CN103684617B - A kind of light divides the method for multiplexing 16-QAM coherent communication system demultiplexing partially - Google Patents

Abstract

The invention discloses a kind of method that light divides multiplexing 16-QAM coherent communication system demultiplexing partially, comprising: the signal y that receiving terminal of communication system is received _tcarry out the digital signal y that analog-to-digital conversion obtains receiving terminal _i; By independent component analysis adaptive learning receiving terminal digital signal y _ifind at t=iT+t ₀moment transmission matrix W _iinverse matrix wherein, T is the intersymbol time interval, t ₀be the time migration of sampling, i is natural number, described transmission matrix W _iin contain white Gaussian noise, phase noise and random polarization state and rotate impact on signal; According to described transmission matrix W _iinverse matrix K _ito the digital signal y of described receiving terminal _icompensate.Method of the present invention compared with prior art, has higher performance.

Description

A kind of light divides the method for multiplexing 16-QAM coherent communication system demultiplexing partially

Technical field

The present invention relates to communication technical field, particularly a kind of light divides the method for multiplexing 16-QAM coherent communication system demultiplexing partially.

Background technology

16 quadrature amplitude modulation (16-QAM) are one of candidate modulation forms in following optical communication system.Compared with Quadrature Phase Shift Keying (QPSK), it can provide higher spectrum utilization efficiency, but needs higher Optical Signal To Noise Ratio (OSNR) cost simultaneously.A point multiplex technique (PDM) can make power system capacity become original 2 times partially, but it needs the polarization damage be subject in receiving terminal is to transmitting procedure to recover.Be generally used for partially dividing the permanent modeling method (CMA) of multiplexing QPSK coherent reception system polarization demultiplexing extend to partially point multiplexing 16QAM system time, encounter two inherent restrictions.One is singularity problem, and namely the two-way of CMA exports and all converges on same source, this is because two of CMA independent convergences cause; Two is that CMA requires signal to there is constant mould long, and the such multimode modulation format of this and 16-QAM not too meets.Therefore, for PDM16-QAM, we need to find the better Deplexing method of performance.

Independent component analysis (ICA) is the method utilizing statistical property to carry out the linear or nonlinear mixing of separation signal.It utilizes the foundation of independence as separation signal of signal, therefore, it is possible to thoroughly eliminate singularity problem.

Summary of the invention

(1) technical problem that will solve

The technical problem to be solved in the present invention is the method finding the better light of a kind of performance partially to divide multiplexing 16-QAM coherent communication system demultiplexing.

(2) technical scheme

In order to solve the problems of the technologies described above, the invention provides a kind of method that light divides multiplexing 16-QAM coherent communication system demultiplexing partially, comprising:

To the signal y that receiving terminal of communication system receives _tcarry out the digital signal y that analog-to-digital conversion obtains receiving terminal _i;

By receiving terminal digital signal y described in independent component analysis adaptive learning _iat t=iT+t ₀moment transmission matrix W _iinverse matrix wherein, T is the intersymbol time interval, t ₀be the time migration of sampling, i is natural number, described transmission matrix W _iin contain white Gaussian noise, phase noise and random polarization state and rotate impact on signal;

According to described transmission matrix W _iinverse matrix K _ito the digital signal y of described receiving terminal _icompensate.

Wherein, described by receiving terminal digital signal y described in independent component analysis adaptive learning _iat t=iT+t ₀moment transmission matrix W _iinverse matrix K _istep specifically comprise:

Consider that signal is the inverse matrix K of the situation of complex random variable, described transmission matrix _imaximum likelihood logarithm Λ (K _i) be expressed as:

Λ(K _i)=log|detK _i| ²+logp(z _i)

Wherein z _i=K _iy _i, p (z _i) be z _iprobability distribution;

Search makes described K _imaximum likelihood logarithm Λ (K _i) maximum K _i.

Wherein, K is made described in the method by adopting natural water surface coatings to carry out upgrading finds _imaximum likelihood logarithm Λ (K _i) maximum K _i, and simultaneously to receiving terminal digital signal y _icarry out whitening processing;

Wherein, described renewal adopts following more new formula:

K _i+1=[I+μH _φ(z _i)]K _i；

Wherein, μ is adjusting learning rate, I representation unit matrix;

$H_{\mathrm{\φ}}\left(z_i\right)=I-z_i{z}_i^H+\mathrm{\φ}\left(z_i\right)z_i^H-z_i\mathrm{\φ}{\left(z_i\right)}^H,$

The conjugate transpose operator of superscript H representing matrix;

$\mathrm{\φ}\left(z_i\right)=\frac{\∂\mathrm{\Λ}\left(K_i\right)}{{\∂K}_i^{*}},$

* Conjugate operator is represented.

Wherein, when considering white Gaussian noise and phase noise, φ (z _i) expression formula be:

$\mathrm{\φ}\left(z_i^n\right)={\mathrm{De}}^{j\left(\arg \right[z_i^n\left]\right)}-z_i^n,$ n=1,2

Wherein (n=1,2) representative is at t=iT+t ₀receiving terminal digital signal after moment n-th polarization branch compensates, represent and get complex variable argument; After compensating, the mould of 16-QAM planisphere is long is distributed as the ring that 3 have one fixed width, and D is the mean value of the radius of outermost side ring and the radius of adapter ring here.

Wherein, described adjusting learning rate μ is determined by method below:

μ=μ ₀·h _i，

$h_i=\mathrm{mean}\left(h_i^n\right),$ (n=1,2)，

$h_i^n=\left|\right|z_i^n|-r_{\mathrm{im}}^n|,$ (n=1,2;m=1,2,3)；

Wherein, μ ₀represent initial learning rate, h _irepresent the module of two polarization branch convergences with mean value, mean operator representation gets the module of two polarization branch convergence with mean value, m represents the m ring of desirable 16-QAM planisphere, represent the radius of the desirable 16-QAM planisphere m ring that the receiving terminal digital signal distance after compensating with the n-th polarization branch is the shortest, || represent and ask modular arithmetic.

Wherein, described method adopts butterfly digital filter to realize, and described butterfly digital filter comprises a classical butterfly structure filter and a convergence metric module.

(3) beneficial effect

The present invention proposes improvement independent component analysis (MICA) method for the inclined decomposition multiplex of PDM16-QAM.The method, while elimination singularity problem, improves the constringency performance of system.And newly propose the method that calculates the convergence of inclined decomposition multiplex, based on this method, the learning rate of MICA adaptively modifying method.

Accompanying drawing explanation

Fig. 1 is the flow chart of embodiment of the present invention Deplexing method;

Fig. 2 is the schematic diagram of embodiment of the present invention convergence module;

Fig. 3 is the structural representation of embodiment of the present invention digital signal processing module;

Fig. 4 is the flow chart that the method for the embodiment of the present invention is realized by butterfly digital filter;

Fig. 5 a and 5b is the test result of CMA and MICA algorithm opposing singularity ability respectively;

Fig. 6 a and 6b is that in different polarization dependent loss (PDL) situation, the probability of singularity problem appears in CMA and MICA respectively;

Fig. 7 a and 7b be method of the present invention respectively amplitude ratio angle θ be π/6 and π/4 time three kinds of algorithm CMA, ICA and MICA error rate (BRE) Performance comparision.

Embodiment

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.Following examples for illustration of the present invention, but are not used for limiting the scope of the invention.

Suppose that the inclined division multiplex signal of input is x _t, after link transmission, the signal of receiving terminal is y _tif the transfer function of link is W _t, then y is had _t=W _tx _t.The object of inclined decomposition multiplex algorithm is when having white Gaussian noise and phase noise, by adaptive study receiving end signal, finds transmission matrix W _tinverse matrix thus reach the object of compensation.

The present embodiment describes a kind of method that light divides multiplexing 16-QAM coherent communication system demultiplexing partially, comprising:

S1: the signal y that receiving terminal of communication system is received _tcarry out the digital signal y that analog-to-digital conversion obtains receiving terminal _i;

S2: by receiving terminal digital signal y described in independent component analysis adaptive learning _iat t=iT+t ₀moment transmission matrix W _iinverse matrix wherein, T is the intersymbol time interval, t ₀be the time migration of sampling, i is natural number, described transmission matrix W _iin contain white Gaussian noise, phase noise and random polarization state and rotate impact on signal;

S3: according to described transmission matrix W _iinverse matrix K _ito the digital signal y of described receiving terminal _icompensate.

ICA algorithm generally adopts the method for maximal possibility estimation to realize.Consider that signal is the situation of complex random variable, maximum likelihood logarithm is expressed as

Λ(K _i)=log|detK _i| ²+logp(z _i)（1）

Wherein z _i=K _iy _i, p (z _i) be z _iprobability distribution.The task of ICA algorithm searches suitable K _imake Λ (K _i) maximum.At this, we use natural water surface coatings to K _iupgrade.In order to ensure orthogonality, simultaneously will to receiving terminal digital signal y _icarry out whitening processing.

Following more new formula is adopted in the present embodiment:

K _i+1=[I+μH _φ(z _i)]K _i（2）

Wherein μ is learning rate (step-length), I representation unit matrix, and

$H_{\mathrm{\φ}}\left(z_i\right)=I-z_i{z}_i^H+\mathrm{\φ}\left(z_i\right)z_i^H-z_i\mathrm{\φ}{\left(z_i\right)}^H---\left(3\right)$

The conjugate transpose operator of superscript H representing matrix.

And $\mathrm{\φ}\left(z_i\right)=\frac{\∂\mathrm{\Λ}\left(K_i\right)}{{\∂K}_i^{*}}---\left(4\right)$

* Conjugate operator is represented.When considering white Gaussian noise and phase noise, φ (z _i) expression formula be:

$\mathrm{\φ}\left(z_i^n\right)={\mathrm{De}}^{j\left(\arg \right[z_i^n\left]\right)}-z_i^n,$ n=1,2（5）

Wherein (n=1,2) represent the signal after two branch roads compensation, represent and get complex variable argument; D is the mean value of the radius of outermost side ring and the radius of adapter ring in 16-QAM planisphere.

Learning rate is the key factor affecting algorithmic statement performance.We have proposed the adjusting learning rate ICA algorithm for partially dividing multiplexing 16-QAM system.Consider that the probability distribution of the 16-QAM planisphere exported after butterfly filter compensation is 3 rings having one fixed width, we using the point after compensating and it should the distance of ring as the module restrained, as shown in Figure 2, it can be expressed as:

$h_i^n=\left|\right|z_i^n|-r_{\mathrm{im}}^n|,(n=1,2;m=\mathrm{1,2,3})---\left(6\right)$

Wherein at t=iT+t after compensating ₀moment (time interval between T is-symbol, t ₀the time migration of sampling) output signal in the n-th polarization branch, the radius (have 3 kind possibilities) of corresponding output signal apart from the shortest ring, || be ask modular arithmetic.

We define

$h_i=\mathrm{mean}\left(h_i^n\right)(n=1,2)---\left(7\right)$

Mean operator representation gets the module of two polarization branch convergences with mean value.

Adjusting learning rate adopts following formula to obtain:

μ=μ ₀·h _i（8）

Wherein μ 0 is initial learning rate.Generally speaking, it is the value making system BER performance best by choosing after a series of test.The present embodiment utilizes the value of convergence measurement to upgrade the learning rate of ICA, reaches and better restrains effect.

Fig. 2 be convergence module schematic diagram (white point represents 16-QAM planisphere ideally, and dotted line ring represents 3 rings of the microscler one-tenth of 16-QAM constellation point mould, stain be in the n-th polarization branch compensate after sampled point convergence measurement standard it is sampled point to it should the distance of ring.）

The present embodiment whole algorithm butterfly digital filter realizes, and its structure as shown in Figure 3.It comprises a classical butterfly structure filter and a convergence metric module.Wherein be through the signal that other signal process parts are input to filter, n=1,2 represent two polarization states respectively.K ₁₁, K ₁₂, K ₂₁and K ₂₂it is matrix K _ielement, be also simultaneously 4 tap coefficients of butterfly filter.

As shown in Figure 4, after signal is input to described butterfly filter, butterfly filter is according to the K calculated respectively for the flow chart of the present embodiment method realized by butterfly digital filter _iand adjusting learning rate carries out filtering process to signal, the signal after last output filtering.

Build the optical transmission system of a 40Gbaud/s to verify the lifting of MICA to systematic function.Signal introduce by the additive white Gaussian noise introduced by image intensifer, transmitting terminal and local oscillations phase noise, the change at random of polarization state and the impact of polarization associated injury, and do not consider the impact of chromatic dispersion (CD) and polarization mode dispersion (PMD).In system, total live width of transmitting terminal and receiving terminal laser is 1MHz, and the polarization state change at random (namely random polarization state rotates) that optical fiber causes is expressed as:

$T=\left[\begin{array}{cc}\cos \mathrm{\θ}& e^{-\mathrm{j\φ}}\sin \mathrm{\θ}\\ -e^{\mathrm{j\φ}}\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]--\left(9\right)$

Wherein θ is amplitude ratio angle, and it is relevant with the amplitude component of light signal on two mutual perpendicular polarisation state, and meets tan θ=A ₂/ A ₁(A in formula ₁, A ₂represent the amplitude of light signal on two mutual perpendicular polarisation state), φ is the phase difference of light signal on two mutual perpendicular polarisation state.

(1) ability of singularity problem is resisted

First the ability that MICA resists singularity problem is investigated.The performance of CMA and MICA algorithm is compared by testing all possible polarization state situation.The span of amplitude ratio angle θ and phase difference is during test, OSNR is 20dB.Result as shown in figure 5 a and 5b (white represent there is no singularity problem, black represent there occurs singularity problem).

Result shows that CMA exists can there is singularity problem in neighbouring (black part), but MICA singularity problem can not occur.

Polarization Dependent Loss (PDL) can increase the weight of singularity problem.For convenience's sake, we suppose that PDL occurs in two polarization branch just.Under at this, we discuss different PDL situation, the performance of CMA and MICA, as shown in figures 6 a and 6b.Result shows that PDL can increase the weight of the singularity problem of CMA: the angular range of singularity occurs and probability all increases along with the increase of two branch power gaps, and systematic function is by PDL grievous injury; MICA is not then subject to the impact of PDL all the time, still can ensure systematic function two branch power differences up to during 6dB.Visible, MICA algorithm has the ability of very strong opposing singularity problem.

(2) OSNR performance

Choose π/4, θ angle of CMA algorithm generation singularity problem respectively and there are not π/6, θ angle of singularity problem, test the OSNR performance of CMA, ICA and MICA tri-kinds of algorithms, result as shown in figs. 7 a and 7b.When θ=π/6, three kinds of algorithms can normally work.The similar nature of ICA and CMA, and MICA best performance.Be 10 in the error rate ^-3time (forward error correction threshold value), MICA can provide the OSNR of 1dB to promote.And when θ=π/4, CMA is because singularity problem cisco unity malfunction, and consistent during same θ=π/6 of the performance of ICA with MICA.Compared with existing algorithm (CMA, ICA), MICA at least can improve the OSNR of 1dB.

Above execution mode is only for illustration of the present invention; and be not limitation of the present invention; the those of ordinary skill of relevant technical field; without departing from the spirit and scope of the present invention; can also make a variety of changes and modification; therefore all equivalent technical schemes also belong to category of the present invention, and scope of patent protection of the present invention should be defined by the claims.

Claims (5)

1. light divides a method for multiplexing 16-QAM coherent communication system demultiplexing partially, it is characterized in that, comprising:

To the signal y that receiving terminal of communication system receives _tcarry out the digital signal y that analog-to-digital conversion obtains receiving terminal _i;

By receiving terminal digital signal y described in independent component analysis adaptive learning _iat t=iT+t ₀moment transmission matrix W _iinverse matrix wherein, T is the intersymbol time interval, t ₀be the time migration of sampling, i is natural number, described transmission matrix W _iin contain white Gaussian noise, phase noise and random polarization state and rotate impact on signal;

According to described transmission matrix W _iinverse matrix K _ito the digital signal y of described receiving terminal _icompensate;

Described by receiving terminal digital signal y described in independent component analysis adaptive learning _iat t=iT+t ₀moment transmission matrix W _iinverse matrix K _istep specifically comprise:

Consider that signal is the inverse matrix K of the situation of complex random variable, described transmission matrix _imaximum likelihood logarithm Λ (K _i) be expressed as:

Λ(K _i)＝log|detK _i| ²+logp(z _i)

Wherein z _i=K _iy _i, p (z _i) be z _iprobability distribution;

Search makes described K _imaximum likelihood logarithm Λ (K _i) maximum K _i.

2. the method for claim 1, is characterized in that, makes K described in being found by the method adopting natural water surface coatings to carry out upgrading _imaximum likelihood logarithm Λ (K _i) maximum K _i, and simultaneously to receiving terminal digital signal y _icarry out whitening processing;

Wherein, described renewal adopts following more new formula:

K _i+1＝[I+μH _φ(z _i)]K _i；

Wherein, μ is adjusting learning rate, I representation unit matrix;

$H_{\mathrm{\φ}}\left(z_i\right)=I-z_i{z}_i^H+\mathrm{\φ}\left(z_i\right)z_i^H-z_i\mathrm{\φ}{\left(z_i\right)}^H,$

The conjugate transpose operator of superscript H representing matrix;

$\mathrm{\φ}\left(z_i\right)=\frac{\∂\mathrm{\Λ}\left(K_i\right)}{\∂K_i^{*}},$

* Conjugate operator is represented.

3. method as claimed in claim 2, is characterized in that, when considering white Gaussian noise and phase noise, and φ (z _i) expression formula be:

$\mathrm{\φ}\left(z_i^n\right)={\mathrm{De}}^{j(\arg \[z_i^n\])}-z_i^n,n=1,2$

Wherein representative is at t=iT+t ₀receiving terminal digital signal after moment n-th polarization branch compensates, represent and get complex variable argument, j represents complex symbol; The mould of the 16-QAM planisphere after compensation is long is distributed as the ring that 3 have one fixed width, and D is the mean value of the radius of outermost side ring and the radius of adapter ring here.

4. method as claimed in claim 3, it is characterized in that, described adjusting learning rate μ is determined by method below:

μ＝μ ₀·h _i，

$h_i=mean\left(h_i^n\right),(n=1,2),$

$h_i^n=\left|\right|z_i^n|-r_{im}^n|,(n=1,2;m=1,2,3);$

Wherein, μ ₀represent initial learning rate, h _irepresent the module of two polarization branch convergences with mean value, mean operator representation gets the module of two polarization branch convergence with mean value, m represents the m ring of desirable 16-QAM planisphere, represent the radius of the desirable 16-QAM planisphere m ring that the receiving terminal digital signal distance after compensating with the n-th polarization branch is the shortest, || represent and ask modular arithmetic.

5. the method for claim 1, is characterized in that, described method adopts butterfly digital filter to realize, and described butterfly digital filter comprises a classical butterfly structure filter and a convergence metric module.