Method for transmitting a sequence of data symbols, corresponding device for transmission, signal, method for receiving, device for receiving and computer program

Abstract

A method is provided for transmitting a sequence of data symbols including at least two data symbols of distinct values, delivering an electromagnetic wave carrying an orbital angular momentum. The method includes, for at least one data symbol to be transmitted: a bijective selection of an order of orbital angular momentum associating, with each distinct value of a data symbol, a distinct order of orbital angular momentum, and delivering a selected order of orbital angular momentum that is representative, by bijection, of the value of the at least one data symbol to be transmitted; and transmitting the electromagnetic wave carrying an orbital angular momentum, the order of orbital angular momentum of which corresponds to the selected order of orbital angular momentum.

Claims

1. A method for transmitting a sequence of data symbols comprising at least two data symbols of distinct values, delivering an electromagnetic wave carrying an orbital angular momentum, wherein the method comprises, for at least one data symbol to be transmitted, the following acts performed by a transmission device: a bijective selection of an order of orbital angular momentum associating, with each distinct value of a data symbol, a distinct order of orbital angular momentum, and delivering a selected order of orbital angular momentum that is representative, by bijection, of the value of said at least one data symbol to be transmitted, and transmitting said electromagnetic wave carrying an orbital angular momentum, the order of orbital angular momentum of which corresponds to said selected order of orbital angular momentum, wherein the method further comprises the following acts implemented by the transmission device prior to said bijective selection: receiving a binary data string, determining the maximum absolute value of order of orbital angular momentum that can be transmitted by the transmission device, forming said sequence of data symbols from said binary string, said act of forming taking account of said absolute maximum value of order of orbital angular momentum.

2. The method for transmitting according to claim 1, wherein said order of orbital angular momentum is selected when it is equal to the value of the data symbol to be transmitted.

3. The method for transmitting according to claim 1, wherein said act of forming corresponds to an N-state modulation, N being an integer equal to twice the absolute maximum value of the order of orbital angular momentum plus one.

4. The method for transmitting according claim 1, wherein, when said transmission device comprises a radiofrequency transmission device comprising a plurality of sending elements, said method for transmitting furthermore comprises an act of series-parallel replication of said order of the orbital angular momentum selected, delivering said order of orbital angular momentum at input of each sending element from said plurality of sending elements.

5. A device for transmitting a sequence of data symbols comprising at least two data symbols of distinct values, delivering an electromagnetic wave carrying an orbital angular momentum, wherein the device comprises, for at least one data symbol to be transmitted: a module configured to make a bijective selection of an order of orbital angular momentum associating, with each distinct value of a data symbol, a distinct order of orbital angular momentum, and deliver a selected order of orbital angular momentum representing, by bijection, the value of said at least one data symbol to be transmitted, and a transmitter, which transmits said electromagnetic wave carrying an orbital angular momentum, the order of the orbital angular momentum of which corresponds to said selected order of orbital angular momentum, wherein the device is further configured to, prior to said bijective selection: receive a binary data string, determine the maximum absolute value of order of orbital angular momentum that can be transmitted by the transmission device, form said sequence of data symbols from said binary string, taking account of said absolute maximum value of order of orbital angular momentum.

6. A method comprising: receiving, by a receiving device, a signal transmitted in the form of an electromagnetic wave carrying an angular momentum delivering an estimation of a data symbol of a sequence of data symbols comprising at least two data symbols of distinct values, said electromagnetic wave carrying an orbital angular momentum having an order of orbital angular momentum selected bijectively during the transmission of said signal so as to represent, by bijection, the value of said data symbol, and estimating, by the receiving device, the value of said data symbol, implementing an act of detecting said order of orbital angular momentum, wherein said detecting implements a determining of a phase gradient comprising: shaping said signal in vector form, unwrapping of a phase of each term of said vector form and of determining a phase of the product of the terms of said vector form, obtaining said order of estimated orbital angular momentum implementing a division of said phase of the product of the terms of said vector form multiplied by the term (L1), L being an integer corresponding to a maximum absolute value of the order of orbital angular momentum capable of being received, multiplied by two.

7. The method for receiving according to claim 6, wherein said detecting implements a Fourier transform of said signal.

8. The method for receiving according to claim 6, wherein said detecting is a detection by maximum likelihood.

9. The method for receiving according to claim 8, wherein said detecting by maximum likelihood is iterative and uses a Fisher information matrix.

10. The method for receiving according to claim 6, wherein the method further comprises a preliminary act of equalizing said signal in baseband.

11. A device comprising: a receiver, which is configured to receive a signal transmitted in the form of an electromagnetic wave carrying an angular momentum, delivering an estimation of a data symbol of a sequence of data symbols comprising at least two data symbols of distinct values, said electromagnetic wave carrying an orbital angular momentum presenting an order of orbital angular momentum selected bijectively during the transmission of said signal so as to represent, by bijection, the value of said data symbol, and an estimator of the value of said data symbol, implementing a detector of said order of orbital angular momentum, wherein said detector is configured for determining of a phase gradient comprising: shaping said signal in vector form, unwrapping of a phase of each term of said vector form and of determining a phase of the product of the terms of said vector form, obtaining said order of estimated orbital angular momentum implementing a division of said phase of the product of the terms of said vector form multiplied by the term (L1), L being an integer corresponding to a maximum absolute value of the order of orbital angular momentum capable of being received, multiplied by two.

12. A non-transitory computer-readable medium comprising a computer program stored thereon, comprising instructions to implement a method of transmitting a sequence of data symbols comprising at least two data symbols of distinct values, delivering an electromagnetic wave carrying an orbital angular momentum, when this program is executed by a processor of a transmission device, wherein the instructions configure the transmission device to perform the following acts, for at least one data symbol to be transmitted: a bijective selection of an order of orbital angular momentum associating, with each distinct value of a data symbol, a distinct order of orbital angular momentum, and delivering a selected order of orbital angular momentum that is representative, by bijection, of the value of said at least one data symbol to be transmitted, and transmitting said electromagnetic wave carrying an orbital angular momentum, the order of orbital angular momentum of which corresponds to said selected order of orbital angular momentum, and wherein the instructions further configure the transmission device to perform the following acts prior to said bijective selection: receiving a binary data string, determining the maximum absolute value of order of orbital angular momentum that can be transmitted by the transmission device implementing said method for transmitting, forming said sequence of data symbols from said binary string, said act of forming taking account of said absolute maximum value of order of orbital angular momentum.

Description

4. LIST OF FIGURES

(1) Other characteristics and advantages of the invention shall appear more clearly from the following description of a particular embodiment given by way of a simple, illustratory and non-exhaustive example and from the appended figures, of which:

(2) FIG. 1 already described with reference to the prior art illustrates the helical wavefront of an electromagnetic wave carrying an orbital angular momentum,

(3) FIG. 2 already described with reference to the prior art illustrates a radiofrequency transceiver system for transmission-reception of an electromagnetic wave carrying an orbital angular momentum,

(4) FIG. 3 presents the main steps of the method for transmitting according to one embodiment of the invention,

(5) FIG. 4 is a schematic representation of a radiofrequency transmission device according to one example of the invention,

(6) FIGS. 5A and 5B derived from the prior art respectively represent the general principle of a optical transmission module for transmitting an electromagnetic wave presenting an orbital angular momentum of a predetermined order and the corresponding waveguide architecture,

(7) FIG. 6 is a representation of a spatial localization of a reception element of a radiofrequency reception device according to the invention,

(8) FIG. 7 presents the main steps of the method for receiving according to the invention,

(9) FIGS. 8 to 10 illustrate different examples of implementation of the method for receiving according to the invention,

(10) FIGS. 11 and 12 respectively illustrate the simplified structure of a transmission device implementing a technique of transmission, and a device for receiving implementing a technique of reception according to one particular embodiment of the invention.

5. DESCRIPTION OF ONE EMBODIMENT OF THE INVENTION

5.1 General Principle

(11) The general principle of the invention relies on a novel technique for transmitting information by electromagnetic waves based on the use of the orbital angular momentum.

(12) The order of orbital angular momentum of the electromagnetic wave to be transmitted in effect directly represents the symbol value of data to be sent, a bijective relationship being established according to the invention between the order of orbital angular momentum and the symbol value of the data to be transmitted.

(13) Thus, as compared with the prior-art techniques where the properties of the orbital angular momentum are essentially used to generate orthogonal channels available for the transportation of information associated with a multiplexing of information, the present invention proposes to dedicate an order of orbital angular momentum to the representation of only one value of data symbols.

(14) The technique according to the invention increases spatial diversity and can especially be applied in short-range transmission, for example to transmit identification data.

(15) At reception, the rebuilding of the data symbol sent is simple and efficient because it can be deduced by a single inversion of the bijective relationship used when sending to select the order of orbital angular momentum to be used to generate the electromagnetic wave.

(16) Here below, referring to FIG. 3, we present the main steps implemented by a method of transmission according to one embodiment of the invention.

5.2 Description of Examples of Implementation of the Method of Transmission

(17) According to one particular example of implementation, the method for transmitting according to the invention receives (31) at input M pieces of binary data to be transmitted {d}.sub.1:M, M being an integer and d being a binary value equal to 1 or 0.

(18) In addition, the method implements a step (32) for determining the maximum absolute value of order l.sub.max of the orbital angular momentum capable of being transmitted by the transmission device used.

(19) For example, when the transmission device has N=5 sending elements, the maximum absolute value of order l, also called mode, of orbital angular momentum that can be encoded distinctly is then such that abs(l)<N/2, giving l.sub.max=2, so that l{2, 1, 0, 1, 2}.

(20) According to another example, if the transmission device has N=8 sending elements available, the possible values, also called modes, of the order l of orbital angular momentum which can be encoded distinctly are such that N/2l<N/2 so that l{4, 3, 2, 1, 0, 1, 2, 3}.

(21) Transmission modules are used to transmit an electromagnetic wave carrying an orbital angular momentum with a predetermined order, are for example represented in FIGS. 4 and 5A, 5B pertaining respectively to a radiofrequency transmission and to an optical transmission.

(22) In particular, the radiofrequency transmission module (44) of FIG. 4 has eight elements (T.sub.0, T.sub.1, T.sub.2, T.sub.3, T.sub.4, T.sub.5, T.sub.6, T.sub.7) and is therefore capable of generating electromagnetic waves carrying an orbital angular momentum, of which the order l{4, 3, 2, 1, 0, 1, 2, 3}.

(23) It must also be noted that other transmission modules capable of exciting an orbital angular momentum have been devised, for example a parabolic reflector that is classic but twisted in order to induce a phase azimuthal distribution as described by F. Tamburini et al. (Encoding many channels on the same frequency through radio vorticity: first experimental test, New Journal of Physics, Vol 14, 2012, 033001), or again a phase blade as described by R. Niemiec (Excitation d'un moment angulaire orbital (OAM) d'une onde en bande millimtrique, partir d'une lame de phase (Excitation of an orbital angular momentum (OAM) of a millimeter-band wave from a phase plate), 18.sup.me Journe Nationales Microondes, 15-17 May 2013).

(24) According to another example, illustrated by FIGS. 5A and 5B, an optical transmission module (5000 and 5001) corresponding to a photonic integrated circuit made of silicon can also be used to generate an electromagnetic wave carrying an orbital angular momentum with a predetermined order l as described by N. K. Fontaine et al. (Efficient multiplexing and demultiplexing of free-space orbital angular momentum using photonic integrated circuits, Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2012 and the National Fiber Optic Engineers Conference, pages 1 to 3, 4-8 Mar. 2012).

(25) Such an optical transmission module comprises especially a circular network coupler (54) and a star coupler (51). The circular network coupler is especially based on the use of monomode apertures (54) sending or collecting light. This light is then guided to the star coupler (51) by means of optical waveguides (53), the length of which is adapted to the location of the aperture in the wavefront considered in order to convert an azimuth phase (50) representing the order of the orbital angular momentum corresponding to the number of rotations of the phase per wavelength, and a variation of amplitude into linear phase variations (52). FIG. 5A represents an optical transmission module capable of generating electromagnetic waves carrying an orbital angular momentum, of which the order l{2, 1, 0, 1, 2}, while FIG. 5B represents an optical transmission module capable of generating electromagnetic waves carrying an orbital angular momentum, of which the order l{4, 3, 2, 1, 0, 1, 2, 3, 4}.

(26) These existing transmission modules, conventionally used to transport information associated with information multiplexing, cannot be used as such to implement the invention because there is no relationship between the value of the data symbol to be transmitted and the order of the orbital angular momentum.

(27) The step (31) for receiving M binary data to be transmitted and the step (32) for determining the maximum absolute value of order l.sub.max of the orbital angular momentum capable of being transmitted by the transmission device used are independent and can be implemented successively, according to any order whatsoever or in parallel as shown in FIG. 3.

(28) Once these two steps have been performed, the method according to the embodiment shown in FIG. 3 implements a step (33) for forming a sequence of data symbols from the binary string, in taking account of the maximum absolute value of order l.sub.max of the orbital angular momentum.

(29) In other words, the string of digital symbols {d}.sub.1:M, M being an integer and d being a binary value equal to 1 or 0, is encoded in an alphabet of data symbols defined by the possible orders (or again states) of the orbital angular momentum, these orders being demarcated by the maximum absolute value of order l.sub.max of the orbital angular momentum capable of being transmitted by the previously determined transmission device.

(30) According to one particular example of implementation, the step for forming corresponds to an N-state modulation, N being an integer equal to twice said maximum absolute value of order of orbital angular momentum plus one.

(31) For example, for a radiofrequency transmission device or an optical transmission device, the step for forming corresponds to an N-state pulse amplitude modulation, called a PAM N-ary modulation.

(32) Such a PAM N-ary modulation (42) is especially illustrated in FIG. 4, as is a set of bits of the binary string 1011..01 represented by a data symbols, the value of which in the constellation is 2, 1, 0, 4. The correspondence between the binary sequence 1011..01 and the representation or mapping in the constellation is for example set up by means of an encoding such as a Gray encoding or any other means used to establish such a mapping.

(33) A quadrature phase shift keying (QPSK) modulation or again a 16-state quadrature amplitude modulation (16QAM) is also used to associate a value of mapping of the data symbol in the constellation (also called a state value) with a group of several bits.

(34) It must be noted that the term value is understood to mean any piece of information used to localize a data symbol in a constellation. Such a value can therefore correspond to an integer value associated with a position number in the constellation, but also a pair of coordinates in the plane of the constellation.

(35) Once the data symbols have been shaped and their value in the constellation defined, the method according to the invention implements a step of bijective selection (34) of an order of orbital angular momentum associating, with each distinct value of data symbols, a distinct order of orbital angular momentum and delivering a selected order of orbital angular momentum representing, by bijection, the value of said at least one data symbol to be transmitted.

(36) Thus, by making the order of orbital angular momentum carry the value of the symbol, a spatial modulation is created.

(37) This aspect is especially illustrated in FIG. 4 where said method of transmission is implemented by a radiofrequency transmission device (40) comprising a plurality of sending elements (T.sub.0, T.sub.1, T.sub.2, T.sub.3, T.sub.4, T.sub.5, T.sub.6, T.sub.7).

(38) The bijective selection (34) according to the invention of an order of orbital angular momentum is implemented by a selection module (45).

(39) According to the example illustrated in FIG. 4, the order of orbital angular momentum is selected when it is equal to the value of the data symbol to be transmitted. Thus, according to this example, the bijective relationship between the order of orbital angular momentum and the value representing the data symbol in the constellation is therefore a relationship of identity, in other words a relationship of equality, between the value representing the data symbol in the constellation and the order of orbital angular momentum.

(40) Such a bijective selection based on an equality between the value representing the data symbol in the constellation and the order of orbital angular momentum is not possible unless the mode of formation and representation of data symbols in the constellation delivers an integer value.

(41) In other words, when the data symbol is represented by the value 4 in the constellation, an order of orbital angular momentum l=4 is selected. As a consequence, the order of angular momentum directly represents the value of the information to be transmitted.

(42) When the value corresponds for example to a pair of coordinates in the constellation plane, the bijective selection is based on a bijective relationship associating with each distinct pair of coordinates a distinct order of orbital angular momentum.

(43) Then, with regard to the embodiment represented in FIG. 4 representing a radiofrequency transmission device (40), the method of transmission furthermore comprises a step of series-parallel replication (43) of the order of orbital angular momentum selected l=4 so that it is delivered at input of each sending element (T.sub.0, T.sub.1, T.sub.2, T.sub.3, T.sub.4, T.sub.5, T.sub.6, T.sub.7).

(44) Once the bijective selection of the order of orbital angular momentum to be transmitted is done, the method according to the invention implements a step (35) for transmitting said electromagnetic wave carrying an orbital angular momentum, the order of orbital angular momentum of which corresponds to said selected order of orbital angular momentum.

(45) An example of this transmission is for example illustrated by FIG. 4, where the order of orbital angular momentum l=4 has been selected and transmitted by N=8 sending elements corresponding to eight sending radiofrequency antennas.

(46) The signal (35) transmitted by the eight radiofrequency antennas (T.sub.0, T.sub.1, T.sub.2, T.sub.3, T.sub.4, T.sub.5, T.sub.6, T.sub.7) forming the network of circular antennas corresponding to the transmission module (44) is therefore transmitted in the following form:

(47) $x=\frac{1}{\sqrt{N}}\left[\begin{array}{c}1\\ e^{j2\frac{l}{N}}\\ \mathrm{.Math.}\\ e^{j2\frac{l\left(N-1\right)}{N}}\end{array}\right]$
where l represents the N-ary information symbol to be transmitted.

(48) Thus, with regard to the illustration of FIG. 4, when l=4, the antenna T.sub.6 generates an electromagnetic wave, the expression of which comprises a term

(49) $\frac{1}{\sqrt{N}}{e}^{j2\frac{\left(-4\right)*6}{N}}.$

(50) It must be noted that the steps for receiving (31), determining (32), forming and replication (43) are optional, their implementation can be eliminated when the transmission device directly receives the values representing the constellation, each data symbol to be transmitted and/or when the transmission device uses a single sending element such as an optical waveguide.

(51) In addition, the steps of the method for receiving according to the invention are repeated as many times successively as there are data symbols in the sequence of data symbols transmitted preliminarily.

5.3 Description of Examples of Implementation of the Method of Reception

5.3.1 Case of a Transmission Channel without Fading

(52) The received signal r, corresponding to the signal transmitted according to the method of transmission described here above has the following expression: r=Hx+n,

(53) where H is the matrix representing the channel 12 between the transmission device T and the reception device R as represented by FIG. 1 and represents solely the free-space loss in a communication between these two devices and n such that n(0,.sup.2I.sub.N), a complex Gaussian noise, for example a circular complex Gaussian noise received by each of the reception elements, the reception elements corresponding to radiofrequency antennas when the communications system (formed by at least one transmission device and at least one reception device) is a radiofrequency communications system.

(54) It must be noted that for a radiofrequency communications system, it is quite possible to implement a system comprising N sending elements and N receiving elements as to implement a system comprising N.sub.E sending elements and N.sub.R reception elements, N.sub.E and N.sub.R being distinct.

(55) In the case of an NN radiofrequency communications system, the matrix H representing the channel can be written as

(56) $H=\frac{}{4}\left[\begin{array}{cccc}\frac{e^{-jk{d}_{11}}}{d_{11}}& \frac{e^{-j{\mathrm{kd}}_{12}}}{d_{12}}& \mathrm{.Math.}& \frac{e-j{\mathrm{kd}}_{1N}}{d_{1N}}\\ \frac{e^{-j{\mathrm{kd}}_{21}}}{d_{21}}& & & \\ \mathrm{.Math.}& & & \mathrm{.Math.}\\ \frac{e^{-j{\mathrm{kd}}_{N1}}}{d_{N1}}& \mathrm{.Math.}& \mathrm{.Math.}& \frac{e-j{\mathrm{kd}}_{\mathrm{NN}}}{d_{\mathrm{NN}}}\end{array}\right]$
with

(57) $k=\frac{2}{}$
being the number of waves, d.sub.mn being the distance between the n.sup.th sending element and m.sup.th reception element, with:

(58) $d_{\mathrm{mn}}=\sqrt{a^2+\frac{z_m^2}{{\cos }^2{}_m}-2{\mathrm{az}}_m\tan {}_m\cos \left({}_m-{}_n\right)}$
where is the radius of the sending antenna, z.sub.m is the distance between the plane of the sending antenna and that of the receiving antenna, .sub.m is the pointing angle on the reception antenna m in spherical coordinates, .sub.m is the azimuth of the sensor of the reception antenna in spherical coordinates and

(59) ${}_n={\left\{\frac{2n}{N}\right\}}_{n=0,\mathrm{.Math.},N-1}$
is the angular position of the sending elements in the plane of the antenna network, these parameters being illustrated by FIG. 6.

(60) Here below, referring to FIG. 7, we present the main steps implemented by a method for receiving according to one embodiment of the invention.

(61) According to one particular example of implementation, the method for receiving according to the invention inputs (71) an electromagnetic wave O.sub.EM.

(62) According to the invention, the electromagnetic wave O.sub.EM carries an orbital angular momentum having an order of orbital angular momentum selected bijectively during the transmission of the signal so as to represent the value of a data symbol by bijection.

(63) Once this step for receiving has been performed, the method according to the embodiment shown in FIG. 7 implements a step of estimation (72) of the value of the data symbol transmitted, comprising a step (721) for detecting the order of orbital angular momentum {circumflex over (l)} of the electromagnetic wave O.sub.EM.

(64) Once the order of the orbital angular momentum {circumflex over (l)} of the electromagnetic wave O.sub.EM has been detected, the method for receiving according to the invention determines (722) the value Vs representing, in the constellation, the data symbol transmitted. This determining especially implements an inversion Inv.sub.B of the bijective relationship having allowed the selection of the order of orbital angular momentum {circumflex over (l)}.

(65) Then, starting from the value Vs, one or more bits D_bits are determined (723) by correspondence between the value Vs of representation in the constellation (known as demapping) and a binary set comprising at least one bit, for example through a decoding such as a Gray decoding.

(66) A) Detection of the Order of Orbital Angular Momentum Based on the Implementing of a Fourier Transform.

(67) The signal r is received (71) by the reception module 81 of the reception device 80 illustrated in FIG. 8, comprising for example a plurality of reception elements (optical or radiofrequency elements as represented in FIG. 8) and belonging to a communications system NN.

(68) For example, when the reception device is a radiofrequency or optical reception device, a baseband conversion is applied.

(69) A fast Fourier transform (FFT) is then applied (821) to the received vector r[m], m{0, . . . , N1}, N being an integer corresponding to the number of reception elements so that y the resultant vector is expressed as follows:

(70) $\begin{array}{c}y=F_{N}r=F_N\mathrm{Hx}+F_{N}n\\ =F_N\left(h.Math.x\right)+\tilde{n}\\ =F_{N}h{F}_{N}x+\tilde{n}\\ =\tilde{h}{}_{ln}+\tilde{n}\end{array}$
with {tilde over (h)}=F.sub.Nh being the Fourier transform of the first row h of the transmission channel between the N sending elements and the first reception element. By property, the FFT of the vector x is a dirac function .sub.ln such that:

(71) ${}_{ln}=\{\begin{array}{cc}1& \mathrm{sil}=n\\ 0& \mathrm{sil}n\end{array}$
in addition and are respectively the circular convolution operators and Hadamard product (in other words the term-to-term product).

(72) Thus, by construction, a single input of y contains the information on the order l of orbital angular momentum used.

(73) Without noise n, the single non-zero input of y gives the order l of the orbital angular momentum used. For example, if N=8 and l transmitted=4, then:

(74) ${}_{ln}=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ 1\\ 0\\ 0\\ 0\end{array}\right]\mathrm{and}\mathrm{as}a\mathrm{consequence}$$y=\left[\begin{array}{c}{y}_0\\ y_1\\ y_2\\ y_3\\ y_4\\ y_5\\ y_6\\ y_7\end{array}\right]=\left[\begin{array}{c}{\tilde{h}}_0\\ {\tilde{h}}_1\\ {\tilde{h}}_2\\ {\tilde{h}}_3\\ {\tilde{h}}_4\\ {\tilde{h}}_5\\ {\tilde{h}}_6\\ {\tilde{h}}_7\end{array}\right]\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ 1\\ 0\\ 0\\ 0\end{array}\right]+\left[\begin{array}{c}{\tilde{n}}_0\\ {\tilde{n}}_1\\ {\tilde{n}}_2\\ {\tilde{n}}_3\\ {\tilde{n}}_4\\ {\tilde{n}}_5\\ {\tilde{n}}_6\\ {\tilde{n}}_7\end{array}\right]=\left[\begin{array}{c}{\tilde{n}}_0\\ {\tilde{n}}_1\\ {\tilde{n}}_2\\ {\tilde{n}}_3\\ {\tilde{h}}_4+{\tilde{n}}_4\\ {\tilde{n}}_5\\ {\tilde{n}}_6\\ {\tilde{n}}_7\end{array}\right]$

(75) Finally, the decision on the order l of orbital angular momentum used during the transmission is based on the detection of the maximum energy of the elements constituting the vector y, in assuming that the channel undergoes no fading.

(76) After a parallel-series conversion (822) of the elements constituting the vector y to create a block of N elements in a row y=[y[0], . . . y[N1]], the detection of the order l of orbital angular momentum used during the transmission is then implemented by means of an energy detector such that: {circumflex over (l)}=max.sub.i|y.sub.i|.sup.2, with i[0,N1]. In other words, the absolute value squared is taken on the elements constituting the vector y, i.e. |y.sub.i|.sup.2 and the maximum index i gives the value of the order l of the orbital angular momentum used, with the following rule: If maximum index i.sub.max

(77) 0$\left\{0,\mathrm{.Math.}.Math.\frac{N-1}{2}.Math.\right\}$ is such that then {circumflex over (l)}=i.sub.max if i.sub.max{N1/2+1, . . . , N1} then {circumflex over (l)}={N/2, . . . , 1}.

(78) Finally, once the order {circumflex over (l)} of the orbital angular momentum of the electromagnetic wave O.sub.EM is detected, the method for receiving according to the invention determines D_Vs (824) the value Vs representing, in the constellation, the data symbol transmitted in implementing an inversion of the bijective relationship that has enabled the selection of the order of orbital angular momentum {circumflex over (l)}.

(79) Then, from the value Vs, one or more bits are determined (824) by correspondence between the value Vs of representation in the constellation (demapping) and a binary set comprising at least one bit, using for example a decoding such as the Gray decoding.

(80) B) Detection by Maximum Likelihood of the Order of Orbital Angular Momentum.

(81) Here below, we present a variant of an embodiment with regard to the detection described here above based on the implementation of a Fourier transform.

(82) The present variant is based on a detection by maximum likelihood (or scoring).

(83) According to this alternative embodiment, the signal r is received (71) by the reception module 81 and then, assuming that the value of the angle of aperture .sub.m (represented in FIG. 6) is also unknown, it is necessary to estimate the vector =[l,].sup.T maximizing the density of probability (ddp) p(y;) of the received signal. In assuming that .sub.m=,m{1, . . . , N} the density of probability is expressed in the following form:

(84) $p\left(y;\right)=\frac{1}{{}^{2M}}{e}^{-\frac{1}{{}^2}\underset{m=0}{\overset{M-1}{.Math.}}{.Math.y\left[m\right]-\frac{\cos }{4z}{e}^{-jk\frac{z}{\cos }\underset{n=0}{\overset{N-1}{.Math.}}{e}^{jl{}_n}{e}^{jak\sin \cos \left({}_m-{}_n\right)}}.Math.}^2.}$
The following relationship is obtained: max.sub.p(y;)max.sub. ln p(y;).

(85) According to one alternative implementation, the search for the vector is implemented by successive iterations from an initial state of and from the Fisher information matrix I, especially the value of at the instant k+1, is such that:

(86) ${{}_{k+1}={}_k+I^{-1}\left(\right)\frac{\ln p\left(y;\right)}{}.Math.}_{={}_k},$
with I(), the Fisher information matrix on the parameters , and the generic term of which is:

(87) ${\left\{I\left(\right)\right\}}_{i,j}=\frac{{}^2\ln p\left(y,\right)}{{}_i{}_j}.$

5.3.2 Case of any Unspecified Transmission Channel

(88) The received signal r, corresponding to the signal transmitted according to the method for transmitting described here above, always has the expression: r=Hx+n,

(89) where H is the matrix representing the channel 12 between the transmission device T and the reception device R as represented in FIG. 1, such that H.sup.MN of which each element h.sub.m,n is constituted by the free space loss part as well as a complex coefficient .sub.mn(0,1) the gain of which is a Rayleigh relationship,

(90) In distant field, the expression of the element h.sub.m,n is the following:

(91) $h_{m,n}={}_{\mathrm{mn}}\frac{\cos {}_m}{4z}{e}^{-jk\frac{z}{\cos {}_m}{e}^{j\mathrm{ak}\sin {}_m\cos \left({}_m-{}_n\right)}}.$

(92) The signal r is received (71) by the reception module 81 of the reception device 90, illustrated by FIG. 9, comprising for example a plurality of M reception elements (optical or radiofrequency as represented in FIG. 9) and belonging to a communications system NM, with MN, N and M representing respectively the number of sending elements and the number of reception elements.

(93) According to one example of implementation of the method for receiving according to the invention in any unspecified channel, an estimator (91) is implemented to estimate the data vector sent x and implements an equalization (912) by maximum likelihood (MV), this equalization being optimal because it has a minimum variance for the estimation of the data vector sent x.

(94) Such an equalization (912) is implemented after estimation (911) of the transmission channel H and self-correlation of the noise so that: {circumflex over (x)}=(H.sup.HC.sup.1H).sup.1H.sup.HC.sup.1s

(95) where H.sup.H is the conjugate transpose matrix of H, In addition, C is the matrix of covariance of the noise such that C=[nn.sup.H].sup.MM.

(96) The signal received after processing is then expressed by the following equation:
{circumflex over (x)}=x+(H.sup.HC.sup.1H).sup.1H.sup.HC.sup.1n.

(97) Thus, the vector {circumflex over (x)} is an estimate of the vector x plus a noise vector, each constituent element of which is a complex number.

(98) Once this estimation of the received signal has been made, the detection (82) of the order l of the orbital angular momentum used during the transmission is based on the implementation of a Fourier transform as described here above with reference to FIG. 8.

(99) According to another alternative, after estimation and equalization (101) as described here above or by using any other type of equalizer such as a zero forcing (ZF) equalizer, a decision feedback equalizer, or again an equalizer based on a minimum mean square error (MMSE) equalizer, the detection (82) of the order l of the orbital angular momentum used during the transmission can also be implemented by means of a determining of a phase gradient as illustrated by FIG. 10.

(100) Such a determining of a phase gradient comprises: a step for shaping said signal in vector form, a step of unwrapping of the phase of each term of said vector form and determining (102) the phase of the product of the terms of said vector form, a step (103) for obtaining said estimated order of orbital angular momentum implementing a division of the phase of the product of the terms of said vector form by the term (L1), L being an integer corresponding to said maximum absolute value of order of orbital angular momentum capable of being received multiplied by two.

(101) For example, in the case of a radiofrequency transmission module with N sending elements, L=N.

(102) In other words, the phase of the product of the terms of the vector {circumflex over (x)} is estimated and then divided by (L1) such that

(103) $\hat{l}=\frac{\left(\underset{i=0}{\overset{L-1}{.Math.}}\hat{x}\left[i\right]\right)}{\left(L-1\right)}=\frac{\underset{i=0}{\overset{L-1}{.Math.}}\frac{2li}{L}+{}_i}{\left(L-1\right)},$
with .sub.i as a random phase term due to the Gaussian noise filtered by means of an equalization by maximum likelihood (MV). Without noise, .sub.i=0i{0, . . . , L1}.

(104) More specifically, the phase of the vector {circumflex over (x)} is determined by phase unwrapping, i.e. when the phase gradient between two measurement point exceeds , the phase measured is corrected by an addition of a multiple of 2. Methods for running the phase making it possible to determine a multiple of this kind are especially disclosed in another context by M. Desvignes et al (Droulement de phase: application la correction de distorsions gomtriques en IRM (Phase unwrapping: geometric distortions correction on MRI), Traitement du Signal 2000, Volume 17, n4, pages 313 to 324).

(105) Naturally, the phase measurement at each point is disturbed by a noise term, but this noise term is attenuated by preliminary equalization.

(106) When there is no noise, such a detector enables a perfect detection of the order l of the orbital angular momentum used during the transmission because by using the mathematical development of L1 integers, the following is obtained:

(107) $\underset{i=0}{\overset{L-1}{.Math.}}\frac{2li}{L}=l\left(L-1\right).$

(108) In a noisy channel, it can be noted that the greater the value of L the lower will be the noise

(109) $\frac{{}_i}{\left(L-1\right)}$
for the estimation of l.

5.4 Structure of the Transmission and Reception Devices

(110) Referring now to FIGS. 11 and 12 respectively, we shall now describe the simplified structure of a device for transmitting and the structure of a device for receiving according to one particular embodiment of the invention.

(111) As illustrated in FIG. 11, such a transmission device comprises a memory 1110 comprising a buffer memory, a processing unit 1111, equipped for example with a microprocessor P, and driven by the computer program 1112, implementing the method for transmitting according to one embodiment of the invention.

(112) At initialization, the code instructions of the computer program 1112 are for example loaded into a RAM and then executed by the processor of the processing unit 1111. The processing unit 1111 inputs at least one binary string of data. The microprocessor of the processing unit 1111 implements the steps of the method of transmission described here above according to the instructions of the computer program 1112 to generate an electromagnetic wave carrying an orbital angular momentum, of which the order of the orbital angular momentum represents, by bijection, the value of the data symbol to be transmitted. To this end, the device for transmitting comprises, in addition to the buffer memory 1110, a module for bijective selection of an order of orbital angular momentum associating, with each distinct data symbol value, a distinct order of orbital angular momentum and delivering a selected order of orbital angular momentum that is representative, by bijection, of the value of said at least one data symbol to be transmitted, and a module for transmitting said electromagnetic wave carrying an orbital angular momentum, for which the order of the orbital angular momentum corresponds to said selected order of orbital angular momentum.

(113) These modules are driven by the microprocessor of the processing unit 1111.

(114) As illustrated in FIG. 12, a reception device according to the invention for its part comprises a memory 1210 comprising a buffer memory, a processing unit 1211, equipped for example with a microprocessor P, and driven by the computer program 1212, implementing the method for receiving according to one embodiment of the invention

(115) At initialization, the code instructions of the computer program 1212 are for example loaded into a RAM and then executed by the processor of the processing unit 1211. The processing unit 1211 inputs an electromagnetic wave carrying an orbital angular momentum. The microprocessor of the processing unit 1211 implements the steps of the method for receiving described here above according to the instructions of the computer program 1212 to estimate the data symbols transmitted. To this end, the reception device comprises, in addition to the buffer memory 1210, an estimator of the value of the data symbol implementing a detector of said order of orbital angular momentum.

(116) These modules are driven by the microprocessor of the processing unit 1211.

(117) Although the present disclosure has been described with reference to one or more examples, workers skilled in the art will recognize that changes may be made in form and detail without departing from the scope of the disclosure and/or the appended claims.