RU2730051C1 - Radiation pattern recovery method - Google Patents

Abstract

FIELD: radio electronics.

SUBSTANCE: invention relates to radio electronics and can be used to extend the service life of radio complexes. In the method of reconstructing a radiation pattern (RP), determining

a function of model distribution of the field strength phase in a PAA aperture, at which the model radiation pattern –

coincides in the predetermined view sector (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂) with deformed RP PAA – ƒ_d(θ, ϕ). Based on results of comparison of

with F₀(x, y) – function of design distribution of field intensity in PAA aperture, phase corrections are determined and introduced into distribution of phase of intensity of electromagnetic field in aperture PAA, which provide forming ƒ_red(θ, ϕ) – reduced RP PAA, which in sector in review (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂) coincides with design RP – f₀(θ, ϕ). Disclosed is a special procedure for restoring the main lobe RP.

EFFECT: restoration of design RP flat PAA only on the basis of knowledge of design parameters of flat PAA and type of deformed RP.

1 cl, 2 dwg

Description

The invention relates to the field of electronics and can be used to extend the service life of radio complexes by restoring the directional patterns of the phased antenna arrays deformed during operation, which are part of these radio complexes.

Known invention is a method of compensating for deformations of directional patterns (DP) of phased antenna arrays (PAA) [1]. In the known method, the deformations of the antenna pattern are compensated for, caused by changes in the position of the radiating elements of the HEADLIGHTS during operation as a result of mechanical or temperature effects. The goal is to restore the PAA gain (KU) to its design value. With this method, for each antenna element, a certain value of the phase correction of the radiated field is randomly generated and set. With the help of a reference antenna, the value of the PA PAA obtained after phase correction is determined and compared with the design value. The iterative process is repeated in accordance with the genetic algorithm until the design value of the PA PAR is restored.

The disadvantages of the known invention include:

- the need to use an additional reference antenna to analyze the quality of the pattern recovery;

- this method restores only the magnitude of the gain at the radiation maximum, without taking into account such essential parameters of the reconstructed pattern as the direction of the pattern's main lobe, the width of the pattern's main lobe, the level of side lobes, etc.

Features of the present invention that match those of the analogue:

- determination and installation of compensating phase correction in the antenna elements, which ensures restoration of the design RP of the phased array.

где

- исходная энергетическая ДН антенны, λ_ij - множители Лагранжа, находят значения C_nm - коэффициентов Фурье разложения функции фазового распределения поля в плоской апертуре антенны Ф(х,у) и определяют Ф(х,у) по формуле

, где k - волновое число свободного пространства, l - максимальный линейный размер апертуры антенны. Реализуют Ф(х,у) в апертуре антенны, что обеспечивает формирование провалов в ДН в направлениях прихода помех.Known invention - a method of adaptive suppression of spatial interference [2] in which a method is proposed for converting the antenna pattern, the closest in its technical essence to the patented invention, which is adopted as a prototype of the present invention. In the known invention, a sequence of two-dimensional orthonormal polynomials P _nm (x, y) is constructed from ρ ₀ (x, y), a given function of the normalized amplitude distribution of the main polarization component of the electromagnetic field strength in the aperture of a flat PAA. For each direction of interference arrival (θ _ij , ϕ _ij ), where i is the number of the side lobe of the pattern, j is the number of the sector in the side lobe; minimizing the functionality

Where

- the initial energy antenna pattern, λ _ij - Lagrange multipliers, find the values of C _nm - the Fourier coefficients of the expansion of the phase distribution function of the field in the flat aperture of the antenna Ф (x, y) and determine Ф (x, y) by the formula

, where k is the wavenumber of free space, l is the maximum linear size of the antenna aperture. F (x, y) is implemented in the antenna aperture, which ensures the formation of dips in the pattern in the directions of interference arrival.

The disadvantages of the prototype include the fact that it does not consider the possibility of using the proposed method for converting the antenna pattern in the problems of restoring deformed antenna patterns.

Features of the present invention that match those of the prototype:

- using the representation of the phase distribution function of the field strength in the antenna aperture in the form of an expansion in a Fourier series in orthogonal polynomials P _nm (x, y);

- use of data on the design parameters of the antenna system and geometric parameters of the antenna aperture;

- determination and installation in the antenna aperture of the required phase distribution of the electromagnetic field, ensuring the formation of the required pattern.

The present invention, a method for recovering the directional pattern, solves the problem of restoring the design RP of flat PARs, the phase distribution of the field in the flat aperture of which is deformed during operation.

The technical result of the present invention is to ensure the restoration of the design RP of flat PAR. The problem of reconstructing the antenna pattern is solved only on the basis of knowledge of the design parameters of a plane PAA and the type of deformed pattern. When reconstructing the pattern, knowledge of the distorted phase distribution in the phased array aperture and the use of additional measuring equipment to control the parameters of the recovered pattern are not required. For radio complexes installed on spacecraft (SC), the invention makes it possible to extend the life of the spacecraft.

The essence of the patented method for recovering the directional pattern is illustrated by a description of examples of its implementation and drawings, which show:

FIG. 1. Scheme of a multi-element flat PAR.

FIG. 2. Comparison of design, deformed and reconstructed radiation patterns.

FIG. 1, fig. 2 introduced the following notation:

1 _r - antenna element, 2 _r - controlled phase shifter of the antenna element 1 _r , 3 - microwave splitter, 4 - control unit; 5 - design directional diagram f ₀ (θ, ϕ); 6 - deformed radiation pattern f _d (θ, ϕ); 7 - reconstructed directional pattern f _Voc (θ, ϕ).

The present invention has various implementations. The choice of a specific implementation of the present invention is due to the functional objectives, scope and conditions of its practical use.

1. A method for recovering the directional pattern, which ensures the restoration of the pattern in a given view sector of the pattern and includes the creation of a flat phased array, consisting of antenna elements 1 _r , controlled phase shifters 2 _r , microwave splitter 3 and control unit 4 (see Fig. 1).

For a flat PAR, the following are known: ƒ ₀ (θ, ϕ) is the design energy RP, where θ, ϕ are the spherical coordinates of the observation point; (θ ₀ , ϕ ₀ ) is the direction of the main lobe of the design energy BP; ƒ _d (θ, ϕ) is the deformed energy DP, which arose as a result of impacts on the PAA during operation; (θ _d , ϕ _d ) - direction of the main lobe of the deformed energy pattern; (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ) - sector of the DP survey, in which the design DP is restored; δ is the threshold value of the coefficient of mismatch between the design and reconstructed radiation patterns in the sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ); Ω (x, y) - the area of the aperture of the flat PAR; x, y - coordinates of a point in the plane of the phased array aperture; K is the total number of antenna elements; x _r , y _r - coordinates of the phase centers of the antenna elements numbered r, where r = 1, ..., K; Ф ₀ (x, y) is the design function of the distribution of the phase of the electromagnetic field strength in the phased array aperture; Ф ₀ (x _r , y _r ) - the values of Ф ₀ (x, y), which were installed in the aperture at the points of placement of the antenna elements numbered r when the HEADLIGHTS were put into operation, where r = 1, ..., K, ρ ₀ ( x, y) - design amplitude distribution of the electromagnetic field strength in the aperture; P _nm (x, y) is the set of orthonormal harmonics, where (n, m) are the harmonic numbers; λ is the working wavelength.

The set P _nm (x, y) is the orthonormal harmonics of the expansion of the function ρ ₀ (x, y) in the domain Ω (x, y), where (n, m) are the numbers of the harmonics, which are found by a well-known method [3].

The deformed pattern for PAA, which can be serviced at ground sites, is measured according to standard methods.

For the HEADLIGHTS installed on the spacecraft in operation, data on ƒ _d (θ, ϕ) are obtained during the processing of data from the fields of special ground-based meters (SPI), which make it possible to measure the signal values of the PAA SC-SPI radio lines in a wide range of values (θ, ϕ ) [5, 6, 7].

The size of the view sector of the DN - (θ ₁ θ ≤ ₂ , ϕ _{1 2} ) is set in accordance with the tasks at hand by the user of the HEADLIGHT, taking into account the fact that with an increase in the view sector the volume of computational procedures sharply increases.

- функцию модельного распределения фазы напряженности поля в апертуре ФАР, при котором модельная диаграмма направленности -

совпадает в секторе обзора (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂) с деформированной энергетической ДН ФАР - ƒ_д(θ,ϕ). По результатам сравнения

и Ф₀(х,у) определяют и вносят фазовые поправки в распределение фазы напряженности электромагнитного поля в апертуре ФАР, которые обеспечивают формирование ƒ_вос(θ,ϕ) - восстановленной ДН ФАР, которая в секторе обзора (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂) совпадаете f₀(θ,ϕ).When implementing the method for recovering the directional pattern, determine

is the function of the model distribution of the field strength phase in the phased array aperture, at which the model radiation pattern is

coincides in the viewing sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ) with the deformed energy RP of the HEADLIGHT - ƒ _d (θ, ϕ). By comparison

and Ф ₀ (x, y) determine and introduce phase corrections to the distribution of the phase of the electromagnetic field in the aperture of the HEADLIGHTS, which provide the formation of _ƒos (θ, ϕ) - the reconstructed pattern of the HEADLIGHTS, which in the survey sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ) match f ₀ (θ, ϕ).

During the implementation of the invention, the following operations are performed.

представляют в виде отрезка ряда Фурье

, где

, где

,

,

- коэффициенты ряда Фурье.

are represented as a segment of the Fourier series

where

where

,

,

are the coefficients of the Fourier series.

,

,

и минимальные значения М, N, при которых достигается требуемое совпадение

с ƒ_д(θ,ϕ) в секторе обзора (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂).The values sought are

,

,

and the minimum values M, N at which the required coincidence is achieved

with ƒ _d (θ, ϕ) in the viewing sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ).

,

используют то обстоятельство, что направление главного лепестка ДН задает

- линейная составляющая функции

.In determining

,

use the fact that the direction of the main lobe of the pattern

- linear component of the function

...

Therefore, in accordance with [4] from the system of equations:

,

где a ₁₁, b₀₁, b₁₁ - коэффициенты линейных ортонормированных гармоник Р₁₀(х,у)=a_11x+а₁₀, P₀₁(x,y)=b_11y+b_01x+b₁₀, и определяют функцию

.according to the known direction of the main lobe of the deformed pattern - (θ _d , ϕ _d ) find the coefficients

,

where a ₁₁ , b ₀₁ , b ₁₁ are the coefficients of linear orthonormal harmonics P ₁₀ (x, y) = a _11x + a ₁₀ , P ₀₁ (x, y) = b _11y + b _01x + b ₁₀ , and determine the function

...

модельную диаграмму направленности -

представляют в виде

In determining

model radiation pattern -

represent in the form

и фиксированных значениях М, N, функционал

, где

- величина комплексно сопряженная

, и последовательно увеличивая значения М, N, определяют минимальные значения

и

, где

при которых выполняется неравенство:

, где

. Неравенство:

является условием совпадения

с ƒ_д(θ,ϕ) в секторе обзора (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂) с заданной точностью. По известным

определяют функцию

.Minimizing, for a known function

and fixed values of M, N, functional

where

- complex conjugate value

, and sequentially increasing the values of M, N, determine the minimum values

and

where

at which the inequality holds:

where

... Inequality:

is a match condition

with ƒ _d (θ, ϕ) in the viewing sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ) with a given accuracy. According to famous

define the function

...

, используя полученные значения

,

,

,

вычисляют

- значения

в точках размещения антенных элементов под номерами r, где r=1, …, K.According to the formula

using the obtained values

,

,

,

calculate

- values

at the points where the antenna elements are numbered r, where r = 1, ..., K.

, где r=1, …, K, - значения фазовых поправок, при введении которых в деформированное распределения фазы напряженности поля в апертуре ФАР обеспечивается восстановление в секторе обзора (θ₁≤θ≤θ₂, ϕ₁≤ϕ≤ϕ₂) проектной диаграммы направленности ФАР.Calculate

, where r = 1, ..., K, are the values of the phase corrections, when introduced into the deformed distribution of the field strength phase in the phased array aperture, restoration in the viewing sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ) of the design phased array radiation patterns.

With the control of controlled phase shifters 4 and _r 2 block in the phase distribution field intensity at points FAS aperture with coordinates x _r, y _r added phase shift ΔF _r, where r = 1, ..., K.

2. The second variant of the patented method for restoring the directional pattern of a planar phased array antenna is its modification in cases in which only the direction of the main lobe of the antenna pattern is restored.

When implementing this option, it is used that the direction of the main lobe of the antenna pattern is determined only by linear elements of the expansion of the phase distribution function of the field strength in the PAA aperture in the Fourier series in terms of linear orthonormal harmonics P ₁₀ (x, y) = a _11x + a ₁₀ , P ₀₁ (x , y) = b _11y + b _01x + b ₁₀ .

In accordance with [4] from the system of equations:

,

, вычисляют

, где r=1, …, K, - значения линейной составляющей разложения проектной функции распределения фазы напряженности электромагнитного поля в апертуре ФАР в ряд Фурье.according to the known direction of the main lobe of the design BP - (θ ₀ , ϕ ₀ ), find the coefficients

,

, calculate

, where r = 1, ..., K, are the values of the linear component of the expansion of the design function of the distribution of the phase of the electromagnetic field strength in the PAA aperture in the Fourier series.

From the system of equations:

,

, вычисляют

, где r=1, …, K, - значения линейной составляющей разложения деформированной функции распределения фазы напряженности электромагнитного поля в апертуре ФАР в ряд Фурье.according to the known direction of the main lobe of the deformed pattern - (θ _d , ϕ _d ) find the coefficients

,

, calculate

, where r = 1,…, K, are the values of the linear component of the expansion of the deformed phase distribution function of the electromagnetic field strength in the PAA aperture in the Fourier series.

, где r=1, …, K, - значения фазовых поправок в деформированное распределения фазы напряженности поля в апертуре ФАР, при которых обеспечивается восстановление направления главного лепестка диаграммы направленности ФАР.Calculate values

, where r = 1,…, K, are the values of phase corrections to the deformed phase distribution of the field strength in the PAA aperture, at which the direction of the main lobe of the PAA radiation pattern is restored.

With the control of controlled phase shifters 4 and _r 2 block in the phase distribution field intensity at points FAS aperture with coordinates x _r, y _r added phase shift ΔF _r, where r = 1, ..., K.

To confirm the feasibility and effectiveness of the patented method for recovering the radiation pattern, mathematical modeling of the procedure for recovering the radiation pattern was carried out, the results of which are illustrated in Fig. 2.

The simulation was carried out for a linear antenna array of 10 elements (K = 10), with the interelement distance x _r -x _r-1 = λ / 2, the array length L = 4.5λ. The design BP with the direction of the main lobe θ ₀ = 0 is shown in pos. 4 fig. 2. The deformed BP with the direction of the main lobe θ _d = 3.5 angular degrees is shown in pos. 5 fig. 2.

The recovery of the pattern was carried out in the view sector (- 30 angular degrees. ≤θ≤30 angular degrees.) At a given value δ = 5 * 10 ^-4 .

потребовалось учитывать три первые гармоники.The restored DN is shown in pos. 3 fig. 2. When restoring to a segment of the Fourier series

it was necessary to take into account the first three harmonics.

As seen in FIG. 2 the coincidence of the reconstructed and design directional patterns in the viewing sector (-30 angular degrees ≤θ≤30 angular degrees) was made with high accuracy with the realized value δ = 3 * 10 ^-4 .

Thus, the patented method for recovering the directional pattern is practically realizable and provides the declared technical result - it ensures the recovery of the pattern only on the basis of knowledge of the design parameters of the plane PAA and the type of the deformed pattern.

Literature

1. Seong-Ho Son, Soon-Young EomDaen, Soon-IkJeon, Woon-Bong Hwang, US 7,994,980 B2

2. Patent No. 2488928 Russian Federation, IPC H01Q 21/00. Method of adaptive suppression of spatial noise / Bondarev V.E., Gusevsky V.I., Duplenkova M.D .; applicant and patentee of OKB MEI JSC - No. 2012137999, app. 09/06/2012; publ. 07/27/2013 Bul. No. 21.

3. Suetin PK, Orthogonal polynomials in two variables. M .: Science, 1976, p. 32

4. Zelkin E.G., Kravchenko V.F., Gusevsky V.I. Constructive approximation methods in antenna theory. - M .: Sains-press, 2005, p. 363

5. TerraSAR-X Calibration Results. M. Schwerdt; B. Brautigam; M. Bachmann; B. Doring; D. Schrank; J. Hueso Gonzalez. IGARSS 2008 - 2008 IEEE International Geoscience and Remote Sensing Symposium. 7-11 July 2008.

. IEEE TRANSACTIONS ON GEOSOENCE AND REMOTE SENSING, VOL. 48, NO. 2, FEBRUARY 2010.6. TerraSAR-X Antenna Calibration and Monitoring Based on a Precise Antenna Model. Markus Bachmann, Marco Schwerdt, and Benjamin

... IEEE TRANSACTIONS ON GEOSOENCE AND REMOTE SENSING, VOL. 48, NO. 2, FEBRUARY 2010.

7. IN-ORBIT CALIBRATION OF THE TANDEM-X SYSTEM. Marco Schwerdt, Jaime Hueso Gonzalez, Markus Bachmann, et al. 2011 IEEE International Geoscience and Remote Sensing Symposium.

Claims (2)

1. The method of restoration of the radiation pattern includes the creation of a flat phased antenna array (PAR), consisting of antenna elements, controlled phase shifters, a microwave splitter and a control unit, for a flat PAR are known: ƒ ₀ (θ, ϕ) - design energy radiation pattern , where θ, ϕ are the spherical coordinates of the observation point; (θ ₀ , ϕ ₀ ) is the direction of the main lobe of the design energy BP; ƒ _d (θ, ϕ) - deformed energy MD: (θ _d , ϕ _d ) - direction of the main lobe of the deformed energy MD; (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ) - the survey sector in which the design BP is restored; δ is the threshold value of the coefficient of mismatch between the design and reconstructed radiation patterns in the sector (θ ₁ ≤θ≤θ ₂ , ϕ ₁ ≤ϕ≤ϕ ₂ ); Ω (x, y) is the aperture area of the flat PAA; x, y - coordinates of a point in the plane of the phased array aperture; K is the total number of antenna elements; x _r , y _r - coordinates of the phase centers of antenna elements numbered r, where r = 1,…, K .; Ф ₀ (x, y) is the design function of the distribution of the phase of the electromagnetic field strength in the phased array aperture; Ф ₀ (x _r , y _r ) - the values of Ф ₀ (x, y) at the points of placement of antenna elements numbered r, where r = 1, ..., K; ρ ₀ (x, y) - design amplitude distribution of the electromagnetic field strength in the phased array aperture; P _nm (x, y) is the set of orthonormal harmonics, where (n, m) are the harmonic numbers; λ - operating wavelength, characterized in that

- the model function of the phase distribution of the field strength in the PAA aperture is represented as a segment of the Fourier series

where

,

,

,

are the coefficients of the Fourier series, from the system of equations

find the coefficients

,

, where a ₁₁ , b ₀₁ , b ₁₁ are the coefficients of linear orthonormal harmonics P ₁₀ (x, y) = a _11x + a ₁₀ , P ₀₁ (x, y) = b _11y + b _01x + b ₁₀ , define the function

, the model radiation pattern -

represent in the form

minimizing, for a known function

and fixed values of M, N, functional

where

- complex conjugate value

and successively increasing the values of M, N, determine the minimum values

and

Where

at which the inequality holds:

where

define the function

, calculate

- values

at the points of placement of antenna elements numbered r, where r = 1, ..., K, calculate

Where r = 1, ..., K, with the control unit and the controllable phase shifters in the phase distribution of field intensity at points FAS aperture with coordinates x _r, y _r added phase shift ΔF _r, where r = 1, ..., K. 2. A method for restoring the directional pattern of a flat phased antenna array according to claim 1, characterized in that, the direction of the main lobe of the antenna pattern is restored, for which from the system of equations

, where a ₁₁ , b ₀₁ , b ₁₁ are the coefficients of the known linear orthonormal harmonics P ₁₀ (x, y) = a _11x + a ₁₀ , P ₀₁ (x, y) = b _11y + b _01x + b ₁₀ , find the coefficients

,

, calculate

, where r = 1, ..., K, from the system of equations

, find the coefficients

calculate

where r = 1, ..., K, calculate the values

where r = 1,…, K.

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