CN102868662A - Channel estimation method for PDM-CO-OFDM (Pulse Duration Modulation-Coherent Optical-Orthogonal Frequency Division Multiplexing) system - Google Patents

Abstract

Translated fromChinese

本发明用于PDM-CO-OFDM系统的信道估计方法，涉及数字信息的传输中的应用多频码的系统，步骤是：在PDM-CO-OFDM系统发送端对离散导频格式进行设计与选取，发送信息数据及导频数据；在接收端将接收到的信息数据及导频数据，利用最小二乘算法即LS算法对正交频分复用符号进行导频点信道估计；在频域进行线性插值，将得到的插值结果进行多小波去噪；在时域进行线性插值，将插值结果进行符号内频域平均，完成联合去噪；降噪处理后的信道特性经矩阵求逆运算；最后估计出发送数据。本发明基于离散导频，结合多小波与符号内频域平均的联合降噪进行信道估计，克服了相关现有OFDM信道估计方法的计算量增大和增大系统开销的缺陷。

The channel estimation method used in the PDM-CO-OFDM system of the present invention relates to a system using multi-frequency codes in the transmission of digital information. The steps are: designing and selecting the scattered pilot format at the sending end of the PDM-CO-OFDM system , send information data and pilot data; at the receiving end, use the least squares algorithm (LS algorithm) to perform pilot point channel estimation on OFDM symbols with the received information data and pilot data; in the frequency domain Linear interpolation, perform multi-wavelet denoising on the obtained interpolation results; perform linear interpolation in the time domain, average the interpolation results in the frequency domain within the symbol, and complete joint denoising; the channel characteristics after denoising processing are calculated by matrix inversion; finally Estimated sent data. The present invention is based on scattered pilots, and combines multi-wavelet and intra-symbol frequency domain average joint noise reduction to perform channel estimation, and overcomes the defects of increased calculation amount and increased system overhead of related existing OFDM channel estimation methods.

Description

The channel estimation methods that is used for the PDM-CO-OFDM system

Technical field

Technical scheme of the present invention relates to the system of the application multifrequency code in the transmission of digital information, specifically is used for the channel estimation methods of PDM-CO-OFDM system.

Background technology

Current, people sharply increase the demand of message capacity, and the research of speed fiber optic communication systems has attracted people to pay close attention to greatly.The evolution of vast capacity optical fiber transmission network, oneself becomes one of the following mainstream development direction in present international communication field.Palarization multiplexing coherent light ofdm system, namely the PDM-CO-OFDM system because its two-forty, high spectrum utilization, high receiving sensitivity and ability of anti-multipath are strong, are approved to become and is realized at a high speed long a solution apart from optical signal transmission.Yet because the time variation of fiber channel, at system receiving terminal, channel estimation methods becomes one of key technology of the direct PDM-CO-OFDM of impact systematic function.

Existing based on the non-blind algorithm for estimating of the most employing of OFDM channel estimation methods, according to inserted mode, be divided into again block pilot tone, Comb Pilot and scattered pilot.CN201010034537.1 discloses in the optical OFDM system adaptive channel estimation method based on training sequence and Cyclic Prefix (CP), although can improve the precision of channel estimating, but the method adopts recursive least squares (RLS) to carry out channel estimating, has increased amount of calculation.CN201010580496.6 has disclosed a kind of channel estimation methods that improves the coherent optical communication system performance, compare with conventional method, systematic function is the highest to improve 2 dB, but the method is based on training sequence, the system spectrum utilance is reduced, increase overhead.CN201010132219.9 has reported in the optical OFDM system judgment feedback channel estimation method based on training sequence, although can improve precision and the systematic function of channel estimating, reduced the insertion frequency of training sequence, but still there is the defective that increases overhead in the method with respect to scattered pilot.

Summary of the invention

Technical problem to be solved by this invention is: the channel estimation methods that is provided for the PDM-CO-OFDM system, be a kind of channel estimation methods in conjunction with the average associating noise reduction of frequency domain in many small echos and the symbol based on scattered pilot, the amount of calculation that has overcome relevant existing OFDM channel estimation methods increases and increases the defective of overhead.

The present invention solves this technical problem the technical scheme that adopts: being used for the channel estimation methods of PDM-CO-OFDM system, is a kind of channel estimation methods in conjunction with the average associating noise reduction of frequency domain in many small echos and the symbol based on scattered pilot, and step is:

The first step designs and chooses the scattered pilot form at PDM-CO-OFDM system transmitting terminal, sends information data and pilot data

Carry out the design of pilot frequency design at the transmitting terminal X of PDM-CO-OFDM system and two polarization directions of Y, take S_f=6, S_T1=4 and S_T2=3, be the scattered pilot pattern, pilot tone is identical at frequency domain insertion interval, and it is identical that time domain is inserted the interval, but just identical every an OFDM symbol inserted mode that contains pilot tone at frequency domain, when sending pilot tone on the directions X, sends spacing wave on the Y-direction;

Second step, utilizing least-squares algorithm at the PDM-CO-OFDM system receiving terminal is that the LS algorithm carries out pilot tone point channel estimating to OFDM symbol

At the PDM-CO-OFDM system receiving terminal, the information data that the transmitting terminal that receives is sent and pilot data are according to the LS algorithm principle, estimate the characteristic of channel at the pilot tone point place of X, Y polarization direction, in PDM-CO-OFDM system channel estimation model, i symbol and k the fine channel response Jones matrix of subcarrier glazing obtain by the LS channel estimating:

$H_{i,k}=\left[\begin{array}{cc}{H}_{\mathrm{xx}}& H_{\mathrm{xy}}\\ H_{\mathrm{yx}}& H_{\mathrm{yy}}\end{array}\right]$

Suppose two frequency pilot sign t_xAnd t_yExperienced same channel effect, the frequency pilot sign that then receives is:

$r_1\left(k\right)=\left[\begin{array}{c}{r}_{1x}\left(k\right)\\ r_{1y}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{xx}}{t}_x\left(k\right)\\ H_{\mathrm{yx}}{t}_x\left(k\right)\end{array}\right],$$r_2\left(k\right)=\left[\begin{array}{c}{r}_{2x}\left(k\right)\\ r_{2y}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{xy}}{t}_y\left(k\right)\\ H_{\mathrm{yy}}{t}_y\left(k\right)\end{array}\right]$

Then, channel matrix can be obtained by following formula:

$H_{i,k}=\left[\begin{array}{cc}{H}_{\mathrm{xx}}& H_{\mathrm{xy}}\\ H_{\mathrm{yx}}& H_{\mathrm{yy}}\end{array}\right]=\left[\begin{array}{cc}{r}_{1x}\left(k\right)/t_x\left(k\right)& r_{2x}\left(k\right)/t_y\left(k\right)\\ r_{1y}\left(k\right)/t_x\left(k\right)& r_{2y}\left(k\right)/t_y\left(k\right)\end{array}\right]$

Obtain thus the characteristic of channel at information data, pilot data and pilot tone point place;

The 3rd step, carry out linear interpolation at frequency domain, the interpolation result that obtains is carried out many Wavelet Denoising Methods

Choose the many small echos of CL3 and carry out denoising, concrete steps are:

3.1 select odd to carry out preliminary treatment, be about to the channel response H that the LS estimation obtains by frequency domain interpolation_{I, k}Carry out the idol sampling and be assigned to respectively C with strange sampling_i⁰And C_i¹Obtain original coefficient: C_i⁰=H_{I, 2k},

3.2 many wavelet decomposition

According to following two formulas

$c_{j-1,k}=\frac{\sqrt{2}}{2}\underset{n}{\mathrm{\Σ}}{c}_{j,n}{H}_{n-2k}^{*}$

$d_{j-1,k}=\frac{\sqrt{2}}{2}\underset{n}{\mathrm{\Σ}}{c}_{j,n}{G}_{n-2k}^{*}$

Carry out wavelet decomposition more than 6 times, obtain the wavelet coefficient { d of different layers_{J-1, k},

3.3 the wavelet coefficient thresholding is processed, at first definite threshold is

σ wherein_jBe that noise criteria is poor under each yardstick, obtain by following formula is approximateAdopt afterwards the soft-threshold method to process, reach many Wavelet Denoising Methods purpose,

3.4 many wavelet reconstructions

According to following formula

${\hat{c}}_{j,k}=\frac{\sqrt{2}}{2}(\underset{n}{\mathrm{\Σ}}{c}_{j-1,n}{H}_{k-2n}+\underset{n}{\mathrm{\Σ}}{d}_{j-1,n}{G}_{k-2n})$

Finish many wavelet reconstructions, obtain after the reconstruct

3.5 reprocessing, by

Reduction obtains channel response

The 4th step, carry out linear interpolation in time domain, interpolation result is carried out in the symbol frequency domain average, finish the associating denoising

The frequency domain averaging method is processed in the symbolization, namely in above-mentioned i the symbol, and the channel matrix H of k subcarrier_{I, k}, be with the front m of subcarrier k and rear m, being averaging of (2m+1) individual adjacent sub-carriers channel matrix altogether carried out obtaining by time domain interpolation behind many Wavelet Denoising Methods to the 3rd stepCarry out frequency domain averaging method processing denoising in the symbol again, finish the associating denoising, the channel matrix that obtains k subcarrier is expressed as:

$H_{{i,k}^{\′}}^{\′}=\frac{1}{\min (k_{\max },k^{\′}+m)-\max (k_{\min },k^{\′}-m)+1}\underset{k=k^{\′}-m}{\overset{k^{\′}+m}{\mathrm{\Σ}}}{H}_{i,k}$

In the formula, k_MaxAnd k_MinBe respectively minimum and maximum subcarrier sequence number, exceed [k in the summation of following formula right-hand member_Min, k_Max] subcarrier do not exist, their channel matrix is set to zero;

In the 5th step, the characteristic of channel after the noise reduction process is through matrix inversion operation

With the characteristic of channel matrix after the associating denoising of the 4th step

Invert, obtain

In the 6th step, estimate the transmission data

The inverse matrix of the channel matrix of being obtained through matrix inversion operation by the characteristic of channel in the 5th step and by information data and pilot data that the second step that receiving terminal receives obtains estimates and sends data and be

${\stackrel{\‾}{x}}_{\mathrm{ik}}=y_{\mathrm{ik}}\·{H_{i,k}^{\′}}^{-1}=y_{\mathrm{ik}}\·{H_{i,k}^{\′}}^{*}/{\left|H_{i,k}^{\′}\right|}^2,$Wherein, i=1 ..., Nf; K=1 ..., Nsc.

Above-mentioned channel estimation methods for the PDM-CO-OFDM system describedly sends spacing wave on the Y-direction when directions X sends pilot tone, adopt the QAM modulation, establishes the frequency pilot sign that sends on X, the Y polarization direction and is:

$t_x=\begin{array}{c}\left[\begin{array}{c}{t}_x\\ 0\end{array}\right]\end{array},$$t_y=\left[\begin{array}{c}0\\ t_y\end{array}\right]$

In the formula, t_xAnd t_yBe X and Y-direction data pilot symbol, Y and directions X correspondence position send 0 pilot tone, namely as directions X transmission t_xThe time, the correspondence position of Y-direction sends 0.

Above-mentioned channel estimation methods for the PDM-CO-OFDM system, formation and the principle of described PDM-CO-OFDM system are that those skilled in the art know.

The invention has the beneficial effects as follows: compared with prior art, the remarkable advantage of channel estimation methods of the present invention is:

(1) the inventive method is the channel response that obtains by time domain interpolation behind many Wavelet Denoising Methods carrying out, and carries out in the symbol frequency domain averaging method again and processes denoising, finishes the associating denoising, obtains the total data point characteristic of channel behind the noise reduction.

(2) in optical OFDM system, prior art adopts block pilot tone or Comb Pilot, and these two kinds of pilot tone estimated performances are better, but overhead is larger.The scattered pilot that the inventive method adopts when reducing overhead, carries out the compensation of channel estimating and phase noise.

(3) design of pilot frequency format reduces the phase mutual interference between two polarization directions, simplifies the form of transmission matrix, and has improved the availability of frequency spectrum, has reduced to a great extent the expense of system.

(4) overcome the sensitiveness of LS algorithm to noise, kept simultaneously the simplicity of algorithm, had certain real-time tracking channel time-frequency characteristic ability, and can further resist the transmission damage.

To further prove outstanding substantive distinguishing features and the significant progress of the inventive method in the following examples.

Description of drawings

The present invention is further described below in conjunction with drawings and Examples.

Fig. 1 is the schematic process flow diagram that the present invention is used for the channel estimation methods of PDM-CO-OFDM system.

Fig. 2 is the PDM-CO-OFDM system channel estimation model schematic diagram based on pilot tone;

Fig. 3 is the inventive method directions X pilot design pattern schematic diagram;

Fig. 4 is the inventive method Y-direction pilot design pattern schematic diagram;

Fig. 5 is many Wavelet Denoising Methods flow chart;

Fig. 6 is the signal constellation (in digital modulation) figure without channel estimating;

Fig. 7 is the signal constellation (in digital modulation) figure that direct channels is estimated;

Fig. 8 is the signal constellation (in digital modulation) figure of ISFA denoising channel estimating;

Fig. 9 is the signal constellation (in digital modulation) figure of the inventive method associating denoising channel estimating;

Figure 10 is that the ber curve after the various channel estimating compares schematic diagram

Embodiment

Embodiment illustrated in fig. 1 showing, the flow process that the present invention is used for the channel estimation methods of PDM-CO-OFDM system is: at PDM-CO-OFDM system transmitting terminal the scattered pilot form is designed and chooses, send information data and pilot data → at receiving terminal with the information data and the pilot data that receive, to utilize least-squares algorithm be the LS algorithm carries out pilot tone point channel estimating → carry out linear interpolation at frequency domain to OFDM symbol, the interpolation result that obtains is carried out many Wavelet Denoising Methods → carry out linear interpolation in time domain, interpolation result is carried out in the symbol frequency domain average, finish after associating denoising → noise reduction process the characteristic of channel through matrix inversion operation and at receiving terminal with the information data that receives and pilot data → estimate transmission data.

Showing of PDM-CO-OFDM system channel estimation model based on pilot tone shown in Figure 2, suppose that the pilot frequency sequence that PDM-CO-OFDM system transmitting terminal inserts is

The sequence that receives is y_{I, k}, therefrom extract the pilot frequency sequence that receives

Then their pass is:

Utilize least square (LS) method criterion, i.e. min{ (Y-H_LSX)^H(Y-H_LSX) }, the LS that namely obtains the characteristic of channel at pilot tone place estimates:

After oneself knows the channel response of pilot frequency locations, can obtain the channel information that non-pilot symbol is put by the filtering interpolation algorithm, namely obtain the transfer function H of whole channel after the interpolation.At this moment, by inverse transformation, the transmission data that we can namely recover to obtain estimating are

Embodiment illustrated in fig. 3 showing, the square of black represents pilot tone among the figure.Frequency direction is placed 1 every 6, and time orientation is placed 1 every 7, but just identical every an OFDM symbol inserted mode that contains pilot tone at frequency domain.The square ofmark 0 represents to be 0 pilot tone herein, and corresponding Y-direction is in this relevant position data inserting pilot tone.

Embodiment illustrated in fig. 4 showing, the square of black represents pilot tone among the figure.Frequency direction is placed 1 every 6, and time orientation is placed 1 every 7, but just identical every an OFDM symbol inserted mode that contains pilot tone at frequency domain.The square ofmark 0 represents to be 0 pilot tone herein, and corresponding directions X is in this relevant position data inserting pilot tone.

Many Wavelet Denoising Methods flow chart illustration shown in Figure 5 shows, at first selects odd to carry out preliminary treatment, is about to the channel response H that the estimation of LS algorithm obtains by frequency domain interpolation_{I, k}Carry out the idol sampling and be assigned to respectively C with strange sampling_i⁰And C_i¹Obtain original coefficient: C_i⁰=H_{I, 2k},Then carry out many wavelet decomposition, obtain the wavelet coefficient { d of different layers_{J-1, k}; Then carry out the wavelet coefficient thresholding and process, at first definite threshold T_j, adopt afterwards the soft-threshold method to process, reach many Wavelet Denoising Methods purpose; Carry out afterwards many wavelet reconstructions, obtain after the reconstruct

Finish at last reprocessing, by${\hat{H}}_{i,k}=[H_{i,2k},H_{i,2k-1}]={\hat{c}}_{j,k},$Reduction obtains

Signal constellation (in digital modulation) figure without channel estimating shown in Figure 6 demonstrates without channel estimating and balanced signal constellation point and is distributed as annular.

The signal constellation (in digital modulation) figure that direct channels shown in Figure 7 is estimated, the signal constellation point that demonstrates after direct channels is estimated to process obviously concentrates near the 4QAM ideal constellation point, but the sensitivity owing to noise disperses still a lot of in the constellation point of periphery, and the mistake symbol is also more accordingly.

The signal constellation (in digital modulation) figure of ISFA denoising channel estimating shown in Figure 8 demonstrates ISFA denoising channel estimating more concentrated than the direct channels estimation, and the mistake symbol still less.

The planisphere of the inventive method associating denoising channel estimating shown in Figure 9 demonstrates associating denoising channel estimating constellation point distribution slight change, no longer is circular distribution, and more concentrated than ISFA denoising channel estimating constellation point.

Embodiment illustrated in fig. 10 show after the various channel estimating ber curve relatively, as can be seen from the figure the inventive method estimates that based on the PDM-CO-OFDM system channel of scattered pilot the associating denoising effect is best.Be 10 in bit error rate^-3The time, the inventive method estimates that based on the PDM-CO-OFDM system channel of scattered pilot with the channel estimating that does not add denoising be that the performance of general LS channel estimating is compared the improvement that 0.95～0.97dB is arranged, and compares the improvement that 0.19～0.21dB is arranged with the channel estimating performance that only has the ISFA denoising.The inventive method estimates that based on the PDM-CO-OFDM system channel of scattered pilot the Optical Signal To Noise Ratio of associating denoising namely reaches the BER upper bound 10 of forward error correction about 14.4dB^-3Requirement.

Embodiment

In optical OFDM system, prior art adopts block pilot tone or Comb Pilot, and these two kinds of pilot tone estimated performances are better, but overhead is larger.The scattered pilot of employing of the present invention when reducing overhead, carries out the compensation of channel estimating and phase noise.

The first step designs and chooses the scattered pilot form at PDM-CO-OFDM system transmitting terminal, sends information data and pilot data

By the Multi simulation running experiment, integrated system expense and estimated performance two aspects are considered, are carried out taking S in the design of pilot frequency design at the transmitting terminal X of PDM-CO-OFDM system and two polarization directions of Y_f=6, S_T1=4 and S_T2=3, be the scattered pilot pattern of optimum.Fig. 3 and Figure 4 shows that X that the present embodiment adopts and the scattered pilot pattern of two polarization directions of Y.Pilot tone is identical at frequency domain insertion interval, and it is identical that time domain is inserted the interval, but just identical every an OFDM symbol inserted mode that contains pilot tone at frequency domain.Simultaneously, the phase mutual interference of signal on two polarization directions when directions X sends pilot tone, sends spacing wave on the Y-direction, adopts the QAM modulation, establishes the frequency pilot sign that sends on X and the Y polarization direction and is:

${\mathrm{<figure-callout\; label="t"\; filenames="120921163145.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=\left[\begin{array}{c}{\mathrm{<figure-callout\; label="t\; x"\; filenames="120921163145.png,120921163149.png"\; state="\{\{state\}\}">t</figure-callout>}}_x\\ 0\end{array}\right],$$t_2=\left[\begin{array}{c}0\\ t_y\end{array}\right]---\left(1\right)$

In the formula, t_xAnd t_yBe X and Y-direction data pilot symbol, Y and directions X correspondence position send 0 pilot tone, namely as directions X transmission t_xThe time, the correspondence position of Y-direction sends 0, pilot frequency design as shown in Figure 3 and Figure 4.

Second step utilizes least-squares algorithm that OFDM symbol is carried out pilot tone point channel estimating at the PDM-CO-OFDM system receiving terminal

At the PDM-CO-OFDM system receiving terminal, the information data that the transmitting terminal that receives is sent and pilot data estimate the characteristic of channel at the pilot tone point place of X and Y polarization direction according to the LS algorithm principle.The present embodiment shows that at Fig. 2 i symbol and K subcarrier glazing fibre channel response Jones matrix obtain by the LS channel estimating, are expressed as in the model that the PDM-CO-OFDM system channel estimates:

$H_{i,k}=\left[\begin{array}{cc}{H}_{\mathrm{xx}}& H_{\mathrm{xy}}\\ H_{\mathrm{yx}}& H_{\mathrm{yy}}\end{array}\right]---\left(2\right)$

Suppose frequency pilot sign t_xAnd t_yExperienced same channel effect, the frequency pilot sign that then receives is:

$r_1\left(k\right)=\left[\begin{array}{c}{r}_{1x}\left(k\right)\\ r_{1y}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{xx}}{t}_x\left(k\right)\\ H_{\mathrm{yx}}{t}_x\left(k\right)\end{array}\right],$$r_2\left(k\right)=\left[\begin{array}{c}{r}_{2x}\left(k\right)\\ r_{2y}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{xy}}{t}_y\left(k\right)\\ H_{\mathrm{yy}}{t}_y\left(k\right)\end{array}\right]---\left(3\right)$

Then, channel matrix can be obtained by following formula:

$H_{i,k}=\left[\begin{array}{cc}{H}_{\mathrm{xx}}& H_{\mathrm{xy}}\\ H_{\mathrm{yx}}& H_{\mathrm{yy}}\end{array}\right]=\left[\begin{array}{cc}{r}_{1x}\left(k\right)/t_x\left(k\right)& r_{2x}\left(k\right)/t_y\left(k\right)\\ r_{1y}\left(k\right)/t_x\left(k\right)& r_{2y}\left(k\right)/t_y\left(k\right)\end{array}\right]---\left(4\right)$

Obtain thus the characteristic of channel at information data, pilot data and pilot tone point place.

The 3rd step, carry out linear interpolation at frequency domain, the interpolation result that obtains is carried out many Wavelet Denoising Methods

Commonly used in the prior art have the many small echos of small echo more than two kinds: GHM and many small echos of CL.

To given signal f (t), use$c_{j-1,k}=(c_{j-1,\mathrm{<figure-callout\; label="k"\; filenames="120921163145.png"\; state="\{\{state\}\}">k</figure-callout>}}^1,c_{j-1,k}^2,\&CenterDot;\&CenterDot;\&CenterDot;,c_{j-1,k}^r)$With$d_{j-1,k}=(d_{j-1,\mathrm{<figure-callout\; label="k"\; filenames="120921163145.png"\; state="\{\{state\}\}">k</figure-callout>}}^1,d_{j-1,k}^2,\&CenterDot;\&CenterDot;\&CenterDot;,d_{j-1,k}^r)$The scale coefficient and the wavelet coefficient that represent respectively many wavelet transformations, the former approaches part, and the latter is detail section.It is { c that many wavelet decomposition algorithm requires initial original coefficient_{J, k}, many wavelet decomposition are { c_{J, k}Be transformed into { c_{J-1, k}, { d_{J-1, k}Process, namely

$c_{j-1,k}=\frac{\sqrt{2}}{2}\underset{n}{\mathrm{\&Sigma;}}{c}_{j,n}{H}_{n-2k}^{*}---\left(5\right)$

$d_{j-1,k}=\frac{\sqrt{2}}{2}\underset{n}{\mathrm{\&Sigma;}}{c}_{j,n}{G}_{n-2k}^{*}---\left(6\right)$

H_kAnd G_kLow pass and the high pass filter matrix of many small echos of adopting.

Inverse process is many wavelet reconstructions, is expressed as follows:

${\hat{c}}_{j,k}=\frac{\sqrt{2}}{2}(\underset{n}{\mathrm{\&Sigma;}}{c}_{j-1,n}{H}_{k-2n}+\underset{n}{\mathrm{\&Sigma;}}{d}_{j-1,n}{G}_{k-2n})---\left(7\right)$

The many small echos of CL3 that the present embodiment is chosen in the many small echos of CL carry out denoising, its flow chart as shown in Figure 5, step is:

3.1 select odd to carry out preliminary treatment, be about to the channel response H that the LS estimation obtains by frequency domain interpolation_{I, k}Carry out the idol sampling and be assigned to respectively C with strange sampling_i⁰And C_i¹Obtain original coefficient: C_i⁰=H_{I, 2k},

3.2 many wavelet decomposition.Carry out wavelet decomposition more than 6 times according to formula (5) and (6), obtain the wavelet coefficient { d of different layers_{J-1, k},

3.3 the wavelet coefficient thresholding is processed, at first definite threshold is

σ wherein_jBe that noise criteria is poor under each yardstick, obtain by following formula is approximate

Adopt afterwards the soft-threshold method to process, reach many Wavelet Denoising Methods purpose,

3.4 many wavelet reconstructions are finished many wavelet reconstructions according to formula (7), obtain after the reconstruct

3.5 reprocessing, by${\hat{H}}_{i,k}=[H_{i,2k},H_{i,2k-1}]={\hat{c}}_{j,k},$Reduction obtains

The 4th step, carry out linear interpolation in time domain, interpolation result is carried out in the symbol frequency domain average, finish the associating denoising

Frequency domain averaging method (hereinafter to be referred as ISFA) is processed in the symbolization, namely in above-mentioned i the symbol, and the channel matrix H of k subcarrier_{I, k}, be with the front m of subcarrier k and rear m, being averaging of (2m+1) individual adjacent sub-carriers channel matrix altogether carried out obtaining by time domain interpolation behind many Wavelet Denoising Methods to the 3rd stepCarry out frequency domain averaging method processing denoising in the symbol again, finish the associating denoising, the channel matrix that obtains k subcarrier is expressed as:

$H_{{i,k}^{\&prime;}}^{\&prime;}=\frac{1}{\min (k_{\max },k^{\&prime;}+m)-\max (k_{\min },k^{\&prime;}-m)+1}\underset{k=k^{\&prime;}-m}{\overset{k^{\&prime;}+m}{\mathrm{\&Sigma;}}}{H}_{i,k}---\left(8\right)$

In the formula, k_MaxAnd k_MinBe respectively minimum and maximum subcarrier sequence number, exceed [k in the summation of following formula right-hand member_Min, k_Max] subcarrier do not exist, their channel matrix is set to zero, finishes thus the associating denoising, obtains the total data point characteristic of channel behind the noise reduction.

In the 5th step, the characteristic of channel after the noise reduction process is through matrix inversion operation

With the characteristic of channel matrix after the associating denoising of the 4th step

Invert, obtain

In the 6th step, estimate the transmission data

The inverse matrix of the channel matrix of being obtained through matrix inversion operation by the characteristic of channel in the 5th step and by information data and pilot data that the second step that receiving terminal receives obtains estimates and sends data and be

${\stackrel{\&OverBar;}{x}}_{\mathrm{ik}}=y_{\mathrm{ik}}\&CenterDot;{H_{i,k}^{\&prime;}}^{-1}=y_{\mathrm{ik}}\&CenterDot;{H_{i,k}^{\&prime;}}^{*}/{\left|H_{i,k}^{\&prime;}\right|}^2---\left(9\right)$

Wherein, i=1 ..., Nf; K=1 ..., Nsc.

The present embodiment adopts optical communication software that the PDM-CO-OFDM system is carried out modeling, Digital Signal Processing (being called for short DSP) part adopts the mode of associative simulation to realize, according to above method this PDM-CO-OFDM system is carried out channel estimating, acquired results is referring to Fig. 6～Figure 10.

Simulation parameter that the present embodiment adopts arranges as follows: the length that sends pseudo random sequence is 2¹⁵-1, system's speed is 80Gb/s, and OFDM symbol data frame length is N_Spf=16, FFT points N_c=1024, adopt the 4QAM modulation system; The major parameter of fiber model is: the loop of Optical Fiber Transmission gets 10, and each loop length is 100km, and loss factor is 0.22dB/km, and abbe number is 16ps/ (nmkm), and chromatic dispersion gradient is 0.08ps/ (nm²Km), PMD Coefficient is

Fig. 6～Figure 10, provided estimate without channel estimating, direct channels under the condition of 15dB Optical Signal To Noise Ratio and 1000km Transmission Fibers, signal constellation (in digital modulation) figure after ISFA denoising channel estimating and the associating denoising channel estimating.

Fig. 6 shows that the signal constellation point without channel estimating and equilibrium is distributed as annular, take GVD (Group Velocity Dispersion) as main channel dispersion effect so that the constellation point on each subcarrier produces different phase rotatings, produces final annular and distributes.Fig. 7 shows that the signal constellation point after direct channels is estimated to process obviously concentrates near the 4QAM ideal constellation point, but owing to the sensitivity to noise, disperses still a lot of in the constellation point of periphery, and the mistake symbol is also more accordingly.Fig. 8 and Fig. 9 show that the constellation point that adopts ISFA denoising channel estimating and associating denoising channel estimating is more concentrated than the direct channels estimation, the mistake symbol still less, the constellation point distribution slight change of associating denoising channel estimating no longer be circular distribution, and constellation point is more concentrated.Figure 10 is that direct channels is estimated, the error rate of system performance curve of ISFA denoising channel estimating, many Wavelet Denoising Methods channel estimating and the associating denoising channel estimating of m=5.Estimate that based on the PDM-CO-OFDM system channel of scattered pilot the associating denoising effect is best by Figure 10 explanation.Be 10 in bit error rate^-3The time, the present embodiment method estimates that based on the PDM-CO-OFDM system channel of scattered pilot with the channel estimating that does not add denoising be that the performance of general LS channel estimating is compared the improvement that 0.94～0.98dB is arranged, and compares the improvement that 0.1～0.3dB is arranged with the channel estimating performance that only has the ISFA denoising.The present embodiment method estimates that based on the PDM-CO-OFDM system channel of scattered pilot the Optical Signal To Noise Ratio of associating denoising namely reaches the BER upper bound 10 of forward error correction at 14.2～14.6dB^-3Requirement.

The formation of the system of PDM-CO-OFDM described in above-described embodiment and principle are that those skilled in the art know.

Claims (2)

1. be used for the channel estimation methods of PDM-CO-OFDM system, it is characterized in that: be a kind of channel estimation methods in conjunction with the average associating noise reduction of frequency domain in many small echos and the symbol based on scattered pilot, step is:

The first step designs and chooses the scattered pilot form at PDM-CO-OFDM system transmitting terminal, sends information data and pilot data

Carry out the design of pilot frequency design at the transmitting terminal X of PDM-CO-OFDM system and two polarization directions of Y, take S_f=6, S_T1=4 and S_T2=3, be the scattered pilot pattern, pilot tone is identical at frequency domain insertion interval, and it is identical that time domain is inserted the interval, but just identical every an OFDM symbol inserted mode that contains pilot tone at frequency domain, when sending pilot tone on the directions X, sends spacing wave on the Y-direction;

Second step, utilizing least-squares algorithm at the PDM-CO-OFDM system receiving terminal is that the LS algorithm carries out pilot tone point channel estimating to OFDM symbol

At the PDM-CO-OFDM system receiving terminal, the information data that the transmitting terminal that receives is sent and pilot data are according to the LS algorithm principle, estimate the characteristic of channel at the pilot tone point place of X, Y polarization direction, in PDM-CO-OFDM system channel estimation model, i symbol and k the fine channel response Jones matrix of subcarrier glazing obtain by the LS channel estimating:

$H_{i,k}=\left[\begin{array}{cc}{H}_{\mathrm{xx}}& H_{\mathrm{xy}}\\ H_{\mathrm{yx}}& H_{\mathrm{yy}}\end{array}\right]$

Suppose two frequency pilot sign t_xAnd t_yExperienced same channel effect, the frequency pilot sign that then receives is:

$r_1\left(k\right)=\left[\begin{array}{c}{r}_{1x}\left(k\right)\\ r_{1y}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{xx}}{t}_x\left(k\right)\\ H_{\mathrm{yx}}{t}_x\left(k\right)\end{array}\right],$$r_2\left(k\right)=\left[\begin{array}{c}{r}_{2x}\left(k\right)\\ r_{2y}\left(k\right)\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{xy}}{t}_y\left(k\right)\\ H_{\mathrm{yy}}{t}_y\left(k\right)\end{array}\right]$

Then, channel matrix can be obtained by following formula:

$H_{i,k}=\left[\begin{array}{cc}{H}_{\mathrm{xx}}& H_{\mathrm{xy}}\\ H_{\mathrm{yx}}& H_{\mathrm{yy}}\end{array}\right]=\left[\begin{array}{cc}{r}_{1x}\left(k\right)/t_x\left(k\right)& r_{2x}\left(k\right)/t_y\left(k\right)\\ r_{1y}\left(k\right)/t_x\left(k\right)& r_{2y}\left(k\right)/t_y\left(k\right)\end{array}\right]$

Obtain thus the characteristic of channel at information data, pilot data and pilot tone point place;

The 3rd step, carry out linear interpolation at frequency domain, the interpolation result that obtains is carried out many Wavelet Denoising Methods

Choose the many small echos of CL3 and carry out denoising, concrete steps are:

3.1 select odd to carry out preliminary treatment, be about to the channel response H that the LS estimation obtains by frequency domain interpolation_{I, k}Carry out the idol sampling and be assigned to respectively C with strange sampling_i⁰And C_i¹Obtain original coefficient: C_i⁰=H_{I, 2k},

3.2 many wavelet decomposition

According to following two formulas

$c_{j-1,k}=\frac{\sqrt{2}}{2}\underset{n}{\mathrm{\&Sigma;}}{c}_{j,n}{H}_{n-2k}^{*}$

$d_{j-1,k}=\frac{\sqrt{2}}{2}\underset{n}{\mathrm{\&Sigma;}}{c}_{j,n}{G}_{n-2k}^{*}$

Carry out wavelet decomposition more than 6 times, obtain the wavelet coefficient { d of different layers_{J-1, k},

3.3 the wavelet coefficient thresholding is processed, at first definite threshold is

σ wherein_jBe that noise criteria is poor under each yardstick, obtain by following formula is approximate

Adopt afterwards the soft-threshold method to process, reach many Wavelet Denoising Methods purpose,

3.4 many wavelet reconstructions

According to following formula

${\hat{c}}_{j,k}=\frac{\sqrt{2}}{2}(\underset{n}{\mathrm{\&Sigma;}}{c}_{j-1,n}{H}_{k-2n}+\underset{n}{\mathrm{\&Sigma;}}{d}_{j-1,n}{G}_{k-2n})$

Finish many wavelet reconstructions, obtain after the reconstruct

3.5 reprocessing, by

Reduction obtains channel response

The 4th step, carry out linear interpolation in time domain, interpolation result is carried out in the symbol frequency domain average, finish the associating denoising

The frequency domain averaging method is processed in the symbolization, namely in above-mentioned i the symbol, and the channel matrix H of k subcarrier_{I, k}, be with the front m of subcarrier k and rear m, being averaging of (2m+1) individual adjacent sub-carriers channel matrix altogether carried out obtaining by time domain interpolation behind many Wavelet Denoising Methods to the 3rd stepCarry out frequency domain averaging method processing denoising in the symbol again, finish the associating denoising, the channel matrix that obtains k subcarrier is expressed as:

$H_{{i,k}^{\&prime;}}^{\&prime;}=\frac{1}{\min (k_{\max },k^{\&prime;}+m)-\max (k_{\min },k^{\&prime;}-m)+1}\underset{k=k^{\&prime;}-m}{\overset{k^{\&prime;}+m}{\mathrm{\&Sigma;}}}{H}_{i,k}$

In the formula, k_MaxAnd k_MinBe respectively minimum and maximum subcarrier sequence number, exceed [k in the summation of following formula right-hand member_Min, k_Max] subcarrier do not exist, their channel matrix is set to zero;

In the 5th step, the characteristic of channel after the noise reduction process is through matrix inversion operation

With the characteristic of channel matrix after the associating denoising of the 4th stepInvert, obtain

In the 6th step, estimate the transmission data

The inverse matrix of the channel matrix of being obtained through matrix inversion operation by the characteristic of channel in the 5th step and by information data and pilot data that the second step that receiving terminal receives obtains estimates and sends data and be

${\stackrel{\&OverBar;}{x}}_{\mathrm{ik}}=y_{\mathrm{ik}}\&CenterDot;{H_{i,k}^{\&prime;}}^{-1}=y_{\mathrm{ik}}\&CenterDot;{H_{i,k}^{\&prime;}}^{*}/{\left|H_{i,k}^{\&prime;}\right|}^2,$Wherein, i=1 ..., Nf; K=1 ..., Nsc.

2. described channel estimation methods for the PDM-CO-OFDM system according to claim 1 is characterized in that: describedly send spacing wave on the Y-direction when directions X sends pilot tone, adopt the QAM modulation, establish the frequency pilot sign that sends on X, the Y polarization direction and be:

$t_x=\begin{array}{c}\left[\begin{array}{c}{t}_x\\ 0\end{array}\right]\end{array},$$t_y=\left[\begin{array}{c}0\\ t_y\end{array}\right]$

In the formula, t_xAnd t_yBe X and Y-direction data pilot symbol, Y and directions X correspondence position send 0 pilot tone, namely as directions X transmission t_xThe time, the correspondence position of Y-direction sends 0.

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