EP0718911A1 - Beam forming array for radiofrequency antenna with fast Fourier transform and device using such array, in particular for space applications - Google Patents

Abstract

The network includes using two-layer architecture to perform a hexagonal bidimensional discrete Fourier transform on input signals whose number is a multiple (R) of the square of another integer (N). The first layer (5) performs a unidimensional discrete Fourier transform on the rows and contains NxN cells (51a-54d), with each having R inputs and outputs. The second layer consists of R independent sets (7-9) of cells (71-98), each having N inputs and outputs. The second layer performs a unidimensional discrete Fourier transform on the columns. The sets of cells in the second layer are interconnected by groups of row/column links (79, 89 99), and the layers themselves are interconnected by row/column links (6).

Description

The invention relates to a beam shaping network for radio frequency antenna implementing the Fast Fourier Transform, which will be called in the following, for reasons of simplification, "FFT" (commonly used abbreviation of the English expression "Fast Fourier Transform").

It also relates to a hardware structure implanting such a network.

The invention applies advantageously, but not exclusively, to the field of antennas of the phase antenna array type for the generation of multiple beams for applications on board satellites.

Conventional beam radiofrequency conformers, for applications comprising a large number of synthesized beams and a large number of radiating element on the antenna, are hardly usable, because of their mass. Rather, we use intermediate frequency beam (IF) conformers, or even digital baseband conformers, with the impact in power consumption that this implies.

The article by P.S. Hall and S.J. Vetterlein: "Review of Radio Frequency Beamforming Techniques for Scanned and Multiple Beam Antennas", pages 293-303, published in "IEE Proceedings", Vol. 137, Pt. H., N ° 5, October 1990, reviews the main techniques used for the conformation of radiofrequency beams.

Among these, the so-called "Butler Matrix" technique, described in paragraph 4.2 of this article (see also figure 15), allows a compact layout with a minimum of coupling circuits. A priori, such Butler matrices are suitable for the realization of linear networks. With regard to phase control planar arrays implementing rectangular arrangements of radiating elements, it is possible to install the beam shaper using also linear Butler matrices.

• 1) Les tolérances de fabrication : quand la taille de la matrice s'accroît, les décalages de fréquence entre les éléments rayonnants adjacents deviennent plus faible. Une commande plus fine des caractéristiques de phase s'avère nécessaire. On peut admettre, comme rappelé dans l'article précité, que la taille maximale d'une matrice de Butler, mettant en oeuvre la technologie dite "microstrip" (microruban), est de 64×64.
• 2) La topologie complexe des connexions (cheminement) entre couches de coupleurs : comme il est aisé de le constater sur la figure 1 annexée à la présente description, pour une matrice de Butler, de dimensions 16×16, un cheminement complexe de lignes de connexions est nécessaire. Les circuits du conformateur de faisceau à matrice de Butler se répartissent selon deux niveaux (Niveaux 1 et 2), comprenant chacun quatre cellules, Cel₁ à Cel₄ et Cel'₁ à Cel'₄, respectivement. Aux liaisons 1 à 16 correspondent seize liaisons 1' à 16'. Une très grande isolation électrique entre ces liaisons est nécessaire. Cette complexité rend les technologies du type "plan" (connues sous le sigle anglo-saxon "planar" : guides à rubans, lignes microbandes) difficiles à mettre en oeuvre.
• 3) Les exigences concernant les transitions entre faisceaux : Si on considère une antenne réseau linéaire comprenant N éléments rayonnants, un conformateur de faisceaux à matrice de Butler, de dimensions N×N, génère un jeu de N faisceaux avec des niveaux de transition de -4 dB.

However, the maximum size of a Butler matrix (and therefore the maximum number of beams and radiating elements of the antenna) is limited by several factors, as shown below:

• 1) Manufacturing tolerances: when the size of the matrix increases, the frequency offsets between the adjacent radiating elements become smaller. A finer control of the phase characteristics is necessary. We can admit, as recalled in the aforementioned article, that the maximum size of a Butler matrix, implementing the technology called "microstrip" (microstrip), is 64 × 64.
• 2) The complex topology of connections (routing) between layers of couplers: as it is easy to see in FIG. 1 appended to this description, for a Butler matrix, of dimensions 16 × 16, a complex routing of lines of connections is required. The circuits of the Butler matrix beam former are divided into two levels (Levels 1 and 2), each comprising four cells, Cel ₁ to Cel ₄ and Cel ' ₁ to Cel' ₄ , respectively. Connections 1 to 16 correspond to sixteen connections 1 'to 16'. Very high electrical insulation between these connections is necessary. This complexity makes technologies of the "plan" type (known under the acronym "planar": ribbon guides, microstrip lines) difficult to implement.
• 3) The requirements concerning the transitions between beams: If we consider a linear array antenna comprising N radiating elements, a beam conformator with Butler matrix, of dimensions N × N, generates a set of N beams with transition levels of - 4 dB.

This level is certainly too low for the preferred applications targeted by the invention, namely space applications. A level of the order of -1 dB is required. A well-known solution is to oversize the former and use only part of the die. As an example, using a 2N × 2N matrix , we obtain a transition level of -1.5 dB.

It is however easy to understand that this oversizing of the Butler matrix beam shaper has a direct impact on its mass, on its manufacturing tolerances and increases the difficulties linked to the complexity of the connections.

In addition, for space applications, array antennas are normally used with a hexagonal grid topology instead of rectangular. Greater efficiency is obtained with regard to compactness: the number of radiating elements required, as is well known, is less, for the same coverage. However, in this case, a simple layout of the row / column type, as described in relation to the Butler matrix conformers, is no longer possible.

Another configuration was proposed by GG Chadwick et al., In: "An Algebraic Synthesis Method for RN ² Multibeam Matrix Network", published in "Antenna Applications Symposium", Monticello (Illinois, USA), September 23-25, 1981, "Proceedings". This configuration is very similar to the concept of "Butler matrix": these two configurations constitute, in reality, a direct implementation in radio frequency of the "FFT" algorithm.

Although interesting, this configuration however brings the same remarks as previously with regard to the mass, the manufacturing tolerances, the routing of the connections and the transition levels between adjacent beams.

In addition, as is clear from FIG. 12 of the aforementioned publication, a large number of phase-shifting circuits, placed on two levels, is used. Finally, the circuits are not very modular. With the exception of cells with three inputs and three outputs, there are no repetitive modules.

However, as is well known, when one is in the presence of very complex circuits, this aspect is very important for the aspects of manufacturing costs, possibilities of integration and ease of testing. For example, a module is naturally easier to produce and less expensive to replace, in the event of a defect, than a complex circuit. Known technology limits integration to circuits of a certain size and complexity. Relatively uncomplicated repetitive circuits can therefore be produced in the form of integrated circuits, the reliability of which is generally greater than that of discrete circuits. Finally, without being exhaustive, the complexity of the test programs increases, generally in a non-linear fashion, with the complexity of the circuits to be tested.

In summary, it can be admitted that the technology of radiofrequency antennas, in particular for space applications (antennas on satellite), imposes a certain number of constraints, some of which will now be recalled.

Generally, the antenna has a hexagonal shape. However, in the context of the invention, the antenna may also be of triangular shape.

It is first of all necessary to implement an efficient architecture (the term "efficient" must be understood in terms of technology and low complexity). The signal processing algorithm must use Discrete Fourier Transform, which will be called in the following, for reasons of simplification, "DFT" (abbreviation of the commonly used Anglo-Saxon expression "Discrete Fourier Transform") . This "DFT" operates on a series of signals for sampling power supply of the radiating elements of the type antenna. hexagonal, such that the coefficients resulting from the "DFT" are also sampling of the hexagonal type in the domain of the transform (that is to say representing the center of the beams).

The requirement for hexagonal type sampling in the origin domain (generally called "time domain" in the signal processing technique) is essentially due to the usually hexagonal shape of the antenna. The requirement for hexagonal type sampling in the transform domain (generally called "frequency domain" in the signal processing technique) comes from the fact that it allows more efficient coverage when the beams coincide with a hexagonal grid.

The invention therefore sets itself the aim of solving this problem, namely to offer both an efficient architecture and compatible with current integration technologies, the efficiency being expressed in terms of low mass, of simple implementation. , reliability and easy testing; and an optimized algorithm, the term "optimized" must in turn be included in criteria for technological rather than mathematical optimization.

• en ce que la première couche de circuits est constituée d'une rangée de N ² cellules munies chacune de R entrées et de R sorties, chaque cellule recevant un signal présent sur l'une desdites N _t entrées et effectuant, sur les signaux présents sur ses R entrées, une transformée discrète de Fourier unidimensionnelle ;
• en ce que la seconde couche de circuits est constituée de R jeux indépendants de cellules, munies chacune de N entrées et N sorties, chaque jeu comportant une première et une seconde rangée de N cellules, chaque cellule effectuant, sur les signaux présents sur ses N entrées, une transformée discrète de Fourier unidimensionnelle ; chacune des sorties des cellules de ladite seconde rangée commandant un desdits éléments rayonnants ;
• en ce que lesdites première et seconde couches de circuits sont reliées par un premier ensemble d'interconnexions, établissant des connexions entre les sorties des cellules de ladite rangée de N ² cellules et les entrées des N cellules de la première rangée des R jeux indépendants de cellules ; les sorties de rang i de chaque cellule étant connectées, chacune, à l'une des entrées de cellule du jeu indépendant de même rang ; avec i ∈ {l, R};
• et en ce que lesdites première et seconde rangées de cellules de chacun desdits R jeux indépendants sont reliées par un second ensemble d'interconnexions, établissant des connexions entre les sorties des N cellules de la première rangée et les entrées des N cellules de la seconde rangée ; la sortie de rang j de chaque cellule du premier rang étant connectée à une entrée de la cellule de même rang de la seconde rangée ; avec j ∈ {l, N}.

The subject of the invention is therefore a beam shaping network for radiofrequency antenna comprising a determined number of radiating elements for the generation of multiple beams, said shaping network comprising a determined number of signal inputs, a number of signal outputs control of radiating elements equal to said predetermined number of signal inputs and effecting a discrete two-dimensional hexagonal Fourier transform on the input signals, characterized in that said predetermined number of inputs and outputs being equal to N _t , with N _t = R × N ² , R and N being whole numbers, the circuits composing said beam shaping network are divided into first and second layers of circuits performing, respectively, a discrete one-dimensional Fourier transform of lines and a discrete transform of One-dimensional fourier of columns;

• in that the first layer of circuits consists of a row of N ² cells each provided with R inputs and R outputs, each cell receiving a signal present on one of said N _t inputs and performing, on the signals present on its R inputs, a discrete one-dimensional Fourier transform;
• in that the second layer of circuits consists of R independent sets of cells, each provided with N inputs and N outputs, each set comprising a first and a second row of N cells, each cell carrying out, on the signals present on its N starters, a discrete transform of One-dimensional Fourier; each of the outputs of the cells of said second row controlling one of said radiating elements;
• in that said first and second circuit layers are connected by a first set of interconnections, establishing connections between the outputs of the cells of said row of N ² cells and the inputs of N cells of the first row of R independent sets of cells; the outputs of rank i of each cell being connected, each, to one of the cell inputs of the independent game of the same rank; with i ∈ {l, R };
• and in that said first and second rows of cells of each of said R independent sets are connected by a second set of interconnections, establishing connections between the outputs of the N cells of the first row and the inputs of the N cells of the second row ; the output of row j of each cell of the first row being connected to an input of the cell of the same rank of the second row; with j ∈ {l, N }.

The invention also relates to a structure for the mechanical implantation of such a network.

• La figure 1 illustre schématiquement un conformateur de faisceaux à matrice de Butler de dimensions 16×16 selon l'art connu ;
• La figure 2 représente schématiquement la topologie d'une région élémentaire du support des éléments rayonnants d'une antenne du type antenne réseau à commande de phase ;
• La figure 3 représente schématiquement la duplication de cette région élémentaire sur un fragment plus important du support ;
• La figure 4 représente schématiquement une région du support des éléments rayonnants pour un réseau hexagonal de dimensions 27×27 ;
• La figure 5 illustre schématiquement l'architecture fonctionnelle d'un conformateur de faisceaux du type hexagonal selon l'invention de dimensions 27× 27 ;
• La figure 6 illustre schématiquement l'architecture fonctionnelle d'un conformateur de faisceaux du type hexagonal selon l'invention de dimensions 27× 27, incorporant des commutateurs ;
• Les figures 7 et 8 illustrent le schéma fonctionnel et la topologie des circuits d'une cellule de base de dimension 3×3 utilisée de façon répétée pour la réalisation du conformateur de la figure 5 ;
• La figure 9 illustre la topologie des circuits d'une cellule de base de dimension 3×3 utilisée de façon répétée pour la réalisation des conformateurs des figures 5 ou 6, selon un second mode de réalisation ;
• La figure 10 illustre une variante de ce second mode de réalisation ;
• La figure 11 illustre schématiquement l'architecture fonctionnelle d'un conformateur de faisceaux du type hexagonal selon l'invention de dimensions 48× 48 ;
• Les figures 12 et 13 illustrent le schéma fonctionnel et la topologie des circuits d'une cellule de base de dimension 4×4 utilisée de façon répétitive pour la réalisation du conformateur de la figure 11 ;
• La figure 14 illustre la topologie des circuits d'une cellule de base de dimension 4×4 utilisée de façon répétée pour la réalisation du conformateur de la figure 11, selon un second mode de réalisation ;
• La figure 15 illustre schématiquement un premier exemple d'implantation physique d'un conformateur de faisceaux ;
• La figure 16 illustre schématiquement un deuxième exemple d'implantation physique d'un conformateur de faisceaux, particulièrement approprié pour un conformateur de grandes dimensions ;
• La figure 17 illustre schématiquement un troisième exemple d'implantation physique de ce conformateur de faisceaux, particulièrement approprié pour un conformateur de très grandes dimensions;
• La figure 18 illustre la réalisation d'un cheminement d'interconnexions mettant en oeuvre la technologie dite "planar" ;
• La figure 19 illustre un exemple de réalisation de ligne de transmission du type ruban pouvant être utilisée comme élément de liaison.

Finally, it relates to the application of this network to the control of radio frequency antennas of the phase control network type for the generation of multiple beams, in particular of a hexagonal grid antenna on board a satellite.

• FIG. 1 schematically illustrates a beam shaping machine with Butler matrix of dimensions 16 × 16 according to the prior art;
• FIG. 2 schematically represents the topology of an elementary region of the support of the radiating elements of an antenna of the network antenna type with phase control;
• FIG. 3 schematically represents the duplication of this elementary region on a larger fragment of the support;
• FIG. 4 schematically represents a region of the support of the radiating elements for a hexagonal network of dimensions 27 × 27;
• FIG. 5 schematically illustrates the functional architecture of a beam former of the hexagonal type according to the invention of dimensions 27 × 27;
• FIG. 6 schematically illustrates the functional architecture of a beam former of the hexagonal type according to the invention of dimensions 27 × 27, incorporating switches;
• FIGS. 7 and 8 illustrate the functional diagram and the topology of the circuits of a basic cell of dimension 3 × 3 used repeatedly for the production of the shaper of FIG. 5;
• FIG. 9 illustrates the topology of the circuits of a basic cell of dimension 3 × 3 used repeatedly for the production of the conformers of FIGS. 5 or 6, according to a second embodiment;
• FIG. 10 illustrates a variant of this second embodiment;
• FIG. 11 schematically illustrates the functional architecture of a beam former of the hexagonal type according to the invention of dimensions 48 × 48;
• FIGS. 12 and 13 illustrate the functional diagram and the topology of the circuits of a basic cell of dimension 4 × 4 used repeatedly for the production of the shaper of FIG. 11;
• FIG. 14 illustrates the topology of the circuits of a basic cell of dimension 4 × 4 used repeatedly for the production of the shaper of FIG. 11, according to a second embodiment;
• FIG. 15 schematically illustrates a first example of physical layout of a beam shaper;
• FIG. 16 schematically illustrates a second example of physical layout of a beam former, particularly suitable for a large former;
• FIG. 17 schematically illustrates a third example of physical layout of this beam former, particularly suitable for a very large former;
• FIG. 18 illustrates the making of an interconnection path using the so-called "planar"technology;
• FIG. 19 illustrates an exemplary embodiment of a ribbon-type transmission line that can be used as a connecting element.

As has been recalled, among the constraints of radiofrequency technology, it is necessary to implement an efficient architecture which operates the "DFT" transform of a two-dimensional sequence of signals with hexagonal sampling (that is to say, signal inputs to an antenna element which is placed on a grid of hexagonal topology) so that the coefficients resulting from the "DFT" are also with hexagonal sampling in the domain of the transform (representing the center of the beams).

• 1. Il doit être fait usage d'une décomposition lignes/colonnes ;
• 2. L'architecture doit être modulaire et faire appel à un très petit nombre de blocs fonctionnels (un ou deux) qui sont répétés et dont la complexité reste compatible avec les contraintes des technologies d'intégration habituelles à ce type d'application ;
• 3. L'architecture doit offrir un degré de modularité additionnel tel que plusieurs blocs fonctionnels puissent être interconnectés pour former un bloc que l'on peut qualifier de "macro bloc" et qui peut être utilisé dans différentes parties de l'architecture dans sa globalité ;
• 4. Le nombre de déphaseurs associés aux interconnexions doit être minimisé.

The architecture must have the following characteristics:

• 1. Use must be made of a row / column breakdown;
• 2. The architecture must be modular and use a very small number of functional blocks (one or two) which are repeated and whose complexity remains compatible with the constraints of the usual integration technologies for this type of application;
• 3. The architecture must offer an additional degree of modularity such that several functional blocks can be interconnected to form a block which can be described as "macro block" and which can be used in different parts of the architecture as a whole. ;
• 4. The number of phase shifters associated with the interconnections must be minimized.

The mathematical algorithm implemented in the beam former according to the invention must be compatible with the constraints of the architecture which have just been mentioned.

We will first recall the main properties and characteristics of a two-dimensional hexagonal "DFT" algorithm. Only the characteristics necessary for the invention will be explained in detail, the mathematical basis of such a transform being well known per se. We can again advantageously refer, for example, to the article by GG Chadwick et al. cited above for a more detailed explanation of this algorithm applied to radio frequency antennas of the phase control network type.

• 1. Il est tout d'abord nécessaire de déterminer les régions du support des deux domaines de transformée, c'est-à-dire d'établir, dans l'espace bidimensionnel d'origine, comment sont répartis les éléments rayonnants de l'antenne et, dans l'espace bidimensionnel de transformée, comment sont répartis les centres des faisceaux. Ces deux régions de support sont caractérisées par deux nombres, à savoir N ₁ et N ₂ , et sont dotées d'une forme sensiblement hexagonale comme illustré par la figure 2.
  Les éléments d'indice i, El _i , sont donc compris dans un hexagone repéré par rapport à deux axes arbitraires orthonormés yx. Le côté inférieur, de dimension N ₁ , est confondu avec l'axe x et le côté supérieur, de dimension N ₁ +1, est parallèle à cet axe x. Les côtés latéraux, de dimensions N ₂ et N ₂ +1, sont inclinés par rapport à l'axe x d'un angle α et d'un angle (π - α), respectivement, avec α peu différent de 45° dans l'exemple décrit. La légère asymétrie simplifie beaucoup l'explication des calculs mathématiques, mais n'a pas d'incidence sur le système selon l'invention, car dans un cas réel, seuls les éléments nécessaires à l'intérieur de la région de support peuvent être sélectionnés, région qui peut avoir une forme symétrique.
• 2. Dans une deuxième étape, la périodicité de la matrice N est déterminée. Celle-ci constitue une matrice caractéristique de la transformée bidimensionnelle utilisée dans le cadre de l'invention. Elle doit être sélectionnée de telle manière qu'elle concerne un signal à échantillonnages hexagonal dont la transformée de Fourier est aussi un signal à échantillonnages hexagonal. Cette matrice peut prendre la forme suivante :
  
• 3. Dans une troisième étape, on écrit les transformées de Fourier Discrètes (Directe) et Inverse : "DFT" et "IDFT". Elles peuvent être déterminées à partir des équations suivantes :
  
  

The steps described below are followed:

• 1. It is first of all necessary to determine the regions of the support of the two transform domains, that is to say to establish, in the original two-dimensional space, how are the radiating elements of the antenna and, in the two-dimensional transform space, how the centers of the beams are distributed. These two support regions are characterized by two numbers, namely N ₁ and N ₂ , and have a substantially hexagonal shape as illustrated in FIG. 2.
  The elements of index i , El _i , are therefore included in a hexagon identified with respect to two arbitrary orthonormal axes yx. The lower side, of dimension N ₁ , coincides with the x axis and the upper side, of dimension N ₁ + 1, is parallel to this x axis . The lateral sides, of dimensions N ₂ and N ₂ +1, are inclined relative to the x axis by an angle α and an angle (π - α), respectively, with α little different from 45 ° in l example described. The slight asymmetry greatly simplifies the explanation of mathematical calculations, but does not affect the system according to the invention, because in a real case, only the elements necessary inside the support region can be selected, a region which can have a symmetrical shape.
• 2. In a second step, the periodicity of the matrix N is determined. This constitutes a characteristic matrix of the two-dimensional transform used in the context of the invention. It must be selected in such a way that it concerns a signal with hexagonal samples, the Fourier transform of which is also a signal with hexagonal samples. This matrix can take the following form:
  
• 3. In a third step, we write the Discrete (Direct) and Inverse Fourier transforms: "DFT" and "IDFT". They can be determined from the following equations:
  
  

[n] étant l'une des représentations possibles de cette classe.The expression L _{I / N} is an algebraic sequence called the modulo n residue sequence of the algebraic sequence LI, which is a two-dimensional lattice of integers. In particular, L _{I / N} is a series of equivalence classes, whose generic class [ n ] is given by the expression: $$\text{[n] =}\mathit{\text{{m, n}}\text{∈}{\mathit{\text{L}}}_{\mathit{\text{I}}}\text{as such manner that}\mathit{\text{not}}\text{=}\mathit{\text{m (mod N)}}}$$

[n] being one of the possible representations of this class.

[k] est une des représentations possibles de cette classe.Similarly, L _{I / N} ^T is a sequence of modulo N ^T residues of LI, and therefore a sequence of equivalence classes, for which a generic class [k] is given by the expression: $$\text{[}\mathit{\text{k}}\text{] =}\mathit{\text{{d, k}}\text{∈}{\mathit{\text{L}}}_{\mathit{\text{I}}}\text{as such manner that}{\mathit{\text{k = j (mod N}}}^{\mathit{\text{T}}}\mathit{\text{)}}}$$

[ k ] is one of the possible representations of this class.

We will consider one of the suites, for example more L _{I / N.} The number of classes of residues The following _{I / N} is called the L indexes in _I L _N. The number of residue classes, and therefore of points to consider in equation (3), becomes equal to | det ( N ) |, which is itself equal to [(2N ₁ x N ₂ ) + N ₂ ² ] (See Equation (1)). There are an infinite number of possible selections for the representative sequences of L _{I / N} since the number of representations of a given equivalence class is infinite.

In a fourth step, the input values x (n) of equation (3) are determined (or alternatively the input values X (k) of equation (2)).

• a) Dans un espace bidimensionnel comprenant les éléments rayonnants comme illustré par la figure 2, on définit deux nouveaux axes, respectivement n ₁ et n ₂ , n ₁ étant confondu avec l'axe x et n ₂ formant un angle α avec cet axe (c'est-à-dire étant confondu avec le côté de dimension N ₂ + 1 de l'hexagone). En outre, chaque élément rayonnant est repéré par rapport à ces nouveaux axes : x(n ₁ , n ₂ ).
• b) On génère ensuite, comme illustré plus particulièrement par la figure 3 (duplications Rp_i), une extension périodique du signal x(n ₁ , n ₂ ) en générant des répétitions du signal original définies comme : $${\mathit{\text{x(n}}}_{\mathit{\text{1}}}\text{- (}{\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{×<figure-callout id="2" label="N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ <figure-callout id="2" label="r" filenames="imgf0001.png,imgf0003.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{×(<figure-callout id="1" label="N" filenames="imgf0001.png,imgf0002.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{+ N}}}_{\mathit{\text{2}}}{\mathit{\text{), n}}}_{\mathit{\text{2}}}\text{- (}{\mathit{\text{r}}}_{\mathit{\text{1}}}\text{x}{\mathit{\text{<figure-callout id="2" label="2N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">2N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ r2xN}}}_{\mathit{\text{2}}}\mathit{\text{)) ;}}$$
  
  N ₁ et N ₂ étant les nombres entiers précédemment définis et r₁ et r₂ des nombres arbitraires, et dont les coordonnées sont exprimées par rapport aux axes n ₁ et n ₂ . Ces répétitions permettent de couvrir entièrement l'espace bidimensionnel. Le jeu initial de points x(n ₁ , n ₂ ), avant répétition, est appelé période fondamentale. La relation suivante est satisfaite : $${\mathit{\text{x(<figure-callout id="1" label="n" filenames="imgf0001.png,imgf0002.png" state="{{state}}">n</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{, n}}}_{\mathit{\text{2}}}{\mathit{\text{) = x(n}}}_{\mathit{\text{1}}}\text{- (}{\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{×<figure-callout id="2" label="N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ <figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{×(<figure-callout id="1" label="N" filenames="imgf0001.png,imgf0002.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{+ N}}}_{\mathit{\text{2}}}{\mathit{\text{)), n}}}_{\mathit{\text{2}}}\mathit{\text{-}}\text{(}{\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{<figure-callout id="2" label="x2N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">x2N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ <figure-callout id="2" label="r" filenames="imgf0001.png,imgf0003.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{×N}}}_{\mathit{\text{2}}}\mathit{\text{))}}$$
  
  r ₁ et r ₂ étant des entiers arbitraires.
• c) Finalement, on peut effectuer une correspondance entre x(n) et x(n(1)) et x(n(2)) dans la représentation étendue, n(1) et n(2) étant définis comme les deux coordonnées qui définissent la représentation des classes d'équivalence [n] de L _I/N . $$\mathit{\text{X(n) = x(n(1), n(2))}}$$
  
  $$\text{avec}\mathit{\text{n = n(1), n(2))}}$$
  

The following procedure is followed (only the case of determining x (n) is illustrated, since we carry out equivalent operations to determine X (k) ):

• a) In a two-dimensional space comprising the radiating elements as illustrated in FIG. 2, two new axes are defined, respectively n ₁ and n ₂ , n ₁ being coincident with the axis x and n ₂ forming an angle α with this axis ( that is to say being confused with the side of dimension N ₂ + 1 of the hexagon). In addition, each radiating element is identified with respect to these new axes: x (n ₁ , n ₂ ).
• b) Next, as illustrated more particularly by FIG. 3 (Rp _i duplications), a periodic extension of the signal x (n ₁ , n ₂ ) is generated by generating repetitions of the original signal defined as: $${\mathit{\text{x (n}}}_{\mathit{\text{1}}}\text{- (}{\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{× <figure-callout id="2" label="N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ <figure-callout id="2" label="r" filenames="imgf0001.png,imgf0003.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{× (<figure-callout id="1" label="N" filenames="imgf0001.png,imgf0002.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{+ N}}}_{\mathit{\text{2}}}{\mathit{\text{), not}}}_{\mathit{\text{2}}}\text{- (}{\mathit{\text{r}}}_{\mathit{\text{1}}}\text{x}{\mathit{\text{<figure-callout id="2" label="2N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">2N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ r2xN}}}_{\mathit{\text{2}}}\mathit{\text{));}}$$
  
  N ₁ and N ₂ being the integers previously defined and r ₁ and r _{2 being} arbitrary numbers, the coordinates of which are expressed relative to the axes n ₁ and n ₂ . These repetitions make it possible to fully cover the two-dimensional space. The initial set of points x (n ₁ , n ₂ ), before repetition, is called the fundamental period. The following relationship is satisfied: $${\mathit{\text{x (<figure-callout id="1" label="n" filenames="imgf0001.png,imgf0002.png" state="{{state}}">n</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{, not}}}_{\mathit{\text{2}}}{\mathit{\text{) = x (n}}}_{\mathit{\text{1}}}\text{- (}{\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{× <figure-callout id="2" label="N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ <figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{× (<figure-callout id="1" label="N" filenames="imgf0001.png,imgf0002.png" state="{{state}}">N</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{+ N}}}_{\mathit{\text{2}}}{\mathit{\text{)), not}}}_{\mathit{\text{2}}}\mathit{\text{-}}\text{((}{\mathit{\text{<figure-callout id="1" label="r" filenames="imgf0001.png,imgf0002.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{<figure-callout id="2" label="x2N" filenames="imgf0001.png,imgf0003.png" state="{{state}}">x2N</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{+ <figure-callout id="2" label="r" filenames="imgf0001.png,imgf0003.png" state="{{state}}">r</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{× N}}}_{\mathit{\text{2}}}\mathit{\text{)))}}$$
  
  r ₁ and r ₂ being arbitrary integers.
• c) Finally, we can make a correspondence between x (n) and x (n (1)) and x (n (2)) in the extended representation, n (1) and n (2) being defined as the two coordinates that define the representation of the equivalence classes [n] L _{I / N.} $$\mathit{\text{X (n) = x (n (1), n (2))}}$$
  
  $$\text{with}\mathit{\text{n = n (1), n (2))}}$$
  

• a) Détermination des éléments (jeu des représentations [n]) de L _I/N (ou alternativement de L _I/N ^T );
• b) détermination des valeurs de x(n) selon l'équation (3) (ou alternativement de X(k) selon l'équation (2)) ;
• c) Application de l'équation (2) pour la "DFT" (Directe) ou pour la "IDFT".

From this result, it becomes possible to determine an architecture of the beam shaping network according to the invention. The preceding steps can be summarized as follows:

• a) Determination of the elements (set of representations [ n ]) of L _{I / N} (or alternatively of L _{I / N} ^T ) ;
• b) determination of the values of x (n) according to equation (3) (or alternatively of X (k) according to equation (2));
• c) Application of equation (2) for the "DFT" (Direct) or for the "IDFT".

Up to this point, the procedure has consisted in a simple reformulation of the problem according to an appropriate algebraic representation. In reality, the "DFT" of equation (2) does not use a fast algorithm and, consequently, does not meet any of the criteria set by the invention.

Since the periodicity matrix (equation (1)) is not a diagonal matrix, it is not possible to carry out a row / column decomposition in equation (2), which is the first condition required by the invention to get an efficient implantation.

• a) Décomposition de la matrice périodique N en ce qu'il est appelé une forme normale de Smith. Cette décomposition est toujours possible. On obtient une relation matricielle de la forme : $$\mathit{\text{N = U.D.V}}$$
  
  relation dans laquelle U et V sont des matrices unimodulaire entières (c'est-à-dire pour lesquelles la relation suivante est satisfaite : det(U) = det(V) = 1, et D est une matrice diagonale entière de la forme :
  
  matrice dans laquelle d ₁ est un diviseur de d ₂ .
• b) Substitution de l'équation (8) dans l'équation (3) par laquelle on obtient :
  
        avec k ∈ L _I/N ^T .

To solve this first problem, it is necessary to perform the following steps:

• a) Decomposition of the periodic matrix N into what is called a normal Smith form. This breakdown is always possible. We obtain a matrix relation of the form: $$\mathit{\text{N = UDV}}$$
  
  relation in which U and V are whole unimodular matrices (i.e. for which the following relation is satisfied: det ( U ) = det ( V ) = 1, and D is an integer diagonal matrix of the form:
  
  matrix in which d ₁ is a divisor of d ₂ .
• b) Substitution of equation (8) in equation (3) by which we obtain:
  
  with k ∈ L _{I / N} ^T.

By defining n̂ = U ^-1 .n (11) and k̂ = (V ^-1 ) ^T .k (12), equation (10) can be rewritten as follows:

Since the matrix D is a diagonal matrix, equation (13) therefore describes a conventional rectangular "DFT", with a row / column decomposition.

It should be noted that the new variables introduced (see (11) and (12)) are isomorphic with the variables n and k , respectively. In addition, they only assume a rearrangement in the input and output data which does not involve additional calculations. Finally, it should be noted that, the parameters of a particular problem being fixed, that is to say the geometry of the antenna and of the bundles, the aforementioned rearrangement has no impact on the resulting material. It is just necessary to know how to associate the "DFT" inputs with the radiating elements and the "DFT" outputs with the beams, which can be deduced from equation (11).

With a) and b), a first objective of the invention leading to an efficient hardware implementation, that is to say the row / column decomposition, is achieved.

The objective of breaking down into large modular blocks (which have been qualified in the above as "macro blocks") is also achieved. These blocks are repeated in architecture.

It is also interesting to note that all the rows of "DFT" are identical among themselves and that this is also true for the columns. It is therefore necessary to determine only one of these blocks.

In addition, the large two-dimensional "DFT" has been reduced to two smaller "DFT". The first step for calculating an "FFT" has therefore been carried out.

To achieve the other objectives set by the invention, it is necessary to carry out additional steps. Each of these two one-dimensional "DFT" will now be broken down into a set of small modular blocks, compatible with the limitations of integration technologies commonly used for this type of application. These blocks can be reused many times in the shaping network according to the invention.

• de Russel M. Mersereau : "The Processing of Hexagonally Sampled Two-Dimensional Signals", paru dans "Proceedings of the IEEE", vol. 67, No. 6, juin 1979, pages 930-949 ;
• de Russel M. Mersereau et la. : "The Processing of Periodically Sampled Multidimensional Signals", paru dans "IEEE Transactions on ASSP", vol. 31, février 1983, pages 188-194 ;
• et de Abderrezac Guessoum et al. : "Fast Algorithms for the Multidimensional Discrete Fourier Transform" paru dans IEEE Transactions on ASSP", vol. 34, août 1986, pages 937-943.

To do this, it is necessary to work further independently, the rows and columns of the one-dimensional "DFT" and to have recourse to the well-known "FFT" algorithm for one-dimensional "DFT", that is to say ie the so-called "radix" algorithm (radix-2, radix-3, radix-4, etc.), the decomposition into prime factors, etc. The selection of the algorithm depends on the size of the one-dimensional "DFT". A review of these algorithms can be found in the following articles:

• by Russel M. Mersereau: "The Processing of Hexagonally Sampled Two-Dimensional Signals", published in "Proceedings of the IEEE", vol. 67, No. 6, June 1979, pages 930-949;
• by Russell M. Mersereau and the. : "The Processing of Periodically Sampled Multidimensional Signals", published in "IEEE Transactions on ASSP", vol. 31, February 1983, pages 188-194;
• and from Abderrezac Guessoum et al. : "Fast Algorithms for the Multidimensional Discrete Fourier Transform" published in IEEE Transactions on ASSP ", vol. 34, August 1986, pages 937-943.

Although the previous decomposition can be effective in practice (cases where the size of the network and the number of beams can be adjusted so as to obtain well-conditioned numbers), an alternative procedure, which further minimizes the number of phase shifters, can be implemented when det ( D ) can be expressed as the product of two numbers (ie p and q ) which are prime to each other. In this case, the decomposition into "DFT" of smaller dimension can be carried out directly in the case in two dimensions and not independently in the case in one dimension. This case can be considered as an extension of the theory of the decomposition of the one-dimensional "FFT" into prime factors, which is known under the Anglo-Saxon name "MPFA" (for Algorithm of Matrix in Prime Factors).

• Les jeux de "DFT" unidimensionnelles de grandes dimensions se réduisent à des blocs "DFT" de faibles dimensions, répétés de nombreuses fois tout au long de l'architecture ;
• Les déphaseurs dans les stades intermédiaires entre lignes et colonnes ne sont plus nécessaires ; le nombre de déphaseurs est donc réduit.

These two approaches to decomposition make it possible to obtain a hardware architecture which satisfies all the requirements which the invention had set for itself, that is to say, in addition to the requirements already mentioned, the following requirements:

• Large one-dimensional "DFT" sets are reduced to small "DFT" blocks, repeated many times throughout the architecture;
• The phase shifters in the intermediate stages between rows and columns are no longer necessary; the number of phase shifters is therefore reduced.

Generally, with the normal parameters to be considered in a satellite communications application, the large two-dimensional "FFT" will consist of a layer of simple one-dimensional "DFT" (of order 3 or 4) for the "DFT" lines and at more than two layers of one-dimensional "DFT" of small dimension for the one-dimensional "DFT" of columns. There are therefore three layers in total.

We will now describe the hardware architecture of beam shapers according to the invention.

To fix the ideas, we will consider two cases: a first case concerning an architecture of a beam former of moderate size, in this case a hexagonal beam former of size 27 × 27, and a second case concerning a beam former more complex, in this case a 48 × 48 size beam former.

According to the procedure which has just been recalled, it is first of all necessary to determine the regions of the support, that is to say of the antenna. If we admit that N ₁ = N ₂ = 3, the total number of radiating elements will be equal to 2 × N ₁ x N ₂ + N ₂ ² , that is 27 radiating elements and 27 beams. The region of the support is illustrated in FIG. 4: elements El ₁ to El ₂₇ .

We determine the matrix N : If we refer again to equation (1), the matrix N becomes:

We determine the values of the elements [ n ] of L _{I / N} and the elements [ k ] of L _{I / N} T :

et

The selection is not unique since, as indicated, there are endless representations of each class. You can choose the game below.

and

Note that since N is symmetric, [ n ] and [ k ] have the same sets of values.

The values of x (n) are then determined and they are connected to the elements El _i of the antenna (see FIG. 4):

• a) Décomposition de la matrice N dans sa forme normale de Smith :
  
• b) Réécriture de la "DFT" sous la forme d'une "DFT" rectangulaire :
  
  et
  
  

We deduce the architecture "FFT":

• a) Decomposition of the matrix N in its normal Smith form:
  
• b) Rewriting of the "DFT" in the form of a rectangular "DFT":
  
  and
  
  

Equation (21) determines the input and output rearrangements.

• a) En ce qui concerne la "DFT" unidimensionnelle de ligne, celle-ci est une "DFT" 3 points, elle est donc réduite à son expression minimale.
• B) La "DFT" unidimensionnelle de colonne est une "DFT" de 9 points. Il est donc possible d'utiliser l'algorithme de décomposition lignes/colonnes radix-3.

The one-dimensional "FFT" algorithm is then used for the one-dimensional row and column "DFT":

• a) With regard to the one-dimensional "DFT" of line, this one is a "DFT" 3 points, it is thus reduced to its minimal expression.
• B) The one-dimensional column "DFT" is a 9 point "DFT". It is therefore possible to use the radix-3 row / column decomposition algorithm.

   dans laquelle il a été défini les expressions suivantes :

Equation (19) can be rewritten as follows:

in which the following expressions have been defined:

C (n ₂ , k ₁ ) can be defined as follows:

By substituting (25) in (22), we obtain:

The following variable changes are then made: $$\begin{gathered} {\mathit{\text{not}}}_{\mathit{\text{2}}}\mathit{\text{= 3p + q}}\text{with}\mathit{\text{p}}\text{∈ (0,1,2) and}\mathit{\text{q}}\text{∈ (0,1,2)} \\ {\mathit{\text{<figure-callout id="2" label="k" filenames="imgf0001.png,imgf0003.png" state="{{state}}">k</figure-callout>}}}_{\mathit{\text{2}}}\mathit{\text{= 3r + s}}\text{with}\mathit{\text{r}}\text{∈ (0,1,2) and}\mathit{\text{s}}\text{∈ (0,1,2)} \end{gathered}$$

We then obtain equation (28):

et $$\mathit{\text{E}}\left(\mathit{\text{q}}\text{,}{\mathit{\text{k}}}_{\text{1}}\text{,}\mathit{\text{s}}\right)\text{=}\mathit{\text{D}}\left(\mathit{\text{q}}\text{,}{\mathit{\text{k}}}_{\text{1}}\text{,}\mathit{\text{s}}\right)\text{exp(-}\mathit{\text{j}}\frac{\text{2π}}{\text{9}}\mathit{\text{s}}\text{·}\mathit{\text{q}}\text{)}$$

   et en substituant (30) dans (28), on obtient finalement :

   ou de façon équivalente (équation (32)):

Calling :

and $$\mathit{\text{E}}\left(\mathit{\text{q}}\text{,}{\mathit{\text{<figure-callout id="1" label="k" filenames="imgf0001.png,imgf0002.png" state="{{state}}">k</figure-callout>}}}_{\text{1}}\text{,}\mathit{\text{s}}\right)\text{=}\mathit{\text{D}}\left(\mathit{\text{q}}\text{,}{\mathit{\text{<figure-callout id="1" label="k" filenames="imgf0001.png,imgf0002.png" state="{{state}}">k</figure-callout>}}}_{\text{1}}\text{,}\mathit{\text{s}}\right)\text{exp (-}\mathit{\text{j}}\frac{\text{2π}}{\text{9}}\mathit{\text{s}}\text{·}\mathit{\text{q}}\text{)}$$

and by substituting (30) in (28), we finally obtain:

or equivalent (equation (32)):

The inverse transform can be obtained simply by conjugating the exponentials, normalizing by the determinant of D and changing the variables (equation (33)):

The architecture of the beam former can be determined so that it satisfies these equations (32) and (33), that is to say so that the transforms "DFT" and "IDFT" are carried out.

FIG. 5 illustrates the architecture of a hexagonal beam former CFH, of dimensions 27 × 27, according to the invention.

The rearrangement of the output elements is identified by the references El ₁ to El ₂₇ . These references correspond to those of the radiating elements of FIG. 4. This rearrangement is derived from equation (21).

As is clear from FIG. 5, the CFH hexagonal beam former according to the invention comprises only two main layers of circuits. In addition, it uses only one kind of cell, very simple, in this case circuits performing a one-dimensional "DFT" 3 points.

More precisely, the CFH hexagonal beam former includes four sets of cells: 1 to 4, the set referenced 4 constituting one of the circuit layers.

This layer includes nine identical cells or modules, 41 to 47, performing a one-dimensional 3-point "DFT". Such a module will be described later with reference to FIG. 6. The inputs of these cells, referenced e ₁ to e ₂₇ , from top to bottom in FIG. 5, are in number equal to the number of elements El _i .

The second layer of circuits includes three games, referenced 1 to 3. Each of these games has 9 inputs and 9 outputs. Each set consists of two rows of 3 basic cells, each performing a 3-point "DFT". The two rows are connected by paths of the line / column links incorporating phase shifters: 111 to 133, 211 to 233 and 311 to 333, called CLC ₁ to CLC ₃ respectively, for games 1 to 3. Each game is provided with identical topology. The three outputs of the first module, for example module 11, are each connected to 0 ° phase shifters: 111, 112 and 113. In other words, the output signals are not phase shifted. The three outputs of the second module, for example module 12, are connected, respectively to 0 °, 40 ° and 80 ° phase shifters: 121, 122 and 123.

The three outputs of the third module, for example module 13, are connected, respectively to 0 °, 80 ° and 160 ° phase shifters: 131, 132 and 133. The outputs of the first phase shifters of each set, for example 111, 121 and 131, are connected to one of the three inputs (from top to bottom in FIG. 5) of the first module of the second row, for example module 14. The outputs of the second phase shifters of each set, for example 112, 122 and 132, are connected to one of the three inputs of the second module of the second row, for example module 15. The outputs of the third phase shifters of each set, for example 113, 123 and 133, are connected to one of the three inputs of the third module of the second row, for example module 16.

The outputs of the cells, 14 to 16, 24 to 26 and 34 to 36, of the second row of sets 1 to 3 are connected to the radiating elements in the following order, in accordance with the aforementioned rearrangement: El ₁ , El ₁₃ , El ₁₆ , El ₂ , El ₁₄ , El ₁₇ , El ₃ , El ₁₅ , El ₁₈ , El ₆ , El ₂₀ , El ₂₃ , El ₇ , El ₂₁ , El ₄ , El ₁₉ , El ₂₂ , El ₅ , El ₁₂ , El ₂₆ , El ₉ , El ₂₄ , El ₂₇ , El ₁₀ , El ₂₅ , El ₈ and El ₁₁ (from top to bottom in the figure).

For their shares, the first outputs of the first three cells, 41 to 43, of set 4, are connected to the first inputs of cells, 11 to 13, of the first row of set 1. Likewise, the first outputs of the following three cells , 44 to 46, are connected to the second inputs of the three cells, 11 to 13, and the first outputs of the last three cells, 47 to 49, to the third inputs of the three cells, 11 to 13.

This interconnection diagram is repeated for the second outputs of all the cells of the first set which are connected to the second inputs of the sets of the second layer. It is finally the same for the third outputs which are connected to one of the third inputs of the cells of the second circuit layer.

This arrangement of row / column links bears the general reference 4a.

The architecture of the hexagonal beam former according to the invention is therefore perfectly regular. In addition, it proves to be much less complex than the architecture of an equivalent hexagonal beam former according to the known art, such as that described, for example, in the aforementioned article by Chadwick. The number of phase shifters is reduced to a minimum, according to one of the aims of the invention.

The hexagonal beam shaping architecture CFH which has just been described lends itself to very easy integration of a matrix of radiofrequency switches. By directly incorporating this matrix into the architecture of the shaper, a high degree of beam switching possibility is obtained. More precisely, the resulting architecture performs both the functions corresponding to a hexagonal beam former and those corresponding to a beam changer.

FIG. 6 schematically illustrates such an architecture, in the particular example of a hexagonal beam former CFH ', of dimensions 27 × 27. It takes up, in its entirety, the architecture of the shaper of FIG. 5 which it is useless to rewrite.

The main difference is the addition of three layers of switches, Co ₁ to Co ₃ , respectively. Each layer comprises nine matrixes of switches of dimensions 3 × 3: Co ₁₁ to Co ₁₉ , for the first layer Co ₁ ; Co ₂₁ to Co ₂₉ , for the second layer Co ₂ ; Co ₃₁ to Co ₃₉ , for the third layer Co ₃ .

The first layer Co ₁ is inserted between the inputs, e ₁ to e ₂₇ , and the inputs of the 3 × 3 cells, 41 to 49, of the circuits 4.

The second layer Co ₂ is interposed between the outputs of the set of row / column connections 4a and the inputs of the cells of dimensions 3 × 3, 41 to 49.

Finally, the third layer Co ₃ is inserted between the outputs of the three sets of row / column links, CLC ₁ to CLC ₃ , and the inputs of the 3 × 3 cells, 41 to 49.

It can be seen that the architecture of the beam shaping CFH 'remains completely symmetrical.

By initializing all twenty-seven 3 × 3 switch matrices to an appropriate state, we can theoretically obtain 6 ²⁷ permutations of real beams in space, corresponding to each beam input port.

In reality, this technique does not allow the implantation of all the above permutations. However, the number of permutations is extremely high. Experience shows that it is sufficient for most applications.

This solution is to be compared to the conventional solution which would have consisted, in order to obtain the same result, in the implementation of a complete matrix of switches of dimensions 27 × 27 with a beam conformator in cascade.

Different architectures are known for the realization of the radio frequency switch function ("crossbar", reconfigurable circuits, divider-power mixer circuits, etc.). In general, circuit layouts are limited by the insulation that can be reached between ports, insulation that decreases with the size of the switch matrix and / or with the associated insertion losses.

If the architecture according to the invention is implemented, which allows the incorporation of the switching function in the conforming function, it is possible to obtain good isolation: each signal propagates only through the switching circuits of a matrix of dimension 3 × 3, for a hexagonal beam former of dimensions 27 × 27. The increase in insertion losses is negligible.

FIG. 7 very schematically illustrates the functional diagram of a circuit performing a one-dimensional "DFT" 3 points on three input signals, referenced I ₁ to I ₃ . The output signals are referenced O ₁ to O ₃ . By way of example, it may be cell 11, it being understood that all the cells are identical. It is a conventional circuit diagram, well known to those skilled in the art and which need not be described further. It is only useful to note that the connections between the inputs and the signal output O ₃ are free of phase shifters. It is the same between I ₁ and O ₁ . The direct links I ₂ -O ₂ and I ₃ -O ₃ include a phase shifter 120 °, ϕ ₂₂ and ϕ ₃₃ respectively. The I ₂ -O ₃ and I ₃ -O ₂ cross links include a 240 ° phase shifter, ϕ ₂₃ and ϕ ₃₂ respectively.

The basic cells 11 to 49 (FIG. 5) can be produced by using miniaturization technologies, for example the technology known by the Anglo-Saxon name "GaAs MMIC" (for Monolithic Microwave Integrated Circuits on Gallium Arsenide ). Depending on the dimensions of the base cell, one or more "MMICs" chips will be required to integrate the cell. In the example described, the basic cell can be produced as illustrated in FIG. 8. The cell 11, the functional diagram of which is illustrated by FIG. 7, is physically produced using radiofrequency "MMICs", integrating the circuits CI-1 to CI-3, each forming a 90 ° / 3 dB hybrid technology sub-cell, each having two inputs and two outputs, one of the outputs being 90 ° phase shifted. The CI-2 sub-cell performs an asymmetrical division of the electrical power received, in the sense that 2/3 of the power is transmitted to the port marked "0" and 1/3 of the power to the port marked "-90". The number of "MMICs" depends on the technological design. A solution based on a single chip is feasible if the total size of the chip remains compatible with the integration technologies used in the field. The phase shift is obtained using capacitors and inductors, with localized constants, in the wavelength band "L" or "S". The additional phase shifters ϕ _-90 , ϕ ₊₃₀ and ϕ ₊₆₀ provide the phase shifts 120 ° and 240 ° of Figure 6. The phase shifters 111 to 333 of Figure 5 could also be included in the "MMICs".

The integrated circuit (s) "MMICs is (are) advantageously included (s) in a single microwave package.

It is easy to see that the architecture described which allows the use of a "MMIC" technology is very advantageous, from several points of view.

We can indeed hope for an electrical behavior very similar from one cell to another (both with regard to the phase shift and the amplitude of the signals delivered). Manufacturing tolerances and related problems are therefore minimized.

Likewise, due to the very simple nature of "MMICs", in passive circuits based on circuits comprising only capacitors and inductances, a very high efficiency can be achieved during the manufacture of these, with low costs associated with this return.

It is still possible to improve the topology of 3 × 3 basic cells. FIG. 9 schematically illustrates the topology of a 3 × 3 cell according to a preferred embodiment of the invention.

As before, it is assumed that it is cell 11, it being understood that all the cells are identical.

The three inputs, labeled I ₁ to I ₃ , and the three outputs, labeled O ₁ to O _{3, have been shown} .

As previously also, capacitors and inductances are used, with localized constants, in the wavelength band "L" or "S". The inductors are all marked "L" and the capacitors "C", because these elements are all identical. This constitutes a first simplification.

In addition, it is easy to see on examining FIG. 9 that the topology of the circuit is extremely simple.

• En entrée, chaque borne d'entrée, I₁ à I_3, est reliée aux deux autres par une inductance L ;
• En sortie, chaque borne d'entrée, O₁ à O₃, est reliée aux deux autres par une inductance L ;
• Chaque borne d'entrée, I₁ à I₃, est reliée à une borne de sortie, O₁ à O₃ respectivement, par une inductance L; plus précisément à la borne de sortie de même rang ;
• Enfin, chaque borne, d'entrée, I₁ à I₃, ou de sortie, O₁ à O₃, est connectée au potentiel de la terre M_a par une capacité C.

The implementation rules are as follows:

• At the input, each input terminal, I ₁ to I _3, is connected to the other two by an inductance L;
• At the output, each input terminal, O ₁ to O ₃ , is connected to the other two by an inductance L;
• Each input terminal, I ₁ to I ₃ , is connected to an output terminal, O ₁ to O ₃ respectively, by an inductance L; more precisely to the output terminal of the same rank;
• Finally, each terminal, input, I ₁ to I ₃ , or output, O ₁ to O ₃ , is connected to the earth potential M _a by a capacity C.

The cell is extremely symmetrical and therefore easy to produce.

This 3 × 3 cell configuration allows, at a minimum, integration on a single "MMIC". It is actually possible to integrate several cells on a single "MMIC" of larger dimensions, which is not possible to do simply for the cells produced in accordance with FIG. 8.

• La fonction désirée est obtenue avec un nombre d'inductances et de capacités plus réduits ;
• Toutes les capacités ont la même valeur pour un même type de cellule, ce qui va permettre de procéder à un réglage des circuits du conformateur de faisceaux comme il va l'être montré ci-après.

The advantages specific to this topology are as follows:

• The desired function is obtained with a smaller number of inductances and capacities;
• All the capacities have the same value for the same type of cell, which will make it possible to adjust the circuits of the beam shaper as will be shown below.

Since all the "MMICs" circuits used in a given beam former come from the same wafer in manufacturing, all the capacities will have values with very similar errors compared to the theoretical nominal values calculated. Naturally, this error can correlatively generate phase and amplitude errors, errors which must be compensated for.

This problem can be easily resolved if each of the capacitors C is replaced by a fixed capacitor C 'of lower value in parallel on a MESFET type transistor, which functions as a capacitor of variable value. It suffices to modify the gate control voltage.

Figure 10 illustrates such an arrangement. The capacitance C ′ is placed in parallel with a transistor T _r of the MESFET type whose source and drain are at the potential of the earth M _a . Naturally, this particular configuration is adopted for all the capacities of a 3 × 3 cell.

Since all the capacities used in all the basic 3 × 3 cells, in the entire hexagonal beam former, have the same value, it suffices to control all the grids by a single control voltage, V _c , to be able to adjust all the capacities belonging to the same type of cell to obtain the desired nominal capacity value. It has indeed been indicated, above, that all the errors resulting from the manufacture were very similar. It follows that phase and amplitude errors can be minimized in a very simple way.

This state of affairs alone allows a very significant increase in the maximum dimensions of the beam shaper that can be reached.

We will now describe the architecture of a hexagonal beam former with a more complex structure. To fix the ideas, we consider the case of a beam conformator of dimensions 48 × 48.

The same steps are followed as in the case of the former described above.

We choose N ₁ = N ₂ = 4, or in total, as just indicated, 3 × N ₁ ² = 3 × N ₂ ² = 48 elements.

We determine the periodicity of the matrix N (see (1)):

We then decompose the matrix N into its normal Smith form:

Note that in this case det ( D ) = 48 = 3 × 16, i.e. it can be written as the product of two prime numbers between them ( p = 3, q = 16). As has been pointed out, this case presents more ease for the decomposition of the "DFT" using the Prime Factor Matrix Algorithm ("MPFA"). The algorithm is as follows:

$${\mathit{\text{P}}}_{\mathit{\text{2}}}{\mathit{\text{= D}}}_{\mathit{\text{1}}}{\mathit{\text{·V}}}_{\mathit{\text{1}}}$$

$${\mathit{\text{Q}}}_{\mathit{\text{1}}}{\mathit{\text{= D}}}_{\mathit{\text{2}}}{\mathit{\text{·V}}}_{\mathit{\text{1}}}$$

$${\mathit{\text{Q}}}_{\mathit{\text{2}}}{\mathit{\text{= U·D}}}_{\mathit{\text{2}}}$$

   et les relations suivantes : $${\mathit{\text{n = D}}}_{\text{2}}{\mathit{\text{·U}}}^{\text{-1}}{\mathit{\text{·n}}}_{\text{1}}{\mathit{\text{+ D}}}_{\text{1}}{\mathit{\text{.U}}}^{\text{-1}}\text{·}{\mathit{\text{n}}}_{\text{2}}\mathit{\text{(mod N)}}$$

$$\mathit{\text{k}}\text{=}{\mathit{\text{V}}}^{\text{T}}\text{·}{\mathit{\text{D}}}_{\text{2}}\text{· (}{\mathit{\text{V}}}^{\text{-1}}\text{)·}{\mathit{\text{k}}}_{\text{1}}\text{+}{\mathit{\text{V}}}^{\mathit{\text{T}}}\text{·}{\mathit{\text{D}}}_{\text{1}}\text{· (}{\mathit{\text{V}}}^{\text{-1}}\text{) ·}{\mathit{\text{k}}}_{\text{2}}\text{(mod}{\mathit{\text{N}}}^{\mathit{\text{T}}}\text{)}$$

We can define the following matrices: $${\mathit{\text{<figure-callout id="1" label="P" filenames="imgf0001.png,imgf0002.png" state="{{state}}">P</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{= U · D}}}_{\mathit{\text{1}}}$$

$${\mathit{\text{<figure-callout id="2" label="P" filenames="imgf0001.png,imgf0003.png" state="{{state}}">P</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{= <figure-callout id="1" label="D" filenames="imgf0001.png,imgf0002.png" state="{{state}}">D</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{· V}}}_{\mathit{\text{1}}}$$

$${\mathit{\text{<figure-callout id="1" label="Q" filenames="imgf0001.png,imgf0002.png" state="{{state}}">Q</figure-callout>}}}_{\mathit{\text{1}}}{\mathit{\text{= <figure-callout id="2" label="D" filenames="imgf0001.png,imgf0003.png" state="{{state}}">D</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{· V}}}_{\mathit{\text{1}}}$$

$${\mathit{\text{<figure-callout id="2" label="Q" filenames="imgf0001.png,imgf0003.png" state="{{state}}">Q</figure-callout>}}}_{\mathit{\text{2}}}{\mathit{\text{= U · <figure-callout id="2" label="D" filenames="imgf0001.png,imgf0003.png" state="{{state}}">D</figure-callout>}}}_{\mathit{\text{2}}}$$

and the following relationships: $${\mathit{\text{n = <figure-callout id="2" label="D" filenames="imgf0001.png,imgf0003.png" state="{{state}}">D</figure-callout>}}}_{\text{2}}{\mathit{\text{· U}}}^{\text{-1}}{\mathit{\text{·not}}}_{\text{1}}{\mathit{\text{+ <figure-callout id="1" label="D" filenames="imgf0001.png,imgf0002.png" state="{{state}}">D</figure-callout>}}}_{\text{1}}{\mathit{\text{.U}}}^{\text{-1}}\text{·}{\mathit{\text{not}}}_{\text{2}}\mathit{\text{(mod N)}}$$

$$\mathit{\text{k}}\text{=}{\mathit{\text{V}}}^{\text{T}}\text{·}{\mathit{\text{<figure-callout id="2" label="D" filenames="imgf0001.png,imgf0003.png" state="{{state}}">D</figure-callout>}}}_{\text{2}}\text{· (}{\mathit{\text{V}}}^{\text{-1}}\text{) ·}{\mathit{\text{<figure-callout id="1" label="k" filenames="imgf0001.png,imgf0002.png" state="{{state}}">k</figure-callout>}}}_{\text{1}}\text{+}{\mathit{\text{V}}}^{\mathit{\text{T}}}\text{·}{\mathit{\text{<figure-callout id="1" label="D" filenames="imgf0001.png,imgf0002.png" state="{{state}}">D</figure-callout>}}}_{\text{1}}\text{· (}{\mathit{\text{V}}}^{\text{-1}}\text{) ·}{\mathit{\text{k}}}_{\text{2}}\text{(mod}{\mathit{\text{NOT}}}^{\mathit{\text{T}}}\text{)}$$

In which n ₁ ∈ L _{I / P1} , n ₂ ∈ L _{I / Q2} , k ₁ ∈ L _{I / (QI)} ^T , k ₂ ∈ L _{I / (P2)} ^T , n ∈ L _{I / N} , and k ∈ L _{I / N} T.

We introduce new variables: $$\begin{gathered} {\widehat{\mathit{\text{not}}}}_{\text{1}}\text{=}{\mathit{\text{U}}}^{\text{-1}}\text{·}{\mathit{\text{not}}}_{\text{1}}\text{(mod}{\mathit{\text{D}}}_{\text{1}}\text{)} \\ {\widehat{\mathit{\text{not}}}}_{\text{2}}\text{=}{\mathit{\text{U}}}^{\text{-1}}\text{·}{\mathit{\text{not}}}_{\text{2}}\text{(mod}{\mathit{\text{D}}}_{\text{2}}\text{)} \\ {\widehat{\mathit{\text{k}}}}_{\text{1}}\text{=}{\mathit{\text{<figure-callout id="2" label="D" filenames="imgf0001.png,imgf0003.png" state="{{state}}">D</figure-callout>}}}_{\text{2}}\text{.}{\mathit{\text{V}}}^{\text{-1}}\text{·}{\mathit{\text{k}}}_{\text{1}}\text{(mod}{\mathit{\text{D}}}_{\text{1}}\text{)} \\ {\widehat{\mathit{\text{k}}}}_{\text{2}}\text{=}{\mathit{\text{<figure-callout id="1" label="D" filenames="imgf0001.png,imgf0002.png" state="{{state}}">D</figure-callout>}}}_{\text{1}}\text{·}{\mathit{\text{V}}}^{\text{-1}}\text{·}{\mathit{\text{k}}}_{\text{2}}\text{(mod}{\mathit{\text{D}}}_{\text{2}}\text{)} \end{gathered}$$

It is then easy to rewrite the two-dimensional "DFT" of dimensions 48 × 48 in the form:

From there, we can derive an architecture comprising a row / column decomposition, the row part of which consists of a one-dimensional 3-point "DFT" and each of the three column "DFT" consists of a two-dimensional 4 × 4 rectangular "FFT" .

The initial two-dimensional "DFT" was converted into an "FFT" algorithm requiring only the calculation of a "DFT" of order 3 for the first level and of order 4 for the second and third levels. Only two types of one-dimensional "DFT" modules are used, 3 × 3 and 4 × 4 respectively.

FIG. 11 illustrates the architecture allowing the installation of a hexagonal beam former CFH ", according to the invention, of dimensions 48 × 48.

This architecture, as before, comprises two layers of circuits, comprising set 5 (one-dimensional "DFT" of order 3) for the first layer of circuits and sets 7 to 9 ("FFT" rectangular 4 × 4) for the second circuit layer.

The first set 5 is made up of 16 unidimensional 3 × 3 "DFT" cells, all identical, marked 51a - 54a, 51b - 54b, 51c - 54c and 51d - 54d (from bottom to top of Figure 11). Each cell has four inputs and four outputs. Only the extreme inputs e ' ₁ and e' ₄₈ have been identified so as not to overload the figure.

Sets 7 to 9 are made up of one-dimensional 4 × 4 "DFT" cells, also all identical, arranged in two rows of 4 modules to form what has been called above the second and third levels. The first row includes cells 71 to 74, 81 to 84 and 91 to 94, for sets 7, 8 and 9, respectively. The second row includes cells 75 to 78, 85 to 88 and 95 to 98, for sets 7, 8 and 9, respectively. The two rows of cells are interconnected by line / column link paths marked 79, 89 and 99 for sets 7, 8 and 9, respectively. These paths are similar (well than slightly more complex) to those described in more detail with regard to the architecture of FIG. 5, relating to a hexagonal beam former of dimensions 27 × 27. They must check equation (44). To fix the ideas, with regard to set 7, the first outputs of modules 71 to 74 are each connected to an input of cell 75, directly or via an additional phase shifter (in a similar manner to FIG. 5), the second outputs of cells 71 to 74 are each connected to an input of cell 76, and so on. It is the same, naturally for games 8 and 9.

Likewise, the first and second layers of circuits are interconnected by a path of connections, marked 6, and which will be described in more detail below.

The 48 outputs of cells 75 to 78, 85 to 88 and 95 to 98 are connected to the 48 radiating elements of the antenna (not shown in the figure).

The architecture of the hexagonal beam former according to the invention, according to this second embodiment, is therefore perfectly regular. In addition, it also turns out to be much less complex than the architecture of an equivalent hexagonal beam former according to known art such as, for example, than that described in the aforementioned article by Chadwick.

Naturally, as in the case of the 27 × 27 hexagonal beam former, shown in FIG. 5, it is possible to combine the functions "former" and "switches". According to this alternative embodiment (not shown), it suffices to add three layers of switching matrices, in a manner similar to what has been described in relation to FIG. 6, that is to say between the inputs and the 3 × 3 cells of circuits 5; between the outputs of the row / column connection assembly 6 and the cells of dimensions 4 × 4, 71 to 94; and between the outputs of the row / column connection sets, 79 to 99, and the inputs of the 4 × 4 cells, 75 to 98.

The matrices of the first layer have the same dimensions as the switching matrices described with reference to FIG. 6 since they must deliver signals on the three cell inputs of dimensions 3 × 3. On the other hand, and for a similar reason, the matrices of the second and third layers are of 4 × 4 dimensions, the cells to be served being of 4 × 4 dimension.

In general, for a hexagonal beam former of dimensions R × N ² , the elementary matrices of switching circuits will have respective dimensions R × R, for the first layer, and N × N for the second and third layers.

The 3 × 3 “DFT” modules (51a to 54d) can be produced identically to the modules described in relation to FIGS. 7 and 8.

An embodiment of the 4 × 4 “DFT” modules will now be described with reference to FIGS. 12 and 13.

FIG. 12 very schematically illustrates the functional diagram of a one-dimensional 4 × 4 “DFT” calculation cell, for example the cell constituting the module 71; it being understood that all the modules 71 to 98 are identical.

The signal inputs have been marked I ₁ to I ₄ and the outputs O ₁ to O ₄ . All inputs are connected to all outputs (trellis), some directly (i.e. without phase shift): I ₁ to all outputs, I ₂ to O ₁ , I ₃ to O ₁ and O3, d ' others via phase shifters. I ₂ is connected to O ₂ by a phase shifter φ _'22 90 ° to O ₃ by a phase shifter φ' ₂₃ 180 ° and O ₄ by a phase shifter φ _'24 270 °. Likewise I ₃ is connected to O ₂ by a 180 ° phase shifter _{32 '32} and to 04 by a 180 ° phase shifter ₃₄ ' ₃₄ also. Finally, I ₄ is connected to O ₂ by a phase shifter ϕ _'42 by 270 °, to O ₃ by a phase shifter ϕ' ₄₃ by 180 ° and to O ₄ by a phase shifter ϕ _'44 by 90 °.

As with the 3 × 3 cells, the 4 × 4 cells can be produced in the form of modules based on “MMIC” in Gallium Arsenide (AsGa).

FIG. 13 illustrates an example of integration of the basic cell "DFT" 4 × 4, for example cell 71, the functional diagram of which has just been recalled. The module includes one or more "MMICs" in hybrid technology, integrating circuits CI-41 to CI-44 with two inputs and two outputs, including a direct output (without phase shift, indicated by an arrow in the figure) and a phase-shifted output 180 °. The circuit CI-43 receives, at the input, the input signals I ₁ and I ₄ . In the context of the invention, the term "hybrid technology" means that it is a circuit with four ports: two input ports and two output ports. They have the particularity that a signal present on a first input port (I ₁ for example for the CI-43 circuit) is divided into two signals of the same power and of the same phase, transmitted to the two output ports, and that '' a signal present on the second input port (indicated by an arrow in figure 13: I ₂ for example for the CI-43 circuit) is divided into two signals of the same power and of opposite phase, transmitted to the two ports of exit. The circuit CI-44 receives as input the signals of the inputs I ₂ and I ₃ . The direct output of the CI-43 circuit is crossed and connected to the first input of the CI-42 circuit (left in the figure). The phase-shifted output of circuit CI-44 is crossed and transmitted to the second input of circuit CI-42 (right in the figure). The exit direct from circuit CI-44 is transmitted, via an additional phase shifter ϕ-90 to the second input of circuit CI-42 and the phase-shifted output of circuit CI-41 is transmitted to the first input of circuit CI-41. The first and second outputs of the CI-41 circuit constitute the outputs O ₁ and O ₃ , respectively. The first and second outputs of the CI-42 circuit constitute the outputs O ₂ and O ₄ , respectively.

As with the 3 × 3 cells, it is still possible to improve the topology of the 4 × 4 base cells. FIG. 14 schematically illustrates the topology of a 4 × 4 cell according to a preferred embodiment of the invention.

As before, it is assumed that it is cell 71, it being understood that all the cells are identical.

We have represented the four inputs, marked I ₁ to I ₄ , and the four outputs, marked O ₁ to O ₄ .

As previously also, capacitors and inductors are used, with localized constants, in the wavelength band "L" or "S". The inductors are all marked "L" and the capacitors "C", because these elements are all identical.

• En entrée, chaque borne d'entrée, I₁ à I₄, est reliée aux deux autres par une inductance L ;
• En sortie, chaque borne d'entrée, O₁ à O₄, est reliée aux deux autres par une inductance L ;
• Chaque borne d'entrée, I₁ à I₄, est reliée à une borne de sortie, O₁ à O₄ respectivement, par une inductance L; plus précisément à la borne de sortie de même rang ;
• Enfin, chaque borne, d'entrée, I₁ à I₄, ou de sortie, O₁ à O₄, est connectée au potentiel de la terre M_a par une capacité C.

The implementation rules are similar to what was previously indicated:

• At the input, each input terminal, I ₁ to I ₄ , is connected to the other two by an inductance L;
• At the output, each input terminal, O ₁ to O ₄ , is connected to the other two by an inductance L;
• Each input terminal, I ₁ to I ₄ , is connected to an output terminal, O ₁ to O ₄ respectively, by an inductance L; more precisely to the output terminal of the same rank;
• Finally, each terminal, input, I ₁ to I ₄ , or output, O ₁ to O ₄ , is connected to the earth potential M _a by a capacity C.

The cell is extremely symmetrical and therefore easy to produce.

This 4 × 4 cell configuration allows, at a minimum, their integration on a single "MMIC" and it is actually possible to integrate several cells on a single "MMIC" of larger dimensions.

The advantages specific to this topology are identical to those mentioned for 3 × 3 cells.

Therefore, it is also possible to simply compensate for errors on the capacity values actually obtained compared to the values nominal calculated by replacing these capacities by a fixed capacity C 'in parallel on a transistor T _r of MESFET type.

We will now describe examples of physical implantation of hexagonal beam shapers according to the invention.

In examples of practical implementation, it is necessary to distinguish three cases of implantation according to the complexity of the circuits of the hexagonal beam former in accordance with the invention.

A distinction can be made between dimensions which will be called "normal", "large" and "very large", the latter being the most general case.

This distinction is essentially linked to the more or less significant possibilities of integration allowed by the technologies used.

In addition, as indicated, if the preferred embodiment of the basic cells is used (see FIGS. 10 and 14), the integration rate can be increased in large proportions.

FIG. 15 illustrates a first example of layout for a low complexity shaper ("normal" dimensions), for which the basic cells have been integrated on single "MMICs". This example corresponds to a CFH hexagonal beam shaper of dimensions 27 × 27, as described in FIG. 5. The same references have been kept to designate the elements thereof.

The CFH hexagonal beam former is installed in "2D", that is to say on a plane, for example a printed circuit board PCB. It comprises three layers of "MMICs" grouping, respectively, cells 4, cells 11 to 33 of the first row and cells 14 to 36 of the third row. The interconnection lines of assemblies 4a and CLC ₁ to CLC ₃ are produced in multilayer technology. Examples of practical implementation will be detailed below.

In reality this approach could be applied to more complex conformers, of dimensions up to typically 144 × 144. The mass and dimensions would then be reduced to their strict minimum; in the order of hundreds of grams for the mass and size of a standard printed circuit.

FIG. 16 illustrates an example of physical layout of a CFH hexagonal beam former according to the invention of larger dimensions: second case mentioned above. To fix the ideas and not to overly complicate the description, we will resume, as before, the example of the CFH 27 × 27 hexagonal beam conformator described in with reference to FIG. 5. It will however be assumed that it is not possible to integrate all the cells of a level on a single "MMIC".

The connections between the two layers of circuits: set 4, on the one hand, and sets 1 to 3, on the other hand, can be carried out simply using connectors, referenced C ₁ to C ₃ . In the embodiment illustrated in this FIG. 16, the base cells, 41 to 49, of the first layer of circuits are arranged on as many flat supports (printed circuit boards for example), all parallel to one another. An exemplary embodiment will be detailed below, in relation to the description of FIG. 18. The three sets, 1 to 3, making up the second layer of circuits, are each arranged on a support, also flat. These three planes are arranged at right angles to the planes formed by the supports of cells 41 to 49. As indicated, the first outputs of all the cells in set 4, are connected, only, to the inputs of set 1, the second outputs at the inputs of game 2 and the third outputs at the inputs of game 3. It is therefore easy to carry out in these circumstances the connection path connecting the first layer of circuits (set 4) to the second layer of circuits (sets 1 to 3), since the respective supports are in orthogonal planes. In practical terms, the connectors C ₁ to C ₃ can be made integral with the supports of the cells 41 to 49. It then suffices to insert the three supports of the sets 1 to 3 in these connectors. No link crossing is necessary.

Finally, FIG. 17 illustrates an example of installation of a very large hexagonal beam former. To fix the ideas and not to overly complicate the description, we will resume, as previously, the example of the CFH 48 × 48 hexagonal beam shaping machine described with reference to FIG. 11. It will however be assumed that the you cannot integrate all the cells of a level on a single "MMIC".

The mechanical installation of this CFH 'hexagonal beam shaper, of dimensions 48 × 48, can no longer be carried out as simply as in the case of a less complex shaper (such as that described with reference to FIG. 16 for example, from which we have used the conventions for references).

The assembly is carried out on the faces of a cube-shaped support S. The sixteen 4 × 4 "DFT" modules can be grouped on a first side S ₁ of this cube and rearranged in the form of a matrix comprising 4 rows and 4 columns of modules: 51a-54a, 51b-54b, 51c-54c and 51d-54d, respectively. Each module has three input connections, only two of which, e ' ₁ and e' ₄₈ , for all the modules have been identified so as not to overload the figure unnecessarily.

The three sets 7, 8 and 9 of the second layer of circuits are arranged, for their part, on three faces of the cube, for example the upper face (in the figure) S ₂ , the face S ₃ , opposite the face S ₁ , and the underside S ₄ .

Advantageously, these faces are provided with four connectors, parallel to each other, in which will be inserted plates of rectangular parallelepiped shape, supports for modules 71-74, 81-84 and 91-94, for games 7, 8 and 9, respectively. In order not to unnecessarily overload the figure, only the assembly of the face S ₂ has been identified and detailed (set 7). It should however be clear that this assembly is repeated in a similar manner on the faces S ₃ and S ₄ , for games 8 and 9.

The connectors fixed to the face S ₂ are marked C ₇₁ to C ₇₄ . In each of these connectors a plate is inserted, supporting the modules 71 to 74, respectively. The routing of the links (79, 89 and 99) interconnecting the first row of modules to the second row of modules makes it possible to physically carry out this routing in a very simple manner. It suffices to produce these modules (for example, modules 75 to 78) also in the form of plates. Four rows of connectors, C ₇₅ to C ₇₈ , of module modules 71 to 74 are made integral, on the sides opposite to the connectors C ₇₁ to C ₇₄ . In addition, as illustrated in the figure, the connectors C ₇₅ to C ₇₈ are _mutually parallel and orthogonal to the connectors C ₇₁ to C ₇₄ . In each of these connectors is one of the plates, 75 to 78, respectively. As noted, this arrangement is repeated for games 8 and 9, arranged on the sides S ₃ and S ₄ . Each module has four output connections, of which only one, El ' ₁ , for all the modules has been identified so as not to overload the figure unnecessarily.

The routing 6 of connections between the outputs of the modules 51a to 54d of the set 5, on the one hand, and the inputs of the modules of the first row of the other sets, on the other hand, being more complex than in the case illustrated by the Figure 5, these connections can no longer be made simply using connectors. The sixteen modules 51a to 54d comprising a total of 48 outputs (four per module), the connections 6 between the face S ₁ and the three other faces can be produced, for example, using 48 coaxial cables. The outgoing bundle 60 of 48 cables is divided into three sub-bundles of 16 cables: 61, 62 and 63, distributed at the inputs of the modules of sets 7, 8 and 9, respectively. Naturally, as is well known to those skilled in the art, these cables will have to be adapted in phase and in insertion loss. We will also choose the constituent materials so that they have good temperature stability.

This material layout can be extended to more complex beam shapers. As the dimensions of these become larger, we can use the two free faces of the cube. When the complexity increases further, we can use, not a cube, but a polyhedral structure. Naturally, the structure of the basic cells constituting the modules also changes with the complexity of the hexagonal beam former.

In summary, it should be clearly understood that the material structure of the hexagonal beam former, shown in FIG. 16 (of dimensions 27 × 27 in the example illustrated), is a particular case which can be described as "limit" by compared to the more general structure shown in Figure 17. Indeed, it can be argued, in this particular case, that the supporting structure could have been reduced to its simplest expression, that is to say to a plane. The connectors C ₁ to C ₃ play a role similar to the role played by the connectors C ₇₄ to C ₇₈ . It is no longer useful to have recourse to a bundle of coaxial cables, the connections between the cells of the first layer of circuits (4) and the second layer of circuits (1 to 3) being able to take place directly. The modules of the second and third levels were, due to the low complexity of the circuits, arranged on a single wafer, which made it possible to eliminate the assembly using connectors between these modules as in the case of the shaper of dimensions 48 × 48 which has just been described (FIG. 17).

For reasons of standardization, a cubic or even polyhedral structure could also have been used to mechanically implant the hexagonal beam shaper, of dimensions 27 × 27. In this case, the modules 41 to 43 (set 4: FIG. 5) would be arranged on the face S ₁ and the modules of the sets 1 to 3 (FIG. 5) on the faces S ₂ to S ₃ , respectively. Likewise, the second and third levels could have been separated. The interconnections would then be made using connectors playing a role similar to connectors C ₇₁ to C ₇₈ . The interconnections between the modules of the set 4 and the other modules could then be carried out, also, by using coaxial cables. However, it can be seen that this structure, while remaining consistent with the teaching of the invention, would however be more complex than that described with regard to FIG. 16.

• a) Une rangée de N ² cellules "DFT" unidimensionnelles d'ordre R×R. Cette rangée est disposée sur une des faces de la structure polyédrique précitée. Ces cellules peuvent naturellement être réarrangées sur cette face selon une organisation matricielle lignes/colonnes comme il ressort de la figure 12. Chaque cellule peut être réalisée sous forme de modules comprenant un ou plusieurs "MMIC" sur AsGa (voir figures 7 ou 11, par exemple).
• b) R jeux indépendants de cellules "DFT" unidimensionnelles, chacun comprenant deux rangées (deuxième et troisième niveaux) de N cellules, chacune d'ordre N×N. Chacun de ces R jeux indépendants est disposé sur une des faces restantes de la structure polyédrique. En outre, chacun de ces jeux est implanté sous la forme d'un empilement de modules à deux étages. Le premier étage est constitué des N cellules de la première rangée, chacun étant enfiché dans un connecteur supporté par la face précitée. Le deuxième étage est constitué des N modules de la seconde rangée, chacun étant enfiché dans un connecteur supporté par les modules de la seconde rangée, les connecteurs des premier et second étages étant disposés orthogonalement entre eux comme illustré sur la figure 17.

In general, a hexagonal beam former with N _t = R × N ² inputs, R and N being whole numbers, is made up as follows, using a polyhedral structure:

• a) A row of N ² one-dimensional "DFT" cells of order R × R. This row is arranged on one of the faces of the above-mentioned polyhedral structure. These cells can naturally be rearranged on this face according to a row / column matrix organization as shown in FIG. 12. Each cell can be produced in the form of modules comprising one or more "MMICs" on AsGa (see Figures 7 or 11, by example).
• b) R independent sets of one-dimensional "DFT" cells, each comprising two rows (second and third level) of N cells, each of order N × N. Each of these R independent sets is arranged on one of the remaining faces of the polyhedral structure. In addition, each of these games is implemented in the form of a stack of two-stage modules. The first stage consists of the N cells of the first row, each being plugged into a connector supported by the aforementioned face. The second stage consists of the N modules of the second row, each being plugged into a connector supported by the modules of the second row, the connectors of the first and second stages being arranged orthogonally to one another as illustrated in FIG. 17.

The material constituting the cubic structure, or more generally polyhedral, must be used as support. Various materials can be chosen. We will select a light material such as aluminum.

If one wishes to incorporate the "switching" function (see FIG. 6), the complexity of the switching matrices follows the same rules, as indicated. Indeed, they are square matrices M × M with M = N or M = R, depending on whether they serve the inputs of cells of dimensions N × N or R × R.

The connectors of the second stage establish the necessary interconnections between the modules of the second and third levels, in a manner very similar to what has been described in relation to FIG. 17. The interconnections between the outputs of the N ² modules of the first level and the inputs of the other modules require N _t connections (trellis). They can be carried out, as before, using N _t coaxial cables, adapted in phase and in insertion losses, and stable in temperature.

For the interconnections between the first and the second level, the general rule can be stated as follows: the outputs of rank i of each cell are each connected to one of the cell inputs of the independent game similarly rank ; with i ∈ {1, R }. Likewise, for the connections between the cells of the first and second row in each of the R independent sets of cells, the rule is as follows: the output of row j of each cell of the first row is connected to an input of the cell of the same second row rank; with j ∈ {1, N }. These rules only generalize what has been described in detail with regard to Figures 5 and 11

Finally, if we can further increase the degree of integration, in particular by using 3 × 3 or 4 × 4 cells implanted according to the teaching of FIGS. 9 and 14, respectively, we can implant the whole of the beam shaper hexagonal on a simple multilayer printed circuit board.

We have not considered the additional phase shifters between levels, however, as indicated, they can be integrated into the modules or, at the very least, produced on the support plates of these modules.

As far as the routing of the connections inside the modules is concerned, these are difficult to achieve by using the so-called "planar" techniques, due to the necessary crossings of these connections, when considering a single plan.

One can naturally think of using jumpers or similar elements. However, this solution would lead to a degradation of the radiofrequency insulation.

To solve this problem, it is possible to use planar multilayer technology, with radio frequency crossings.

Figure 18 illustrates such an arrangement. The set of module 1 in FIG. 5 was taken as an example. This set comprises two rows of three 3 × 3 one-dimensional "DFT" cells: 11-13 and 14-16, respectively. It is assumed that it is produced on a single support which merges with the set 1 itself.

No problem arises for the input-output of the set of modules 1, because there are no crossings.

On the other hand, the connections between the modules of the two rows are effected by means of transmission lines arranged on two levels of a dielectric. The latter also serves as a support for cells or modules 11 to 16. The links 110 (cell 11 to cell 14), 111 (cell 11 to cell 15), 122 (cell 12 to cell 15), 132 (cell 13 to cell 15 ) and 133 (cell 13 to cell 16) occupies only one level (upper plane). On the other hand, the links 112 (cell 11 to cell 16), 121 (cell 12 to cell 14), 123 (cell 12 to cell 16) and 131 (cell 13 to cell 14) occupy two levels (upper and lower planes). Each of these links is divides into three sections: 112-112'-112 ", 121-121'-121", 123-123'-123 "and 131-131'-31", respectively. The "lower" transmission lines are connected to the "upper" transmission lines using radio frequency feed-throughs: 1120-1121, 1210-1211, 1230-1231 and 1310-1311, respectively.

The dielectric material, taking into account the frequency range used, is of the type known as "soft" substrates. More specifically, the material used can be, for example, Teflon, loaded or not with ceramic, or alumina.

As is well known, adaptation elements or circuits may be necessary near the radio frequency crossings.

Different technological variants can be implemented.

One of these variants is illustrated in FIG. 19. Ribbon-type lines ("stripline") are used, in thick or thin film depending on the precise application and the manufacturing methods involved. The element shown, in section, in this figure comprises three parallel metallic ground planes PM ₁ , PM ₂ and PM ₃ and, between these ground planes, two layers, D ₁ and D ₂ , forming supports, of dielectric material. Two metallic ribbon lines, an upper line L ₁ and a lower line L ₂ , are buried in the dielectric supports, respectively in D ₁ and D ₂ . At the places where an interconnection must be made between the lines L ₁ and L ₂ , provision is made for a radiofrequency crossing TR ₁ in the form of a metallized hole. Naturally, an orifice of larger diameter, or more generally of larger dimensions, is produced in the intermediate ground plane M ₂ . The latter plays the role of radio screen between the two lines L ₁ and L ₂ . This arrangement therefore ensures a very high level of radiofrequency insulation.

Another solution, not illustrated, would be to provide a waveguide line on one level and a ribbon line on the other. This solution offers a minimum of complexity, however the radiofrequency insulation is not as important as that offered by the ribbon lines. However, a sufficient degree of insulation can be achieved by increasing the thickness of the dielectric.

Other solutions are still possible. In all cases, to carry out the interconnection link routing, two levels of transmission lines are necessary, with a good level of radiofrequency isolation between lines and low losses at crossings. Depending on the frequency ranges considered, thin or thick film technologies, substrates made of flexible materials or ceramic, with radiofrequency feedthroughs such as metallized holes or pins ("pins").

Finally, when complexity becomes very important, it is necessary to call on other solutions: connectors, coaxial cables, etc., as explained with reference to FIG. 17.

   relation dans laquelle :

• N _r est le nombre de modules de base R×R ;
• M _r est la masse de chacun de ces modules, incluant les boîtiers et les connecteurs ;
• N _n est le nombre de modules de base N×N ;
• M _n est la masse de chacun de ces modules, incluant les boîtiers et les connecteurs ;
• N _t est le nombre total d'entrées du conformateur de faisceau hexagonal ;
• M _c est la masse d'un câble coaxial, incluant les connecteurs d'extrémité.

The mass of the hexagonal beam former, for a hexagonal grid antenna, can be estimated as follows: $${\mathit{\text{Mass = (N}}}_{\mathit{\text{r}}}{\mathit{\text{× M}}}_{\mathit{\text{r}}}{\mathit{\text{) + (N}}}_{\mathit{\text{not}}}{\mathit{\text{× M}}}_{\mathit{\text{not}}}{\mathit{\text{) + (N}}}_{\mathit{\text{t}}}{\mathit{\text{× M}}}_{\mathit{\text{vs}}}\mathit{\text{)}}$$

relationship in which:

• N _r is the number of basic modules R × R ;
• M _r is the mass of each of these modules, including the boxes and connectors;
• N _n is the number of basic modules N × N;
• M _n is the mass of each of these modules, including the boxes and connectors;
• N _t is the total number of inputs of the hexagonal beam former;
• M _c is the mass of a coaxial cable, including the end connectors.

To fix the ideas, in the case of a hexagonal beam former, of dimensions 48 × 48, implanted as illustrated in figure 17, with R = 3 and N = 4, using the proposed technology, and with the following estimates: M _r = 25 g, M _n = 35 g and M _c = 20 g, the total mass would be around 2.2 Kg.

The mass per node "BFN" (from the Anglo-Saxon "BeamForming Network") is less than 1 g. The number of nodes is defined as the product of the number of beams by the number of radiating elements. In the known art, a ratio of 10 g per node is commonly accepted as a reference ratio when total mass estimates are made for conforming networks of radiofrequency beams, using the usual technologies in the field.

The architecture of the invention therefore allows a reduction in the total mass in a ratio of about 1 to 10.

It should be clear that the invention is not limited only to the examples of embodiments precisely described, in particular in relation to FIGS. 2 to 19. In particular, the integration of the basic cells into modules can be carried out by using other technologies. Interconnections can also be carried out, as has been shown, by using various technologies: multilayers, coaxial cables, etc.
order networks of a triangular-shaped grid antenna, which do not need to be contiguous or to be hexagonal at the periphery.

Finally, it is possible to interpose, between the beam shaping network and the radiating elements of the invention, conventional amplitude weighting means, including the special case of zero weighting (for the radiating elements absent), which allows to obtain very simply beam forms with significant overlap.

Although particularly suitable for space applications, the invention cannot be confined to this single type of application. It applies to all radio frequency antennas of the network antenna type with phase control for the generation of multiple beams.

Claims (22)

Beam shaping network (CFH, CFH ') for radiofrequency antenna comprising a determined number of radiating elements ( El ₁ to El ₂₇ ) for the generation of multiple beams, said shaping network (CFH, CFH') comprising a determined number of signal inputs ( e ₁ to e ₂₇ ), a number of radiating element control signal outputs ( El ₁ to El ₂₇ ) equal to said predetermined number of signal inputs ( e ₁ to e ₂₇ ) and effecting on the signals of inputs a discrete two-dimensional hexagonal Fourier transform, characterized in that said predetermined number of inputs and outputs being equal to N _t , with N _t = R × N ² , R and N being whole numbers, the component circuits said beam shaping network (CFH, CFH ") are divided into first and second layers of circuits performing, respectively, a one-dimensional discrete Fourier transform of lines and a discrete Fouri transform one-dimensional columns; in that the first layer of circuits consists of a row (4, 5) of N ² cells (41 to 49, 51a to 54d) each provided with R inputs and R outputs, each cell receiving a signal present on the one of said N _t inputs and effecting, on the signals present on its R inputs, a discrete one-dimensional Fourier transform; in that the second layer of circuits consists of R independent sets (1 to 3, 7 to 9) of cells, each provided with N inputs and N outputs, each set comprising a first (11 to 13, 22 to 23 31 to 33; 71 to 74, 81 to 84, 91 to 94) and a second row (14 to 16, 24 to 26, 34 to 36; 75 to 78, 85 to 88, 95 to 98) of N cells, each cell performing , on the signals present on its N inputs, a discrete one-dimensional Fourier transform; each of the outputs of the cells of said second row controlling one of said radiating elements; in that said first and second circuit layers are connected by a first set of interconnections (4a, 6), establishing connections between the outputs of the cells of said row of N ² cells and the inputs of N cells of the first row R independent sets of cells; the outputs of rank i of each cell being connected, each, to one of the cell inputs of the independent game of the same rank; with i ∈ {1, R }; and in that said first and second rows of cells of each of said R independent sets are connected by a second set of interconnections (CLC ₁ to CLC ₃ , 79, 89 99), establishing connections between the outputs of the N cells of the first row and the entries of the N cells of the second row; the output of row j of each cell of the first row being connected to an input of the cell of the same rank of the second row; with j ∈ {1, N }. Network (CFH ') according to claim 1, characterized in that it further comprises arrays of beam switching circuits, and in that these circuits are divided into a first layer (Co ₁ ) disposed between said signal inputs determined number (e ₁ -e ₂₇ ) and said first layer of circuits (4) of N ² cells, in a second layer (Co ₂ ) disposed between the outputs of said first set of interconnections (4a, 6) and the cells (11 to 33) of the first row of said R independent sets, and a third layer (Co ₃ ) disposed between the outputs of said second set of interconnections (CLC ₁ to CLC ₃ ) and the cells (14 to 36) of the second row of said R independent games. Network (CFH ') according to claim 2, characterized in that the switching matrices are square matrices, in that the switching matrices of the first layer (Co ₁ ) are of dimension R × R, and in that the matrices of the second and third layers are matrices of dimensions N × N. Network (CFH) according to any one of claims 1 to 3, characterized in that, N _t being equal to 27, N being equal to 3 and R being equal to 3, all the cells (41 to 49, 11 to 36 ) performing the one-dimensional Discrete Fourier Transform are identical and include 3 inputs and 3 outputs. Network (CFH ") according to any one of claims 1 to 3, characterized in that N _t being equal to 48, N being equal to 4 and R being equal to 3, all the cells (51a to 54d) performing the Transform Discrete Fourier of said row (5) of N ² cells are identical and include 3 inputs and 3 outputs and in that all cells (71 to 98) performing the Unidimensional Discrete Fourier Transform of the first and second rows of said R games independent (7, 8, 9) are identical and include 4 inputs and 4 outputs. Network (CFH, CFH ', CFH ") according to any one of claims 1 to 5, characterized in that said cells performing a discrete Fourier transform are produced in the form of at least one microwave monolithic integrated circuit chip in Gallium arsenide. Network (CFH, CFH ', CFH ") according to claim 6, characterized in that said chips are passive circuits in hybrid technology based on capacitors and inductors with constants located in L or S frequency bands. Network (CFH, CFH ', CFH ") according to claim 7, characterized in that said cells (11, 71) being of dimensions X × X , with X integer equal to N or to R , these cells are produced by connecting each input (I ₁ to I ₄ ) to an output of the same rank (O ₁ to O ₄ ) by an inductance (L) of determined value, by connecting each input (I ₁ to I ₄ ) to the [X-1] other inputs (I ₁ to I ₄ ) by an inductor (L) of the same determined value, by connecting each output (O ₁ to O ₄ ) to the [X-1] other outputs (O ₁ to O ₄ ) by an inductor (L ) of the same determined value, and by connecting each input (I ₁ to I ₄ ) and each output (O ₁ to O ₄ ) to the earth potential (M _a ) by capacitors (C) of the same first value determined. Network (CFH, CFH ', CFH ") according to claim 8, characterized in that each capacity (C) consists of a fixed capacity (C') of a second of determined value less than said first value determined in parallel on a MESFET type transistor (T _r ), the gate (G) of which is connected to said fixed capacitance (C ') and the source and drain of which are connected to the earth potential (M _a ) so as to form a variable capacitance, and in that a control voltage (V _c ) is applied to the gate (G) so as to modify the value of the composite capacitance formed by said fixed capacitance (C ') and said transistor (T _r ) so as to obtain said first determined value. Network (CFH, CFH ', CFH ") according to claim 9, characterized in that said control voltage (V _c ) is unique and applied to all cells. Network (CFH, CFH ', CFH ") according to any one of claims 6 to 10, characterized in that said chips are implanted on substrates of dielectric material and in that the interconnections (111 to 133) between chips are made by multilayer transmission lines, the connections between layers being made by radio frequency crossings (1120 to 1231). Network (CFH, CFH ', CFH ") according to claim 11, characterized in that said transmission lines (L ₁ , L ₂ ) are produced in the form of microstrip lines comprising first and second external metallic ground planes (M ₁ and M ₃ ), an intermediate ground plane (M ₂ ) disposed between the first and second metallic ground plane and forming a screen between said transmission lines (L ₁ , L ₂ ), in that the three planes (M ₁ to M ₃ ) are parallel to each other, in that the volume between these and the intermediate plane is filled with a dielectric material (D ₁ , D ₂ ), in that said transmission lines consist of metallic ribbons (L ₁ , L ₂ ) embedded in the dielectric materials (D ₁ , D ₂ ) and arranged parallel to said planes (M ₁ to M ₃ ), and in that the interconnections between these lines are made by metallized holes forming radiofrequency crossing (Tr ₁ ), said intermediate plane (M ₂ ) having openings (Tr ₂ ) of larger section than the section of these crossings, so as to allow free passage to said crossings (Tr ₁ ). Structure for the mechanical implantation of a network (CFH) according to any one of Claims 1 to 12, characterized in that, the said cells being produced in the form of monolithic microwave integrated circuit chips, they are implanted on a multilayer printed circuit (PCB), and in that said first and second sets of interconnections (CLC ₁ to CLC ₃ ) are installed in the form of multilayer transmission lines on said printed circuit board (PCB). Structure for the mechanical implantation of a network (CFH ") according to any one of claims 1 to 12, characterized in that it comprises a frame (S) in the form of a polyhedron, in that the cells (51a to 51b) said row (5) of N ² cells are arranged on a first face (S ₁ ) of said polyhedron (S) and in that each of said R independent sets (7, 8, 9) is arranged on the remaining R faces (S ₂ , S ₃ , S ₄ ) of said polyhedron (S). Structure according to claim 14, characterized in that said N ² cells are arranged on said first face of the polyhedron (S) according to a matrix configuration of N columns and N rows. Structure according to Claims 14 or 15, characterized in that the cells of the first (71 to 74) and second (75 to 78) rows of said R independent sets (7) being produced in the form of monolithic microwave integrated circuit chips, each cell (71 to 74, 75 to 78) is arranged on a flat substrate of rectangular parallelepiped shape, in that the faces (S ₂ to S ₄ ) on which these R games are arranged are each provided with a first set of N connectors (C ₇₁ to C ₇₄ ), mutually parallel, in each of which is plugged one of said planar substrates supporting a cell (71 to 74) of the first row, so as to constitute, with N _t additional connection lines, said first set of interconnections (6), establishing connections between the outputs of the cells of said row of N ² cells and the inputs of N cells of the first row of R independent sets of cells, in that these s ubstrates support, on the side opposite the insertion side in the connectors (C ₇₁ to C ₇₄ ), a second set of N connectors (C ₇₅ to C ₇₈ ), these connectors being parallel to each other and orthogonal to the connectors (C ₇₁ to C ₇₄ ) of said first set, so as to constitute said second set of interconnections (79), establishing direct connections between the outputs of the N cells of the first row and the inputs of the N cells of the second row. Structure according to claim 16, characterized in that said N _t additional connection lines are formed by coaxial cables (60), a first end of which is connected to one of the outputs of the cells of said row (5) of N ² cells (51a to 54d) and the second end at one of the inputs of the N cells (71 to 74, 81 to 84, 91 to 94) of the first rows of said R independent sets (7, 8, 9), via the one of said connectors of the first set (C ₇₁ to C ₇₄ ), supported by one of the faces (S ₂ to S ₃ ) of said polyhedron (S). Structure according to any one of Claims 14 to 17, characterized in that, R being less than or equal to 5, said structure (S) is a cube. Structure for the mechanical installation of a network (CFH) according to any one of claims 1 to 4 or 5 to 13, characterized in that, N _t being equal to 27, N being equal to 3 and R being equal to 3, the cells being produced in the form of monolithic microwave integrated circuit chips, each cell of said row of N ² cells (42 to 48) is arranged on an independent flat substrate, of rectangular parallelepiped shape, these N flat substrates being parallel between them, in that the cells of each of said R independent sets (1, 2, 3), are arranged on a common planar substrate, of rectangular parallelepiped shape, these R planar substrates being parallel to each other, in that said N planar substrates are arranged orthogonally to said R flat substrates, and in that said N flat substrates support on one of their side R connectors (C ₁ , C ₂ , C ₃ ) in each of which is plugged one of said R substrates planes so as to form said first set of connections. Structure according to claim 19, characterized in that said second set of connections is produced by multilayer transmission lines (111 to 133) between cells of the first (11 to 13, 21 to 23, 31 to 33) and second (14 to 16, 24 to 26, 34 to 36) rows of said R independent sets (1, 2, 3), the connections between layers being made by radiofrequency crossings (1120 to 1231). Application of a network (CFH, CFH ', CFH ") according to any one of claims 1 to 13 to the control of radio frequency antennas of the network type with phase control for the generation of multiple beams. Application according to claim 21, characterized in that the radiating elements ( El ₁ to El ₂₇ ) of said antenna are arranged on a hexagonal grid and in that the antenna is carried on a satellite.

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