CN109217934B

CN109217934B - A Polarization Demultiplexing Algorithm Based on Maximum Likelihood Independent Component Analysis

Info

Publication number: CN109217934B
Application number: CN201811098227.9A
Authority: CN
Inventors: 杨彦甫; 范林生; 张群
Original assignee: Harbin Institute of Technology Shenzhen
Current assignee: Harbin Institute of Technology Shenzhen
Priority date: 2018-09-20
Filing date: 2018-09-20
Publication date: 2020-04-21
Anticipated expiration: 2038-09-20
Also published as: CN109217934A

Abstract

The invention provides a polarization demultiplexing algorithm based on the maximum likelihood independent component analysis method, uses ML-ICA to estimate the inverse Jones matrix W , and uses the input and output mutual information of the X polarization state and the Y polarization state to maximize, thereby To achieve the purpose of polarization demultiplexing. The beneficial effect of the present invention is that it can be used for any modulation format, and can tolerate a large IQ imbalance at the same time.

Description

Polarization demultiplexing algorithm based on maximum likelihood independent component analysis method

Technical Field

The invention relates to communication, in particular to a polarization demultiplexing algorithm based on a maximum likelihood independent component analysis method.

Background

With the advent of large data centers and the increase in communication traffic, communication capacity is increasing. Coherent optical communication systems combining digital signal processing techniques and advanced modulation formats are known as effective solutions for increasing system capacity. Among them, the Polarization Division Multiplexed (PDM) coherent optical communication system multiplies the system capacity by transferring information using two Polarization states of an optical signal. However, due to defects and random birefringence effects in the optical fiber, polarization crosstalk often exists between signals in two polarization states. Therefore, polarization multiplexing systems require a reliable polarization demultiplexing algorithm to separate the two aliased polarization state signals.

Conventional polarization demultiplexing algorithms, such as Constant Modulus Algorithm (CMA), multimode algorithm (MMA), rely on fixed reference constellation points and therefore can only be used for fixed modulation formats. However, when there is IQ imbalance, modulation nonlinearity or modulation format change in the system, the reference constellation point will change. At this time, the performance of the conventional polarization demultiplexing algorithm may be seriously degraded, and even the convergence fails.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a polarization demultiplexing algorithm based on a maximum likelihood independent component analysis method, which can be used for any modulation format and can tolerate larger IQ imbalance.

The invention provides a polarization demultiplexing algorithm based on a maximum likelihood independent component analysis method,

estimating an inverse Jones matrix W by using ML-ICA, and using input and output mutual information of an X polarization state and a Y polarization state to achieve the maximum, thereby realizing the purpose of polarization demultiplexing;

U＝WZ

wherein Z is an input signal and U is an output signal;

the cost function of the mutual information maximization algorithm is as follows:

J(W)＝H(U)＝-E{ln P_U(U)} (1)

wherein E and

respectively representing the operations of calculating the expectation and the partial derivative; h, (U), P_U(U), g (U), and tanh (U) represent an entropy function, a Probability Density Function (PDF), an Activation function (Activation function), and a tangent function, respectively, of the output signal;

according to the principle of gradient descent, the information content of the inverse jones matrix is:

wherein

As an evaluation function (Score function);

to avoid matrix inversion, natural gradients are referenced:

W_k+1＝W_k+ΔW_k(8)

ΔW_k＝(I+φ(U_k)U_k ^H)W_k(9)

φ(U_k)＝-2tanh(U_k) (10)

wherein I represents a unit array, subscript "_X/Y"represents the X polarization state and the Y polarization state, subscript" k "represents a time sequence number, and the ML-ICA iteratively updates the parameters of the butterfly filter according to the principle of a mutual information maximization algorithm (infomax), thereby realizing polarization demultiplexing.

The invention has the beneficial effects that: can be used for any modulation format, and can tolerate larger IQ imbalance.

Drawings

Fig. 1 is a schematic diagram illustrating the principle of the polarization demultiplexing algorithm based on the maximum likelihood independent component analysis method according to the present invention.

FIG. 2 is a schematic diagram of PDM-QPSK polarization demultiplexing of a polarization demultiplexing algorithm based on maximum likelihood independent component analysis of the present invention.

FIG. 3 is a schematic diagram of PDM-16QAM polarization demultiplexing of a polarization demultiplexing algorithm based on maximum likelihood independent component analysis.

FIG. 4 is a schematic diagram of PDM-16QAM polarization demultiplexing when IQ imbalance exists in a polarization demultiplexing algorithm based on maximum likelihood independent component analysis of the present invention.

Detailed Description

The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.

The invention provides a polarization demultiplexing algorithm based on a maximum likelihood independent component analysis method, which considers constellation point distortion caused by system damage and the requirements of various modulation formats in a dynamic optical network. The algorithm can be used for any modulation format, and can tolerate larger IQ imbalance.

A polarization demultiplexing algorithm based on Maximum likelihood independent component analysis (ML-ICA) estimates an inverse Jones matrix W by using the ML-ICA, and maximizes input and output mutual information of X and Y polarization states, thereby realizing the purpose of polarization demultiplexing.

U＝WZ

Where Z is the input signal and U is the output signal.

The cost function of the mutual information maximization algorithm (Infmax) is:

J(W)＝H(U)＝-E{ln P_U(U)} (1)

wherein E and

representing the operations of calculating the desired and partial derivatives, respectively. H, (U), P_U(U), g (U), and tanh (U) represent an entropy function, a Probability Density Function (PDF), an Activation function (Activation function), and a tangent function, respectively, of the output signal.

wherein

As an evaluation function (Score function).

To avoid matrix inversion, natural gradients are referenced:

the implementation of the present invention is shown in fig. 1.

W_k+1＝W_k+ΔW_k(8)

ΔW_k＝(I+φ(U_k)U_k ^H)W_k(9)

φ(U_k)＝-2tanh(U_k) (10)

Wherein I represents a unit array. Subscript "_X/Y"represents the X and Y polarization states. The subscript "k" represents a time series number. The ML-ICA iteratively updates the parameters of the butterfly filter according to the principle of infomax, thereby implementing polarization demultiplexing, as in fig. 1.

ML-ICA was tested in a PDM system with a signal-to-noise ratio of 20dB and a baud rate of 14 Gbaud. The polarization demultiplexing algorithm based on the maximum likelihood independent component analysis method provided by the invention is used for polarization multiplexing of PDM-QPSK, PMD-16QAM and PMD-16QAM with IQ imbalance (4dB amplitude imbalance and 40-degree phase imbalance), and the result is shown in figures 2-4. The result shows that the invention can be used for polarization demultiplexing of different modulation formats and has strong tolerance to IQ imbalance.

The invention provides a polarization demultiplexing algorithm based on a Maximum likelihood independent component analysis method, and provides a Maximum likelihood independent component analysis algorithm (ML-ICA) for recovering a polarization state of a coherent optical communication system. The scheme maximizes the mutual information between the input signal and the output signal according to the maximum likelihood method, thereby achieving the purpose of polarization demultiplexing. The scheme has the characteristic of code pattern independence, and can tolerate larger In-phase/quadrature component (IQ) imbalance and modulation nonlinearity.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims

1. a polarization demultiplexing algorithm based on maximum likelihood independent component analysis method, is characterized in that:

The inverse Jones matrix W is estimated by the maximum likelihood independent component analysis method, and the input and output mutual information of the X polarization state and the Y polarization state are used to achieve the maximum, so as to achieve the purpose of polarization demultiplexing;

U=WZ

Where Z is the input signal, U is the output signal;

The cost function of the mutual information maximization algorithm is:

J(W)=H(U)=-E{ln P _U (U)} (1)

where E and

Represent the operations of finding expectation and finding partial derivatives, respectively; H(U), P _U (U), g(U), and tanh(U) represent the entropy function, probability density function, activation function and tangent function of the output signal, respectively; According to the principle of gradient descent, the information content of the inverse Jones matrix is:

in

is the evaluation function (Score function);

To avoid matrix inversion, quote the natural gradient:

W _k+1 =W _k +ΔW _k (8)

ΔW _k =(I+φ(U _k )U _k ^H )W _k (9)

φ(U _k )=-2tanh(U _k ) (10)

where I represents the unit matrix, the subscript " _X/Y " represents the X polarization state and the Y polarization state, and the subscript "k" represents the time sequence number. The maximum likelihood independent component analysis method iteratively updates the butterfly according to the principle of mutual information maximization algorithm. parameters of the type filter, thereby realizing polarization demultiplexing.