I / Q CODING METHOD FOR A WDM TRANSMISSION SYSTEM OVER AN OPTICAL FIBER

Description

DOMAINE TECHNIQUE

[0001] The present invention relates to the field of fiber optic communications and more particularly to wavelength division multiplexing or WDM communications ( Wavelength Division Multiplexing ). ÉTAT DE LA TECHNIQUE ANTÉRIEURE

[0002] Commonly used WDM communication systems over optical fibers achieve transmission rates of the order of several Tb / s. Different types of WDM systems are known in the state of the art, some being defined in wavelengths (CWDM for Coarse Wavelength Division Multiplexing ) and others, more recent, being defined in frequencies (DWDM for Dense WDM). The difference between CWDM and DWDM systems is essentially the spacing between transmission channels. When the transmission channels are contiguous or even overlapping, we speak respectively of a WDM superchannel ( superchannel ) and Nyquist superchannel ( Nyquist superchannel ). The term WDM will be used in the following in its general sense and will cover the different types of systems mentioned above.

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

[0004] First of all, the increase in the density of WDM transmission channels and correlatively the bringing together of the subcarriers, leads to an increase in the level of inter-channel interference or ICI ( Inter Channel Interference ). This interference can be combated by adopting an ideally rectangular shaping of the channels in the frequency domain, in other words by a waveform according to a sync function in the time domain (so-called Nyquist shaping). Of course, in practice the shaping is imperfect and residual inter-channel interference remains.

[0005] Then, different dispersion phenomena such as chromatic dispersion or CD ( Chromatic Dispersion ), 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, while the first two can be digitally compensated at reception, the latter cannot be due to its non-unitary nature, which degrades the performance of WDM transmission systems in terms of BER as a function of the bit rate, and therefore of transmission capacity.

[0006] Elie Awad's thesis "Emerging space-time coding techniques for optical fiber transmission systems", published in 2015, proposed the use of space-time coding techniques to combat the degradation of transmission capacity due to PDL. 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] 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 9, 2015, pp. 27434-27447.

[0008] This method of precoding on orthogonal polarizations has been illustrated schematically in Fig. 1 .

[0009] 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).

[0010] 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.

[0011] The precoding method described in this article, however, only applies to a single-carrier transmission system and not to a WDM transmission system.

[0012] WO 2016 / 145,493 describes a method comprising the features of the preamble of claim 1.

[0013] An object of the present invention is therefore to provide a WDM transmission method over optical fiber which makes it possible to achieve high transmission capacities despite PDL and interference between adjacent channels while requiring only a single use of a transmission channel to transmit a block of information symbols. EXPOSÉ DE L'INVENTION

[0014] The present invention is defined by a WDM transmission method on polarization duality optical fiber, intended to transmit, during channel use, 2N symbols belonging to a modulation constellation in the complex plane, N being the number of WDM channels used for transmission, said method comprising: 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 2 N complex transmit symbols, each complex transmit symbol modulating a first state and a second polarization state of a WDM 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] According to a first example, the first permutation may be composed of an even plurality of transpositions and the second permutation is composed of an odd plurality of transpositions, or vice versa.

[0017] The first rotation and the second rotation can be chosen to be the same.

[0018] Alternatively, the first orthogonal linear transformation can be chosen equal to the identity.

[0019] Whatever the embodiment, the complex scalar, α, can be advantageously chosen such that α 2 N < is not a real positive.

[0020] The complex scalar can for example be equal to j with j 2 < = -1. In this case, the number N can be chosen odd with N ≥ 3. BRÈVE DESCRIPTION DES DESSINS

[0021] 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 pre-coding on two orthogonal polarizations; The Fig. 2 schematically represents a WDM transmission device on optical fiber with IQ coding according to a general embodiment of the invention; The Fig. 3 schematically represents a WDM transmission device on optical fiber with IQ coding according to a preferred embodiment of the invention; The Fig. 4 schematically represents a WDM transmission device on optical fiber with IQ coding according to a first exemplary embodiment of the invention; The Fig. 5 schematically represents a WDM transmission device on optical fiber with IQ coding according to a second exemplary embodiment of the invention; The Figs. 6A-6C show the gain provided by a WDM transmission device according to the invention for different assumptions of number of channels; The Figs 7A-7C show the gain provided by a WDM transmission device according to the invention for different PDL hypotheses in the optical fiber. EXPOSÉ DÉTAILLÉ DE MODES DE RÉALISATION PARTICULIERS

[0022] In the following, we will consider a WDM transmission system over optical fiber and assume that this fiber is classically affected by PDL attenuation, in other words 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 (EDFA) which create energy losses and fluctuations in the optical signal to noise ratio or OSNR (Optical Signal to Noise Ratio). On the other hand, dispersive effects in the fiber such as chromatic dispersion (CD) and polarization dispersion (PMD) will be ignored since these effects can be effectively corrected by channel equalization in the receiver DSP.

[0023] The effect of PDL attenuation for a WDM channel (and a single spatial mode) 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].

[0024] The WDM transmission system uses a plurality N of WDM channels (wavelengths or subcarriers), each WDM 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 WDM channel. The number N is generally chosen to be high, in the order of several tens or even several hundreds. In any case N > 1 and, preferably, N > 2.

[0025] The idea behind the present invention is to separate the real and imaginary parts of the different modulation symbols and to make them undergo separate orthogonal linear transformations before recombining them in the complex plane to then modulate with the obtained symbols the different wavelengths / the different subcarriers of the WDM multiplex. This performs an averaging of the PDL attenuation on the different polarization states and the different WDM channels.

[0026] There Fig. 2 schematically represents a WDM transmission device on optical fiber according to a general embodiment of the invention.

[0027] The data to be transmitted at each transmission interval is in the form of 2N information symbols, for example 2N 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.

[0028] The information symbols themselves may result from source coding and / or channel coding, in a manner known per se.

[0029] 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.

[0030] 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 .

[0031] 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 .

[0032] 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.

[0033] 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 < must not be a positive real. 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 , X̃ whose complex elements, x̃ 1,..., x̃ 2 N, are emission symbols respectively used to modulate the 2N polarization states of N WDM channels. More precisely, the component of a first polarization state (for example, a horizontal polarization component) of a WDM 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 channel will be given by ( x̃ n ), or vice versa.

[0034] Ultimately, the vector X̃ can be expressed, up to a multiplicative coefficient, in the form: X ˜ = FX R + αGX I

[0035] According to a variant not shown, the first transformed vector is multiplied by the complex scalar value α in 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 .

[0036] There Fig. 3 schematically represents a WDM transmission device on optical fiber according to a preferred embodiment of the invention.

[0037] 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 .

[0038] 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 X = 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.

[0039] Advantageously, the complex scalarα is not a standard, in other words N is chosen odd with N ≥ 3.

[0040] The complex elements x̃ 1 ,...,x̃ 2 N of the vector X̃ are respectively used to modulate the 2N polarization states of N WDM subcarriers / wavelengths.

[0041] There Fig. 4 schematically represents a WDM transmission device on optical fiber with IQ coding according to a first exemplary embodiment of the invention.

[0042] 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 .

[0043] 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 .

[0044] 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 .

[0045] 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.

[0046] 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

[0047] 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 .

[0048] There Fig. 5 schematically represents a WDM transmission device on optical fiber with IQ coding according to a second exemplary embodiment of the invention.

[0049] 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 .

[0050] 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 permutation P trivial or not in ℝ 2 N .

[0051] The first vector and the second transformed vector are here combined to form the complex vector X̃ symbols intended to modulate the 2 N polarization states as before.

[0052] In all cases, the received optical signal is demultiplexed into WDM channel (wavelength or subcarrier) and polarization state then equalized to compensate for chromatic dispersion (CD). The MIMO 2 channel N ×2 N is then estimated, for example using an LS algorithm ( Least Squares ) àfrom 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 ) aimed at multiplying the received signal by the pseudo-inverse of the channel matrix, namely X ˜ ^ = H H H − 1 H H Y where Ĥ is of size 2 N × 2 N is the estimated matrix of the MIMO channel.

[0053] 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 2N real parts and a second vector X̃ t consisting of the 2N 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.

[0054] THE Figs. 6A-6C show the gain provided by a WDM transmission device according to the invention for different hypotheses of number of WDM channels.

[0055] It was assumed that the value of PDL, Γ dB was identical for all WDM channels and equal to 5dB, the polarization rotation, φ was equal to π / 2.

[0056] The optical fiber consisted of 10 sections of 100 km each, with a constant wavelength gain optical amplifier being provided between consecutive sections. The symbol rate was 12 Gbaud and the modulation constellation was 16-QAM. The sub-bands corresponding to the different WDM channels were non-overlapping and the signals transmitted in each sub-band were shaped by a raised cosine root filter with a roll-off factor of 0.1.

[0057] The chosen method of implementation was that of the Fig. 5 with P = Id 2 N .

[0058] The estimation at reception was carried out using an ML estimator.

[0059] There Fig. 6A gives the bit error rate (BER) as a function of the optical signal-to-noise ratio (OSNR) in the fiber for N = 2 wavelengths. In this case, we have α 2 N< =1 but we nevertheless observe a gain (of OSNR) of 2dB compared to a non-IQ coded WDM system, the difference with the ideal channel (Gaussian channel) being only 0.6 dB.

[0060] There Fig. 6B gives the BER as a function of the OSNR for N = 3 wavelengths. In this case, we have α 2 N < = -1. We observe a gain of 2.6dB greater than in the previous case and the difference with the ideal channel is negligible, in other words the effect of the PDL is almost entirely corrected by averaging.

[0061] There Fig. 6C gives the BER as a function of the OSNR for N = 5 wavelengths. The property α 2 N < = -1 is still verified and the performances obtained are substantially the same as for N = 3.

[0062] THE Figs 7A-7C show the gain provided by a WDM transmission device according to the invention for different PDL hypotheses in the optical fiber.

[0063] We place ourselves in the previous case where N = 3 wavelengths but different PDL configurations are considered.

[0064] In Fig. 7A , it was assumed that the PDL, Γ db , was identical on the three channels and equal to 5dB. The IQ coding according to the present invention allows to achieve a gain of 1.8 dB compared to the uncoded case and only presents a deviation of 1dB compared to the Gaussian channel.

[0065] In Fig. 7B it was assumed that the PDL, Γ db , on channels 1 and 3 was 3dB and 5dB on channel 2. The rotation angles φ 1 , φ 2, φ 3 are drawn at random from a uniform probability distribution on [- π,π ]. The IQ coding according to the present invention achieves a gain of 2 dB compared to the uncoded case and only has a deviation of 0.6 dB compared to the Gaussian channel.

[0066] Finally, in Fig. 7Cit was assumed that the PDL at the output of each optical amplifier followed a Gaussian law and that, consequently, the probability distribution of the PDL at the fiber output followed a Maxwell distribution. The mean of the PDL was chosen to be equal to 5dB. Here again, the transmission method according to the present invention makes it possible to achieve, in the worst case, a gain of 1dB compared to the uncoded case.

Claims

1. WDM 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 WDM 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; characterized in that the transmission method comprises : 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 WDM channel.

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

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