CN104205678B - Nonlinear and crossing polarization alleviates algorithm - Google Patents

Abstract

Presents relates to optical transmission system.Especially, the method and system alleviated of the cross-polarization modulation (XPOLM) during presents relates to optical transmission system.Describe and be adapted to be reception by the coherent optical heterodyne communicatio (200) representing the optical signal that the optical transport channel of XPOLM is transmitted.The optical signal received includes the first polarized component and the second polarized component.First polarized component and the second polarized component include the M of referred to as MPSK respectively^aryPhase shift keying symbols sequence, M is integer, and M > 2.Coherent optical heterodyne communicatio (200) including: conversion and processing unit (201,202), is adapted to be and generates digital signal set based on the optical signal received；Polarization demultiplexing unit (203), is adapted to be the second complex number components in the first two dimension (referred to as plural number) component and the second polarization axle this digital signal set being demultiplexing as in the first polarization axle；And XPOLM compensating unit (204), it is adapted to be and the first complex number components and the second complex number components are transformed in Stokes Space, thus produce Stokes' parameter set；Based on this Stokes' parameter set, determine the first polarization axle and the rotation of the second polarization axle；And convert the first complex number components and the second complex number components by the rotation of the first polarization axle and the second polarization axle determined by basis, to determine the first complex number components that XPOLM compensates and the second complex number components that XPOLM compensates.

Description

Nonlinear and crossing polarization alleviates algorithm

Technical field

Presents relates to optical transmission system.Especially, the cross-polarization modulation during presents relates to optical transmission system (XPOLM) the method and system alleviated.

Background technology

The optical transmission system using point multiplexing (PDM) or polarization switch (PS) partially may be referred to as cross-polarization modulation (XPOLM) restriction of nonlinear effect.Particularly, when having based on (non-zero dispersion phase shifter optical fiber) NZ-DSF cable PDM-BPSK (binary phase shift keying), PDM-QPSK (QPSK) or PS-QPSK is used to modulate lattice on submarine cable During formula, XPOLM is probably the effect of restriction.

Fig. 1 a and 1b shows the friendship of the PDM-BPSK of 40G bit/s on the optical transmission chain of typical dispersion management The effect of fork Polarization Modulation.In the situation of Fig. 1 a, the power of the optical signal injected than non-linear threshold (NLT) low 1dB, and And in the situation of Fig. 1 b, the power 1dB higher than NLT injected.Two figures all indicate forward error correction (FEC) limit 102, 112.When the power of optical signal is higher than NLT, XPOLM becomes leading distortion effect, has Q²The stability of the factor Impact, from the Q Fig. 1 a²Q in Fig. 1 b that the factor 101 compares²The variance of the increase of the factor 111, it can be seen that this shadow Ring.

In view of above-mentioned, there are the needs of effect for alleviating the XPOLM at the photoreceiver of optical transmission system.

Summary of the invention

According to an aspect, describe a kind of coherent optical heterodyne communicatio.This coherent optical heterodyne communicatio is adapted to be reception by exhibition The optical signal that the optical transport channel of existing cross-polarization modulation (XPOLM) is transmitted.Especially, this coherent optical heterodyne communicatio is adapted to be Alleviate the distortion (such as polarizing rotation) caused by XPOLM.The optical signal received generally includes the first polarized component and second Polarized component.By way of example, the optical signal received can be partially to divide multiplexing (PDM) or polarization switch (PS) signal. First polarized component and the second polarized component can include M respectively^aryPhase-shift keying (PSK) (MPSK) symbol sebolic addressing, M is integer, and M >2。

This coherent optical heterodyne communicatio may include that conversion and processing unit, is adapted to be based on the optical signal next life received Become digital signal set.This conversion and processing unit can include for the optical signal received is converted into analogue signal set Relevant frequency mixer and photodiode.Multiple analog-digital converters (ADC) can be used to be converted into this analogue signal set Digital signal set.Additionally, this conversion and processing unit can include digital signal processor to process this digital signal collection Close, such as, be used for compensating dispersion (CD).So, this digital signal set can be that CD compensates.

This coherent optical heterodyne communicatio may further include: polarization demultiplexing unit, is adapted to be this digital signal set It is demultiplexing as the second such as 2D component in first in the first polarization axle such as two dimension (2D) component and the second polarization axle.First Polarization axle and the second polarization axle can be basically about orthogonal.First component and second component can be the first complex number components With the second complex number components.First component can be included in (follow-up) the first complex sampling sequence at follow-up moment k, k= 1 ..., K, K are integers, K > 1.In a similar fashion, the second complex number components can be included in the second plural number at follow-up moment k Sample sequence.

Additionally, this coherent optical heterodyne communicatio includes XPOLM compensating unit.This XPOLM compensating unit is adapted to be first multiple Number component and the second complex number components transform in Stokes Space, thus produce Stokes' parameter set.By example Mode, the first complex number components and the second complex number components can be complex number components X_kAnd Y_k.This Stokes' parameter set can include The S being defined below_1,k, S_2,k, S_3,kIn one or more:

S_0,k=| X_k|²+|Y_k|²

S_1,k=(| X_k|²-|Y_k|²)/S_0,k

$S_{2,k}=2\mathrm{Re}\left\{X_k{Y}_k^{*}\right\}/S_{0,k}$

$S_{3,k}=-2\mathrm{Im}\left\{X_k{Y}_k^{*}\right\}/S_{0,k}$

So, this XPOLM compensating unit can be configured to, the first sample sequence and second at these moment k Sample sequence X_kAnd Y_k, determine the Stokes' parameter sequence of sets S at these moment k respectively_1,k, S_2,kAnd/or S_3,k。

First complex number components and the second complex number components can be indicated in Jones space.MPSK in Stokes Space The quantity in the site of symbol sebolic addressing relatively can be reduced compared with the quantity in the site in Jones space.In other words, these The point (compared to the quantity of the point in Jones space) of the minimizing quantity that MPSK symbol can be mapped in Stokes Space. This multipair few mapping is for coming from the first complex sampling sequence and the second complex sampling sequence in relatively short time interval It is favourable for determining reliable statistics, thus allows the tracking to the distortion (rotation) caused by XPOLM and compensation.

This XPOLM compensating unit can be configured to, and determines that first is inclined based on this Stokes' parameter collection is incompatible Shake axle or component and the second polarization axle or the rotation of component.Especially, this XPOLM compensating unit can be configured to, based on Stokes' parameter sequence of sets at these moment k, k-1 ..., k-N determine the first polarization axle at these moment k and The rotation of the second polarization axle, wherein N is the length of observation window.For this purpose, this XPOLM compensating unit can be adapted For, perform the statistical analysis of Stokes' parameter sequence of sets.By way of example, this XPOLM compensating unit can be fitted Join for, from this Stokes' parameter collection incompatible determine covariance coefficient and use these covariance coefficients for characteristic vector/ Eigenvalues analysis.

This XPOLM compensating unit can be configured to, by the first polarization axle determined by basis and the second polarization axle Rotate the first complex number components and the second complex number components, to determine that the first complex number components that XPOLM compensates and XPOLM compensate The second complex number components.Especially, this XPOLM compensating unit can be configured to, by determined by basis at these moment k Locate the rotation of the first polarization axle and the second polarization axle to be rotated in the first complex sampling sequence at these moment k and the second plural number The second of sample sequence, the first complex sampling sequence compensated with the XPOLM determined at these moment k and XPOLM compensation is multiple Number sample sequence.In other words, this XPOLM compensating unit can be configured to, and uses based on the system determined for particular moment k Rotate determined by meter, be rotated in the first complex sampling at particular moment k and the second complex sampling.This statistics can be base Any feedback or training program is not used to individually determine in the optical signal received.As result, this XPOLM compensates Unit is adapted to be, and compensates the XPOLM distortion (rotation) of relatively rapid change.

This Stokes' parameter set can cross over multidimensional Stokes Space.This XPOLM compensating unit can be adapted For by subspace fitting to Stokes' parameter sequence of sets, wherein the subspace of institute's matching has lower than Stokes Space Dimension.By way of example, this subspace can be complex number plane (such as in the case of MPSK, and M > 2), or This subspace can be 1D line (such as in the case of BPSK or PS-QPSK).This XPOLM compensating unit can be adapted to be, Subspace based on institute's matching, such as, based on this 2D plane or this 1D line, determine the first polarization axle and the rotation of the second polarization axle Turn.

As noted above, this XPOLM compensating unit can be adapted to be, based on the stoke at these moment k This parameter sets sequence, determines the covariance coefficient of Stokes' parameter at these moment k.Additionally, this XPOLM compensates Unit can be adapted to be, based on determined by covariance coefficient at these moment k, determine at these moment k The characteristic vector of the covariance matrix of Stokes' parameter.In this situation, this XPOLM compensating unit can be adapted to be, Eliminate the ambiguity in the direction of characteristic vector determined by the follow-up moment, be therefore prevented from characteristic vector direction (and Rotation as result) uncontrolled vibration.The rolling average across N number of moment can be used to determine these covariance systems Number, wherein N is typically smaller than K.It is typically based on the speed by the change caused by XPOLM to select N.By way of example, should XPOLM compensating unit can be adapted to be, and for multiple different time lags, determines at least one in Stokes' parameter The auto-correlation function of Stokes' parameter.May then based on this auto-correlation function to determine that quantity N in moment is (or for really The length of the time interval of these covariance coefficients fixed).

The optical signal received can be PDM bpsk signal or PS QPSK signal.In such a case, this XPOLM Compensating unit can be adapted to be, the characteristic vector of covariance matrix is defined as the feature corresponding with eigenvalue of maximum to Amount.In another embodiment, the optical signal received can be PDM mpsk signal and M > 2.In such a case, should XPOLM compensating unit can be adapted to be, and determines the feature that the characteristic vector with minimal eigenvalue of covariance matrix is corresponding Vector.Additionally, this XPOLM compensating unit can be configured to, determine determined by characteristic vector and acquiescence axle between angle And rotary shaft.This XPOLM compensating unit can based on angle determined by Stokes Space and determined by rotate Axle, determines the first complex number components and the conversion of the second complex number components or rotation.Especially, this XPOLM compensating unit can be with base In the formula provided in the detailed description part of presents, determine the first complex number components and the rotation of the second complex number components Turn.

This XPOLM compensating unit can be adapted to be, and based on the long-time statistical derived from Stokes' parameter set, determines Relative phase drift between first complex number components and the second complex number components, is followed by the 2nd XPOLM compensating unit and is adapted to be, The complex number components that the complex number components compensated by oneth XPOLM and the 2nd XPOLM compensate transforms in Stokes Space, thus produces Raw other Stokes' parameter set.2nd XPOLM compensating unit can be with similar with this (first) XPOLM compensating unit Mode is adapted.Especially, the 2nd XPOLM compensating unit can be adapted to be, based on the short-term derived from Stokes' parameter Statistics, alleviates the first complex number components and the XPOLM of the second complex number components.Especially, the 2nd XPOLM compensating unit can be fitted Join for, based on the short term statistics derived from other Stokes' parameter set, the complex number components compensated from an XPOLM and the The complex number components that two XPOLM compensate, determines what the first complex number components that other XPOLM compensates and other XPOLM compensated Second complex number components.The time interval considered by the long-time statistical corrected for relative phase can be more than for short term statistics institute The time interval considered.So, this photoreceiver can include multiple XPOLM compensating unit, and these XPOLM compensating units are fitted Join for using across adding up determined by different time interval (such as across the sampling of varying number N), compensate phase with friction speed To phase drift and XPOLM effect.

According to further aspect, describe the cross-polarization modulation in a kind of optical signal for alleviating reception (XPOLM) method.The optical signal received includes the first polarized component and the second polarized component.First polarized component and second Polarized component includes MPSK symbol sebolic addressing respectively, and M is integer, and M > 2.The method included based on the optical signal next life received Become digital signal set.The method continues at the first complex number components this digital signal set being demultiplexing as in the first polarization axle With the second complex number components in the second polarization axle.Additionally, the first complex number components and the second complex number components are converted to Stokes In space, thus produce Stokes' parameter set.The method continues at based on this Stokes' parameter set, determines that first is inclined The axle and second that shakes polarizes transformation of axis or rotation, and continues at by the first polarization axle determined by basis and the second polarization axle Conversion or rotate the first complex number components and the second complex number components, with determine the first complex number components that XPOLM compensates and The second complex number components that XPOLM compensates.

According to further aspect, describe a kind of software program.This software program can be adapted at processor Or the execution on hardware embodiment, and for performing the side summarized in this document when being implemented on the computing device Method step.

According on the other hand, describe a kind of storage medium.This storage medium can include software program, this software program It is adapted to execution on a processor, and for performing when being implemented on the computing device to be summarized in this document Method step.

According to further aspect, describe a kind of computer program.This computer program can include performing Instruction, these executable instructions for performing the method step summarized in this document when being performed on computers.

It should be noted that, the method and system of the preferred embodiment including it as summarized in the present patent application, permissible Individually or with additive method disclosed in this document and system in combination use.Additionally, institute in the present patent application All aspects of the method and system of general introduction can at random combine.Especially, each feature of claim can be with arbitrarily side Formula is mutually combined.

Accompanying drawing explanation

Explain the present invention the most in an exemplary fashion, in the accompanying drawings:

Fig. 1 a and 1b illustrates the effect of the cross-polarization modulation of the function of the power as the optical signal transmitted；

Fig. 2 a shows the block diagram of the exemplary optical receiver including XPOLM compensating unit；

Fig. 2 b shows the block diagram of the example filter group used in polarization demultiplexing unit；

Fig. 3 shows the block diagram of example XPOLM compensating unit；

Fig. 4 a to 4c illustrates the exemplary components of XPOLM compensating unit；

Fig. 5 a and 5b shows exemplary experimental result；

Fig. 6 illustrates the Stokes' parameter S for PDM-QPSK (QPSK) signal₁、S₂And S₃；And

Fig. 7 illustrates the determination of the example rotation rotating to be feature with 3D in Stokes Space.

Detailed description of the invention

As pointed by background section, XPOLM the distortion caused becomes the quality for optical transmission system Key factor, especially when operating optical transmission system with optimal power (such as with NLT or higher than NLT).For compensating The various schemes of XPOLM can be used.By way of example, it is possible to use being referred to as the concrete arteries and veins of intertexture zero (iRZ) Die-cut cut (carving) scheme.This arrangement reduces XPOLM, but can not be used to fully compensate for XPOLM.Additionally, this The scheme of kind makes answering machine (including photoreceiver) more expensive and is appropriate only for as the high-performance field of undersea transmission system etc Scape.Other scheme can utilize (in-line) polarization mode dispersion (PMD) in line.But, typical submarine cable has very Low PMD and PMD can not be added to existing cable.Generally speaking, it is impossible to interpolation PMD, thus it is directed at based on PMD Scheme is incompatible with old system.Another method is at Lei Li et al. " Nonlinear Polarization Crosstalk Canceller for Dual-Polarization Digital Coherent Receivers ", The XPOLM determining auxiliary described in OFC2010, Paper OWE3 compensates DSP scheme.But, the performance of this scheme is Limited and Q²Factor gain is using relatively small value as coboundary.Other method can be less than the injection merit of below NLT Rate.But, this has many defects.Particularly, existing system reduces injecting power the most possible.Additionally, The reduction of injecting power typically results in the average Q factor of suboptimum.

So, exist for a kind of effectively low cost for compensating XPOLM at the receiver of optical transmission system The needs of scheme.In this document, it is proposed that use blind backoff algorithm compensates the XPOLM in the DSP of coherent optical heterodyne communicatio.Carry Discuss and above analyzed, at Poincare sphere (it is intended to indicate that the method for polarization state of light), the nonlinear scattering caused by XPOLM. Geometry lexical or textual analysis is combined with the linear regression technique according to mathematical statistics, describe one and can follow the trail of and compensate quickly The algorithm of the XPOLM distortion of change.The special advantage of proposed algorithm is: described algorithm is in terms of Q factor gain Highly effective and this algorithm complexity is relatively low, thus this algorithm can be such as real in ASIC (special IC) Execute.Additionally, this algorithm is blind, i.e. this algorithm does not utilize feedback circuit and need not data slave part.

Hereinafter, described in the situation of PDM-BPSK modulation format, it is used for compensating the system and method for XPOLM.So And, it should be noted that this system and method is also applied to other modulation formats, and (wherein M represents arbitrary integer to such as PDM-MPSK And the wherein quantity of M instruction constellation point) and PS-QPSK.

Fig. 2 a illustrates example coherent optical heterodyne communicatio 200.Coherent optical heterodyne communicatio 200 includes that front end 201, front end 201 are joined Be set to be converted into the optical signal received a pair complex digital signal, the most each digital signal include homophase phase component and Quadrature phase component.For this purpose, front end 201 can include coherent detector and analog-digital converter (ADC) group.Additionally, It is (such as, one or more to one or more digital signal processors of digital signal that photoreceiver 200 includes processing this ASIC), in order in detector unit 208, recover the data transmitted.This generally includes CD and compensates 202 the process of digital signal (dispersive estimates, CDE), polarization demultiplexing 203, estimating carrier frequencies (CFE) 205, carrier phase estimate (CPE) 206 and poor Decompose code (Diff.Dec.) 207.

In other words, the optical signal received at Coherent Transporder 200 is advanced through light front end 201, wherein along with relevant Local oscillator (LO) in frequency mixer and pulse (beating), light detection and analog digital conversion are performed.Digitized signal Being passed to the DSP stage, the DSP stage includes: dispersive estimates/compensation (CDE) 202, permanent mould for polarization demultiplexing and equilibrium Algorithm (CMA) 203, estimating carrier frequencies/correction (CFE) 205, two independent carrier phase estimation/correction box 206, difference Decoding 207 and detection 208.

So, the process at photoreceiver 200 generally includes polarization demultiplexing and balanced unit (constant modulus algorithm, CMA) 203.Polarization demultiplexing unit 203 can include one or more equalization filter, and it is equal that these equalization filters are used for channel Weigh and/or for polarization demultiplexing.Polarization demultiplexing unit 203 generally includes four FIR (the limited arteries and veins arranged with butterfly structure Punching response) group 270 (seeing Fig. 2 b) of wave filter 271.The filter tap (tap) of these FIR filter 271 can include It is determined continuously in the feedback circuit of adaptation unit 272 and adaptive.Adaptation unit 272 can perform in " blind " mode continuously The CMA algorithm of matched filter tap.In other words, CMA algorithm is based only upon the digital signal derived from the optical signal received To sampling, determine the filter tap of FIR filter 271.Filter tap is typically determined so that demultiplexing at polarization Prearranged signals characteristic is represented with the filtered signal of unit downstream (i.e. after utilizing FIR filter group 270 filtering).Pass through The mode of example, for the signal of unit amplitude, CMA can attempt minimizing at the output of polarization demultiplexing unit 203 Error term E=(| s_out|-1)²Value, wherein | s_out| it is output signal s of polarization demultiplexing unit 203_outIntensity (or Person's amplitude).So, CMA algorithm is based on relevant pre-of fixing intensity (or amplitude) with the two of the optical signal received polarizations Determine characteristics of signals and operate.In addition to other things, polarization demultiplexing unit 203 is configured to offer two at its output Individual complex digital signal, the two complex digital signal is about orthogonal.

Godard (IEEE Tr.Comm, vol.28, no.11.pp.1867-1875,1980) describes CMA algorithm, and Its description is incorporated by reference into.Additionally, at Proceedings of ECOC 2006 paper of in JIUYUE, 2006 cannes of france Document " the Digital Equalization of 40Gbit/s per Wavelength of the S.J.Savory of Th2.5.5 et al. Transmission over 2480km of Standard Fiber without Optical Dispersion Compensation " in discuss CMA.The description of the CMA in this document is incorporated to from there through quoting.

Additionally, this process includes blind XPOLM equalizer (blind-XPolE) 204, it is also referred herein as XPOLM and compensates Unit 204.In the examples shown of Fig. 2 a, after blind-XPolE 204 is just placed on CMA 203, so blind-XPolE 204 is not Utilize the signal operation for it of original detection.Alternatively, blind-XPolE 204 utilizes the output of polarization demultiplexing unit 203 The orthogonal complex digital signal at place.As indicated above, the polarization demultiplexing unit 203 using CMA utilizes and is received The predetermined knowledge that the intensity (amplitude) of optical signal is relevant, in order to two orthogonal polarization axes of the optical signal that demultiplexing is received.CMA The most only it is adapted to be the relatively slow rotation following the trail of polarization axle.So, CMA is not the most adapted to be tracking and compensates by rapidly The distortion (i.e. rotating) that the XPOLM of phenomenon is caused, the XPOLM of rapid phenomenon result in fast-changing rotation (in nanosecond In the range of).It is generally not capable of using feedback scheme (such as the situation of CMA) or study loop to follow the trail of or compensate these Rapid Variable Design Rotation.

In view of above-mentioned, XPOLM compensating unit 204 utilizes the sampling derived from the optical signal received, without feedback Loop or study loop.As result, XPOLM compensating unit 204 can follow the trail of and compensate the light received caused by XPOLM The fast-changing rotation of signal.Fig. 3 illustrates the high-level block diagram of the example of blind-XPolE 204.Blind-XPolE 204 includes Jones (Jones) arrives Stokes (Stokes) module 301, and it is configured to map signal 311 from Jones space (that is, will Jones's vector transformation) to Stokes Space (that is, to set or the Stokes Vector of Stokes' parameter).Additionally, blind- XPolE 204 includes average 302 (also referred to as covariance determines unit 302) of covariance matrix, and it is configured to hold in the palm based on this The sequence of gram this parameter determines that covariance is added up.Covariance matrix average 302 be followed by linear regression axle matching 303 (also by It is referred to as covariance analysis unit 303), it is configured to the lowest mean square of the signal constellation (in digital modulation) in digital simulation Stokes Space Line.It addition, blind-XPolE 204 includes module 304, module 304 is for calculating inverse Jones matrix in Jones space Channel is changed.Especially, inverse Jones matrix unit 304 (also referred to as spin matrix determines unit 304) determines for making rotation The spin matrix that signal 311 in Jones space in unit 305 rotates, thus produces the signal 312 that XPOLM compensates.

Generally speaking, the core calculations compensated for XPOLM performs in Stokes Space.This is favourable, because Quantity in the possible incoming symbol 311 of the input of XPOLM compensating unit is mapped in Stokes Space reduce number The possible point (compared to Jones space) of amount, so that being determined to become of reliable statistics based on the symbol reducing quantity can Can, and so that for the tracking of the change (being caused by XPOLM) rapidly of the rotation of the polarization of optical signal received and Compensation is possibly realized.

Input signal (or incoming symbol) 311 is two polarization tributary X at the output of CMA unit 203_kAnd Y_k.Use with The two is polarized tributary X by lower equation_kAnd Y_kIt is transformed in Stokes Space:

S_0,k=| X_k|²+|Y_k|²

S_1,k=(| X_k|²-|Y_k|²)/S_0,k

$S_{2,k}=2\mathrm{Re}\left\{X_k{Y}_k^{*}\right\}/S_{0,k}$

$S_{3,k}=-2\mathrm{Im}\left\{X_k{Y}_k^{*}\right\}/S_{0,k}$

Wherein k is the index (in brief, k can be referred to as the moment) of the symbol at mark particular moment, and wherein S_1,k, S_2,k, S_3,kIt it is the Stokes' parameter 411 forming Stokes Vector.Conversion mentioned above Jones to stoke This module 301 performs (seeing Fig. 4 a).So, Jones is configured to the symbol in Jones space to Stokes module 301 Number sequence (X_kAnd Y_k) the 311 symbol sebolic addressing S being converted in Stokes Space_1,k, S_2,k, S_3,k411.It should be noted that, X_kAnd Y_k It it is complex values.

Following step is that covariance matrix is average.In other words, size N is used_MAMoving average filter, by this Symbol sebolic addressing S in lentor space_1,k, S_2,k, S_3,k411 are used for determining covariance coefficient C_nm,k.Illustrate association in fig. 4b Variance determines the block diagram of unit 302.Use following rolling average equation to determine covariance coefficient C_nm,k, and n, m=1 ..., 3:

MA: moving average filter:

Rolling average length: N_MA=2N+1

In superincumbent equation, point () represents product S_n,k S_m,k.As result, it is thus achieved that covariance matrix C, it is Symmetrical and positive definite:

$C=\left[\begin{array}{ccc}{C}_{11}& C_{12}& C_{13}\\ C_{12}& C_{22}& C_{23}\\ C_{13}& C_{23}& C_{33}\end{array}\right]$

So, covariance determines that unit 302 is configured to for each k, i.e. for each moment k, determines covariance system Number C_nm,kSet or covariance matrix C.Covariance coefficient C for moment k_nm,kSet or covariance matrix C can by with Determine the spin matrix for compensating the XPOLM at moment k.

For this purpose, XPOLM compensating unit 204 utilizes performed in covariance analysis unit 303 linear time Return axle matching (the linear regression axle matching being referred to as in figure 3).Can characteristic vector/eigenvalue based on covariance matrix C Analyze and perform linear regression axle matching.For PDM-BPSK modulated signal, the characteristic vector corresponding with eigenvalue of maximum can Following axle to be used to identify in Stokes Space: symbol sebolic addressing is mapped on these axles or around these axles. In preferable (the most undistorted) situation, PDM-BPSK symbol X_kAnd Y_kBe mapped in Stokes Space two possible Point, (S_1,k,S_2,k,S_3,k)=(0 ,-1,0) and (S_1,k,S_2,k,S_3,k)=(0 ,+1,0).Covariance matrix be C's and eigenvalue of maximum Corresponding characteristic vector should indicate the axle of the point including that the two is possible.This axle, i.e. this characteristic vector, it is possible to by with It is rotated in the PDM-BPSK symbol X at moment k_kAnd Y_k, thereby compensate for XPOLM.

For having M > the PDM-MPSK signal of the higher order of 2, such as PDM-QPSK, possible constellation point is positioned at stoke In this space by axle S_2,kAnd S_3,kIn the plane of definition.This is shown in the Poincare sphere 600 of Fig. 6, its axis S_2,kAnd S_3,k 601,602 it is shown as crossing over plane 604.It can be seen that the cloud 605 that PDM-QPSK symbol is formed at around ideal constellation point, Point (the S that ideal constellation point is positioned in plane 604_1,k,S_2,k,S_3,k)=(0 ,-1,1), (S_1,k,S_2,k,S_3,k)=(0,1,1), (S_1,k,S_2,k,S_3,k)=(0 ,-1 ,-1) and (S_1,k,S_2,k,S_3,k)=(0,1 ,-1) place.Additionally, illustrate S₁Axle 603, it is with flat Face 604 is orthogonal.When lacking XPOLM, S₁Axle 603 can be confirmed as the corresponding with minimal eigenvalue of covariance matrix C Characteristic vector.This axle 603 uniquely identifies plane 604 and can be by the case of PDM-MPSK modulated signal (M > 2) It is used for determining spin matrix.

For showing for the efficiently calculating of the characteristic vector of PDM-BPSK and PDM-MPSK (M > 2) (such as PDM-QPSK) Example scheme illustrates below:

$1.\stackrel{\‾}{C}=(C_{11}+C_{22}+C_{33})/3$

$2.D_{11}=C_{11}-\stackrel{\‾}{C};D_{22}=C_{22}-\stackrel{\‾}{C};D_{33}=C_{33}-\stackrel{\‾}{C}$

$3.p=(D_{11}^2+D_{22}^2+D_{33}^2+{2C}_{12}^2+{2C}_{13}^2+{2C}_{23}^2)/6$

$4.q=(D_{11}{D}_{22}{D}_{33}+2C_{12}{C}_{13}{C}_{23}-C_{12}^2{D}_{33}^2-C_{13}^2{D}_{22}-C_{23}^2{D}_{11})/2$

$7.A=\left[\begin{array}{c}{C}_{11}-\mathrm{\λ}\\ C_{12}\\ C_{13}\end{array}\right]B=\left[\begin{array}{c}{C}_{12}\\ C_{22}-\mathrm{\λ}\\ C_{23}\end{array}\right]$

8.v=A × B.

$9.v\←\frac{v}{\left|\right|v\left|\right|}$

It should be noted that, what the direction of characteristic vector typically obscured.In order to prevent the vibration in the direction of characteristic vector, permissible Use following alignment scheme so that the ambiguity removed in characteristic vector direction:

If ${\stackrel{\→}{V}}_{k+1}\·{\stackrel{\→}{V}}_k\≥0,$ SoOtherwise

This technology can be referred to as three-dimensional and open, because it is similar to opening for phase place, but its operation is in 3-dimensional In Stokes Space.The technology of opening is shown in the vector diagram 420 of Fig. 4 c.If it can be seen that characteristic vector v_k413 tools It is related to characteristic vector v subsequently_k+1The rightabout of 414, characteristic vector v the most subsequently_k+1The direction of 414 is reverse, by This maintains the direction of these characteristic vectors.

Once have determined that characteristic vector v of covariance matrix C_k413 is (relative with minimum or eigenvalue of maximum respectively Should), inverse Jones matrix unit 304 (also referred to as spin matrix determines unit 304) determines that spin matrix, and this spin matrix is used In Jones space, symbol sebolic addressing 311 is rotated in using rotary unit 305.The feature that inverse Jones matrix module 304 will be calculated DUAL PROBLEMS OF VECTOR MAPPING is multiplied by incoming Jones's vector 311 to 2x2 plural number Jones matrix J, this matrix J, in order to equilibrium XPOLM.

Spin matrix J can determine as follows.In Stokes Space, determined by characteristic vector by means of three-dimensional revolve Turn can in the case of PDM-BPSK with S₂Axle be directed at, and in the case of PDM-QPSK with S₁Axle is directed at.With Stokes Any rotation in space is corresponding, there is the two-dimensional transform of equivalent in Jones space.Assume the spy of general three-dimensional rotation Levy the axle being to rotate701 and the plane 703 vertical with rotary shaft 701 in the angle of rotation702, such as institute in Fig. 7 Illustrate.Correspondent transform in Jones space is:

Wherein:

$I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]{\mathrm{\σ}}_1=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]{\mathrm{\σ}}_2=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]{\mathrm{\σ}}_3=\left[\begin{array}{cc}0& -j\\ j& 0\end{array}\right]$

$\stackrel{\→}{\mathrm{\σ}}={({\mathrm{\σ}}_1,{\mathrm{\σ}}_2,{\mathrm{\σ}}_3)}^T$

The output assuming linear regression axle fitting module isWherein in the case of PDM-BPSK to AmountShould be with S₂Axle is directed at, and wherein vector in the case of PDM-MPSK (M > 2) (such as PDM-QPSK)Should be with It is perpendicular to S_2,k、S_3,kThe S of plane 604₁Axle 603 is directed at.It is to say, in the case of PDM-BPSK,It is S₂Axle withIt Between angle, andIt isWith along S₂The cross product of the unit vector of axle.PDM-MPSK's (M > 2) (such as PDM-QPSK) In situation, S₂Axle is by S₁Axle replaces.Jones matrix J (also referred to as spin matrix) for PDM-BPSK is then given by:

$J_{\mathrm{BPSK}}=\left[\begin{array}{cc}{J}_{11}& J_{12}\\ J_{21}& J_{22}\end{array}\right]$

And

$J_{11}=\cos \left[\frac{1}{2}a\cos \left(v_k^2\right)\right]+j\frac{v_k^3}{\sqrt{{\left(v_k^1\right)}^2+{\left(v_k^3\right)}^2}}\sin \left[\frac{1}{2}a\cos \left(v_k^1\right)\right],$

$J_{12}=-\frac{v_k^1}{\sqrt{{\left(v_k^1\right)}^2+{\left(v_k^3\right)}^2}}\sin \left[\frac{1}{2}a\cos \left(v_k^1\right)\right],$

$J_{21}=-\frac{v_k^1}{\sqrt{{\left(v_k^1\right)}^2+{\left(v_k^3\right)}^2}}\sin \left[\frac{1}{2}a\cos \left(v_k^1\right)\right],$ And

$J_{22}=\cos \left[\frac{1}{2}a\cos \left(v_k^2\right)\right]-j\frac{v_k^3}{\sqrt{{\left(v_k^1\right)}^2+{\left(v_k^3\right)}^2}}\sin \left[\frac{1}{2}a\cos \left(v_k^1\right)\right]$

And for PDM-MPSK (M > 2) (such as PDM-QPSK) it is:

$J_{\mathrm{MPSK}}=\left[\begin{array}{cc}\cos \left[\frac{1}{2}a\cos \left(v_k^1\right)\right]& -\frac{-v_k^2+j{v}_k^3}{\sqrt{{\left(v_k^2\right)}^2+{\left(v_k^3\right)}^2}}\sin \left[\frac{1}{2}a\cos \left(v_k^1\right)\right]\\ \frac{-v_k^2-j{v}_k^3}{\sqrt{{\left(v_k^2\right)}^2+{\left(v_k^3\right)}^2}}\sin \left[\frac{1}{2}a\cos \left(v_k^1\right)\right]& \cos \left[\frac{1}{2}a\cos \left(v_k^1\right)\right]\end{array}\right]$

Details for the calculating of Jones matrix (spin matrix) J provides at Kogelnik, H.；Nelson,L.E.； Gordon,J.P.,“Emulation and inversion of polarization-mode dispersion,” Lightwave Technology, Journal of, in vol.21, no.2, pp.482-495, Feb.2003, it is by quoting And be incorporated to.

In other words, can state that inverse Jones matrix module 304 is configured to determine that characteristic vectorWith corresponding acquiescence (it is S in the case of PDM-BPSK to axle₂Axle, and at PDM-MPSK, M > it is S in the case of 2₁Axle 603) between angle. Additionally, inverse Jones matrix module 304 is configured to determine that following rotary shaft: determined by angle will be used in this rotary shaft Around.Then angle determined by with is transformed to Jones space from Stokes Space, thus around the rotation of rotary shaft Produce spin matrix J mentioned above.So, inverse Jones matrix module 304 generates a kind of unitary transformation, this unitary transformation etc. Imitate in by characteristic vectorTake S to₂Axle (in the case of PDM-BPSK) or take S to₁Axle (at PDM-MPSK, M > situation of 2 In) Stokes Space rotation process.

Finally, in rotary unit 305, calculate XPOLM as follows compensate symbol

$\left[\begin{array}{c}{\hat{X}}_k\\ {\hat{Y}}_k\end{array}\right]=J\left[\begin{array}{c}{X}_k\\ Y_k\end{array}\right]$

Wherein J is J_BPSKOr J_QPSK。

Fig. 5 a show three kinds of different situations of use (do not compensate 501, use determine orientation method 502 and use blind- XpolE 503) the probability density function (pdf) 500 in linear-scale.INF and error free waveform through binary marks Corresponding.It can be seen that the pdf of the blind-XpolE described in use presents produces notable pdf binary for INF. Fig. 5 b shows (do not compensate 511, use decision orientation method 512 and use blind-XpolE 513) probability in logarithmic scale The pdf 510 of density function (pdf) 500.It can be seen that at probability 10E-2, blind-XpolE algorithm shows relative to not mending Repay the gain of the 1.6dB of situation.

When lacking XPOLM, typical coherent receiver Q²The factor is floated at below 0.5dB.But, there is XPOLM Time, Q²The factor is floated and is reached up to 5dB, and this ratio does not has big 10 times of value during XPOLM.These floatings can be divided by their probability Cloth function (pdf) comes quantitatively.From Fig. 5 a and 5b it can be seen that the use to blind-XpolE makes about the one of measured waveform Half is error free.

Proposed algorithm implements the quick scattering around a kind of acquiescence constellation point for correction on Poincare sphere Method.The hypothesis of blind-XpolE is: on average, and the signaling point position in Stokes Space is in correct constellation point, i.e. It is ± S for PDM-BPSK₂.This assumes to be probably mistake in some cases.In such a case, it is possible to use double Phase algorithm.XPOLM is corrected, there is relatively long average window N_MA1The first blind-XpolE block can be to have subsequently The shorter averaging window lengths N suitably selected_MA2The second blind-XpolE block.In this dual-stage configures first piece is put down All go out noise and XPOLM, and the mean state of polarization can be corrected to be suitable for the requirement of second piece.Second piece such as institute the most above Operate as description, have been concentrated in correct constellation point for the most correctly assuming this signal averaging.

This algorithm can be configured to length N being adaptive to for determining covariance_MA.Side based on Stokes Vector The statistical analysis of difference, to N_MASelf adaptation be possible.For PDM-BPSK modulation format, it may be considered that Stokes' parameter S₂。S₂Auto-correlation be that there is the function in the equal monotone decreasing in positive number side and negative side that peak value is zero.Can be by for difference Delayed n and cross over k and come product S_2,k S_2,k+nIt is averaged, to determine S₂Auto-correlation.Observable the two of auto-correlation function At half maximum of side, full duration (FWHM) indicates for N_MAProbable value.In the case of PDM-MPSK M > 2, can be with Similar mode considers S₁Auto-correlation function.

This algorithm can be scaled up to PS-QPSK (polarization shift or polarization switch QPSK) modulation format.Due at PS- Phase correlation between two polarized components in the case of QPSK, this modulation format has identical with PDM-BPSK Pang Add the expression on Lay ball.Due to the signal in blind-XpolE Algorithm Analysis Stokes Space, so it works well equally And the mode identical with PDM-BPSK is used for PS-QPSK.But, for PS-QPSK, this algorithm may need to be embedded into In suitable DSP block.For the order of DSP block may is that polarization demultiplexing (it is generally not capable of utilizing CMA to complete because PS-QPSK with CMA is incompatible), the blindest-XpolE and be finally the phase ambiguity block that PS-QPSK is typically required.

As already indicated above, blind-XpolE algorithm can be adapted to and PDM-MPSK (M > 2) (such as PDM- QPSK) modulation format works together.As illustrated in FIG. 6, signal expression on Poincare sphere is in the feelings of PDM-MPSK (M > 2) Condition is different.Geometry lexical or textual analysis should correspondingly be modified, and should identify PDM-QPSK constellation point and cross over it and determined Unique plane of position.This is corresponding to calculating the characteristic vector corresponding with the minimal eigenvalue of the covariance matrix of signal.This calculation Other parts of method are identical with the algorithm for PDM-BPSK.PDM-QPSK as already indicated above, on Poincare sphere Represent four points 605 including in plane 604.Contrary with the situation of PDM-BPSK, in PDM-QPSK, blind-XpolE 304 marks Know constellation plane 604, by " minimum " characteristic vector (indicated by the arrow 603 in Fig. 6) of the covariance matrix of signal Be given.

In this document, it has been described that for compensating the method and system of the XPOLM in optical transmission system.These methods The conversion from Jones space to Stokes Space is utilized, in order to reduce the number in site (constellation point for different) with system Amount, so that the determination of the reliable statistics on short observation window is possibly realized, and to relatively quick Tracking and the compensation of XPOLM phenomenon are possibly realized.These method and systems can be complicated with relatively low calculating in the digital domain Degree is implemented, without applying XPOLM compensation method in light level.

It should be noted that, this description and accompanying drawing only illustrate the principle of proposed method and system.Therefore it will be appreciated that Although those skilled in the art embodies the former of the present invention by designing that be not explicitly described herein or illustrate Manage and be included in the various layouts in its spirit and scope.Additionally, all examples described herein are the brightest Really it is intended to be only used for instructing purpose with the principle of the method and system proposed by auxiliary reader understanding and by inventor's tribute The concept in order to promote this area offered, and be to be interpreted as being not restricted to the most concrete example recorded and condition.Additionally, Principle, aspect and the embodiment of notebook invention and all statements of their concrete example herein are intended to contain them Equivalent.

Additionally, it should be noted that the assembly of the step of various method described above and described system can be by warp The computer of programming performs.In this article, some embodiments also attempt to overlay program storage device, such as numerical data storage Medium, these program storage devices are machines or computer-readable and can perform machine or computer is executable Instruction repertorie encodes, and wherein said instruction performs some in the step of described method described above or all steps Suddenly.Program storage device it may be that such as, the magnetic storage medium of digital memory, such as Disk and tape, hard drives or The readable digital data storage medium of person's light.Each embodiment alsos attempt to cover and is programmed to execute the described of method described above The computer of step.

Additionally, it should be noted that software can be performed by using specialised hardware and can be associated with suitable software Hardware, the function of various elements described in this patent document is provided.When provided by a processor, these functions can With by single specialized processor, by single shared processor or provided by multiple individual processors, these multiple individual at Some individual processors in reason device can be shared.Additionally, to the clearly use of term " processor " or " controller " not Should be interpreted to refer exclusively to be able to carry out the hardware of software, and can be impliedly without including digital signal with limiting Processor (DSP) hardware, network processing unit, special IC (ASIC), field programmable gate array (FPGA), it is used for storing The read only memory (ROM) of software, random access storage device (RAM) and nonvolatile memory.Can also include that other are normal Hardware that is that advise and/or that customize.

Finally, it is to be noted that any block diagram herein illustrates the concept of the illustrative circuit of the principle embodying the present invention View.Similarly, it will be appreciated that any flow chart, flow chart, state transition diagram, false code etc. represent can substantially table The various processes showing in computer-readable medium and so performed by computer or processor, regardless of whether clearly Show such computer or processor.

Claims (15)

1. a coherent optical heterodyne communicatio, is adapted to be and receives the optical signal transmitted by optical transport channel, and described coherent light connects Receipts machine includes:

-conversion and processing unit, be adapted to be and generate digital signal set based on the optical signal received, and wherein said light passes Defeated channel represents cross-polarization modulation XPOLM, and the optical signal wherein received includes the first polarized component and the second polarization Component, and wherein said first polarized component and described second polarized component include M respectively^aryPhase-shift keying (PSK) MPSK symbol sequence Row, M is integer, and M > 2；

-polarization demultiplexing unit, is adapted to be and is demultiplexing as described digital signal set answering along the first of the first polarization axle Number component and the second complex number components along the second polarization axle, wherein said first complex number components is included at follow-up moment k The first complex sampling sequence, k=1 ..., K, K are integers, K > 1；And

-XPOLM compensating unit, is adapted to be:

-described first complex number components and described second complex number components are transformed in Stokes Space, thus produce stoke This parameter sets；

-based on described Stokes' parameter set, determine described first polarization axle and described second polarization transformation of axis；And

-by converting described first plural number according to the described conversion of described first polarization axle determined and described second polarization axle Component and described second complex number components, to determine the first complex number components that XPOLM compensates and the second plural number point that XPOLM compensates Amount.

Coherent optical heterodyne communicatio the most according to claim 1, wherein:

-described second complex number components is included in the second complex sampling sequence at described follow-up moment k；

-described XPOLM compensating unit is adapted to be:

-described first complex sampling sequence at described moment k and described second complex sampling sequence, determine respectively in institute State the Stokes' parameter sequence of sets at moment k；

-based on described Stokes' parameter sequence of sets, determine described first polarization axle and described second at described moment k Polarization transformation of axis；And

-become by described first polarization axle at described moment k determined by basis and described second polarization transformation of axis Change the described first complex sampling sequence at described moment k and described second complex sampling sequence, to determine respectively described The second complex sampling sequence that first complex sampling sequence of the XPOLM compensation at moment k and XPOLM compensate.

Coherent optical heterodyne communicatio the most according to claim 2, wherein:

-described Stokes' parameter sets spans three-dimensional Stokes Space；

-described XPOLM compensating unit is adapted to be subspace fitting to described Stokes' parameter sequence of sets；

The subspace of-institute matching has the dimension lower than described Stokes Space；And-described XPOLM compensating unit quilt It is adapted for subspace based on institute's matching and determines described first polarization axle and the rotation of described second polarization axle.

Coherent optical heterodyne communicatio the most according to claim 2, wherein said XPOLM compensating unit is adapted to be:

-based on the described Stokes' parameter sequence of sets at described moment k, determine described at described moment k this The covariance coefficient of Stokes parameter；And

-based on determined by described covariance coefficient at described moment k, determine this torr described at described moment k The characteristic vector of the covariance matrix of gram this parameter.

Coherent optical heterodyne communicatio the most according to claim 4, wherein:

-described XPOLM compensating unit is adapted to be the use rolling average across N number of moment to determine described covariance coefficient；And And

-N speed based on the change caused by XPOLM.

Coherent optical heterodyne communicatio the most according to claim 5, wherein said XPOLM compensating unit is adapted to be:

-for multiple time lags, determine the auto-correlation letter of at least one Stokes' parameter in described Stokes' parameter Number；And

-determine N based on described auto-correlation function.

Coherent optical heterodyne communicatio the most according to claim 4, wherein said XPOLM compensating unit is adapted to be elimination follow-up Moment at determined by the ambiguity in direction of characteristic vector.

Coherent optical heterodyne communicatio the most according to claim 4, wherein:

-the optical signal that received is partially to divide multiplexing PDM bpsk signal or polarization switch PSQPSK signal；And

-described XPOLM compensating unit be adapted to be the feature corresponding with eigenvalue of maximum determining described covariance matrix to Amount.

Coherent optical heterodyne communicatio the most according to claim 4, wherein:

-the optical signal that received is PDM mpsk signal and M > 2；And

-described XPOLM compensating unit be adapted to be the feature corresponding with minimal eigenvalue determining described covariance matrix to Amount.

Coherent optical heterodyne communicatio the most according to claim 4, wherein said XPOLM compensating unit is adapted to be:

-determine determined by angle between acquiescence axle in characteristic vector and described Stokes Space；

-rotary shaft is defined as with determined by the perpendicular axle of the plane crossed over of characteristic vector and described acquiescence axle；And

-based on described angle and described rotary shaft, determine described first polarization axle and the described rotation of described second polarization axle.

11. coherent optical heterodyne communicatios according to claim 1, wherein:

-described XPOLM compensating unit is adapted to be, and based on the long-time statistical derived from described Stokes' parameter set, determines The second complex number components that first complex number components of described XPOLM compensation and described XPOLM compensate；

-described coherent optical heterodyne communicatio includes the 2nd XPOLM compensating unit, is adapted to be:

The second complex number components that-the first complex number components of being compensated by described XPOLM and described XPOLM compensate transforms to this torr described In gram this space, thus produce other Stokes' parameter set；And

-based on the short term statistics derived from described other Stokes' parameter set, the first plural number compensated from described XPOLM The second complex number components that component and described XPOLM compensate determines the first complex number components that other XPOLM compensates and other The second complex number components that XPOLM compensates；

-the time interval that considered by described long-time statistical is more than the time interval considered by described short term statistics.

12. coherent optical heterodyne communicatios according to claim 1, wherein said first polarization axle and described second polarization axle about It is orthogonal each other.

13. 1 kinds of coherent optical heterodyne communicatios, are adapted to be and receive the optical signal transmitted by optical transport channel, and described coherent light connects Receipts machine includes:

-conversion and processing unit, be adapted to be and generate digital signal set based on the optical signal received, and wherein said light passes Defeated channel represents cross-polarization modulation XPOLM, and the optical signal wherein received includes the first polarized component and the second polarization Component, and wherein said first polarized component and described second polarized component include M respectively^aryPhase-shift keying (PSK) MPSK symbol sequence Row, M is integer, and M > 2；

-polarization demultiplexing unit, is adapted to be and is demultiplexing as described digital signal set answering along the first of the first polarization axle Number component and the second complex number components along the second polarization axle, wherein said first complex number components is included at follow-up moment k The first complex sampling sequence, k=1 ..., K, K are integers, K > 1；And

-XPOLM compensating unit, is adapted to be:

-described first complex number components and described second complex number components are transformed in Stokes Space, thus produce stoke This parameter sets；

-based on described Stokes' parameter set, determine described first polarization axle and described second polarization transformation of axis；And

-by converting described first plural number according to the described conversion of described first polarization axle determined and described second polarization axle Component and described second complex number components, to determine the first complex number components that XPOLM compensates and the second plural number point that XPOLM compensates Amount；Wherein:

-described first complex number components and described second complex number components are complex number components X_kAnd Y_k；And

-described Stokes' parameter set includes the one or more elements in last three elements in list below:

S_0,k=| X_k|²+|Y_k|²

S_1,k=(| X_k|²-|Y_k|²)/S_0,k

$S_{2,k}=2\mathrm{Re}\left\{X_k{Y}_k^{*}\right\}/S_{0,k}$

$S_{3,k}=-2Im\left\{X_k{Y}_k^{*}\right\}/S_{0,k}.$

14. 1 kinds of coherent optical heterodyne communicatios, are adapted to be and receive the optical signal transmitted by optical transport channel, and described coherent light connects Receipts machine includes:

-conversion and processing unit, be adapted to be and generate digital signal set based on the optical signal received, and wherein said light passes Defeated channel represents cross-polarization modulation XPOLM, and the optical signal wherein received includes the first polarized component and the second polarization Component, and wherein said first polarized component and described second polarized component include M respectively^aryPhase-shift keying (PSK) MPSK symbol sequence Row, M is integer, and M > 2；

-polarization demultiplexing unit, is adapted to be and is demultiplexing as described digital signal set answering along the first of the first polarization axle Number component and the second complex number components along the second polarization axle, wherein said first complex number components is included at follow-up moment k The first complex sampling sequence, k=1 ..., K, K are integers, K > 1；And

-XPOLM compensating unit, is adapted to be:

-described first complex number components and described second complex number components are transformed in Stokes Space, thus produce stoke This parameter sets；

-based on described Stokes' parameter set, determine described first polarization axle and described second polarization transformation of axis；And

-by converting described first plural number according to the described conversion of described first polarization axle determined and described second polarization axle Component and described second complex number components, to determine the first complex number components that XPOLM compensates and the second plural number point that XPOLM compensates Amount；Wherein:

-described first complex number components and described second complex number components are indicated in Jones space；And

The quantity in the site of-MPSK symbol sebolic addressing in described Stokes Space and the site in described Jones space Quantity compares and is reduced.

The method of 15. 1 kinds of cross-polarization modulation XPOLM in the optical signal alleviating reception, described method includes:

-generating digital signal set based on the optical signal received, the optical signal wherein received includes the first polarized component With the second polarized component, and wherein said first polarized component and described second polarized component include M respectively^aryPhase-shift keying (PSK) MPSK symbol sebolic addressing, M is integer, and M > 2；

-described digital signal set is demultiplexing as in the first polarization axle be referred to as the first complex number components the first two dimensional component and The second complex number components in second polarization axle, wherein said first complex number components is included in the first plural number at follow-up moment k Sample sequence, k=1 ..., K, K are integers, K > 1；And

-described first complex number components and described second complex number components are transformed in Stokes Space, thus produce stoke This parameter sets；

-based on described Stokes' parameter set, determine described first polarization axle and the rotation of described second polarization axle；And

-by rotating described first plural number according to the described rotation of described first polarization axle determined and described second polarization axle Component and described second complex number components, to determine the first complex number components that XPOLM compensates and the second plural number point that XPOLM compensates Amount.