RU2497141C1 - Method for multi-signal direction-finding of radio sources at same frequency for circular antenna system - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: speed of direction-finding is increased using an efficient algorithm for identifying radio signal parameters. In particular, bearings are obtained in a circular antenna system via preliminary input of a system of equations into the computer, said system being derived for a specific pre-measured circular antenna system and at given values of azimuths θk in given ranges: $$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=1}^K{\displaystyle \sum _{l=1}^N(u_i\exp (j{\alpha }_i){\xi }_i^{\cos {\gamma }_m+tg{\theta }_{il}\sin {\gamma }_m})}};$$

m∈[1,M] ξ_i=exp(j(2πR/λ)cosθ_icosβ_i) u_iexp(jα_i) is the complex amplitude of the signal of the i-th radio source; R is the radius of the antenna system; λ is the wavelength of the signal emitted by the radio source; α_i is the initial phase of the i-th signal; γ_m is the angle between a line passing through the centre of the antenna system and the m-th element of the antenna system and the line of origin of the azimuths; M is the number of elements (dipoles) of the circular antenna system; K is the number of radio sources; N is the number of given azimuth samples; at the output of the solution of said system of equations, values of parameters of amplitudes u_iexp(jα_i) and values ξ_i are obtained, which, along with given values θ_i, are transmitted to the input of the unit for calculating elevation bearings β_i through an arccosine function based on the condition: ξ_i=exp(j(2πR/λ)cosθ_icosβ_i).

EFFECT: high rate of direction-finding when receiving radio signals of multiple radio sources operating at the same frequency using circular antenna systems consisting of low-directivity elements.

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Description

The invention relates to radio engineering, in particular to direction finding. Multi-signal direction finding of radio emission sources (IRI) takes place in the process of monitoring the electronic environment in the case of multipath propagation of radio waves, exposure to deliberate and unintentional interference, signal reflections from various objects and layers of the atmosphere.

The direction finding problem is incorrect. Most methods of multi-signal direction finding at a single frequency described in the literature rely on statistical methods for testing hypotheses, on the maximum likelihood method, superresolving methods (for example, MUSIC), etc. However, the IR direction finding problem cannot be solved reliably using statistical methods, the reliability of the result of which is determined by the accuracy of the obtained estimates of signal parameters; nor by the least squares method (OLS) due to nonlinearity and poor conditionality of the system of equations being solved; nor by superresolving methods that give acceptable results only at high signal to noise ratios and do not provide the resolution of IRI, which have similar bearings.

All methods of direction finding have much in common: the radio signals of the sources are received by means of an antenna system (AS), complex signal amplitudes are obtained at the outputs of the antenna elements (amplitude-phase distribution (AFR) vector), and the values of the signal parameters are determined from these data. The difference is in what algorithms process the signals recorded by the antenna system.

Known methods of direction finding with high resolution [1, 2].

In the patent [2], the problem is solved using l _P -regularization. This method requires a lot of time to process the signal, which does not allow it to be applied in an operational environment, and by qualified operators, because in the method it is necessary for each measurement to set the values of the regularization parameter and the exponent of the regularizing (functional. There are no unambiguous approaches for their selection.

Therefore, as a prototype, the method described in the patent [1] is adopted: The method of multi-signal direction finding of radio sources at a single frequency includes receiving a multi-beam signal via a multi-element speaker, synchronously converting an ensemble of received signals depending on the time and number of the drug element into digital signals, the conversion of digital signals into a signal-vector AFR y (u, θ, β), which describes the distribution of amplitudes and phases on the elements of the AS.

The prototype method has the following disadvantages:

- designed for linear rather than circular speakers;

- for a circular AS, it is not possible to reduce the problem to a system of algebraic equations in which unknown variables have integer exponents;

- it is impossible to exclude unknown signal amplitudes at the first stage of solving the problem, thereby separately determining the amplitudes of the signals and bearings of the emitters;

- additional operation is not always required for the separate determination of azimuthal θ and elevational β bearings.

These shortcomings do not allow the use of the prototype in real conditions for which speakers that are more compact and widespread than linear speakers.

The proposed method is free from these disadvantages and is a parametric method of multi-signal direction finding at a single frequency. Signals are considered deterministic, subject to additive interference, the parameter estimates of which are to be determined. A circular speaker consisting of several weakly directed elements (vibrators) is considered as an AS. One of the vibrators is selected as the phase center (the point with respect to which the phases of the signals arriving at the elements of the antenna system are measured).

They set the task of determining the following parameters present on the airwaves:

- amplitudes (power) of the emitted signals;

- azimuthal and elevation bearings of Iran,

- exclusion of an additional operation for separate determination of azimuthal θ and elevation β bearings,

- to increase the speed of performing a sequence of simple mathematical operations that do not require large computational costs.

The objective of the invention is to reduce the processing of real IRI signals to the simplest formulas in order to minimize the computational processing time for determining the bearing.

In the invention, the problem is solved as follows: a method of multi-signal direction finding of radio emission sources (IRI) at a single frequency includes receiving a multi-beam signal using a multi-element speaker, synchronously converting an ensemble of received signals, depending on the time and number of the speaker element, into digital signals, converting digital signals into signal-vector of amplitude-phase distribution (AFR) y (u, θ, β), which describes the distribution of the amplitudes u and phases determining θ and β on the AC elements - azimuthal and elevation bearings of the IRI accordingly. In this case, bearings are obtained in a circular AS by first introducing into the calculator a system of equations for the m-th element of the AS formed for a specific pre-dimensioned circular AS (and with given values of the vector in azimuth bearings in a given range):

; m∈[1,M] $$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K{\displaystyle \sum _{l=\mathrm{one}}^N(u_i\exp (j{\alpha }_i){\xi }_i^{\cos {\gamma }_m+tg{\theta }_{il}\sin {\gamma }_m})}}$$

; m∈ [1, M]

where ξ _i = exp (j (2πR / λ) cosθ _i cosβ _i );

u _i exp (jα _i ) is the complex amplitude of the signal of the i-th IRI;

R is the radius of the speaker;

λ is the wavelength of the signal emitted by the IRI;

α _i is the initial phase of the i-th signal;

γ _m is the angle between the line drawn through the center of the AS and its m-th element of the AS, and the reference line of azimuth bearings;

M - the number of elements (vibrators) of a circular speaker;

K is the number of different IRI signals (or the number of IRI);

N is the number of specified discrete azimuth bearing;

then, at the output of the solution of the indicated system of equations, the values of the amplitude parameters u _i exp (jα _i ) and the values of ξ _i are obtained, which, together with the given values of θ _i, are input to the block for calculating elevation bearings β _i through the arccosine sanction from the condition: ξ _i = exp ( j (2πR / λ) cosθ _i cosβ _i ).

The proposed method is as follows through operations:

1. Only the range of azimuth bearings θ is specified, in which the emitted signals can be, for example, from 0 to 360 degrees. The vector of these values or a system of such vectors is one of the characteristics of a circular AS and is formed prior to measurements.

2. A system of algebraic equations of dimension M by N is formed, M is the number of elements AC, N is the number of discrete azimuth bearings in the selected range (usually this range is 360 °, then in the simplest case with a constant step Δθ of change in the azimuth bearing θ number of discrete N = 360 / Δθ). AC equations have the following form:

$$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K{\displaystyle \sum _{l=\mathrm{one}}^N(u_i\exp (j{\alpha }_i){\xi }_i^{\cos {\gamma }_m+tg{\theta }_{il}\sin {\gamma }_m});m\in [\mathrm{one,}M](\mathrm{one})}}$$

This system of equations is also one of the characteristics of a circular speaker and is formed prior to measurements.

3. Physical radio signals from K IRI are received in real time by means of a circular speaker system containing M elements (vibrators).

4. Get the complex amplitudes of the signals at the outputs of the antennas (vector AFR). The mth element of the AFR vector has the form

$$y_m={\displaystyle \sum _{i=\mathrm{one}}^K{u}_i\exp \left\{j{\varphi }_m({\theta }_i,{\beta }_i)\right\}+n_m(2)}$$

where K is the number of IRI, u _i is the amplitude of the signal of the i-th IRI, φ _m (θ _i , β _i ) is the phase of the signal of the i-th IRI on the m-th AC element (vibrator), depending on the azimuthal and elevation bearings i- Iran θ _i and β _i, respectively, n _m is the noise occurring on the m-th element (vibrator), including the noise of the world background and equipment.

5. The complex amplitudes of the signals at the outputs of the antennas (AFR vector) are supplied to the calculator through the M-channel analog-to-digital converter (ADC), then the AFR recovery unit, that is, obtaining discrete complex values of the signal envelopes.

The procedure for determining the parameters in the parameter identification block is carried out on the basis of synchronous measurement of the outputs of the elements of the M-element circular AS at time t (note: it is possible to increase the number of equations in system (1) to increase the accuracy of the solution by taking into account the values of the AFR vector obtained at different times )

The output y _{m of the} m-th element of a circular speaker has the form

$$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K{u}_i\exp (j(2\pi R/\lambda )\cos ({\theta }_i-{\gamma }_m)\cos {\beta }_i+{\alpha }_{{}^i})}(3)$$

where u is the vector of amplitudes (powers) of the signals emitted by the IRI;

θ, β are the vectors of the azimuthal and elevation bearings of the IRI, respectively;

R is the radius of the speaker;

λ is the wavelength of the signal emitted by the IRI;

α _i - the initial phase of the i-th signal (i-th IRI);

γ _m is the angle between the line drawn through the center of the AS and its m-th element, and the reference line of azimuth bearings.

We apply the simplest transformations to (3)

. $$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K{y}_i\exp (j{\alpha }_i)\exp (j(2\pi R/\lambda )\cos ({\theta }_i-{\gamma }_m)\cos {\beta }_i)}$$

.

We denote $${\xi }_i=\exp (j(2\pi R/\lambda )\cos ({\theta }_i)\cos {\beta }_i).(\mathrm{four})$$

Then ((2πR / λ) cos (θ _i -γ _m ) cosβ _i ) / ((2πR / λ) cos (θ _i ) cosβ _i ) = cosγ _m + tgθ _i sinγ _m .

Hence ((2πR / λ) cos (θ _i -γ _m ) cosβ _i ) = ((2πR / λ) cos (θ _i ) cosβ _i ) (cosγ _m + tgθ _i sinγ _m )

or

$$\begin{array}{l}\exp (j(2\pi R/\lambda )\cos ({\theta }_i-{\gamma }_m)\cos {\beta }_i)=\\ {(}^{\exp }={\xi }_i^{\cos {\gamma }_m+tg{\theta }_i\sin {\gamma }_m},t.e.\end{array}$$

$$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K(u_i\exp (j{\alpha }_i)={\displaystyle \sum _{i=\mathrm{one}}^K{u}_i\exp (j{\alpha }_i){\xi }_i^{\cos {\gamma }_m+tg{\theta }_i\sin {\gamma }_m};m\in [\mathrm{one,}M],(5)}}$$

A _i = u _i exp (jα _i ) is the complex amplitude of the i-th signal.

для каждого поступающего сигнала, например, θ∈[0,360], Δθ=1 (тогда N=360/1=360). Получаем систему, в которой для каждого i-го сигнала задается набор значений θ_il:We obtained a system of algebraic equations (5). To solve it, a grid in θ is formed in the calculator $$(\theta \ne \frac{\pi }{2}\pm n\pi )$$

for each incoming signal, for example, θ∈ [0.360], Δθ = 1 (then N = 360/1 = 360). We obtain a system in which for each ith signal a set of values θ _il is set:

$$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K{\displaystyle \sum _{l=\mathrm{one}}^N(u_i\exp (j{\alpha }_i){\xi }_i^{\cos {\gamma }_m+tg{\theta }_{il}\sin {\gamma }_m});m\in [\mathrm{one,}M].(6)}}$$

6. The introduced transformation (4) allows us to divide the determination of signal parameters into two steps, which ensures a more stable solution to noise. The solution process consists of two steps: first, from system (6) we find estimates of the complex amplitude u _i exp (jα _i ), θ _i, and ξ _i . Knowing ξ _i and θ _i , by definition (4) we find the elevation bearing β _i by means of the trigonometric function arccosine.

7. The previously entered system of equations (6) enters the calculator for given azimuth values θ _il and the AFR vector. At the output of the calculator, the complex amplitude u _i exp (jα _i ) and the values of θ _i and ξ _i are obtained. The values θ _i and ξ _i are supplied to the calculation unit of the elevation bearing β _i according to definition (4).

8. The variances of the obtained estimates are defined as the variances of the function of a random argument. Based on the obtained dispersions, the corresponding confidence intervals are constructed [3].

The operation of the method is illustrated in Fig.1 - structural diagram of the direction finding device.

The above method has a high speed, because does not contain operations that require large computational costs.

Example

.A circular speaker is set with two elements (vibrators) spaced 30 degrees apart, that is, γ _i = 0; $${\gamma }_2=\frac{\pi }{6}$$

.

We write the first and second equations for system (6) for two signals. In the example, we reflect the fact that for each signal the series of values of the azimuthal bearing θ can be different (for example, over the entire 360 degree interval, the discreteness of the azimuthal bearing change can be different - from fractions to several degrees):

$$\begin{array}{l}{y}_{\mathrm{one}}(u,\theta ,\beta )=u_{\mathrm{one}}\exp (j{\alpha }_{\mathrm{one}}){\xi }_{\mathrm{one}}^{\cos 0+tg{\theta }_{\mathrm{eleven}}\sin 0}+...+u_{\mathrm{one}}\exp (j{\alpha }_{\mathrm{one}}){\xi }_{\mathrm{one}}^{\cos 0+tg{\theta }_{\mathrm{1,360}}\sin 0}+\\ +u_2\exp (j{\alpha }_2){\xi }_2^{\cos 0+tg{\theta }_{2.1}}{}^{\sin 0}+...+u_2\exp (j{\alpha }_2){\xi }_2^{\cos 0+tg{\theta }_{\mathrm{2,360}}\sin 0}\end{array}$$

$$\begin{array}{l}{y}_2(u,\theta ,\beta )=u_{\mathrm{one}}\exp (j{\alpha }_{\mathrm{one}}){\xi }_{\mathrm{one}}^{\cos \frac{\pi }{6}+tg{\theta }_{\mathrm{eleven}}\sin \frac{\pi }{6}}+...+u_{\mathrm{one}}\exp (j{\alpha }_{\mathrm{one}}){\xi }_{\mathrm{one}}^{\cos \frac{\pi }{6}+tg{\theta }_{\mathrm{1,360}}\sin \frac{\pi }{6}}+\\ +u_2\exp (j{\alpha }_2){\xi }_2^{\cos \frac{\pi }{6}+tg{\theta }_{2.1}\sin \frac{\pi }{6}}+...+u_2\exp (j{\alpha }_2){\xi }_2^{\cos \frac{\pi }{6}+tg{\theta }_{\mathrm{2,360}}\sin \frac{\pi }{6}}\end{array}$$

For given values of y ₁ (u, θ, β), ..., y ₂ (u, θ, β) and θ, solving the reduced system of equations, we find estimates of the desired parameters. Note that for a specific circular AS, the system of equations (6) (excluding the column y ₁ (u, θ, β), ..., y ₂ (u, θ, β) will be compiled in advance.

For a new measurement (observation) of the same AS, it is enough to introduce a new column of measured values y ₁ (u, θ, β), ..., y ₂ (u, θ, β). And then, in the process of the system’s operation, only a specific measurement result for all elements (vibrators) of circular AC is introduced into the computer — only the left side of equations (6), that is, the values y ₁ (u, θ, β), ..., y ₂ (u, θ, β) and θ.

Thus, to obtain bearings it is sufficient to perform a sequence of simple mathematical operations that do not require large computational costs.

Information sources

1. Greshilov A.A. Patent RU 2380719, IPC G01S 5/04, publ. 01/27/2010.

2. Greshilov A.A., Plohuta P.A. Patent RU 2382379, IPC G01S 5/04, publ. 02/20/2010.

3. Greshilov A.A. Mathematical decision-making methods: Textbook for universities. - M.: Publishing House of MSTU. N.E. Bauman, 2006 .-- 584 p.

Claims (1)

A method of multi-signal direction finding of radio emission sources (IRI) at a single frequency, which includes receiving a multi-beam signal by means of a multi-element antenna system (AC), synchronously converting an ensemble of received signals depending on the time and number of an AC element into digital signals, converting digital signals into a signal the amplitude-phase distribution (AFD) vector y (u, θ, β), which describes the distribution of amplitudes and phases containing θ and β on the AC elements, the azimuthal and elevation bearings of the IRI, respectively, differing in m that receiving bearings carried in a circular speaker by prior administration of a computer system of equations generated for a particular pre obrazmerennoy circular speaker and for given values of azimuth bearings θ in predetermined ranges:
$$y_m(u,\theta ,\beta )={\displaystyle \sum _{i=\mathrm{one}}^K{\displaystyle \sum _{l=\mathrm{one}}^N(u_i\exp (j{\alpha }_i){\xi }_i^{\cos {\gamma }_m+tg{\theta }_{il}\sin {\gamma }_m})}}$$

; m∈ [1, M],
where ξ _i = exp (j (2πR / λ) cosθ _i cosβ _i );
u _i exp (jα _i ) is the complex amplitude of the signal of the i-th IRI;
R is the radius of the speaker;
λ is the wavelength of the signal emitted by the IRI;
α _i is the initial phase of the i-th signal;
γ _m is the angle between the line drawn through the center of the AS and its m-th element of the AS, and the reference line of azimuth bearings;
M - the number of elements (vibrators) of a circular speaker;
K is the number of different IRI signals (or the number of IRI);
N is the number of specified discrete azimuth bearing;
Further, at the output of the solution of the indicated system of equations, the values of the parameters of the amplitudes u _i exp (jα _i ) and the values of ξ _i are obtained, which, together with the given values of θ _i, are input to the block for calculating elevation bearings β _i through the arccosine function from the condition: ξ _i = exp ( j (2πR / λ) cosθ _i cosβ _i ).