Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms
The Joint Time-Frequency Transforms (JTFT) are employed to identify the time-frequency distribution of dispersed ultra short impulse signals transmitted through unknown propagation channels in the presence of noise. The channel dispersive effect can be corrected by pre-distorting the transmitted sig...
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Deng, H. 2017-07-02T16:48:04Z 2017-07-02T16:48:04Z 2002 Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms / H. Deng // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 451-454. — Бібліогр.: 7 назв. — англ. 1027-9636 https://nasplib.isofts.kiev.ua/handle/123456789/122358 The Joint Time-Frequency Transforms (JTFT) are employed to identify the time-frequency distribution of dispersed ultra short impulse signals transmitted through unknown propagation channels in the presence of noise. The channel dispersive effect can be corrected by pre-distorting the transmitted signals or using matched filter at receiver from the estimated time-frequency. Simulation results show both Short Time Fourier Transform (STFT) and Adaptive Local Cosine Transform (ALCT) are effective to correct the dispersive effects for ultra-short impulse signals. Совместное частотно-временное преобразование (JTFT) используется для идентификации частотно-временного распределения диспергированных ультракоротких импульсных сигналов, прошедших через неизвестные каналы распространения в присутствии шума. Дисперсионный эффект канала можно откорректировать предварительным искажением передаваемого сигнала или использованием согласованного фильтра на приемнике. Результаты моделирования показывают, что и коротковременное преобразование Фурье (STFT), и адаптивное локальное косинусное преобразование являются эффективными для коррекции эффектов дисперсии ультракоротких импульсных сигналов. Спільне частотно-часове перетворення (JTFT) використовується для ідентифікації частотно-часового розподілу диспергованих ультракоротких імпульсних сигналів, що пройшли крізь невідомі канали розповсюдження у присутності шуму. Дисперсійний ефект каналу може бути відкоректований попереднім спотворенням сигналу, що передається, або застосуванням узгодженого фільтра на вході приймача. Результати моделювання вказують, що і короткочасове перетворення Фур’є (STFT), і адаптивне локальне косинусне перетворення є ефективними для корекції ефектів дисперсії ультракоротких імпульсних сигналів. en Радіоастрономічний інститут НАН України Радиофизика и радиоастрономия Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms Коррекция дисперсионного эффекта для ультракоротких импульсных сигналов с помощью совместного частотно-временного преобразования Корекція дисперсійного ефекту для ультракоротких імпульсних сигналів за допомогою спільного частотно-часового перетворення Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms |
| spellingShingle |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms Deng, H. |
| title_short |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms |
| title_full |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms |
| title_fullStr |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms |
| title_full_unstemmed |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms |
| title_sort |
dispersive effect correction for ultra-short impulse signals using joint time-frequency transforms |
| author |
Deng, H. |
| author_facet |
Deng, H. |
| publishDate |
2002 |
| language |
English |
| container_title |
Радиофизика и радиоастрономия |
| publisher |
Радіоастрономічний інститут НАН України |
| format |
Article |
| title_alt |
Коррекция дисперсионного эффекта для ультракоротких импульсных сигналов с помощью совместного частотно-временного преобразования Корекція дисперсійного ефекту для ультракоротких імпульсних сигналів за допомогою спільного частотно-часового перетворення |
| description |
The Joint Time-Frequency Transforms (JTFT) are employed to identify the time-frequency distribution of dispersed ultra short impulse signals transmitted through unknown propagation channels in the presence of noise. The channel dispersive effect can be corrected by pre-distorting the transmitted signals or using matched filter at receiver from the estimated time-frequency. Simulation results show both Short Time Fourier Transform (STFT) and Adaptive Local Cosine Transform (ALCT) are effective to correct the dispersive effects for ultra-short impulse signals.
Совместное частотно-временное преобразование (JTFT) используется для идентификации частотно-временного распределения диспергированных ультракоротких импульсных сигналов, прошедших через неизвестные каналы распространения в присутствии шума. Дисперсионный эффект канала можно откорректировать предварительным искажением передаваемого сигнала или использованием согласованного фильтра на приемнике. Результаты моделирования показывают, что и коротковременное преобразование Фурье (STFT), и адаптивное локальное косинусное преобразование являются эффективными для коррекции эффектов дисперсии ультракоротких импульсных сигналов.
Спільне частотно-часове перетворення (JTFT) використовується для ідентифікації частотно-часового розподілу диспергованих ультракоротких імпульсних сигналів, що пройшли крізь невідомі канали розповсюдження у присутності шуму. Дисперсійний ефект каналу може бути відкоректований попереднім спотворенням сигналу, що передається, або застосуванням узгодженого фільтра на вході приймача. Результати моделювання вказують, що і короткочасове перетворення Фур’є (STFT), і адаптивне локальне косинусне перетворення є ефективними для корекції ефектів дисперсії ультракоротких імпульсних сигналів.
|
| issn |
1027-9636 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/122358 |
| citation_txt |
Dispersive Effect Correction for Ultra-Short Impulse Signals Using Joint Time-Frequency Transforms / H. Deng // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 451-454. — Бібліогр.: 7 назв. — англ. |
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2025-11-25T23:07:39Z |
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2025-11-25T23:07:39Z |
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| fulltext |
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4, pp. 451-454
DISPERSIVE EFFECT CORRECTION FOR ULTRA
SHORT IMPULSE SIGNALS USING JOINT TIME-
FREQUENCY TRANSFORMS
Hai Deng
Department of Electrical Engineering, The University of New Orleans
New Orleans, LA 70148-2215, USA
E-mail: Hai.Deng@uno.edu
The Joint Time-Frequency Transforms (JTFT) are employed to identify the time-frequency distribution of
dispersed ultra short impulse signals transmitted through unknown propagation channels in the presence of noise.
The channel dispersive effect can be corrected by pre-distorting the transmitted signals or using matched filter at
receiver from the estimated time-frequency. Simulation results show both Short Time Fourier Transform (STFT)
and Adaptive Local Cosine Transform (ALCT) are effective to correct the dispersive effects for ultra-short im-
pulse signals.
1. Introduction
Ultra-short impulse signals, which possess ultra-wide
bandwidth, have been widely used in the wireless
communication systems and impulse radars for
ground penetration and target identification. Because
the system transmits pulses of very short duration on
the order of a nanosecond, the signal contains fre-
quencies ranging from near-DC to a few GHz. If the
impulse signals are transmitted through a dispersive
medium such as the ionosphere, there are usually
different unknown time delays at the receivers for the
different frequency components in the signal. Hence,
to detect the dispersed signal from noise we need an
effective time-frequency analysis algorithm to deter-
mine the time-frequency distribution of the received
signal. Joint time-frequency transform (JTFT) is a
useful tool for representing and analyzing time-
frequency distribution of wideband signals [1]. The
short-time Fourier transform (STFT), employing a
fixed local time window size as the analysis window,
is the most basic JTFT method [2]. For time-varying
wideband signals, usually it is impossible to find an
optimal window size to efficiently represent the en-
tire signal using the STFT. The adaptive local cosine
transform (ALCT) recently has been proposed for
adaptive time-frequency analysis [3, 4]. It uses multi-
scale basis functions and their time-shift versions to
represent time-varying signals. Since time-varying
signals have different frequency characteristics at
different time locations and over different durations,
the ALCT is well suited for analyzing such signals.
One typical scenario requiring the detection of noisy
time-varying signals is in receiving ultra-wideband
signals after propagation through a dispersive chan-
nel. An example is the recently proposed ultra-short
wideband impulse radio system [5]. If the impulse
radio signals are transmitted through a dispersive
medium such as the ionosphere, there are usually
different unknown time delays at the receivers for the
different frequency components in the signal. Hence,
to detect the dispersed signal from noise we need an
effective time-frequency analysis algorithm to deter-
mine the time-frequency distribution of the received
signal. Due to the time-varying feature of the dis-
persed wideband signal, we expect JTFT to be effec-
tive in estimating the signal time-frequency charac-
teristics and detecting the subsequently arrived dis-
persed pulses from noise by correlation processing.
In this paper, ALCT algorithm is briefly described
(readers are referred to [1, 2] about STFT), then the
effectiveness of JTFT is demonstrated by correcting
the noisy dispersed wideband impulse signals using
ALCT and STFT.
2. Adaptive Local Cosine Transform
(ALCT)
A local cosine basis of ( )2 ℜL is defined from a co-
sine-IV basis of [ ]2 0,1L by multiplying a translation
and dilation of each vector with a smooth window
( )pg t [3]. An orthonormal local cosine basis of
( )2 ℜL is defined as follows:
( ){
( ) ( )
,
N, Z
2 1cos ,
2
p k
p
p
p p k p
g t
t a
g t k
l l
π
∈ ∈
=
− +
(1)
Hai Deng
452 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4
where p is an index of the time interval, k is a fre-
quency index, and pa and pl denote respectively the
position and support of the window pg . The win-
dows are usually overlapping, and need to satisfy
symmetry and quadrature properties.
The adaptive local cosine transform tries to find
a group of window parameters { },p pa l for the basis
in (1) to represent a signal most efficiently. To
quickly search for the best local cosine basis for a
signal, we restrict the segmentation of the time axis
to the intervals of dyadic sizes, and thus the fast algo-
rithm proposed in [6] to search for the best wavelet
packet basis can be used to search for the best local
cosine basis using a binary tree. Suppose a signal
exists in the interval [ ]0,T , and the maximum level
of the decomposition in the tree is J , the length of
the equally divided intervals on level j is 2 jT−
( )0 j J≤ ≤ . A fast algorithm is available to com-
pute the decompositions on the level j from the re-
sults on the level 1j − . With an additive cost func-
tion, the same pruning algorithm used in [6, 7] is
applicable to finding the best local cosine basis from
a fully decomposed tree. Usually the entropy func-
tion or the energy concentration function is defined
as the cost function to measure the efficiency (spar-
sity) of the transformed signal. The total computa-
tional cost for the best local cosine basis search and
transform is about ( )2logO Jn N . Readers are re-
ferred to [6, 7] for a detailed description of the search
algorithm.
3. Detection and Estimation of Noisy,
Dispersive Signals Using ALCT
A Gaussian monocycle used in impulse radio, as
shown in Fig. 1(a), is ultra short wideband impulse. It
is transmitted through a distance of D in the iono-
sphere. The phase delay for the signal component at
frequency f is given by:
( )
2
2 1 pfD
f f
c f
φ π = − , (2)
where c is the speed of light in free space and pf is
the plasma frequency of the ionosphere and is de-
pendent on the electron density. The instantaneous
group delay is then given by
2
1
2
1
d
p
d D
df f
c
f
φτ
π
= =
−
. (3)
The above equation indicates that the time delays for
different frequency components are different and the
time-frequency distribution of the received signal
through the ionosphere is a non-linear curve. Hence, a
time-frequency analysis tool is necessary to effec-
tively identify such a signal. Fig. 1(b) shows the dis-
−1 −0.5 0 0.5 1
−2
−1
0
1
2
Time (ns)
G
au
ss
ia
n
M
on
oc
yc
le
(a)
0 150 300 450
−0.4
−0.2
0
0.2
0.4
Time (ns)
D
is
pe
rs
ed
G
au
ss
ia
n
M
on
oc
yc
le
(b)
0 50 100 150 200 250
−4
−2
0
2
4
Time (ns)
D
ire
ct
P
ro
ce
ss
in
g
R
es
ul
t
(c)
Fig. 1.
(a) The Gaussian monocycle used in impulse radio.
(b) The dispersed Gaussian monocycle after propa-
gation through a dispersive medium.
(c) The direct correlation processing result
Dispersive Effect Correction for Ultra Short Impulse Signals Using Joint Time-Frequency Transforms
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 453
persed signal after the Gaussian monocycle in
Fig. 1(a) travels 300 km through ionosphere with
9pf = MHz. Usually the received signals are cor-
rupted by additive white Gaussian noise (AWGN)
with the transmission. For the dispersed received sig-
nal with AWGN with a signal-to-noise ratio (SNR) of
3.5− dB, the direct correlation processing result is
shown in Fig. 1(c). It is observed that the dispersive
effect leads to the loss of the high range resolution
and the received signal is almost undetectable in the
noise due to significant SNR loss from the dispersion.
In order to correct the dispersive effect, the time delay
vs. frequency characteristics in (3) is needed for the
propagation channel. Since the original signal has
zero time-delay for all frequencies, the joint time-
frequency trajectory of the received signal is exactly
the group delay vs. frequency characteristic in (3).
With JTFT processing, the energy of the dis-
persed signal is automatically concentrated in the
time-frequency domain. At the same time, the trans-
formed AWGN remains un-correlated. Therefore the
SNR is improved in the JTF domain. To recover the
signal from noise we need to apply a hard threshold
to the transformed signal. A time-domain template is
formed by inverse-transforming the signal in JTFT
domain for subsequent correlation processing to cor-
rect for the channel dispersion. Fig. 2(a) is the ALCT
processing result of the noise-corrupted received sig-
nal shown in Fig. 1(c). Fig. 2(b) is the correlation
processing result with a dispersed pulse using the
template recovered through ALCT. From Fig. 1(c) to
50
100
150
200
250
Time/256ns
F
re
qu
en
cy
/1
6G
H
z
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
(a)
0 100 200 300 400 500
−8
−4
0
4
8
12
Time (ns)
P
ro
ce
ss
in
g
R
es
ul
t
(b)
Fig. 2.
(a) The time-frequency distribution of the dispersed
signal shown in Fig. 1(c) using the adaptive lo-
cal cosine transform (ALCT).
(b) The correlation processing result using the re-
covered template using ALCT
1
2
3
4
5
6
7
8
9
10
Time/256ns
F
re
qu
en
cy
/1
6G
H
z
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
(a)
0 100 200 300 400 500
−8
−4
0
4
8
12
Time (ns)
P
ro
ce
ss
in
g
R
es
ul
t
(b)
Fig. 3.
(a) The time-frequency distribution of the dispersed
signal shown in Fig. 1(c) using the STFT.
(b) The correlation processing result using the re-
covered template using STFT
Hai Deng
454 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4
Fig. 2(b), one finds that the processing leads to a
much more detectable signal through the matched
filtering processing. The similar processing results of
the same signal in Fig. 1(c) using the STFT are
shown in Figs. 3(a,b). It is observed that the resulting
SNR is higher by using the ALCT processing than
using STFT because of the adaptive window sizes
used along the time axis.
4. Conclusions
Simulations results show that the dispersed ultra-
wideband signals are completely buried in noise at
the receiver without any time-frequency processing,
yet can be reliably detected and restored with either
STFT or ALCT processing. However the Signal-to-
Noise Ratio (SNR) achieved is much higher through
ALCT processing. Furthermore, based on the time-
frequency characteristics found using ALCT process-
ing, it is also possible to transmit pre-distorted ultra-
wideband pulse signals to completely compensate for
the channel dispersive effect. Furthermore, based on
the time-frequency characteristics found using JTFT
processing, it is also possible to transmit pre-
distorted signals to completely compensate the chan-
nel dispersive effect.
References
1. L. Cohen. Time-Frequency Analysis. Prentice Hall,
Englewood Cliffs, NJ (1995).
2. D. Gabor. J. IEE, V93, 429, (1946).
3. H.S. Malvar, D.H. Staelin. IEEE Trans. Acoust.,
Speech, and Signal Proc., V37, 553, (1989).
4. H. Deng, Hao Ling. Microwave Opt. Tech. Lett., V35,
150, (2002).
5. M.Z. Win, R.A. Scholtz. IEEE Comm. Lett., V2, 36,
(1998).
6. R.A. Coifman, M.V. Wicherhauser. IEEE Trans. Info.
Theory, V32, 712, (1999).
7. H. Deng, H. Ling. IEEE Trans. Antennas Propagat.,
V47, 674, (1999).
КОРРЕКЦИЯ ДИСПЕРСИОННОГО
ЭФФЕКТА ДЛЯ УЛЬТРАКОРОТКИХ
ИМПУЛЬСНЫХ СИГНАЛОВ С
ПОМОЩЬЮ СОВМЕСТНОГО
ЧАСТОТНО-ВРЕМЕННОГО
ПРЕОБРАЗОВАНИЯ
Хай Денг
Совместное частотно-временное преобразование
(JTFT) используется для идентификации частотно-
временного распределения диспергированных ультра-
коротких импульсных сигналов, прошедших через не-
известные каналы распространения в присутствии шу-
ма. Дисперсионный эффект канала можно откорректи-
ровать предварительным искажением передаваемого
сигнала или использованием согласованного фильтра
на приемнике. Результаты моделирования показывают,
что и коротковременное преобразование Фурье (STFT),
и адаптивное локальное косинусное преобразование
являются эффективными для коррекции эффектов дис-
персии ультракоротких импульсных сигналов.
КОРЕКЦІЯ ДИСПЕРСІЙНОГО ЕФЕКТУ
ДЛЯ УЛЬТРАКОРОТКИХ
ІМПУЛЬСНИХ СИГНАЛІВ ЗА
ДОПОМОГОЮ СПІЛЬНОГО
ЧАСТОТНО-ЧАСОВОГО
ПЕРЕТВОРЕННЯ
Хай Денг
Спільне частотно-часове перетворення (JTFT) ви-
користовується для ідентифікації частотно-часового
розподілу диспергованих ультракоротких імпульсних
сигналів, що пройшли крізь невідомі канали розповсю-
дження у присутності шуму. Дисперсійний ефект кана-
лу може бути відкоректований попереднім спотворен-
ням сигналу, що передається, або застосуванням узго-
дженого фільтра на вході приймача. Результати моде-
лювання вказують, що і короткочасове перетворення
Фур’є (STFT), і адаптивне локальне косинусне пере-
творення є ефективними для корекції ефектів дисперсії
ультракоротких імпульсних сигналів.
|