RU2690317C1 - Polyharmonic signal detection method - Google Patents

Abstract

FIELD: physics.SUBSTANCE: present invention relates to hydroacoustics, specifically to methods of detecting a polyharmonic signal on a background of additive interference. Result of the present invention is high noise-immunity of the polyharmonic signal detector by more correct consideration of the Doppler effect namely, its broadband signal compression (stretching) properties. Invention is based on formation of a filter with frequencies arranged in accordance with a logarithmic law.EFFECT: such polyharmonic signals are approximants of a hyperbolic signal but differ by simple signal and reception, since they do not require broadband receivers, since each component can be emitted and received separately in component.1 cl, 5 dwg

Description

The present invention relates to the field of underwater acoustics, namely to methods for detecting a polyharmonic signal in the background of additive interference.

As it is known, the main task of detecting hydroacoustic signals is to make a decision about the presence or absence of a useful signal from an object in the observed input process [1-4]. This is a complex task that places the highest demands on the receiving system, since signal detection usually occurs with minimal signal-to-interference ratio (SIR). The decision on the presence of a signal is made by exceeding the receiver’s response to a set threshold selected based on one of the statistical criteria for given probabilities of correct detection and false alarm.

Currently, to solve this problem, the most widespread are complex signals, which, compared to simple signals, have a more complex structure and, therefore, their description is carried out in a functional space. To describe harmonic signals, it is enough to know a numerical vector characterized by amplitude (A), frequency (ω ₀ ), phase (ϕ), then to describe a complex signal, the concept of a complex spectrum is introduced as a function of frequency, which includes the amplitude spectrum and phase spectrum.

Complicated broadband signals in underwater acoustics allow us to solve the problem of good resolution in speed and range, but the generation of such signals, even taking into account digital methods, is a rather complicated procedure, so the use of polyharmonic (multi-frequency) signals seems promising.

Analysis of polyharmonic signals shows that their use is associated with the generation of harmonic signals of different frequencies and radiation of the same duration. The sum of these harmonics allows you to get complex signals that implement a good resolution in range and speed. FIG. one

The main disadvantage of such signals is that the kinematics of the objects being located leads to the compression of such a spectrum, and since the receiving device is designed to shift individual harmonics, in general, the Doppler effect leads to large energy losses due to the mismatch of the mathematical model of the Doppler effect and the processing tool.

The description of such a signal is formally reduced to numerical vectors including (amplitude (A), frequency (ω ₀ ), phase (ϕ)) harmonic components [1, 5, 6].

A known method for detecting narrow-band noise with discrete components of a PSD is, in fact, a multichannel power receiver (prototype) [1, p. 92-95]. This method is a sequential execution of operations: multichannel narrowband bandpass filtering (to form separate frequency channels), quadratic detection, integration and comparison with a threshold.

The proposed method for detecting wideband polyharmonic signals is that before performing the procedures of multi-channel narrowband bandpass filtering (to form separate frequency channels), quadrature detection, integration and comparison with a threshold (in each frequency channel), the frequency setting is performed according to the narrowband ratio:

We also require that for each component of the polyharmonic signal the relation be satisfied

We define the last relation as the "condition of equal-backwardness". Next, we determine the number of components of the polyharmonic signal, which occupies a certain frequency band.

We have:

Further:

(каждая отдельная компонента является узкополосным сигналом).The last relation took into account the fact that

(each individual component is a narrowband signal).

Similarly, the intervals between the components of a polyharmonic signal:

, то из последнего соотношения нетрудно получитьBecause

then it is not difficult to get from the last relation

An illustration of component frequency and bandwidth dependencies is shown in FIG. 1., where a is the dependence of the frequency of a component on its number i, b is the dependence of the bandwidth of a component on its number i.

The graphs show a monotonous increase and frequency of the PS component and the corresponding spectral bands. What generally confirms the fact that the wider the spectrum of PS, the more components it contains.

We double the frequency, the sampling interval will be halved. Since T = n⋅Δt, the duration of the signal T will decrease accordingly.

The number of degrees of freedom of a harmonic signal is twice the number of its periods, so the duration of the signal with constant n will vary.

A temporal representation of the polyharmonic signal standing out of 4 harmonics is shown in FIG. 2 - where the time representation of a polyharmonic signal consisting of 4 harmonics is presented

FIG. 3 shows an illustration of the module of the complex spectrum of a polyharmonic signal consisting of 4 harmonics.

Simulation conditions: number of samples 1024; the number of degrees of freedom is 30; FFT (Fast Fourier Transform) FFT execution base - 512.

In general, the simulation analysis shows that with an increase in the number of components, they become closer and closer to each other, and in the time representation it becomes more and more like a hyperbolic signal. Consequently, its properties also approach the properties of a hyperbolic signal.

It should be noted that:

- generation of a polyharmonic signal is simpler than, for example, hyperbolic or any other type of complex signals;

- by varying the start of generation and the amplitude of each component, it is possible to obtain signals that are quite complex in their structure, possessing the required qualities;

- the amplitude and phase spectra can be described using the vectors of numbers, not functions, which greatly simplifies the analysis of polyharmonic signals;

- it seems promising to use PS when implementing adaptive signal processing methods.

When processing signals, in which the indicator narrowband is determined by the following expression:

This definition of narrowband can be set on the class of multiplicative or hyperbolic signals [9]. Next, from the expression (5) we get:

Denote the total signal bandwidth as:

тогда получим:Set

then we get:

For example, when ƒ ₁ = 100, ΔFm = 1000, k = 0.1, we get N≈30.

Those. the number of multiplicative components is 30. By the multiplicative component we mean a hyperbolic harmonic. Thus, a class of polyharmonic multiplicative signals can be introduced. In general, you can see that such signals have all the properties of hyperbolic signals, but they will have good resolution in speed and acceleration of the target, which the hyperbolic signal cannot “boast”. Complex multiplicative signals make it possible to obtain good resolution and range, which makes research in this direction promising.

For the sake of correct frequencies, let’s take S as the area between the frequencies

The area of the figure can be found by the formula

S = constant

Find the connection between the frequencies using the formula (12)

ƒ _{i + 1} = ƒ ₁ ⋅exp {S}

The frequency difference is determined by the expression

Δƒ ₁ = ƒ _{i + 1} -ƒ ₁ = ƒ ₁ ⋅exp {S} -ƒ ₁

A hyperbolic illustration of the arrangement of the PS components is presented in FIG. 4. The narrowband coefficient is equal to

- гиперболический синус;

- hyperbolic sine;

так как число каналов N должно быть большим, применяя замечательный предел ln[1+x]≈х, при

получаем замечательное соотношениеGiven that 5 is significantly less than 1,

since the number of channels N must be large, applying the remarkable limit ln [1 + x] ≈x, with

we get a wonderful ratio

Thus, the narrowband condition is related to the equality of the areas under the hyperbolic curve.

Determine the number of channels N. To do this, find the total bandwidth of the polyharmonic signal ΔFm:

нетрудно получить:Further, using ln [1 + x] ≈х, with

easy to get:

For example, when ƒ ₁ = 100, ΔFm = 1000, k = 0.1, we get N≈48.

As can be seen, the number of channels under the same initial conditions is somewhat different from each other. This is due to the fact that the definition of narrowband differ among themselves for different classes of signals.

In active sonar due to mutual kinematics of the source and receiver, the most important factor to be taken into account when implementing optimal reception is the Doppler effect, in the prototype and also in all modern means, as a rule, the Doppler effect is taken into account by filtering through Doppler channels and the true The Doppler effect is not a frequency shift, but a compression (extension) of the spectrum signal. For narrowband signals, this does not play a significant role, but the higher the ratio of the band to the signal frequency, the stronger the negative effect of substitution of compression by a shift will be manifested. In [4, 5], it was shown how the signal-to-noise ratio at the output drops significantly as the signal bandwidth increases and the Doppler effect shift model is observed. In works [6], a broadband hyperbolic signal is used, which is invariant to the Doppler effect, but its generation and emission present considerable difficulties in practical implementation, which makes its use problematic.

In the proposed method it is proposed to use its approximation by a polyharmonic signal whose frequencies are logarithmically ”and instead of the frequency band of the filter matched with the bands of the emitted signal instead of the HFM signal. Since the frequencies are arranged according to the logarithmic law, the Doppler effect is taken into account exactly as compression (tension), and not shift. In essence, the additive shift is replaced by the logarithmic ln (αω) = lnω + lnα, accurate accounting of the Doppler effect can increase the noise immunity to the potential since the exact Doppler model is taken into account, in general, the device implementing this method can be represented by the diagram of FIG. five.

List of used sources

1. A.N. Yakovlev, G.P. Short range sonars. L .: Shipbuilding, 1983. 200 p. (Prototype, pp. 92-95).

2. Tikhonov V. I. Optimal reception of signals. M .: Radio and communication, 1983, 320 p. (Analog, p. 80-87).

3. G. Van-Tris. The Theory of Detection, Evaluation, and Modulation, Vol. 1, Moscow: Sov. Radio, 1972, 744 p.

4. Van Tris, T. The Theory of Detection, Evaluation, and Modulation, Vol. 3, Moscow: Sov. Radio, 1977, 661 p.

5. UrikR. Basics hydroacoustics. L .: Shipbuilding, 1978,446 p.

6. Zaraysky V.A., Tyurin A.M. The theory of sonar. L .: BMA, 1975, 604 p.

7. Bolgov V.M., Plakhov DD, Yakovlev V.E. Acoustic noise and interference on ships. L .: Shipbuilding, 1984, 192 p.

8. Olshevsky V.V. Statistical methods in sonar. L .: Shipbuilding, 1983, 280 p.

9. Butgrsky E.Yu. Signal uncertainty function on a transform group. Information and space. 2008. №3. with. 31-39.

Claims (1)

The method of detecting a broadband signal, containing the operations of forming a broadband signal and its reception, including operations of multi-channel matched filtering, threshold comparison and deciding on the presence or absence of a signal in the adopted implementation, characterized in that in order to increase the efficiency of signal processing under the conditions of the Doppler effect by using The exact model additionally includes the operation of forming a special broadband signal, namely a polyharmonic signal, in which The ratio of each frequency component to its band is a constant value that corresponds to the operation of generating a polyharmonic signal that approximates a hyperbolic signal that is invariant with respect to the Doppler effect, a multi-channel matched filtering operation on a logarithmic frequency scale.

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