Dispersive distortions of the fractal ultra-wideband signals in plasma media
The results of numerical modeling of dispersive distortions of the model high-frequency fractal ultra-wideband (UWB) signals propagating in linear and parabolic plasma layers are considered. The character of the dispersive distortions appeared is described and the corresponding numerical character...
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Chernogor, L.F. Lazorenko, O.V. Onishchenko, A.A. 2019-02-14T14:25:02Z 2019-02-14T14:25:02Z 2018 Dispersive distortions of the fractal ultra-wideband signals in plasma media / L.F. Chernogor, O.V. Lazorenko, A.A. Onishchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 135-138. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 41.20.Jb, 52.35.Hr, 52.65.−y, 94.20.Bb https://nasplib.isofts.kiev.ua/handle/123456789/147349 The results of numerical modeling of dispersive distortions of the model high-frequency fractal ultra-wideband (UWB) signals propagating in linear and parabolic plasma layers are considered. The character of the dispersive distortions appeared is described and the corresponding numerical characteristics are estimated. Special attention is paid to the comparison of the results with similar ones obtained for non-fractal ultra-short UWB signals. Розглядаються результати числового моделювання дисперсійних викривлень модельних високочастотних фрактальних надширокосмугових (НШС) сигналів, що поширюються в лінійному та параболічному плазмових шарах. Описується характер дисперсійних спотворень, що виникають, оцінюються відповідні числові характеристики. Особлива увага приділяється порівнянню даних результатів з отриманими раніше аналогічними результатами для нефрактальних високочастотних ультракоротких НШС-сигналів. Рассматриваются результаты численного моделирования дисперсионных искажений модельных высокочастотных фрактальных сверхширокополосных (СШП) сигналов, распространяющихся в линейном и параболическом плазменных слоях. Описывается характер возникающих дисперсионных искажений и оцениваются соответствующие числовые характеристики. Особое внимание уделяется сравнению данных результатов с полученными ранее аналогичными результатами для нефрактальных высокочастотных ультракоротких СШП-сигналов. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Коллективные процессы в космической плазме Dispersive distortions of the fractal ultra-wideband signals in plasma media Дисперсійні викривлення фрактальних надширокосмугових сигналів у плазмових середовищах Дисперсионные искажения фрактальных сверхширокополосных сигналов в плазменных средах Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Dispersive distortions of the fractal ultra-wideband signals in plasma media |
| spellingShingle |
Dispersive distortions of the fractal ultra-wideband signals in plasma media Chernogor, L.F. Lazorenko, O.V. Onishchenko, A.A. Коллективные процессы в космической плазме |
| title_short |
Dispersive distortions of the fractal ultra-wideband signals in plasma media |
| title_full |
Dispersive distortions of the fractal ultra-wideband signals in plasma media |
| title_fullStr |
Dispersive distortions of the fractal ultra-wideband signals in plasma media |
| title_full_unstemmed |
Dispersive distortions of the fractal ultra-wideband signals in plasma media |
| title_sort |
dispersive distortions of the fractal ultra-wideband signals in plasma media |
| author |
Chernogor, L.F. Lazorenko, O.V. Onishchenko, A.A. |
| author_facet |
Chernogor, L.F. Lazorenko, O.V. Onishchenko, A.A. |
| topic |
Коллективные процессы в космической плазме |
| topic_facet |
Коллективные процессы в космической плазме |
| publishDate |
2018 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Дисперсійні викривлення фрактальних надширокосмугових сигналів у плазмових середовищах Дисперсионные искажения фрактальных сверхширокополосных сигналов в плазменных средах |
| description |
The results of numerical modeling of dispersive distortions of the model high-frequency fractal ultra-wideband
(UWB) signals propagating in linear and parabolic plasma layers are considered. The character of the dispersive
distortions appeared is described and the corresponding numerical characteristics are estimated. Special attention is
paid to the comparison of the results with similar ones obtained for non-fractal ultra-short UWB signals.
Розглядаються результати числового моделювання дисперсійних викривлень модельних високочастотних фрактальних надширокосмугових (НШС) сигналів, що поширюються в лінійному та параболічному плазмових шарах. Описується характер дисперсійних спотворень, що виникають, оцінюються відповідні числові характеристики. Особлива увага
приділяється порівнянню даних результатів з отриманими раніше аналогічними результатами для нефрактальних високочастотних ультракоротких НШС-сигналів.
Рассматриваются результаты численного моделирования дисперсионных искажений модельных высокочастотных
фрактальных сверхширокополосных (СШП) сигналов, распространяющихся в линейном и параболическом плазменных
слоях. Описывается характер возникающих дисперсионных искажений и оцениваются соответствующие числовые характеристики. Особое внимание уделяется сравнению данных результатов с полученными ранее аналогичными результатами для нефрактальных высокочастотных ультракоротких СШП-сигналов.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147349 |
| citation_txt |
Dispersive distortions of the fractal ultra-wideband signals in plasma media / L.F. Chernogor, O.V. Lazorenko, A.A. Onishchenko // Вопросы атомной науки и техники. — 2018. — № 4. — С. 135-138. — Бібліогр.: 9 назв. — англ. |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №4(116) 135
DISPERSIVE DISTORTIONS OF THE FRACTAL ULTRA-WIDEBAND
SIGNALS IN PLASMA MEDIA
L.F. Chernogor1, O.V. Lazorenko1, A.A. Onishchenko1,2
1V.N. Karazin Kharkiv National University, Kharkov, Ukraine;
2Kharkiv National University of Radio Electronics, Kharkov, Ukraine
E-mail: Leonid.F.Chernogor@univer.kharkov.ua; Oleg.V.Lazorenko@karazin.ua;
Andrey.Onishchenko@nure.ua
The results of numerical modeling of dispersive distortions of the model high-frequency fractal ultra-wideband
(UWB) signals propagating in linear and parabolic plasma layers are considered. The character of the dispersive
distortions appeared is described and the corresponding numerical characteristics are estimated. Special attention is
paid to the comparison of the results with similar ones obtained for non-fractal ultra-short UWB signals.
PACS: 41.20.Jb, 52.35.Hr, 52.65.−y, 94.20.Bb
INTRODUCTION
Being proposed by D.L. Moffatt [1] and
E.M. Kennaugh [2], in the last thirty years, the ultra-
wideband (UWB) signals have revolutionized many
brunches in science and technologies [3].
The main advantage of the UWB signals over the
narrowband and wideband ones is that the first of them
carry the volume of information, which is / 1nn n >>
times more than the second of them are able to carry ( n
and nn are the relative bandwidths for the UWB and
narrowband signal respectively). The relative bandwidth
of a signal is given by the relation
max min max min2( ) / ( )f f f fn = - + , where minf and maxf
are the minimal and the maximal frequencies of spectral
density function (SDF) of the one-dimensional Fourier
transform (OFT) [4]. The relative bandwidth is
0.2 2n£ < for the UWB signals, is 0 0.01n< £ for
the narrowband signals and is 0.01 0.2n< < for the
wideband signals [4].
Solving the problems of the UWB signal application
in radar, communication and remote radio sounding of
different objects and media, it is necessary to estimate
the dispersive distortions appeared in plasma media. In
the late 1990s, the authors had shown that such distor-
tions for the ultra-short UWB (USUWB) signals can be
significant in many cases [4, 5] and, therefore, should be
taken into account.
In the mid-2000s, the authors had proposed a new
UWB signal class named as the fractal UWB (FUWB)
signals [4, 6, 7]. Such signals unite the advantages of
the UWB and the fractal signals and, for example, have
very high noise immunity. Thus, the idea to estimate the
dispersive distortions of the FUWB signals appeared
during their propagation in plasma layers seems to be
actual and useful.
The purpose of the paper is to calculate the set of
numerical characteristics, which are able to describe the
dispersive distortions of the model FUWB signals ap-
peared during their propagation in the model linear and
parabolic plasma layers, and to compare the results ob-
tained with ones for USUWB model signals.
1. FUWB SIGNAL MODEL
As long as the paper volume is very limited, only
one FUWB signal model was chosen. There are no limi-
tations to perform the calculations listed below for other
FUWB signal models, for example, for those proposed
in [8]. In this paper, we consider the FUWB signal
model based on the Weierstrass function [4, 7]:
( ) ( )
( )( )
2 4
2
0
2 4 1
( ) 1
cos 2
,
1
D
M
D n n
n
n
D M
s t b
b sb t
b
p y
-
-
=
- +
é ù= - ´ê úë û
+
´
-
å
where t is the dimensionless time, normalized on the
signal duration, b is the time scale parameter, s is the
frequency scale parameter, D is the fractal dimension
of the signal, 1 2D< < , ny is the phase distributed
randomly at the interval 0,2pé ùë û , M is the harmonics
number (if M ® ¥ , a mathematical fractal is ob-
tained). The main advantage of this model is the possi-
bility to build the signals with different fractal dimen-
sion values. At the Fig. 1 the model FUWB signal with
1.5D = and model USUWB signal are shown.
The fractal dimension value D for the model
FUWB signal travelling in the plasma medium will be
estimated with the Hurst exponent ( H ) calculation
technique usage. In bounds of the generalized Brownian
motion model, they are connected with 2D H= - [9].
2. DISPERSIVE DISTORSION MODELING
In this paper, only the dispersive distortions ap-
peared due to phase velocity dispersion existence are
considered. Moreover, only the high-frequency (HF)
FUWB signals are used. A UWB signal is called as a
HF UWB signal, if min pf f>> , where pf is the plasma
frequency [4, 5].
Fig. 1. Model UWB (a) and FUWB (b) signals
and their OFT SDF modules (c and d) correspondently
mailto:Leonid.F.Chernogor@univer.kharkov.ua
ISSN 1562-6016. ВАНТ. 2018. №4(116) 136
Fig. 2. Dispersive distortions of the FUWB signal ( 1.5D = , 9
0 10f = Hz, 1.84n = ) appeared in the parabolic
plasma layer with 7
max( ) 10pf z = Hz, max 200z = km for different distances: a – 0z = km; b – 10z = km;
c – 20z = km; d – 30z = km; e – 40z = km; f – 50z = km; g – 60z = km; h – 70z = km;
i – 80z = km; j – 90z = km; k – 100z = km; l – 110z = km; m – 120z = km; n – 130z = km;
o – 140z = km; p – 150z = km; q – 160z = km; r – 170z = km; s – 180z = km; t – 200z = km
In such case, the amplitude of the electric field in a
semi-infinite ( 0z ³ ), isotropic plasma medium at the
distance z from the bound is given by the relation
( , ) ( ) ( , )exp( 2 )E t z S f K f z i ft dfp
+¥
-¥
= ò ,
where the OFT SDF of the signal ( ) ( , 0)s t E t= is given as
( ) ( )exp( 2 )S f s t i ft dtp
+¥
-¥
= -ò .
The function ( , )K f z given by the relation
( , ) ( , )exp( ( , ))K f z K f z i f zf= -
describes the effect of the plasma media, in which a
signal ( )s t propagates. As far as the absorption disper-
sion effects are not considered in this paper, we have
( , ) 1K f z = . The phase is given as
0
( , ) 2 ( , )
z
f
f z n f z dz
c
f p ¢ ¢= ò .
For the HF UWB signals, the dispersion low given
by the relation
2
2
2
( )
( , ) 1 pf z
n f z
f
= -
is applied. We use two plasma layer models, namely,
the linear layer model given by the relation
2 2 min
max
max min
( ) ( )p p
z z
f z f z
z z
-
=
-
ISSN 1562-6016. ВАНТ. 2018. №4(116) 137
Fig. 3. Dispersive distortions of the FUWB signal ( 1.5D = , 9
0 10f = Hz, 1.84n = ) appeared in the parabolic
plasma layer with 7
max( ) 10pf z = Hz, max 200z = km, dynamical Hurst exponent ( )H t and its error ( )dH t
for different distances: a, b, c – 0z = km; d, e, f – 10z = km; g, h, i – 20z = km; j, k, l – 30z = km;
m, n, o – 50z = km; p, q, r – 100z = km; s, t, u – 150z = km; v, w, x – 200z = km
and parabolic layer model given by the relation
2
2 2 max
max
max min
( ) ( ) 1p p
z z
f z f z
z z
é ùæ ö-ê ú÷ç ÷= - çê ú÷ç ÷ç -ê úè ø
ë û
,
where min max[ , ]z z zÎ .
If we investigate the UWB signal propagation in the
Earth’s ionosphere, we should use the following parame-
ters: min 100z = km, max 300z = km, max( ) 10pf z = MHz
for the daytime ionosphere and max( ) 10pf z = MHz
for the night ionosphere.
3. ANALYSIS RESULTS
For non-fractal HF USUWB signals [6 - 8], the dis-
persive distortions appeared during their propagation in
plasma media with phase dispersion only contain the
delays of the signal leading edge fT ( 0/ sT t t= is a
dimensionless time) and envelope maximum of a signal
mT (when such envelope has been formed), the increas-
ing of the relative signal duration 0/s st t ( st and 0st
are current and initial signal durations) and the decreas-
ing of the relative amplitude of the signal envelope
ISSN 1562-6016. ВАНТ. 2018. №4(116) 138
max max 0/E E ( maxE and max 0E are current and initial
signal envelope amplitudes). The values of the effects
appeared depend on the traveling distance z , the plasma
layer model and the relations between m,
0 min max( ) / 2f f f= + and pf . Such dispersive distor-
tions called as ‘traditional’ ones can be very significant.
For example, for daytime ionosphere described above
for 9
0 10f = Hz and µ = 0.2…1.6 we have τs/τs0 =
1.4…68, Ťf = 3.4…6.6, Ťm = 3.8…16.8, Emax/Emax0 =
0.75…0.21 and for 10
0 10f = Hz and µ = 0.2…1.6 we
have τs/τs0 = 1.0…1.6, Ťf = 0.0…1.0, Ťm = 0.3…2.0,
Emax/Emax0 = 1.00…0.55.
For FUWB signals, the character of dispersive dis-
tortions has some differences. As far as their OFT SDF
is appeared to be more complex than ones for USUWB
signals (see Fig. 1,c), and most importantly, to be fractal
(see Fig. 1,d), the new peculiarities of the dispersive
distortions occur. At the Fig. 2 they are clearly shown at
the sample of the model FUWB signal described on the
Fig. 1,b. First, there are all dispersive distortions ap-
peared for USUWB signal. But being formed by high-
frequency part of the OFT SDF, the main fractal struc-
ture of the FUWB signal is appeared to be almost not
changed. Moreover, as it is shown more clearly at the
Fig. 3, remaining fractal ( 0 1H< < ), it has the same
place in the signal and its Hurst exponent H is slightly
decreasing, when the traveling distance z increases.
Other parts of the signal are appeared to be non-fractal
( 1H ³ ). Being estimated in the sliding window with
the width 1TD = , the Hurst exponent becomes a de-
pendence on time ( )H t and can be called as dynamical
one. Second, the distorted signal is appeared to be am-
plitude modulated in time domain. This explains by the
fractal structure of the OFT SDF for FUWB signal.
Third, for FUWB signal (see Fig. 1,b) the ‘traditional’
dispersive distortions described above are appeared to
be more significant than for corresponding USUWB
signal (see Fig. 1,a). This can be explained by the fact
that having the same 0f , the FUWB signal has a bigger
relative bandwidth n ( 1.57UWBn = , 1.84FUWBn = ).
CONCLUSIONS
Main fractal structure of the HF FUWB signal trav-
eled in plasma media with phase dispersion only is ap-
peared to be almost not changed.
Due to fractal OFT SDF, the distorted HF FUWB
signal is appeared to be amplitude modulated.
As far as having the same mean frequency, the
FUWB signals have bigger relative bandwidth, than the
same USUWB signals have, the ‘traditional’ dispersive
distortions of the HF FUWB signals in plasma media
are appeared to be more significant.
REFERENCES
1. D.L. Moffatt, R.J. Puskar. Subsurface Electromag-
netic Pulse Radars // Geophysics (41). 1976, № 3,
p. 506-518.
2. E.M. Kennaugh. 1981. The K-Pulse Concept // IEEE
Transactions on Antennas and Propagation (29).
1981, № 2, p. 327-331.
3. H.F. Harmuth. Nonsinusoidal Waves for Radar and
Radio Communication. New-York: “Academic
Press”, 1981.
4. O.V. Lazorenko, L.F. Chernogor. Ultrawideband Sig-
nals and Processes: Monograph. Kharkov: V.N. Kara-
zin Kharkiv National University, 2009.
5. O.V. Lazorenko and L.F. Chernogor. Dispersive
Distortions of High-Frequency, Super Wide-Band
Radio Signals in the Interplanetary Plasma // Tele-
communications and Radio Engineering. 1997,
v. 51, № 5, p. 19-21.
6. O.V. Lazorenko, L.F. Chernogor. Fractal ultrawide-
band signals // Radio Physics and Radio Astronomy
(10). 2005, № 1, p. 62-84.
7. O.V. Lazorenko, A.A Potapov, L.F. Chernogor.
Fractal Ultrawideband Signals. Informational securi-
ty: the encryption methods / Ed.-in-ch. E.M. Suha-
rev. Moscow: “Radiotechnika”, 2011 (in Russian).
8. L.F. Chernogor, O.V. Lazorenko, A.A. Onishchenko.
New Models of the Fractal Ultra-Wideband Signals
// Proc. 8th International Conference on Ultrawide-
band and Ultrashort Impulse Signals, September 5-
11, 2016, Odessa, Ukraine. Odessa, 2016, p. 89-92.
9. А.А. Potapov. Fractals in Radio Physics and Radar:
The Sample Topology. M.: “University book”, 2005.
Article received 24.06.2018
ДИСПЕРСИОННЫЕ ИСКАЖЕНИЯ ФРАКТАЛЬНЫХ СВЕРХШИРОКОПОЛОСНЫХ СИГНАЛОВ
В ПЛАЗМЕННЫХ СРЕДАХ
Л.Ф. Черногор, О.В. Лазоренко, А.А. Онищенко
Рассматриваются результаты численного моделирования дисперсионных искажений модельных высокочастотных
фрактальных сверхширокополосных (СШП) сигналов, распространяющихся в линейном и параболическом плазменных
слоях. Описывается характер возникающих дисперсионных искажений и оцениваются соответствующие числовые ха-
рактеристики. Особое внимание уделяется сравнению данных результатов с полученными ранее аналогичными резуль-
татами для нефрактальных высокочастотных ультракоротких СШП-сигналов.
ДИСПЕРСІЙНІ ВИКРИВЛЕННЯ ФРАКТАЛЬНИХ НАДШИРОКОСМУГОВИХ СИГНАЛІВ
У ПЛАЗМОВИХ СЕРЕДОВИЩАХ
Л.Ф. Черногор, О.В. Лазоренко, А.А. Онищенко
Розглядаються результати числового моделювання дисперсійних викривлень модельних високочастотних фракталь-
них надширокосмугових (НШС) сигналів, що поширюються в лінійному та параболічному плазмових шарах. Описуєть-
ся характер дисперсійних спотворень, що виникають, оцінюються відповідні числові характеристики. Особлива увага
приділяється порівнянню даних результатів з отриманими раніше аналогічними результатами для нефрактальних висо-
кочастотних ультракоротких НШС-сигналів.
introduction
1. FUWB signal model
2. DIspersive distorsion modeling
3. Analysis results
Conclusions
references
Дисперсионные искажения фрактальных сверхширокополосных сигналов в плазменных средах
Дисперсійні викривлення фрактальних надширокосмугових сигналів у плазмових середовищах
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