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Methodology for Assessing Synchronization Conditions in Telecommunication Devices Advances in Science, Technology and Engineering Systems Journal Vol. 5, No. 2, 320-327 (2020) ASTESJ www.astesj.com ISSN: 2415-6698 Special Issue on Multidisciplinary Sciences and Engineering Methodology for Assessing Synchronization Conditions in Telecommunication Devices Juliy Boiko*,1, Ilya Pyatin1, Oleksander Eromenko2, Oleg Barabash3 1Khmelnytskyi National University, Department of Telecommunications and Radio Engineering, 29016, Ukraine 2Khmelnytskyi National University, Department of Physics and Electrical Engineering, 29016, Ukraine 3State University of Telecommunications, Department of Mathematics, 03110, Ukraine A R T I C L E I N F O A B S T R A C T Article history: This paper represents analysis of principles providing maximally reliable delay estimation Received: 11 January, 2020 of signal synchronization devices in telecommunication. Clock synchronization schemes on Accepted: 10 March, 2020 the base of stochastic models, graph-analytic interpretation, analytical functional Online: 23 March, 2020 description and their parameters selection in case of real complex hindrance are analyzed. Dependences between dispersion of maximally reliable estimation of synchronization Keywords: devices and signal to noise ratio (SNR) are represented. Analytical expressions and Synchronization dependences are obtained for deviation of synchronization error with respect to SNR at the Modulation output of discriminator. Diagrams of state are formed for assessment of digital Dispersion of Error synchronization device in case of error state. Calculated error of numerical solution of the Interpolation equation of a stationary grid method. We obtain the schedule of the distribution of the Timing Error probability density synchronization errors for different values of the normalized time. The Signal to Noise Ratio functions performed by the symbolic synchronization circle, features of the construction of the timing error detector (TED) are analyzed. The Gardner, Early-Late, Mueller & Muller TED, their error and the S-curve equation are investigated. The dependence of the relative timing error on the SNR is obtained. The article examines the effects of interpolation and decimation conditions in the forming filters of digital communication systems. 1. Introduction that qualitatively influence the factors contributing to the noise immunity of modern information processing systems [2,3]. The This paper is an extension of work originally presented in coherent and quasicoherent methods for signal receiving require conference name "Quality Assessment of Synchronization phase locked loop (PLL) frequency as obligate component which Devices in Telecommunication" that is published in 2019 IEEE forms the reference signal from the received oscillation [4]–[6]. To 39th International Conference on Electronics and Nanotechnology receive discrete information a system needs clock, word and frame (ELNANO) [1]. synchronization. The important task of synchronization, which is The proposed paper (additionally) presents experimental to form reference oscillation at the receiving side of wireless results for evaluating the effect of interpolation conditions and connection, in most of the cases, becomes complicated due to decimation for energy gain of telecommunication facilities on influence of noise, which distorts the received signal, and in some phase shift keying modulation, as well as comparative analysis of cases due to random character of the signal itself [2]. error detectors of symbol synchronization of coherent Such events entail fluctuational phase deviation, which is communication network with QPSK modulation has done. formed by reference oscillation synchronization system. The The main purpose of the presented results is to supplement and effectiveness of data transmission lowers consequently because of summarize information on the specifics and nature of losses in transmission of data required for not only synchronization synchronization conditions in the means of determining the factors but also for the signal search time and transition onto monitoring mode for all synchronization systems of the receiver. This raises *Corresponding Author : Juliy Boiko, Khmelnytskyi National University, 29016 the question of improving synchronization system especially in Ukraine, [email protected] www.astesj.com 320 https://dx.doi.org/10.25046/aj050242 J. Boiko et al. / Advances in Science, Technology and Engineering Systems Journal Vol. 5, No. 2, 320-327 (2020) case of using in communication systems frequency, phase and signal is represented analogously as the following: 푈(푡) = quadrature methods of digital modulation [7]–[9]. 푈0 ∑푖 푆푖 ℎ(푡 − 푇 − ξ), h(t)=1, 0≤t≤T, h(t)=0, t ∈ (0,T). Papers [4,5] represent linear and nonlinear analysis of clock Thus, the pulses sequence is given U0 - having rectangular form synchronization devices. Probability of acquisition and probability h(t), which represents binary character data stream 푆푖 ∈ {+1, −1}, of cycle slip are estimated. The main factors, which increase an n(t) - Gaussian white noise. The research is conducted in order to error in increasing and decreasing reliability of system identify discriminatory and fluctuational characteristics. The synchronization in time, are analyzed. synchronization error is specified by γ = (ξ − ξ̂)/푇. The pulse The represented research is conducted in progress of results sequences to identify synchronization error are represented in Fig. published in [3]–[6]. We use various stochastic models with 2. expanded technical interpretation of Markov’s modeling, cumulant method and method for statistic linearization. Besides, upgrading circuit structure of the manipulated signal receiver in order to optimize it by using solutions aimed at removing reverse effect, synthesis of the receiver structure with synchronization devices and defining character of signal to noise ratio influence on accuracy of synthesized clock synchronization devices are important. The research outcome represents novelty, which consists in using stochastic model to describe synchronization error. Significance of the research consists in estimating clock transition distribution density. The criteria and algorithm is developed to provide optimal operation of synchronizer in condition of Figure 2: Pulse sequences in synchronization system hindrance. The dispersion of fluctuational error in synchronization system 2. Stochastic Model of Synchronization System is to be defined using the equation of Markov’s random process, which density of probability distribution P=P (γ, t) is expressed by 2.1. Semigraphical Interpretation of Clock Synchronization Fokker-Planck equation [10,11]: Systems In article [1], [7], a stochastic model of a synchronization dγ + kα(γ) = k h(γ)n(t), 0 t, () system was proposed. Model of synchronization system is dt described by stochastic equations in accordance to the scheme Fig. 1. The following symbols are used: ξ=ξ(t) - input influence, ξ̂ = γ(0) P0(γ). ξ̂(푡) - influence assessment, γ = γ(푡) = (ξ(푡) − ξ̂(푡))/ 푇 - normalized synchronization error, ρ(γ) - discriminatory where P0(γ) - initial density distribution of synchronization characteristics, h(γ) - fluctuation characteristics, n(t) - Gaussian error. white noise, f(ε) - transient pulse function of the linear dynamic element, which describes the effect of processing output signal and P 1 2 = − (A(γ)P) + ((γ)P), P(γ,0) = P (γ) () adjustment of the clock generator frequency Fig.1. t γ 2 γ 2 0 2 where U0(γ)=-kα(γ), Z(γ)=k S (0, γ). The solution of equation (2) at synchronization system 휕푃 stationary mode = 0 is found as: 휕푡 γ 2 −1 2h0 χ0n(U) + dh(U) / dU () P(γ) = c exp− dU , γ 1/ 2 h(U) Figure 1: The research clock synchronization scheme 0 Assumption is made that: the influence is slow process, stable where χ0=4/U0kT - parameter opposite to normalized noise due to large amount of symbol intervals; assessment of the target band of the synchronization system linear model [12]-[15]; influence is a slow process; normalizing random processes and 1/ 2 γ 2 fluctuation of discriminator’s output signal is the condition to be 2h0 χ0n (U) + dh(U) / dU - normalizing c = 2 exp− dU dγ used; spectral density G(ω, γ) is assumed stable in the tract h(U) 0 0 transmission frequency band G(0, γ) and fluctuation component is constant. represented as the white noise. Synchronization system accuracy is assessed by dispersion of The synchronization system is described as automatic control normalized synchronization error: system. The input influence is represented as r(t)=U(t)+n(t). The www.astesj.com 321 J. Boiko et al. / Advances in Science, Technology and Engineering Systems Journal Vol. 5, No. 2, 320-327 (2020) 1/ 2 operators are replaced with difference ones. Initial conditions are: 2 2 () σγ = 2 γ P(γ)dγ Pk,0=1, k ∈ (0, ±N), P-N,l=PN,l, PN+1,l=P-N+1,l, P-N-1,l=PN-1,l. 0 References testify that solution is possible to find at the new layer on conditions mentioned above [16]. The stability condition of the 2 The mathematical modeling will be performed and error difference scheme is worthy to mention: δ/ξ < D0/2. dispersion influence will be assessed in dependence on signal to The equation (5) rewritten with recurrent formulas becomes: noise ratio for some values of χ0 parameter. In particular Fig. 3 2 demonstrates assessment carried out for δ0=δ0opt (h0 ). δ δ Pk,l +1 = Pk,l + (αk +1Pk +1,l − αk −1Pk −1,l )+ ( hk +1Pk +1,l − 2hk Pk,l + hk −1Pk −1,l ) 2ξ 2 D0ξ δ δ () Pk,l +1 = Pk,l + (αk +1Pk +1,l − αk −1Pk −1,l )+ (hk +1Pk +1,l − 2hk Pk,l + hk −1Pk −1,l ) 2ξ 2 D0ξ l=0,1,2, … ω(φ, τ)=1/2π·(chτ-chτ·cosφ). The error should be assessed by comparing grid functions of two types – the accurate and the numerical solutions; and by finding Δ=(ωa(φ,τ)-ωn(φ,τ)/ωa(φ,τ))·100% along the layers in nodes of selected grid. This approach will be used to assess error of clock synchronization. Fig. 4 shows transient process, Fig. 5 – dependences of numerical solution (6), and Fig. 6 represents graphs, which describe process of setting on stationary mode at -3 error probability p0=10 , in case of minimum shift keying (GMSK) digital modulation [1].
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