Improvement of Signal Reception Reliability at Satellite Spectrum Monitoring System

Extensively increasing numbers of radio electronic devices significantly complicate the electromagnetic situation under conditions of radio frequency spectrum deficiency and require improvement in the functions and mechanisms of spectrum monitoring systems. Today, in the framework of the existing ground-borne spectrum monitoring system, it is impossible to qualitatively perform the functions and problems of spectrum monitoring. Spectrum (radio) monitoring is one of the main techniques for spectrum load estimation to solve problems of perspective management of the radio frequency spectrum with the purpose of developing new radio technologies. Therefore, the problem of improving the effectiveness of spectrum monitoring does not lose relevance. When solving such problems, one of the most important factors is the extraction of an effective signal with background noise and interference. Therefore, the effectiveness of the Kalman filter application for satellite-based radio monitoring systems is considered in this study. The proposed method for detecting radio signals using Kalman filters makes it possible to make correct decisions with high accuracy. The simulation results show that Kalman filters work effectively even at a negative signal-to-noise ratio (90% and higher), adapting to the original signal at different noise dispersions in a noisy signal. It can be concluded that this method can be successfully applied to solve problems of detecting sources of radiation of a certain frequency according to the signal registered by the onboard receiver of the satellite spectrum monitoring system. The influence of the Kalman filter decision-making speed on the results of radio signal processing was estimated.

the radio frequency spectrum (RFS), RFS has become an 23 increasingly deficient natural resource. Under such condi- 24 tions of deficiency, RFS requires improvement in the func- 25 tions and mechanisms of regulation and management [1], [2], 26 [3], [4], [5], [6], [7]. At present, new approaches to RFS man-27 agement have appeared, including dynamic/opportunistic 28 The associate editor coordinating the review of this manuscript and approving it for publication was Hamed Azami . spectrum access, spectrum sharing and licensed/unlicensed 29 spectrum aggregation, cognitive radio, and software-defined 30 networks. All these methods are directed toward achieving 31 the best and most scientific use of RFS [7], [8], [9], [10]. 32 Radio control of RFS use (spectrum radio monitoring) is one 33 of the ways of estimating its load for solving problems of 34 perspective management of the radio frequency spectrum, 35 with the aim of developing new wireless technology [11]. 36 Radio monitoring of the radio frequency spectrum is a col-37 lection, treatment, analysis, and storage of information about 38 the state of the radio frequency spectrum and identification of 39 violations of the rules of spectrum use. However, at present, 40 VOLUME 10,2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ spectrum monitoring is performed based on ground-borne 41 means of radio control systems [12], [13], [14]. Using

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The rest of the paper is organized as follows: in Section II 77 the analysis of the radio channels of a low-orbit satellite sys-78 tem to assess the real signal levels is presented; in Section III 79 signal evaluation using the Kalman filter in a satellite mon- ing a low-orbiting small spacecraft to fulfil radio monitoring.

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The analysis of the signal level at the input of the measuring 89 onboard receiver of the radio monitoring system showed that 90 for most ground-borne radio-electronic means, the signal-to-91 interference ratio is more than 10 dB, which is acceptable 92 for satellite radio monitoring systems. However, to increase 93 radio monitoring quality, effective methods for improving the 94 detection reliability and recognition of radio signals from 95 radio emission sources are required [21], [22], [23], [24], 96 [25], [26], [27]. To estimate the detection reliability of radio 97 signals from radio emission sources there has been carried 98 out an analysis of telemetry signal levels of the Earth dis-99 tance probing satellite system KazEOSat-2 (Figure 1), the 100 signals were obtained as a result of measurements in a period 101 from September, the 5 th to October, the 20 th , 2020 and from 102 January to June 2021 on the base of national company 103 ''Kazakhstan Garysh Sapary''. The technical parameters of the distance probing of Earth 105 space system KazEOSat-2 are listed in Table 1. The receiving and data treatment equipment of ground 107 complex was used to monitor the radio channels of the satel-108 lite system KazEOSat-2 for signal levels assessment. The 109 power of the ground signal transmitter was 47 dBWt.

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Measurements of the telemetry signal levels in the zone 111 of radio visibility at the input of the on-board measuring 112 receiver range from −85 dBm to −120 dBm, and the altitude 113 of the average resolution satellite KazEOSat-2 was 630 km. 114 FIGURE 2. Magnitude of telemetry signals levels on the input of on-board measuring receiver in period from September, the 5 th to October, the 19 th , 2020.
Such a signal level is optimal from the point of view of satel-115 lite radio monitoring.

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To increase the quality of radio monitoring, it is necessary    In a satellite spectrum monitoring system to determine 149 parameters and the current position of radio emission sources 150 it is suggested to use radio receiving equipment placed 151 onboard a small low-orbit satellite. It is assumed that at a 152 specific time on the input of the onboard measuring receiver, 153 the observation is fixed, which is the measured value (z).

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At this point, a useful signal (x) distortion owing to 155 interference n (noise) is observed. Here, n is a random vari-156 able that appears in the measurement and when transmitted 157 through the connection channel. Therefore, on the input of the 158 measuring on-board receiver, one defines not the true values 159 of the signal parameters (by which the radio emission source 160 parameters are determined), but the distorted ones. The task 161 of the on-board measuring receiver is to determine the useful 162 signal (x) most reliably. However, one can only approximate 163 the values of the radio emission source signal parameters (x), 164 denoting the values asẋ.

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When receiving a signal from an on-board receiver, it is 166 suggested that it is a product of a certain dynamic process, 167 and correspondingly, a mathematical model of the system is 168 in the following form: where x is the vector of states of the system and F(x, t) is the 171 function describing the evolution of the system.

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When determining radio emission source parameters using a 178 satellite spectrum monitoring system on the basis of one low-179 orbit small spacecraft, let us suppose that one deals with the 180 problem of detecting a harmonic signal (carrying oscillation), 181 which has the following form: However, this form does not satisfy the requirements of 184 the Kalman filter. Let us represent this in differential form. 185 To achieve this, one needs to find differential equations that 186 have a solution in the form of (2). Before applying Kalman 187 filters, it is necessary to solve a transitional problem -to find 188 a system of differential equations. Solving these differential 189 equations, one can find function (2), and if this requirement 190 is true, then one can use these differential equations in the 191 logic of the Kalman filter application. Furthermore, we write 192 an equation that describes the dynamics of the harmonic 193 oscillator: Then, the differential equation order is reduced. To reduce 196 the order, one should introduce additional parameters, such as 197 Hence, Here the speed is variable.

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Thus, the mathematical model of the process generating a 203 harmonic oscillator has the following form: Here x -is represented as a set of discrete values.

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From (5), it is necessary to obtain a differential equation 207 that has the following form: From equation (6), one obtains a final solution that pro- Thus, the signal to be defined is represented in accordance 215 with equation (7) in the form where ε k -the model error, which is related to the mathe- including errors that occur during the rotation of the Earth k -error of the measuring 222 equipment).

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If the condition η k is true, then η k is the actual 224 noise effect.

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Hence, Here, v k dt is a term that controls the evolution of the 228 system, ε k -model error, x k is the real value of the signal, z k is 229 the value obtained from the output of the on-board measuring 230 receiver, η k -the noise. Where ε k and η k are random values.

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The mathematical expectances of the random values ε k and 232 η k are assumed to be as follows: Thus, it is assumed that the noise does not possess any con-

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The Kalman filter algorithms then follow. For this, one 238 needs to find the optimal value of signal y k which is unknown.

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If values x k and z k are available, then y k is an optimal value 240 of the golden mean between x k and z k , and here, U k = v k dt.
242 Hence, to find the optimal value of the golden mean it is 243 necessary to introduce weight coefficient k (optimal value 244 of the golden mean will depend on the coefficient), here 245 Further one should minimize e k+1 = x k+1 − y k+1 . This is 248 done in the following way: Having solved the equation, one obtains the following: Finally, for Kalman filter coefficient the following expres-253 sion is obtained: In Figures 3 and 4, graphs of the measured signal depend-256 ing on time with the effect of different noise levels are illus-257 trated. In the figure, along the horizontal axis, the numbers 258 of signal counts are shown, the counts measure and make 259 calculations at discrete time moments, and along the vertical 260 axis, the model values of the signal are given. Thus, in the 261 figures, graphs of the dependence of the signal levels on 262 different noise levels are represented. In the graphs, the red 263 curve denotes the initial signal, and the blue curve denotes 264 the initial signal with noise addition. When the magnitude of the root-mean-square deviation of 266 the noise is equal to σ = 0.1, the level of noise generated is 267 significantly less than the level of the initial signal. At this 268 point, the resulting oscillation (blue curve) was similar to 269 the initial signal. At σ = 0.5, the level of noise generated 270 is insignificantly less than that of the initial signal. At this 271 point, the resulting oscillation (blue curve) was greater than 272 the initial signal. At σ = 1, the resulting oscillation (blue 273 curve) becomes greater than the initial signal, that is, the 274 signal-to-interference ratio decreases to a minimum value. 275 At σ = 2, the resulting oscillation (blue curve) became 276 significantly greater than the initial signal, that is, the signal- Thus, as can be seen in the graphs, the signal on the output the Kalman filter adapts to the initial signal. At σ = 2, in 298 the noisy signal, where the signal-to-interference ratio has a 299 negative value, the Kalman filter adapts to the initial signal. 300 In Figure 7, the result of the Kalman filter works with an 301 absent initial signal on the filter input. When an effective 302 determined signal in the noisy signal is absent, the Kalman 303 filter defines the absence of the initial signal by stochastic 304 oscillation with a level close to zero. This means that the 305 Kalman coefficient is successfully applicable when radio 306 monitoring of radio emission sources is used to detect the 307 effective signal availability. For this purpose, we introduce the concept of the similarity 309 coefficient of the filtered signal using a Kalman filter for the 310 initial signal.

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Similarity coefficient is calculated in the following way:

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-the difference between the two signals is calculated 313 (filtered and initial);

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The root-mean-square value of the difference signal was 315 calculated.

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The root-mean-square value of the difference signal is 317 subtracted from the initial signal amplitude. 318 Figure 8 shows the graphs of the dependence of the sim-319 ilarity coefficient on the noise level. As can be seen from to be less than 0.3, it is decided that the initial signal is absent.

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The advantage of this method is that the similarity coef-335 ficient when the initial signal is available has a value 336 greater than the threshold (0.9), even at negative signal-to-337 interference ratios.  For each level of noise, the similarity coefficients are cal-352 culated multiply (in this case, 500 times) for both cases, that 353 is, when the initial signal is present or absent in the measured 354 signal. 355 For the cases where the initial signal is present, the magni-356 tude of the similarity coefficient is analyzed; if it is less than 357 the threshold value (in this case 0.9), then the decision is taken 358 to be incorrect; otherwise, it is taken as correct.

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In cases where the initial signal is absent, the magnitude of 360 the similarity coefficient is analyzed; if it is greater than the 361 threshold value (in this case, 0.3), then the decision is taken 362 to be incorrect; otherwise, it is taken as correct.

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-The relative ratio of correct decisions is calculated, which 364 is an indicator of the reliability of the decisions made in the 365 results of the method application. 366 It is obvious that the method reliability index calculated in 367 this way takes values from 0 to 1. The greater the magnitude 368 of the index, the higher the level of validity and reliabil-369 ity of the proposed method for harmonic signal detection. 370 Figures 9 and 10 show the dependences of the method relia-371 bility index on the signal-to-interference ratio for both cases, 372 with available and unavailable initial signals in the measured 373 signal.

FIGURE 9.
(Dependence of method reliability on signal-to-interference ratio (initial signal is present)). Figure 9, the method reliability index has a 375 very high value of 1 for all positive values of the signal-to-376 interference ratio. However, at negative values of the signal-377 to-interference ratio, the index sharply approaches zero and 378 at −6 dB it achieves its possible minimum value.

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In Figure 8, one can see that the method reliability index 380 with an unavailable initial signal has virtually its maximum 381 possible value, which means that the method works ultra-382 reliably in this case.

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Thus, at a negative signal-to-interference ratio value, the 384 signal level at the input of the filter was greater than 385 0.85 (85%). Hence, when the signal-to-interference ratio is 386 greater than zero, the signal on the input of the on-board 387 measuring receiver is taken with a reliability of more than 388 0.9 (90%). Thus, one can conclude that the probability of the 389 signal to exist and the signal to be taken by the on-board 390 FIGURE 10. (Dependence of method reliability on signal-to-interference ratio (initial signal is absent)).
measuring receiver is more than 0.9 (90%) at zero and a 391 greater signal-to-interference ratio. 392 We estimated the operating speed of the proposed method.

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As can be seen from Figure 11, when the signal-to-394 interference ratio is greater than 0 dB, the correct decision   Figure 12 This assumption is illustrated.

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In Figure 12, the satellite position during its motion is  discussion, BC = 1, and the distance from it to the current 413 satellite position can be found by the following formula: where X A , X B -coordinates of the satellite and emission 416 source respectively.

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Suppose that the attenuation of the signal from the emis-418 sion source obeys the exponential law. Then, the root-mean-419 square deviation of noise at a satellite location is defined by 420 the following formula: where coefficient α is defined by the boundary data of the 423 problem. For instance, if we consider the following: Thus, the further away the satellite is from the emission 428 source, the lower the signal-to-interference ratio will be. 429 Correspondingly, the maximum similarity coefficient cor-430 responds to the satellite position at point C ( Figure 12). 431 Hence, by fixing the satellite coordinates at which the sim-432 ilarity coefficient has its maximum values, one can define the 433 emission source location coordinate as well. 434 VOLUME 10, 2022   Since 2011, she has been working at the IITU. Since October 2018, she 627 has been the Head of the Department of Radio Engineering, Electronics, 628 and Telecommunications, and since October 2019, she has been the Vice-629 Rector for Science and International Affairs of IITU. More than 140 scientific 630 publications have been published in republican and international rating 631 journals, including articles in journals with a high impact factor, copyright 632 certificates on the protection of intellectual property rights, and educational 633 and teaching aids.