HIn with this regard article assesses the noise immunity of high-orbit satellite telecommunication systems with code division of addresses when using a number of broadband noise-like signals with linear frequency modulation as information carrier

Belov, A. S.

Belov, S. P.

Bukhantsov, A. D.

Raczynski, S. A.

Zhilyakov, E. G.

English

DSpace at Belgorod State University

COMPUSOFT, An international journal of advanced computer technology, 8(6), June-2019 (Volume-VIII, Issue-VI) 3217    Cite This Paper: Sergey P.Belov, Evgeniy G.Zhilkov, Sergey A.Raczynski, Aleksandr S.Belov, Andrei S.Belov, Andrei D.Bukhantsov. (2019). Evaluation of noise immunity of high orbital satellite telecommunication systems with broadband noise-like sign, 8(6), COMPUSOFT, An International Journal of Advanced Computer Technology. PP. 3217-3222.   This work is licensed under Creative Commons Attribution 4.0 International License.    EVALUATION OF NOISE IMMUNITY OF HIGH ORBITAL SATELLITE TELECOMMUNICATION SYSTEMS WITH BROADBAND NOISE-LIKE SIGN   Sergey P. Belov *,Evgeniy G. Zhilyakov,Sergey A. Raczynski,  Aleksandr S. Belov,Andrei S. Belov,Andrei D. Bukhantsov   Belgorod State University, 85, Pobedy St., Belgorod, 308015, Russia  Corresponding author:  Sergey P. Belov Dean of the Faculty of IT and PM, Doctor of Technical Sciences, Belgorod State University, 308015, Pobedyst., Russia E-mail: belov@bsu.edu.ru  Abstract: It is known, when using narrow-band signals in high orbital satellite communication systems for organizing exchange of information, the efficiency of allocated frequency and time communication channel resource usage is reduced due to the large uncertainty in the frequency caused at the Doppler Effect and changes time of received signals arrival. In this regard, currently one of the promising directions in the development of methods for constructing channel signals for use as information carriers in modern high-orbit satellite communication systems with code division of addresses, providing communication between remote subscribers in the Northern latitudes, is the use of broadband noise-like signals, which are the result of the use of special codes and new methods of spectrum expansion. However, the priority of usage of one or another signal class in these systems is largely determined by their resistance to Doppler frequency shift. In with this regard article assesses the noise immunity of high-orbit satellite telecommunication systems with code division of addresses when using a number of broadband noise-like signals with linear frequency modulation as information carriers.  Keywords: satellite telecommunication systems, linear frequency modulated signal, a function of uncertainty, noise immunity, pseudo-random sequence.  I. INTRODUCTION One of the most known classes of broadband noise-like signals that are widely used today in high-orbit satellite telecommunication systems with code-division addresses is the so-called FM PRS signals, obtained as a result of phase modulation of high-frequency harmonic oscillation according to the pseudo-random sequence (PRS) [1-6].  The reason to use such signals in these systems is based on large number of partially correlated forms, while it is known that they are not invariant to the Doppler frequency shift, which leads to large time-frequency expenses for searching and synchronizing of FM PRS  Available online at: https://ijact.in Date of  Submission Date of  Acceptance 03/05/2019 15/06/2019 Date of  Publication 30/06/2019 Page numbers 3217-3222 (6 Pages) ISSN:2320-0790 COMPUSOFT, An international journal of advanced computer technology, 8(6), June-2019 (Volume-VIII, Issue-VI) 3218  signals. At the same time, there is a class of broadband noise-like signals with linear frequency modulation (LFM), that are invariant to the Doppler frequency shift and because of that such signals can be used for building of frequency-search less of high-orbit satellite telecommunication systems quite easily [7-8].   However, this class of signals has a small number of partially correlated forms, which does not allow using it in telecommunication systems with code-division of addresses. In works [9-10], it was shown that as carriers of information in satellite telecommunication systems with code-division of addresses it is much more efficient to use LFM FM or PR LFM signals, which combine the positive properties of both LFM and FM PRS signals.  However, a very important aspect related to the quantitative assessment of the influence of the Doppler frequency shift (which, when satellites in high-elliptical orbits, reaches 50 kHz) on the noise immunity of satellite telecommunication systems with code division of addresses of these classes of broadband noise-like signals was not investigated in any of these works.  In this regard, this paper analyzes the effect of this effect on the noise immunity of high-orbit satellite telecommunication systems with broadband noise-like signals.  II. EXPERIMENTS AND RESULTS To estimate the Doppler frequency shift, as is known [4, 8], the uncertainty function (UF) is widely used, which in mathematical form can be represented as  follows:        dttFjtiStiSEFi   2exp21,          (1) where: τ is the time shift between signals, Fд is the Doppler frequency shift, Е is the signal energy, Si(t) is the envelope of the received i -th signal,   tiS. is the complex-conjugate envelope of the i -th signal. For LFM signals, the envelope of which, according to [4], is represented by the expression: 𝑆 𝑡 =  𝑆0. exp⁡(𝑗µ𝑡22)  (2) where S0 is the amplitude of the signal envelope, hereinafter a constant value equal to 1, μ is the slope of the modulation characteristic of the LFM of the radio pulse (rate of change of frequency) associated with the frequency deviation ∆F and the duration of the signal T, ratio TF /2   , The UF graphically, for different values of the Doppler frequency shift (Fд from 0 to 50 kHz) and the magnitude of the signal base B=ΔF*T=1000, is shown in Figure 1.  Figure 1: Values of UF for the LFM signal at B = 1000  For FM PRS signals, the envelope of which, according to [4], is representable by the expression:   0112 2ЭN Эll ЭTt lS t S rect             (3) where τэ is the duration of the element PRS;  N is the number of elements in the PRS; l  is the coefficient characterizing the state of the PRS, takes the values +1 or -1,  1 1( ) 1, ; ( ) 0,2 2rect x при х rect x при х     is a rectangular "cutting off" function, The UF graphically, for different values of the Doppler frequency shift (Fд from 0 to 50 kHz) and the value B = 1000, is shown in Figure. 2.   Figure 2: Values of UF for FM PRS signal at B = 1000, N = 31  For LFM FM signals, the envelope of which, according to [9], is represented by the expression:     20112 2 exp ;2 20;ЭN Эll ЭTt lt TS rect j при tSat othertts                                                 (4) UF in graphical form for the value of the base signal B = 1000, various values of the Doppler frequency COMPUSOFT, An international journal of advanced computer technology, 8(6), June-2019 (Volume-VIII, Issue-VI) 3219  shift (Fд from 0 to 50 kHz) and the number of elements of the PRS 31 and 127, are presented in Figures 3 and 4.  Figure 3: Values of UF for LFM FM signal at B = 1000, N = 31    Figure 4.Values of UF for LFM FM signal at B = 1000, N = 127  For PR LFM signals, the envelope of which, according to [10], is representable by the expression:      210 1 00 0201 00 1 0 00 0exp21 exp2NllNllTT t lt lT NNS rect j t lT NTT t lt lT NNS t S rect j t lT N                                                                                 0 0;10, 1 0NNat T T tN                 (5) where: 1l  is a coefficient characterizing the state of the encoded sequence and taking values of +1 or 0;  ω0- is the average frequency of the LFM radio pulse;  T0-duration LFM radio pulse; τ0 is the delay between the beginning of the LFM of a radio pulse and the beginning of the PRS element corresponding to zero coefficient values 1l ; UF in graphical form for the magnitude of the signal base B=ΔF*To=1000, various values of the Doppler frequency shift (Fд from 0 to 50 kHz) and the number of elements of the PRS 31 and 127, are presented in Figures 5 and 6.   Figure 5: The values of the UF for the PR LFM signal at B = 1000, N = 31    Figure 6: The values of the UF for the PR LFM signal at B = 1000, N = 127  When assessing the noise immunity of satellite telecommunication systems with code-division of addresses, when using the considered classes of signals as carriers of information, we will use the formula given in [11]:    mist 0,5 1 ( )P h                                 (6) Where, 2 202( )2hxh e dx   is the probability integral, ℎ =  𝐸𝑁0  where E  is the signal energy, N0 is the power spectral density  The expediency of applying formula (6) is justified by the fact that the considered classes of signals, as shown by the results of experimental studies of their mutual uncertainty functions (Figure 7– Figure 10), are quasi-orthogonal, i.e.  their values are close to zero.    Figure 7: The values of the MUF for the LFM FM signal at B = 1000, N = 31 COMPUSOFT, An international journal of advanced computer technology, 8(6), June-2019 (Volume-VIII, Issue-VI) 3220    Figure 8: The values of the MUF for the LFM FM signal at B = 1000, N = 127   Figure 9: The values of the UF for the PR LFM signal at B = 1000, Ni=48,Nj=24    Figure 10: The values of the UF for the PR LFM signal at B = 100, Ni=31,Nj=27  To find the numerical values of the error probability, it is necessary to determine the argument of the integral of the probability h for all values of the Doppler frequency shift.  To do this, we first find the maximum values of the UF for each of the considered classes of signals for all values of the Doppler frequency shift, and then multiply the found values of the UF (placed in Table 1) by the selected values of the signal energy to power spectral density (at Fд = 0).  The values of the sought argument selected and obtained as described above, which take into account the effect of the Doppler frequency shift on the selected values of the ratio of the signal energy to the power spectral density, are presented in Table 2.  Table 1:  Maximum values of the uncertainty functions for LFM, PR LFM, LFM FM, FM PRS signals for different values of Doppler frequency shifts:  The values of the Doppler frequency shift (kHz) UF value  for LFM signal UF value for PR LFM N=31 UF value for LFM FM N=31 UF value for LFM FM N=127 The UF value for the FM PRS signal at  N=31 5 0.9995 0.9889 0.9715 0.9374 0.05 10 0.999 0.9651 0.9513 0.8741 0.031 15 0.9985 0.9471 0.9466 0.811 0.061 20 0.998 0.9394 0.9354 0.748 0.0297 25 0.9975 0.9242 0.91 0.685 0.0294 30 0.997 0.9016 0.8962 0.6223 0.027 35 0.9965 0.883 0.8816 0.5596 0.013 40 0.996 0.874 0.8681 0.4971 0.024 45 0.9955 0.8592 0.8413 0.4348 0.004 50 0.995 0.8374 0.8358 0.3692 0.02   Table 2.  Ratio of signal energy to noise power spectral density  The values of 𝐸𝑁0  At Fd= 0   PR LFM, N=31 The values of  𝐸𝑁0  At Fd=10, 30, 50 kHz LFM FM, N=31The values of  𝐸𝑁0  at Fd= 10, 30, 50 kHz LFM FM, N=127 The values of   𝐸𝑁0  atFd=10, 30, 50 kHz 10 kHz 30kHz 50 kHz 10 kHz 30kHz 50 kHz 10 kHz 30kHz 50 kHz 1 0.965 0.901 0.837 0.951 0.896 0.835 0.874 0.622 0.369 2 1.930 1.803 1.674 1.902 1.792 1.671 1.748 1.244 0.738 3 2.895 2.704 2.512 2.853 2.688 2.507 2.622 1.866 1.107 4 3.860 3.606 3.349 3.805 3.584 3.343 3.496 2.489 1.476 5 4.825 4.508 4.187 4.756 4.481 4.179 4.370 3.111 1.846 6 5.790 5.409 5.024 5.707 5.377 5.014 5.244 3.733 2.215 7 6.755 6.311 5.861 6.659 6.273 5.850 6.118 4.356 2.584 8 7.720 7.212 6.699 7.610 7.169 6.686 6.992 4.978 2.953 9 8.685 8.114 7.536 8.561 8.065 7.522 7.866 5.600 3.322 10 9.651 9.016 8.374 9.513 8.962 8.358 8.741 6.223 3.692 11 10.616 9.9176 9.211 10.464 9.858 9.193 9.615 6.845 4.061 12 11.581 10.819 10.048 11.415 10.754 10.029 10.489 7.467 4.430 13 12.546 11.720 10.886 12.366 11.650 10.865 11.363 8.089 4.799 14 13.511 12.622 11.723 13.318 12.546 11.701 12.237 8.712 5.168 15 14.476 13.524 12.561 14.269 13.443 12.537 13.111 9.334 5.538 16 15.441 14.425 13.398 15.220 14.339 13.372 13.985 9.956 5.907 17 16.406 15.327 14.235 16.172 15.235 14.208 14.859 10.579 6.276 18 17.371 16.228 15.073 17.123 16.131 15.044 15.733 11.201 6.645 19 18.336 17.130 15.910 18.074 17.027 15.880 16.607 11.823 7.014 20 19.302 18.032 16.748 19.026 17.924 16.716 17.482 12.446 7.384  Based on the results obtained, Tables 3-5 of  Рmist changes for PR LFM and LFM FM signals were compiled.  Table 3: Changes Pmist PR LFM signal at B = 1000, N = 31          Fd  h2, dB 0 10 kHz 30kHz 50 kHz 5 1.267*10-2 1.4*10-2 1.683*10-2 1.903*10-2 10 7.827*10-4 9.462*10-4 1.338*10-3 1.903*10-3 15 5.367*10-5 7.068*10-5 1.17*10-4 1.96*10-4 20 3.872*10-6 5.55*10-6 1.077*10-5 2.121*10-5  Table 4: Changes of Pmist  LFM FM signal, at B = 1000, N = 31  COMPUSOFT, An international journal of advanced computer technology, 8(6), June-2019 (Volume-VIII, Issue-VI) 3221  Fd h2, dB 0 10 kHz 30kHz 50 kHz 5 1.267*10-2 1.459*10-2 1.714*10-2 2.046*10-2 10 7.827*10-4 1.02*10-3 1.378*10-3 1.92*10-3 15 5.367*10-5 7.921*10-5 1.23*10-4 1.995*10-4 20 3.872*10-6 6.447*10-6 1.15*10-5 2.171*10-5  Table 5: Changes of  Pmist LFM FM signal, at B = 1000, N = 31          Fd h2, dB 0 10 kHz 30kHz 50 kHz 5 1.267*10-2 1.828*10-2 3.887*10-2 8.712*10-2 10 7.827*10-4 1.556*10-3 6.305*10-3 2.734*10-2 15 5.367*10-5 1.467*10-4 1.124*10-3 9.304*10-3 20 3.872*10-6 1.45 *10-5 2.094*10-4 3.29*10-3  III. DISCUSSION Thus, the use of broadband noise-like signals LFM FM and PR LFM in high-orbit modern satellite telecommunication systems with code-division of addresses as the information carriers allows ensuring the stable functioning of these systems under the conditions of Doppler frequency mismatch in real limits of its change. In addition, due to the property of invariance to the Doppler mismatch in frequency within the limits of its real change, the use of the proposed classes of broadband noise-like signals reduces the number of required time-frequency resources of existing communication channels due to the minimum cost of their search and synchronization. IV. CONCLUSION From the data presented in tables 3-5, it can be seen that the change in the Doppler frequency shift in the real range of its change (from 0 to 50 kHz) leads to a decrease in noise immunity of high-orbit satellite telecommunications systems with code division of addresses [12], when used as information carriers FM PRS, LFM FM and PR LFM broadband noise-like signals.  However, it should be noted that the level of noise immunity of high-orbit satellite telecommunications systems when used as information carriers FM PRS signals even with small values of Doppler frequency mismatch is significantly reduced. At the same time, the level of noise immunity of high-orbit satellite telecommunications systems when used as information carriers LFM FM and PR LFM signals decreases slightly over the entire range of real changes in Doppler roassoglasovaniya frequency, which suggests the feasibility of the use of LFM FM and PR LFM broadband noise-like signals in high-orbit satellite telecommunications systems with code division channels. V. REFERENCES [1]. Varakin L.E.,1970. Theory of complex signals, Moscow,Pages:375. Available at: http://bookre.org/reader?file=405705 (accessed 14 May, 2019). (in Russian). [2]. Pestryakov V.B., Afanasyev V.P., Gurvich V.L. and et.1973. Noise-like signals in information transmission systems, Moscow, Pages:424. Available at: https://booksee.org/book/756964(accessed 14 May, 2019).(in Russian). [3]. 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Evaluation of noise immunity of high orbital satellite telecommunication systems with broadband noise-like sign

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Evaluation of noise immunity of high orbital satellite telecommunication systems with broadband noise-like sign

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