A carrier frequency offset estimation method for dual polarization coherent optical communication

Abstract

The application belongs to the technical field of coherent optical communication, and relates to a carrier frequency offset estimation method for dual-polarization coherent optical communication, which comprises the following steps: performing DSP processing on original data at a transmitting end, and modulating the data processed by the DSP processing by using an IQ modulator to generate a dual-polarization coherent optical signal; performing power compensation on the dual-polarization coherent optical signal; receiving the signal at a receiving end, and performing coherent demodulation on the received signal; performing DSP processing on the signal demodulated coherently to obtain a restored signal; performing processing on the signal by using a coarse positioning algorithm and a fine positioning algorithm during the DSP processing to obtain a training sequence; performing carrier frequency offset estimation on the signal optimized according to the training sequence; and performing phase offset compensation and data recovery on the signal according to the carrier frequency offset compensation result. The training sequence in the received signal is accurately positioned by using the coarse positioning algorithm and the fine positioning algorithm, and the carrier frequency offset estimation is performed on the signal based on the training sequence, so that the estimation accuracy is improved.

Description

Technical Field

[0001] This invention belongs to the field of coherent optical communication technology, specifically relating to a carrier frequency offset estimation method for dual-polarization coherent optical communication. Background Technology

[0002] With the rapid growth of global data traffic, the fundamental requirements for long-distance, high-speed, and large-capacity optical fiber transmission have been placed on it. Coherent optical communication, due to its high receiver sensitivity and support for high-order modulation formats such as QPSK and 16-QAM, provides a solution for achieving high-speed, long-distance, and large-capacity transmission. However, in coherent optical transmission systems, due to the limitations of manufacturing processes, it is impossible to make the frequencies of the transmitting laser and the local oscillator (LO) laser exactly the same. The carrier frequency offset mainly comes from the difference in frequencies between the transmitting and receiving lasers. This offset makes demodulation difficult, leading to inter-symbol interference (ISI) and synchronization errors. Therefore, how to achieve high-precision, low-complexity carrier frequency offset estimation in the receiver's DSP has become a key issue in improving the performance of the transmission system.

[0003] Currently, several algorithms have been proposed for estimating carrier frequency offset. For example, the fourth-power frequency offset estimation algorithm, which can only be used for QPSK signals, multiplies the received signal by its complex conjugate, then performs the fourth-power operation, sums the results, takes the amplitude, and divides by 4 to obtain the frequency offset. However, this algorithm has a limited range of estimated frequency offsets. Based on the fourth-power frequency offset estimation algorithm, a 16-QAM feedforward carrier frequency recovery algorithm based on a QPSK segmentation scheme is proposed for the 16QAM modulation format. This algorithm divides the constellation points of the 16QAM signal into two categories, selecting the corresponding QPSK constellation points from the 16QAM constellation points for fourth-power frequency offset estimation. Since only a subset of points is used for frequency offset estimation, the algorithm's performance is degraded. Another commonly used method is to estimate the carrier frequency offset using the Fast Fourier Transform (FFT). The basic idea is to perform an FFT on the amplitude of the received signal, divide the resulting peak frequency by 4 to obtain the frequency offset value. However, due to the need for FFT transformation, the computational complexity of this algorithm is relatively high. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a carrier frequency offset estimation method for dual-polarization coherent optical communication. The method includes: a dual-polarization coherent optical communication system comprising a transmitter, an optical fiber channel, and a receiver; performing DSP processing on the raw data at the transmitter, and modulating the DSP-processed data using an IQ modulator to generate a dual-polarization coherent optical signal; performing power compensation on the dual-polarization coherent optical signal in the optical fiber channel and transmitting it to the receiver; receiving the signal at the receiver and performing coherent demodulation on the received signal; and performing DSP processing on the coherently demodulated signal to obtain the restored signal.

[0005] The DSP processing of the coherently demodulated signal at the receiving end includes: compensating and optimizing the coherently demodulated signal to obtain an optimized signal; calculating the training sequence in the optimized signal; estimating the carrier frequency offset of the optimized signal based on the training sequence; performing frequency offset compensation on the signal based on the carrier frequency offset estimation result; and performing phase offset compensation and data recovery based on the result of frequency offset compensation.

[0006] The beneficial effects of this invention are:

[0007] This invention employs coarse and fine positioning algorithms to accurately locate the training sequence in the received signal, and estimates the carrier frequency offset of the signal based on the training sequence, thereby improving the accuracy of the estimation and reducing the complexity compared to other algorithms. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the principle framework of the carrier frequency offset estimation method for dual-polarization coherent optical communication of the present invention.

[0009] Figure 2 This is a block diagram of the simulation system structure of the present invention;

[0010] Figure 3 This is a diagram showing the results of the coarse localization algorithm of the present invention;

[0011] Figure 4 This is a diagram showing the results of the fine localization algorithm of the present invention;

[0012] Figure 5 The phase of the training sequence of this invention is the result before and after first-order linear fitting based on least squares.

[0013] Figure 6 shows the carrier frequency offset estimation accuracy and range results of the algorithm of the present invention and the comparison algorithm; where (a) is the X polarization state of the comparison algorithm; (b) is the Y polarization state of the comparison algorithm; (c) is the X polarization state of the algorithm of the present invention; and (d) is the Y polarization state of the algorithm of the present invention.

[0014] Figure 7The graph shows the relationship between BER and OSNR of the algorithm of this invention and the comparison algorithm in the simulation system. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] A carrier frequency offset estimation method for dual-polarization coherent optical communication is disclosed. The method includes: a dual-polarization coherent optical communication system comprising a transmitter, an optical fiber channel, and a receiver; comprising: performing DSP processing on raw data at the transmitter and modulating the DSP-processed data using an IQ modulator to generate a dual-polarization coherent optical signal; performing power compensation on the dual-polarization coherent optical signal in the optical fiber channel and transmitting it to the receiver; receiving the signal at the receiver and performing coherent demodulation on the received signal; and performing DSP processing on the coherently demodulated signal to obtain the restored signal.

[0017] The DSP processing of the coherently demodulated signal at the receiving end includes: compensating and optimizing the coherently demodulated signal to obtain an optimized signal; calculating the training sequence in the optimized signal; estimating the carrier frequency offset of the optimized signal based on the training sequence; performing frequency offset compensation on the signal based on the carrier frequency offset estimation result; and performing phase offset compensation and data recovery based on the result of frequency offset compensation.

[0018] Figure 1 This is a schematic diagram illustrating the principle structure of a carrier frequency offset estimation algorithm based on training sequences according to the present invention. The algorithm consists of a training sequence localization module and a frequency offset estimation module.

[0019] Dual-polarization coherent optical communication includes a transmitter, an optical fiber channel, and a receiver. At the transmitter, the raw data undergoes digital signal processing (DSP) and is converted into a dual-polarization coherent optical signal by an IQ modulator powered by a laser. In the optical fiber channel, the signal is transmitted over a long distance through a single-mode fiber and power compensation is performed using an erbium-doped fiber amplifier (EDFA). At the receiver, a coherent receiver performs coherent demodulation using a local oscillator laser and a photodetector, and then the data is processed by the receiver's DSP to reconstruct the original data.

[0020] The training sequence used for frequency offset estimation needs to satisfy the following conditions: the modulation phase cannot be too large, and the real or imaginary part of the training sequence cannot remain unchanged for a long time; the total length of the training sequence is 256 symbols, the second and 255th symbol sequences are 1000, which are used for coarse and fine positioning algorithms of the training sequence; other training sequences used for carrier frequency offset estimation are composed of 1111 and 1010.

[0021] The calculation of the training sequence based on the received signal includes: processing the received signal using a coarse positioning algorithm to obtain the starting position range of the training sequence; using a fine positioning algorithm to precisely locate the starting position range obtained by the coarse positioning algorithm to obtain the starting position of the training sequence; and obtaining the complete training sequence based on the starting position and the set length of the training sequence.

[0022] The algorithm aims to calculate the range of the starting position of the training sequence using a coarse localization algorithm. This includes: setting the window size to 256 symbols, continuously moving the window forward from the first bit of the received data, and using the sum of the absolute values ​​of the phase differences of all symbols within the window before and after fitting as the judgment criterion. The specific process of the algorithm includes the following steps:

[0023] S01: Obtain complex data of the X polarization state from the received data;

[0024] S02: Set the maximum value of the window's starting position index to IndexRange_X, meaning the range of the window's starting position is 1 to IndexRange_X;

[0025] S03: Starting from the first bit of the received data to the IndexRange_X bit, take the next 256 bits of complex data in sequence;

[0026] S04: Take the argument of the complex data in the window to obtain the corresponding phase value;

[0027] S05: Perform phase unwinding on the results obtained in S04;

[0028] S06: Subtract the phase value of the local training sequence from the result of S05 and store it in the CoarsePhaseDifference_X array;

[0029] S07: Perform a first-order linear fit on the data in the CoarsePhaseDifference_X array using the least squares method to obtain the fitted linear expression;

[0030] S08: Calculate the absolute value of the difference between each data point in the CoarsePhaseDifference_X array and its corresponding fitted data;

[0031] S09: Execute S08 on all data in the window, sum all the results obtained from S08, and store them in the array WindowAbsDiffSum_X;

[0032] S10: Repeat S04 to S09 until the IndexRange_X is obtained at the beginning of the window;

[0033] S11: Find the minimum value of the data in the array WindowAbsDiffSum_X. The index value corresponding to the minimum value is the location value of the coarse estimate of the X polarization state, Index_Rough_X.

[0034] S12: Obtain complex data of the Y polarization state from the received data;

[0035] S13: Set the maximum value of the window's starting position index to IndexRange_Y, meaning the range of the window's starting position is 1 to IndexRange_Y;

[0036] S14: Starting from the first bit of the received data to the IndexRange_Y bit, take the next 256 bits of complex data in sequence;

[0037] S15: Take the argument of the complex data in the window to obtain the corresponding phase value;

[0038] S16: Perform phase unwinding on the result obtained in S15;

[0039] S17: Subtract the phase value of the local training sequence from the result of S16 and store it in the CoarsePhaseDifference_Y array;

[0040] S18: Perform the same first-order linear fitting based on least squares as in S07 on the data in the CoarsePhaseDifference_Y array to obtain the fitted linear expression;

[0041] S19: Calculate the absolute value of the difference between each data point in the CoarsePhaseDifference_Y array and its corresponding fitted data;

[0042] S20: Execute S19 on all data in the window, sum all the results obtained from S19, and store them in the array WindowAbsDiffSum_Y;

[0043] S21: Repeat S15 to S20 until the IndexRange_Y is obtained at the beginning of the window;

[0044] S22: Find the minimum value of the data in the array WindowAbsDiffSum_Y. The index value corresponding to the minimum value is the location value of the coarse estimate of the Y polarization state, Index_Rough_Y.

[0045] In this embodiment, a first-order linear fitting algorithm based on the least squares approach is used, including: assuming the data before fitting is (x1, y1)...(x...). i ,y i )…(x m ,y m ), x i and y i These are the index values ​​of the PhaseDifference_X array and the corresponding values ​​within that array, respectively, where m is the length of the data to be fitted. The fitted line is expressed as y = kx + b, where k and b are the slope and intercept of the fitted line, respectively. The expression for the slope k is:

[0046]

[0047] The expression for the intercept b of the fitted line is:

[0048]

[0049] First-order linear fitting algorithms based on the least squares approach include:

[0050] S0701: Calculate the sum of the index values ​​of the data array to be fitted and store it in the variable sum_x;

[0051] S0702: Calculate the sum of the values ​​in all arrays of the data array to be fitted, and store it in the variable sum_y;

[0052] S0703: Calculate the sum of the products of the index and the corresponding value in the data array to be fitted, and store it in the variable sum_xy;

[0053] S0704: Calculate the sum of the squares of the index values ​​of the data array to be fitted, and store the sum in the variable sum_x_squared;

[0054] S0705: Calculate the length of the data array to be fitted and assign it to the variable m;

[0055] S0706: Multiply the result m of S0705 by the result sum_xy of S0703, then subtract the value of multiplying the result sum_x of S0701 by the result sum_y of S0702, and store it in the variable Slope_Numerator;

[0056] S0707: Multiply the result m of S0705 by the result sum_x_squared of S0704, subtract the squared result sum_x of S0701, and store the result in the variable Slope_Denominator.

[0057] S0708: Divide the value of Slope_Numerator by the value of Slope_Denominator to obtain the slope value of the fitted line, and store it in the variable k;

[0058] S0709: Divide the result sum_y of S0702 by the result m of S0705, then subtract the result k of S0708 multiplied by the result sum_x of S0701 divided by the result m of S0705, to obtain the intercept value of the fitted line, which is stored in variable b; return the fitted line expression y = kx + b.

[0059] The starting position of the window is narrowed down to the region near Index_Rough_X (or Index_Rough_Y) obtained from the coarse localization. The difference in the index values ​​corresponding to two consecutive data points with phase abrupt changes within the window is detected. When the difference is 254, the starting position of the window is the accurate starting position of the training sequence. The specific process of the fine localization algorithm includes the following steps:

[0060] S01: Input the parameters required by the algorithm, including the coarsely estimated location value, Index_Rough_X and Index_Rough_Y;

[0061] S02: Set the fluctuation of the window's starting position relative to Index_Rough_X as StartPosVariation_X, that is, the range of the window's starting position is from Index_Rough_X-StartPosVariation_X to Index_Rough_X+StartPosVariation_X.

[0062] S03: Take the received X-polarization state complex data with a length of 256 from the beginning position of the window;

[0063] S04: Take the argument of the complex data in the window to obtain the corresponding phase value;

[0064] S05: Perform phase unwinding on the results obtained in S04;

[0065] S06: Subtract the phase value of the local training sequence from the result of S05 and store it in the FinePhaseDifference_X array;

[0066] S07: Perform a first-order linear fit on the data in the FinePhaseDifference_X array using the least squares method to obtain the fitted linear expression;

[0067] S08: Calculate the distance from each point within the window to the fitted line and store it in the Distance_X array;

[0068] S09: Check the data in the Distance_X array one by one. If the data is greater than 1.2, store its corresponding index in the Point_index_X array.

[0069] S10: Subtract the value of the first element from the value of the second element in the Point_index_X array and add 1, then store the result in the variable L_X;

[0070] S11: If the value of L_X is equal to 254, then the exact starting position of the training sequence in the X polarization state, Index_X, is equal to the starting position of the window at this time; otherwise, repeat S03 to S10.

[0071] S12: Set the fluctuation of the window's starting position relative to Index_Rough_Y, i.e., the range of the window's starting position is from Index_Rough_Y-StartPosVariation_Y to Index_Rough_Y+StartPosVariation_Y.

[0072] S13: Take the received Y-polarization complex data with a length of 256 from the beginning position of the window;

[0073] S14: Take the argument of the complex data in the window to obtain the corresponding phase value;

[0074] S15: Perform phase unwinding on the result obtained in S14;

[0075] S16: Subtract the phase value of the local training sequence from the result of S15 and store it in the FinePhaseDifference_Y array;

[0076] S17: Perform a first-order linear fit on the data in the FinePhaseDifference_Y array using the least squares method to obtain the fitted linear expression;

[0077] S18: Calculate the distance from each point within the window to the fitted line and store it in the Distance_Y array;

[0078] S19: Check the data in the Distance_Y array one by one. If the data is greater than 1.2, store its corresponding index in the Point_index_Y array.

[0079] S20: Subtract the value of the first element from the value of the second element in the Point_index_Y array and add 1, then store the result in the variable L_Y;

[0080] S21: If the value of L_Y is equal to 254, then the exact starting position of the training sequence in the Y polarization state, Index_Y, is equal to the starting position of the window at this time; otherwise, repeat S13 to S20.

[0081] The phase of a signal can be represented as:

[0082] R k =exp{j(θ s (k)+ΔωkT+θ L (k)+θ n (k))}

[0083] Where, θ s (k) represents the modulation phase of the signal with index k. θ L (k) is phase noise caused by the laser linewidth. Since the phase noise changes slowly relative to high-speed symbols, it can be assumed that the phase noise is constant between adjacent symbols. The amplifier's ASE noise is represented by θ. n (k), and the mean phase of the ASE noise is 0. ΔωkT is the phase error caused by the carrier frequency offset to the k-th signal, and ΔωT is the carrier frequency offset value.

[0084] Assume RS k RS represents the k-th training symbol received. k The phase of a signal can be represented by the phase formula for the signal; TS k This represents the original k-th training symbol from the sender. TS k Phase:

[0085] TS k =exp{j(θ s (k))}

[0086] Figure 1 At point a, the received training sequence symbols RS are respectively... k and local training sequence symbols TS k Take the phase angle. Subtract the phase of the local training sequence symbol from the phase of the received training sequence symbol, and remove the modulation phase θ. s (k), this process is completed at point b.

[0087]

[0088] The phase of the training sequence symbols, obtained by subtracting the modulation phase, is shown above. This is achieved by subtracting the modulation phase from the phase of all training sequences. The carrier frequency offset estimate can be obtained by performing a first-order linear fit based on the least squares method. This process is completed at point c.

[0089] In this embodiment, after subtracting the phase value of the local training sequence from the phase value of the training sequence, a first-order linear fitting algorithm based on least squares is used to obtain the fitted line. The slope of the fitted line divided by 2π and then multiplied by the symbol rate is the estimated carrier frequency offset. The specific process of the algorithm includes the following steps:

[0090] S01: Input the parameters required by the algorithm, including: obtaining the accurate starting positions Index_X and Index_Y of the training sequence;

[0091] S02: Take 256 bits of complex data starting from the Index_X position of the received X polarization state data;

[0092] S03: Take the argument angle of the result of S02 to obtain the phase value corresponding to the received training sequence;

[0093] S04: Perform phase unwinding on the results obtained in S03;

[0094] S05: Subtract the phase value of the local training sequence from the result of S04 and store it in the TrainPhaseDifference_X array;

[0095] S06: Perform a first-order linear fit on the data in the TrainPhaseDifference_X array using the least squares method to obtain the slope Xfe of the fitted line;

[0096] S07: Divide the Xfe obtained in S06 by 2π and then multiply by the corresponding symbol rate to get the estimated carrier frequency offset of the X polarization state, EstFreqOffset_X.

[0097] S08: Take 256 bits of complex data starting from the Index_Y position of the received Y polarization state data;

[0098] S09: Take the argument angle of the result of S08 to obtain the phase value corresponding to the received training sequence;

[0099] S10: Perform phase unwinding on the results obtained in S09;

[0100] S11: Subtract the phase value of the local training sequence from the result of S10 and store it in the TrainPhaseDifference_Y array;

[0101] S12: Perform a first-order linear fit on the data in the TrainPhaseDifference_Y array using the least squares method to obtain the slope Yfe of the fitted line;

[0102] S13: Divide the Yfe obtained in S12 by 2π and multiply by the corresponding symbol rate to get the estimated carrier frequency offset value of the Y polarization state, EstFreqOffset_Y.

[0103] This embodiment verifies the invention through a specific example. The total number of bits to be transmitted is set to 524288, the transmission rate is 200 Gbit / s, the data modulation format is 16QAM, dual polarization is used for transmission, and the length of the training sequence for the positioning and frequency offset estimation algorithms is set to 256 symbols. Furthermore, the maximum values ​​of the window start position index (IndexRange_X and IndexRange_Y) in the coarse positioning of the algorithm are set to 200; the fluctuation magnitudes (StartPosVariation_X and StartPosVariation_Y) of the window start position relative to the coarse positioning result in the fine positioning of the algorithm are set to 4. Figure 2 The diagram shows the structure of the simulation system; Table 1 shows the specific parameters of the simulation system.

[0104] Table 1. Parameters of the simulation system based on training sequence localization and frequency offset estimation

[0105]

[0106] Figure 3 This is the result of the training sequence undergoing a coarse localization algorithm. Based on... Figure 3 As shown, phase peaks appeared at the 1st, 254th, and 256th symbols. Compared with the phase of the local training sequence, it can be seen that the starting position of the training sequence obtained by the coarse localization algorithm has shifted forward by one position compared with the accurate starting position.

[0107] Figure 4 for Figure 3 The result after coarse localization followed by fine localization algorithm. Based on... Figure 4 As shown, peaks appear at the 2nd and 255th symbols, consistent with the positions of peaks in the local training sequence. Therefore, the coarse and fine localization algorithms in this invention can obtain the accurate starting position of the training sequence, achieving the function of training sequence localization.

[0108] Figure 5In the frequency offset estimation algorithm of this invention, the result of subtracting the local phase from the phase of the training sequence and performing a first-order linear fitting based on the least squares method is as follows. It can be seen that the phase value of the training sequence, after first-order linear fitting, becomes a straight line, and the slope of this line divided by 2π and multiplied by the corresponding symbol rate is the estimated value of the carrier frequency offset.

[0109] To illustrate the advantages of the algorithm of the present invention in this embodiment, a frequency offset estimation algorithm based on the fourth power FFT is used for comparison. The number of points used for FFT estimation in this algorithm is 4096, and this algorithm is referred to as the comparison algorithm.

[0110] Figure 6 illustrates the specific performance of the two algorithms in terms of accuracy and range for estimating carrier frequency offset. It can be seen that when the carrier frequency offset is between 1 GHz and 6 GHz, the accuracy of the algorithm of this invention is superior to the comparative algorithm. Furthermore, regarding the estimable range, the simulation results given in Figures 6(a) and (b) show that when the carrier frequency offset is greater than 6 GHz, the estimated frequency offset value of the comparative algorithm differs significantly from the actual frequency offset value; while the algorithm of this invention can still accurately estimate the frequency offset when the carrier frequency offset is greater than 6 GHz. Simulation tests show that the estimation range of the algorithm of this invention is -17 GHz to 17 GHz.

[0111] Figure 7 The figure shows the bit error rate (BER) as a function of the injected optical signal-to-noise ratio (OSNR) for two different frequency offset estimation algorithms under X-polarization and Y-polarization conditions in simulations. It can be seen that the algorithm of this invention, compared to the comparative algorithm, achieves a lower bit error rate (BER) of 3.8 × 10⁻⁶. -3 An improvement of approximately 0.3 dB in OSNR can be achieved at the HD-FEC hard decision threshold.

[0112] Table 2 shows the computational complexity of the two algorithms. In the comparison algorithms, a single symbol undergoing a fourth power operation requires 1.5 complex multiplications, and an N-point FFT computation requires (N / 2)log2N complex multiplications. Here, N is the number of symbols used for fourth power FFT estimation of frequency offset, set to 4096 in the simulation; N... tr The length of the training sequences used for localization and frequency offset estimation is set to 256 in the simulation. It can be calculated that the comparative algorithm requires 159,744 actual additions and 122,880 actual multiplications; while the algorithm of this invention requires only 2,297 actual additions, 2,570 actual multiplications, and 256 argument operations. This shows that the computational complexity of the algorithm of this invention is reduced by approximately 98.1% compared to the comparative algorithm.

[0113] Table 2 Comparison of computational complexity

[0114]

[0115] In summary, the algorithm for localization and carrier frequency offset estimation based on training sequences proposed in this invention for dual-polarization coherent optical communication can accurately locate the training sequence and has lower computational complexity compared to other algorithms. This demonstrates the advantages of the algorithm and provides a selection criterion for frequency offset estimation in coherent optical communication.

[0116] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A carrier frequency offset estimation method for dual-polarization coherent optical communication, wherein the dual-polarization coherent optical communication system includes a transmitter, an optical fiber channel, and a receiver, characterized in that, include: The raw data is processed by DSP at the transmitting end, and the data processed by DSP is modulated by IQ modulator to generate a dual-polarization coherent optical signal. In the optical fiber channel, power compensation is performed on the dual-polarization coherent optical signal, and it is transmitted to the receiving end; the receiving end receives the signal and performs coherent demodulation on the received signal. The coherently demodulated signal is processed by DSP to obtain the restored signal. The DSP processing of the coherently demodulated signal at the receiving end includes: compensating and optimizing the coherently demodulated signal to obtain an optimized signal; calculating the training sequence in the optimized signal; estimating the carrier frequency offset of the optimized signal based on the training sequence; performing frequency offset compensation on the signal based on the carrier frequency offset estimation result; and performing phase offset compensation and data recovery based on the result of frequency offset compensation. Calculating the training sequence based on the received signal includes: setting the training sequence length; processing the received signal using a coarse positioning algorithm to obtain the starting position range of the training sequence; using a fine positioning algorithm to precisely locate the starting position range obtained by the coarse positioning algorithm to obtain the starting position of the training sequence; and obtaining the complete training sequence based on the starting position and the set training sequence length. Estimating the carrier frequency offset of the optimized signal includes: Step 1: Initialize the TrainPhaseDifference_X and TrainPhaseDifference_Y arrays; Step 2: Take 256 bits of complex data starting from the Index_X position of the received X polarization state data; Step 3: Take the argument of the 256-bit complex data to obtain the phase value corresponding to the received training sequence; Step 4: Perform phase unwrapping on the phase values, subtract the phase values ​​of the local training sequence from the phase unwrapping result, and store it in the TrainPhaseDifference_X array; Step 5: Perform a first-order linear fit on the data in the TrainPhaseDifference_X array using the least squares method to obtain the slope Xfe of the fitted line; Step 6: Divide Xfe by 2π and multiply by the corresponding symbol rate to obtain the estimated carrier frequency offset value EstFreqOffset_X for the X polarization state; Step 7: Take 256 bits of complex data starting from the Index_Y position of the received Y polarization state data; Step 8: Take the argument angle of the complex data of the Y polarization state to obtain the phase value corresponding to the received training sequence; Step 9: Perform phase unwrapping on the phase value corresponding to the Y polarization state data phase angle, subtract the phase value of the local training sequence from the phase unwrapped data, and store it in the TrainPhaseDifference_Y array; Step 10: Perform a first-order linear fit on the data in the TrainPhaseDifference_Y array using the least squares method to obtain the slope Yfe of the fitted line; Step 11: Divide Yfe by 2π and multiply by the corresponding symbol rate to obtain the estimated carrier frequency offset value of the Y polarization state, EstFreqOffset_Y.

2. The carrier frequency offset estimation method for dual-polarization coherent optical communication according to claim 1, characterized in that, Compensation and optimization of the coherently demodulated signal include IQ compensation, dispersion compensation, polarization mode dispersion compensation, matched filtering, clock recovery, and channel equalization.

3. The carrier frequency offset estimation method for dual-polarization coherent optical communication according to claim 1, characterized in that, The total length of the training sequence is 256 symbols, of which the sequence of the 2nd and 255th symbols is 1000, and the sequences of the other symbols are composed of 1111 or 1010.

4. The carrier frequency offset estimation method for dual-polarization coherent optical communication according to claim 1, characterized in that, The processing of the received signal using a coarse localization algorithm includes: Step 1: Set the window size to 256 symbols and the maximum value of the window's starting position index, IndexRange_X; initialize the CoarsePhaseDifference_X array and the WindowAbsDiffSum_X array; obtain the complex data of the X polarization state from the received signal; Step 2: Starting from the first bit of the received data to the IndexRange_X bit, take the next 256 bits of complex data in sequence to obtain the window complex data; Step 3: Take the argument of the complex data in the window to obtain the phase value corresponding to the complex data in the window; Step 4: Perform phase unwrapping on the phase values, subtract the phase unwrapping result from the phase values ​​of the local training sequence, and store the subtraction result in the CoarsePhaseDifference_X array; Step 5: Perform a first-order linear fit on the data in the CoarsePhaseDifference_X array using the least squares method; Step 6: Calculate the difference between each data point in the CoarsePhaseDifference_X array and its corresponding first-order linear fit data, and take the absolute value of the difference; Step 7: When all the data in the window has completed the absolute value calculation, sum all the absolute values ​​and store the summation result in the array WindowAbsDiffSum_X; Step 8: Repeat steps 3 to 7 until the starting position of the window is obtained as IndexRange_X; Step 9: Find the minimum value of the data in the array WindowAbsDiffSum_X. The index value corresponding to the minimum value is the location value Index_Rough_X for the coarse estimation of the X polarization state. Step 10: Set the maximum value of the window start position index to IndexRange_Y, initialize the CoarsePhaseDifference_Y array and the WindowAbsDiffSum_Y array, and obtain the complex data of the Y polarization state from the received data; Step 11: The complex data processing method for the Y-polarization state is the same as that for the X-polarization state, to obtain the coarsely estimated location value Index_Rough_Y for the Y-polarization state.

5. The carrier frequency offset estimation method for dual-polarization coherent optical communication according to claim 4, characterized in that, First-order linear fitting of the data based on the least squares method includes: Step 51: Calculate the sum of the index values ​​in the fitted data set to obtain sum_x; Step 52: Calculate the sum of all data in the fitted data set to obtain sum_y; Step 53: Calculate the sum of the products of the index and the corresponding value in the data array to be fitted, and obtain sum_xy; Step 54: Calculate the sum of the squares of the index values ​​of the data array to be fitted, and obtain sum_x_squared; Step 55: Calculate the length m of the data array to be fitted; Step 56: Calculate the slope k of the fitted line based on the length m, sum_x, sum_y, sum_xy, and sum_x_squared; Step 57: Calculate the intercept b of the fitted line based on the slope value k, sum_x, sum_y and length m; obtain the expression of the fitted line based on the slope and intercept of the fitted line, and complete the first-order linear fitting based on the least squares method.

6. The carrier frequency offset estimation method for dual-polarization coherent optical communication according to claim 5, characterized in that, The expression for the slope k of the fitted line is: The expression for the intercept b of the fitted line is: Where m is the length of the data array to be fitted, x i To fit the i-th index value in the data set, y i Let be the i-th data value in the fitted data set, and k be the slope of the fitted line.

7. The carrier frequency offset estimation method for dual-polarization coherent optical communication according to claim 1, characterized in that, The fine-positioning algorithm is used to accurately locate the starting position range obtained by the coarse-positioning algorithm, including: S1. Initialize the FinePhaseDifference_X array, Distance_X array, and Point_index_X array; set the fluctuation value of the window's starting position relative to Index_Rough_X; calculate the initial position range of the window based on the coarsely estimated positioning value Index_Rough_X and the fluctuation value. S2. Take the received X-polarization state complex data with a length of 256 from the beginning position of the window; S3. Take the argument of the complex data in the window to obtain the phase value corresponding to the complex data in the window; S4. Perform phase unwrapping on the phase values, subtract the phase unwrapping result from the phase values ​​of the local training sequence, and store the result of the subtraction in the FinePhaseDifference_X array; S5. Perform a first-order linear fit on the data in the FinePhaseDifference_X array using the least squares method to obtain the fitted line; S6. Calculate the distance from all points within the window to the fitted line and store the distances in the Distance_X array; S7. Set a threshold. Compare the data in the Distance_X array with the threshold. If the data is greater than the set threshold, store its corresponding index in the Point_index_X array. S8. Subtract the value of the first element from the value of the second element in the Point_index_X array and add 1, then store the result in the variable L_X; S9. If the value of L_X is equal to 254, then the exact starting position of the training sequence in the X polarization state, Index_X, is equal to the starting position of the window at this time; otherwise, repeat S2 to S8. S10. Initialize the FinePhaseDifference_Y array, Distance_Y array, and Point_index_Y array; set the fluctuation value of the window's starting position relative to Index_Rough_Y; calculate the initial position range of the window based on the coarsely estimated positioning value Index_Rough_Y and the fluctuation value. S11. Take the received Y-polarization state complex data with a length of 256 from the beginning position of the window; S12. The processing method for complex data of Y polarization state is the same as that for complex data of X polarization state, to obtain the accurate starting position Index_Y of the training sequence of Y polarization state.

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