CN101895499B

CN101895499B - Method for demultiplexing polarization by using constant rotation sign training sequence

Info

Publication number: CN101895499B
Application number: CN201010213192.6A
Authority: CN
Inventors: 乔耀军; 赵源; 纪越峰
Original assignee: Beijing University of Posts and Telecommunications
Current assignee: Beijing University of Posts and Telecommunications
Priority date: 2010-06-30
Filing date: 2010-06-30
Publication date: 2014-11-19
Anticipated expiration: 2030-06-30
Also published as: CN101895499A

Abstract

The invention belongs to the field of optical communication, and is applied to the polarization demultiplexing of a polarization diversity multiplexing coherent optical communication system. According to the invention, for the problem of the polarization demultiplexing in the polarization diversity multiplexing coherent optical communication system, a special training sequence and related algorithms are designed. Through the method, a coherent receiver can fast, automatically and accurately perform the polarization demultiplexing. As the track of the training sequence, viewed from a planisphere, rotates along a unit circle after sign power is normalized, the training sequence provided by the invention is called a constant rotation sign training sequence. The invention discloses two processing algorithms for the constant rotation sign training sequence, which are a frequency-domain algorithm and a time-domain algorithm respectively, wherein the frequency-domain algorithm can be combined with frequency-domain dispersion compensation without adding a frequency spectrum calculation module. Through the method, the receiver does not need synchronizing with an initial position of the training sequence.

Description

Method for demultiplexing polarization by using constant rotation symbol training sequence

Technical Field

The invention belongs to the field of optical communication, and is applied to a polarization diversity multiplexing coherent optical communication system for polarization demultiplexing.

Background

Coherent optical communication can not only improve the spectrum efficiency by using a high-order modulation technology and a polarization diversity multiplexing technology, but also dynamically compensate signal damage by using an adaptive digital signal processing technology. Is an important technology with wide application prospect. In a polarization diversity multiplexing coherent optical communication system, a transmitting end inputs two paths of optical signals with mutually vertical polarization directions into an optical fiber for transmission. Fig. 1 shows an input signal of a polarization diversity multiplexing system. Optical signals traveling through optical fibers are subject to polarization mode dispersion in the optical fiber. Polarization mode dispersion causes the polarization state of an optical signal to rotate. As shown in fig. 2. Furthermore, optical fiber polarization mode dispersion is random, resulting in random rotation of the polarization state of an optical signal transmitted through the optical fiber. The polarization state of the optical signal at the receiving end is shown in fig. 3.

As shown in fig. 4, at a receiving end of the polarization diversity multiplexing coherent optical communication system, a polarization beam splitter 402 splits a received signal 401 into two optical signals with mutually perpendicular polarization states, and the two optical signals respectively enter an X polarization branch 403 and a Y polarization branch 404. A local Laser (LO)405 emits laser light having the same or close carrier frequency as the optical signal, and the laser light is divided into two paths, and the two paths enter two 90 ° mixers 406 and 407 with the signals of the X-polarization branch 403 and the Y-polarization branch 404, respectively. The outputs of the two 90 ° mixers are received by a photodiode 408 and converted into an electrical signal, which is sampled by an analog-to-digital converter (ADC)409, resulting in a baseband digital signal 410 of the received optical signal 401. The baseband digital signal enters the DSP module 411 to perform operations such as dispersion compensation, clock synchronization, polarization demultiplexing, polarization mode dispersion compensation, demodulation, and recover the original data 412.

The polarization beam splitter 402 at the receiving end is fixed in orientation, i.e., receives signals in two fixed polarization directions perpendicular to each other. In general, these two polarization directions cannot be aligned with the two polarization directions of the optical signal reaching the receiving end, respectively. This causes a portion of the optical signal in each of the two polarization directions to enter the X-polarization branch 403 and the Y-polarization branch 404 at the receiving end. The received signals on X polarization branch 403 and Y polarization branch 404 are a superposition of the transmitted signals in both polarization directions. Generally, the coherent receiver (fig. 4) uses a butterfly filter 506 in a Digital Signal Processing (DSP) module (fig. 5) to perform polarization demultiplexing, and setting a reasonable value for the butterfly filter is the key for polarization demultiplexing.

The invention aims to solve the problem of polarization demultiplexing of a polarization diversity multiplexing coherent optical communication system.

Disclosure of Invention

The invention is suitable for a polarization diversity multiplexing coherent optical communication system, and the modulation mode of the system can be MPSK (M is more than or equal to 4) or MQAM (M is more than or equal to 4). The invention designs a special training sequence and a related algorithm aiming at the problem of polarization demultiplexing in a polarization diversity multiplexing coherent optical communication system. By adopting the method, the coherent receiver can quickly, automatically and accurately carry out polarization demultiplexing. The training sequence provided by the invention is characterized in that after the symbol power is normalized, the track of the training sequence is rotated along a unit circle seen on a constellation diagram, and therefore, the training sequence is named as a constant rotation symbol training sequence. The two polarization directions of the transmitting terminal respectively transmit a certain length of symbol sequences with different and constant rotation speeds, wherein the meaning of the different rotation speeds includes different rotation rates or different rotation directions (for example, clockwise rotation in one polarization direction and counterclockwise rotation in the other polarization direction). The coherent receiver knows the rotation speed of the training sequences transmitted by the transmitting end in both polarization directions. The invention provides two processing algorithms aiming at a constant rotation symbol training sequence. The two algorithms are used for a receiving end, and can endow the butterfly filter 506 with proper weight values for polarization demultiplexing.

One of these two algorithms requires calculating the frequency spectrum of the received signal and estimating the channel transfer function matrix from the frequency domain of the received signal, thereby initializing the butterfly filter 506. Therefore, this algorithm is named a frequency domain algorithm. The algorithm mainly comprises the following steps:

(1) subjecting the received training sequence to a Discrete Fourier Transform (DFT) to compute a frequency spectrum;

(2) finding a peak from the spectrum;

(3) estimating a channel transfer function from the peak value;

(4) the weights of the butterfly filter are initialized with the inverse of the transfer function.

The frequency difference between the Local Oscillator (LO)405 and the transmitted optical signal carrier in the coherent receiver can also be conveniently estimated from the locations where the spectral peaks occur.

Another algorithm belongs to the least mean square error (LMS) algorithm, which is processed in the time domain of the received signal to optimize the weights of the butterfly filter 506. Therefore, this algorithm is named time-domain algorithm. The algorithm mainly comprises the following steps:

(1) calculating the angle of two-branch output signals (complex number) of the butterfly filter at the last moment;

(2) calculating the expected value of the output signal at the current moment according to the angle of the output signal at the previous moment and the rotation speed of the training sequence symbol of the polarization branch circuit;

(3) and the difference between the expected value of the output signal at the current moment and the actual value of the output signal at the current moment is used as an error signal of the LMS algorithm.

Drawings

FIG. 1: a transmission signal schematic diagram of a polarization diversity multiplexing system;

FIG. 2: a schematic diagram of randomly rotating the polarization state of a transmitted optical signal by fiber polarization mode dispersion;

FIG. 3: a schematic diagram of a receiving end initially receiving a polarization state of an optical signal;

FIG. 4: a receiver of a polarization diversity multiplexing coherent optical communication system;

FIG. 5: a DSP module in a receiver of the polarization diversity multiplexing coherent optical communication system;

FIG. 6: a constellation diagram of a polarization diversity multiplexing QPSK system, and a rotation schematic diagram of a constant rotation symbol training sequence on the constellation diagram;

FIG. 7: a frequency domain algorithm structure chart for carrying out polarization demultiplexing by using a constant rotation symbol training sequence;

FIG. 8: a detailed flow chart of a frequency domain algorithm;

FIG. 9: a time domain algorithm structure chart for carrying out polarization demultiplexing by using a constant rotation symbol training sequence;

FIG. 10: time domain algorithm detailed flow chart.

Detailed Description

Receiver of polarization diversity multiplexing optical communication system as shown in fig. 4, the coherent receiver includes a front-end processing part 413 and a Digital Signal Processing (DSP) module 411. The front-end processing section 413 changes the optical signal into a baseband digital signal 410. The DSP module 411 processes the baseband digital signal 410, performs clock synchronization, compensates for various signal impairments, and demodulates to recover the data 412. The details of the DSP block 411 are shown in fig. 5, where the output 510 of the DSP block corresponds to 412 in the coherent receiver and the inputs 501, 502 of the DSP block are connected to the baseband digital signal 410 in the coherent receiver. Note that input x of the DSP circuit_in501，y_in502 is a complex number, with 410 having the relationship:

x_in＝x_Re+i×x_Im

y_in＝y_Re+i×y_Im

input signal x_in501，y_in502 first enters 503 for dispersion compensation and clock synchronization. Output x of the dispersion compensation and clock synchronization module 503_p504、y_p505 are synchronized signals, which then enter butterfly filter 506 for polarization demultiplexing, polarization mode dispersion compensation, and residual dispersion compensation. The butterfly filter 506 is composed of 4 complex filters 511, 512, 513, 514 and two adders 515, 516. The weights h of the complex filters 511, 512, 513, 514_xx、h_xy、h_yx、h_yyIs a complex number, and can be a one-dimensional or multi-dimensional vector. The operation of the butterfly filter 506 is:

x_out＝x_p*h_xx+y_p*h_xy

y_out＝x_p*h_xy+y_p*h_yy

wherein, the variables in the formula are complex numbers; is a convolution operation; x is the number of_out507，y_out508 is the filter output; appropriately setting the weight h of the filter_xx、h_xy、h_yx、h_yyI.e., polarization demultiplexing. The outputs 507, 508 of the butterfly filter enter a phase recovery and demodulation block 509 to obtain demodulated data 510.

Linear channel model for polarization diversity multiplexing optical communication system

The transmission signal of the polarization diversity multiplexing system has the following time domain and frequency domain representations:

<math> <mrow> <mover> <mi>s</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>s</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

<math> <mrow> <mover> <mi>S</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

where x, y are two mutually perpendicular polarization directions.

The time and frequency domain representations of the received signal are:

<math> <mrow> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>r</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>r</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

<math> <mrow> <mover> <mi>R</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>R</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

channel transmission matrix:

channel transmission equation:

constant rotation symbol training sequence

The training sequence provided by the invention is characterized in that after the symbol power is normalized, the track of the training sequence is rotated along a unit circle seen on a constellation diagram, and therefore, the training sequence is named as a constant rotation symbol training sequence. The two polarization directions of the transmitting terminal respectively transmit a certain length of symbol sequences with different and constant rotation speeds, wherein the meaning of the different rotation speeds includes different rotation rates or different rotation directions (for example, clockwise rotation in one polarization direction and counterclockwise rotation in the other polarization direction).

Signal on X polarization at angular frequency ω on constellation diagram_xRotating:

s_x(t)＝exp(iφ_x)exp(iω_xt)

wherein phi is_xIs the initial phase of the training sequence, t 0, 1, 2.

Signal on Y polarization at angular frequency ω on constellation diagram_yRotating:

s_y(t)＝exp(iφ_y)exp(iω_yt)

wherein phi is_yIs the initial phase of the training sequence, t 0, 1, 2.

Note that the rotational speeds in the X, Y polarization directions are not the same, i.e., ω_x≠ω_y。

For example, for QPSK signals, ω_x，ω_yAre respectively taken asThe rotation direction of the training sequence on the constellation diagram is shown in fig. 6. The constellation diagram of the training sequence transmitted in the X polarization direction is shown in the diagram 605, and the phases of the symbol sequence are sequentially And so on. The constellation diagram of the training sequence transmitted in the Y polarization direction is shown in fig. 610, and the phases of the symbol sequence are sequentiallyAnd so on.

Frequency domain representation of the signal on the X polarization direction transmit:

<math> <mrow> <msub> <mi>S</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <msub> <mi>iφ</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>ω</mi> <mo>=</mo> <msub> <mi>ω</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>ω</mi> <mo>&NotEqual;</mo> <msub> <mi>ω</mi> <mi>x</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

frequency domain representation of the transmitted signal in the Y polarization direction:

<math> <mrow> <msub> <mi>S</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <mi>i</mi> <msub> <mi>φ</mi> <mi>y</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>ω</mi> <mo>=</mo> <msub> <mi>ω</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>,</mo> </mtd> <mtd> <mi>ω</mi> <mo>&NotEqual;</mo> <msub> <mi>ω</mi> <mi>y</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

will S_x(ω)，S_yThe expression of (ω) is substituted into the signaling equation:

obtaining:

R_x(ω)＝H_xx(ω_x)exp(iφ_x)+H_xy(ω_y)exp(iφ_y)

R_y(ω)＝H_yx(ω_x)exp(iφ_x)+H_yy(ω_y)exp(iφ_y)

frequency domain algorithm for polarization demultiplexing with constant rotation symbol training sequence:

FIG. 7 is a structural diagram of a frequency domain algorithm, where a transmitting end transmits a constant rotation symbol training sequence, and x is reached to an input end of a butterfly filter_p701、y_p702. The output of the butterfly filter is x_out705、y_out706。x_p701、y_p702 enters a channel transfer function estimator 704, and the estimator 704 estimates the channel transfer function and assigns initial values to the weights of the butterfly filter 703 according to the transfer function. The assigned butterfly filter 703 can smoothly perform polarization demultiplexing. Fig. 8 is a flowchart of the transfer function estimator 704. Discrete Fourier Transform (DFT) modules 803, 804 apply to the input signal x_p801、y_p802 find the frequency spectrum, the frequency spectrum is R_x(ω)805 and R_y(ω) 806. Frequency spectrum R_x(ω)805 and R_y(ω)806 are input to peak fetching modules 807, 808, respectively. Peaking modules 807, 808 vs R_x(omega) and R_y(ω) at ω ═ ω_xAnd ω ═ ω_yThe point with the maximum absolute value, namely the peak value, is searched nearby, and 4 peak values are found in total, wherein the peak values are respectively as follows:

1.R_x(ω) at ω ═ω_xThe size of the nearby peak is h₁＝H_xx(ω_x)exp(iφ_x) The peak position is ω ═ ω₁；

2.R_x(ω) at ω ═ ω_yThe size of the nearby peak is h₂＝H_xy(ω_y)exp(iφ_y) The peak position is ω ═ ω₂；

3.R_y(ω) at ω ═ ω_xThe size of the nearby peak is h₃＝H_yx(ω_x)exp(iφ_x) The peak position is ω ═ ω₃；

4.R_y(ω) at ω ═ ω_yThe size of the nearby peak is h₄＝H_yy(ω_y)exp(iφ_y) The peak position is ω ═ ω₄。

The peak magnitudes 812, 813 are input to a matrix 814 that is used to estimate the channel transfer function, and the peak locations 809, 810 can estimate the frequency difference 811 between the Local Oscillator (LO)405 and the optical carrier of the signal. Module 814 estimates a channel transfer function matrix from the spectral peaks. The specific operation is as follows: spectrum R_x(omega) and R_yThe peaks in (ω) constitute the matrix H':

h' can be written as:

wherein,

it is assumed that the length of the unit impulse response of the channel transfer function is 1. Thus, its Fourier transform H_xx(ω)，H_xy(ω)，H_yx(ω)，H_yy(ω) is equal over all ω. The channel transfer function can be estimated:

inverting H 'to H'^-1And is H'^-1And giving a weight value to the butterfly filter. The overall transfer function of the channel and the butterfly filter is:

<math> <mrow> <msub> <mi>H</mi> <mi>total</mi> </msub> <mo>=</mo> <msup> <mi>H</mi> <mrow> <mo>′</mo> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>H</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mi>HΦ</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>·</mo> <mi>H</mi> <mo>=</mo> <msup> <mi>Φ</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>HH</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>Φ</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>exo</mi> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>iφ</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>exp</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>-</mo> <mi>iφ</mi> </mrow> <mi>y</mi> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

note that the overall transfer function has been successfully polarization demultiplexed by multiplying the input signal in the x and y polarization directions by a phase factor exp (-i φ), respectively_x)，exp(-iφ_y) This phase factor can be removed in a subsequent phase recovery and demodulation module 509.

The matrix inversion module 816 uses the inverse of H' and assigns initial values to the weights of the butterfly filters.

The inverse of H' is:

if the weight vector h of the butterfly filter_xx，h_xy，h_yx，h_yyThe length is 1, then the initial values are respectively set as:

h_{xx} = \frac{h_{4}}{h_{1} h_{4} - h_{2} h_{3}},

h_{xy} = \frac{- h_{2}}{h_{1} h_{4} - h_{2} h_{3}}

h_{yx} = \frac{- h_{3}}{h_{1} h_{4} - h_{2} h_{3}},

h_{yy} = \frac{h_{1}}{h_{1} h_{4} - h_{2} h_{3}}

if so, the weight vector h of the butterfly filter_xx，h_xy，h_yx，h_yyIf the length is greater than 1, the weight vector is maximizedThe weight value in the middle is set as the upper value, and the weight values in the rest positions are set as 0. The above is a frequency domain algorithm for polarization demultiplexing with a constantly rotating symbol training sequence.

According to the frequency spectrum R of the received signal_x(ω)805 and R_yThe frequency difference 811 between the Local Oscillator (LO)405 and the signal carrier can be conveniently estimated at the location 809,810 where the peak occurs in (ω) by:

setting: r is the angular frequency of the received signal omega_r(ii) a L is the local laser output optical signal, whose baseband is represented as:

wherein ω is_LIs the angular frequency, ω, of the LO_rIs the angular frequency of the signal(s),the initial phase difference of the LO and the received signal and the phase noise of the LO are included.

r and L are input to a 90 ° mixer, and the signal received by the PD is:

wherein Δ ω ═ ω_L-ω_rIs the frequency difference of the LO and the signal.

From the above analysis, it can be seen that when the LO has a frequency difference from the carrier frequency of the signal, the received signal will rotate on the constellation diagram with an angular frequency of- Δ ω. Viewed from the frequency domain, the frequency difference enables PD to receiveThe spectrum of the signal is shifted by- Δ ω from the spectrum of the received signal r. If r is a constant rotation symbol training sequence, its peak will not appear at ω after DFT_xOr ω_yAbove, but offset by- Δ ω T_sWherein T is_sIs one symbol period. R_x(ω) at ω ═ ω_xThe position of the nearby peak is ω ═ ω₁Should satisfy-delta-omega-T_s＝ω₁-ω_xThe frequency difference Δ f can be estimated by the following equation:

wherein T is_sIs the symbol period. Also can use omega in combination₁，ω₂，ω₃，ω₄To improve the accuracy of the frequency offset estimation.

Time domain algorithm for polarization demultiplexing with constant rotation symbol training sequence:

the algorithm belongs to a least mean square error (LMS) algorithm. Algorithm structure diagram as shown in fig. 9, LMS algorithm block 904 uses input x of butterfly filter 903_p901、y_p902 and output x_out905、y_out906 updates the weights of the butterfly filter 903. After a plurality of iterations, the weight h of the butterfly filter 903_xx907，h_xy908，h_yx909，h_yy910 will converge to the inverse of the channel transfer function matrix and thus successfully depolarise multiplex. The basic idea of the time domain algorithm is to exploit the properties of a constant rotation symbol training sequence: in the training sequence, the phase of the symbol transmitted in the X polarization direction is followedOne total increase ω from the previous one_x. The phase of the transmitted symbol in the Y polarization direction being increased by ω from the former one_y. In addition, the symbols should be on the unit circle on the constellation diagram. Thus, the error signal of the LMS algorithm is:

wherein x is_out905 is the output signal of the butterfly filter branch x at the present moment, x_out' is the output signal at the last moment,is the output x of the last time input x branch_outAngle of' i.e.ε_xError for branch x; y is_out906 is the output signal of the butterfly filter y branch at the present moment, y_out' is the output signal at the last moment,is the output y of the last time input y branch_outAngle of' i.e.ε_yThe error of the y branch.

The weight h of the butterfly filter 903 is updated by the following formula_xx907，h_xy908，h_yx909，h_yy910：

<math> <mrow> <msub> <mi>h</mi> <mi>xx</mi> </msub> <mo>&RightArrow;</mo> <msub> <mi>h</mi> <mi>xx</mi> </msub> <mo>-</mo> <mfrac> <mi>μ</mi> <mn>2</mn> </mfrac> <mfrac> <mrow> <mi>d</mi> <msup> <mrow> <mo>|</mo> <msub> <mi>ϵ</mi> <mi>x</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mi>d</mi> <msub> <mi>h</mi> <mi>xx</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>h</mi> <mi>xx</mi> </msub> <mo>+</mo> <mi>μ</mi> <msub> <mi>ϵ</mi> <mi>x</mi> </msub> <msup> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>*</mo> </msup> </mrow> </math>

<math> <mrow> <msub> <mi>h</mi> <mi>xy</mi> </msub> <mo>&RightArrow;</mo> <msub> <mi>h</mi> <mi>xy</mi> </msub> <mo>-</mo> <mfrac> <mi>μ</mi> <mn>2</mn> </mfrac> <mfrac> <mrow> <mi>d</mi> <msup> <mrow> <mo>|</mo> <msub> <mi>ϵ</mi> <mi>x</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mi>d</mi> <msub> <mi>h</mi> <mi>xy</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>h</mi> <mi>xy</mi> </msub> <mo>+</mo> <mi>μ</mi> <msub> <mi>ϵ</mi> <mi>x</mi> </msub> <msup> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>*</mo> </msup> </mrow> </math>

<math> <mrow> <msub> <mi>h</mi> <mi>yx</mi> </msub> <mo>&RightArrow;</mo> <msub> <mi>h</mi> <mi>yx</mi> </msub> <mo>-</mo> <mfrac> <mi>μ</mi> <mn>2</mn> </mfrac> <mfrac> <mrow> <mi>d</mi> <msup> <mrow> <mo>|</mo> <msub> <mi>ϵ</mi> <mi>y</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mi>d</mi> <msub> <mi>h</mi> <mi>yx</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>h</mi> <mi>yx</mi> </msub> <mo>+</mo> <mi>μ</mi> <msub> <mi>ϵ</mi> <mi>y</mi> </msub> <msup> <msub> <mi>x</mi> <mi>p</mi> </msub> <mo>*</mo> </msup> </mrow> </math>

<math> <mrow> <msub> <mi>h</mi> <mi>yy</mi> </msub> <mo>&RightArrow;</mo> <msub> <mi>h</mi> <mi>yy</mi> </msub> <mo>-</mo> <mfrac> <mi>μ</mi> <mn>2</mn> </mfrac> <mfrac> <mrow> <mi>d</mi> <msup> <mrow> <mo>|</mo> <msub> <mi>ϵ</mi> <mi>y</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mi>d</mi> <msub> <mi>h</mi> <mi>yy</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>h</mi> <mi>yy</mi> </msub> <mo>+</mo> <mi>μ</mi> <msub> <mi>ϵ</mi> <mi>y</mi> </msub> <msup> <msub> <mi>y</mi> <mi>p</mi> </msub> <mo>*</mo> </msup> </mrow> </math>

Where μ is the step size of the LMS algorithm and x is the complex conjugate operation.

FIG. 10 is update h_xx907, updating h_xy908，h_yx909，h_yy910 are similar. Input x of the butterfly filter_p1002 and output x_out1001 is the input to the update algorithm, ω_x1007 and μ 1012 are parameters of the update algorithm. x is the number of_out1001 enters an angle extractor 1003, the obtained angle passes through a time delay 1006 and then passes through an adder 1008 and omega_x1007 and the result is calculated by block 1009x_out1001 into a sign inverter 1005, and through an adder 1010 andare added to obtainx_p1002 into a conjugator 1004 and then into a multiplier 1011 with parameters μ 1012 and ε_x1015 are multiplied to obtain h_xxCorrection amount of (u) ∈_xy_p ^*1016. Correction quantities 1016 and h_xx1014 add 1013, the result of addition 1017 being h_xxThe new value of (c). h is_xxThe new value output 1018 updates the butterfly filter weights. The above is a time domain algorithm for polarization demultiplexing with a constantly rotating symbol training sequence.

Main technical advantages

Aiming at the problem of polarization demultiplexing in a polarization diversity multiplexing coherent optical communication system, the invention designs a special training sequence called as a training sequence using a constant rotation symbol and a correlation algorithm comprising a frequency domain algorithm and a time domain algorithm. By adopting the method, the coherent receiver can quickly, automatically and accurately carry out polarization demultiplexing. The most important advantage of using a constant rotation symbol training sequence is that the receiver does not need to synchronize with the transmitted training sequence, i.e. the receiver does not need to know the initial phase of the transmitted training sequence.

The invention provides two processing algorithms aiming at a constant rotation symbol training sequence, namely a frequency domain algorithm and a time domain algorithm. The frequency domain algorithm has the advantage that the weights of the butterfly filter can be directly estimated from the frequency spectrum of the received signal. If a coherent receiver compensates for dispersion in the frequency domain, it is necessary to obtain the spectrum of the received signal. The frequency domain algorithm can directly use the spectrum without adding an additional module for calculating the spectrum.

The time domain algorithm has the advantage that the butterfly filter weights are updated by using a least mean square error (LMS) algorithm, and the complexity of the algorithm is low.

Claims

1. A method for polarization demultiplexing in a polarization diversity multiplexed coherent optical communication system using a constantly rotating symbol training sequence, the method comprising the steps of:

(1) in the initialization stage of a communication system, a transmitting end respectively transmits constant rotation symbol training sequences with different rotation speeds in two polarization directions;

(2) the coherent receiver receives and processes the training sequence, initializes the weight of the butterfly filter, and thus performs polarization demultiplexing,

the method for the coherent receiver to initialize the weight of the butterfly filter includes a frequency domain algorithm and a time domain algorithm,

the frequency domain algorithm comprises the following steps:

(1) performing discrete Fourier transform on the received training sequence to calculate a frequency spectrum;

(2) finding a peak from the spectrum;

(3) estimating a channel transfer function from the peak value;

(4) the weights of the butterfly filter are initialized with the inverse of the transfer function,

the time domain algorithm comprises the following steps:

(1) calculating the angle of the output signals of the two branches of the butterfly filter at the first moment;

(2) calculating an expected value of the output signal at the current moment according to the angle of the output signal at the previous moment and the symbol rotation speed of the training sequence of the polarization branch circuit;

(3) and taking the difference between the expected value of the output signal at the current moment and the actual value of the output signal at the current moment as an error signal of the time domain algorithm.

2. The method of claim 1, wherein the training sequence is rotated at a constant speed along a unit circle as viewed on a constellation diagram after being normalized by the symbol power, and the different rotation speeds include different rotation speeds or different rotation directions.