I / Q coding method for WDM communication systems via optical fiber

Abstract

The present invention relates to a method for dual-polarized WDM transmission over optical fiber, which uses a specific I / Q coding to combat the effects of PDL. The modulation symbols transmitted in 2N polarization states on N wavelengths are decomposed (220) into real and imaginary values. A first orthogonal linear transform (230-1) is applied to the vector of real values ​​thus obtained, and a second orthogonal linear transform (230-2), different from the first, is applied to the vector of imaginary values ​​thus obtained. In JPEG2024530267000060.jpg7170 A complex scalar that solves the 8170 irreducible polynomial is multiplied with either the first or second transformation vector before the two transformation vectors are summed (240) to provide a vector of transmit symbols for modulating the different polarization states of the WDM channel.

Description

[Technical Field]

[0001] This invention relates to the field of optical fiber communications, and more particularly to wavelength division multiplexing (WDM) communications. [Background technology]

[0002] Commonly used WDM communication systems via optical fibers achieve transmission rates of several Tb / s. In recent technology, different types of WDM systems are known, including those defined by wavelength (Coarse Wavelength Division Multiplexing: CWDM) and, more recently, by frequency (Dense WDM: DWDM). The difference between CWDM and DWDM systems is fundamentally the spacing between transmit channels. When the transmit channels are consecutive or overlapping, they are called WDM superchannels and Nyquist superchannels, respectively. The term WDM is used in a general sense below, covering the various types of systems described above.

[0003] The use of high modulation orders and multiplexing with orthogonal polarization has made it possible to further increase the capacity of these communication systems, but this progress is now facing various limitations.

[0004] First, the density of WDM transmission channels increases, and in correlation, subcarrier integration increases, leading to an increase in inter-channel interference level, or ICI (inter-channel interference). This interference can be countered by shaping the channels into an ideal rectangle in the frequency domain, in other words, by employing a waveform that follows a synchronization function in the time domain (the so-called Nyquist shaping). Of course, in reality, the shaping is imperfect, and residual inter-channel interference remains.

[0005] Subsequently, different dispersion phenomena such as chromatic dispersion (CD), polarization mode dispersion (PMD), and polarization-dependent loss (PDL) increase the error rate (BER) in different channels. However, while the first two can be digitally compensated for during reception, the last one cannot be compensated for due to its non-unitarity, resulting in a decrease in the performance of the WDM transmission system in terms of BER depending on the bit rate and therefore the transmission capacity.

[0006] To counteract the reduction in transmission capacity caused by PDL, the use of spatiotemporal coding techniques is proposed in Elie Awad's thesis entitled "Emerging space-time coding techniques for optical fiber transmission systems," published in 2015. However, these coding techniques complicate transmitters and receivers because blocks of transmitted information symbols are coded over several consecutive transmission intervals or TTIs (Time Transmission Intervals), and more generally, over multiple channel uses or CUs (Channel Uses).

[0007] A method for precoding with orthogonal polarization to counteract the capacitance reduction caused by PDL is described in the paper entitled "Improved polarization dependent loss tolerance for polarization multiplexed coherent optical systems by polarization pairwise coding" by C. Zhu et al., published in J. Lightwave Technology, vol. 34 no. 8, pp. 1746-1753, 2016.

[0008] This method of precoding with orthogonal polarization is schematically shown in Figure 1.

[0009] The transmitted information symbols (binary words) are converted into symbols of the modulation constellation in the q-element symbol modulators 110-1 and 110-2. The acquired modulation symbols x1 and x2 are then rotated by an angle θ in the complex plane using their respective rotation modules 120-1 and 120-2 to obtain the rotated symbols.

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[0010] Optical signals, whose orthogonal polarization components are modulated by radiation symbols X1 and X2 respectively, are transmitted via optical fiber.

[0011] However, the precoding method described in this article applies only to single-carrier transmission systems and not to WDM transmission systems. [Prior art documents] [Non-patent literature]

[0012] [Non-Patent Document 1] Elie Awad's thesis entitled 「Emerging space-time coding techniques for optical fiber transmission systems」, published in 2015

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0013] [[ID=*14]]Therefore, an object of the present invention is to propose a WDM transmission method via an optical fiber that enables achieving a high transmission capacity by using the transmission channel only once to transmit a block of information symbols, despite PDL and interference between adjacent channels.

Means for Solving the Problems

[0014] The present invention is defined by a WDM transmission method via an optical fiber having polarization duality, and aims to transmit 2N symbols belonging to a modulation constellation in the complex plane during the use of one channel, where N is the number of WDM channels used for transmission, and this method separates these symbols into a real part and an imaginary part in order 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. applies a first orthogonal linear transformation to the first vector in order to provide a first transformation vector. In order to provide a second transformation vector, a second orthogonal linear transformation different from the first orthogonal linear transformation is applied to the second vector. To provide a vector consisting of 2N complex radiating symbols, before the two transformation vectors are summed,

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[0015] According to a preferred embodiment, the first linear transformation is

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[0016] According to the first example, the first permutation can consist of multiple even transposes, the second permutation can consist of multiple odd transposes, and vice versa.

[0017] The first and second rotations can be the same.

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

[0019] In any embodiment, the complex scalar α is advantageously α 2N It can be chosen such that it is not a positive real number.

[0020] A complex scalar can be equal to, for example, j, where j 2 = -1. In this case, the numerical value N can be an odd number such that N ≥ 3.

[0021] Other features and advantages of the present invention will become apparent from reading the preferred embodiments of the invention described with reference to the accompanying drawings. [Brief explanation of the drawing]

[0022] [Figure 1] As already explained, this is a schematic diagram of an optical fiber transmission device that uses precoding in two orthogonal polarizations. [Figure 2] This figure schematically represents a WDM transmission device via optical fiber using IQ coding according to a general embodiment of the present invention. [Figure 3] This figure schematically represents a WDM transmission device via optical fiber using IQ coding according to a preferred embodiment of the present invention. [Figure 4] This figure schematically represents a WDM transmission device via optical fiber using IQ coding according to a first embodiment of the present invention. [Figure 5] This figure schematically represents a WDM transmission device via optical fiber using IQ coding according to a second embodiment of the present invention. [Figure 6A] This figure shows the gain provided by the WDM transmission device according to the present invention for different hypotheses regarding the number of channels. [Figure 6B] This figure shows the gain provided by the WDM transmission device according to the present invention for different hypotheses regarding the number of channels. [Figure 6C] This figure shows the gain provided by the WDM transmission device according to the present invention for different hypotheses regarding the number of channels. [Figure 7A] This figure shows the gain provided by the WDM transmission device according to the present invention for different PDL hypotheses in optical fibers. [Figure 7B] This figure shows the gain provided by the WDM transmission device according to the present invention for different PDL hypotheses in optical fibers. [Figure 7C] This figure shows the gain provided by the WDM transmission device according to the present invention for different PDL hypotheses in optical fibers. [Modes for carrying out the invention]

[0023] In the following, we consider a WDM transmission system via optical fiber, assuming that this fiber is classically affected by PDL attenuation, in other words, that 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, particularly doped fiber optical amplifiers (EDFAs) that cause energy loss and variations in the optical signal-to-noise ratio or OSNR. However, dispersion effects in the fiber, such as chromatic dispersion (CD) and polarization dispersion (PMD), can be effectively compensated for by channel equalization within the receiver DSP and are therefore abstracted away.

[0024] The effect of PDL attenuation on WDM channels (and single spatial modes) is applied to the two polarization states. PDL It can be represented by a matrix.

[0025]

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[0026] During the ceremony,

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[0027] A WDM transmission system uses multiple N WDM channels (wavelengths or subcarriers), with each WDM channel associated with two polarization states. Therefore, at each transmission moment, in other words, each use of a channel, the transmission system can transmit 2N modulation symbols, with one symbol transmitted per polarization state and per WDM channel. N is generally chosen to be a high value, typically in the tens, or even hundreds. In any case, N > 1, preferably N > 2.

[0028] The underlying idea of ​​this invention is to separate the real and imaginary parts of different modulation symbols, apply separate orthogonal linear transformations to them, recombine them in the complex plane, and then modulate different wavelengths / different subcarriers of WDM multiplexing with the resulting symbols. Thus, it performs averaging of PDL attenuation across different polarization states and different WDM channels.

[0029] Figure 2 schematically shows a WDM transmission device via optical fiber according to a general embodiment of the present invention.

[0030] The data transmitted at each transmission interval is in the form of 2N information symbols, for example, 2N q-element words of q ≤ log2Q, where Q is the radix of the modulated alphabet. The modulated alphabet can be, in particular, the Q~QAM alphabet.

[0031] Informational symbols may be derived from source coding and / or channel coding in ways that are known in themselves.

[0032] In all cases, 2N information symbols are converted into 2N modulation symbols in the q-element symbol modulators 210-1, ..., 210-2N, respectively. The odd indices of these symbols correspond to the first polarization state, and the even indices correspond to the second polarization state orthogonal to the first polarization state. Each of these modulation symbols corresponds to the following x1, ..., x 2N It is shown as follows, and then decomposed into real and imaginary parts by the separation module I / Q220.

[0033] The real part of each of these modulation symbols

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[0034] Similarly, the imaginary part of the modulation symbol is,

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[0035] It is advantageous to choose the orthogonal linear transformations F and G separately. For example, one of them is a direct orthogonal linear transformation, in other words, the corresponding matrix is ​​a special orthogonal group.

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[0036] Next, the second transformation vector is:

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[0037] The first and second transformation vectors, multiplied in this way, are finally added together in adder 250.

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[0038] Therefore, vector

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[0040] In a modified example not shown, the first transformation vector is multiplied by a complex scalar value α instead of the second transformation vector, and the first transformation vector thus multiplied is then summed with the second transformation vector to form a vector

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[0041] Figure 3 schematically shows a WDM transmission device via optical fiber according to a preferred embodiment of the present invention.

[0042] Modules 310-1, ..., 310-2N, 320, 330-1, and 330-2 perform the same functions as modules 210-1, ..., 210-2N, 220, 230-1, and 230-2 in Figure 2, respectively.

[0043] Unlike the embodiment shown in Figure 2, the first and second transformation vectors are coupled by the I / Q coupling module 340.

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[0044] Conveniently, the complex scalar α is not a norm; in other words, N can be an odd number such that N ≥ 3.

[0045] Vector

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[0046] Figure 4 schematically shows a WDM transmission device via optical fiber using IQ coding according to the first embodiment of the present invention.

[0047] Modules 410-1, ..., 410-2N, 420, 430-1, 430-2, and 440 perform the same functions as modules 310-1, ..., 310-2N, 320, 330-1, 330-2, and 340 in Figure 3, respectively.

[0048] In this embodiment, the first linear transformation is direct, i.e.,

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[0049] The second linear transformation is the composition of this rotation R and

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[0050] The permutation can also 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.

[0051] The permutation can be a cycle, in which case the second linear transformation is represented by the matrix PR, where P ∈ {Φ, Φ 2 ,..., Φ 2N-1} is the set of possible permutations (excluding the trivial permutation), and Φ is a cyclic permutation matrix, defined by the following formula.

[0052]

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[0053] 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 the imaginary part X I , and the composition of rotation and permutation and / or reflection (S)PR / S(P)R can be applied to the vector of the real part X R .

[0054] Figure 5 schematically shows a WDM transmission device via optical fiber using IQ coding according to a second embodiment of the present invention.

[0055] Modules 510-1, ..., 510-2N, 520, 530, and 540 perform the same functions as modules 310-1, ..., 310-2N, 320, 530-2, and 540 in Figure 3, respectively.

[0056] In this exemplary embodiment, the first linear transformation is trivial and the identity matrix is ​​trivial.

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[0057] Here, the first vector and the second transformation vector are complex vectors of symbols for modulating 2N polarization states as described above.

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[0058] In all cases, the received optical signal is separated into WDM channels (wavelength or subcarrier) and polarization states, and then equalized to compensate for chromatic dispersion (CD). The 2N × 2N MIMO channels are then estimated, for example, from pilot symbols using the LS (least squares) algorithm. The symbols transmitted by the transmission device are then used with a MIMO decoder to obtain the pseudo-inverse of the channel matrix, i.e., the received signal.

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[0059]

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[0060] Figures 6A to 6C show the gain provided by the WDM transmission device according to the present invention for different hypotheses regarding the number of WDM channels.

[0061] PDL value, Γ dB We assumed that this was the same for all WDM channels and equal to 5dB, and that the polarization rotation φ was equal to π / 2.

[0062] The optical fiber consisted of 10 sections, each 100 km long, with optical amplifiers having constant wavelength gain between consecutive sections. The symbol rate was 12 Gbaud, and the modulation constellation was 16-QAM. The subbands corresponding to different WDM channels did not overlap, and the signals transmitted in each subband were shaped by a cosine root raised to the power of a filter with a roll-off coefficient of 0.1.

[0063] The selected embodiment is P=Id in Figure 5. 2N It belonged to them.

[0064] The estimation at the time of reception was performed using an ML estimator.

[0065] Figure 6A shows the bit error rate (BER) as a function of the optical signal-to-noise ratio (OSNR) in an N=2 wavelength fiber. In this case, α 2N Although the value is 1, a gain of 2 dB (OSNR) is still observed compared to a non-IQ coded WDM system, and the difference from the ideal channel (Gaussian channel) is only 0.6 dB.

[0066] Figure 6B shows BER as a function of OSNR at N=3 wavelengths. In this case, α 2N = -1. A gain 2.6 dB greater than in the previous case is observed, and the deviation from the ideal channel is negligible; in other words, the effect of PDL is almost completely corrected by averaging.

[0067] Figure 6C shows BER as a function of OSNR at N=5 wavelengths. 2N The property of =-1 was re-examined, and the performance obtained was almost the same as in the case of N=3.

[0068] Figures 7A to 7C show the gain provided by the WDM transmission device according to the present invention for different PDL hypotheses in optical fibers.

[0069] In the previous case, we considered N=3 wavelengths, but let's consider a different PDL configuration.

[0070] In Figure 7A, the value of PDL is Γ dB It was assumed that the three channels were identical and equal to 5 dB. IQ coding according to the present invention can achieve a gain of 1.8 dB compared to the uncoding case and shows only a 1 dB deviation compared to the Gaussian channel.

[0071] In Figure 7B, the value of PDL is Γ dB This assumes that the level is 3dB in channels 1 and 3, and 5dB in channel 2. Rotation angle

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[0072] Finally, in Figure 7C, it is assumed that the PDL at the output of each optical amplifier follows a Gaussian law, and consequently, that the probability distribution of the PDL at the fiber output follows a Maxwell distribution. The mean of the PDL was selected to be equal to 5 dB. Here again, the transmission method according to the present invention makes it possible to achieve a gain of 1 dB compared to the uncoded case, even in the most unfavorable case. [Explanation of symbols]

[0073] 110-1 q-element symbol modulator 110-2 q-element symbol modulator 120-1 Rotary Module 120-2 Rotation Module 210 q original symbol modulator 220 Separate Module I / Q 230-1 First Linear Combination Module 230-2 Second Linear Combination Module 240 multiplier 250 Adder 340 I / Q coupling module

Claims

1. A WDM transmission method via a polarization-duplex optical fiber, which transmits 2N symbols belonging to a modulation constellation in the complex plane during a single use of one channel, wherein N>1 is the number of WDM channels used for transmission. To provide a first vector consisting of the real part of these symbols and a second vector consisting of the imaginary part of these same symbols, the symbols are separated into the real part and the imaginary part (220-520), To provide a first transformation vector, a first orthogonal linear transformation (230-1, ..., 430-1) is applied to the first vector. In order to provide a second transformation vector, a second orthogonal linear transformation (230-2, ..., 530-2), which is different from the first orthogonal linear transformation, is applied to the second vector. In order to provide a vector consisting of 2N complex radiating symbols, before the two transformation vectors are summed, [Math 1] in [Math 2] A complex scalar, which is the solution to an irreducible polynomial from , is multiplied by the first or second transformation vector, so that each complex transmit symbol modulates the first state and second polarization state of the WDM channel. A WDM transmission method characterized by the following features.

2. The first linear transformation described above is [Math 3] A composition of a first rotation and a first nontrivial permutation and / or a first nontrivial reflection in, the second linear transformation is [Math 4] A WDM transmission method via an optical fiber having polarization duplexity according to claim 1, characterized in that it is a combination of a second rotation and a second non-trivial permutation and / or a second non-trivial reflection in .

3. A WDM transmission method via an optical fiber having polarization duplexity according to claim 2, characterized in that the first permutation is composed of a plurality of even transposes, and the second permutation is composed of a plurality of odd transposes.

4. A WDM transmission method via an optical fiber having polarization duplexity according to claim 3, characterized in that the first rotation and the second rotation are the same.

5. The WDM transmission method via an optical fiber having polarization duplexity according to claim 2, characterized in that the first orthogonal linear transformation is an identity matrix.

6. The aforementioned complex scalar α is α 2N A WDM transmission method via an optical fiber having polarization duplexity according to claim 1, characterized in that the number is selected such that it is not a positive real number.

7. The aforementioned complex scalar is equal to j, and j 2 A WDM transmission method via an optical fiber having polarization duplexity according to claim 5, characterized in that = -1.

8. A WDM transmission method via an optical fiber having polarization duplexity according to claim 7, characterized in that the numerical value N is odd and N ≥ 3.

9. The WDM transmission method via an optical fiber having polarization duplexity according to Claim 2, characterized in that the first permutation is composed of a plurality of odd transposes and the second permutation is composed of a plurality of even transposes.

10. The WDM transmission method via an optical fiber having polarization duplexity according to claim 9, characterized in that the first rotation and the second rotation are the same.

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