RU2314610C1 - Method for power optimization of phased antenna array - Google Patents

Abstract

FIELD: antenna engineering.

SUBSTANCE: proposed method for power optimization of phased antenna array involves weighing signals received by each radiator. Weighting coefficients are found as functional error minimizing vector determined by using data on direction to signal source and on distribution of interference sources. Used as maximizing functional is ratio of signal power in desired direction to sum of noise and interference values. Weighting coefficients of N - 2 antennas, where N is total number of phased array antennas, and 2M is number of antennas with independent weighting coefficients, are assumed to equal product of source weighting coefficients by weighting coefficient X⁰ common for these antennas, found by solving optimization problem. Order of matrices incorporated in error functional is reduced to 2M + 1. Vector

is normalized in compliance with expression

- x⁰ which ensures constant weighting coefficients of N - 2M antennas of array, where vector

is error minimizing functional.

EFFECT: enhanced responsiveness of antenna array in interference environment.

1 cl, 3 dwg, 1 tbl

Description

The invention relates to antenna technology and can be used for optimal control of weighing devices in the channels of phased array antennas (PAR) according to the criterion of the maximum signal to noise ratio + interference.

There is a method of energy optimization of the PAR [1], the essence of which is to weight the signals received by each emitter using weight coefficients, according to which the weight coefficients are found as a vector that minimizes the error functional, which is determined by using information about the direction to the signal source and about the distribution of interference sources, and as the maximized functional, the ratio of the signal power in a given direction to the sum of noise and interference received a ntennoy.

A disadvantage of the known method for energy optimization of PARs is that the optimization of PARs is achieved by changing the weights in all elements, and the weights are determined as a result of an iterative procedure, which complicates the implementation of the method and also impedes the implementation of the known algorithm in real time, especially with large sizes of the PAR .

Also known is a method of energy optimization of a monopulse antenna array (MAP) with joint beam formation [2], the essence of which is to weight the signals received by each emitter using complex weighting coefficients (CVCs), divide these signals into two channels, sum the signals from the same name the outputs of the dividers with the corresponding progressively increasing and decreasing phase shift, ensuring the deviation of each beam by an angle of ± ΔΘ, and the subsequent formation of the sum and difference diagrams, for example avlennosti (DN). In this case, KVK are found as the main vector of a beam of Hermitian shapes corresponding to the maximum characteristic number of a beam of rank 2M + 1, which is determined by using information about the direction to the signal source and the distribution of interference sources, and the signal power is selected as the first and second Hermitian beam shapes, respectively in the total channel and the sum of the noise and interference powers in the rays of the monopulse group, and the complex weights of the N-2M part of the MAP elements, where N is the total number of MAP elements, and 2M is the number of elements with independent KVK, take equal to the product of the initial weighting coefficients, providing the orientation of the equal signal direction (RSN) to the signal source, common to these elements KVK I _p determined from the solution of the optimization problem, after which the KVK of all elements are normalized to the value of I _p .

The disadvantage of this method [2] is the impossibility of its implementation in relation to PAR, since the known method involves changing the complex weighting factors, i.e. and amplitudes and phases of the currents, whereas in the PAR only the phases of the currents change.

The proposed method is aimed at eliminating these disadvantages of the known methods.

The structural diagram of the device operating according to this method is presented in figure 1. Figure 2 presents the headlights after optimization by the method [1] and after optimization by this method. Figure 3 shows the differences in phase distributions obtained by known and claimed methods from the initial phase distribution.

Consider the essence of the proposed method. As in the prototype [1], the signals received by each emitter are weighed using weighting factors, which are found as a vector that minimizes the error functional, which is determined by using information about the direction to the signal source and the distribution of interference sources, and as a maximized functional respectively, the ratio of the signal power in a given direction to the sum of the noise and interference received by the antenna is selected. In this case, the weighting coefficients of N-2M elements of the phased antenna array, where N is the total number of elements of the phased antenna array, and 2M is the number of elements with independent weighting coefficients, are taken equal to the product of the initial weighting coefficients, ensuring the orientation of the main maximum of the radiation pattern to the signal source, by the total weight coefficient X ⁰ for these elements, determined from the solution of the optimization problem.

, минимизирующий функционал ошибки, который нормируют в соответствии с выражением

, в связи с чем весовые коэффициенты неадаптируемых N-2M элементов не изменяют.However, unlike the prototype, the order of the matrices included in the error functional is reduced to 2M + 1, and the vector is chosen as the optimal vector of weight coefficients

minimizing the error functional, which is normalized in accordance with the expression

, and therefore the weights of non-adaptable N-2M elements do not change.

, минимизирующий функционал ошибки, который нормируют в соответствии с выражением

, в связи с чем весовые коэффициенты неадаптируемых N-2M элементов не изменяют.A comparative analysis of the inventive method and prototype shows that in the inventive method the conditions for performing the weighing operation are changed. When determining the vector of weight coefficients, the order of the matrices included in the error functional is reduced to 2M + 1, and the vector is selected as the optimal vector of weight coefficients

minimizing the error functional, which is normalized in accordance with the expression

, and therefore the weights of non-adaptable N-2M elements do not change.

Consider the proposed method for energy optimization of the PAR, assuming that the direction to the signal source is Θ ₀ and the distribution of noise and interference in the space T (Θ) is known.

Taking into account the structural diagram of the optimized PAR, presented in figure 1, for optimization we use a functional of the form:

where f (Θ) is the directivity pattern of the linear equidistant PAR, determined with a uniform amplitude distribution I = 1 by the expression [1]:

where u (Θ) = kd (sinΘ-sinΘ ₀ ); P = (N-1) / 2; k is the wave number; d is the grid pitch; Ψ _p is the phase shift of the ith element of the PARS relative to the value corresponding to the in-phase mode of operation (in (2) it was taken into account that for an equidistant PAR with identical emitters, the phases of the elements located symmetrically with respect to the center of the grating are equal but opposite in sign, therefore, in what follows all transformations are given relative to P elements), moreover:

- начальная фаза р-го элемента ФАР (в случае начального синфазного возбуждения ФАР

); x_р<<1 - малое возмущение фазы р-го элемента ФАР; р=1, 2,..., Р.

- the initial phase of the p-th element of the PAR (in the case of the initial in-phase excitation of the PAR

); x _p << 1 - small perturbation of the phase of the r-th element of the PAR; p = 1, 2, ..., R.

Denominator (1) is written under the assumption that the dimensions of the emitters along the x axis are infinite, the radiation occurs in the half-space z> 0, and expression (2), as in the prototype [1], is written for the case of identical PAR emitters.

Substituting (3) in (2) and further into the denominator (1) for the selected functional, we obtain:

where B is a square symmetric matrix of the Pth order with elements:

β is a valid P-dimensional column vector with elements:

f ⁰ (Θ) is the daylight of the unperturbed headlamp; α is a scalar quantity defined by the expression:

x is the column vector of unknown phase perturbations, which are taken into account with plus for the PAR elements (Fig. 1) from N-P + 1st to Nth, and for the PAR elements from 1st to Pth, with a minus sign .

The expression in the denominator (4) represents the error functional.

As shown in the prototype [1], the maximum of functional (4) provides the vector x ^m defined by the expression:

while the maximum of functionality is equal to:

. Далее вектор Ψ⁰+х^м трактуют как новые начальные значения и получают возмущения второго порядка. Итерационную процедуру продолжают до тех пор, пока значение максимизируемого функционала увеличивается.Expression (8) determines the first-order perturbations with respect to the initial values

. Next, the vector Ψ ⁰ + x ^{m is} treated as new initial values and second-order perturbations are obtained. The iterative procedure is continued until the value of the maximized functional increases.

Let us analyze the changes in the conditions of weighing the signals received by the PAR elements, the proposed method, for this we consider the radiation pattern of the PAR in more detail. Substituting (3) in (2) and revealing the sum of the cosine arguments, we obtain:

Further, considering that x _p << 1 and, accordingly, cos (x _p ) ≈1, a sin (x _p ) ≈x _p , from (10) we get:

In accordance with the proposed method, the weighting coefficients of N-2M elements of the phased antenna array are taken equal to the product of the initial weighting coefficients, ensuring the orientation of the main maximum of the radiation pattern to the signal source, to the weight coefficient X ^o common to these elements.

Further, as in the prototype [1], all transformations are given for P = (N-1) / 2 lattice elements, which is due to the accepted assumptions on the PAR symmetry. Accordingly, the number of elements with independent weights in the given expressions is taken equal to M. With this in mind, from (11) we obtain:

- мерный вектор-столбец с элементами:Where

- dimensional column vector with elements:

- мерный вектор-столбец неизвестных весовых коэффициентов с элементами:

- dimensional column vector of unknown weights with elements:

.Thus, the radiation pattern of the headlamps is represented by the function P-M + 1-dimensional vector of unknown weights

.

Substituting (12) in the denominator (1) and performing the transformations, we obtain:

where In ^d is a square symmetric matrix PM + 1st order with elements:

β ^d - real P-M + 1-dimensional column vector with elements:

порядка Р-М+1 (или для общего случая N-2M+1), минимизирующий функционал ошибки, входящий в знаменатель (17):Thus, as a result of changing the weighing operation by the proposed method, the order of the matrices included in the error functional (denominator (15)) decreases from P to P-M + 1. In the general case, without taking into account the PAR symmetries, the order of the matrices included in the error functional decreases from N to N-2M + 1. Accordingly, the solution to the optimization problem is a vector

of order Р-М + 1 (or for the general case N-2M + 1), minimizing the error functional included in the denominator (17):

As before, expression (18) defines the first-order perturbations; therefore, the iterative procedure is continued until the value of the maximized functional increases.

его значения нормируют в соответствии с выражением:After defining the vector

its values are normalized in accordance with the expression:

As a result of such normalization, the phases of non-adaptable elements do not change and correspond to the initial phase distribution.

The operation of the device operating according to the proposed method can be illustrated using figure 1. Information Θ ₀ about the direction to the signal source and about the distribution of interference sources T (Θ) in space is fed to the inputs 2 and 3 of the weighting factor calculator 3, functioning in accordance with (18) and (19). The signals received by the first M and the last M elements 1 of the phased antenna array are weighed using weighing devices 5, to which the signals of the calculator 3 are received.

The signals received by non-adaptable PAR elements (M + 1 through N-M) are weighted by weighting factors 6, which provide the orientation of the maximum radiation pattern to the signal source. After that, the signals of all elements enter the adder 7, at the output of which 8 a beam pattern is formed.

In Fig.2 a continuous line shows the beam corresponding to the known optimization method, and a dashed line shows the radiation pattern of the headlamp optimized by the proposed method. The vertical line in figure 2 shows the direction of arrival of the interfering signal.

The calculations were performed for an array of non-directional emitters with parameters N = 29, P = 14, y ₀ = 0.5λ, at Θ ₀ = 20 ⁰ , and also the function T (Θ) of the following form:

Two sublattices are distinguished at the edges of the FAR, five elements in each (M = 5), respectively, the order of the matrices included in functional (4) is reduced from 14 to 6, t, taking into account assumptions on the symmetry of the lattice [1], .e. more than twice (for the general case of solving the optimization problem from 29 to 10).

The simulation results showed that in the case of exposure to interference of the form (20), the signal-to-noise + interference ratio before optimization is -0.1 dB, and after optimization by known and claimed methods, respectively 18.95 and 18.94 dB, which indicates the high efficiency of the claimed method, while the result of the claimed method is achieved by changing the phases only in a third (10 out of 29) PAR elements with a uniform amplitude distribution.

The presented results correspond to the fifth iteration. It should be noted that the inversion procedure of the matrix included in the denominator of maximized functionals (4) and (15) is repeated at each iteration, therefore, the computational efficiency of the proposed method increases with each iteration, because in accordance with the proposed method, a smaller order matrix is used to determine the weight coefficients .

Figure 3, the solid line represents the difference between the initial phase distribution and the phase distribution corresponding to the known method, and the dashed line shows the difference between the initial phase distribution and the phase distribution obtained by the proposed method.

As can be seen from figure 3, in the case of the implementation of the proposed method, the phases of the elements from 6 to 24 do not change with respect to the initial in-phase excitation, which is a technical effect of the proposed method, which significantly simplifies the discrete control circuits of the PAR. The phase values (in degrees) for different methods are shown in table 1.

The proposed method can also be applied to headlamps with identical directional and to headlamps with non-identical (for example, distorted by mutual connections) emitters.

The source of information

1. Cheng D.K. Optimization techniques for antenna arrays // IEEE Proc. 1971. V. 59. No. 12. P.1664.

2. Patent No. 2255396 of the Russian Federation. The method of energy optimization of monopulse antenna arrays with joint beam formation / Bashly PN, Manuilov BD, Bogdanov VM // B.I. 2005. No. 18.

Claims (1)

A method of energy optimization of a phased array antenna, based on the weighting of the signals received by each emitter, using weight coefficients, according to which the weight coefficients are found as a vector that minimizes the error functional, which is determined by using information about the direction to the signal source and the distribution of interference sources , and as the maximized functional, the ratio of the signal power in a given direction to the sum of the noise and interference received by the ant moreover, and the weighting coefficients of N-2M elements of the phased antenna array, where N is the total number of elements of the phased antenna array, and 2M is the number of elements with independent weighting coefficients, taken equal to the product of the initial weighting coefficients, ensuring the orientation of the main maximum of the radiation pattern to the signal source, in common for these elements a weighting factor ⁰ X determined from the solution of the optimization problem, characterized in that the order of the matrices included in the error functional is reduced to 2M + 1, and to honors the optimal weight vector is selected vector

minimizing the error functional, which is normalized in accordance with the expression

, and therefore the weights of non-adaptable N-2M elements do not change.

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