresnel filtering and multiple scattering. In the weak scintillation re- gime, the f-’/’ dependence of the correlation distance is an indication that the controlling factor is the Fresnel filtering.
As the frequency decreases, decorrelation due t o multiple scattering becomes important and the correlation distance decreases with frequency. The maximum correlation distance will occur at a frequency somewhere between those two limit- ing cases. Experimental data clearly bear out this prediction.
For phmeflwfCtUgfhns, since the Fresnel filtering is not effee tive, the correlation time is almost a constant with possible decomhtion effects at the low end of the frequency spectrum when multiple scattering becomes important.
The power spectra for the intensity, the phase as well as the quadrature components of the field are also studied in Section IV. In the case of weak scintillation, the theoretical predic- tions agree very well with observational results. For strong scintillations, however, only qualitative comparisons are possible.
Some experimental results on the average field and the coherence function are also presented in Section IV and com- pared with theoretical computations.
In studying the temporal behavior of the signal in Section V, the importance of one-position two-frequency mutual coher- ence function is stressed. One convenient way of describing the temporal behavior is t o use temporal moments. For many applications one is interested only in quantities such as the mean arrival time, the mean pulsewidth, and the pulse skew- ness. These quantities can be related t o temporal moments.
A method developed to compute these temporal moments is reviewed in Section V. Although the method is general and capable, at least formally, of computing temporal moments to any order, the algebraic complexities increase rapidly as one moves to higher order moments. At present, analytical expres- sions up to the fifth order have been derived in the literature.
Once the beginning few moments are known, an orthogonal polynomial expansion technique can be used t o construct the approximate mean pulse shape. Very few data sets are avail- able against which accurate comparison can be made t o verify these theoretical results. Some numerical experiments are available, which suggest good agreement.
PROCEEDINGS O F THE IEEE, VOL. 70, NO. 4, APRIL 1982
The subject matter reviewed in this paper is expected t o have applications in transionospheric communications. These appli- cations are only touched upon in this review. Interested readers should consult several publications [ 199
I ,
[ 2 101.Another topic that has not been included in this review is the subject of generating mechanisms for the ionospheric ir- regularities. There are fast developing activities in that area.
Interesting readers are referred t o several recent review papers on that subject 1481, [2091.
It is fair t o state that, thanks to the coordinated observa- tional programs and advances in theoretical studies, our under- standing of the phenomenon of radio wave scintillation in the ionosphere has improved quite significantly. We are now in a better position t o apply this knowledge t o the two major areas mentioned in the Introduction that have helped t o sustain the interests of ionospheric scintillation study. The first is the application t o improve the transionospheric communication systems, involving channel modeling prediction, design of adaptive system, etc. The other area is the application to the investigation of the geophysical processes that generates these irregularities. This will involve the search for more effective methods t o deduce from scintillation data the important geophysical parameters, in other words, the inversion problem, Future progresses is expected in these two directions,
ACKNOWLEDGMENT
C. H. Liu would like t o thank the Department of Electrical Engineering, National Taiwan University, for their hospitality and assistance during his stay in the Department where part of the work was carried out.
REFERENCES
J. S. Hey, S. J. Parsons, and J. W. Phillips, “Fluctuations in cos- mic radiation at radiofrequencies,” Nature (London), vol. 158, p. 247, 1946.
F. G. Smith, C. G. Little, and A.C.B. Lovell, “Origin of the fluctuations in the intensity of radio waves from galactic sources,”
Nature, vol. 165, pp. 422-424, 1950.
C. G. Little, “The origin of the fluctuations on galactic radio A. Hewish, “The diffraction of galactic radio waves as a method noise,” Ph.D. thesis, Univ. of Manchester, 1952.
of investigating the irregular structure of the ionosphere,”
T. R. Hartz, “Radio star scintillations and the ionosphere,”
Can. J. Phys., vol. 33, pp. 476-482, 1955.
R. S. Lawrence, J . L. Jespersen, and R. C. Lamb, “Amplitude Res. Nat. Bur. Stand., vol. 65D (Radio Prop.), no. 4, pp. 333- and angular scintillations of the radio source cygnus-A ” J.
350, 1961.
C. G. Little, G. C. Reid, E. Stiltner, and R. P. Memtt, “ A n served at frequencies of 223 and 456 megacycles per second experimental investigation of the scintillation of radio stars ob- from a location close to the auroral zone,” J. Geophys. Res., H.J.A. Chivers, “The simultaneous observation of radio star Phys.,vol. 17, pp. 181-187, 1960a.
scintillations on different radiofrequencies,” J. A m o s . Terresr.
PTOC. ROY. SOC.,VOI. A214, pp. 492-514, 1952.
VOI. 67, pp. 1763-1784, 1962.
- , “Radio s t a r scintillations and spread-F echoes,” J. A m o s . I. R. Koster, “Some measurements of the ,jrregularity giving rise t o radio star scintillation at the equator,” J. Geophys. Res.,
wave radiated from artificial satellite 19578,” J. A tmos. Terresr.
G. S. Kent, “High-frequency fading observed on the 4 0 Mc/s Terrest. PhYS., VOl. 25, PP. 468-472, 1963.
VOl. 68, Pp. 2579-2590, 1963.
Phys., VOI. 16, pp. 10-20, 1959.
K. C. Yeh and G. W. Swenson, Jr., “The siintillation of radio signals from satellites,” J . Geophys. Res., vol. 64, pp. 2281- 2286, 1959.
logical study of scintillation on satellite radio signals, Spring K. C. Yeh, G . W. Swenson, Jr., and J. P. McClure, A phenomeno-
L. Liszka, “A study of ionospheric irregularities using satellite URSI Meeting, Washington D C , 1963.
transmissions at 54 Mc/s,” Arkiv. Geofysik, vol. 4, 227-246, 1963b.
. .
YEH AND LIU: RADIO WAVE SCINTILLATIONS IN THE IONOSPHERE 357
[ I s ] D. G. Singleton and G. J. Lynch, “The scintillation of the radio transmissions from Explorer 7,” J. Atmos. Terresr. Phys., vol.
[ 161 J. Aarons, H. E. Whitney, and R. S. Allen, “Global morphology of ionospheric scintillation,” Proc. IEEE, vol. 59, pp. 159- 1 7 2 , 1 9 7 1 .
[ 1 7 ) N. I . Skinner, R. F. Kelleher, J. B. Hacking, and C. W. Benson,
“Scintillation fading of signals in the SHF band,” Nature, [ 181 R. R. Taur, “Ionospheric scintillation a t 4 and 6 GHz,” COMSAT [ 191 K. Davies, R. B. Fritz, R. N. Grubb,and J. E. Jones, “Some early
Tech. Rev., vol. 3, pp. 145-163, 1973.
results from the ATS-6 radio beacon experiment,” Radio Sci., vol. 10, pp. 785-799,1975.
[ 201 E. J. Fremouw, R. L. Leadbrand, R. C. Livingston, M. D. Cousins, C. L. Rino, B. C. Fair, and R. A. Long, “Early results from the DNA wideband satellite experiments: Complex signal scintilla- [ 2 1 ] C. L. Rino, R. T. Tsunoda, J. Petriceks, R. C. Livingston, M. C.
tion,” Radio Sci.,vol. 13, pp. 167-187, 1978.
Kelley, and K. D. Baker, “Simultaneous rocket-borne beacon and in situ measurements of equatorial spread F-intermediate wavelength results,” J. Geophys. Res., vol. 86, pp. 241 1-2420, [ 2 2 ] H. G. Booker, J. A. Ratcliffe, and D. H. Shinn, “Diffraction
1981.
from an irregular screen with applications t o ionospheric prob- lems,” Philos. Trans. Roy. SOC. London, Ser. A, vol. 242, pp.
(231 J . A. Ratcliffe, “Some aspects of diffraction theory and their application t o t h e ionosphere,” Rep. Prop. Phys., vol. 19, pp.
[ 2 4 ] Yu. N. Barabenenkov, Yu. A. Kravtsov, S. M. Rytov, and V. I . Tatarskii, “Status of the theory of propagation of waves in a randomly inhomogeneous medium,” Sow. Phys. Uspekhi, vol.
13, pp. 551-575,1971.
[ 2 5 1 I. Aarons, “Global morphology of ionospheric scintillations,”
this issue, pp. 360-378.
[ 2 6 l Yu. A. Kravtsov, S. M. Rytov, and V. I. Tatarskii, “Statistical problems in diffraction theory,” Sov. Phys.-Usp., vol. 18, pp.
2 4 , pp. 3 5 3 - 3 7 4 , 1 9 6 2 .
V O ~ . 232, PP. 19-21, 1971.
579-607, 1950.
188-267,1956.
1271 M. Y. Youakim, C. H. Liu, and K. C. Yeh, “Generation of 118-130,1975.
- .
random hypersurfaces,” J . Comp. Phys., vol. 8, pp. 382-391, [ 2 8 ] -, “A numerical study of rays in random media,” Appl. Sci.
1971.
Res., vol. 28, pp. 223-238, 1973.
[ 2 9 ] -, “Light beams and radiation patterns in random media,”
Appl. Sci. Res., vol. 2 9 , pp. 259-272, 1974.
[ 301 H. G. Booker and H. W Wells, “Scattering of radio waves by the F-region of t h e ionosphere,” J . Geophys. Res., vol. 4 3 , pp. 249- 2 5 6 , 1 9 3 8 .
[ 4 4 ] P. L. Dyson, J . P. McClure, and W. B. Hanson, ‘.In-situ measure- ments of the spectral characteristics of F region ionospheric [ 4 5 ] R. C. Sagalyn, M. Smiddy, and J. Wisnia, “Measurement and irregularities,” J . Geophys. Res.,vol. 79, pp. 1497-1502, 1974.
interpretation of ion density distribution in the daytime F- region,” J. Geophys. Res., vof. 69, p. 199, 1973.
[ 4 6 ] H. G . Booker, “The role of acoustic gravity waves in the genera- tion of spread F and ionospheric scintillation,” J. Atmos. Ten.
[ 4 7 ] K, C. Yeh, H. Soicher, and C. H. Liu, “Observations of equatorial ionospheric bubbles by the radio propagation method,” J.
Geophys. Res.,vol. 84, pp. 6589-6594, 1979.
[ 4 8 ] B. G. Fejer and M. C. Kelley, “Ionospheric irregularities,”
Rev. Geophys. Space Phys., vol. 18, pp. 401-454, 1980.
[ 4 9 ] A.D.R. Phelps and R. C. Sagalyn, “Plasma density irregularities in the high-latitude topside ionosphere,” J. Geophys. Res., [ S O ] W. J. Myers, R. J. Gjeldum, C. H. Liu, and K. C. Yeh, “A study of ionospheric scintillations of phase and quadrature com- ponents,” J. Geophys. Res.,vol. 8 4 , pp. 2039-2048, 1979.
[ 5 1 ] R. Umeki, C. H. Liu, and K. C. Yeh, “Multifrequency spectra of ionospheric amplitude scintillations,” J. Geophys. Res., vol. 82, [ 5 2 ] J. R. Jokippi and J . V. Hollweg, “Interplanetary scintillation
and the structure of solar wind fluctuations,” Astrophys. J . , [ 5 3 ] K. C. Yeh, C. H. Liu, and M. Y. Youakim, “A theoretical study
scattering,”Radio Sci., vol. 10, pp. 97-106, 1975.
of the ionospheric scintillation behavior caused by multiple [54) R. F. Woodman and S. Basu, “Comparison between in situ
spectral measurements of the F region irregularities and back- scatter observations at 3 m wavelength,” Geophys. Res. Len., 1551 R. Tsunoda, “Backscatter measurements of 1 1 cm equatorial [ 561 J . spread D. Huba and Firregularities,”Geophys. S. L.Osakow, “On Res. Lerr.,vol. 7, p. 848, 1980. the 1 1 cm irregularities during equatorial spread F,” J. Geophys. Res., vol. 86, pp. 829-832, [ 5 7 ] I. P. Shkarofsky, “Generalized turbulence space-correlation and
wave-number spectrum-function pairs,” Can. J. Phys., vol. 4 6 , [ S S ] V. I. Tatarskii, “The effects of the turbulent atmosphere o n wave [ 5 9 ] R. A. Silverman, “Fading of radio waves scattered by dielectric
propagation,”Nat.Tech.Inform.Service, Springfield,VA, 1971.
[ 6 0 ] -, “Remarks on the fading of scattered radio waves,” Trans.
turbulence,” J. A p p l . Phys.,vol. 2 8 , pp. 506-511, 1957.
[ 6 1 ] I. P. Shkarofsky, “Turbulence functions useful for probes and for scattering analysis,” Can. J . Phys., vol. 4 6 , pp. 2683-2702, PhyS.,vol. 4 1 , pp. 501-515,1979.
VOI. 81, Pp. 515-523, 1976.
pp. 2752-2760, 1977.
~ 0 1 . 160, pp. 745-753, 1970.
VOl. 5 , pp. 869-872, 1978.
1981.
pp. 2133-2153,1968.
IRE,vol. AP-6, P. 378, 1958.
[ 3 1 ] S p e n d Issue: Fifty Years of the Ionosphere, J. A m o s . Terr. 1968.
Phys., vol. 36, no. 1 2 , Dec. 1974. 162) R. W. Fredricks and F. V. Coroniti, “Ambiguities in the de- [ 321 J. R. Herman, “Spread F and ionospheric Fregion irregularities,” duction of rrest frame fluctuation spectrums from spectrums Rev. Geophys.,vol. 4 , p p . 255-299, 1966. computed in moving frames,” J . Geophys. Res., vol. 81, pp.
[ 3 3 ] W. E. Gordon, “Incoherent scattering of radio waves by free 5591-5595,1976.
electrons with applications to space exploration by radar,” [ 6 3 ] 8. H. Brig@, “Ionospheric irregularities and radio scintillations,”
1341 D. T. Farlev. “Radio wave scattering from the ionosohere.” in (641 F. Du Castel, Tropospheric Radiowave ProDaPation Bevond the
PrOC. IRE, V O ~ . 4 6 , pp. 1824-1829, 1958. Contemp. Phys., vol. 16, pp. 469-488, 1975.
- .
Merhods of Experimental Physics, R . H. Lovberg and
H.
R.Grien, Eds. New York: Academic Press, 1971, vol. 9 B , ch. 14.
[ 3 5 ] J . V. Evans, “High power radar studies of the ionosphere,”
[ 3 6 ] J. P. McClure and R. F. Woodman, “Radar observations of equatorial spread-F in a region of electrostatic turbulence,”
J. Geophys. Res.,vol. 7 7 , pp. 5617-5671, 1972.
(371 R. F. Woodman and C. LaHoz, “Radar observations of F region equatorial irregularities,” J. Geophys. Res., vol. 81, pp.
[ 3 8 ] H. G. Booker, “The use of radio stars to study irregular re- fraction of radio waves in the ionosphere,” Proc. IRE, vol. 46, PrOc. IEEE,vol. 63, pp. 1636-1650,1975.
5447-5466,1976.
139) K. C. Yeh and G. W. Swenson, Jr., “F-region irregularities pp. 2 9 8 - 3 1 4 , 1 9 5 8 .
. .
studied by scintillation of signals from satellites,” J. Res. Not.
[ 4 0 ) L. J. Procello and L. R. Hughes, “Observed fme structure of a Bur. Srand. (Radio Sci.), vol. 68D, pp. 881-894, 1964.
phase perturbation induced during transauroral propagation,”
[ 4 1 ] T. J. Elkins and M. D. Papagiannis, “Measurement and interpre- J. Geophys. Res., vol. 7 3 , pp. 6337-6346, 1968.
tation of power spectrums of ionospheric scintillation at sub- auroral location,” J . Geophys. Res., vol. 74, pp. 4105-4115, 1969.
[ 4 2 1 C. L. Rufenach, “Power law wave number spectrum deduced from ionospheric scintillation observations,” J. Geophys. Res., [ 4 3 ] J. P. McCIure and W. B. Hanson, “A catalog of ionospheric F region irregularity behavior based on OGO-6 retarding potential analyzer data,” J. Geophys. Res., vol. 7 8 , p. 7431, 1973.
VOl. 77, pp. 4 7 6 1 - 4 7 7 2 , 1 9 7 2 .
Horizon. Oxford, England: Pergamon, 1966.-
[ a s ] A. Hewish, “The diffraction of radio waves in passing through a phase-changing ionosphere,” Proc. Roy. SOC. London, Ser. A, (661 J. A. Fejer, “Diffraction of waves in passing through an irregular
refracting medium,” Proc. Roy. SOC. London, Ser. A, vol. 220, [ 6 7 ] E. N. Bramley, “The diffraction of waves by our irregular
refracting medium,” Proc. Roy. SOC. London, Ser. A, vol. 225, [ 6 8 ] S. A. BowhiU, “The scattering of radio waves by an extended
randomly refracting medium,” J . A m o s . Terr. Phvs.. vol. 20.
V O ~ . 209, pp. 81-96, 1951.
pp. 4 5 5 - 4 7 1 , 1 9 5 3 .
pp. 515-518,1954.
- ,
pp. 9-18, 1960.
[ 6 9 ] R. P. Mercier, “Diffraction by a screen causing large random phase fluctuations,” Proc. Camb. Phil. SOC., vol. 5 8 , pp. 382- 4 0 0 . 1 9 6 2 .
[ 7 0 ] B.
H.
Briggs and I. A. Parkin, “On the variation of radio star and satellite scintillations with zenith angle,” J. Atmos. Terr.[ 7 1 ] E. E. Salpeter, “Interplanetary scintillations, I. Theory,”
Phys.,vol. 25, pp. 339-352,1963.
AsRoDhvs. J.. VOI. 147. , DO.
- _
433-448. 1967 I .[ 7 2 ] R. B k k l e y , “Diffraction by a random phase screen with very large RMS phase deviation, 1 and 2,” Aust. J . Phys., vol. 2 4 , pp.
351-396, 1971.
(731 C. L. Rufenach, “Ionospheric scintillation by a random phase screen spectral approach,” Radio Sci., vol. 10, pp. 155-161, [ 7 4 ] K. 1975. Davies, R. B. Fritz, R. N. Grubb, and J. E. Jones, “ATS-6
radio beacon experiments: The f m t year,” IEEE Trans. Aerosp.
358 PROCEEDINGS O F THE IEEE, VOL. 70, NO. 4 , APRIL 1982
[ 7 5 ] M. H. Cohen and E. J. Gundermann, “Interplanetary scintilla- Electron. Syst., vol. AES-11, pp. 1103-1 107, 1975.
tions, 4 . Observations near the Sun,” Astrophys. J., vol. 155, [ 7 6 ] D. S. Intriligator and J. H. Wolfe, “Preliminary power spectra of the interplanetary plasma,” Astrophys. J., vol. 162,pp. L187- (771 C. C. L190, 1970. Counselman I11 and J. M. Rankin, “Multipath delay distortion of radio pulses from NP 0532,” Astrophys. J., vol.
[ 7 8 ] E. Jakeman and I. G. McWhirter, “Correlation function de- pendence of scintillation behind a deep random phase screen,”
[ 7 9 ] K. G. Budden and B. J . Uscinski, “Teh scintillation of extended radio sources when the receiver has a finite bandwidth,” Proc.
Roy. SOC. (London), vol. A316, pp. 315-339, 1970.
[SO] D. G. Singleton, “Saturation and focusing effecting in radio star and satellite scintillations,” J. A m o s . Terr. Phys., vol. 32, [ 8 1 ] V. I. Shishov, “Dependence of the form of the scintillation
inhomogeneities. communication, I. A phase screen,” Radio- spectrum on the form of the spectrum of refractive-index
[ 8 2 ] V. H. Rumsey, “Scintillations due to a concentrated layer with phys. Quantum Electron., vol. 17, pp. 1287-1296, 1974.
a power-law turbulence spectrum,” Radio Sci., vol. 10, pp.
(831 M. Marians, “Computed scintillation spectra for strong tur- bulence,”RadioSci.,vol. 10, pp. 115-119, 1975.
[ 8 4 ] A. M. Drokhorov, F. V. Bunkin, K. S. Gochelasvily, and V. I.
Shishov, “Laser irradiance propagation in turbulent media,”
Proc. IEEE,vol. 63, pp. 790-811, 1975.
[ a s ] R. L. Fante, “Comparison of theories for intensity fluctuations [ 8 6 ] C. L. Rino, “A power law phase screen model for ionospheric
instrong turbulence,”RadioSci.,vol. 11, pp. 215-219, 1976.
scintillation 2. Strong scatter,” Radio Sci., vol. 14, pp. 1147- 1 1 5 5 , 1 9 7 9 .
[ 8 7 ] D. L. Fried, “Test of the Rytov approximation,” J. Opt. SOC.
Amer., vol. 57, pp. 268-269, 1967.
[ 8 8 ] W. P. Brown, “Validity of the Rytov approximation,” J. O p t . SOC. Amer., vol. 57, pp. 1539-1543, 1967.
I891 J. B. Keller, “Accuracy and validity of the Born and Rytov approximations,” J. O p t . SOC. Amer., vol. 59, pp. 1003-1004, 1969.
[ 9 0 ] R. K. Crane, “Spectra of ionospheric scintillation,” J. Geophys.
[ 9 1 ] A. W. Wernik and C. H. Liu, “Application of the scintillation theory to ionospheric irregularities studies,” Artificial Satellites, [ 9 2 ] B. Chytil, “The distribution of amplitude scintillation and the
conversion of scintillation indices,” J. Armos. Terr. Phys., vol.
[ 9 3 ] K. Bischoff and B. Chytil, “A note on scintillation indices,”
[ 9 4 ] H. E. Whitney, C. Malik, and J. Aarons, “A proposed index for Planer. Space Sci., vol. 17, pp. 1066-1069, 1969.
measuring ionospheric scintillation,” Planer. Space Sci., vol. 17, [ 9 5 ] D. G. Singleton, “Power spectra of ionospheric scintillations,”
J. Armos. Terr. Phys.,vol. 36, pp. 113-134, 1974.
[ 9 6 ] K. G. Budden, “The amplitude fluctuations of the radio wave scattered from a thickionosphericlayer with weakirregularities,”
PP. 645-663,1969.
166, PP. 513-523, 1971.
J. Phya A,vol. 10, pp. 1599-1643,1977.
pp. 187-208, 1970.
107-114,1975.
Res., VOI. 81, pp. 2041-2050, 1976.
VOl. 10, Pp. 37-58,1975.
29, PP. 1175-1177, 1967.
PP. 1069-1073, 1969.
[ 9 7 ] -, “The theory of the correlation of amplitude fluctuations of J. A m o s . Terr. Phys.,vol. 27, pp. 155-172, 1965.
radio signals at two frequencies, simultaneously scattered by the ionosphere,” J. A m o s . T e n . P h y s . , vol. 27, pp. 883-897, [ 9 8 ] L. S. Taylor, “Effects of layered turbulence on oblique waves,”
1965.
[ 9 9 ] C. L. Rino and E. J . Fremouw, “The angle dependence of singly Radio Sci., vol. 10, pp. 121-128, 1975.
scattered wavefields,” J. A m o s . Terr. Phys., vol. 39, pp. 859- 8 6 8 , 1 9 7 7 .
1001 C. L. Rho, R. C. Livingston, and S. J . Matthews, “Evidence for sheet-like auroral ionospheric irregularities,” Geophys. Res.
Lett., vol. 5, pp. 1039-1042, 1978.
1011 K. C. Yeh, “Propagation of spherical waves through an iono- Srand., Sec. D., vol. 6 6 , pp. 621-636, 1962.
sphere containing anistropic irregularities,” J. Rea Nat. Bur.
1021 C. 8. Liu, “Cross-correlation function of spherical waves J. A m o s . Terr. Phys., vol. 28, pp. 385-395, 1966.
propagating through a slab containing anisotropic irregularities,”
1 0 3 1 A. I. Kon and V. J. Feizulin, “Fluctuations in the parameters of spherical waves propagating in a turbulent atmosphere,” Radio- phys. Quant. Elecnon., vol. 13, pp. 71-74, 1970.
1041 L. A. Chernov, “The method of parabolic equation in the theory of wave propagation in a medium with random inhomogeneities”
(in Russian), in Rec. 3nj All-Union Symp. rhe Diffraction of Waves. Moscow,U.S.S.R.: Nauka, 1964, p. 224.
[ 1 0 5 1 A. Ishimaru, Wave Propagation and Scattering in Random Medicr.
New York: Academic Press, 1978, vol. 2, ch. 20.
[ 1 0 6 ) L. C. Lee, ‘Wave propagation in a random medium: A complete set of moment equations with different wavenumbers,” J. Math.
(1071 C. H. Liu, A. W. Wernik, K. C. Yeh,andM.Y. Youakim,“Effects of multiple scattering on scintillation of transionospheric radio signals,” Radio Sci., vol. 9 , pp. 599-607, 1974.
[ l o 8 1 C. H. Liu, A. W. Wernik, and K. C. Yeh, “Propagation of pulse trains through a random medium,” IEEE Trans Antennas Phys., VOI. 15, pp. 1431-1435, 1974.
1091 A. Ishimaru and Propagat., vol. AP-22, pp. 624-627, 1974. S. T. Hong, “Multiple scattering effects on in a random distribution of particles,” Radio Sci., vol. 10, pp.
coherent bandwidth and pulse distortion of a wave propagating
1101 V. A. Alimov and L. M. Erukhimov, “Waveform and statistical characteristics of a pulsed signal past a layer with random in- homogeneities,” Radiophys. Quantum. Electron., vol. 1 1 , pp.
637-644,1975.
2 6 8 - 2 7 8 . 1 9 6 8 .
[ 1111 C. H. Liu and A. W. Wernik, “A characterization of transiono- spheric fading communication channel,” IEEE Trans. Commun., [ 1121 S. J. Ulaszek, C. H. Liu, and K. C. Yeh, “A study of signal
decorrelation through the ionosphere,” IEEE Trans. Commun., [ 1 1 3 ] C. H. Liu and K. C. Yeh, “Frequency and spatial correlation
functions in a fading communication channel through the iono- [ 1 1 4 ] M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, and VI. V.
sphere,”Radio Sci., vol. 10, pp. 1055-1061, 1975.
Pokasov, “Similarity relations and their experimental verifica- Laser Beam Propagation in the Armosphere, J. W. Strohbehn, tion for strong intensity fluctuations of laser radiation,” in Ed. Berlin: Springer-Verlag, 1978, pp. 107-127.
[ 11 5 1 C. L. Rino and C. H. Liu, “On the parameterization of intensity scintillation of transionospheric radio signal,” Radio Sci., t o be published.
[ 1161 V. I. Shishov, “Theory of wave propagation in random media,”
[ 1171 W. P. Brown, “Fourth moment of a wave propagating in a Radiophys. Quanr. Electron., vol. 11, pp. 500-505, 1968.
random medium,” J . Opt. SOC. Amer., vol. 62, pp. 966-971, 1972.
v01. COM-23, pp. 773-776, 1975.
vol. COM-24, pp. 1191-1194, 1976.
1181 R. L. Fante, “Comparison of theories for intensity fluctuations in strong turbulence,”Radio Sci., vol. 11, pp. 215-220, 1976.
1191 R. L. Fante, “Intensity scintillation of an EM wave in extremely strong turbulence,” ZEEE Trans. Antenna Propagar., vol. AP- 1201 P. L. Chow, “Applications of functional 25, pp. 266-268, 1977. space integrals t o wave propagation in random media,” J. Math. Phys., vol. 13, pp.
121 ] R. Dashen, “Path integral for waves in random media,” J . Marh.
1221 C. M. Rose and M. Besieris, “Nth-order multifrequency coherence functions: A functional path integral approach,”J. Math. Phys., 1224-1236,1972.
Phys., V O ~ . 20, pp. 894-920, 1979.
VOI. 20, PP. 1530-1540. 1979.
[ 1 2 3 ] S.Y.Lee,C.H.Liu,and~K.C.Yeh,‘Wavesinrandomcontinuum described by path integrals,” in Research Topics in EM Wave [ 1 2 4 ] J . W. Strohbehn, “Line-of-sight wave propagation through the
Theory, J. A. Kong, Ed. New York: Wiley, 1981, ch. 2.
turbulent atmosphere,” Proc. ZEEE, vol. 56, pp. 1301-1318, 1968.
(1251 C. L. Rino, R. C. Livingston, and H. E. Whitney, “Some new results on the statistics of radio wave scintillation 1. Empirical evidence for G a w i a n statistics,” J. Geophys. Res., vol. 8 1 , pp.
[ 1 2 6 ] J. W. Strohbehn, T. I.Wang,and J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,”
Radio Sci., vol. 10, pp. 59-70, 1975.
[ 1 2 7 ] C. C. Heyde, “On a property of the log normal distributions,”
[ I 2 8 1 V. I. Klyatskin, “Asymptotic behavior of the fluctuations of J. R o y . Sratirt. SOC., M I . B25, pp. 392-393, 1963.
intensity of a plane light wave propagating in a turbulent medium,” Sov. Phys. JETP, vol. 33, pp. 703-705, 1971.
[ 1291 D. A. de Wolf, “Strong irradiance fluctuations in turbulent air:
Rane waves,” J. Opt. SOC. Amer., vol. 63, pp. 171-179, 1973.
[130] K. Furutsu, “Statistical theory of wave propagation in random Amer., vol. 62, pp. 240-254, 1972.
medium and the irradiance distribution function,” J. Opt. SOC.
[ 131 ] Y. Furuhama, “Probability distribution ofirradiance fluctuations of beam waves in a weakly turbulent atmosphere,” Radio Sci., [ 1321 T. I. Wang and J. W. Strohbehn, “Perturbed log-normal distribu- tion of irradiance fluctuations,” J. Opt. SOC. Amer., vol. 64, pp.
[ 1331 K. C. Yeh and C. H. Liu, Theory oflonospheric Waves. New (1341 -, “Wave propagation in a random medium with anisotropic
2051-2058,1976.
VOl. 11, pp. 763-774, 1976.
9 9 4 - 9 9 9 , 1 9 7 4 .
York: Academic Press, 1972.