IQ DENSE CODING METHOD AND DEVICE FOR SDM COMMUNICATION SYSTEM ON OPTICAL FIBER

Abstract

The present invention relates to a method and a device for dual-polarisation, fiber-optic SDM transmission. The transmission method uses specific I/Q coding that makes it possible to combat the effects of PDL. The modulation symbols to be transmitted on the 2N polarisation states of the N basic spatial channels are broken down into real and imaginary values (220). A real vector composed by concatenating these real values and imaginary values is then constructed. A first invertible linear transformation, represented by a dense real matrix, is applied (230) to the resulting real vector to provide a transformed real vector. Complex transmission symbols are formed by I/Q combination (240) of the components of the transformed vector, the transmission symbols then modulating the different polarisation states of the basic spatial channels.

Claims

1. SDM transmission method on dual polarization optical fiber, intended to transmit, during channel use, 2N symbols belonging to a modulation constellation in the complex plane, N>1 being the number of elementary spatial channels used for transmission, wherein: said symbols undergo a separation into real part and imaginary part to provide a real vector of size 4N formed by the 2N real parts of these symbols and the 2N imaginary parts of these same symbols; an invertible linear transformation represented by a dense real matrix of size 4N4N is applied to the real vector to provide a transformed real vector; 2N complex emission symbols are obtained by performing an IQ combination of 2N components of a first set of components of the transformed real vector respectively with the 2N components of a second set of components of the transformed real vector, the first and second sets being disjoint, each complex emission symbol modulating a first state and a second state of polarization of an elementary spatial channel.

2. SDM transmission method on dual polarization optical fiber according to claim 1, characterized in that said real vector is formed by the concatenation of a first vector composed of the real parts of the modulation symbols and of a second vector composed of the imaginary parts of these same symbols.

3. SDM transmission method on dual polarization optical fiber according to claim 1, characterized in that the first set of components of the transformed real vector is composed of the first 2N components of this vector and that the second set of components of the transformed real vector is composed of the last 2N components of this vector.

4. SDM transmission method on polarization dual optical fiber according to claim 1, characterized in that the characteristic polynomial of the dense real matrix does not have real roots.

5. SDM transmission method on dual polarization optical fiber according to claim 4, characterized in that the dense real matrix is a rotation matrix in the R.sup.4N space.

6. SDM transmission method on dual polarization optical fiber according to claim 1, characterized in that the elementary spatial channels are propagation modes in the optical fiber.

7. SDM transmission method on dual polarization optical fiber according to claim 1, characterized in that the optical fiber is of the multicore type and that the elementary spatial channels are different cores of said fiber.

8. SDM transmission device on optical fiber with polarization duality, intended to transmit, during a channel use, 2N symbols belonging to a modulation constellation in the complex plane, N>1 being the number of elementary spatial channels used for the transmission, wherein it comprises: a first module configured to separate each of said symbols into a real part and an imaginary part to provide a real vector of size 4N formed by the 2N real parts of these symbols and the 2N imaginary parts of these same symbols; a second linear combination module configured to apply an invertible linear transformation, represented by a dense real matrix of size 4N4N, to the real vector to provide a transformed real vector; a third IQ combining module configured to respectively combine 2N components of a first set of components of the transformed real vector with 2N components of a second set of components of the transformed real vector, the first and second sets being disjoint, so as to generate 2N complex emission symbols, each complex emission symbol modulating a first polarization state and a second polarization state of an elementary spatial channel.

9. SDM transmission device on optical fiber with polarization duality according to claim 8, characterized in that the first module is configured to form said real vector by concatenating a first vector composed of the real parts of the modulation symbols and a second vector composed of the imaginary parts of these same symbols.

10. SDM transmission device on optical fiber with polarization duality according to claim 8, characterized in that the third module is configured so that the first set of components of the transformed real vector is composed of the first 2N components of this vector and that the second set of components of the transformed real vector is composed of the last 2N components of this vector.

11. SDM transmission device on optical fiber with polarization duality according to claim 8, characterized in that the characteristic polynomial of the dense real matrix does not have real roots.

12. SDM transmission device on optical fiber with polarization duality according to claim 11, characterized in that the dense real matrix is a rotation matrix in the R.sub.4N space.

13. SDM transmission device on optical fiber with polarization duality according to claim 8, characterized in that the elementary spatial channels are propagation modes in the optical fiber.

14. SDM transmission device on optical fiber with polarization duality according to claim 8, characterized in that the optical fiber is of the multicore type and that the elementary spatial channels are different cores of said fiber.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Other features and advantages of the invention will appear on reading a preferred embodiment of the invention, described with reference to the attached figures among which:

[0035] FIG. 1, already described, schematically represents a fiber optic transmission device using pre-coding on two orthogonal polarizations;

[0036] FIG. 2 schematically represents an SDM transmission device on optical fiber with dense IQ coding according to a general embodiment of the invention;

[0037] FIG. 3 schematically represents an SDM transmission device on optical fiber with dense IQ coding according to a preferred embodiment of the invention.

DESCRIPTION OF THE EMBODIMENTS

[0038] We will consider in the following a spatial diversity transmission system (SDM) on optical fiber. Spatial diversity can be due to the plurality of modes and/or cores in the fiber. In the case of a conventional multimode fiber, the core diameter is large enough to allow the propagation of several modes at the considered wavelength. In the case of a multi-core fiber, propagation takes place in a plurality of elementary cores of the fiber. The case of a bundle of single-mode fibers with reduced cladding thickness is subsequently assimilated to a multi-core fiber.

[0039] The SDM transmission systems considered below can be of one and/or the other type, it being understood that the elementary spatial channels are then propagation modes and/or cores of an optical fiber.

[0040] We will further assume that the optical fiber is classically affected by PDL attenuation, that is, that the different states of polarization (SOP) in the fiber do not undergo the same attenuation. It is recalled that PDL attenuation is generally introduced by optical elements between fiber sections, in particular doped fiber optical amplifiers (EDFA) which create energy losses and fluctuations in the optical signal to noise ratio (OSNR). Polarization dispersion (PMD) will be ignored, however, as this effect can be effectively corrected by channel equalization in the receiver's DSP.

[0041] An SDM channel model was described in the article by A. Abouseif et al. entitled Channel model and optimal core scrambling for multi-core fiber transmission system, Optics communications, Volume 454, 2020. The elementary spatial channels correspond to the different cores of a multi-core fiber (MCF) and/or to the different modes of a multi-mode fiber (MMF).

[0042] The effect of PDL attenuation for an elementary spatial channel can be expressed by the matrix H.sub.PDL applying to both polarization states:

[00001]$\begin{array}{cc}{H}_{\mathrm{PDL}}=D_{}{R}_{}{B}_{}& \left[\mathrm{Math}.1\right]\end{array}$

[0043] Where

[00002]$D_{}=\left(\begin{array}{cc}\sqrt{1+}& 0\\ 0& \sqrt{1-}\end{array}\right)$

is the gain matrix,

[00003]$R_{}=\left(\begin{array}{cc}\cos & -s\mathrm{in}\\ \sin & \cos \end{array}\right)$

is the polarization rotation matrix and

[00004]$B_{}=\left(\begin{array}{cc}{e}^i& 0\\ 0& e^i\end{array}\right)$

is the birefringence matrix with [0,1] defining the PDL value, .sub.dB=10 log .sub.10() with =(1+)/(1) and , [, ]. The SDM transmission system uses a plurality N of elementary spatial channels, each elementary spatial channel being associated with two polarization states. Thus, at each transmission instant, in other words at each use of the channel, the transmission system can transmit 2N modulation symbols, one symbol being transmitted per polarization state and per elementary spatial channel. The number N is generally chosen to be high, of the order of several tens or more. In any case N>1.

[0044] The idea behind the present invention is to separate the real parts and the imaginary parts of the different modulation symbols and to subject all the real and imaginary parts of the different symbols to an invertible linear transformation. This results in an averaging of the PDL attenuation and the CDL and/or MDL attenuation over the different polarization states and the different elementary spatial channels.

[0045] FIG. 2 schematically represents an SDM transmission device on optical fiber according to a general embodiment of the invention.

[0046] The data to be transmitted at each transmission interval is in the form of 2N information symbols, for example 2N q-ary words with qlog .sub.2Q where Q is the cardinality of the modulation alphabet. The modulation alphabet can notably be a Q-QAM alphabet.

[0047] The information symbols themselves may result from source coding and/or channel coding, in a manner known per se.

[0048] In all cases, the 2N information symbols are respectively converted into 2N modulation symbols in the q-ary modulators with symbol 210-1, . . . , 210-2N. The odd indices of these symbols correspond to a first polarization state and the even indices to a second polarization state, orthogonal to the first one. Each of these modulation symbols, noted in the sequence x.sub.1, . . . , x.sub.2N, is then subjected to a decomposition into a real part and an imaginary part in the separation module I/Q, 220.

[0049] The real parts R(x.sub.1), . . . , R(x.sub.2N) and the imaginary parts I(x.sub.1), . . . , I(x.sub.2N) form a real vector X.sub.R of R.sup.4N which is supplied to the linear combination module 230.

[0050] In the figure, the real vector X.sub.R is obtained by separately grouping the real parts and the real parts of the modulation symbols x.sub.1, . . . , x.sub.2N, i.e. X.sub.R=(R(x.sub.1) . . . R(x.sub.2N) I(x.sub.1) . . . I(x.sub.2N)).sup.T. However, in general the vector X.sub.R can be obtained by concatenating in any way the real parts and the imaginary parts of these symbols, i.e. [0051] X.sub.R=(R(x.sub.1) . . . R(x.sub.2N)I(x.sub.1) . . . I(x.sub.2N)).sup.T where represents any permutation of the 2N components.

[0052] The first module 230 combines the elements of X.sub.Rby means of an invertible linear transformation, F, represented by a matrix FGL(4N, R), a linear group of dimension 4N on R, to provide a transformed vector, X.sup..sub.R, in R.sup.4N. The linear transformation is chosen such that the matrix F (representative of F in the canonical basis of R.sup.4N is dense (or full), that is to say that it does not contain any zero. Advantageously, the matrix F is chosen such that its characteristic polynomial has no root in R, in other words such that it has no eigen space. This property ensures efficient mixing of the components of the X.sub.R vector and consequently averaging of the PDL.

[0053] The transformed vector, X.sup..sub.R, can be expressed in the following form:

[00005]$\begin{array}{cc}{\tilde{X}}_R={\mathrm{FX}}_R=\left(\begin{array}{c}{f}_1({R\left(x_i\right)}_{i=1,.Math.,4N},{I\left(x_i\right)}_{i=1,.Math.,4N}\\ .Math.\\ .Math.\\ f_{4N}\left({R\left(x_i\right)}_{i=1,.Math.,4N},I{\left(x_i\right)}_{i=1,.Math.,4N}\right)\end{array}\right)& \left[\mathrm{Math}.2\right]\end{array}$ [0054] where f.sub.1, f.sub.2, . . . , f.sub.4N are linear forms on R.sup.4N.

[0055] The first 2N elements and the last 2N elements of X.sup..sub.R are then combined two by two in an I/Q combination module, 240, to give a complex vector X.sup..sub.C, of dimension 2N:

[00006]$\left[\mathrm{Math}.3\right]$${\tilde{X}}_C=\left(\begin{array}{c}{f}_1\left({R\left(x_i\right)}_{i=1,.Math.,4N},{I\left(x_i\right)}_{i=1,.Math.,4N}\right)+{\mathrm{jf}}_{2N+1}\left({R\left(x_i\right)}_{i=1,.Math.,4N},{I\left(x_i\right)}_{i=1,.Math.,4N}\right)\\ .Math.\\ .Math.\\ f_{2N}\left({R\left(x_i\right)}_{i=1,.Math.,4N},I{\left(x_i\right)}_{i=1,.Math.,4N}\right)+{\mathrm{jf}}_{4N}\left({R\left(x_i\right)}_{i=1,.Math.,4N},{I\left(x_i\right)}_{i=1,.Math.,4N}\right)\end{array}\right)$

[0056] More generally, we can form a first partial transformed vector X.sup.1.sub.R, of size 2N by selecting 2N components of the vector X.sup..sub.R and a second partial transformed vector, X.sup.2.sub.R, also of size 2N, by selecting the remaining 2N components, the complex vector then being obtained as X.sup..sub.C=X.sup.1.sub.R+j X.sup.2.sub.R.

[0057] In any case, the complex elements x.sup..sub.1, . . . , x.sup..sub.2N of the vector X.sup.1.sub.C are respectively used to modulate the 2N polarization states of the N elementary SDM channels.

[0058] FIG. 3 schematically represents a WDM transmission device on optical fiber according to a preferred embodiment of the invention.

[0059] Modules 310-1, . . . , 310-N, 320, 330, 340 respectively perform the same functions as modules 210-1, 210-N, 220, 230, 240 of FIG. 2.

[0060] This embodiment is a special case of that shown in FIG. 2 in that the linear transformation here is a rotation in the R.sup.4N space.

[0061] Note that the fact that the matrix must be full immediately excludes trivial rotation matrices I.sub.4N or -I.sub.4N where I.sub.4N is the identity matrix of size 4N.

[0062] Furthermore, since the dimension of space is even, the rotation matrix does not have an eigen (invariant) space.

[0063] Again, the vector X.sub.R can be obtained by concatenating in any way the real parts and the imaginary parts of the modulation symbols x.sub.1, . . . , x.sub.2N. Similarly, the complex vector X.sup..sub.C can be obtained as X.sup..sub.C=X.sup.1.sub.R+jX.sup.2.sub.R from partial transformed vectors X.sup.1.sub.R, X.sup.2.sub.R constructed by selecting for each a set of 2N components of the transformed vector, the sets of components associated with these two vectors being disjoint.

[0064] Finally, the complex lments x.sup..sub.1, . . . , X.sup..sub.2N of the vector X.sup..sub.C are respectively used to modulate the 2N polarization states of the N elementary SDM channels.

[0065] In the embodiments presented in FIGS. 2 and 3, the dense IQ coding is applied to all the SDM elementary channels. However, alternatively, the dense IQ coding may be applied by blocks of spatial channels (mode block and/or core block), the invertible linear transformations, for example the rotations, being able to be chosen distinct from one block of spatial channels to another.

[0066] Finally, although the present invention has been presented in the context of a dual polarization state optical fiber, those skilled in the art will understand that the dense IQ coding method described above can be applied in the case of a single polarization state.

[0067] In all cases, the received optical signal is demultiplexed both spatially (by propagation mode and/or by core) and by polarization. According to a first variant, a channel estimation and a corresponding equalization can be carried out elementary spatial channel by elementary spatial channel. According to a second variant, the channel estimation and the corresponding equalization can be carried out globally on all the elementary spatial channels, i.e. a 2N2N MIMO channel. In both cases, the channel estimation can be based on pilot symbols. For this purpose, we can use CAZAC (Constant Amplitude Zero Auto Correlation) sequences, for example Zadoff-Chu sequences.

[0068] In the case of a 2N2N MIMO channel equalization, the symbols transmitted by the transmission device can be estimated using a MIMO decoder using an ML (Maximum Likelihood) estimate or more simply a ZF (Zero Forcing) estimate aimed at multiplying the received signal by the pseudo-inverse of the channel matrix, namely =(H.sup.HH).sup.1H.sup.HY where {circumflex over ()}H of size 2N2N is the estimated matrix of the MIMO channel. Alternatively, in an elementary spatial channel by elementary spatial channel equalization, the estimation of the symbols transmitted is carried out from N matrices {circumflex over ()}H.sub.i, i=1, . . . , N, each of these matrices corresponding to an elementary spatial channel. It should be noted that this operation does not include the inversion of the linear transformation represented by the matrix F.

[0069] After separating the real and imaginary parts of each of the components of .sub.C, we construct from these components a real vector, R, of size 4N. For example, if the embodiment illustrated in FIG. 2 or FIG. 3 was used in the broadcast, a first vector consisting of the 2N real parts and a second vector consisting of the 2N imaginary parts could be formed, then the first vector and the second vector could be concatenated to obtain the real vector R.

[0070] We then apply the inverse orthogonal transformation F.sup.1 to the vector R to obtain a vector {circumflex over ()}X.sub.R, then the inverse of the permutation applied to the emission on its components.

[0071] For example, when the real vector has been obtained by grouping the real parts and the imaginary parts of the modulation symbols, the first 2N components of the vector {circumflex over ()}X.sub.R give an estimate of the real parts R({circumflex over ()}x.sub.1), . . . , R({circumflex over ()}x.sub.2N) and the last 2N components give an estimate of the imaginary parts I({circumflex over ()}x.sub.1), . . . , I({circumflex over ()}x.sub.2N) of the transmitted modulation symbols.