CN106789793A - For the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update - Google Patents

Abstract

The invention discloses a kind of LMS methods without frequency difference difference feedback updated for adaptive equalizer coefficients, it is related to coherent light communication technical field.The LMS methods are comprised the following steps：X polarized receptions signal and Y polarized receptions signal to adaptive equalizer carry out time domain equalization；Define the error formula of above-mentioned time domain equalization；Defined according to above-mentioned error, adaptive equalizer coefficients are updated using gradient algorithm, to ensure that adaptive equalizer persistently tracks the change of polarization state, and without frequency difference and the feedback for differing.The present invention can make the renewal of adaptive equalizer coefficients eliminate the reliance on frequency difference and the feedback for differing, even if running into extreme polarization state change, coherent optical communication system also can be tracked correctly, it is ensured that the robustness of system.

Description

For the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update

Technical field

The present invention relates to coherent light communication technical field, be specifically it is a kind of for adaptive equalizer coefficients update Without LMS (Least mean square, lowest mean square) method of frequency difference difference feedback.

Background technology

The theoretical and experiment of coherent light communication starts from the eighties.Coherent optical communication system be acknowledged as with sensitivity it is high, The characteristics of frequency selectivity is good, spectrum efficiency is high, these features are conducive to the raising of message capacity.In addition, in coherent light communication In, the damage of dispersion and polarization mode dispersion to signal is all linear damage, and now communication channel can be modeled as LTI system System, therefore can just be compensated by complicated DSP (Digital Signal Processing, the Digital Signal Processing) technology of appropriateness Linear damage, so that the chromatic dispersion problem of puzzlement industry becomes relatively easy solution.And in 40G, 100G optic communication epoch, phase Dry optic communication is combined with Digital Signal Processing, and obtains huge business success.Consider spectrum efficiency and OSNR The requirement of tolerance limit, 100G commercial systems use the PM-QPSK (Polarization based on coherent light communication Multiplexed Quadri Phase Shift Keying, palarization multiplexing quadriphase PSK) technology.

Due to the progress of electronic technology so that the cost of DSP is greatly lowered, the coherent optical communication system of a new generation generally draws Enter DSP technologies.After using intrinsic light carrier demodulated signal light, ADC (Analog-Digital Converter, mould are reused Number converter) electronic signal after demodulating of sampling, finally carry out Digital Signal Processing.Shown in Figure 1, coherent light communication is received The flow of the Digital Signal Processing of machine is generally：Dispersion compensation → clock recovery → adaptive equalization → carrier auxiliary (estimate by frequency difference Meter and compensation) → carrier auxiliary (differing estimation with compensation) → bit decision.

Adaptive equalizer is the chief component of Digital Signal Processing, plays polarization demultiplexing and residual chromatic dispersion compensation Effect, is generally made up of linear equalizer with adaptive equalization coefficient update algorithm.Coherent light communication used and enter 2 × 2 more Have more adaptive equalizer, two polarization signals after output equilibrium.

At present, the more popular adaptive equalization coefficient update algorithm that can be used for PM-QPSK is CMA (Constant Modulus Algorithms, constant modulus algorithm).Because CMA does not need training sequence, and need not in advance compensate frequency difference, relatively Simply and with certain robustness, it is widely used by main flow commercial system.The error defined formula of constant modulus algorithm is：

Wherein,For the X ports of adaptive equalizer export,For the Y-port of adaptive equalizer is exported, | | For modulus is calculated, 1 is the permanent mould size of setting, and n is data sequence number.The coefficient update formula of adaptive equalizer is according to formula (1), the error formula given by (2) is drawn by gradient algorithm.

But, what CMA algorithms were utilized is QPSK (Quadri Phase Shift Keying, quadriphase PSK) signal Permanent model's point, it is impossible to distinguish tracked polarization state, thus algorithm may mistake restrain, make two of adaptive equalizer it is defeated Go out all one polarization states of output.When polarization state occur and quickly changing, when such as aerial optical cable is acutely rocked under typhoon, CMA can Tracked polarization state can be lost, and mistake converges to two outputs all one polarization states of output of balanced device, brings system Collapse.

And as improved LMS (Least mean square, lowest mean square) algorithm based on training sequence, due to making First order statistic, can track faster polarization variations than CMA.Also, due to the guide function of training sequence, self adaptation Balanced device can export the polarization state corresponding to training sequence used.But, in coherent optical communication system, due to for demodulation There is frequency difference and differ in local laser, with originator laser so when using LMS algorithm, it is necessary to from frequency difference thereafter and phase Difference compensating module introduces frequency difference with calculating of the feedback for error signal, its specific error calculation formula is differed：

Wherein, D^xWith D^yIt is expected data, is the training sequence numerical value being known a priori by, Δ f is frequency difference, and T is code-element period, Φ_xWith Φ_yThe respectively difference of X, Y polarization signal, n is data sequence number.

But, the problem of existing LMS methods is：In actual signal processing, frequency difference estimation with differ estimation All rely on the correct output of adaptive equalizer.In the system of actual deployment, although in most cases polarization state change is slow Slowly, but the polarization variations being exceedingly fast instantaneously are likely to occur, now it cannot be guaranteed that the correct output of adaptive equalizer, no correct Frequency difference can not correctly work with feedback, existing LMS methods is differed, so not ensured that using existing LMS methods and being Existence of the system under the polarization variations being exceedingly fast.

The content of the invention

The invention aims to overcome the shortcomings of above-mentioned background technology, there is provided one kind is used for adaptive equalizer coefficients The LMS methods without frequency difference difference feedback for updating, can make the renewal of adaptive equalizer coefficients eliminate the reliance on frequency difference and differ Feedback, even if running into extreme polarization state change, system also can be tracked correctly, it is ensured that the robustness of system.

To achieve the above objectives, the present invention is adopted the technical scheme that：There is provided one kind is used for adaptive equalizer coefficients more The new LMS methods without frequency difference difference feedback, the LMS methods are comprised the following steps：

S1：To the X polarized reception signals [Ein of adaptive equalizer^x] and Y polarized reception signals [Ein^y] to carry out time domain equal Weigh, the formula of time domain equalization is：

Wherein,WithThe respectively output of adaptive equalizer X polarization signals and Y polarization signals, F^xx、F^xy、F^yx、F^yyIt is four adaptive equalizer coefficients, n is sequence number, and L is adaptive equalizer series, and l is that self adaptation is equal Weighing apparatus series sequence number；

S2：The error formula for defining above-mentioned time domain equalization is：

Error (n)=| Error_xy1 (n) |²+|Error_xy2(n)|², wherein：

In formula, D^x、D^yIt is expected data, is previously known training sequence numerical value；It is the X ends of adaptive equalizer Mouth output,For the Y-port of adaptive equalizer is exported；| | for modulus is calculated, []^*To take conjugation；

S3：Defined according to above-mentioned error, adaptive equalizer coefficients are updated using gradient algorithm, to ensure adaptive equalization Device persistently tracks the change of polarization state, and without frequency difference and the feedback for differing.

On the basis of above-mentioned technical proposal, the formula that adaptive equalizer coefficients are updated described in step S3 is：

In above-mentioned formula, * is conjugate of symbol, and g represents the g times renewal, μ₁、μ₂It is the small coefficient for using as needed.

On the basis of above-mentioned technical proposal, in step S3, the μ in the formula for updating adaptive equalizer coefficients₁ And μ₂May be the same or different.

On the basis of above-mentioned technical proposal, in step S3, the μ in the formula for updating adaptive equalizer coefficients₁ And μ₂Span be 1~10^-9。

On the basis of above-mentioned technical proposal, in step S3, when adaptive equalizer updates adaptive equalizer coefficients, meeting Lock the difference Φ of X polarization signals_xWith the difference Φ of Y polarization signals_ySo that Φ_x=Φ_y；Also, when sef-adapting filter just Really during output, the output of adaptive equalizer X polarization signalsWith the output of Y polarization signalsRespectively：

Wherein, j is plural number, and Δ f is frequency difference, and T is code-element period；And the frequency difference Δ f in above-mentioned output formula will be in error It is eliminated in formula.

On the basis of above-mentioned technical proposal, under QPSK application scenarios, training sequence previously known described in step S2 Columns value need to meet claimed below when being pre-designed：D^x(n)/D^yN () equably takes 1, j, -1, four numerical value of-j.

The beneficial effects of the present invention are：

(1) present invention has identical frequency difference with the spy for differing using the two paths of signals demodulated in coherent optical communication system Point, it is proposed that the error formula of new follow-on X, Y polarization signal.Using follow-on error formula, it is capable of achieving without frequency Difference and the LMS algorithm for differing feedback.Compare traditional LMS algorithm have to rely on frequency difference with differ feedback for, this method due to The coefficient update of adaptive equalizer eliminates the reliance on frequency difference and differs feedback, even if running into extreme polarization state change, system Can correctly track, it is ensured that the robustness of system, meet actually used demand.

(2) present invention is realized simply, with very strong practicality；And of the invention use is not limited to coherent light communication neck Domain, it is applied widely.

Brief description of the drawings

Fig. 1 is the Digital Signal Processing flow chart of coherent optical communication receiver in the prior art；

Fig. 2 is the LMS side without frequency difference difference feedback updated for adaptive equalizer coefficients in the embodiment of the present invention The flow chart of method.

Specific embodiment

Below in conjunction with the accompanying drawings and specific embodiment the present invention is described in further detail.

It is shown in Figure 2, the embodiment of the present invention provide it is a kind of for adaptive equalizer coefficients update without frequency difference phase The LMS methods of difference feedback, comprise the following steps：

Step S1：To the X polarized reception signals [Ein of adaptive equalizer^x] and Y polarized reception signals [Ein^y] carry out when Domain is balanced, and the formula of time domain equalization is：

Wherein,WithThe respectively output of adaptive equalizer X polarization signals and Y polarization signals, F^xx、F^xy、F^yx、F^yyIt is four adaptive equalizer coefficients, n is sequence number, and L is adaptive equalizer series, and l is that self adaptation is equal Weighing apparatus series sequence number, is transferred to step S2.

Step S2：The error formula for defining above-mentioned time domain equalization is：

Error (n)=| Error_xy1 (n) |²+|Error_xy2(n)|², (7)

In formula, D^x、D^yIt is expected data, is previously known training sequence numerical value；It is the X ends of adaptive equalizer Mouth output,For the Y-port of adaptive equalizer is exported；| | for modulus is calculated, []^*To take conjugation, step S3 is transferred to.

It is understood that when training sequence numerical value is pre-designed, D^x(n) and D^yN the difference of () should uniformly take all Value may be obtained.By taking QPSK as an example, that is, require, in project training sequential digit values, to meet D^x(n)/D^yN () equably takes 1, J, -1, four numerical value of-j, wherein, j is plural number.

Step S3：According to above-mentioned error defined formula (7)~(9), adaptive equalizer coefficients are updated using gradient algorithm, To ensure that adaptive equalizer persistently tracks the change of polarization state, and without frequency difference and the feedback for differing.

Wherein, the coefficient update formula of adaptive equalizer is：

In above-mentioned formula, * is conjugate of symbol, and g represents the g times renewal, μ₁、μ₂The small coefficient for using as needed is, Both may be the same or different, and μ₁And μ₂Span can be 1~10^-9。

Further it will be understood that when adaptive equalizer updates adaptive equalizer coefficients, X polarization signals can be locked Difference Φ_xWith the difference Φ of Y polarization signals_ySo that Φ_x=Φ_y, so that the coefficient update of adaptive equalizer is no longer Rely on the feedback of difference；Also, when sef-adapting filter is correctly exported, the output of adaptive equalizer X polarization signalsWith the output of Y polarization signalsRespectively：

Wherein, j is plural number, and Δ f is frequency difference, and T is code-element period；And the frequency difference Δ f in above-mentioned output formula will be in error It is eliminated in formula, so that the coefficient update of adaptive equalizer eliminates the reliance on the feedback of frequency difference.

As can be seen from the above-described embodiment, the present invention is realized simply, with very strong practicality.Due to adaptive equalizer Coefficient update eliminate the reliance on frequency difference and differ feedback, even if running into extreme polarization state change, system also can correctly be tracked, protected The robustness of system has been demonstrate,proved, actually used demand has been met.

The present invention is not limited to the above-described embodiments, for those skilled in the art, is not departing from On the premise of the principle of the invention, some improvements and modifications can also be made, these improvements and modifications are also considered as protection of the invention Within the scope of.The content not being described in detail in this specification belongs to prior art known to professional and technical personnel in the field.

Claims (6)

1. it is a kind of to differ the LMS methods fed back without frequency difference for what adaptive equalizer coefficients updated, it is characterised in that should LMS methods are comprised the following steps：

S1：To the X polarized reception signals [Ein of adaptive equalizer^x] and Y polarized reception signals [Ein^y] time domain equalization is carried out, when Formula is in a balanced way in domain：

$E_{out}^X\left(n\right)=\underset{l=-L+1}{\overset{L-1}{\Σ}}{F}^{xx}\left(l\right)\[{\mathrm{Ein}}^x(n-l)\]+\underset{l=-L+1}{\overset{L-1}{\Σ}}{F}^{xy}\left(l\right)\[{\mathrm{Ein}}^y(n-l)\]$

$E_{out}^Y\left(n\right)=\underset{l=-L+1}{\overset{L-1}{\Σ}}{F}^{yx}\left(l\right)\[{\mathrm{Ein}}^x(n-l)\]+\underset{l=-L+1}{\overset{L-1}{\Σ}}{F}^{yy}\left(l\right)\[{\mathrm{Ein}}^y(n-l)\]$

Wherein,WithThe respectively output of adaptive equalizer X polarization signals and Y polarization signals, F^xx、F^xy、 F^yx、F^yyIt is four adaptive equalizer coefficients, n is sequence number, and L is adaptive equalizer series, and l is adaptive equalizer level Number sequence number；

S2：The error formula for defining above-mentioned time domain equalization is：

Error (n)=| Error_xy1 (n) |²+|Error_xy2(n)|², wherein：

$\mathrm{Error}\_\mathrm{xy}1\left(n\right)=D^x\left(n\right){\left[D^y\left(n\right)\right]}^{*}-E_{\mathrm{out}}^X\left(n\right){\left[E_{\mathrm{out}}^Y\left(n\right)\right]}^{*},$

$Error\_xy2\left(n\right)=E_{out}^X\left(n\right)-E_{out}^Y\left(n\right)D^x\left(n\right)/D^y\left(n\right);$

In formula, D^x、D^yIt is expected data, is previously known training sequence numerical value；For the X ports of adaptive equalizer are defeated Go out,For the Y-port of adaptive equalizer is exported；| | for modulus is calculated, []^*To take conjugation；

S3：Defined according to above-mentioned error, adaptive equalizer coefficients are updated using gradient algorithm, to ensure that adaptive equalizer is held The change of continuous tracking polarization state, and without frequency difference and the feedback for differing.

2. it is as claimed in claim 1 to be used for the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update, its It is characterised by：Described in step S3 update adaptive equalizer coefficients formula be：

$\begin{array}{c}{F}^{xx}(l,g+1)=F^{xx}(l,g)+4{\mathrm{\μ}}_{1}Error\_xy1\left(n\right)E_{out}^Y\left(n\right){\[{\mathrm{Ein}}^x(n-l)\]}^{*}\\ -4{\mathrm{\μ}}_{2}Error\_xy2\left(n\right){\[{\mathrm{Ein}}^x(n-l)\]}^{*}\end{array};$

$\begin{array}{c}{F}^{xy}(l,g+1)=F^{xy}(l,g)+4{\mathrm{\μ}}_{1}Error\_xy1\left(n\right)E_{out}^Y\left(n\right){\[{\mathrm{Ein}}^y(n-l)\]}^{*}\\ -4{\mathrm{\μ}}_{2}Error\_xy2\left(n\right){\[{\mathrm{Ein}}^y(n-l)\]}^{*}\end{array};$

$\begin{array}{c}{F}^{yx}(l,g+1)=F^{yx}(l,g)+4{\mathrm{\μ}}_1{\[Error\_xy1\left(n\right)\]}^{*}{E}_{out}^X\left(n\right){\[{\mathrm{Ein}}_x^x(n-l)\]}^{*}\\ +4{\mathrm{\μ}}_{2}Error\_xy2\left(n\right){\[D^x\left(n\right)/D^y\left(n\right)\]}^{*}{\[{\mathrm{Ein}}^x(n-l)\]}^{*}\end{array};$

$\begin{array}{c}{F}^{yy}(l,g+1)=F^{yy}(l,g)+4{\mathrm{\μ}}_1{\[Error\_xy1\left(n\right)\]}^{*}{E}_{out}^X\left(n\right){\[{\mathrm{Ein}}^y(n-l)\]}^{*}\\ +4{\mathrm{\μ}}_{2}Error\_xy2\left(n\right){\[D^x\left(n\right)/D^y\left(n\right)\]}^{*}{\[{\mathrm{Ein}}^y(n-l)\]}^{*}\end{array};$

In above-mentioned formula, * is conjugate of symbol, and g represents the g times renewal, μ₁、μ₂It is the small coefficient for using as needed.

3. it is as claimed in claim 2 to be used for the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update, its It is characterised by：In step S3, the μ in the formula for updating adaptive equalizer coefficients₁And μ₂May be the same or different.

4. it is as claimed in claim 2 to be used for the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update, its It is characterised by：In step S3, the μ in the formula for updating adaptive equalizer coefficients₁And μ₂Span be 1~10^-9。

5. it is as claimed in claim 1 to be used for the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update, its It is characterised by：In step S3, when adaptive equalizer updates adaptive equalizer coefficients, the difference Φ of X polarization signals can be locked_x With the difference Φ of Y polarization signals_ySo that Φ_x=Φ_y；Also, when sef-adapting filter is correctly exported, adaptive equalizer X The output of polarization signalWith the output of Y polarization signalsRespectively：

$E_{out}^X\left(n\right)=D^x\left(n\right)\exp (j2\mathrm{\π}n\mathrm{\Δ}fT+{\mathrm{j\Φ}}_x);$

$E_{out}^Y\left(n\right)=D^y\left(n\right)\exp (j2\mathrm{\π}n\mathrm{\Δ}fT+{\mathrm{j\Φ}}_y);$

Wherein, j is plural number, and Δ f is frequency difference, and T is code-element period；And the frequency difference Δ f in above-mentioned output formula will be in error formula In be eliminated.

6. it is as claimed in claim 5 to be used for the LMS methods without frequency difference difference feedback that adaptive equalizer coefficients update, its It is characterised by：Under QPSK application scenarios, training sequence numerical value previously known described in step S2 need to expire when being pre-designed Foot is claimed below：D^x(n)/D^yN () equably takes 1, j, -1, four numerical value of-j.