RU2484496C1 - Method of detecting frequency-shift keyed radio signals - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method of detecting frequency-shift keyed radio signals involves performing analogue-to-digital conversion of the input signal, calculating the amplitude spectrum for sampling a signal of given length, estimating the position and width of the spectrum of the radio signal, filtering the ratio signal on the spectrum into two equal parts, calculating envelopes of the filtered components, calculating the cross correlation coefficient for the obtained envelopes, making a decision on associating the received signal with a class of frequency-shift keyed signals based on comparison of the calculated cross correlation coefficient with a predetermined threshold.

EFFECT: wider class of detected frequency-shift keyed radio signals, high probability of correct detection of frequency-shift keyed radio signals with 4 or more frequency components, shorter detection time.

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Description

The invention relates to pattern recognition, in particular to recognition of the type of modulation of radio signals, and can be used in automated technical means of signal recognition.

A known method for detecting a frequency-modulated signal with unknown parameters [1], based on determining the maximum modulus of the correlation sum of samples of the reference and input signals in the parameter space: signal frequency and its derivative. The signal samples are divided into segments of the same length, the samples of the discrete Fourier transform of the segments are calculated, the correlation sums are calculated by summing the samples of the discrete Fourier transform of the segments multiplied by complex coefficients, the maximum modulus of the correlation sum is determined and its value is compared with the threshold.

The disadvantage of this method is the relatively low probability of correct recognition of P _ol frequency-modulated radio signals with a low signal to noise ratio and significant computational costs due to the need for the formation of reference signals.

Closest to the proposed invention is a known method for recognizing frequency-manipulated (FM) radio signals with unknown parameters [2], including analog-to-digital conversion of the input signal, calculating the amplitude spectrum for sampling a signal of a given length, determining the position of the frequency components in the spectrum of the radio signal, filtering the frequency the components of the spectrum, calculating their envelopes, calculating the cross-correlation coefficient r between them, deciding on the classification of the received signal as a class sou frequency-manipulated based on a comparison of r with a predetermined threshold value.

Compared with the previous method, in the prototype method, the probability of correct recognition of P _{ol of} frequency-manipulated radio signals when exposed to noise and interference is increased and the recognition process time is reduced by using the value of the cross-correlation coefficient between the envelopes of the individual frequency components of the signal.

The disadvantages of the prototype method are:

1. Recognition of a limited number of FM radio signals (FM with two frequency positions (FM2) and dual FM2). This follows from the description of the prototype method.

2. Low probability of correct recognition of FM radio signals with more than two frequency components. The use of the prototype method for the recognition of these radio signals leads to a significant reduction in the probability of their correct recognition. Figure 1 presents a graph of the dependence of the probability of correct recognition of the frequency-manipulated signals P _ol by the prototype method from the total number of frequency components M. The decrease in P _ol is due to a decrease in the correlation between the envelopes of two separate frequency components with an increase in their total number. Figure 2 presents a graph of the correlation coefficient r between two envelopes of individual frequency components from the total number of frequency components of the FM radio signal. Theoretical calculations are carried out in accordance with formula 1 [3, p. 171]:

$$r_{xy}=\frac{K_{xy}}{{\sigma }_x{\sigma }_y},\text{(one)}$$

- корреляционный момент;Where: $$K_{xy}={\displaystyle \sum _i{\displaystyle \sum _j(x_i-m_x)(y_i-m_y)p_{ij}}}$$

- correlation moment;

x _i and y _j - discrete values of random variables X and Y;

m is the average value;

σ is the standard deviation;

p _ij is the probability of taking a value (x _i , y _j );

3. Large computational costs in the recognition of FM radio signals. This is due to the following operations: filtering and calculating the envelopes of all determined (detected) frequency components, removing the constant component from the envelopes, calculating the cross-correlation coefficient between all pairs of envelopes, inverting one envelope in each pair when calculating the cross-correlation coefficient.

Achievable technical result of the claimed method is to expand the class of recognizable frequency-manipulated radio signals, increase the likelihood of correct recognition of frequency-manipulated radio signals with the number of frequency components from 4 or more, as well as reduce the time of their recognition.

To achieve the specified technical result in the method of recognizing frequency-manipulated signals, an analog-to-digital conversion of the input signal is performed, the amplitude spectrum for sampling a signal of a given length is calculated, the position and width of the spectrum of the radio signal are estimated, the radio signal is filtered by the spectrum into two equal parts, the envelope of the filtered components is calculated, calculation of the cross-correlation coefficient for the obtained envelopes, the decision on the classification of the received signal as a class of frequency-manip Rowan based on a comparison of the calculated cross-correlation coefficient with a predetermined threshold value.

Common features of the prototype and the proposed method are analog-to-digital conversion of the input signal, calculation of the amplitude spectrum for sampling a signal of a given length, determining the position of the frequency components in the spectrum of the radio signal, filtering the frequency components of the spectrum, calculating their envelopes, calculating the cross-correlation coefficient r between them, making a decision on assigning the received signal to the class of frequency-manipulated based on a comparison of the calculated coefficient r with a predetermined threshold th value of r _then .

Distinctive features of the proposed method from the prototype are:

1. Assessment of the position and width of the spectrum of the radio signal.

2. Filtering the radio signal over the spectrum into two equal parts.

3. Calculation of the envelopes of the filtered parts of the radio signal without removing the constant component and inversion.

4. The cross-correlation coefficient r is calculated for one pair of envelopes.

5. As a condition for making a decision, r <r _{pores are used} .

The technical result is an extension of the class of recognizable FM radio signals and an increase in the probability of correct recognition of FM radio signals with the number of frequency components from 4 or more, achieved by using the property of FM radio signals, which consists in the fact that at a reference moment the signal is present at only one frequency. This allows us to consider the FM signal as the sum of amplitude-manipulated signals with different radio frequencies. The calculation of the common envelope of several frequency components leads to the content of all the included frequency components in it. This is because when calculating the envelope of the signal, the radio frequency is eliminated.

Thus, a pair of common envelopes, each of which contains the sum of the envelopes of the individual frequency components, can be obtained by dividing the FM signals in the spectrum into two parts. In this case, time instants of a unit voltage in one envelope always correspond to time instants of zero voltage in another. As a result, the correlation between the obtained envelopes of the filtered components of the FM signal will be negative even in the absence of noise r → -1.

The technical result is a reduction in the recognition time of FM radio signals, achieved by reducing the number of computational operations. In particular, the radio signal is filtered according to the spectrum into only two parts (and not according to the number of frequency components), the envelopes of the filtered parts of the radio signal are calculated without removing the constant component and inversion, the cross-correlation coefficient is calculated for one pair of envelopes, the comparison with the threshold value is performed once . The decision condition has the form r <r _then .

The analysis of the level of existing technology made it possible to establish that analogues, characterized by a combination of features identical to all the features of the claimed technical solution, are absent. This indicates the conformity of the claimed method to the condition of patentability "novelty." The search results for well-known solutions in this and related fields of technology in order to identify features that match the features of the claimed object that are different from the prototype showed that they do not follow explicitly from the prior art. The prior art also did not reveal the popularity of the impact provided by the essential features of the claimed invention, the transformations on the achievement of the specified technical result. Therefore, the claimed invention meets the condition of patentability "inventive step".

The method is illustrated by illustrations in which are presented:

figure 3 is a generalized structural recognition scheme;

figure 4 - amplitude spectrum of the FM8 signal and filter bandwidth;

5 - envelopes of the filtered components of the FM8 signal;

6 is a graph of the dependence of R _PR frequency-manipulated signals from SNR for a duration of ten parcels.

The method of recognition of frequency-manipulated signals consists of the following steps (figure 3):

Stage 1. An analog-to-digital conversion of the input signal. It can be carried out, for example, based on the method of quadrature sampling [4, p. 154].

The result of quadrature sampling is a digital signal S [t], which is a sequence of complex samples of the input analog signal S (t).

Stage 2. Calculation of the amplitude spectrum for sampling a signal of a given length. It can be implemented, for example, based on fast discrete Fourier transform algorithms [4, p. 294]. The sample length n is calculated by the formula 2:

$$n=2^k,\text{(2)}$$

where: k is a positive integer. The value of k is selected from the condition that the probability of the joint occurrence of zero and single premises on the sample duration is not lower than 0.95. Such a probability is provided for a sample length of six elementary premises (the probability of the joint occurrence of zero and one is 0.96875). For example, at a manipulation speed of B = 10 baud and a sampling frequency of 8 kHz, n = 8192 and k = 13. The result of a discrete Fourier transform is a sequence of complex samples. The amplitude spectrum of the digital signal S [t] is calculated as the modulus of the complex number and is a sequence of material samples S [f].

Step 3. Assessment of the position and width of the spectrum of the radio signal Δf _s . It can be carried out, for example, by the methods of power ratio or measurement by the level of L dB [5, p. 199]. In the first case, Δf _c is defined as the width of the occupied frequency band of the radio emission, beyond which a given part of the total average power of the radio transmitter is radiated (usually the radiated powers outside the lower and upper limits of the occupied band are assumed to be the same and 0.5% is chosen). In the second case, the bandwidth of the radiation frequency is the zone beyond which any component of the spectrum is at least L dB less than the predefined reference level (for FM signals, L is set by the level of the non-manipulated carrier or 0 dB). The result of estimating the occupied frequency band is the lower f _n and the upper f _{in the} frequency of the radio emission, which characterize its position on the frequency axis. The width of the spectrum of the radio signal is calculated as Δf _c = f _in -f _n .

Stage 4. Filtering the radio signal over the spectrum into two equal parts Δf ₁ and Δf ₂ (figure 4). Can be performed, for example, in the frequency domain by suppressing spectral components that do not fall into the estimated width of the spectrum of the radio signal Δf _c . Since filtering RF signal carried on two equal parts spectrum, it suppressed the components of the initial spectral component to f _n and by (f _n + f _c) / 2 to the last spectral component for the band Δf ₁ for band Δf ₂ - from initial spectral component to (f _n + f _in ) / 2 and from f _to to the last spectral component. The bandwidth is calculated by the formula 3:

$$\mathrm{<figure-callout\; id="1"\; label="\Delta \; f"\; filenames="00000013.png,00000015.png"\; state="\{\{state\}\}"><figure-callout\; id="2"\; label="\Delta \; f"\; filenames="00000010.png,00000015.png"\; state="\{\{state\}\}">\Delta \; </figure-callout></figure-callout>}{f}_{}{}_{}{}_{\mathrm{1,2}}=\frac{\mathrm{one}}{2}\Delta f_{\mathrm{from}}.\text{(3)}$$

The passbands are chosen the same from the condition that the probability of the manifestation of the components of the FM radio signal and the signal-to-noise ratio (SNR) in each of the bands are respectively the same. The filtering result is two sequences of samples of the first U ₁ [f] and second U ₂ [f] halves of the spectrum of the radio signal.

Step 5. The calculation of the envelopes of the filtered components (figure 5). It can be carried out, for example, on the basis of amplitude detection or the Hilbert transform [4, p. 512, 276]. The result is two sequences of envelope samples U ₁ [t] and U ₂ [t], filtered by the spectrum of the parts of the radio signal. In figure 5, U ₁ [t] and U ₂ [t] for clarity, spaced voltage.

Step 6. The calculation of the cross-correlation coefficient r between the two obtained envelopes U ₁ and U ₂ is performed according to the formula (4) [3, p. 171].

$$r=\frac{{\displaystyle \sum \left(U_{\mathrm{one}}[i]-{\overline{U}}_{\mathrm{one}}\right)\left(U_2[i]-{\overline{U}}_2\right)}}{\sqrt{{\displaystyle \sum {\left(U_{\mathrm{one}}[i]-{\overline{U}}_{\mathrm{one}}\right)}^2{\displaystyle \sum {\left(U_2[i]-{\overline{U}}_2\right)}^2}}}}\text{(four)}$$

и $${\overline{U}}_2$$

- средние значения огибающих U₁ и U₂ соответственно.Where: $${\overline{U}}_{\mathrm{one}}$$

and $${\overline{U}}_2$$

- average values of the envelopes U ₁ and U _2, respectively.

Step 7. Comparison of the cross-correlation coefficient r with a threshold value of r _then . The value of r between the envelopes can vary from -1 (FM signal) to 0. Therefore, the threshold value was calculated by the criterion of an ideal observer and is -0.5.

Stage 8. Making a decision on classifying the received signal as a frequency-manipulated class. The decision is made when the condition r <r _then .

The study of the feasibility of the proposed method was carried out on an electronic computer (computer) according to the method of statistical testing Monte Carlo.

Stage 1 was implemented by an analog-to-digital converter (sound card) of a computer. The input of signals to the computer was carried out at a low frequency.

To implement stages 2 ... 8, software was developed in the C ++ programming language using the Visual Studio 2008 integrated development environment.

During the experiment, FM radio signals of the high frequency range with various modulation parameters were recognized in the analysis band of 4 kHz. The experimental results are presented in Fig.6. The probability of correct recognition of FM signals (FM2, 4, 8, 16, 32, 64) at a 6 dB SNR is 0.95 (when using the prototype method for recognizing FM4, 8, 16, 32, 64 signals in the absence of noise, P _pr decreases from 0.843 to zero). This value of the probability of correct recognition is provided at the sample length of the analyzed signal in 10 packages, which for modulation speeds from 10 to 300 baud is from 0.02 to 0.6 seconds.

Recognition time is determined by the time costs of each computational operation. So for the prototype method, the recognition time t _p is determined by the following components:

$$t_p=t_{\mathrm{at}.\mathrm{from}.}+t_{\mathrm{about}c}+M{t}_f+M{t}_{\mathrm{about}g}+M{t}_{P.\mathrm{from}.}+I{t}_{\mathrm{and}n\mathrm{at}}+K{t}_r+K{t}_{\mathrm{from}R}\text{(5)}$$

where: t _VS - time calculation of the amplitude spectrum;

t _sc - time to evaluate the position of the frequency components;

t _f - filtering time of one frequency component;

t _og - calculation time of the envelope of one filtered component;

t _ps - time to remove the constant component from one envelope;

t _inv is the inversion time of one envelope;

t _r is the calculation time r between one pair of envelopes;

t _cf is the time of comparison of one calculated r with a threshold value;

M is the total number of frequency components;

I is the number of inverted envelopes;

K is the number of times the cross-correlation coefficient is calculated.

When recognizing by the claimed method, the recognition time t ' _p is determined by the following components:

$$t{\text{'}\text{'}}_p=t_{\mathrm{at}.\mathrm{from}.}+t_{\mathrm{about}c}+2t_f+2t_{\mathrm{about}g}+t_r+t_{\mathrm{from}R}\text{(6)}$$

In the formula 6 there are no temporary components t _p.s. and t _inv , a components t _f , t _og , t _r , t _cp do not depend on the total number of frequency components of the signal. In the simplest case, when only the FM2 radio signal is exposed to recognition (without interference), t _p will exceed t ' _p by 2t _ps + t _inv , in the general case - at (M-2) t _f + (M- 2) t _og + Mt _ps + It _inv + (K-1) t _r + (K-1) t _cf. The recognition time for FM radio signals by the claimed method t ' _p for any number of frequency components remains the same and is determined by formula 6.

Thus, the conducted experimental studies confirmed the claimed technical result - expanding the class of recognizable frequency-manipulated radio signals, increasing the likelihood of correct recognition of frequency-manipulated radio signals with the number of frequency components from 4 or more, as well as reducing the time of their recognition.

Literature

1. Patent No. 2154837, Russian Federation, IPC ⁷ G01S 7/285. A method for detecting a linear frequency modulated signal with unknown parameters. / A.G. Aganin, A.V. Bogdanov et al., Applicant and patent holder of OKB Travers LLC, Application No. 99113134/09 of 06.16.1999, published on 08.20.2000.

2. Patent No. 2236693, Russian Federation, IPC ⁷ G01S 13/52, G06K 9/00. A method for recognizing frequency-manipulated radio signals with unknown parameters. / A.V.Dovgiy, V.O. Egurnov et al., Applicant and patent holder, Military University of Communications, Application No. 2003122963/09 of July 21, 2003, published September 20, 2004.

3. Ventzel E.S. Probability Theory: A Textbook for Stud. universities. / Elena Sergeevna Wentzel. - 9th ed. - M.: Publishing Center "Academy", 2003. - 576 p.

4. Sergienko A.B. Digital signal processing: textbook. allowance. / A.B.Sergienko. - 3rd ed. - SPb .: BHV-Petersburg, 2011 .-- 768 p.

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Claims (1)

A method for recognizing frequency-manipulated radio signals, including analog-to-digital conversion of the input signal, calculating the amplitude spectrum for sampling a signal of a given length, determining the position of the frequency components in the spectrum of the radio signal, filtering the frequency components of the spectrum, calculating their envelopes, calculating the cross-correlation coefficient r between them, accepting decisions on assigning the received signal to the class of frequency-manipulated based on a comparison of the calculated coefficient r with a preset nnym threshold r _pores, characterized in that when determining the frequency components of the position estimate position and width of the radio spectrum, with the frequency components filtration divide the spectrum into two equal parts and the envelope is calculated only for them, thus not removed DC component and does not perform the inversion, the coefficient r is calculated for the obtained pair of envelopes and r <r _pores are used as a condition for making a decision.

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