IQ CODING METHOD FOR AN SDM COMMUNICATION SYSTEM ON AN OPTICAL FIBER

Description

TECHNICAL FIELD

[0001] The present invention relates to the field of optical fiber communications and more particularly to spatial multiplexing or SDM communications. (Spatial Division Multiplexing). STATE OF THE PRIOR ART

[0002] Progress in recent years in reducing attenuation in single-mode optical fibers has enabled them to almost reach their theoretical transmission capacities. Spatial multiplexing (SDM) optical communication systems based on multimode and / or multicore optical fibers (or even bundles of single-mode fibers with reduced gain thickness, referred to below as multicore optical fibers) make it possible to overcome this limit by taking advantage of spatial multiplexing between different modes and / or between different cores of an optical fiber.

[0003] The use of high modulation orders and multiplexing on orthogonal polarizations have made it possible to further increase the capacity of SDM communication systems, but these advances now come up against various limitations.

[0004] First, increasing the number of modes / cores leads to an increase in the level of interference between the elementary channels associated with the different modes / cores.

[0005] Then, different dispersion phenomena such as mode dispersion or MDL ( Dispersion Loss Mode ), the core dispersion or CDL ( Core Dispersion Loss ), polarization dispersion or PMD ( Polarization Mode Dispersion ) and polarization dependent attenuation or PDL ( Polarization Dependent Loss) increase the error rate (BER) in the different channels. However, if the effects due to MDL, CDL and PMD can be compensated digitally at reception, those due to PDL cannot be due to its non-unitary nature, which degrades the performance of SDM transmission systems in terms of BER as a function of the flow rate, and therefore of transmission capacity.

[0006] In Akram Abouseif's thesis "Emerging DSP techniques for multi-core fiber transmission systems", published in 2015, it was proposed to use space-time coding techniques to combat the degradation of transmission capacity due to CDL. However, these coding techniques complicate the transmitter and the receiver since the block of information symbols to be transmitted is coded over several successive transmission intervals or TTIs ( Time Transmission Intervals ) and, more generally, on several channel uses or CUs ( Channel Uses).

[0007] Similarly, it was proposed in the thesis of El Mehdi Amhoud et al. entitled “Coding techniques for spatial multiplexing on optical fiber systems”, 2018, to use space-time coding techniques to combat the degradation of transmission capacity due to MDL.

[0008] An orthogonal polarization precoding method to combat capacity reduction due to PDL was described in the article by C. Zhu et al. titled "Improved polarization dependent loss tolerance for polarization multiplexed coherent optical systems by polarization pairwise coding" published in Optics Express, vol. 23, no. 21, October 19th, 2015, pp. 27434-27447.

[0009] This method of precoding on orthogonal polarizations has been illustrated schematically in Fig. 1 .

[0010] The information symbols (binary words) to be transmitted are converted into symbols of a modulation constellation in the modulators q -area with symbol 110-1 and 110-2. The modulation symbols obtained, x 1 , x 2 are then rotated by an angle θ in the complex plane by means of the respective rotation modules 120-1 and 120-2 to obtain rotated symbols, x 1 θ , x 2 θ . The real part of the first rotated symbol and the real part of the second rotated symbol are combined at 130-1 to provide a first emission symbol, x ˜ 1 = ℜ x 1 θ + jℜ x 2 θ , carried by a first polarization component (e.g., a horizontal polarization state). Similarly, the imaginary part of the first rotated symbol and the imaginary part of the second rotated symbol are combined at 130-2 to provide a second emission symbol x ˜ 2 = ℑ x 1 θ + jℑ x 2 θ , carried by a second component of polarization orthogonal to the first (for example a state of vertical polarization).

[0011] The light signal whose orthogonal polarization components have been respectively modulated by the emission symbols X 1 , X 2 is then transmitted over the optical fiber.

[0012] The precoding method described in this article, however, only applies to a single-mode / single-core fiber optic transmission system and not to an SDM optical communication system.

[0013] An object of the present invention is therefore to propose a method of SDM transmission over optical fiber (multimode and / or multicore) which makes it possible to achieve high transmission capacities despite PDL and interference between elementary spatial channels (interference between different modes and / or different cores) while requiring only a single use of transmission channel to transmit a block of information symbols. STATEMENT OF THE INVENTION

[0014] The present invention is defined by a method of SDM transmission on optical fiber with polarization duality, intended to transmit, during channel use, symbols belonging to a modulation constellation in the complex plane, being the number of elementary spatial channels used for transmission, said method being original in that: said symbols undergo a separation into real parts and imaginary parts to provide a first vector consisting of the real parts of these symbols and a second vector consisting of the imaginary parts of these same symbols; a first orthogonal linear transformation is applied to the first vector to provide a first transformed vector; a second orthogonal linear transformation, distinct from the first, is applied to the second vector to provide a second transformed vector; a complex scalar, solution of an irreducible polynomial of ℝ X in □ is multiplied to the first or second transformed vector, before the two transformed vectors are summed to provide a vector consisting of complex emission symbols, each complex emission symbol modulating a first state and a second polarization state of an elementary spatial channel.

[0015] According to a preferred embodiment, the first linear transformation is the composition of a first rotation with a first non-trivial permutation and / or a first non-trivial reflection in ℝ 2 N and that the second linear transformation is the composition of a second rotation with a second non-trivial permutation and / or a second non-trivial reflection in ℝ 2 N .

[0016] The first permutation may consist of an even plurality of transpositions and the second permutation may then consist of an odd plurality of transpositions, or vice versa. For example, the first rotation and the second rotation are identical.

[0017] According to an exemplary embodiment, the first orthogonal linear transformation is the identity.

[0018] Whatever the mode of realization the complex scalar, α such as α 2 N < is not a real positive.

[0019] For example, the complex scalar is equal to j with j 2<=-1. In this case, the number N is advantageously chosen odd with N ≥ 3.

[0020] Elementary spatial channels can be propagation modes in optical fiber.

[0021] When the optical fiber is of the multi-core type, the elementary spatial channels can be made up of different cores of said fiber BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Other characteristics and advantages of the invention will appear on reading a preferred embodiment of the invention, described with reference to the attached figures among which: There Fig. 1 , already described, schematically represents a device for transmission on optical fiber using a pre-coding technique on two orthogonal polarizations; The Fig. 2schematically represents an SDM transmission device on optical fiber with IQ coding according to a general embodiment of the invention; The Fig. 3 schematically represents an SDM transmission device on optical fiber with IQ coding according to a preferred embodiment of the invention; The Fig. 4 schematically represents an SDM transmission device on optical fiber with IQ coding according to a first exemplary embodiment of the invention; The Fig. 5 schematically represents an SDM transmission device on optical fiber with IQ coding according to a second exemplary embodiment of the invention; The Fig. 6 shows on an example the gain provided by an SDM transmission device according to the invention. DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

[0023] In the following, we will consider a spatial diversity (SDM) transmission system 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 wavelength considered. In the case of a multicore fiber, the 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 assimilated in the following to a multicore fiber.

[0024] 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.

[0025] We will further assume that optical fiber is classically affected by PDL attenuation, i.e., that the different polarization states 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 (EDFAs) which create energy losses and fluctuations in the optical signal to noise ratio (OSNR). Polarization dispersion (PMD) will be ignored, however, since this effect can be effectively corrected by channel equalization in the receiver DSP.

[0026] The effect of PDL attenuation in an elementary spatial channel can be expressed by the matrix H PDL applying to both polarization states: H PDL = D γ R φ B β Or D γ = 1 + γ 0 0 1 − γ is the gain matrix, R φ = cos φ − sin φ sin φ cos φ is the polarization rotation matrix and B β = exp iβ 0 0 exp iβ is the birefringence matrix with γ ∈ [0,1] defining the value of PDL, Γ dB = log 10 (Γ), with Γ = 1 + γ 1 − γ And φ , β ∈ [ -π , π ].

[0027] 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 2 N 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 dozen or more. In any case N > 1 and, preferably, N > 2.

[0028] The idea behind the present invention is to separate the real parts and the imaginary parts of the different modulation symbols and to make them undergo distinct orthogonal linear transformations before recombining them in the complex plane to then modulate the light signal with the different elementary spatial channels / polarizations. An averaging of the PDL attenuation is thus carried out on the different polarization states and the different elementary spatial channels.

[0029] There Fig. 2 schematically represents an SDM transmission device on optical fiber according to a general embodiment of the invention.

[0030] The data to be transmitted at each transmission interval is in the form of 2 N information symbols, e.g. 2 N words q -areas with q ≤ log 2 Q Or Qis the cardinal of the modulation alphabet. The modulation alphabet can notably be an alphabet Q -QAM.

[0031] The information symbols themselves may result from source coding and / or channel coding, in a manner known per se.

[0032] In any case, the 2 N information symbols are respectively converted into 2 N modulation symbols in modulators q -area 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. Each of these modulation symbols, noted in the following x 1,..., x 2 N , is then subjected to a decomposition into a real part and an imaginary part in the I / Q separation module, 220.

[0033] The respective real parts of these modulation symbols ( x1),..., ( x 2 N ) form a vector X R of ℝ 2 N which is supplied to a first linear combination module 230-1. This first module combines these real parts by means of a first orthogonal linear transformation, F , represented by a matrix F ∈ O 2 N , ℝ , to provide a first transformed vector, X̃ R , In ℝ 2 N .

[0034] Similarly, the imaginary parts of the modulation symbols form a vector X I of ℝ 2 N which is supplied to a second linear combination module, 230-2. This second module combines these imaginary parts by means of a second orthogonal linear transformation, G , represented by a matrix G ∈ O 2 N , ℝ , to provide a second transformed vector, X̃ I , In ℝ 2 N .

[0035] Orthogonal linear transformationsF And G are advantageously chosen to be distinct. For example, one of them could be a direct orthogonal linear transformation, in other words the corresponding matrix will be an element of the special orthogonal group SO 2 N , ℝ , and the other will be an indirect orthogonal linear transformation.

[0036] The second transformed vector is then multiplied by 240 a complex scalar value α , solution of a polynomial of ℝ X , irreducible in . Preferably, α will be chosen not to be a norm of an element in the complex plane, in other words α 2 N < should not be a real positive.

[0037] The first transformed vector and the second transformed vector thus multiplied are finally summed in the adder 250 to provide a vector of ℂ 2 N , X whose complex elements, x̃ 1 , ..., x̃ 2 N, are emission symbols respectively used to modulate the 2N polarization states of N elementary spatial channels. More precisely, the component of a first polarization state (for example, a horizontal polarization component) of an elementary spatial channel of index n will be given by ( x̃ n ) and that of a second polarization state (for example a vertical polarization component) of this elementary spatial channel will be given by ( x̃ n ), or vice versa.

[0038] Ultimately, the vector X̃ can be expressed, up to a multiplicative coefficient, in the form: X ˜ = FX R + αGX I

[0039] According to a variant not shown, the first transformed vector is multiplied by the complex scalar value αin place of the second transformed vector, the first transformed vector thus multiplied then being summed with the second transformed vector to provide the vector X̃ .

[0040] There Fig. 3 schematically represents an SDM transmission device on optical fiber according to a preferred embodiment of the invention.

[0041] The modules 310-1,...,310-2N, 320, 330-1 and 330-2 here respectively fulfill the same functions as the modules 210-1,...,210-2N, 220, 230-1 and 230-2 in the Fig. 2 .

[0042] Unlike the embodiment illustrated in Fig. 2 , the first transformed vector and the second transformed vector are combined by the I / Q combination module, 340, to form the complex vector X̃ = X̃ R + j X̃ I In ℂ 2 N . In other words, this embodiment is deduced as a particular case from the general embodiment with α = j , the I / Q combination module here replacing the 240 multiplier and the 250 adder.

[0043] Advantageously, the complex scalar α is not a standard, in other words N is chosen odd with N ≥ 3.

[0044] Complex elements x̃ 1 , ... , x̃ 2 N of the vector X̃ are respectively used to modulate the 2N polarization states of N elementary spatial channels.

[0045] There Fig. 4 schematically represents an SDM transmission device on optical fiber with IQ coding according to a first exemplary embodiment of the invention.

[0046] Modules 410-1,...,410-2N, 420, 430-1, 430-2, 440 respectively perform the same functions as modules 310-1,...,310-2N, 320, 330-1, 330-2 and 340 of the Fig. 3 .

[0047] This embodiment example is a special case of the preferred embodiment of the Fig. 3 in that the first linear transformation is direct, that is, a rotation R in space in ℝ 2 N .

[0048] The second linear transformation results from the composition of this rotation R with a non-trivial permutation P In ℝ 2 N and / or a non-trivial reflection S In ℝ 2 N . By non-trivial permutation we mean a permutation distinct from the identity Id ℝ 2 N . By non-trivial reflection we mean a reflection distinct from − Id ℝ 2 N .

[0049] The permutation can be composed of an even number of transpositions in which case the second linear transformation is still a rotation, or it can be composed of an odd number of such transpositions.

[0050] The permutation can be cyclic, the second linear transformation then being represented by the matrix PR Or P ∈ { Φ , Φ 2< ,..., Φ 2 N -1<} set of all possible permutations (except the trivial permutation) and where Φ is the cyclic permutation matrix defined by: Φ = 0 1 0 ⋯ 0 0 0 1 ⋯ 0 ⋮ ⋱ ⋱ ⋮ 0 0 ⋯ 0 1 1 0 ⋯ 0 0

[0051] As in the general case, the roles of the first and second linear transformations can be interchanged. In other words, the rotation R can be applied to the vector of imaginary parts X I and the compound of rotation and permutation and / or reflection ( S ) PR / S ( P )R can be applied to the vector of real parts X R .

[0052] There Fig. 5 schematically represents an SDM transmission device on optical fiber with IQ coding according to a second exemplary embodiment of the invention.

[0053] Modules 510-1,...,510-2N, 520, 530, 540 respectively perform the same functions as modules 310-1,...,310-2N, 320, 530-2 and 540 of the Fig. 3 .

[0054] This embodiment example is a special case of the preferred embodiment of the Fig. 3 in that the first linear transformation is trivial and equal to the identity Id ℝ 2 N , and that the second linear transformation results from the composition of this rotation R with a trivial permutation P or not in ℝ 2 N .

[0055] The first vector and the second transformed vector are here combined to form the complex vector X̃symbols intended to modulate the 2 N polarization states as before.

[0056] In all cases, the received optical signal is demultiplexed spatially (by propagation mode and / or by core) and by polarization. The MIMO 2 channel N × 2 N can be estimated, for example using an LS algorithm ( Least Squares ) à from pilot symbols. The symbols emitted by the transmitting device can then be estimated using a MIMO decoder using ML estimation ( Maximum Likelihood) or, more simply, a ZF estimate (Zero Forcing) aiming to multiply the received signal by the pseudo-inverse of the channel matrix, namely X ˜ ^ = H H H − 1 H H Y Or Ĥ size 2 N × 2 N is the estimate of the MIMO channel.

[0057] After separating the real and imaginary parts of each of the components of X ˜ ^ and formation of a first vector X R made up of 2 N real parts and a second vector X I made up of 2 N imaginary parts, we apply a first inverse orthogonal transformation F -1< to the first vector X R and a second inverse orthogonal transformation G -1< to the second vector, multiplied by α -1< , α -1< X I . We can then estimate the real and imaginary parts of the modulation symbols from the same-rank components of the vectors thus obtained.

[0058] There Fig. 6 shows on an example the gain provided by an SDM transmission device according to the invention for N = 4 elementary spatial channels, here elementary cores of a multicore fiber (MCF).

[0059] It was assumed that the value of PDL, Γ dBwas identical for all elementary spatial channels and equal to 4.5 dB, the polarization rotation, φ was equal to π / 2.

[0060] The optical fiber consisted of 10 sections of 100 km each, with a constant-gain optical amplifier for the different modes being provided between consecutive sections. The symbol rate was 12 Gbaud and the modulation constellation was 16-QAM.

[0061] The chosen method of implementation was that of the Fig. 5 with P = Id 2 N .

[0062] The estimation at reception was carried out using an ML estimator.

[0063] There Fig. 6 gives the bit error rate (BER) as a function of the optical signal-to-noise ratio (OSNR) in the multicore fiber. In this case, we have α 2 N < = 1 but we nevertheless observe a gain (of OSNR) of more than 1 dB compared to a non-IQ coded SDM system.

Claims

1. SDM transmission method over optical fiber with polarization duality, intended to transmit, during one channel use, 2N symbols belonging to a modulation constellation in the complex plane, N > 1 being the number of spatial elementary channels used for transmission, wherein: said symbols undergo a separation into real part and imaginary part (220-520) to provide a first vector consisting of the real parts of these symbols and a second vector consisting of the imaginary parts of these same symbols; a first orthogonal linear transformation (230-1,..,430-1) is applied to the first vector to provide a first transformed vector; a second orthogonal linear transformation (230-2,..,530-2), distinct from the first, is applied to the second vector to provide a second transformed vector; a complex scalar, solution of an irreducible polynome from ℝ X in is multiplied to the first or to the second transformed vector, before the two transformed vectors are summed to provide a vector consisting of 2N complex emission symbols, each complex transmission symbol modulating a first state and a second polarization state of a spatial elementary channel.

2. SDM transmission method over optical fiber with polarization duality according to claim 1, characterized in that the first linear transformation is the composition of a first rotation with a first non-trivial permutation and / or a first non-trivial reflection in ℝ 2 N and that the second linear transformation is the composition of a second rotation with a second non-trivial permutation and / or a second non-trivial reflection in ℝ 2 N .

3. SDM transmission method over optical fiber with polarization duality according to claim 2, characterized in that the first permutation is composed of an even plurality of transpositions and that the second permutation is composed of an odd plurality of transpositions, or vice versa.

4. SDM transmission method over optical fiber with polarization duality according to claim 3, characterized in that the first rotation and the second rotation are identical.

5. SDM transmission method over optical fiber with polarization duality according to claim 2, characterized in that the first orthogonal linear transformation is identity.

6. SDM transmission method over optical fiber with polarization duality according to one of the preceding claims, characterized in that the complex scalar, α is chosen such that α2N is not a positive real.

7. SDM transmission method over optical fiber with polarization duality according to claim 5, characterized in that the complex scalar is equal to j with j2= - 1.

8. SDM transmission method over optical fiber with polarization duality according to claim 7, characterized in that the number N is odd with N ≥ 3.

9. SDM transmission method over optical fiber with polarization duality according to one of the preceding claims, characterized in that the spatial elementary channels are propagation modes in the optical fiber.

10. SDM transmission method over optical fiber with polarization duality according to one of claims 1 to 8, characterized in that the optical fiber is of the multi-core type and that the elementary spatial channels are different cores of said fiber.