=Paper=
{{Paper
|id=Vol-2533/paper16
|storemode=property
|title=Simulation Model and Practical Realization of Barker-Like Codes
|pdfUrl=https://ceur-ws.org/Vol-2533/paper16.pdf
|volume=Vol-2533
|authors=Ivan Tsmots,Oleg Riznyk,Vasyl Rabyk,Yurii Kynash,Mykhailo Dendiuk,Olga Myaus,Michal Gregus ml.
|dblpUrl=https://dblp.org/rec/conf/dcsmart/TsmotsRRKDMG19
}}
==Simulation Model and Practical Realization of Barker-Like Codes==
<pdf width="1500px">https://ceur-ws.org/Vol-2533/paper16.pdf</pdf>
<pre>
    Simulation Model and Practical Realization of Barker-
                        Like Codes

              Ivan Tsmots1[0000-0002-4033-8618], Oleg Riznyk1[0000-0002-3815-043X],

             Vasyl Rabyk2[0000-0003-2655-0812], Yurii Kynash1[0000-0002-3762-3215],

           Mykhailo Dendiuk3[0000-0002-7631-022X], Olga Myaus1[0000-0001-5332-7080]

                              Michal Gregus4[0000-0001-6207-1347]
                    1 Lviv Polytechnic National University, Lviv, Ukraine

    {ivan.tsmots, riznykoleg, yuk.itvs, myausolya2016@gmail.com}
                2 Ivan Franko National University of Lviv, Lviv, Ukraine

                                   rabykv@ukr.net
                 3 Ukrainian National Forestry University, Lviv, Ukraine

                                   dendiuk@ukr.net
            4 Comenius University in Bratislava, Bratislava, Slovak Republic

                          michal.gregusml@fm.uniba.sk



       Abstract. In the work we presented method of getting barker-like codes. It was
       implemented on the basis of numerical lines, that is, knots. The presented algo-
       rithm was realized on FPGA EP3C16F484N6, Altera. We have reviewed the
       main advantages, areas of use and peculiarities of barker-like codes. Besides, it
       was given functional diagram of the DS-SS system. The barker-like code gen-
       erator and its frequency domain simulation were performed in VHDL language.

       Keywords: Autocorrelation function, Barker code, Barker-like code, DS-SS,
       FPGA, Hardware implementation, Numerical ruler-bundle.


1      Introduction

The noise immunity and sensitivity of the pseudorandom code sequence primarily
depends on its parameters. The length of the code may be the same, but the sequence
parameters are different. Therefore, in the radio system of transmission information
selecting pseudorandom code sequence is very important [1].
   We propose to consider Barker's signals, because they are the ones that cause the
greatest interest among scholars. They are also referred to as signals with a low level
of side lobes of the autocorrelation function (ACF). It's interesting that a low level of
side lobes provides a high value of the main lobe of the ACF. Basically, these signals
will be built and researched on a numerical sequence from -1 to 1 [2].
   However, it is known [3] that when the value of ACF does not exceed unit (exclud-
ing the main petal), and Barker's signals occupy odd positions that are more than 13,
then they simply disappear, that is, they do not exist. Among the known Barker sig-

Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0)
2019 DCSMart Workshop.
2


nals, the maximum ratio of the main petal to other petals is 13. But in the course of
research, the ratio of barker-like code signals equal to 14 or more was found [4].
Therefore, it makes sense to continue research in this direction.
   So far there is no universal algorithm that provides an acceptable quality signal
processing in all radar tasks [5]. In connection with this, the task of each modern radar
station is to provide a constantly updated set of algorithms and signals that, when they
are used jointly, are capable of solving certain tasks [6]. The electronic properties of
materials to radar systems can be calculated by methods from first principles [7].
   The paper presents the development of methods for synthesizing noise-like codes
with the use of barker-like sequences for encoding and decoding data [8]; the devel-
opment of simulation model of the synthesis of noise-like codes according to different
criteria (by the functions of autocorrelation, by the length of the sequence and by the
number of detected and corrected errors) [9]; realization of received sequences on
FPGA [10]. The subject of research is the ACF-function of the model of barter-like
codes and methods for its finding [11].


2      Review of the Literature

An urgent problem in our time is the protection of real-time data transmission with
onboard systems, protection of their impedance and secrecy, and the general increase
of strong cryptography. After all, these systems must meet the requirements for ener-
gy consumption, prices and general parameters in general. It is for this purpose that
there are noise-like signals. They have a fairly high impedance over high-bandwidth
interference with high power, can split subscribers by codes, have high protection
against multi-beam propagation, provide secrecy of data transmission. In addition,
noise signals have high resolution, even when positioned in radar and navigational
measurements.
   Many scientists have been working on the development of methods and means of
silent coding in their time. Most of them used noise-like codes based on Barker se-
quences. For instance: M. Kelman and F. Rivest - the algorithm of encoding and de-
coding in real time with the use of sequences Barker [12]; P. Kim and E. Jang - re-
search noisy codes are presented on the basis of sequences Goley and Barker;
R. Nilawar and D, Bhalerao [13] - wireless data protection and data transmission sys-
tems that works in real time with certain parameters; S. Omar and F. Kassem - the
solution of the problems of the ambiguity using methods with links to a Barker se-
quence [14]; S. Matsuyuki and A. Tsuneda - examples of the application of noise-
coding codes in control systems, communication codes (the auto-collegial function is
minimal) [15] and others.
   After analyzing the scientific materials presented above, we concluded that it is
impossible to find the Barker code for lengths greater than 13. Moreover, we found
that the construction of barker-like sequences of any length is still an unresolved
problem in our time. Regular methods of their construction were not yet developed. It
follows that the known Barker codes can be used only for signals having a small
base [16].
                                                                                        3


   Since finding sequences longer than 13 that are similar to the Barker sequence,
with the lowest possible value of the lateral petals is a major problem in our time, the
regular method of constructing these codes proposed by us is actual. The method is
based on ideal ring nodes. With its help, it is possible to realize the implementation of
software and hardware components in order to synthesize small-scale real-time data
transmission systems [17].


3      Problem Statement

We use Barker codes in communication networks with its extended range. After com-
parative analysis, it was found that Barker codes have more advantages than other
pseudo-noise (PN) codes. In addition, they are well befit for Direct Sequence-Spread
Spectrum (DS-SS). In systems DS-SS in each of the transmitted bits is embedded a
certain sequence of chips. It is called a noise-like code. This is done in order to ex-
pand the spectrum of the narrowband signal. Each chip is represented as a rectangular
pulse line with a duration that is one time smaller than the duration of the information
bit. Figure 1 rep-presents the expansion of the spectrum for two information bits [18].




        Fig. 1. The extension of the signal spectrum Barker code whose length is N=7.

  Here, the Barker code is used instead of the pseudo-noise code. Its length is N=7.
On this figure is marked: d t – information signal (two bits), Tb – period of each bit,
bct – Barker code, Tc – the period of each chip, txt – the converted signal which is
generated when the transmission of signals d t and bct through an XOR element with
a denial.
   The transmitter is governed by regenerating the signal of txt. This is done using the
Binary Phase Shift Keying (BPSK) method. A method of demodulation of BPSK
restores the modulated signal in the receiver [19]. Functional diagram of the system
DS-SS are shown in Fig. 2.




            Fig. 2. The figuration of the functional scheme of the DS-SS system.
4


   The PN-sequence generator is one of the main blocks in each DS-SS system. A
range consisting of N of elements of a j for 1  j  N , which taking values +1 and -
1, make Barker's sequence. They must alternate so that the condition has being ful-
filled:

                                  N −i
                                    a j a j +i  1 ,                                (1)
                                   j =1

where 1  i  N .
   Barker codes provide optimal reception, because they have minimum level of side
lobes ACF. Well-known sequences of Barker have a length 2  N  13 [20].
   Sequence the ACF of the Barker code is a finite discrete sequence, which is formed
by performing convolution on the sequence and its own copy:
                                          N− j
                                 R j =  ai ai*+ j ,                                 (2)
                                          i =1

where the discrete index between the sequence and its copy in time is indicated.
   This designation indicates a complex conjugate value. From the general properties
of the autocorrelation function, it follows that it is symmetric with respect to the main
lobe.
   The mainlobe level (ML) is a module for the ACF coefficient for zero’s displace-
ment j = 0 . The level of the main petal has the greatest value and is equal to own
length. Peak sidelobe level (PSL) is defined as the maximum absolute value among
the coefficients of the autocorrelation function for a non-zero shift 1≤j<N [21]:

                                       N− j        
                            PSL = max   ai ai + j  .                              (3)
                                       i =1        

   In the Barker codes, the side petals never exceed 1. The ratio of the side lobes to
their peak ratio has become a widespread application in our time. It is measured in
decibels:

                                              PSL 
                             PSLR = 20 log10      .                                (4)
                                              ML 

  As an example, consider the Barker code which length is N=13 (+1, +1, +1, +1,
+1, -1, -1, +1, +1, -1, +1, -1, +1), for which PSL=1, ML=13 і PSLR=-22.279 dB. Its
ACF is depicted in the Fig. 3.
                                                                                        5




              Fig. 3. Autocorrelation of Barker sequence whose length is N=13.


4      Algorithm of Synthesis of Barker-Like Codes

In the general case, a sequence K N = (k1, k2 ,..., kN ) is called a simple numerical ring
bundle (SNRB) of order of N on a sequence of N numbers. On it all the amounts dial
the values of all L N numbers starting from the given one. In a simpler version, these
amounts exhaust the values of the natural range numbers 1, 2, …, L N [22].
   Provided that the range of successive values of the amounts discussed above begins
with а, then the total sum of all numbers in this range will be determined as the ra-
tio [23]:

                                       K ( K + 2a − 1)
                                SN =                   .                              (1)
                                              2

   The relationship between the number of the K methods for realizing the sums on
the N - sequence, the multiplicity of R , and the sum of L N all numbers is expressed
by the formula [24]:

                                 ( LN − 1) R = K − 1 .                                (6)

   Sealing procedure is an important parameter of a system that uses barker-like
codes. It consists in transforming the noise-like signal received by the receiver into
the required information signal. In this case, the processing factor shows the degree of
improvement of the signal-to-noise ratio. In the general case, B0 is equal to:

                                             C 
                                B0 = 10log10  k  ,                                  (7)
                                              Ci 

where Ck – the frequency of receiving pseudorandom sequence chips (chip / sec), C i
– speed of information transmission (bit/sec). For the system with C i =1 Mbit/sec and
6


 Ck =13 MChip/sec, each bit of information is encoded by a pseudo-random sequence
of 13 bits. When processing, the advantage will be B0 =11.14 dB. In this case, the
efficiency of the information transmission system will be maintained if the useful
input signal is reduced by 11.14 dB.
    In addition, the algorithm for the synthesis of barker-like codes on the basis of nu-
merical ring bundles (NRB). It consists in using the minimum value of the autocorre-
lation function of the discrete signal [25]. This algorithm is as follows:

• it is necessary to choose a variant of the NRB of the given order N . It should be
  necessary length L N and multiplicity R . To do this, you need to apply the algo-
  rithm of selective displacements (for 2  N  12 ), then the asymmetric branching
  algorithm (for 12  N  18 ) f, j and the algorithm for constructing the NRB on the
  basis of ideal ring joints (for 18  N );
• •to construct an L N -position code  i , i=1, 2, …, L N with a one-level periodic
  autocorrelation function based on the selected NRB variant (k1, k2 ,..., kN ) , where in
  the N positions of the code with sequence numbers x l , l = 1,2,..., N to place the
    symbols "1", and in the other L N − N positions - the symbols "-1".

    The sequence numbers x l is determined from the formula:

                                         l
                                xl  1 +  ki  ( mod LN ) .                                (8)
                                        i =1

   The sequence we received defines a pulse sequence that has a property called "no
more R-matches." It is also the minimum value of the auto-correlation function. If you
choose another variant of the NRB with the same parameters (if it exists), then we
will receive other pulse sequences with the same property.
   The paper [26] presents barker-like codes, whose lengths are L N =14 … 40. For
each of the lengths L N of these codes, the level of the side lobes of the normalized
correlation function is minimal. The calculation of unique codes for each L N length
was carried out with the help of the NRB.
   For an example, we will consider building a barker-like code based on the above
algorithm. The construction will be carried out for LN = 21 , N = 12 , R = 7 [27].
First, you need to do the following steps:

• there are only four variants of the shortest simple NRB of order N = 12 . All of
  them are based on the algorithm of selective movements [28]. We need to choose
  the first version of the NRB, for which: (1, 1, 1, 1, 1, 2, 4, 2, 1, 4, 1, 2);
• carry up a sequence in which the length of the code is LN = 21 .

   To do this, you must place the "1" characters in twelve positions ( N = 12 ). We
calculate these positions by the formula (4). The remaining positions need to be filled
in with "-1" characters: 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1.
                                                                                                   7


   Received a barker-like code for which PSLR=-20.42, its ACF is depicted in Fig. 4.
From this figure, we see that PSL=2, the level of the main petal is equal to ML=21.
Number of variants with a minimum level of ACF - 12.




                 Fig. 4. Autocorrelation of Barker sequence whose length is N=21.

   Software that simulates the operation of NRB-based barker-like codes has been de-
veloped. The general layout of the program and the results when the sum of the entered
NRB is greater than or equal to the length of the code similar to the barker-like code is
shown in Fig. 5a and Fig. 5b.




                         a                                               b

    Fig. 5. A general view of a program and results that simulates the work of barker-like codes
                                          based on NRB.


5        Realization of Barker-Like Codes on FPGA

In the course of the research, the FPGA EP3C16F484N6 of the Cyclone III family of
the Altera company, which is part of the DE0 booth [29], was used. With its help,
barker-like codes and Barker codes had been implemented. The development was
done in VHDL hardware programming language in Quartus II development environ-
ment using development libraries. We needed to perform parallel computing with a
large amount of data, so we used FPGA. They have a fairly large number of hardware
on their crystal. For example, the FPGA EP3C16F484 includes 15,484 logical ele-
8


ments (LEs), 56 M9K units, 56 multipliers 18x18, a large number of implemented IP
cores [30]. FPGA supports high-speed interfaces with external memory.
   LE is the smallest element of logic in the architecture of the family Cyclone III.
Each LE has four inputs, a four-inputs conversion table (LUT), a register, and an out-
put logic [31].
   The sequential parallel shift register determines the basis of the barker-like code
generator. The scheme of its generation is depicted in Fig. 6. The dimension of the
barker-like code is N=28.




            Fig. 6. Figuration of the barker-like code generation scheme (N=28).

    This register stores the value 0x9FB2B94 (1001111110110010101110010100B). It
is the initial value for the offset.
    The character generator barker-like codes of length N=28 (CB_28) shown in
Fig. 7.




                       Fig. 7. The appearance of the symbol CB_28.

   Input of the generator of the barker-like code which dimension is N = 28 : Clk –
the input of register of pulses to the case of a sequential parallel shift; Load (active
signal level "1") – a signal to load the source data into a register. The output of the
CB_28 generator is a barker-like code with a dimension of N=28. During each Clk
synchronization pulse, the off-set is executed for one bit to the left of the D_Out array
[27..0] and record the input value of the D_In register REG_S_PAR to the lower
grade D_Out [0]. Timing diagrams of the generator are shown in the Fig. 8 [32].




         Fig. 8. Time charts of the barker-like code the dimension of which is N=28.
                                                                                                9


   As for barker-like codes of arbitrary dimension N = 14...40 , they can be realized in
a similar way. However, you must keep in mind that the hardware resources that are
needed for this will change. For example, in order to implement a barker-like code
generator with dimension N = 28,29 (out of 15,408) logical elements, 28 registers
and 3 (out of 347) FPGA EP3C16F484 outputs are required [33].


6      Conclusion

Thus, in the course of the work, an algorithm for the synthesis of barker-like codes,
having a dimension N = 14...40 , was developed. Autocorrelation functions for these
codes were investigated. Barker-like codes were implemented on the Altera firmware
of the FPGA family of EP3C16F484 Cyclone III and modeling their work in a time
sequence.


References
 1. Nazarkevych, M., et. al.: Detection of regularities in the parameters of the ateb-gabor
    method for biometric image filtration. In.: Eastern-Еuropean journ. of enterprise technolo-
    gies, № 1(2), pp. 57–65. (2019)
 2. Medykovskyy, M., et. al.: Methods of protection document formed from latent element lo-
    cated by fractals. In.:2015 Xth Int. Scient. and Techn. Conf. Comp. Sci. and Infor. Techn.
    (CSIT), pp. 70-72. Lviv, Ukraine (2015), doi: 10.1109/STC-CSIT.2015.7325434
 3. Ahmad, J., et. al.: Barker-coded thermal wave imaging for non-destructive testing and
    evaluation of steel material. In: IEEE Sensors Journ., vol. 19, no. 2, pp. 735-742 (2019).
    doi:10.1109/JSEN.2018.2877726
 4. Riznyk O., et. al.: Information Encoding Method of Combinatorial Configuration. In 2007
    9th Int. Conf. - The Experience of Designing and Applications of CAD Systems in Mi-
    croelectronics, pp. 370-370. Lviv-Polyana, Ukraine (2007). doi: 10.1109/CADSM.2007.
    4297583
 5. Tsmots, I., et. al.: Structure and software model of a parallel-vertical multi-input adder for
    FPGA implementation. In: 2016 XIth Int. Scie. and Techn. Conf. Comp. Sci. and Infor.
    Techn. (CSIT), pp. 158-160. Lviv, Ukraine (2016), doi: 10.1109/STC-CSIT.2016.7589894
 6. DE0 User Manual. Development and Education Board. http://esca.korea.ac.kr/teaching/
    FPGA_boards/DE0/DE0_User_Manual.pdf
 7. Kellman, M.R., et. al.: Node-pore coded coincidence correction: coulter counters, code de-
    sign, and sparse deconvolution. In: IEEE Sensors Journ., vol. 18, no. 8, pp. 3068-3079
    (2018). doi:10.1109/JSEN.2018.2805865
 8. Izonin, I., et. al. An approach towards missing data recovery within loT smart system. Pro-
    cedia Comp. Sci., 155, 11-18, (2019)
 9. Tkachenko, R., et. al. A non-iterative neural-like framework for missing data imputation.
    Procedia Comp. Sci., 155, 319-326, (2019)
10. Wang, M., et. al.: Pseudo Chirp-Barker-Golay coded excitation in ultrasound imaging. In:
    2018 Chinese Control and Decision Conf. (CCDC), pp. 4035-4039. Shenyang (2018).
    doi:10.1109/CCDC.2018.8407824
11. Syrotyuk, S.V., et. al.:The exact formula for an energy band spectrum gradient within the
    new completely orthogonalized plane wave method. In: Physica Status Solidi (B) Basic
10


    Research, 200 (1), pp. 129-136. (1997). doi: 10.1002/1521-3951(199703)200:1<129::
    AID-PSSB129>3.0.CO;2-#
12. Riznyk, O., et. al.: Transformation of information based on noisy codes. In: 2018 IEEE
    Second Int. Conf. on Data Stream Mining & Processing (DSMP), pp. 162-165. Lviv,
    Ukraine (2018). doi:10.1109/DSMP.2018.8478509
13. Riznyk, O., et. al.: Information encoding method of combinatorial configuration. In: 2007
    9th Intern. Conf. - The Experience of Designing and Applications of CAD Systems in Mi-
    croelectronics, pp. 370-370. Lviv-Polyana, Ukraine (2007). doi:10.1109/CADSM.2007.
    4297583
14. Kim, P., et. al.: Barker-sequence-modulated golay coded excitation technique for ultra-
    sound imaging. In: 2016 IEEE Int. Ultrasonics Symp. (IUS), pp. 1-4. Tours (2016).
    doi:10.1109/ULTSYM.2016.7728737
15. Oleg, R., et. al.: Information technologies of optimization of structures of the systems are
    on the basis of combinatorics methods. In: 2017 12th Int. Scient. and Techn. Conf. on
    Comp. Sci. and Infor. Techn. (CSIT), pp. 232-235. Lviv, Ukraine (2017).
    doi:10.1109/STC-CSIT.2017.8098776
16. Omar, S.M., et. al.: A novel barker code algorithm for resolving range ambiguity in high
    PRF radars. In: 2015 Europ. Radar Conf. (EuRAD), pp. 81-84. Paris (2015).
    doi:10.1109/EuRAD.2015.7346242
17. Wang, S., et. al.: Research on low intercepting radar waveform based on LFM and barker
    code composite modulation. In: 2018 Int. Conf. on Sensor Networks and Signal Processing
    (SNSP), pp. 297-301. Xi'an, China (2018). doi:10.1109/SNSP.2018.00064
18. Rosli1, S.J., et. al.: Design of Binary Coded Pulse Trains with Good Autocorrelation Prop-
    erties for Radar Communications. In: 2018 MATEC Web of Conf., doi:10.1051/ matec-
    conf/201815006016
19. Lakshmi, C. R., et. al.: Barker coded thermal wave imaging for anomaly detection. In:
    2018 Conf. on Signal Processing And Communication Engineering Systems (SPACES),
    pp.198-201.Vijayawada (2018). doi: 10.1109/SPACES.2018.8316345
20. Li, J., et. al.: A 3-Gb/s Radar Signal Processor Using an IF-Correlation Technique in 90-
    nm CMOS. In: IEEE Transactions on Microwave Theory and Techniques, vol. 64, no. 7,
    pp. 2171-2183 (2016). doi: 10.1109/TMTT.2016.2574983
21. Dua, G., et. al.: Applications of barker coded infrared imaging method for characterisation
    of glass fibre reinforced plastic materials. In: Electronics Letters, vol. 49, no. 17, pp. 1071-
    1073 (2013). doi: 10.1049/el.2013.1661
22. Riznyk, O., et. al.: Synthesis of non-equidistant location of sensors in sensor network. In:
    2018 XIV-th Int. Conf. on Perspective Technologies and Methods in MEMS Design
    (MEMSTECH), pp. 204-208. Lviv, Ukraine (2018). doi:10.1109/MEMSTECH.2018.
    8365734
23. Nilawar, R.C., et. al.: Reduction of SFD bits of WiFi OFDM frame using wobbulation
    echo signal and barker code. In: 2015 Int. Conf. on Pervasive Computing (ICPC), pp. 1-3.
    Pune (2015). doi:10.1109/PERVASIVE.2015.7087095
24. Sekhar, S., et. al.: Comparative analysis of offset estimation capabilities in mathematical
    sequencesfor WLAN. In: 2016 Int. Conf. on Communication Systems and Networks
    (ComNet), pp. 127-131. Thiruvananthapuram (2016). doi:10.1109/CSN.2016.7824000
25. Xia, S., et. al.: Application of pulse compression technology in electromagnetic ultrasonic
    thickness measurement. In: 2018 IEEE Far East NDT New Technology & Application Fo-
    rum (FENDT), pp. 37-41. Xiamen, China (2018). doi:10.1109/FENDT.2018.8681975
                                                                                           11


26. Banket, V., et. al.: Composite Walsh-Barker sequences. In: 2018 9th Int. Conf. on Ul-
    trawideband and Ultrashort Impulse Signals (UWBUSIS), pp. 343-347. Odessa (2018).
    doi:10.1109/UWBUSIS.2018.8520220
27. Chunhong, Y., et. al.: The superiority analysis of linear frequency modulation and barker
    code composite radar signal. In: 2013 Ninth Int. Conf. on Computational Intelligence and
    Security, pp. 182-184. Leshan (2013). doi:10.1109/CIS.2013.45
28. Riznyk, O., et. al.: Composing method of anti-interference codes based on non-equidistant
    structures. In: 2017 XIIIth Int. Conf. on Perspective Technologies and Methods in MEMS
    Design (MEMSTECH), pp. 15-17. Lviv, Ukraine (2017). doi:10.1109/MEMSTECH.
    2017.7937522
29. Riznyk, O., et. al.: The Method of Encoding Information in the Images Using Numerical
    Line Bundles. In: 2018 IEEE 13th Int. Scientific and Technical Conf. on Comp. Sci. and
    Infor. Techn. (CSIT), pp. 80-83. Lviv, Ukraine (2018). doi:10.1109/STC-
    CSIT.2018.8526751
30. Riznyk, O., et. al.: A synthesis of barker sequences is by means of numerical bundles. In:
    2017 14th Int. Conf. The Experience of Designing and Application of CAD Systems in
    Microelectronics (CADSM), pp. 82-84. Lviv, Ukraine (2017). doi:10.1109/CADSM.
    2017.7916090
31. Riznyk, V., et. al.: Information Encoding Method of Combinatorial Optimization. In.:
    2006 Int. Conf. Modern Problems of Radio Engineering, Telecommunications, and Comp.
    Sci., pp. 357-357. Lviv-Slavsko (2006), doi: 10.1109/TCSET.2006.4404550
32. Holubnychyi, A.: Generalized binary barker sequences and their application to radar tech-
    nology. In.: 2013 Signal Processing Symp. (SPS), pp. 1-9. Serock (2013), doi:
    10.1109/SPS.2013.6623610
33. Tsmots, I., et. al. (2020) Implementation of FPGA-Based Barker’s-Like Codes. In:
    Lytvynenko V., Babichev S., Wójcik W., Vynokurova O., Vyshemyrskaya S., Radetskaya
    S. (eds) Lecture Notes in Computational Intelligence and Decision Making. ISDMCI 2019.
    Advances in Intelligent Systems and Computing, vol 1020. Springer, Cham, doi.:
    10.1007/978-3-030-26474-1_15

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