Nonlinear equalization method of ultra-high-order QAM coherent optical transmission system

Abstract

The invention relates to the technical field of coherent light transmission, and discloses a nonlinear equalization method of an ultra-high-order QAM coherent light transmission system, which comprises the following steps: acquiring a damaged digital signal after a signal to be transmitted is transmitted; iQ orthogonalization is carried out on the X polarization state and the Y polarization state of the damaged digital signal, in-phase components and orthogonal components of the X polarization state and the Y polarization state are obtained and expressed as XI, XQ, YI and YQ, and optimized in-phase components and optimized orthogonal components of the X polarization state and the Y polarization state are obtained through dispersion compensation, clock recovery, multimode operation, frequency offset estimation and carrier phase recovery in sequence; for the X polarization state and the Y polarization state, the optimized in-phase component and the optimized orthogonal component are used as input, an improved Wollaston polynomial equalizer is input, combined equalization is carried out through Wollaston series, corresponding X polarization state estimation digital signals and Y polarization state estimation digital signals are output, and equalization digital signals are obtained through fusion. And completing nonlinear equalization of the damaged digital signal.

Description

Technical Field

[0001] The invention relates to the technical field of coherent optical transmission, and in particular to a nonlinear equalization method for an ultra-high-order QAM coherent optical transmission system. Background Art

[0002] With the continuous expansion of data centers and the increasing popularity of cloud services, the expected demand of each user in the future optical access network will reach the order of gigabits per second. In order to meet the growing demand for data transmission rates, the next generation of optical fiber communication systems requires higher spectral efficiency. Therefore, how to improve the spectral efficiency of the system has become a core research topic.

[0003] In this regard, high-order modulation formats can effectively increase spectral efficiency by increasing the number of bits carried by each symbol. At the same time, the application of probability shaping (PS) and geometric shaping (GS) technology has become the focus of increasing channel capacity and transmission distance in coherent optical communication systems. Furthermore, by jointly coding with FEC, that is, applying the probability amplitude shaping (PAS) scheme, the BER performance of the system can be effectively improved and the reliability of information transmission can be increased. However, the Euclidean distance between adjacent constellation points of ultra-high-order quadrature amplitude modulation (QAM) signals increases exponentially with the increase of the modulation order. Any defects in devices or links that may be ignored when using low-order modulation formats may seriously affect the performance of the system. Optical signals will encounter nonlinear impairments during propagation. In systems with high-order modulation formats or high-speed transmission, these impairments will significantly affect the signal quality, thereby limiting the transmission capacity of the system.

[0004] Among the nonlinear compensation algorithms proposed so far, digital back propagation (DBP) is considered to be a promising method. It uses a split-step Fourier algorithm to iteratively compensate for nonlinear effects at the transmitter or receiver. This algorithm can effectively eliminate deterministic nonlinear crosstalk between signals and is therefore recognized as a benchmark solution for compensating fiber nonlinearity. However, the algorithm has high computational complexity and is not suitable for short-distance transmission. In recent years, neural networks have flourished in optical communication applications due to their powerful learning ability, and several neural network equalization schemes for optical channel equalization have been proposed. However, a major challenge is that neural network-based algorithms usually have high computational complexity and how to implement an interpretable neural network model. In addition, for the equalization of ultra-high-order QAM signals, neural network equalizers cannot achieve ideal results. Therefore, both digital back propagation and neural network-based methods have the problem of high computational complexity in short-distance transmission.

[0005] In addition, the Volterra nonlinear equalizer (VNLE) has a strong effect on alleviating the nonlinear distortion of the signal and can compensate for the nonlinear inter-symbol interference caused by the transceiver or the Kerr effect. However, the general single-input single-output (SISO) Volterra nonlinear equalizer (VNLE) is more suitable for pulse amplitude modulation (PAM) signals, and is not applicable to QAM signals with in-phase components and orthogonal components. And because ultra-high-order QAM signals are more susceptible to system damage, nonlinear damage is a key limiting factor. For higher optical signal-to-noise ratios (OSNR), the system is more susceptible to nonlinearity, and the traditional single-input single-output (SISO) Volterra nonlinear equalizer (VNLE) still has the problem of unstable bit error rate results after equalization. Summary of the invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the problem in the prior art that the nonlinear distortion and bit error rate of the signal transmitted in the ultra-high-order QAM coherent optical transmission system cannot be balanced, resulting in inaccurate transmission signals.

[0007] In order to solve the above technical problems, the present invention provides a nonlinear equalization method for an ultra-high-order QAM coherent optical transmission system, comprising:

[0008] Obtaining the damaged digital signal output after the signal to be transmitted is transmitted through the ultra-high-order QAM coherent optical transmission system;

[0009] Performing IQ orthogonalization on the X polarization state and the Y polarization state of the damaged digital signal respectively to obtain an in-phase component XI and an orthogonal component XQ of the X polarization state, and an in-phase component YI and an orthogonal component YQ of the Y polarization state;

[0010] Let XI, XQ, YI and YQ respectively undergo dispersion compensation, clock recovery, multi-mode operation, frequency offset estimation and carrier phase recovery in sequence to obtain the optimized in-phase component and optimized orthogonal component of the X polarization state, and the optimized in-phase component and optimized orthogonal component of the Y polarization state;

[0011] For both the X polarization state and the Y polarization state, the optimized in-phase component and the optimized orthogonal component are used as inputs to the improved Volterra polynomial equalizer, and the Volterra series is used for joint equalization to output the corresponding X polarization state estimation digital signal and Y polarization state estimation digital signal;

[0012] Based on the X polarization state estimation digital signal and the Y polarization state estimation digital signal, an equalized digital signal is obtained by fusion, thereby completing nonlinear equalization of the damaged digital signal.

[0013] Preferably, the improved Volterra polynomial equalizer is expressed as:

[0014] z*(n)=V 1 [uI (n),u Q (n)]+jV 2 [u I (n),u Q (n)];

[0015] Among them, u I (n) and u Q (n) respectively represent the optimized in-phase component and the optimized orthogonal component of the polarization state signal currently input, z*(n) represents the estimated digital signal; j represents the imaginary part; V 1 With V 2 is the Volterra series, expressed as

[0016] l i represents the window length before and after the center of the sliding window of the i-th order term in the improved Volterra polynomial equalizer; the total window length of the i-th order term of the improved Volterra polynomial equalizer is expressed as: L i =2l i +1; i represents the i-th order term of the improved Volterra polynomial equalizer, i∈[1,2,3]; W represents the set of tap coefficients, defined as w 1 、w 2 With w 3 denote the tap coefficients of the first-order term, the second-order term and the third-order term of the improved Volterra polynomial equalizer respectively; represents the transpose of the tap coefficient of the i-th order term; The complex number symbol received at the center of the sliding window of the i-th order term is defined as U 1 , U 2 with U 3 The complex symbols of the sliding window centers of the first-order, second-order, and third-order terms, respectively; n represents the nth symbol in the current input polarization state signal, k 1 , k 2 With k 3 is the preset sliding window coefficient of the i-th order term; represents the Kronecker product, defined as

[0017] Preferably, the nonlinear augmentation operator A generated by N products of the received signal vector U(n) is used to define the augmented received signal vector v(n)=A[U(n)], and the improved Volterra polynomial equalizer is expressed as:

[0018] z*(n)=W T v(n);

[0019] Wherein, U(n) represents the received signal vector of the polarization state signal currently input with a length of L, and the expression is U(n)=[u(n-1),u(n),…,u(n+1)] T ; N represents the total order of the improved Volterra polynomial equalizer; W T Represents the transpose of a set of tap coefficients.

[0020] Preferably, a horizontal cascade set V of the augmented received signal vector v(n)=A[U(n)] is obtained, and the improved Volterra polynomial equalizer is expressed as:

[0021] z*=W T V;

[0022] Among them, z * =[z * (1),z * (2),…,z * (K)] is the shift input vector, K represents the preset window movement times; the horizontal cascade set is expressed as V = [v(1), v(2),…, v(K)].

[0023] Preferably, the number of taps N of the improved Volterra polynomial equalizer is MVPE , expressed as:

[0024]

[0025] Where P represents the total order of the improved Volterra polynomial equalizer, 1≤i≤P; L i represents the total window length of the i-th order term of the improved Volterra polynomial equalizer, and ! represents the factorial operation.

[0026] Preferably, the improved Volterra polynomial equalizer is optimized using an adaptive method of recursive least squares method based on the error between the signal to be transmitted and the equalized digital signal.

[0027] Preferably, the step of obtaining a damaged digital signal output after the signal to be transmitted is transmitted by an ultra-high-order QAM coherent optical transmission system comprises:

[0028] After preprocessing, the signal to be transmitted is input into the transmitting end of the ultra-high-order QAM coherent optical transmission system, and the corresponding optical signal is generated through the waveform generator and IQ modulator;

[0029] The optical signal is amplified and regulated through the transmission route and then sent to the receiving end;

[0030] The receiving end performs denoising and filtering on the received optical signal, inputs it into an oscilloscope, performs analog-to-digital conversion, and outputs a damaged digital signal.

[0031] Preferably, the signal to be transmitted is preprocessed, including:

[0032] The signal to be transmitted is passed through a constant composition distribution matcher to generate a specified amplitude sequence, and is mapped into a binary bit sequence according to a Gray code;

[0033] After combining the binary bit sequence with the preset bit sequence, LDPC encoding is performed to obtain a coded sequence;

[0034] Input the coded sequence into the interleaver for interleaving, obtain I-channel data information and Q-channel data information, and generate an interleaved signal;

[0035] The interleaved signal is up-sampled, root-raised cosine filtered, and channel tilt compensated to obtain a pre-processed signal to be transmitted.

[0036] Preferably, the step of amplifying and adjusting the optical signal through the transmission route and then sending it to the receiving end comprises:

[0037] Amplifying the optical signal by a first erbium-doped fiber amplifier and outputting the amplified optical signal;

[0038] The amplified optical signal is adjusted to the preset input optical power by using a variable optical attenuator and input into a standard single-mode optical fiber for transmission;

[0039] The second erbium-doped fiber amplifier amplifies the optical signal transmitted by the standard single-mode optical fiber and inputs the amplified signal to the receiving end.

[0040] Preferably, the receiving end performs denoising and filtering on the received optical signal, inputs the signal into an oscilloscope, performs analog-to-digital conversion, and outputs a damaged digital signal, including:

[0041] De-noising the received optical signal using an optical bandpass filter to obtain a de-noised optical signal;

[0042] The denoised optical signal is input into the coherent receiver together with the local oscillator light, and the denoised optical signal is converted into an electrical signal using an oscilloscope to obtain the damaged digital signal output.

[0043] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0044] The nonlinear equalization method of the ultra-high-order QAM coherent optical transmission system of the present invention obtains the in-phase component and the orthogonal component of the signal to be transmitted in the X polarization state and the Y polarization state as multiple inputs, and inputs them into the improved Volterra polynomial equalizer with multiple inputs and outputs proposed by the present invention, and jointly equalizes the in-phase component and the orthogonal component in the X polarization state or the Y polarization state, further compensating for the nonlinear damage of the system, and can obtain a stable equalization result. The improved Volterra polynomial equalizer proposed by the present invention is based on a dual-input real-valued Volterra series, which includes not only the terms in each branch, but also the cross terms between the I path and the Q path, and only retains one of the cross terms, removes repeated cross terms, reduces the calculation complexity, reduces the transmission bit error rate, improves the nonlinear equalization effect, and makes the signal transmitted through the ultra-high-order QAM coherent optical transmission system more accurate and safe.

[0045] The present invention optimizes the improved Volterra polynomial equalizer by using an adaptive method of recursive least squares method, which is not adversely affected by the covariance matrix condition and can update the inverse covariance matrix in each new sample, thereby effectively avoiding the problem of ill-conditioning and improving the equalization effect of the optimized improved Volterra polynomial equalizer. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0047] Figure 1 It is a flowchart of the steps of the nonlinear equalization method of the ultra-high-order QAM coherent optical transmission system provided by the present invention;

[0048] Figure 2 (a) is a model diagram of a typical Volterra transceiver. Figure 2 (b) is a model diagram of the p-order Volterra nonlinear equalizer;

[0049] Figure 3 It is a structural diagram of the improved Volterra polynomial equalizer;

[0050] Figure 4 It is a comparison chart of the NGM I performance of 4096-QAM signal transmitted back-to-back under MVPE and VNLE equalization;

[0051] Figure 5 It is a comparison chart of NGM I performance of 4096-QAM signal transmitted back-to-back under MVPE-LC and LMS+DD-LMS equalization;

[0052] Figure 6This is a comparison chart of NGMI performance of 4096-QAM signal transmitted back-to-back under MVPE+MVPE-LC and VNLE+LMS+DD-LMS equalization;

[0053] Figure 7 This is the NGM I performance comparison chart of 4096-QAM signal under MVPE+MVPE-LC and VNLE+LMS+DD-LMS equalization for 80km SSMF transmission;

[0054] Figure 8 This is a diagram of the experimental setup of the 4096-QAM 80km SSMF coherent optical transmission system;

[0055] Fig. 9 It is the flow chart of the digital signal processing algorithm at the receiving end of the system. DETAILED DESCRIPTION

[0056] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0057] Reference Figure 1 As shown, the step flow chart of the nonlinear equalization method of the ultra-high-order QAM coherent optical transmission system of the present invention comprises the following specific steps:

[0058] S101: Acquire a damaged digital signal output after the signal to be transmitted is transmitted through an ultra-high-order QAM coherent optical transmission system;

[0059] S102: performing IQ orthogonalization on the X polarization state and the Y polarization state of the damaged digital signal respectively, obtaining an in-phase component XI and an orthogonal component XQ of the X polarization state, and an in-phase component YI and an orthogonal component YQ of the Y polarization state;

[0060] S103: Let XI, XQ, YI and YQ respectively undergo dispersion compensation, clock recovery, multi-mode operation, frequency offset estimation and carrier phase recovery in sequence to obtain the optimized in-phase component and optimized quadrature component of the X polarization state, and the optimized in-phase component and optimized quadrature component of the Y polarization state;

[0061] S104: for the X polarization state and the Y polarization state, the optimized in-phase component and the optimized orthogonal component are input to the improved Volterra polynomial equalizer, and the Volterra series is used for joint equalization to output the corresponding X polarization state estimated digital signal and Y polarization state estimated digital signal;

[0062] S105: Based on the X polarization state estimation digital signal and the Y polarization state estimation digital signal, an equalized digital signal is obtained by fusing, thereby completing nonlinear equalization of the damaged digital signal.

[0063] Reference Figure 2 As shown, Figure 2 (a) is a model diagram of a typical Volterra transceiver. Figure 2 (b) is a model diagram of a p-order Volterra nonlinear equalizer; in order to mitigate the nonlinear distortion caused by optoelectronic devices, such as the nonlinear response of the I / Q modulator, the square-law detection of the PD, and the nonlinearity of the amplifier and laser, a p-order Volterra nonlinear equalizer (VNLE) can be used to compensate. A typical Volterra transceiver model and a VNLE in series are shown in Figure 1. Figure 2 As shown in (a) and (b), x is the transmitted symbol and h is the coefficient corresponding to different times of x. Similarly, in the equalizer, y is the received symbol and w is the coefficient corresponding to different times of y. The p-order Volterra nonlinear equalizer is the inverse of the transmitter model. By calculating the error between the transmitter signal and the equalized signal, the adaptive algorithm is used to continuously update the equalizer coefficients to obtain the optimal p-order Volterra nonlinear equalizer, which can be expressed as: Where x*(n) is the estimate of the nth symbol sent, y(n) is the nth symbol received, and wi is the coefficient of the i-th product of y.

[0064] In this embodiment, the ordinary VNLE is extended to a dual-input model to construct a MIMO Volterra Polynomial Equalizer (MVPE), which takes the real and imaginary parts of the signal as input. Based on this, the received complex signal will be equalized using two separate MVPEs with the real and imaginary parts as outputs. Figure 3 As shown, it is a structural diagram of the improved Volterra polynomial equalizer; the improved Volterra polynomial equalizer is expressed as: z*(n)=V 1 [u I (n),u Q (n)]+jV 2 [u I (n),u Q (n)];

[0065] Among them, u I (n) and u Q (n) respectively represent the optimized in-phase component and the optimized orthogonal component of the polarization state signal currently input, z*(n) represents the estimated digital signal; j represents the imaginary part; V 1 With V 2 is the Volterra series, expressed as

[0066] l i represents the window length before and after the center of the sliding window of the i-th order term in the improved Volterra polynomial equalizer; the total window length of the i-th order term of the improved Volterra polynomial equalizer is expressed as: L i =2l i+1; i represents the i-th order term of the improved Volterra polynomial equalizer, i∈[1,2,3]; W represents the set of tap coefficients, defined as w 1 、w 2 With w 3 denote the tap coefficients of the first-order term, the second-order term and the third-order term of the improved Volterra polynomial equalizer respectively; represents the transpose of the tap coefficient of the i-th order term; The complex number symbol received at the center of the sliding window of the i-th order term is defined as U 1 , U 2 with U 3 The complex symbols of the sliding window centers of the first-order, second-order, and third-order terms, respectively; n represents the nth symbol in the current input polarization state signal, k 1 , k 2 With k 3 is the preset sliding window coefficient of the i-th order term; represents the Kronecker product, defined as

[0067] In this embodiment, the nonlinear augmentation operator A generated by the N products of the received signal vector U(n) is used to define the augmented received signal vector v(n)=A[U(n)], and the improved Volterra polynomial equalizer is expressed as: z*(n)=W T v(n); where U(n) represents the received signal vector of the polarization state signal currently input with a length of L, and is expressed as U(n) = [u(n-1), u(n), …, u(n+1)] T ; N represents the total order of the improved Volterra polynomial equalizer; W T Represents the transpose of a set of tap coefficients.

[0068] In this embodiment, a horizontal cascade set V of the augmented received signal vector v(n)=A[U(n)] is obtained, and the improved Volterra polynomial equalizer is expressed as: * =W T V; where z * =[z * (1),z * (2),…,z * (K)] is the shift input vector, K represents the preset window movement times; the horizontal cascade set is expressed as V = [v(1), v(2),…, v(K)].

[0069] Specifically, the number of taps N of the improved Volterra polynomial equalizer is MVPE , expressed as:

[0070]

[0071] Where P represents the total order of the improved Volterra polynomial equalizer, 1≤i≤P; L i represents the total window length of the i-th order term of the improved Volterra polynomial equalizer, and ! represents the factorial operation.

[0072] The nonlinear equalization method of the ultra-high-order QAM coherent optical transmission system of the present invention obtains the in-phase component and the orthogonal component of the signal to be transmitted in the X polarization state and the Y polarization state as multiple inputs, and inputs them into the improved Volterra polynomial equalizer with multiple outputs proposed by the present invention, and jointly equalizes the in-phase component and the orthogonal component in the X polarization state or the Y polarization state, further compensating for the nonlinear damage of the system, and can obtain a stable equalization result. And the improved Volterra polynomial equalizer proposed by the present invention, based on the dual-input real-valued Volterra series, not only includes the terms in each branch, but also includes the cross terms between the I path and the Q path, and only retains one of the cross terms, removes repeated cross terms, reduces the calculation complexity, reduces the transmission bit error rate, improves the nonlinear equalization effect, and makes the signal transmitted by the ultra-high-order QAM coherent optical transmission system more accurate and safe.

[0073] In an embodiment of the present invention, based on the error between the signal to be transmitted and the equalized digital signal, the improved Volterra polynomial equalizer is optimized by using an adaptive method of the recursive least squares method. The present invention optimizes the improved Volterra polynomial equalizer by using an adaptive method of the recursive least squares method, which is not adversely affected by the covariance matrix condition and can update the inverse covariance matrix in each new sample, thereby effectively avoiding the problem of ill-conditioning and improving the equalization effect of the optimized improved Volterra polynomial equalizer.

[0074] Based on the above embodiments, in an embodiment of the present invention, the effect of the nonlinear equalization method of the ultra-high-order QAM coherent optical transmission system provided by the present invention is verified. Specifically, the nonlinear equalization process includes:

[0075] The third-order improved Volterra polynomial equalizer can be expressed as:

[0076] z*(n)=V 1 [u I (n),u Q (n)]+jV 2 [u I (n),u Q (n)];

[0077] in, represents the Kronecker product, defined as Vector W and is defined as The equalizer is based on a dual-input real-valued Volterra series, which includes not only the terms in each branch but also the cross terms between I and Q. Therefore, the nonlinear impairments of I and Q paths can be jointly equalized.

[0078] For the p-order Volterra nonlinear equalizer, assume that the memory length before and after the sliding window center is l i , the memory length of the i-th order term is L i =2l i +1 gives the coefficients w of the p-order Volterra nonlinear equalizer i The number of (number of taps) is:

[0079] However, for the improved Volterra polynomial equalizer, as the polynomial order increases, the coefficient w i The number of will grow exponentially, and the complexity of the problem increases dramatically. By observing the cross terms generated by the Kronecker product, we can find that they are similar. For example, when i = 2, (x 1 x 2 ) and (x 2 x 1 ) are similar, and only one of them can be retained. Therefore, based on the above model, the computational complexity can be reduced by retaining only one of the cross terms between the signals and removing the repeated cross terms, which can reduce the amount of calculation required for the number of coefficients from 2i to (i+1). That is, the coefficient w of the p-order improved Volterra polynomial equalizer is i The number of (number of taps) can be expressed as:

[0080]

[0081] The amplitude information of M-PAM X = {±1, ±3, ..., ±(M-1)} is used for each I and Q symbol. U(n) is the received signal vector of length L U(n) = [u(n-1), u(n), ..., u(n+1)] T , where (·)T is the transpose of the matrix. Then, the augmented received signal vector v(n) = A[U(n)] is defined using the nonlinear augmentation operator A generated by the N products of U(n). The expression of MVPE can be concisely written as: z*(n) = W T v(n); where W is the tap coefficient vector.

[0082] There are many LS-based algorithms for estimating model coefficients, which are linearly weighted representations of nonlinear cross-terms. In transmission experiments using digital-to-analog converters (DACs), the transmitted symbols x appear with a period K due to the limited memory of the DAC. Therefore, in the absence of noise, the horizontal concatenation of the augmented received signal vector V = [v(1), v(2), …, v(K)] defines the complete set of received signals, where each column group stores the same order of terms, which are cyclically shifted versions of each other. Define z * =[z * (1),z*(2),…,z * (K)] is the shifted input vector, and MVPE can be written as: * =W T V.

[0083] Assume that there is an error vector e = [e(1), e(2), …, e(K)], the actual input vector can be written as: x = w T V+e;

[0084] According to the LS method, the value that minimizes the error criterion is: w = (VV T ) -1 Vx T ;

[0085] When the data matrix column rank is full, the least square method (LS) can provide a unique solution, but the stability of the solution is affected by the condition number. There may be a high correlation between the input data, resulting in an ill-conditioned matrix with a high condition number. LMS has the problem of poor covariance matrix conditions, which may lead to instability and divergence problems. The adaptive method of recursive least squares (RLS) is not adversely affected by the covariance matrix conditions and can update the inverse covariance matrix in each new sample. Therefore, the present embodiment adopts recursive estimation based on RLS to effectively avoid the ill-conditioned fitting problem.

[0086] Reference Figure 4 As shown in the figure, it is a comparison chart of the NGM I performance of 4096-QAM signal under MVPE and VNLE equalization in back-to-back transmission, that is, the normalized generalized mutual information (NGM I) of PS-PDM-4096QAM signal under VNLE and MVPE equalizer structures as a function of optical signal-to-noise ratio (OSNR) during back-to-back (BTB) transmission. In the case of lower optical signal-to-noise ratio, the impact of noise on signal quality is too large, and no model can accurately predict the channel behavior. MVPE and VNLE have similar improvements on signal quality. As the signal-to-noise ratio increases, the required input power increases, and the nonlinear damage to the system increases. Traditional VNLE cannot compensate for nonlinear damage well, such as Figure 4As shown in the triangle curve in the middle, the signal quality after equalization is unstable. However, MVPE shows better equalization performance than VNLE, as shown in Figure 4 As shown in the circular curve and dots in the middle, the signal after MVPE equalization not only has a certain degree of improvement in performance, but also has a more stable signal quality. This is more obvious when the OSNR is 42. From the constellation diagram cut out in the figure, it can be clearly seen that the constellation diagram after MVPE equalization is clearer than the constellation diagram after VNLE equalization. That is to say, when the nonlinearity is strong, the traditional VNLE is not accurate in fitting the nonlinear damage, and may generate additional polynomial noise terms, resulting in unstable equalization performance.

[0087] Reference Figure 5 As shown in the figure, the NGMI performance comparison of 4096-QAM signal under MVPE-LC and LMS+DD-LMS equalization back-to-back transmission is compared, comparing the two algorithms for compensating the residual linear impairment in the digital signal processing algorithm of coherent optical communication: LMS+DD-LMS algorithm and MVPE first-order linear compensation (MVPE-LC) algorithm. When only the final residual linear compensation algorithm is changed without changing the VNLE algorithm, the function of NGM I with OSNR during BTB transmission is as follows Figure 5 As shown in the figure. Considering the 20%-LDPC threshold of 0.828, as shown by the triangle curve in the figure, the LMS+DD-LMS method needs to reach the threshold with an OSNR of 36dB. As shown by the circular curve in the figure, the OSNR required to reach the threshold using MVPE-LC for linear equalization is 33.2dB, which can achieve a gain of 2.8dB compared with the original method.

[0088] Reference Figure 6 As shown in the figure, it is a comparison chart of the NGM I performance of 4096-QAM signal transmitted back-to-back under MVPE+MVPE-LC and VNLE+LMS+DD-LMS equalization; replacing the LMS+DD-LMS equalizer with the MVPE-LC equalizer can improve certain performance, but when the OSNR is between 38dB and 45dB, the average data points obtained are distributed in a broken line shape and cannot fall well near the fitting curve, and the recovered signal quality is unstable. This further verifies that the VNLE used originally cannot compensate for nonlinear damage well when the OSNR increases, that is, when the nonlinearity is enhanced. Therefore, using MVPE and the first-order terms of MVPE at the same time will bring the best performance, and the results are shown in the following figure. Figure 6 As shown in Figure 2, compared with the triangular curve, the circular curve not only has a significant improvement in performance, but also has a more stable signal quality after equalization.

[0089] Reference Figure 7As shown in the figure, it is a NGMI performance comparison chart of 4096-QAM signal under MVPE+MVPE-LC and VNLE+LMS+DD-LMS equalization in 80km SSMF transmission, which shows the performance improvement of PS-PDM 4096-QAM signal in 80km standard single-mode fiber (SSMF) transmission by replacing VNLE and LMS+DD-LMS equalizers with MVPE and MVPE-LC equalizers respectively. As can be seen from the figure, both circular points and triangular points are stably distributed on the fitting curve. This is because the OSNR of the signal will decrease after SSMF transmission, which leads to the phenomenon that the large OSNR nonlinear enhancement will not appear in BTB transmission within the achievable OSNR range, and the result after VNLE equalization will be unstable. At the same time, it can be seen from the curve in the figure that the improved algorithm can also improve the system performance by more than 2dB in 80km SSFM transmission.

[0090] In summary, the embodiment of the present invention proposes a nonlinear equalization method for an ultra-high-order QAM coherent optical transmission system for nonlinear equalization of PS-PDM ultra-high-order QAM signals. By changing the original VNLE single-input single-output structure to a multi-input multi-output structure, the I path and Q path in the X or Y polarization are jointly equalized, and the repeated cross terms between the signals are removed to simplify the computational complexity of the algorithm. In addition, by replacing the LMS and DD-LMS algorithms used to compensate for the residual linear equalization in the algorithm architecture with the first-order linear algorithm of MVPE, the bit error rate performance of the system is further improved. Experimental results show that the improved algorithm can obtain a gain of more than 2dB with basically unchanged complexity.

[0091] Based on the above embodiments, the embodiment of the present invention provides a process for acquiring a damaged digital signal output after the signal to be transmitted is transmitted by an ultra-high-order QAM coherent optical transmission system, including:

[0092] S201: After preprocessing, the signal to be transmitted is input to the transmitting end of the ultra-high-order QAM coherent optical transmission system, and the corresponding optical signal is generated through the waveform generator and the IQ modulator;

[0093] S202: amplifying and adjusting the optical signal through the transmission route and then sending it to the receiving end, including:

[0094] Amplifying the optical signal by a first erbium-doped fiber amplifier and outputting the amplified optical signal;

[0095] The amplified optical signal is adjusted to the preset input optical power by using a variable optical attenuator and input into a standard single-mode optical fiber for transmission;

[0096] The second erbium-doped fiber amplifier amplifies the optical signal transmitted by the standard single-mode optical fiber and inputs the amplified signal to the receiving end.

[0097] S203: The receiving end performs denoising and filtering on the received optical signal, inputs the signal into an oscilloscope, performs analog-to-digital conversion, and outputs a damaged digital signal, including:

[0098] De-noising the received optical signal using an optical bandpass filter to obtain a de-noised optical signal;

[0099] The de-noised optical signal is input into a coherent receiver together with the local oscillator light, and the de-noised optical signal is converted into an electrical signal using a polarization phase distribution fiber mixer and a balanced optical detector;

[0100] The electrical signal is input into the oscilloscope for analog-to-digital conversion to obtain the damaged digital signal output.

[0101] Among them, the signal to be transmitted is preprocessed, including: passing the signal to be transmitted through a constant composition distribution matcher to generate a specified amplitude sequence, and mapping it into a binary bit sequence according to the Gray code; after combining the binary bit sequence with the preset bit sequence, LDPC encoding is performed to obtain a coding sequence; the coding sequence is input into an interleaver for interleaving to obtain I-channel data information and Q-channel data information to generate an interleaved signal; upsampling, root raised cosine filtering and channel tilt compensation are performed on the interleaved signal to obtain the preprocessed signal to be transmitted.

[0102] Specifically, refer to Figure 8 As shown in the figure, it is a diagram of the experimental device of the 4096-QAM 80km SSMF coherent optical transmission system; the digital signal processing (DSP) at the transmitting end and the receiving end is completed by programming. At the transmitting end, the signal sequence generated based on the pseudo-random binary sequence (PRBS) is passed through the constant composition distribution matcher (CCDM) to generate a specified amplitude sequence, and is mapped into a binary bit sequence according to the Gray code. The generated sequence is combined with another part of the bit sequence for LDPC coding, and finally interleaved by the interleaver. The interleaved bit sequence can be used as the data information of the I or Q channel for QAM signal modulation. Then, after upsampling, root raised cosine (RRC) filtering and AWG channel tilt compensation offline digital signal processing (DSP), the signal is sent to an arbitrary waveform generator (AWG) with a sampling rate of 8GSa / s and a resolution of 14 bits for digital-to-analog conversion (DAC), and the electrical signal is used to drive the Mach-Zehnder modulator (MZM) to generate a 4096-QAM optical signal.

[0103] The modulator output signal is amplified by an erbium-doped fiber amplifier (EDFA) and adjusted by a variable optical attenuator (VOA) to the optimal input optical power into the 80km standard single-mode fiber (SSMF). For a 4096-QAM signal, the optimal input optical power is around -4dBm.

[0104] At the receiving end, the signal first passes through an optical bandpass filter (OBPF) to suppress the noise from the EDFA, and then enters the coherent receiver together with the local oscillator (LO) light. The coherent receiver consists of an optical mixer and a photodetector (BPD).

[0105] In this embodiment, both the ECL (external cavity laser) and the LO light source use lasers with a wavelength of 1550.112nm and a line width of about 100kHz. Finally, the electrical signal after analog-to-digital conversion (ADC) is sent to the offline DSP module to compensate for the damage suffered by the signal during transmission.

[0106] Reference Fig. 9 As shown in the figure, it is the digital signal processing algorithm flow chart of the receiving end of the system, that is, the offline DSP processing flow of the ultra-high-order QAM coherent receiver, which mainly includes basic processing units such as resampling, matched filtering, and Gram-Schmidt orthogonalization. The damage caused by chromatic dispersion is compensated by dispersion compensation (CDC) technology. In addition, in order to maintain the clock synchronization of the transmitting and receiving ends and eliminate sampling errors, the Gardner algorithm is used for clock recovery. At the same time, a 1-tap 2×2 multimode algorithm (MMA) is used to polarization demultiplex the signal. After that, the carrier is recovered by the frequency offset estimation (FOE) and carrier phase recovery (CPR) algorithms based on the fourth-order fast Fourier transform (FFT) algorithm. VNLE is used to compensate for the nonlinear effects of optoelectronic devices, and then 4×4MMA is used to alleviate the problem of I\Q imbalance. Finally, two single-polarization LMS and direct decision least mean square (DD-LMS) equalizers are used to jointly equalize the in-phase component and the orthogonal component, thereby compensating for the remaining linear damage at the same time to further improve the bit error rate performance.

[0107] In the experimental architecture of this embodiment, VNLE is replaced with the improved MVPE proposed in this embodiment, and the signal after 4×4MMA equalization is sent to the improved MVPE first-order linear compensation (MVPE-LC) equalizer, that is, the single-polarization LMS and direct decision least mean square (DD-LMS) equalizer are replaced with the first-order linear equalizer of MVPE proposed in this embodiment.

[0108] The nonlinear equalization method of the ultra-high-order QAM coherent optical transmission system of the present invention obtains the in-phase component and the orthogonal component of the signal to be transmitted in the X polarization state and the Y polarization state as multiple inputs, and inputs them into the improved Volterra polynomial equalizer with multiple inputs and outputs proposed by the present invention, and jointly equalizes the in-phase component and the orthogonal component in the X polarization state or the Y polarization state, further compensating for the nonlinear damage of the system, and can obtain a stable equalization result. The improved Volterra polynomial equalizer proposed by the present invention is based on a dual-input real-valued Volterra series, which includes not only the terms in each branch, but also the cross terms between the I path and the Q path, and only retains one of the cross terms, removes repeated cross terms, reduces the calculation complexity, reduces the transmission bit error rate, improves the nonlinear equalization effect, and makes the signal transmitted through the ultra-high-order QAM coherent optical transmission system more accurate and safe.

[0109] The present invention optimizes the improved Volterra polynomial equalizer by using an adaptive method of recursive least squares method, which is not adversely affected by the covariance matrix condition and can update the inverse covariance matrix in each new sample, thereby effectively avoiding the problem of ill-conditioning and improving the equalization effect of the optimized improved Volterra polynomial equalizer.

[0110] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A nonlinear equalization method for an ultra-high-order QAM coherent optical transmission system, characterized in that: include: Obtaining the damaged digital signal output after the signal to be transmitted is transmitted through the ultra-high-order QAM coherent optical transmission system; Performing IQ orthogonalization on the X polarization state and the Y polarization state of the damaged digital signal respectively to obtain an in-phase component XI and an orthogonal component XQ of the X polarization state, and an in-phase component YI and an orthogonal component YQ of the Y polarization state; Let XI, XQ, YI and YQ respectively undergo dispersion compensation, clock recovery, multi-mode operation, frequency offset estimation and carrier phase recovery in sequence to obtain the optimized in-phase component and optimized orthogonal component of the X polarization state, and the optimized in-phase component and optimized orthogonal component of the Y polarization state; For both the X polarization state and the Y polarization state, the optimized in-phase component and the optimized orthogonal component are used as inputs to the improved Volterra polynomial equalizer, and the Volterra series is used for joint equalization to output the corresponding X polarization state estimation digital signal and Y polarization state estimation digital signal; Based on the X polarization state estimation digital signal and the Y polarization state estimation digital signal, an equalized digital signal is obtained by fusion, thereby completing nonlinear equalization of the damaged digital signal.

2. The nonlinear equalization method for the ultra-high-order QAM coherent optical transmission system according to claim 1, characterized in that: The improved Volterra polynomial equalizer is expressed as: z*(n)=V1[u I (n),u Q (n)]+jV2[u I (n),u Q (n)]; Among them, u I (n) and u Q (n) represents the optimized in-phase component and optimized orthogonal component of the current input polarization state signal, z*(n) represents the estimated digital signal; j represents the imaginary part; V1 and V2 are Volterra series, expressed as l i represents the window length before and after the center of the sliding window of the i-th order term in the improved Volterra polynomial equalizer; the total window length of the i-th order term of the improved Volterra polynomial equalizer is expressed as: L i =2l i +1; i represents the i-th order term of the improved Volterra polynomial equalizer, i∈[1,2,3]; W represents the set of tap coefficients, defined as W=[w1,w2,,w 2i ] T ; w1, w2 and w3 represent the tap coefficients of the first order, second order and third order of the improved Volterra polynomial equalizer respectively; represents the transpose of the tap coefficient of the i-th order term; The complex number symbol received at the center of the sliding window of the i-th order term is defined as U1, U2 and U3 represent the complex symbols of the sliding window centers of the first-order term, the second-order term and the third-order term, respectively; n represents the nth symbol in the polarization state signal currently input, and k1, k2 and k3 are the preset sliding window coefficients of the i-th order term; represents the Kronecker product, defined as 3. The nonlinear equalization method for the ultra-high-order QAM coherent optical transmission system according to claim 2, characterized in that: Using the nonlinear augmentation operator A generated by N products of the received signal vector U(n), the augmented received signal vector v(n)=A[U(n)] is defined, and the improved Volterra polynomial equalizer is expressed as: z*(n)=W T v(n); Wherein, U(n) represents the received signal vector of the polarization state signal currently input with a length of L, and the expression is U(n)=[u(n-1),u(n),,u(n+1)] T ; N represents the total order of the improved Volterra polynomial equalizer; W T Represents the transpose of a set of tap coefficients.

4. The nonlinear equalization method for the ultra-high-order QAM coherent optical transmission system according to claim 3, characterized in that: Obtain the horizontal cascade set V of the augmented received signal vector v(n)=A[U(n)], and improve the Volterra polynomial equalizer, which is expressed as: z*=W T V; Among them, z*=[z*(1),z*(2),,z*(K)] is the shift input vector, K represents the preset window movement times; the horizontal cascade set is expressed as V=[v(1),v(2),,v(K)].

5. The nonlinear equalization method for ultra-high-order QAM coherent optical transmission system according to claim 2, characterized in that: Improved number of taps N of Volterra polynomial equalizer MVPE , expressed as: Where P represents the total order of the improved Volterra polynomial equalizer, 1≤i≤P; L i represents the total window length of the i-th order term of the improved Volterra polynomial equalizer, and ! represents the factorial operation.

6. The nonlinear equalization method for ultra-high-order QAM coherent optical transmission system according to claim 1, characterized in that: Based on the error between the signal to be transmitted and the equalized digital signal, the improved Volterra polynomial equalizer is optimized using the adaptive method of recursive least squares method.

7. The nonlinear equalization method for ultra-high-order QAM coherent optical transmission system according to claim 1, characterized in that: The step of obtaining a damaged digital signal output after the signal to be transmitted is transmitted by the ultra-high-order QAM coherent optical transmission system comprises: After preprocessing, the signal to be transmitted is input into the transmitting end of the ultra-high-order QAM coherent optical transmission system, and the corresponding optical signal is generated through the waveform generator and IQ modulator; The optical signal is amplified and regulated through the transmission route and then sent to the receiving end; The receiving end performs denoising and filtering on the received optical signal, inputs it into an oscilloscope, performs analog-to-digital conversion, and outputs a damaged digital signal.

8. The nonlinear equalization method for ultra-high-order QAM coherent optical transmission system according to claim 1, characterized in that: Preprocess the signal to be transmitted, including: The signal to be transmitted is passed through a constant composition distribution matcher to generate a specified amplitude sequence, and is mapped into a binary bit sequence according to a Gray code; After combining the binary bit sequence with the preset bit sequence, LDPC encoding is performed to obtain a coded sequence; Input the coded sequence into the interleaver for interleaving, obtain I-channel data information and Q-channel data information, and generate an interleaved signal; The interleaved signal is up-sampled, root-raised cosine filtered, and channel tilt compensated to obtain a pre-processed signal to be transmitted.

9. The nonlinear equalization method for ultra-high-order QAM coherent optical transmission system according to claim 1, characterized in that: The optical signal is amplified and adjusted through the transmission route and then sent to the receiving end, comprising: Amplifying the optical signal by a first erbium-doped fiber amplifier and outputting the amplified optical signal; The amplified optical signal is adjusted to the preset input optical power by using a variable optical attenuator and input into a standard single-mode optical fiber for transmission; The second erbium-doped fiber amplifier amplifies the optical signal transmitted by the standard single-mode optical fiber and inputs the amplified signal to the receiving end.

10. The nonlinear equalization method for ultra-high-order QAM coherent optical transmission system according to claim 1, characterized in that: The receiving end performs denoising and filtering on the received optical signal, inputs the signal into an oscilloscope, performs analog-to-digital conversion, and outputs a damaged digital signal, including: De-noising the received optical signal using an optical bandpass filter to obtain a de-noised optical signal; The denoised optical signal is input into the coherent receiver together with the local oscillator light, and the denoised optical signal is converted into an electrical signal using an oscilloscope to obtain the damaged digital signal output.

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