The study focuses on reconstructing the amplitude-phase distribution of flat multielement passive and active phased antenna arrays with the use of dynamic radiation patterns, measured with electronical scanning without mechanical rotations and antenna movements. The paper describes the measurement settings of dynamic radiation patterns, necessary for reconstructing the amplitude-phase distribution. Findings of the research show that to reconstruct the amplitude-phase distribution according to dynamic radiation diagrams, there is no need for increased computational resources due to the use of Fourier transformation algorithms. After the method was experimentally verified on the specific samples of active phased antenna arrays, its high efficiency was established. The paper gives the examples of reconstructing the amplitude-phase distribution from dynamic radiation patterns in the presence of malfunctions in active phased array antennas.

Рассмотрены особенности реконструкции амплитудно-фазового распределения плоских многоэлементных пассивных и активных фазированных антенных решеток с использованием динамических диаграмм направленности, измеряемых при электронном сканировании лучом без механических поворотов и перемещений антенны. Описаны параметры измерения динамических диаграмм направленности, необходимые для реконструкции амплитудно-фазового распределения. Установлено, что для реконструкции амплитудно-фазового распределения по данным динамических диаграмм направленности не требуются повышенные вычислительные ресурсы ввиду использования алгоритмов преобразования Фурье. В результате экспериментальной проверки данного метода на конкретных образцах активных фазированных антенных решеток установлена его высокая эффективность. Приведены примеры реконструкции амплитудно-фазового распределения по динамическим диаграммам направленности при наличии неисправностей в активных фазированных антенных решетках.

The problem of determining the amplitude-phase distribution (APD) in the apertures of passive phased antenna arrays (hereinafter – PAA) and active phased antenna arrays (APAA) is gaining ever more importance for the theory and practice of antennas development. This is associated with a necessity to ensure real-time serviceability check of antenna array basic systems at the development stages and during operation of final products.

The currently existing APD reconstruction methods are based on measuring signal parameters in the PAA channels, or imply APD recovery as per the data of field strength measurements in the antennas’ near-, intermediate-, or far-field regions. Among the well-developed methods are those based on resolving systems of linear equations [

In this paper, it is proposed to use for APD reconstruction dynamic radiation patterns (DRP) of PAA [

Basics of APD reconstruction as per DRP

Reconstruction of amplitude distribution (AD) and phase distribution (PD) as per a known DRP consists in calculating excitation parameters in the location points of radiating element centres with application of the inverse Fourier transform [

where Amn, ϕmn – radiator amplitude and phase; s, p – direction grid row number and column number; Fps, ψps – values of DRP amplitude and phase components in direction with angular coordinates (up ,vs ); u, v – angular variables that are direction cosines for selected direction to aperture axes X and Y, respectively; u = sin θ cos j, v = sin θ sin j ; k = 2π / λ – wave number; xn, ym – coordinates of a radiator located in row with number m and column with number n.

Proceeding from expression (1), we shall take the advantage of the inverse fast Fourier transform algorithms to reconstruct APD, which will considerably reduce the time of DRP processing, especially for antenna arrays with apertures having a large electrical size and, consequently, a large number of radiators.

Due to the measurement specifics, radiation pattern of a single radiator in the array does not influence the DRP, therefore, in the first approximation, the DRP can be regarded as directivity multiplier (DM) of the PAA. It is known that the DM of a flat antenna array with equidistant arrangement of radiators along each axis is a 2D periodic function [

Fig. 1. Fragment of PAA aperture with triangular pattern of radiators arrangement

Fig. 2. Arrangement pattern of PAA DM diffraction lobes

For reconstruction of APD in the aperture, it is necessary to have the values of DM in the period region. The size of DM period region depends on spacings between array elements dx and dy (see Fig. 1), normalised to wavelength λ, and is defined by the expressions:

At certain values of dx and dy the DM period boundaries go beyond the visibility scope (see Fig. 2). Electronic scanning allows to direct the PAA beam beyond the visibility scope and measure the level of the received signal. To measure DRP in direction (u1, v1 ) in the aperture, it is necessary to form the phase distribution represented as ϕ (x,y) = 2π (xu1 + yv1), therefore phase advances at spacings dx and dy must be equal to

At large deflections of the beam, phase advances at spacings may exceed 2π, which is technically implementable, as the integer amount of 2π can be left out of consideration in phasing of the radiators.

In accordance with the sampling theorem (the Kotelnikov theorem), DRP should be measured with increments

where Lx and Ly – aperture electrical sizes in X and Y coordinates.

For this reason the total number of DRP measurements, e.g. within a single period region, shall be at least

However, in most practical cases, to reconstruct APD as per DRP it will be sufficient to have the values taken in a region corresponding in shape and size to DM half-period (hereinafter – cell), with parameters TU = 1 /dx, TV = 1 /dy . It makes it possible to bring the number of measurements down to Nmin = [TU / ∆u] [TV / ∆v] ≈ NxNy, which roughly corresponds to the number of radiators in a rectangle delineating PAA aperture. Assuming that for a PAA comprising 1000 radiators the time of a single standard-mode measurement amounts to ≈10 ms, the total DRP measurement time will be just ≈10 s, and APD calculation on a medium-performance personal computer will take fractions of a second.

Notably, a complex-valued DRP carries information on the location coordinates and excitation of the radiators. This is demonstrated by an example of modelling DRP of an APAA with circular aperture (≈ 600 radiators) and reconstructing its APD. If, using the DRP data in a single-cell region (Fig. 3), we reconstruct APD for an aperture of larger size (Fig. 4; hereinafter, the values by axes X and Y correspond to the number of wavelengths) but with the same spacing of radiators, then amplitudes (Fig. 5) and phases can be reconstructed with very high accuracy. Notably, amplitudes of the radiators located beyond the limits of the initial radiating aperture have values close to zero.

Fig. 3. DRP amplitude component

Fig. 4. Example of amplitude distribution reconstruction for an aperture of larger size

Amplitude distribution: Row = 18 .

Fig. 5. Reconstructed amplitude distribution in central aperture row

The effectiveness of the method of APD reconstruction as per a measured DRP can be illustrated by an example of reconstructing excitation of the APAA described above. The initial AD is tapered (AEF = 0.9), with AD random errors σа0 = 0.02. Added to cophased PD are errors with σϕ0 = 10° . Also entered in the aperture were malfunctions in the form of disabled radiators, individual ones and groups of such (black rectangles in Fig. 6), as well as a constant phase addition of +60° in one full row and one half-row (Fig. 7). Additional random APD errors, updated at each PAA beam deflection [

Fig. 6. Initial AD

Fig. 7. Initial PD

The result of APD calculation as per the values of DRP amplitude and phase components lying within a single-cell region almost matches the initial APD: RMS deviation of reconstructed AD from the initial AD was σа ≈ 0.0015, RMS deviation of reconstructed PD from the initial PD – σϕ ≈ 0.2° .

As a result of APD reconstruction, the radiators disabled in the initial aperture (with amplitudes equal to zero) had insignificant amplitude deviations from zero value. However, since phases of those radiators take virtually random values within an interval of ±180°, an additional indicator of a disabled radiator is substantial deviation of its phase value from phases of other elements (Fig. 8).

Fig. 8. Reconstructed PD

Based on the findings obtained, it can be inferred that in the presence of regular excitation errors in the PAA aperture, it should be sufficient for APD reconstruction to have values in that DRP region which corresponds to a single DM cell.

A special case is that when the antenna aperture contains elements uncontrollable in phase (the so-called unphaseable elements). If, for instance, the PAA aperture has a faulty half-row in which element phases do not change in the course of scanning, then the accuracy of APD reconstruction as per DRP region corresponding to the region of a single DM cell drops sharply (Figs. 9, 10).

Fig. 9. Reconstructed PAA AD

In this case, the degradation of APD reconstruction accuracy is caused by lack of DRP data in a single DM cell. Acceptable accuracy of APD reconstruction can be achieved by expanding the DRP processing region to the size of DM period (Figs. 11, 12). Fig. 12 shows the DRP phase component demonstrating phase opposition of DRP diffraction lobes, and Figs. 13, 14 – results of APD reconstruction as per DRP data in the DM period region.

Fig. 11. DRP amplitude component

Fig. 12. DRP phase component

A specific feature of the proposed approach consists in that after reconstruction the unphaseable elements have amplitude close to zero (see Figs. 10, 14), which allows to very accurately determine their position in the aperture. Moreover, in implementation of the proposed approach difficulties may occur concerning separate identification of non-radiating elements and elements uncontrollable in phase. This peculiarity has been verified experimentally.

Fig. 13. Reconstructed PAA AD with unphaseable elements

The basic possibilities for reconstructing APD as per a measured DRP are presented. The use of this method is the most effective for multielement PAA/APAA with flat apertures and equidistant arrangement of radiators, row- and column-wise. For such arrays the DM is a 2D periodic function, which makes the process of DRP measurement and processing considerably easier.

It is shown that with triangular arrangement of radiators in the aperture, in the absence of unphaseable radiators in PAA/APAA, for APD reconstruction it is sufficient to use the DRP data measured in the region of a single DM cell, and in the presence of unphaseable radiators, it is necessary to process the DRP data measured in the region of two DM cells (of the same DM period).

The most important advantages of the considered method are: • possibility to use it for measuring DRP in standard mode of PAA beam scanning; • taking measurements without mechanical rotations and movements; • small time expenditure for measurement and processing; • reliable determination of malfunctions in PAA/APAA excitation and control systems that do not change during scanning; • reliable prediction of directional characteristics in the visibility scope.

The key aspects of the presented results were experimentally verified on samples of APAAs under development.

The authors declare that there are no conflicts of interest present.