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WIDEBAND HF SIGNALS DISPERSION DISTORTION COMPENSATOR BASED ON DIGITAL FILTER BANKS. THEORY AND APPROBATION
The article proposes a computationally effective scheme of the dispersion distortions compensation device, based on the modification of the classical 2M-channel digital filter banks. The main idea of dispersion compensation is equalization of the delay and elimination of the phase shift, because the frequency dispersion of the signal is the delay of the signal at each frequency and the phase shift. The dispersion distortions compensation device involves the set of FIR filters and the delay line. The set of FIR filters eliminate fractional delay are implemented in the compensation scheme by means of the signal re-digitization with the help of the 19-th degree interpolation polynomial. Each of the FIR filters is multiplied by a coefficient that eliminates the certain phase shift. The delay line eliminates the integer part of the delay. Also, this article estimates the required number of channels in a dispersion compensation device based on a bank of digital filters and compares compensation algorithms on the basis of a filter bank and a filter-compensator. Analytical expressions are obtained for the approximate calculation of the maximum and standard deviations of the phase response of the system, reflecting the dependence of the phase response on the number of frequency subchannels, the order of the interpolation polynomial of the interpolator, the length of the polyphase components of the prototype filter, the slope of the dispersion characteristic, and the passband of the filter bank. Besides, a theoretical and experimental study is concluded, the purpose of which is to confirm the performance and efficiency (availability in terms of the signal-to-noise ratio) of the algorithms for compensating for dispersion distortion of broadband signals in the decameter band, embedded in a digital analysis-synthesis filter bank.
DOI: 10.36724/2072-8735-2020-14-4-57-65
Denis S. Chirov,
Moscow Technical University of Communications and Informatics, Moscow, Russia, den-chirov@yandex.ru
Elizaveta O. Lobova,
Moscow Technical University of Communications and Informatics, Moscow, Russia, lizabeth2@mail.ru
Keywords: HF communication, wideband signals, dispersion distortion, digital filter banks, ionosphere
Information about authors:
Denis S. Chirov, Doct. Tech. Sciences, docent, chief researcher at SRD MTUCI, Moscow, Russia Elizaveta O. Lobova, postgraduate student MTUCI, minor researcher at SRD MTUCI, Moscow, Russia
Для цитирования:
Чиров Д.С., Лобова Е.О. Компенсатор дисперсионных искажений широкополосных сигналов декаметрового диапазона, построенный на базе банка цифровых фильтров. Теория и эксперимент // T-Comm: Телекоммуникации и транспорт. 2020. Том 14. №4. С. 57-65.
For citation:
Chirov D.S., Lobova E.O. (2020) Wideband HF signals dispersion distortion compensator based on digital filter banks. Theory and approbation. T-Comm, vol. 14, no.4, pр. 57-65. (in Russian)
Introduction
At present, decameter radio communication is actively used for communication in remote and inaccessible regions of the world. Also, decameter communication is an actual type of radio communication for regions that have suffered serious damage due to natural disasters.
Modem development ofHF communication systems is aimed at increasing the information transmission rate by increasing the frequency band used [1-4]. When receiving signals with an extended spectrum, it becomes necessary to take into account the influence of the frequency dispersion of the ionospheric channel, since it leads to significant distortions of the signal and a decrease in the quality of information reception in general [5-7]. An actual problem is to assess the parameters of the frequency dispersion of the ionospheric channel and develop algorithms and devices for compensating for dispersion distortion of wideband signals [8-10, 13-15].
Also, in broadband data transmission systems, digital filter banks have been actively used for signal processing for a long time [11,12].
Filter banks are used to solve such problems as: estimating the power spectral density in radio monitoring tasks and cognitive radio systems, adaptive rejection of narrow-band interference, efficient message coding, etc. Therefore, for the decameter range, it is relevant to use a filter bank and a dispersion distortion compensation device together. This problem is usually solved by using a special compensator filter (a filter consistent with the characteristics of the channel). However, in order to minimize the overall computational complexity of the algorithms for processing the received signals, it is urgent to introduce an algorithm for compensating dispersion distortions directly into the synthesis system of a bank of digital filters which are somehow used on the receiving side. Therefore, the compensation of dispersion distortions introduced into the bank of digital filters in order to eliminate the aforementioned losses is an urgent task.
Filter Bank for Dispersion Distortion Compensation
As a channel model with a dispersion frequency, a channel model with a linear dependence of the group delay of the signal on the central frequency (linear dispersion characteristic with slope s [3]) is adopted. The transfer function of the ionospheric channel in the absence of multipath signal propagation can be written in the form
U(ttnf) = / e [-/, / 2; / 2] (1)
where fA - is the sampling frequency, S - is the slope of the
dispersion characteristic (inclination).
The phase response of the ionospheric channel is described by a quadratic frequency dependence, and the group propagation delay is described by a linear frequency dependence with the slope S jis / MHz.
Consider a system of banks of digital filters of analysis-synthesis with an ideal recovery. The bank consists of 1M = 64 modulated complex exponent of analysis filters and the same number of synthesis filters [11,12,16]. Let us assume ^ Hk{z)l^=Hk(^) and =Fk(e>^)
are respectively the frequency characteristics of the analysis filters and the synthesis filters, respectively, T = 1 / f \.
We can show that the signal distorted by the ionospheric channel at the output of the A-th analysis filter can be represented as
~xk(n)^xk{n-nkyf!° , (2)
where xk(n) - the signal undistorted by the frequency dispersion at the output of the analysis filter, n - round f -i—- I 4- const
\ T J
- the signal delay in the Jt-th channel of the analysis system, expressed in the sampling intervals T, round (x) is the rounding
function to the nearest whole.
The frequency dispersion of the signal is the signal delay at each frequency and the phase shift (see (2)), and for each frequency the delay and phase shift assume different values. Therefore, in order to eliminate the dispersion distortions, it is necessary to "equalize" the delay, which leads to the introduction into the bank's system of analysis and synthesis of an additional delay
line before the synthesis filters and the phase shift of the
signals . Such a solution does not change the algorithm for calculating the synthesis bank filters in any way and does not depend on their specific type.
Figure I shows a computationally efficient compensation scheme for frequency dispersion of filter banks. To reduce the number of computational operations, the algorithm described in [12, I6J was applied. The main idea of such an algorithm is to represent synthesis filters (and analysis) in the form of a set of polyphase components of the original prototype filter Ek (z),
applying the FFT algorithm, and processing the signal at a low sampling frequency (i.e., before increasing Mtimes).
In this case, it becomes necessary to introduce interpolation filters that compensate fractional delays.
In the proposed scheme, the compensation of group delay is carried out at a low sampling frequency. Moreover, one cannot limit oneself to introducing only compensation delay lines, since the delay compensation error will be times greater (since the sampling interval is times larger).
Therefore, a system of FIR filters Kk(z), k = 0...2M -1,
eliminating fractional delay is implemented in the compensation circuit by means of the signal re-digitization with the help of the
19-th degree interpolation polynomial, and the delay line z eliminating the integer part of the delay , nk = round( f\ sMF0),
round(A') - is a function that separates the integer part of the fractional number. Preliminary M0 times interpolation is performed in order to reduce the signal distortion caused by the non-uniformity of the amplitude response and the nonlinearity of the phase response of the interpolating FIR filter. This allows, by processing one copy of the signal in the frequency domain, to reduce the amplitude-phase distortions that contribute to the interpolation FIR filler with group delay compensation. The value Ma is chosen small: I (without pre-interpolation), 2 or 4. The length of the interpolation FIR filter is equal to ^ = 1.
The impulse response of the interpolation FIR filter is calculated as 19-degree Lagrange polynomial values at the corresponding time instants, provided that the input action, on the basis of which the polynomial coefficients are calculated, was unit-impulse. Moments of time correspond to the fractional delay value, which must be compensated.
wj - >,i-:i -
- *,!/) -
— «.Î
- a _
-M.Î-*-'
^'-Éî
r—71 rii-fi X^* - - „.Η0-
Figure 1. Computationally efficient filter bank with dispersion compensation
The transfer function of the channel-bank of the above filter bank is
f M\
2M-\M-\ ( ^
H,
f
' ' ¡7 ze M
y
ZM"
\ J
-jit/;-!-»(
where
ir.M-I^Î-*)^
,2x ,
1- i
M
m
and
?=o
Fk (z) = z-^M-l-a)E1MA_u (z2x')iJ™" ~ computationally
n=0
efficient representation of the transfer functions of analysis filters and synthesis filters, Eq [~2M) H ¿Vw-i-u (-2W ) — polyphase
components of analysis and synthesis fillers.
The summation over q calculâtes the A'-th coefficient of the inverse discrete Fourier transform (DFT) with the block length 2M (excluding the normalizing factor), where k is the filter index, and summing over it calculates the A-th direct DFT coefficient with the block length 2M
The figures Figure 3 and 4show graphs:
1. Frequency response of the channel + bank with compensation system r(z)| .
2. Frequency response of the aliasing components of the filter bank transfer function taking into account the channel and distortion compensation 7^iasini, (z)| ,,r( .
The calculations were carried out for the bank of 64 filters (2M - 64) w:ith the length of the filter N - 1024, satisfying the ideal reconstruction condition, in which aliasing components are mutually destroyed at the synthesis stage. It can be seen from the indicated dependencies that the superimposed components of the filter bank with compensation for dispersion distortions are not fully compensated, and as a result there is no complete signal recovery at the output of the filter bank.
0.02
-0.02
m ■o
P -0.04
(A £1 <3
-0.06 -o.os
-01
- The Titter bank without distortion compensation
— The Titter bank with distortion compensation
4 -4 m 4 -t 1 2 3 4 5
1, Hz X1Û*
Figure 2. Frequency response of the channel + bank with compensation system
i| ■■
'I '
- The Titter bank without distorton compensation
- The Titter bank with distortion compensation
0 f, Hi
1 5 x105
Figure 3, Frequency response of the aliasing components
of the filter bank transfer function taking into account the channel and distortion compensation
The estimation of the minimum number of filters in the
filter bank to ensure a given level of phase distortion
We can show [17] that the phase response of the useful component of the filter bank without taking into account the channel and without the compensation system is strictly linear and corresponds to the signal delay during processing:
VT(ej°') = v(\-Nj;,). (3)
Then, with compensation, the following condition must be
met
<pTi (eJ,i) -> (j>f (i>) + const. (4)
In other words, the compensation should eliminate the channel effect, which is reflected in the appearance of the quadratic part in the phase response. For comparison, it is convenient to use the phase response of the channel + filter bank system after eliminating the linear part. In view of the above, (4) can be rewritten as
ft, ) = <PTo com'' <5>
where <pT ie*" j - the channel phase response + bank filter system after eliminating the linear part.
Figure 4 shows a graph of the phase response of the channel + system of the useful component of the filter bank transfer function with compensation at s — 80 ps / MHz for a different number of filters after eliminating the linear part corresponding to the signal delay in the filter bank. The figure shows that the more fillers are used, the better the quality of compensation (The channel phase response closer to zero, see the formula (5)), The filler near the frequency ib - ±7T is not taken into account (k ^ M), because leads to a failure in the frequency response at the boundary with one of the neighboring filters, i.e. introduces distortions in the final frequency response of the compensator.
(tp(2xf)) = yp{{litf}df -const
min ■
2M
(6)
where (p - permissible deviation of the phase response from zero, F - frequency range (approximation interval).
The level of quality for minimax criterion is defined as the maximum deviation from the average between the maximum and minimum deviations from zero in the passband, because this average shows general phase shift of the signal and does not distort it. The minimax criterion for a filter bank can be written as
<Pm
max (<p( lirf)) - m (ip ( 2tt/) )
-> min , (7)
2M
where q> . - permissible deviation of the phase response
T^mm max r r r
from average.
It is obvious that the phase deviation from zero is due to residual dispersion distortions of the signal within the passband of individual filters in the filter bank. The more filters there are, the narrower their passband, the less the amount of residual distortion.
We introduce the function
F(M,s,Fs) =
¥C
coh
2 M
x
= P,
(8)
f. Hz „ ios
Figure 4. The phase response of the channel system + the useful component of the transfer function of the filter bank after eliminating ilie linear part fori = 80 / MHz
The necessary number of filters to ensure a given level of phase response deviation can be obtained from the solution of the optimization problem using the root mean square criterion (RMS) or minimax criterion. For both criteria, when solving the optimization problem, the variable parameter is the number of filters 2M.
For a filter bank, the RMS criterion of optimality has the form
where Af = F / 2M - bandwidth of one filter from the filter bank, p. - dispersion coefficient of the channel formed by a
separate filter from the filter bank, A/t(i/j = - channel
coherence band with frequency dispersion. Find F(M,s,Ftj] in such a way that
F(Mts,Fs)Mconst, <pminmax = const (9)
for the considered values of M, s. F and <!> .
S r min rnax
Then from relation (3), 2M can be expressed for a known slope of the dispersion characteristic s , sampling frequency F ,
and a given level
From Figure 4 we can conclude that the phase deviation increases from the central frequency of the passband of a single filter and grows to its boundary. Given the channel model
f A/'? fU*p y J •
We seek (3) taken into account as
(10)
=C,F(M,s,Ft)=Ct
¥
¥c
(ii)
cvh
C, — constant.
As a result of numerical calculations for Mn — 2, /v'jWr = 16 the sets of individual values m. and F( M,s,F ) the de-
Tmmiim \ s ' j /
sired constant C, was found by the least squares method and the expression was found
'0.7073F.y -4v!
J 4
C,-0.7073. (12)
Similarly, an expression was obtained for the standard deviation of the phase m
' Trms
9m
= Q.l(m2F2{M,s,Fs) =
0.575F V ff .v
2 M
C, = 0.575
(13)
Figure 5 shows a comparison of the theoretical (calculated by formulas (7, 8) and experimental dependences of and
m . on the number of filters 2M for four different values of
r mm max
the slope s and for the sampling frequency Ft = 1.5 MHz,
Figure 5 shows that the larger the filter bank (the larger the parameter 2M), the smaller the values of (/>__ and m. can
bank implemented according to the computational scheme has the number of channels determined through 2", where /1 = 2,3,... , then the levels <pnm and <pminmaK can vary greatly change depending on 2M. Therefore, when comparing fixed levels w and w , , if the deviation in the tiller bank reaches
■ rrtti ■ ■ T^ Ini.:\ 7
a lower value than the fixed one, this is indicated in brackets.
Table 1
The comparison of the number of material operations of multiplication and addition, which the filter compensator performs and the filter bank when compensating to achieve the specified values (p
■ii ¡is/MHz tp , rad rrms The number of channels in the filter bank, the length of the interpolation polynomial, and the number of real computational operations of the compensator The number ol'real computational operations of the filter-compensator
40 0.004 64, 10, 80 119
80 0.008 64, 10, 80 119
120 0.013 64, 10, 80 119
160 0.02 (for filter bank -0.015) 64, 10, 80 118
Table 2
The comparison of the number of material operations of multiplication and addition, which the filter compensator performs and the filter bank when compensating to achieve the specified values <n
1 ^rmmniax
2. The compensator in the filter bank for the given values of <pmis requires computational operations less than 1.5 times
than the filter-compensator, and for the given values of (p , ,
it is less than about 2 times.
The comparison of theoretical and experimental compensation results
The signal-to-noise ratio (SNR) at the MF output at the time the signal ends for a computationally efficient filter bank circuit with frequency dispersion compensation is defined as
fP:s
N
P
V m
DFT
X a*"™
(14)
>r/> vomit
2a\
( %T |
I M
t-g.BO.
\ 2 y
where
■BZ-in, 2A/-1 . - J-A-/f
j _j.:—m/, eNon +
H(HHk -it'
-M-zHi+f)) » r&ki+u)4
M
w-hwf
2M-I
Qdi =S x^x«*
JM)
-JJL-X S Ä
, \Hf,FT ) „VDH
m,
DFT ^
y 1«-1 - -J^—i] s zJ2lCnk
+k V S 0 V H F K e mT 1 "l>m
I-1
*=0
■Si ^s / MHz ^minmax * rad The number of channels in the filter batik, the length of the interpolation polynomial, and the number of real computational operations of the compensator The number of real computational operations of the filter-compensator
40 0.015 32, 10, 80 166
80 0.015 (for filter bank -0.0076) 64, 12, 96 182
120 0.02 (for filler bank -0.012) 64, 12, 96 182
160 0.015 64, 12,96 199
From tables 1,2 we can draw the following conclusions: I. The compensator in the filter bank with the same number of channels and computational operations provides approximately the same values of (prn:i and ........., while the compensator filler, due to the large non-uniformity of the phase response, the values of ip and m can differ by an order of
r * T rms ' iron t;]\ J
magnitude w ith the same number of computational operations;
Sr Ur Hki, Ftj. - DFT coefficients of the useful signal, impulse response of the channel, impulse response of the analysis and synthesis filters, respectively, kki - the DFT coefficients of the impulse response of the filter-compensator fractional delay interpolated M! M0 times M / M0, k^. - DFT coefficients of
the impulse response of a 11 Iter matched to a useful signal s ), N
n = 0± N b = —- proportionality coefficient. The M
number of DFT points NDFT was chosen for reasons lhat a cy-
2 rt
clic shift ol the spectrum by —— at normalized frequencies is
M
equivalent to a cyclic shit) of the DFT coefficients in the frequency domain by b,
Also, this section presents the results of an experiment to compensate for dispersion distortion in a wideband signal on a single-hope HP radiolink with a length of - 2900 km. The experiment used a wideband signal with direct spreading of the spectrum with a pseudo-random sequence consisting of 512 symbol and with a rectangular envelope function, the width of the main lobe of (lie signal spectrum was 400 kHz.
3. Ml L-STD-188-1I0D. Departament of Defence interface standart. Interoperability and performance standards for data modems. US Department of Defense. 29 December 2017.
4. D.V. Ivanov. (2006). Methods and mathematical models for study of the propagation of decameter complex signals and correction its dispersion distortions. MarSTU, Yoshkar-Ola.
5. E.M. Lobov, I.S. Kosilov. (2011). Calculation of noise immunity of broadband ionospheric radio links using noise-like signals based on prediction data. T-Comm. Vol. 5. No. 11, pp. 68-70.
6. E.M. Lobov, E.O. Smerdova. (2017). Investigation of the quality of algorithms for estimating the slope of the ionospheric channel dispersion characteristics. Telecommunications. No. 6, pp. 28-31.
7. E.M. Lobov, E.O. Smerdova, N.A. Kandaurov, l.S, Kosilov, B.A. Elsukov. (2017). Optimum estimation and filtering of the ionospheric channel dispersion characteristics slope algorithms. 2017 Stys-tems of signal synchronization, generating and processing in telecommunications (SINKHROINFO), DOI: 10,1109/SiNKHRO!NF0.2017.7997537
8. E.M. Lobov, Lobova E.O., Kandaurov N.A. (2018). Optimum tracking dispersion distortion compensator. Telecommunications. No. 5, pp. 85-89.
9. S.S, Adjemov, E.M, Lobov, N.A. Kandaurov, E.O. Lobova. (2019). Methods and algorithms of broadband HF signals dispersion distortion compensation. 2019 Systems of Signal Synchronization. Generating and Processing in Telecommunications, SYNCHROINFO 2019, Yaroslavl, 1 -3 July 2019, 9 p. DOI: 10,1109/SYNCHROINF0.2019.8814074
10. E.O. Lobova, N.A. Kandaurov, (2019), Experimental Results of Dispersion Distortion Compensation of Wideband Signals with a Device Based on a Digital Filter Bank. 2019 Systems of Signals Generating and Processing in the Field of on Board Communications. SOSG 2019, Moscow,20-21 March 2019,8 p. (DOI: 10.1109/SOSG.2019.8706758)
11. V.V. Vityazev. (2017). Multi-speed signal processing. Mo: cow: Hot line - Telecom, 336 p.
12. H.S. Malvar. (1992). Signal Processing with Lapped Tram forms, Artcch I louse, Norwood, MA. 336 p.
13. E.O. Lobova, E.M. Lobov, B.A. Elsukov. (2018). Broadban Signals Dispersion Distortions Compensator Based on the Digital Filtei Bank. Reports of the 20th International Conference "Digital Signi Processing and its Application - DSPA-2018", Moscow, Russia, Vol.; pp. 487-491.
14. E.O. Lobova, E.M. Lobov, B.A. Elsukov (2018). Wideban signals dispersion distortion compensator based on digital filter bank 2018 Systems of signals generating and processing in the field of o board communications, Moscow, 14-15 March 2018, 4 p. DO I 0.U09/SOSG.201 8.8350615
15. E.M. Lobov, E.O. Lobova, A.A. Kurochkin (2018). Computi tionally simplified realization of the compensator of dispersion disto: tions on the basis of the filter bank. 2018 Systems of Signal Synchron zation, Generating and Processing in Telecommunicate (SYNCHROINFO), Minsk, 4-5 July, 2018, 4 p. DO 10.1109/SYNCHR01NF0.2018.8457058
16. T, Karp, N.J. Flicgc. Modified DFT Filter Banks with Perfei Reconstruction. IEEE Transactions on Circuits and Systems — II: Anc log and Digital Signal Processing, vol. 46, II, pp. 1404-1414, DO 10.1109/82.803480
17. V.S, Priputin, V.R, Magsumov, E.O. Lobova. (2019). Analys of Digital Filter Prototype Design Methods for High-Speed Signal Prt cessing Based on Polyphase Filter Bank. 2019 Systems of Signals Get erating and Processing in the Field of on Board Communication, SOSG 2019. Moscow, 20-21 March 2019, 4 p, DO 10.1109/SOSG.2019.870675!
КОМПЕНСАТОР ДИСПЕРСИОННЫХ ИСКАЖЕНИЙ ШИРОКОПОЛОСНЫХ СИГНАЛОВ ДЕКАМЕТРОВОГО ДИАПАЗОНА, ПОСТРОЕННЫЙ НА БАЗЕ БАНКА ЦИФРОВЫХ ФИЛЬТРОВ.
ТЕОРИЯ И ЭКСПЕРИМЕНТ
Чиров Денис Сергеевич, Московский технический университет связи и информатики, Москва, Россия, den-chirov@yandex.ru Лобова Елизавета Олеговна, Московский технический университет связи и информатики, Москва, Россия, lizabeth2@mail.ru
Аннотация
Предложена вычислительно эффективная схема устройства компенсации дисперсионных искажений, основанная на модификации классической схемы 2М-канального цифрового банка фильтров. Основанная идея компенсации дисперсионных искажений состоит в выравнивании временной задержки и устранении фазового сдвига сигнала, так как частотная дисперсия влияет на сигнал, внося дополнительную групповую задержку и фазовый сдвиг. Устройство компенсации дисперсионных искажений состоит из набора КИХ-фильтров интерполяторов и линии задержки. Набор КИХ-фильтров, устраняющих дробную задержку, реализован в схеме компенсации путем повторной оцифровки сигнала с помощью интерполяционного полинома Лагранжа 19-й степени. Каждый из КИХ-фильтров умножается на коэффициент, который устраняет определенный фазовый сдвиг. Линия задержки необходима для устранения целой части задержки. Также, предложен метод оценки необходимого количества каналов в устройстве компенсации дисперсионных искажений для достижения заданного качества компенсации, количественно определяемого среднеквадратичным и максимальным отклонением ФЧХ системы канал+компенсатор. Предложенный алгоритм компенсации сравнивается с алгоритмом компенсации на основе классического фильтра-компенсатора по качеству и сложности реализации. Получены аналитические выражения для приближенного расчета максимального и среднеквадратичного отклонения ФЧХ системы канал+компенсатор, отражающие зависимость отклонения ФЧХ от числа частотных подканалов, порядка интерполяционного полинома интерполятора, длины полифазных компонент фильтра прототипа, наклона дисперсионной характеристики и полосы пропускания банка фильтров. Представлено теоретическое и экспериментальное исследование, цель которого состоит в том, чтобы подтвердить работоспособность и эффективность (с точки зрения отношения сигнал/шум) алгоритма компенсации дисперсионных искажений широкополосных сигналов в декаметровом диапазоне, встроенного в банк фильтров цифрового анализа-синтеза.
Ключевые слова: декаметровая радиосвязь, широкополосные сигналы, дисперсионные искажения, банк цифровых фильтров, ионосфера.
Литература
1. MIL-STD-188-110C. Departament of Defence interface standart. Interoperability and performance standards for data modems. US Department of Defense. 3 January 2012.
2. Jorgenson M.B., Johnson R.W., Nelson R.W. An Extension of Wideband HF Capabilities // IEEE Military Communications Conference. 2013. рр. 1202-1206.
3. MIL-STD-188-110D. Departament of Defence interface standart. Interoperability and performance standards for data modems. US Department of Defense. 29 December 2017.
4. Иванов Д.В. Методы и математические модели исследования распространения в ионосфере сложных декаметровых сигналов и коррекции их дисперсионных искажений: монография. Йошкар-Ола: Марийский гос. технический ун-т, 2006. 266 с.
5. Лобов Е.М., Косилов И.С. Расчет помехоустойчивости широкополосных ионосферных с применением шумоподобных сигналов на основе данных прогнозирования // T-comm: Телекоммуникации и транспорт, 2011, Т. 5, № 11. С. 68-70.
6. Лобов Е.М., Смердова Е.О. Исследование качества алгоритмов оценки наклона дисперсионной характеристики ионосферного канала // Электросвязь, 2017, №6. С. 28-31.
7. Lobov E.M., Smerdova E.O., Kandaurov N.A., Kosilov I.S., Elsukov B.A. Optimum estimation and filtering of the ionospheric channel dispersion characteristics slope algorithms // Systems of signal synchronization, generating and processing in telecommunications (SINKHROINFO), 2017 (DOI: 10.1109/SINKHROINFO.2017.7997537)
8. Лобов Е.М., Лобова Е.О., Кандауров Н.А. Оптимальный следящий компенсатор дисперсионных искажений широкополосных сигналов // Электросвязь, 2018, №5. С. 85-89.
9. Adjemov S.S., Lobov E.M., Kandaurov N.A., Lobova E.O. Methods and algorithms of broadband HF signals dispersion distortion compensation // 2019 Systems of Signal Synchronization, Generating and Processing in Telecommunications, SYNCHROINFO 2019, Yaroslavl, 1-3 July 2019, 9p. (DOI: 10.1109/SYNCHROINFO.2019.8814074)
10. Lobova E.O., Kandaurov N.A. Experimental Results of Dispersion Distortion Compensation of Wideband Signals with a Device Based on a Digital Filter Bank // 2019 Systems of Signals Generating and Processing in the Field of on Board Communications, SOSG 2019, Moscow, 20-21 March 2019, 8 p. (DOI: 10.1109/SOSG.2019.8706758)
11. Витязев В.В. Многоскоростная обработка сигналов. М.: Горячая линия-Телеком. 2017. 336 с.
12. Malvar H.S. Signal Processing with Lapped Transforms, Artech House, Norwood, MA, 1992, 336 p.
13. Лобова Е.О., Лобов E.M., Елсуков Б.А. Устройство компенсации дисперсионных искажений на базе банка цифровых фильтров // DSPA: Вопросы применения цифровой обработки сигналов, 2018, Т.3, №3. С. 60-65.
14. Lobova E.O., Lobov E.M., Elsukov B.A. Wideband signals dispersion distortion compensator based on digital filter banks // 2018 Systems of signals generating and processing in the field of on board communications, Moscow, 14-15 March 2018, 4 p. DOI: 10.1109/SOSG.2018.8350615
15. Lobov E.M., Lobova E.O., Kurochkin A.A. Computationally simplified realization of the compensator of dispersion distortions on the basis of the filter bank // 2018 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), Minsk, 4-5 July, 2018, 4 p. (DOI: 10.1109/SYNCHROINFO.2018.8457058)
16. Karp T., Fliege N.J. Modified DFT Filter Banks with Perfect Reconstruction // IEEE Transactions on Circuits and Systems - II: Analog and Digital Signal Processing, vol. 46, 11, рр. 1404-1414, DOI: 10.1109/82.803480
17. Priputin V.S., Magsumov V.R., Lobova E.O. Analysis of Digital Filter Prototype Design Methods for High-Speed Signal Processing Based on Polyphase Filter Bank // 2019 Systems of Signals Generating and Processing in the Field of on Board Communications, SOSG 2019, Moscow, 20-21 March 2019, 4p. (DOI: 10.1109/SOSG.2019.8706751)
Информация об авторах:
Чиров Денис Сергеевич, г.н.с., д.т.н., доцент, Московский технический университет связи и информатики, Москва, Россия Лобова Елизавета Олеговна, аспирант, м.н.с., Московский технический университет связи и информатики, Москва, Россия
