WO2019042573A1

WO2019042573A1 - Cross polarization modulation compensator

Info

Publication number: WO2019042573A1
Application number: PCT/EP2017/072086
Authority: WO
Inventors: Huijian Zhang; Hartmut HAFERMANN
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2017-09-04
Filing date: 2017-09-04
Publication date: 2019-03-07

Abstract

The present invention provides a cross polarization modulation, XPolM, compensator (100) for an optical coherent receiver (300). The XPolM compensator includes a receiving section (101), configured to receive digital input signals (102), a tap coefficient estimation unit (103), configured to determine tap coefficients (103tc) based on sequences (102s) of samples in the digital input signals (102), and a filter section (104), configured to obtain XPolM compensated output signals (105), based on the digital input signals (102) and on the tap coefficients (103tc).

Description

CROSS POLARIZATION MODULATION COMPENSATOR

TECHNICAL FIELD

The present invention relates to the field of polarization multiplexed coherent optical communication systems and in particular to a non-linear cross polarization modulation (XPolM) compensator and a method for operating said XPolM compensator. Preferably, the XPolM compensator can be applied in an optical coherent receiver.

BACKGROUND Cross phase modulation (XPM), a nonlinear Kerr effect (also called quadratic electro-optic (QEO) effect) in optical fiber, introduces not only nonlinear phase noise but also inter- polarization crosstalk known as XPolM. XPolM may dominate when polarization division multiplexed wavelength division multiplexed (WDM) signals are propagated over fiber links with periodic chromatic dispersion compensation. US 8849131 B2 and L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. Rasmussen, "Nonlinear Polarization Crosstalk Canceller for Dual-Polarization Digital Coherent Receivers," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWE3, propose a method called nonlinear polarization crosstalk cancellation (NPCC) to estimate and compensate XPolM. These prior art documents show that it is possible to compensate XPolM effects by using digital signal processing with acceptable complexity.

However, NPCC assumes perfect power control and phase recovery, which is not always the case in real products. Furthermore, the estimation method of tap coefficients used to cancel nonlinear polarization crosstalk, is not optimal. In the prior art solution, the tap coefficients are determined from received and hard-decided samples (wherein hard-decided means that samples are mapped to their closest constellation point) in a sample-by-sample fashion and then are averaged. More specifically, in the prior art solution only two off-diagonal components of a 2x2 channel filter matrix are determined when determining the tap coefficients. Because of the assumption of perfect power control of polarization components, the diagonal components are set to unity, i.e. they are not determined.

These drawbacks result in suboptimal performance and precision of conventional NPCC. SUMMARY In view of the above-mentioned disadvantages, the present invention aims to improve the cancellation of nonlinear polarization crosstalk. The present invention has the object to provide a device and a method to efficiently track and compensate XPolM.

The object of the present invention is achieved by the solution provided in the enclosed independent claims. Advantageous implementations of the present invention are further defined in the dependent claims.

In particular, in the proposed solution, tap coefficients are determined using a sequence of samples, obtained from a sequence of symbols, to determine the tap coefficients from a least-squares estimation, instead of determining the tap coefficients based on the hard- decided samples in a sample-by-sample fashion. This is more accurate than the sample-by- sample determination. In particular, power variations and the impact of imperfect phase recovery on determining the tap coefficients are reduced. In addition, no assumptions on the channel matrix are made, so that all of its four components are determined. This accounts for polarization-dependent power fluctuations. Further, according to the present invention, instead of the channel filter matrix, its inverse, the compensator matrix, is obtained from a computation involving a 2x2 matrix inversion. More specifically, in this invention, both the amplitude and phase of the tap coefficients are determined in an optimal way without assuming ideal power control and phase recovery.

These features lead to an overall improved performance in determining tap coefficients and cancelling nonlinear polarization crosstalk compared to the solutions according to the prior art.

A first aspect of the present invention provides a cross polarization modulation, XPolM, compensator for an optical coherent receiver, comprising a receiving section, configured to receive digital input signals, a tap coefficient estimation unit, configured to determine tap coefficients based on sequences of samples in the digital input signals, and a filter section, configured to obtain XPolM compensated output signals, based on the digital input signals and on the tap coefficients.

As XPolM is a time-varying effect and its auto-correlation length in time domain is about tens of sample periods depending on parameters such as baud rate of the signal, channel spacing, number of wavelengths and dispersion map, etc., the advantage of the solution according to the present invention is to provide a fast adaptive and yet accurate estimation method based on a short-term observation of a sequence of samples to calculate tap coefficients for XPolM compensation. As a result, tap coefficients can be determined with high speed and precision and XPolM compensation is improved. In a first implementation form of the XPolM compensator according to the first aspect, the digital input signals comprise a horizontal input signal n and a vertical input signal r_v.

In a second implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the receiving section is further configured to obtain adapted horizontal input signals based on the horizontal input signal n and adapted vertical input signals based on the vertical input signal r_v; and the tap coefficient estimation unit is further configured to determine the tap coefficients based on sequences of samples in the adapted horizontal input signals and based on sequences of samples in the adapted vertical input signals.

In a third implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the adapted horizontal input signals include a first horizontal input signal which is obtained by duplicating the horizontal input signal n, and the adapted vertical input signals include a first vertical input signal which is obtained by duplicating the vertical input signal r_v, and the tap coefficient estimation unit is further configured to determine the tap coefficients based on a sequence of samples in the first horizontal input signal and based on a sequence of samples in the first vertical input signal.

In a fourth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the adapted horizontal input signals further include a second horizontal input signal which is obtained by duplicating the horizontal input signal n, and the adapted vertical input signals further include a second vertical input signal which is obtained by duplicating the vertical input signal r_v, and the tap coefficient estimation unit is further configured to determine the tap coefficients based on sequences of samples in the first and second horizontal input signals and based on sequences of samples in the first and second vertical input signals.

In a fifth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the second horizontal input signal is sliced in the receiving section before it is provided to the tap coefficient estimation unit, and the second vertical input signal is sliced in the receiving section before it is provided to the tap coefficient estimation unit, and the tap coefficient estimation unit is further configured to determine the tap coefficients based on a sequence of samples in the first horizontal input signal, a sequence of samples in the sliced second horizontal input signal, a sequence of samples in the first vertical input signal, and a sequence of samples in the sliced second vertical input signal.

In a sixth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, slicing the second horizontal input signal includes performing a hard decision on the samples in the second horizontal input signal to map the samples in the second horizontal input signal to a closest constellation point, and slicing the second vertical input signal includes performing a hard decision on the samples in the second vertical input signal to map the samples in the second vertical input signal to a closest constellation point. In a seventh implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, a third horizontal input signal is obtained by duplicating the horizontal input signal rh in the receiving section, a third vertical input signal is obtained by duplicating the vertical input signal r_v in the receiving section, and the filter section is further configured to obtain the XPolM compensated output signals based on the tap coefficients, the third horizontal input signal and the third vertical input signal.

In an eighth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the third horizontal input signal is aligned before it is provided to the filter section, the third vertical input signal is aligned before it is provided to the filter section, and the filter section is further configured to obtain the XPolM compensated output signals, based on the tap coefficients, the aligned third horizontal input signal and the aligned third vertical input signal. In a ninth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, aligning the third horizontal input signal includes aligning the third horizontal input signal with the tap coefficients that are determined in and output by the tap coefficient estimation unit, aligning the third vertical input signal includes aligning the third vertical input signal with the tap coefficients that are determined in and output by the tap coefficient estimation unit.

In a tenth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the tap coefficients that are determined in and output by the tap coefficient estimation unit include first tap coefficients whv, second tap coefficients whh, third tap coefficients Wvh, and fourth tap coefficients ww.

In an eleventh implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the filter section is further configured to obtain the XPolM compensated output signals based on the first tap coefficients whv, the second tap coefficients whh, the third tap coefficients Wvh, the fourth tap coefficients Ww, the aligned third horizontal input signal and the aligned third vertical input signal.

In a twelfth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the XPolM compensated output signals include a horizontal output signal Sh and a vertical output signal

Sv.

In a thirteenth implementation form of the XPolM compensator according to the first aspect or according to any previous implementation form of the first aspect, the filter section is further configured to obtain the horizontal output signal Sh by adding a result of multiplying a first duplicate of the aligned third horizontal input signal with the second tap coefficients whh to a result of multiplying a first duplicate of the aligned third vertical input signal with the first tap coefficients whv, and to obtain the vertical output signal Sv by adding a result of multiplying a second duplicate of the aligned third horizontal input signal with the fourth tap coefficients Wvh to a result of multiplying a second duplicate of the aligned third vertical input signal with the third tap coefficients Ww. A second aspect of the present invention provides a method for operating a cross polarization modulation, XPolM, compensator, the method comprising the steps of receiving, by a receiving section of the XPolM compensator, digital input signals, determining, by a tap coefficient estimation unit of the XPolM compensator, tap coefficients based on sequences of samples in the digital input signals, and obtaining, by a filter section of the XPolM compensator, XPolM compensated output signals, based on the digital input signals and on the tap coefficients.

In a first implementation form of the method according to the second aspect, the digital input signals comprise a horizontal input signal n and a vertical input signal r_v. In a second implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the method further includes obtaining, by the receiving section, adapted horizontal input signals based on the horizontal input signal n and adapted vertical input signals based on the vertical input signal r_v; and determining, by the tap coefficient estimation unit, the tap coefficients based on sequences of samples in the adapted horizontal input signals and based on sequences of samples in the adapted vertical input signals.

In a third implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the adapted horizontal input signals include a first horizontal input signal which is obtained by duplicating the horizontal input signal n, and the adapted vertical input signals include a first vertical input signal which is obtained by duplicating the vertical input signal r_v, and the method further includes determining, by the tap coefficient estimation unit, the tap coefficients based on a sequence of samples in the first horizontal input signal and based on a sequence of samples in the first vertical input signal. In a fourth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the adapted horizontal input signals further include a second horizontal input signal which is obtained by duplicating the horizontal input signal n, and the adapted vertical input signals further include a second vertical input signal which is obtained by duplicating the vertical input signal r_v, and the method further includes determining, by the tap coefficient estimation unit, the tap coefficients based on sequences of samples in the first and second horizontal input signals and based on sequences of samples in the first and second vertical input signals. In a fifth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the second horizontal input signal is sliced in the receiving section before it is provided to the tap coefficient estimation unit, and the second vertical input signal is sliced in the receiving section before it is provided to the tap coefficient estimation unit, and the method further includes determining, by the tap coefficient estimation unit, the tap coefficients based on a sequence of samples in the first horizontal input signal, a sequence of samples in the sliced second horizontal input signal, a sequence of samples in the first vertical input signal, and a sequence of samples in the sliced second vertical input signal. In a sixth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, slicing the second horizontal input signal includes performing a hard decision on the samples in the second horizontal input signal to map the samples in the second horizontal input signal to a closest constellation point, and slicing the second vertical input signal includes performing a hard decision on the samples in the second vertical input signal to map the samples in the second vertical input signal to a closest constellation point.

In a seventh implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, a third horizontal input signal is obtained by duplicating the horizontal input signal rh in the receiving section, a third vertical input signal is obtained by duplicating the vertical input signal r_v in the receiving section, and the method further includes obtaining, by the filter section, the XPolM compensated output signals based on the tap coefficients, the third horizontal input signal and the third vertical input signal.

In an eighth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the third horizontal input signal is aligned before it is provided to the filter section, the third vertical input signal is aligned before it is provided to the filter section, and the method further includes obtaining, by the filter section, the XPolM compensated output signals, based on the tap coefficients, the aligned third horizontal input signal and the aligned third vertical input signal. In a ninth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, aligning the third horizontal input signal includes aligning the third horizontal input signal with the tap coefficients that are determined in and output by the tap coefficient estimation unit, aligning the third vertical input signal includes aligning the third vertical input signal with the tap coefficients that are determined in and output by the tap coefficient estimation unit.

In a tenth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the tap coefficients that are determined in and output by the tap coefficient estimation unit include first tap coefficients whv, second tap coefficients whh, third tap coefficients Wvh, and fourth tap coefficients Ww.

In an eleventh implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the method further includes obtaining, by the filter section, the XPolM compensated output signals based on the first tap coefficients whv, the second tap coefficients whh, the third tap coefficients Wvh, the fourth tap coefficients Ww, the aligned third horizontal input signal and the aligned third vertical input signal.

In a twelfth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the XPolM compensated output signals include a horizontal output signal Sh and a vertical output signal Sv. In a thirteenth implementation form of the method according to the second aspect or according to any previous implementation form of the second aspect, the method further includes obtaining, in the filter section, the horizontal output signal Sh by adding a result of multiplying a first duplicate of the aligned third horizontal input signal with the second tap coefficients whh to a result of multiplying a first duplicate of the aligned third vertical input signal with the first tap coefficients whv, and obtaining, in the filter section, the vertical output signal Sv by adding a result of multiplying a second duplicate of the aligned third horizontal input signal with the fourth tap coefficients Wvh to a result of multiplying a second duplicate of the aligned third vertical input signal with the third tap coefficients

Ww. The method of the second aspect and its implementation forms achieve the same advantages as the system of the first aspect and its respective implementation forms. It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

BRIEF DESCRIPTION OF DRAWINGS

The above described aspects and implementation forms of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

Fig. 1 shows a schematic overview of an XPolM compensator according to an embodiment of the present invention.

Fig. 2 shows a schematic overview of an XPolM compensator according to an embodiment of the present invention in more detail. Fig. 3 shows a schematic overview of an optical coherent receiver.

Fig. 4 shows a method according to an embodiment of the present invention.

Fig. 5 shows simulation results of using an XPolM compensator according to an embodiment of the present invention.

Fig. 6 shows simulation results of using an XPolM compensator according to an embodiment of the present invention. DETAILED DESCRIPTION OF EMBODIMENTS

Fig. 1 shows a schematic overview of an XPolM compensator 100 according to an embodiment of the present invention. The XPolM compensator 100 is in particular suitable for an optical coherent receiver as it is going to be described in Fig. 3. Fig. 1 illustrates an XPolM compensator 100 that includes a receiving section 101, a tap coefficient estimation unit 103 and a filter section 104. The receiving section 101 is configured to receive digital input signals 102. The digital input signals 102 can in particular be optical digital input signals or be based on optical signals. Preferably, the term "digital" indicates that the digital input signals 102 are sampled and/or quantized signals. The digital input signals 102 also, but not necessarily, can be binary signals. The tap coefficient estimation unit 103 is configured to determine tap coefficients 103tc based on sequences 102s of samples in the digital input signals 102. The sequences 102s of samples can preferably be obtained from sequences of symbols in the digital input signals 102. In turn, the filter section 104 is configured to obtain XPolM compensated output signals 105, based on the digital input signals 102 and on the tap coefficients 103tc.

Optionally, the digital input signals 102 can comprise a horizontal input signal n and a vertical input signal r_v. More specifically, the horizontal input signal n and the vertical input signal r_v are two distinct input signals, each of which corresponding to a horizontal, respectively to a vertical polarization component of light. Further optionally, the horizontal input signal n and the vertical input signal r_v can be aligned before they are further processed in the XPolM compensator 100.

The tap coefficients 103tc can also be referred to as sets of tap coefficients 103tc. As the digital input signals 102 are comprising a sequence 102s of samples, the tap coefficient estimation unit 103 can estimate each set of the tap coefficients 103tc based on a plurality of horizontal and vertical samples taken from the horizontal input signal rh and the vertical input signal r_v. The sequence 102s can also be referred to as a stream.

A set of tap coefficients 103tc (which can include first tap coefficients whv, second tap coefficients whh, third tap coefficients Wvh, and fourth tap coefficients Ww) can be regarded as four complex numbers that can be used in the filter section 104 to generate XPolM compensated output signals 105 (which can include horizontal and vertical output samples). More specifically, the sequence 102s of samples which is used to generate the set of tap coefficients 103tc can be obtained from the digital input signals 102 by the tap coefficient estimation unit 104 by dividing the horizontal input signal n and the vertical input signal r_v into blocks. These blocks of samples may not overlap, or may be selected from the samples in a sliding window. The individual samples within the sequence may or may not be multiplied by a weight depending on their position in the sequence.

This aspect of determining a set of tap coefficients 103tc from a sequence 102s of samples in the digital input signals 102 instead of determining them from one sample by another in the digital input signals 102, allows for improving efficiency and precision of the XPolM compensator 100 in view of the prior art.

Fig. 2 shows a schematic overview of an XPolM compensator 200 according to an embodiment of the present invention in more detail. The XPolM compensator 200 comprises all features and functionality as described in view of the XPolM compensator 100 in Fig. 1. That is, the XPolM compensator 200 also comprises the receiving section 101, the tap coefficient estimation unit 103 and the filter section 104 and their respective functionality.

Optionally, the receiving section 101 of the XPolM compensator 200 can further be configured to obtain adapted horizontal input signals 201, 202, 203 based on the horizontal input signal n and adapted vertical input signals 204, 205, 206 based on the vertical input signal r_v. For determining the tap coefficients 103tc based on the sequences 102s of samples, the tap coefficient estimation unit is further configured to determine the tap coefficients 103tc based on sequences 102s of samples in the digital input signals 102. The tap coefficient estimation unit 103 can further be configured to determine the tap coefficients 103tc based on sequences of samples in the adapted horizontal input signals 201, 202, 203 and based on sequences of samples in the adapted vertical input signals 204, 205, 206.

Further optionally, the adapted horizontal input signals 201, 202, 203 can include a first horizontal input signal 201 which is obtained by duplicating the horizontal input signal n, and the adapted vertical input signals 204, 205, 206 can include a first vertical input signal 204 which is obtained by duplicating the vertical input signal r_v. The tap coefficient estimation unit 103 can further be configured to determine the tap coefficients 103tc based on a sequence 102s of samples in the first horizontal input signal 201 and based on a sequence 102s of samples in the first vertical input signal 204.

Further optionally, the adapted horizontal input signals 201, 202, 203 can include a second horizontal input signal 202 which is obtained by duplicating the horizontal input signal n, and the adapted vertical input signals 204, 205, 206 can include a second vertical input signal 205 which is obtained by duplicating the vertical input signal r_v. The tap coefficient estimation unit 103 can be configured to determine the tap coefficients 103tc based on sequences 102s of samples in the first and second horizontal input signals 201, 202 and based on sequences 102s of samples in the first and second vertical input signals 204, 205. Further optionally, the second horizontal input signal 202 can be sliced in the receiving section 101 before it is provided to the tap coefficient estimation unit 103, and the second vertical input signal 205 can be sliced in the receiving section 101 before it is provided to the tap coefficient estimation unit 103. The tap coefficient estimation unit 103 can be configured to determine the tap coefficients 103tc based on a sequence 102s of samples in the first horizontal input signal 201, a sequence 102s of samples in the sliced second horizontal input signal 202, a sequence 102s of samples in the first vertical input signal 204, and a sequence 102s of samples in the sliced second vertical input signal 205.

Further optionally, slicing the second horizontal input signal 202 can include performing a hard decision on the samples in the second horizontal input signal 202 to map the samples in the second horizontal input signal 202 to a closest constellation point, and slicing the second vertical input signal 205 can include performing a hard decision on the samples in the second vertical input signal 205 to map the samples in the second vertical input signal 205 to a closest constellation point.

In a specific implementation example of using quadrature phase-shift keying (QPSK) modulation, performing a hard decision corresponds to determining the sign of the in-phase and quadrature components of a signal, as the corresponding constellation set is {1+i, 1-i, -1+1, -1-i} .

In another implementation example, a sample obtained from a hard-decision can serve as a training sequence in the XPolM compensator 200. Further optionally, the first horizontal input signal 201 and the sliced second horizontal input signal 202 can be aligned with each other before being provided to the tap coefficient estimation unit 103. Also, the first vertical input signal 204 and the sliced second vertical input signal 205 can be aligned with each other before being provided to the tap coefficient estimation unit 103.

Further optionally, a third horizontal input signal 203 can be obtained by duplicating the horizontal input signal n in the receiving section 101, and a third vertical input signal 206 can be obtained by duplicating the vertical input signal r_v in the receiving section 101. The filter section 104 can further be configured to obtain the XPolM compensated output signals 105 based on the tap coefficients 103tc, the third horizontal input signal 203 and the third vertical input signal 206.

Further optionally, the third horizontal input signal 203 can be aligned before it is provided to the filter section 104, and the third vertical input signal 206 can be aligned before it is provided to the filter section 104. The filter section 104 can further be configured to obtain the XPolM compensated output signals 105, based on the tap coefficients 103tc, the aligned third horizontal input signal 203 and the aligned third vertical input signal 206. Aligning the third horizontal input signal 203 and/or the third vertical input signal 206 can be implemented by delaying the third horizontal input signal 203 and/or the third vertical input signal 206, e.g. in a delay register. Delaying can e.g. be performed for a predefined amount of time.

Further optionally, aligning the third horizontal input signal 203 can include aligning the third horizontal input signal 203 with the tap coefficients 103tc that are determined in and output by the tap coefficient estimation unit 103, and aligning the third vertical input signal 206 can include aligning the third vertical input signal 206 with the tap coefficients 103tc that are determined in and output by the tap coefficient estimation unit 103.

Further optionally, the tap coefficients 103tc that are determined in and output by the tap coefficient estimation unit 103 can include first tap coefficients whv, second tap coefficients whh, third tap coefficients Wvh, and fourth tap coefficients Ww. Further optionally, the tap coefficients 103tc can be calculated according to the following first equation:

wherein Rh represents a column vector form of at least a part of the first horizontal input signal 201. Rv represents a column vector form of at least a part of the first vertical input signal 204. Dh represents a column vector form of at least a part of the sliced (i.e. the hard decided) second horizontal input signal 202. D_v represents a column vector form of at least a part of the sliced (i.e. hard decided) second vertical input signal 205. More specifically, each of the vectors may correspond to a block out of a plurality of blocks into which the respective signal was divided. Alternatively, each of the vectors may correspond to a sliding window corresponding to the respective signal. R^H represents a Hermitian transpose.

Even though there is a matrix inversion in the above equation, this does not cause a complexity problem, since the equation only includes a 2x2 matrix and the inverse of the matrix is calculated directly instead of resorting to iterative methods.

Further optionally, the tap coefficients 103tc can alternatively be calculated according to the following second equation to which the matrix inversion is already applied:

wherein

Again, Rh represents a column vector form of the first horizontal input signal 201, Rv represents a column vector form of the first vertical input signal 204, Dh represents a column vector form of the sliced (i.e. the hard decided) second horizontal input signal 202, Dv represents a column vector form of the sliced (i.e. hard decided) second vertical input signal 205 and R represents a Hermitian transpose, γ is the inverse of the determinant of the 2x2 matrix.

Optionally, calculating the tap coefficients 103tc according to the above first or second equation also fulfills the following equations and in particular an XPolM compensation matrix (which can also be regarded as the channel matrix), which is defined by:

To compute the tap coefficients 103tc for XPolM compensation, it is assumed that the hard- decided samples Dh and D_v are equal to the samples Th and T_v as they are actually transmitted from a sender to a receiver that employs the XPolM compensator 100 or 200. The tap coefficients whh, whv, Wvh and Ww cannot be determined exclusively based on the received and hard-decided samples Dh and D_v because the corresponding equation system is underdetermined. However, a channel can be determined by assuming that it remains the same over a plurality of samples.

To this end, it can be defined that D_ft = (D_{h l}, ..., D_{h N}), D_v = (D_{h l}, ..., D_{h N}), which similarly also applies for R_¾, R_V .Thus, Dh and D_v can be defined as shown below:

Further optionally, the tap coefficients 103tc can be computed by inverting these two relations. This is achieved by computing the pseudoinverse of a matrix containing the received samples, which corresponds to a least-squares estimation. An equalizer therefore operates over a block of samples at a time. The tap coefficients 103tc can then be used to equalize the samples of the entire block, after which a following block is processed.

Alternatively, a sliding window can be used. In this case, the tap coefficients 103tc are determined for a current window and are used to equalize a number of samples within it.

Then the sliding window is moved by the same number of samples. It is possible to use a weighted window, by assigning different weights to samples within a window. According to the example regarding the second equation, the length of the column vectors Rh, Rv, Dh and D_v may depend on the auto-correlation length of the XPolM effect and may need to be optimized in application.

Further optionally, the filter section 104 can be configured to obtain the XPolM compensated output signals 105 based on the first tap coefficients whv, the second tap coefficients whh, the third tap coefficients Wvh, the fourth tap coefficients Ww, the aligned third horizontal input signal 203 and the aligned third vertical input signal 206.

Further optionally, the XPolM compensated output signals 105 can include a horizontal output signal Sh and a vertical output signal Sv. Further optionally, the filter section 104 can be configured to obtain the horizontal output signal Sh by adding a result of multiplying a first duplicate of the aligned third horizontal input signal 203 with the second tap coefficients whh to a result of multiplying a first duplicate of the aligned third vertical input signal 206 with the first tap coefficients whv, and to obtain the vertical output signal Sv by adding a result of multiplying a second duplicate of the aligned third horizontal input signal 203 with the fourth tap coefficients Wvh to a result of multiplying a second duplicate of the aligned third vertical input signal 206 with the third tap coefficients Ww.

In particular, an output sample in the horizontal polarization is determined from the corresponding input samples in the horizontal and vertical polarization according to Sh = whhRh + whvRv and similar an output sample in the vertical polarization is determined from the corresponding input samples in the horizontal and vertical polarization according to: Sv = WvhRh + WwRv (wherein both equations these are scalar equations).

Further optionally, the filter section 104 can in particular be a butterfly filter section or a 1-tap butterfly filter section. Obtaining any kind of new input signal by duplicating any kind of existing signal can also be regarded as creating an identical copy of the respective signal.

Fig. 3 shows a schematic overview of a typical optical coherent receiver 300. Among others, the optical coherent receiver 300 includes a frontend, analog-to-digital converters (ADC), static filters, an adaptive filter, carrier recovery modules, and a forward error correction (FEC) decoder. The optical coherent receiver 300 also includes the XPolM compensator 100 or 200. The XPolM compensator 100 or 200 is arranged between the carrier recovery modules and the FEC decoder. The digital input signals 102 of the XPolM compensator are the down-sampled signals in horizontal (n) and vertical (r_v) polarization, which can be in a digital domain. Those signals may have experienced static chromatic dispersion compensation, adaptive equalization for polarization mode dispersion (PMD) compensation, polarization de -multiplexing and carrier phase recovery. Digital input signals 102 of samples that have been transmitted simultaneously can be aligned. The corresponding output signals 105 of the XPolM compensator Sh and Sv are fed to the FEC decoder. Fig. 4 shows a method 400 according to an embodiment of the present invention. The method 400 corresponds to the XPolM compensator 100 of Fig. 1, and is accordingly for operating the XPolM compensator 100. The method 400 comprises a step of receiving 401, by a receiving section 101 of and XPolM compensator 100, digital input signals 102. Further, the method 400 comprises a step of determining 402, by a tap coefficient estimation unit 103 of the XPolM compensator 100, tap coefficients 103tc based on sequences 102s of samples in the digital input signals 102. Finally, the method 400 comprises a step of obtaining 403, by a filter section 104 of the XPolM compensator 100, XPolM compensated output signals 105, based on the digital input signals 102 and on the tap coefficients 103tc. Fig. 5 shows simulation results of using an XPolM compensator according to an embodiment of the present invention. More specifically, Fig. 5 shows simulation results of 9 polarization division multiplexing binary phase-shift keying (PDM-BPSK) signals with a launch power of -2 dBm per wavelength over a 4000 km and a 5000 km optical fiber link. The measured bit error rate (BER) and constellation of a central wavelength are shown. It is shown that the method 400 according to the invention improves performance remarkably. Q-factor improvement over the prior art solution (NPCC) is -0.7 dB and 1 dB over baseline (without compensation) at OSNR=15 dB after 5000 km propagation. The Q-factor is a common measure of quality of transmission. From the constellation drawings, it can be seen that after the processing in the XPolM compensator according to the present invention, two constellation clusters are more centralized and widely separated because both the crosstalk and residual phase noise are compensated. In particular, Fig. 5 shows a BER- OSNR relationship 501 according to the simulation, simulation results without using compensation 502, simulation results using prior art XPolM compensation 503 and simulation results using XPolM compensation according to the present invention 504.

Fig. 6 shows simulation results of using an XPolM compensator according to an embodiment of the present invention. More specifically, Fig. 6 shows simulation results of 9 polarization division multiplexing quaternary phase-shift keying (PDM-QPSK) signals with launch power of -2dBm per wavelength over a 2000km and a 3000km optical fiber link. It is shown that the method according to the present invention performs better than NPCC. Q-factor improvement over NPCC is -O. ldB and 1.2 dB over baseline at OSNR=18dB after 3000km transmission. In particular, Fig. 6 shows a BER-OSNR relationship 601 according to the simulation, simulation results without using compensation 602, simulation results using NPCC 603 and simulation results using XPolM compensation according to the present invention 604.

The present invention has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word "comprising" does not exclude other elements or steps and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

1. A cross polarization modulation, XPolM, compensator (100, 200) for an optical coherent receiver (300), comprising

- a receiving section (101), configured to receive digital input signals (102),

- a tap coefficient estimation unit (103), configured to determine tap coefficients (103tc) based on sequences (102s) of samples in the digital input signals (102), and

- a filter section (104), configured to obtain XPolM compensated output signals (105), based on the digital input signals (102) and on the tap coefficients (103tc).

2. The XPolM compensator (100, 200) according to claim 1, wherein the digital input signals (102) comprise a horizontal input signal rh and a vertical input signal r_v.

3. The XPolM compensator (100, 200) according to claim 2, wherein the receiving section (101) is further configured to obtain adapted horizontal input signals (201, 202, 203) based on the horizontal input signal n and adapted vertical input signals (204, 205, 206) based on the vertical input signal r_v; and

wherein the tap coefficient estimation unit (103), is further configured to determine the tap coefficients (103tc) based on sequences of samples in the adapted horizontal input signals (201, 202, 203) and based on sequences of samples in the adapted vertical input signals (204, 205, 206).

4. The XPolM compensator (100, 200) according to claim 3, wherein the adapted horizontal input signals (201, 202, 203) include a first horizontal input signal (201) which is obtained by duplicating the horizontal input signal n, and

wherein the adapted vertical input signals (204, 205, 206) include a first vertical input signal (204) which is obtained by duplicating the vertical input signal r_v, and

wherein the tap coefficient estimation unit (103) is further configured to determine the tap coefficients (103tc) based on a sequence (102s) of samples in the first horizontal input signal (201) and based on a sequence (102s) of samples in the first vertical input signal (204).

5. The XPolM compensator (100, 200) according to claim 4, wherein the adapted horizontal input signals (201, 202, 203) further include a second horizontal input signal (202) which is obtained by duplicating the horizontal input signal n, and

wherein the adapted vertical input signals (204, 205, 206) further include a second vertical input signal (205) which is obtained by duplicating the vertical input signal r_v, and wherein the tap coefficient estimation unit (103) is further configured to determine the tap coefficients (103tc) based on sequences (102s) of samples in the first and second horizontal input signals (201, 202) and based on sequences (102s) of samples in the first and second vertical input signals (204, 205).

6. The XPolM compensator (100, 200) according to claim 5, wherein the second horizontal input signal (202) is sliced in the receiving section (101) before it is provided to the tap coefficient estimation unit (103), and

wherein the second vertical input signal (205) is sliced in the receiving section (101) before it is provided to the tap coefficient estimation unit (103), and

wherein the tap coefficient estimation unit (103) is further configured to determine the tap coefficients (103tc) based on a sequence (102s) of samples in the first horizontal input signal (201), a sequence (102s) of samples in the sliced second horizontal input signal (202), a sequence (102s) of samples in the first vertical input signal (204), and a sequence (102s) of samples in the sliced second vertical input signal (205).

7. The XPolM compensator (100, 200) according to claim 6, wherein slicing the second horizontal input signal (202) includes performing a hard decision on the samples in the second horizontal input signal (202) to map the samples in the second horizontal input signal (202) to a closest constellation point, and

wherein slicing the second vertical input signal (205) includes performing a hard decision on the samples in the second vertical input signal (205) to map the samples in the second vertical input signal (205) to a closest constellation point.

8. The XPolM compensator (100, 200) according to anyone of claims 2 to 7, wherein a third horizontal input signal (203) is obtained by duplicating the horizontal input signal n in the receiving section (101), wherein a third vertical input signal (206) is obtained by duplicating the vertical input signal r_v in the receiving section (101), and wherein the filter section (104) is further configured to obtain the XPolM compensated output signals (105) based on the tap coefficients (103tc), the third horizontal input signal (203) and the third vertical input signal (206).

9. The XPolM compensator (100, 200) according to claim 8, wherein the third horizontal input signal (203) is aligned before it is provided to the filter section (104), wherein the third vertical input signal (206) is aligned before it is provided to the filter section (104), and wherein the filter section (104) is further configured to obtain the XPolM compensated output signals (105), based on the tap coefficients ( 103tc), the aligned third horizontal input signal (203) and the aligned third vertical input signal (206).

10. The XPolM compensator (100, 200) according to claim 9, wherein aligning the third horizontal input signal (203) includes aligning the third horizontal input signal (203) with the tap coefficients (103tc) that are determined in and output by the tap coefficient estimation unit (103), wherein aligning the third vertical input signal (206) includes aligning the third vertical input signal (206) with the tap coefficients (103tc) that are determined in and output by the tap coefficient estimation unit (103).

11. The XPolM compensator (100, 200) according to any one of claims 1 to 10, wherein the tap coefficients (103tc) that are determined in and output by the tap coefficient estimation unit (103) include first tap coefficients whv, second tap coefficients whh, third tap coefficients Wvh, and fourth tap coefficients Ww.

12. The XPolM compensator (100, 200) according to claim 10 and 11, wherein the filter section (104) is further configured to obtain the XPolM compensated output signals (105) based on the first tap coefficients whv, the second tap coefficients whh, the third tap coefficients Wvh, the fourth tap coefficients Ww, the aligned third horizontal input signal (203) and the aligned third vertical input signal (206).

13. The XPolM compensator (100, 200) according to anyone of the preceding claims, wherein the XPolM compensated output signals (105) include a horizontal output signal Sh and a vertical output signal Sv.

14. The XPolM compensator (100, 200) according to claim 13, wherein the filter section (104) is further configured to obtain the horizontal output signal Sh by adding a result of multiplying a first duplicate of the aligned third horizontal input signal (203) with the second tap coefficients whh to a result of multiplying a first duplicate of the aligned third vertical input signal (206) with the first tap coefficients whv, and to obtain the vertical output signal Sv by adding a result of multiplying a second duplicate of the aligned third horizontal input signal (203) with the fourth tap coefficients Wvh to a result of multiplying a second duplicate of the aligned third vertical input signal (206) with the third tap coefficients Ww.

15. A method (400) for operating a cross polarization modulation, XPolM, compensator (100), the method comprising the steps of:

- receiving (401), by a receiving section (101) of the XPolM compensator (100, 200), digital input signals (102),

- determining (402), by a tap coefficient estimation unit (103) of the XPolM compensator (100), tap coefficients (103tc) based on sequences (102s) of samples in the digital input signals (102), and

- obtaining (403), by a filter section (104) of the XPolM compensator (100, 200), XPolM compensated output signals (105), based on the digital input signals (102) and on the tap coefficients (103tc).