RU2249890C1 - Method for shaping lobed directivity pattern of antenna array - Google Patents

Abstract

FIELD: antenna engineering; shaping lobed directivity patterns in amplitude-phase (complex) controlled antenna arrays.

SUBSTANCE: proposed method depends on weighing signals received by each radiator followed by their addition in which complex weighting coefficients are found as Hermitean forms of beam resultant corresponding to highest characteristic of beam number, second Hermitean form of beam being chosen as power mean value of directivity pattern; in determining Hermitean form beam resultant use is made of information about positioning of directivity pattern lobes and their relative level; square of modulus of weighed sum of directivity pattern values in directions of lobes being formed are used as first Hermitean form of beam.

EFFECT: ability of shaping lobed directivity pattern with desired positions and levels of main lobes.

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Description

The invention relates to antenna technology and can be used to form multilobe radiation patterns (AF) in antenna arrays (AR) with amplitude-phase (integrated) control.

There is a method of forming the antenna array bottom with the maximum directional coefficient (KND) [1], based on the weighting of the signals received by each emitter, and their subsequent summation, in which the complex weighting coefficients (KVK) are found as the main beam vector of Hermitian forms corresponding to the largest the characteristic number of the beam, and in determining the main vector of the beam, information is used on the direction of orientation of the maximum of the radiation pattern, and as the first and second Hermitian pM beam used respectively square NAM module into the beam direction and the maximum average power value DV.

The essence of the known method lies in the presentation of KND (here we consider a two-dimensional version)

in the form of a relation of Hermitian forms

In (1) and (2) the following notation is accepted:

φ ₀ - direction of orientation of the maximum of the pattern;

| J〉 is the KVK column vector with elements J _n , where n is the emitter number (n = 1,2, ... N);

[A1] and [B1] are Hermitian matrices of order N with elements

f (φ) is the non-normalized amplitude DN of the system excited by the current | J〉, which can be represented as

Denote by (f) the N-dimensional row vector of non-normalized partial diagrams f _n (φ) of the lattice, the nth emitter of which is excited by a current of unit amplitude.

Since the matrices [A1] and [B1] are Hermitian, D1 (J) is the ratio of Hermitian forms. The Hermitian forms included in (2) define a bunch of forms

which is regular, since the form | J〉 * [B1] · | J〉 is positive definite, due to its physical meaning.

The maximum (2) is equal to the largest characteristic number of the beam of forms (6), and this maximum is achieved only on the main beam vector corresponding to this number [2].

In accordance with [2], the maximum eigenvalue of the hermitian form pencil (6) is the maximum eigenvalue of the matrix [D1], defined as

and the eigenvector corresponding to the maximum eigenvalue of the matrix [D1] will be the solution to the optimization problem (1). When determining the main beam vector, information is used on the direction of orientation of the beam, and the square of the module of the beam in the direction of the maximum of the beam and the average value of the beam in power are used as the first and second Hermitian beam shapes.

The known method provides the maximization of the KND of the lattice with an arbitrary arrangement of elements (linear, arc, ring, flat, etc.).

The disadvantage of this method of maximizing KND is that it provides the possibility of forming only single-beam patterns. In some cases, in practice, the antenna should provide service not in one direction, but in two or three or even more directions, the position of which can vary. The required antenna gain in these directions can generally be different.

The proposed method is aimed at eliminating the aforementioned disadvantage of the known method. The structural diagram of an annular antenna array operating by the proposed method is presented in figure 1. Figure 2 and 3 presents the radiation patterns formed on the basis of the proposed method with a different number of petals and different weights.

Consider the essence of the proposed method. As in the prototype, the signals received by each emitter are weighed with the aid of a KVK, and then they are summed up, and the complex weighting coefficients are found as the main vector of the beam of Hermitian forms corresponding to the largest characteristic number of the beam, and the average value of the diagram is chosen as the second Hermitian shape of the beam focus on power. However, unlike the prototype, in determining the main vector of a hermitic beam, they use information about the orientation directions of the main lobes (“rays”) of the radiation pattern and their relative levels. In this case, as the first Hermitian form of the beam, the square of the module of the weighted sum of radiation pattern values in the directions of the formed petals is selected.

A comparative analysis of the claimed method and prototype shows that the claimed and known methods differ in the mode of performing the weighing operation, since when determining the main vector of a beam of Hermitian forms, information is used on the orientation directions of the lobes of the radiation pattern and their relative levels, and the first Hermitian form of the beam is selected the module square of the weighted sum of radiation pattern values in the directions of the formed lobes.

Consider the proposed method of forming multilobe radiation patterns using the example of an N-element annular antenna array of radius R (Fig. 1), in each channel of which there is a complex weighing device J _n (n = 1,2, ... N). The outputs of all complex weighing devices are connected to the inputs of the adder, the output of which is formed by the radiation pattern f (φ).

комплексных амплитуд токов в излучателях, максимизирующий следующий энергетический функционалTo form “rays” with relative amplitude w _s in the radiation pattern in the directions φ _s (s = 1,2, ... S), we will look for an N-dimensional column vector

complex amplitudes of currents in emitters, maximizing the following energy functional

where fS is the weighted sum of the values of DN f (φ) in S directions

Taking into account (5), the weighted sum of the values of ND in S directions can be represented in the following form:

Here (fs) is an N-dimensional row vector with elements

In this case, the square of the module of the weighted sum of the values of the ND in S directions can be written in the following form:

Here * is the sign of the complex conjugation of the scalar quantity and the Hermitian conjugation of the matrix; [A] denotes a square Hermitian matrix of the Nth order with elements

The same can be written for the denominator (8)

where [B] is the Nth order square Hermitian matrix with elements

As a result, the optimized functional (8) can be reduced to

Since the matrices [A] and [B] are Hermitian, K (J) is the ratio of Hermitian forms. The Hermitian forms included in (16) define a bunch of forms

which is regular, since the form | J〉 * [B] · | J〉 is positive definite, due to its physical meaning.

The maximum (16) is equal to the largest characteristic number of the beam of forms (17), and this maximum is achieved only on the main beam vector corresponding to this number [2].

In accordance with [2], the maximum eigenvalue of the hermitian form pencil (17) is the maximum eigenvalue of the matrix [D], defined as

and the eigenvector corresponding to the maximum eigenvalue of the matrix [D] will be the solution to the optimization problem (8).

The maximum eigenvalue and the corresponding eigenvector of the matrix [D] can be determined by one of the known methods, for example, QR decomposition [3]. However, in this case, you can do simpler. Since the rank of the matrix [A] is equal to unity, the current vector delivering a maximum to the functional (16) can be found analytically from the expression [4]

The operation of the device operating according to the proposed method can be illustrated using figure 1. Information on the directions φ _{s of the} maxima of the formed petals and the corresponding weights w _{s is} supplied to the inputs 1 and 2 of the KVK 3 computer, which operates in accordance with expression (19). The signals received by each emitter 4 are weighed using complex weighing devices 5 in accordance with the CVC determined by calculator 3, after which they are fed to the inputs of the high-frequency adder 6. As a result, the radiation pattern f (φ) having S lobes is formed at the output 7 of the high-frequency adder 6 (“Rays”) with relative levels w _s .

As an example, figure 2 shows a three-petal DN formed by a circular AR with isotropic emitters with the following initial data: the number of emitters N = 36, the lattice pitch λ / 2, the orientation angles of the petals of the DN φ ₁ = 110 °, φ ₂ = 150 °, φ ₃ = 240 °, weights w ₁ = 1, w ₂ = 1, w ₃ = 0.5.

When calculating the radiation patterns of the elements were taken in the form

where φ _n is the angular coordinate of the nth emitter.

The complex amplitudes of the currents in the elements of the AR were found using expression (18), i.e. through the determination of the eigenvalues and eigenvectors of the matrix D, and using the expression (19). As expected, both paths lead to the same result. From figure 2 it is seen that the position of the "rays" (petals) of the NAM and their levels correspond to the set.

Figure 3 shows the possibility of sequential formation using algorithm (19) of a single-leaf (f1 (φ)), two-leaf (f2 ((φ)) and three-leaf (f3 (φ)) MDs. In the first case, a lobe with number s = 1 is formed (i.e., with the weight w ₁ and orientation φ ₁ ), in the second - petals with numbers 1 and 3, and in the third - all three petals shown in Fig. 1.

Thus, the change in the mode of performing the weighing operation, which manifests itself in the fact that when determining the main vector of a beam of Hermitian forms, information is used on the orientation directions of the beam patterns and their relative level, and the square of the module of the weighted sum of the values of the radiation pattern in the directions of the formed petals, provides the formation of multi-petal radiation patterns with predetermined positions and levels of the main petals.

Sources of information

1. E.I. Krupitsky. On the maximum directivity of antennas consisting of discrete emitters // Reports of the Academy of Sciences of the USSR, 1962, v.143, No. 3, p.257-259.

2. F.R. Gantmakher. Matrix theory. - 4th ed. - M.: Science, ch. ed. physical mat. lit., 1988, 552 p.

3. Voevodin VV, Kuznetsov Yu.A. Matrices and calculations. M .: Science, ch. ed. physical mat. lit., 1984, 320 p.

4. Cheng David K. Optimization techniques for antenna arrays, "Proc. IEEE", 1971, 59, No. 12, 1664-1674.

Claims (1)

A method for generating multilobe antenna array radiation patterns based on the weighting of the signals received by each emitter and their subsequent summation, in which the complex weight coefficients are found as the main vector of the Hermitian beam shape, corresponding to the largest characteristic number of the beam, and the average is chosen as the second Hermitian beam shape the value of the radiation pattern in power, characterized in that when determining the main vector of the beam of Hermitian forms, inform information about the directions of orientation of the main lobes of the radiation pattern and their relative level, and as the first Hermitian form of the beam, choose the square of the module of the weighted sum of the values of the radiation pattern in the directions of the formed lobes.

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