RU2487367C2 - Method and apparatus for fast computation of signal uncertainty function based on reverberation interference - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: apparatus for calculating a signal uncertainty function based on reverberation interference has an analogue-to-digital converter whose output is connected to the input of a recirculator, the output of which is connected to the input of a fast Fourier transform computer, the output of which is connected to the first input of a multiplier unit. The apparatus further includes: a negative frequency nulling unit, the input of which is the output of the fast Fourier transform computer, and the output is connected to the first input of the multiplier unit; read-only memory, the output of which is connected to the second input of the multiplier unit, the output of which is the input of a unit for calculating two-dimensional inverse fast Fourier transform, the output of which is connected to the input of a squared modulus computer, the output of which is the output of the apparatus; a control device whose outputs are connected to control inputs of the analogue-to-digital converter, the fast Fourier transform computer, the multiplier, the unit for calculating two-dimensional inverse fast Fourier transform and the squared modulus computer.

EFFECT: high noise-immunity of detecting signals on the background of reverberation interference.

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Description

The present invention relates to the field of sonar and radar, and in particular to methods for coordinated filtering of signals against a background of reverberation noise and devices that implement them, and can also be used in radio and sonar systems to determine the coordinates and parameters of target movement (KPDTS).

, где ν - скорость объекта, с - скорость распространения сигнала, Т - длительность излучаемого сигнала, W - ширина полосы частот излучаемого сигнала.As a rule, in sonar systems, correlation processing takes into account the range [1, 2, 3, 4, 5], the radial velocity of the target. In practice, the resolution of a location system is analyzed based on the uncertainty function (FN) of Woodward. The basis of this analysis is the assumption that the speed of the target is constant within the signal duration and negligible distortion of the modulating function. So in work [6] the permissible Doppler detuning in a sonar is given. It is roughly believed that the approximation of the Doppler effect can be used by a simple shift of the spectrum when the condition $$\frac{2\nu }{c}TW<0.1$$

where ν is the speed of the object, s is the speed of propagation of the signal, T is the duration of the emitted signal, W is the bandwidth of the emitted signal.

It is known that the implementation of optimal reception when solving the problem of detecting signals against a background of reverberation noise is largely determined by the level of knowledge of a priori information about the received signal [7].

Therefore, the received echo signal y (t) is expressed as a convolution of the emitted pulse s (t) with the impulse response of the medium and target h (t). In this way,

$$y\left(t\right)=s\left(t\right)*h\left(t\right).\left(\mathrm{one}\right)$$

Since the number of scatterers and their strength for any moment in the formation of reverberation are functions of distance, both the average value and the variance associated with the envelope will also be functions of distance, i.e. depend on time.

The spectral density of the reverberation noise is a non-stationary function of time and frequency N (f, t) and, up to a time-variable power, can be approximately written

$$N\left(f,t\right)=P\left(t\right){\left|S\left(f\right)\right|}^2,\left(2\right)$$

where S (f) is the spectral density of the signal,

P (t) is the reverb power.

Since the spectral density is the mathematical expectation of the value of the square of the amplitude s _R (t) in the frequency domain, then

$$N\left(t\right)={\left|S\left(f\right)\right|}^{2}K{\sigma }_{an}^2,$$

where K is the number of scattering elements.

From the expression (2) it follows that the spectral density of the reverb, taken from a limited interval, has the same form as the power spectrum of the emitted signal. A change in the reverberation amplitude depends on a change in the distance to the object. Due to the Doppler effect, the frequency of the received signal from the scattering element is shifted by a value proportional to the radial velocity of the target relative to the radio or hydroacoustic station. Given the signals received from the ring zone with the center coinciding with the location of a moving radar or sonar station, we get that the Doppler shift lies in the range from 2V / λ ₀ to -2V / λ ₀ , where V is the relative speed of the target, λ ₀ - wavelength of the carrier frequency of the signal.

It follows that for a probing signal with a bandwidth that is small compared to the carrier, the spectrum of the received signal from a single scatterer approximately repeats the spectrum of the probing signal shifted in frequency by the value of the Doppler shift f _d = 2V / λ ₀ , where V is the relative radial velocity component, λ ₀ is the wavelength corresponding to the carrier frequency of the emitted signal.

Thus, the spectrum of the received signal is the sum of the spectra from individual scatterers with a weight determined by the square of the mutual directivity [7]. Doppler shift within the width of the directivity leads to a broadening of the spectrum of the received signal.

In the range from f ₀ + 2V / λ ₀ to f ₀ -2V / λ _{0, the} power of the reverberation noise decreases by an amount determined by the level of the lateral field of the directivity characteristic. Since the Doppler shift cannot exceed 2V / λ, the spectrum at frequencies above f ₀ + 2V / λ ₀ is determined primarily by the shape of the spectrum of the probe pulse centered at f ₀ + 2V / λ.

Close in technical essence to the proposed invention is the CAVORT system [8] (a system for processing echo signals from targets [9, 10, 11, 12]). This system works as follows: the received pulses are passed through a delay line (LZ) at an intermediate frequency with a total number of taps N. These taps are connected to two rows of mixers. The upper row of mixers produces frequency shifts fν, 2fν, ..., (N-1) fν. The resulting shifts at any time characterize the relative speed of the target. Adjustment of this coordination for targets experiencing acceleration of movement is achieved by a further shift provided by the second row of mixers.

The disadvantage of this method is the complexity of its technical implementation, because the required number of filters is very large and amounts to several hundred. Given the spatial processing, this requires a very large computational cost.

Closest to the proposed invention is a method of matched filtering of the received signal [13].

, где ^- - представляет собой символ комплексного сопряжения. К результату перемножения применяется преобразование Фурье, в результате которого получают спектральную взаимно корреляционную функцию (ВКФ) вида:The considered method makes it possible to isolate a signal in the presence of interference under the conditions of the Doppler effect. The essence of the method is as follows. A probe pulse is emitted into the medium. The input implementation and the reference are multiplied among themselves $$y\left(t\right)\cdot \overline{s\left(-t\right)}$$

where ^- - is a symbol for complex pairing. The Fourier transform is applied to the result of multiplication, as a result of which a spectral cross-correlation function (CCF) of the form is obtained:

$$R_{ys}\left(f\right)={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}Y\left(f_{\mathrm{one}}\right)\overline{S\left(f_{\mathrm{one}}-f\right)d{f}_{\mathrm{one}}},\left(3\right)}$$

where f is the frequency shift of the echo due to the Doppler effect.

The resulting response of the correlation function is compared with a threshold voltage. Processing is carried out in real time, i.e. samples of the input implementation are updated in accordance with the Kotelnikov theorem. Exceeding the threshold value occurs at the time of delay compensation τ = 0. In this case, a decision is made to detect the target, and the moment itself will correspond to the distance to the target. The considered method is optimal from the point of view of signal-to-noise ratio for a deterministic signal in the conditions of "white" noise. In technical solutions, instead of (3), the functional is considered:

$$R_{ys}\left(t,f\right)={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}Y\left(f_{\mathrm{one}}\right)\overline{S\left(f_{\mathrm{one}}-f\right)}}\exp \left(i2\pi f_{\mathrm{one}}t\right)d{f}_{\mathrm{one}}\left(\mathrm{four}\right)$$

In view of the great practical importance, expression (4) is defined as the mutual uncertainty function, for the calculation of which the result is the inverse Fourier transform of multiplying the spectrum of the input implementation and the shifted spectra of the reference signal.

This rule (4) solves the problem of coordinated filtering in the presence of a shift and a Doppler effect in the conditions of “white noise”. However, in sonar systems, in addition to the effects of environmental noise, it is necessary to take into account the effect of reverberation noise. Failure to take into account this effect is manifested in a decrease in the noise immunity of the filtration system.

Expression (4) involves the calculation of convolution by a direct method based on the product of polynomials and containing a large number of operations equal to the product of the degrees of these polynomials.

The aim of the invention is:

1) increasing the speed of computing the mutual function of uncertainty;

2) increasing the noise immunity of the filtering system by taking into account the effect of reverberation noise.

This goal is achieved by applying fast algorithms and forming a reference signal for calculating the mutual uncertainty function taking into account a priori data on the spectral density of the reverberation noise.

1. A method for quickly calculating the uncertainty function of signals taking into account reverberation interference

The essence of the method is as follows. The optimal detector of a deterministic signal against the background of additive interference is a matched filter having a frequency response of the form [7]:

, $$H\left(f,t\right)=\frac{\overline{S\left(f\right)}}{N\left(f,t\right)}$$

,

where S (f) is the complex-valued spectral density of the signal,

N (f, t) is the energy spectral characteristic of the noise.

However, in the presence of the Doppler effect, the reverberation response of the matched filter [14, 12] is defined as:

$$\Theta \left(t,f\right)={\left|{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}Y\left(f_{\mathrm{one}}\right)\frac{\overline{S\left(f_{\mathrm{one}}-f\right)}}{N\left(f_{\mathrm{one}},t\right)}\exp \left(i2\pi f_{\mathrm{one}}t\right)d{f}_{\mathrm{one}}}\right|}^2.\left(5\right)$$

Under the condition Y (f) = S (f) for the values t = 0 and f = 0, the value of the mutual uncertainty function reaches a maximum, which is equal to:

$$K\left(\mathrm{0,0}\right)={\left|{\displaystyle \int \frac{{\left|S\left(f_{\mathrm{one}}\right)\right|}^2}{N\left(f_{\mathrm{one}}0\right)}d{f}_{\mathrm{one}}}\right|}^2.\left(6\right)$$

можно представить:In the operator (5), the spectrum of the reference signal $$\overline{S\left(f_{\mathrm{one}}-f\right)}$$

can be imagined:

$$\overline{S\left(f_{\mathrm{one}}-f\right)}=F_{t_{\mathrm{one}}}\left\{\overline{s\left(-t_{\mathrm{one}}\right)}\exp \left(i2\pi f{t}_{\mathrm{one}}\right)\right\}.\left(7\right)$$

Substituting expression (7) into expression (5), we obtain:

$$\Theta \left(t,f\right)={\left|{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}Y\left(f_{\mathrm{one}}\right)\frac{F_{t_{\mathrm{one}}}\left\{\overline{s\left(-t_{\mathrm{one}}\right)}\exp \left(i2\pi f{t}_{\mathrm{one}}\right)\right\}}{N\left(f_{\mathrm{one}},t\right)}}\exp \left(i2\pi f_{\mathrm{one}}t\right)d{f}_{\mathrm{one}}\right|}^2\left(8\right)$$

We write (8) using the inverse Fourier transform with respect to f ₁ :

$$\Theta \left(t,f\right)={\left|F_{f_{\mathrm{one}}}^{-\mathrm{one}}{F}_{t_{\mathrm{one}}}\left(\overline{s\left(-t_{\mathrm{one}}\right)}\frac{Y\left(f_{\mathrm{one}}\right)}{N\left(f_{\mathrm{one}},t\right)}\exp \left(i2\pi f{t}_{\mathrm{one}}\right)\right)\right|}^2.\left(9\right)$$

Expression (9) allows you to create a way to quickly calculate the mutual uncertainty function taking into account the reverberation noise and is the basis for the proposed method for detecting signals in the presence of reverberation noise.

From an analysis of relation (9), we can conclude that in order to generate the response of the mutual uncertainty function, it is necessary to obtain the result of multiplying the inverted and conjugate reference signal, the spectral characteristics of the input implementation, an array of two-dimensional exponentials, dividing the result of multiplication by the generated energy spectral characteristic of the reverberation:

$$R\left(t_{\mathrm{one}},t,f_{\mathrm{one}},f\right)=\overline{s\left(-t_{\mathrm{one}}\right)}Y\left(f_{\mathrm{one}}\right)\exp \left(i2\pi f{t}_{\mathrm{one}}\right)/N\left(f_{\mathrm{one}},t\right)$$

and applying to the result of dividing R (t ₁ , t, f ₁ , f) the inverse and direct Fourier transforms in the variables f ₁ , t ₁ .

Thus, the use of only multiplication operations and fast algorithms for calculating Fourier transforms to calculate the signal uncertainty function taking into account the reverberation noise allows us to perform calculations more efficiently than calculating the mutual uncertainty function in accordance with the algorithm written by formula (4).

The method for calculating the signal uncertainty function taking into account reverberation noise includes the following operations:

1. Calculation of the Fourier spectrum Y (f ₁ ) of the adopted realization y (t ₁ ) and zeroing the negative frequencies (converting it to the spectrum of the analytical signal): Y _A (f ₁ ) = Y (f), for f> 0 and Y _A ( f ₁ ) = 0 for f≤0.

2. The formation (or extraction from the memory of a previously calculated) two-dimensional array of exponentials E (f, t ₁ ) = exp (i2πft ₁ ).

3. The formation (or extraction from the memory of a pre-simulated) spectral density of the reverberation N (f ₁ , t).

эталонного сигнала s(t₁).4. Integrated pairing and reflection from zero $$\overline{s\left(-t_{\mathrm{one}}\right)}$$

reference signal s (t ₁ ).

, экспонент Е(f, t₁) и сформированной энергетической спектральной характеристикой реверберации N(f₁, t).5. Multiplication of the conjugate reference signal $$\overline{s\left(-t_{\mathrm{one}}\right)}$$

, exponent E (f, t ₁ ) and the generated energy spectral reverberation characteristic N (f ₁ , t).

6. The inverse two-dimensional Fourier transform with respect to t ₁ and f ₁ :

. $$R\left(t,f\right)=F_{f_{\mathrm{one}}}^{-\mathrm{one}}{F}_{t_{\mathrm{one}}}\left(\overline{s\left(-t_{\mathrm{one}}\right)}\frac{Y\left(f_{\mathrm{one}}\right)}{N\left(f_{\mathrm{one}},t\right)}\exp \left(i2\pi f{t}_{\mathrm{one}}\right)\right)$$

.

):7. Quadratic detection of the result of the inverse two-dimensional Fourier transform (calculation of the square of the module $${\left|R\left(t,f\right)\right|}^2$$

):

$$\Theta \left(t,f\right)={\left|F_{f_{\mathrm{one}}}^{-\mathrm{one}}F{t}_{\mathrm{one}}\left(\overline{s\left(-t_{\mathrm{one}}\right)}\frac{Y\left(f_{\mathrm{one}}\right)}{N\left(f_{\mathrm{one}},t\right)}\exp \left(i2\pi f{t}_{\mathrm{one}}\right)\right)\right|}^2.$$

Operations 2-5 do not require an input implementation, and, therefore, can be carried out in advance, and the calculation results are stored in read-only memory (ROM).

The use of additional compared with the prototype operations for signal detection in the presence of the Doppler effect and reverberation interference allowed to obtain positive effects, which include increasing the noise immunity of signal detection, increasing the efficiency of calculating the two-dimensional response of a matched filter.

To verify the operation of the proposed method, modeling was performed in the MathCad system. The simulation result without taking into account the effect of reverberation noise is presented in figure 1, and taking into account the influence of reverberation noise in figure 2.

The proposed method of coordinated filtering under the influence of reverberation noise allows to obtain a gain in noise immunity up to 6 dB.

2. Device for quickly calculating the function of signal uncertainty taking into account reverberation interference

A device that implements the proposed method for detecting signals against a background of reverberation noise is shown in Fig.3. The device contains the following blocks:

1) block 1 - analog-to-digital Converter (ADC);

2) block 2 - recirculator;

3) block 3 - FFT calculator,

4) block 4 - shaper analytical signal (device zeroing negative frequencies),

5) block 5 - ROM,

6) block 6 - complex multiplier,

7) block 7 - calculator inverse two-dimensional FFT,

8) block 8 - calculator square module,

9) block 9 - control device.

Block analog-to-digital Converter 1 is intended to represent the adopted implementation in digital form.

The recirculator block 2 is designed to store the output samples of the ADC (block 1).

The Fast Fourier Transform Unit (FFT) 3 is designed to find the signal spectrum and is widely used in digital signal processing [15].

The analytical signal generating unit 4 is intended for zeroing the FFT samples, the numbers of which are more than half the sample length.

Permanent memory unit (ROM) 5 is designed to store an array of values of the results of multiplication of the complex conjugate reference process, an array of exponentials and the spectral density of the reverberation noise.

The complex multiplication block 6 is designed to multiply the spectrum samples of the adopted implementation with the values stored in ROM.

The inverse fast two-dimensional Fourier transform (FFT) block 7 is designed to find signal samples in the time domain and is widely used in digital signal processing [16].

Block calculator square module 8 is designed to raise to a power of 2 values of samples from the output of block 7.

The block of the control device 9 is designed for synchronous operation of all blocks.

The principle of operation of the device is as follows. The implementation of the input process x (t) is input to the ADC (block 1) with a frequency

discretization satisfying the requirements of the Kotelnikov theorem:

. $$f_{\partial }=\frac{\mathrm{one}}{\Delta t_{\partial }}\ge 2f_{\mathrm{at}}$$

.

. Сформированная, текущая дискретная выборка входного процесса s(n) поступает на вход вычислителя БПФ (блок 3), с выхода которого комплексный спектр S(n) поступает на вход блока формирования аналитического сигнала (блок 4), с выхода которого поступает на вход комплексного перемножителя (блок 6), на другой вход которого поступает вычисленный заранее аналитический эталонный сигнал, хранящийся в ПЗУ (блок 5). Результат перемножения поступает на вход вычислителя обратного двухмерного БПФ (блок 7). С выхода вычислителя обратного двухмерного БПФ (блок 7) результат поступает на вход вычислителя квадрата модуля (блок 8), выход которого является выходом устройства.From the output of the ADC (block 1), discrete samples are fed to the input of the recirculator (block 2), where the current discrete sample s (n) with the length of N-samples is generated and updated with each new sample. The sample length N is determined by the duration of the emitted signal and the sampling interval: $$N=\frac{T_S}{\Delta t_{\partial }}$$

. The generated, current discrete sample of the input process s (n) is fed to the input of the FFT calculator (block 3), from the output of which the complex spectrum S (n) is fed to the input of the analytical signal generating unit (block 4), from the output of which goes to the input of the complex multiplier (block 6), the other input of which receives the calculated in advance analytical reference signal stored in the ROM (block 5). The result of the multiplication is fed to the input of the inverse two-dimensional FFT calculator (block 7). From the output of the inverse two-dimensional FFT calculator (block 7), the result is fed to the input of the module square calculator (block 8), the output of which is the output of the device.

The control device (block 9) synchronizes the operation of the analog-to-digital converter (block 1), the recirculator (block 2), the fast Fourier transform calculator block (block 3), the analytical signal generation block (block 4), ROM (block 5), complex a multiplier (block 6), an inverse two-dimensional FFT calculator (block 7), a module square calculator (block 8).

операций умножения [15]).To implement this method of quickly calculating the signal uncertainty function taking into account reverberation noise, one direct FFT operation and one two-dimensional inverse FFT operation are required (respectively $$\frac{N}{2}{\log }_{2}N+\frac{NM}{2}{\log }_{2}NM$$

multiplication operations [15]).

Literature

1. Kelly. Radar measurement of range, speed and acceleration, Foreign electronics (NR), N2, 1962. - P.35.

2. Patent N 4282589 USA, 1981, The correlation method of measuring range.

3. Patent N 3938147 USA, 1976, FM Doppler range measuring system.

4. Application N 1482816 United Kingdom, Method and device for measuring Doppler frequency shift.

5. Application N 56-41953 Japan, 1981, a Method and apparatus for measuring distance using continuous-wave radar with FM.

6. Kramer. Permissible speed and acceleration detuning in highly sensitive broadband correlation sonars with linear FM, TIIER, t.55, N 5, 1967. - C.3.

7. Burdick B.C. Analysis of sonar systems. L., Shipbuilding, 1988 - S.329-333.

8. Kibler. KEVORT - device for optimal processing of a burst radar signal taking into account the acceleration of targets, ZR N, 1968. - P.27-33.

9. AC No. 537315 (USSR) of 11.30.76. A method for determining the speed of a vessel relative to the bottom.

10. Application N 2605933 Germany, a Method of measuring distance and speed, based on the use of pulsed Doppler radar.

11. Kramer. Permissible detuning of speed and acceleration in highly sensitive broadband correlation sonars with linear FM. TIIER, t.55, N 5, 1967. - C.3.

12. Shmarev E.I. et al. Optical calculation of the signal uncertainty function (review). ЗР N 10, 1981. - С.41-43.

13. Burdick B.C. Analysis of sonar systems. - L .: Shipbuilding, 1988 - Pages. 191-194.

14. Kelly, Wischner. Theory of consistent filtering of targets moving accelerated at high speeds. ZR N 10, 1965. - P.38.

15. The use of digital signal processing. / Ed. Oppenheim E., - M: Mir, 1980 .-- P.284, 417-418.

16. Mirsky G. Electronic measurements. - M .: Radio and communications, 1986. - S.126-140. A.S. N 832490 (USSR) from 05/28/81. Spectrum analyzer.

Claims (1)

A device for calculating the signal uncertainty function taking into account reverberation noise, comprising an analog-to-digital converter, the input of which is input implemented, and the output of which is connected to the input of the recirculator, the output of which is connected to the input of the fast Fourier transform computer, the output of which is connected to the first input of the multiplication unit , characterized in that it is additionally introduced: a unit for zeroing negative frequencies, the input of which is the output of the computer of the fast Fourier transform, and the output with one with a first input of the multiplication unit; read-only memory, the output of which is connected to the second input of the multiplication unit, the output of which is the input of the calculation unit of the two-dimensional inverse fast Fourier transform, the output of which is connected to the input of the square calculator of the module, the output of which is the output of the device; a control device whose outputs are connected to the control inputs of an analog-to-digital converter, a fast Fourier transform calculator, a multiplier, a two-dimensional inverse fast Fourier transform calculator, a square module calculator.

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