Carrier phase disturbance high-tolerance equalization method suitable for fractional oversampling

Abstract

A carrier phase disturbance high-tolerance equalization method suitable for fractional oversampling belongs to the field of optical fiber communication, and comprises the following steps: an input signal is subjected to delay processing by a fractional delay filter and block processing by a block delay module in sequence to obtain an output block; using an equalizer to equalize the input signal; the output of the equalizer is subjected to phase rotation through two stages of phase estimators in sequence; a training sequence or a decision symbol is used as a reference signal, and joint adaptive updating of an equalizer tap and a two-stage phase estimator tap is carried out based on a decision-guided least mean square algorithm. According to the invention, the equalizer with an interval greater than one half is combined with the two-stage phase estimator to realize equalization and carrier phase recovery under fractional oversampling, so that equalization under fractional oversampling can be realized without being influenced by carrier phase disturbance and polarization singularity; the problem that a traditional equalization scheme cannot tolerate carrier phase disturbance under fractional oversampling is solved, and the filtering precision and the equalization stability are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical fiber communication, and in particular relates to a high-tolerance equalization method for carrier phase disturbance under fractional oversampling. Background Art

[0002] In the field of optical communications, in order to achieve greater bandwidth, longer transmission distance and higher receiver sensitivity, coherent optical communication systems that use coherent detection at the receiving end have gradually become mainstream. By using a local oscillator light source, coherent detection can completely retain the amplitude, frequency or phase information of the signal light. Combined with a high-order modulation format, it can effectively improve the system spectrum efficiency. In addition, by amplifying the signal light with a high-power local oscillator light source, coherent detection can significantly improve the receiver sensitivity, thereby increasing the distance of optical signal transmission without relays. However, due to the difficulty in maintaining the same frequency between the local oscillator light source and the transmitting light source and the existence of the laser line width, the frequency and phase of the coherent detection signal will inevitably be disturbed, and will affect the key technology in coherent detection digital signal processing-adaptive equalization.

[0003] In the coherent detection digital signal processing, a half-symbol interval equalizer composed of four butterfly adaptive finite-impulse-response (FIR) filters is generally used to realize polarization demultiplexing, polarization mode dispersion compensation, residual dispersion compensation, sampling phase adjustment, and optical / electrical filtering damage equalization. When the delay tap length is much larger than the system impulse response, the equalizer can effectively realize the above damage compensation function. The tap coefficient update generally adopts a training sequence-based algorithm represented by the least mean square algorithm (LMS) or a blind algorithm represented by the constant modulus algorithm (CMA). The LMS adaptive process is phase-sensitive due to the introduction of the complex amplitude of the reference signal. For systems with large carrier phase disturbances, the FIR filter will track the carrier phase, resulting in unstable filtering, which in turn causes a decrease in equalization performance. The CMA adaptive process utilizes the signal envelope and is not affected by the carrier phase disturbance. However, in the polarization division multiplexing system, the two polarization state outputs converge to the same polarization branch due to polarization correlation, which is the polarization singularity problem. In addition, its tap adaptation rate is much slower than that of LMS, and the residual error is also higher.

[0004] On the other hand, the use of a half-symbol interval equalizer requires the receiving end analog-to-digital converter (ADC) to operate at 2 times the symbol rate sampling. As the demand for optical network traffic continues to grow, the symbol rate of coherent optical communication systems is also increasing. 2 times symbol rate sampling increases the cost and power consumption of the ADC a lot. Therefore, fractional oversampling lower than 2 times the symbol rate is needed to relax the hardware requirements. Accordingly, the equalizer must also be adjusted to be able to operate at a greater than half symbol interval.

[0005] In general, the half-symbol interval equalizer using LMS / CMA is no longer in line with the current development trend of coherent optical communications. Summary of the invention

[0006] In order to solve the problem that traditional equalization schemes under fractional oversampling cannot tolerate carrier phase disturbances, to realize an equalizer under fractional oversampling, and to make its adaptive process efficient and unaffected by carrier phase disturbances and polarization singularity problems, the present invention provides a high-tolerance equalization method for carrier phase disturbances under fractional oversampling.

[0007] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0008] The present invention provides a carrier phase disturbance high tolerance equalization method applicable to fractional oversampling, which mainly includes the following steps:

[0009] The input signal is sequentially delayed by a fractional delay filter and processed by a block delay module to obtain an output block; the input signal is equalized by an equalizer; the equalizer output is sequentially phase rotated by a two-stage phase estimator; a training sequence or a decision symbol is used as a reference signal, and a joint adaptive update of the equalizer tap and the two-stage phase estimator tap is performed based on a decision-guided least mean square algorithm.

[0010] Furthermore, the input signal is two signal sequence streams x(n) and y(n) to be equalized, and the two signal sequences to be equalized are respectively copied and input into K multi-phase branches, each branch contains a fractional delay filter and a block delay module, and the sample rate is M / KT, M / K represents the fractional oversampling factor, M represents the numerator of the fractional oversampling factor, K represents the denominator of the fractional oversampling factor, 1 / KT represents the block rate, 1 / T represents the symbol rate, that is, the equalizer working rate, and the equalizer input is switched between the output blocks of each branch at a rate of 1 / T.

[0011] Furthermore, for the i-th FDF, its k-th tap coefficient H i (k) is calculated as:

[0012]

[0013] Where j represents the parameter in the factorial process, L represents the FDF tap length, and D i represents the expected delay of the i-th FDF, which is calculated as:

[0014]

[0015] in Indicates rounding down; the outputs of the two equalized signal sequence streams x(n) and y(n) after the i-th FDF delay and the i-th BDM block in the i-th branch are:

[0016]

[0017] in It represents the output of the signal sequence stream x(n) to be equalized after the i-th FDF delay in the i-th branch. represents the output of the signal sequence stream y(n) to be equalized after the ith FDF delay in the ith branch, X i (n) represents the output of the signal sequence stream x(n) to be equalized after the i-th FDF delay and the i-th BDM block in the i-th branch, Y i (n) represents the output of the signal sequence stream y(n) to be equalized after the i-th FDF delay and the i-th BDM block, n′=(n-1)M+i, n represents the index of the BDM output block, n′ represents the index of the sequence inside the block, N represents the tap length of the equalizer, [·] T represents the matrix transpose, H i (j) represents the j-th tap coefficient of the i-th FDF.

[0018] Furthermore, the equalizer outputs are:

[0019] r x (m) = X i (n)W xx (m)+Y i (n)W yx (m)#(7)

[0020] r y (m) = X i (n)W xy (m)+Y i (n)W yy (m)#(8)

[0021] where r x (m) represents the output of the signal sequence stream x(n) to be equalized after delay, block division and equalization, r y(m) represents the output of the signal sequence stream y(n) to be equalized after delay, block division and equalization, W pq|p，q∈{x,y} represents a vector composed of N equalizer tap coefficients, m=(n-1)K+i, m represents the equalizer output sequence index, n represents the index of the equalizer input block, i=1, 2,...,K.

[0022] Furthermore, the equalizer tap coefficients are adaptively updated using a decision-guided least mean square algorithm, and the calculation formula is as follows:

[0023] W xx (m+1)=W xx (m)+μe x (m)X i (n) * #(9)

[0024] W xy (m+1)=W xy (m)+μe x (m)Y i (n) * #(10)

[0025] W yx (m+1)=W yx (m)+μe y (m)X i (n) * #(11)

[0026] W yy (m+1)=W yy (m)+μe y (m)Y i (n) * #(12)

[0027] Where W xx (m) indicates that the input in the mth iteration is the X polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the X polarization. W xx (m+1) indicates that in the m+1th iteration, the input is the X polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the X polarization. W xy (m) represents the filter coefficient of the filter whose input is the X polarization component and whose output is the output signal component on the Y polarization in the mth iteration, W xy (m+1) indicates the filter coefficient of the filter whose input is the X polarization component and whose output is the output signal component on the Y polarization in the m+1th iteration, W yx (m) represents the filter coefficient of the filter whose input is the Y polarization component and whose output is the output signal component on the X polarization in the mth iteration, W yx(m+1) indicates the filter coefficient of the filter whose input is the Y polarization component and whose output is the output signal component on the X polarization in the m+1th iteration, W yy (m) indicates that in the m-th iteration, the input is the Y polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the Y polarization. Wyy(m+1) indicates that in the m+1-th iteration, the input is the Y polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the Y polarization. μ indicates the equalizer tap update step size. The superscript * indicates conjugation. i=1, 2, ...K. The equalizer tap update error signal is given by the following formula:

[0028]

[0029] where e x (m) represents the equalizer tap update error signal in the equalized signal sequence stream x(n), e y (m) represents the equalizer tap update error signal in another equalized signal sequence stream y(n), f x (m) represents the tap coefficient of the first-stage phase estimator in the equalized signal sequence x(n), and f y (m) represents the tap coefficient of the first-stage phase estimator in the other signal sequence stream y(n) to be equalized, s x (m) represents the tap coefficient of the second-stage phase estimator in the equalized signal sequence x(n), s y (m) represents the tap coefficient of the second-stage phase estimator in the other signal sequence stream y(n) to be equalized, d x (m) represents the training sequence or decision symbol in the signal sequence stream x(n) to be equalized, d y (m) represents the training sequence or decision symbol in another signal sequence stream y(n) to be equalized.

[0030] Furthermore, the adaptive updating method of the tap coefficients of the first-stage phase estimator in the two-stage phase estimator taps is given by the following formula:

[0031]

[0032] e fx (m) = d x (m)-u x (m)#(17)

[0033] e fy (m) = d y (m)-u y (m)#(18)

[0034] where μ f represents the tap update step size of the first-stage phase estimator, fx (m+1) represents the tap coefficient of the first-stage phase estimator in the updated equalized signal sequence stream x(n), f y (m+1) represents the tap coefficient of the first-stage phase estimator in the updated signal sequence stream y(n) to be equalized, e fx (m) represents the tap update error signal of the first-stage phase estimator in the equalized signal sequence stream x(n), e fy (m) represents the tap update error signal of the first-stage phase estimator in another equalized signal sequence stream y(n), u x (m) = r x (m)f x (m) represents the output of the first-stage phase estimator in the equalized signal sequence x(n), u y (m) = r y (m)f y (m) represents the output of the first-stage phase estimator in another signal sequence stream y(n) to be equalized, the superscript * represents the conjugate, and ε represents a very small positive offset value;

[0035] The adaptive update method of the tap coefficients of the second-stage phase estimator in the two-stage phase estimator taps is given by the following formula:

[0036]

[0037] e sx (m) = d x (m)-v x (m)#(21)

[0038] e sy (m) = d y (m)-v y (m)#(22)

[0039] where μ s represents the tap update step size of the second-stage phase estimator, s x (m+1) represents the tap coefficient of the second-stage phase estimator in the updated equalized signal sequence stream x(n), s y (m+1) represents the tap coefficient of the second-stage phase estimator in the updated signal sequence stream y(n) to be equalized, e sx (m) represents the tap update error signal of the second-stage phase estimator in the equalized signal sequence stream x(n), e sy (m) represents the tap update error signal of the second-stage phase estimator in another equalized signal sequence stream y(n), v x (m) = u x (m)s x(m) represents the output of the second-stage phase estimator in a signal sequence stream x(n) to be equalized, v y (m) = u y (m)s y (m) represents the output of the second-stage phase estimator in another signal sequence stream y(n) to be equalized, the superscript * represents the conjugate, and ε represents a very small positive offset value.

[0040] Furthermore, the carrier frequency offset value Δf in the input block signal of the equalizer is calculated using the phase difference θ(m) between the input and output of the first-stage phase estimator:

[0041] θ(m)=arg{U x，y (m)R x，y (m) *}#(twenty three)

[0042]

[0043] Among them U x，y represents the output u of the first-stage phase estimator x，y The Fourier transform of x，y Represents the equalizer output r x，y The Fourier transform of k θ represents the slope of a series of phase differences θ(m) obtained by linear regression, Indicates the symbol rate.

[0044] Furthermore, in the tracking mode, a block compensation module is used to compensate the carrier frequency offset of the input block signal of the equalizer, and the compensation form is as follows:

[0045] X i (n) · ΔF#(25)

[0046]

[0047] Wherein the symbol · represents vector dot product, ΔF represents a vector of length N, e represents a natural constant, and Δf represents a carrier frequency offset value in the input block signal of the equalizer.

[0048] The beneficial effects of the present invention are:

[0049] The invention provides a high-tolerance equalization method for carrier phase disturbance under fractional oversampling, firstly, the inherent delay caused by fractional oversampling is compensated by fractional delay filters (FDF), and the signal is divided into blocks by a block delay module (BDM); then, the signal is equalized and phase rotated by four equalizers (butterfly adaptive filters) and two-stage single-tap phase estimators, and the tap coefficients of each part are jointly adaptively updated by a decision-directed least mean square (DD-LMS) algorithm. The invention adopts an equalizer with an interval greater than one-half in combination with a two-stage phase estimator to realize equalization and carrier phase recovery under fractional oversampling, and can realize equalization under fractional oversampling, and is not affected by carrier phase disturbance and polarization singularity problems, solves the problem that the traditional equalization scheme under fractional oversampling cannot tolerate carrier phase disturbance, significantly improves the filtering accuracy and equalization stability of the method, and has important application prospects in the field of fractional oversampling digital signal processing involving optical communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The present invention provides a flow chart of a carrier phase disturbance high tolerance equalization method applicable to fractional oversampling.

[0051] Figure 2 Schematic diagram of coherent optical communication system transmission and DSP solution.

[0052] Figure 3 A BER comparison diagram of a carrier phase disturbance high tolerance equalization method under fractional oversampling provided by the present invention at different sampling rates.

[0053] Figure 4 The figure is a comparison chart of Q parameters of three schemes under different residual frequency offsets.

[0054] Figure 5 This is a comparison chart of Q parameters of three schemes at different laser line widths. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0056] In a high-tolerance equalization method for carrier phase disturbance under fractional oversampling provided by the present invention, the main design parameters include: fractional oversampling factor M / K; fractional delay filter tap length L, fractional delay filter tap coefficient H i|i∈{1，2，...，M} ; Equalizer tap length N, equalizer tap coefficient W ij|i，j∈{x，y}, equalizer tap update step size μ, equalizer tap update error signal e x and e y ; The tap coefficient f of the first-stage phase estimator x and f y , the first-stage phase estimator tap update step size μ f , the first-stage phase estimator tap updates the error signal e fx and e fy ; Second stage phase estimator tap coefficient s x and y , the second-stage phase estimator tap update step size μ s , the second-stage phase estimator tap updates the error signal e sx and e sy .

[0057] First, the two signal sequences to be equalized are copied and input into K polyphase branches respectively. Each branch contains a fractional delay filter (FDF) and a block delay module (BDM), namely FDF 1, FDF 2, ... FDF K, BDM 1, BDM 2, ... BDM K. After the input signal is delayed and divided into blocks, it is output as a block of length N. This step compensates for the fixed delay caused by fractional oversampling. The equalizer input switches between the output blocks of each branch at a rate of 1 / T. Then, four equalizers (W xx , W yx , W xy , W yy ) completes the equalization of the input signal, and the equalizer output is then phase-rotated through a two-stage phase estimator in turn to eliminate fast-changing phase fluctuations. Using a training sequence or a decision symbol as a reference signal, the tap coefficients of each part are jointly adaptively updated based on a decision-directed least mean square (DD-LMS) algorithm, wherein the reference signal updated for the equalizer should be adjusted to remove phase fluctuations, while the reference signal updated for the phase estimator should retain its original form. In addition, the carrier frequency offset value between the local oscillator light source and the transmitting light source can be calculated using the coefficients of the first-stage phase estimator. As a further improvement of the present invention, a block compensation module is used in the tracking mode to compensate for the carrier frequency offset of the input block signal of the equalizer (i.e., frequency offset estimation), which effectively improves the stability of the equalization and the accuracy of the phase estimation.

[0058] The present invention provides a carrier phase disturbance high tolerance equalization method suitable for fractional oversampling, such as Figure 1 As shown, the specific implementation steps are as follows:

[0059] In the present invention, the two signal sequence streams to be equalized are x(n) and y(n), respectively, and the sample rate is M / KT, where M / K represents the fractional oversampling factor, M represents the numerator of the fractional oversampling factor, K represents the denominator of the fractional oversampling factor, 1 / KT represents the block rate, and 1 / T represents the symbol rate, i.e., the working rate of the equalizer. The FDF with a tap length of L is implemented based on Lagrange interpolation. For the i-th FDF, its k-th tap coefficient H i (k) is calculated as:

[0060]

[0061] Among them, J represents the parameter in the factorial process, L Denotes the FDF tap length, D i represents the expected delay of the i-th FDF, which is calculated as:

[0062]

[0063] in Indicates rounding down.

[0064] The outputs of the two equalized signal sequence streams x(n) and y(n) after the i-th FDF delay and the i-th BDM block in the i-th branch are:

[0065]

[0066] in It represents the output of the signal sequence stream x(n) to be equalized after the i-th FDF delay in the i-th branch. represents the output of the signal sequence stream y(n) to be equalized after the ith FDF delay in the ith branch, X i (n) represents the output of the signal sequence stream x(n) to be equalized after the i-th FDF delay and the i-th BDM block in the i-th branch, Y i (n) represents the output of the signal sequence stream y(n) to be equalized after the i-th FDF delay and the i-th BDM block, n′=(n-1)M+i, n represents the index of the BDM output block, n′ represents the index of the sequence inside the block, N represents the tap length of the equalizer, [·] T represents the matrix transpose, H i (j) represents the j-th tap coefficient of the i-th FDF.

[0067] The equalizer outputs are:

[0068] r x (m) = X i (n)W xx (m)+Yi (n)W yx (m)#(7)

[0069] r y (m) = X i (n)W xy (m)+Y i (n)W yy (m)#(8)

[0070] where r x (m) represents the output of the signal sequence stream x(n) to be equalized after delay, block division and equalization, r y (m) represents the output of the signal sequence stream y(n) to be equalized after delay, block division and equalization, W pq|p，q∈{x，y} represents a vector composed of N equalizer tap coefficients, m=(n-1)K+i, m represents the index of the equalizer output sequence, n represents the index of the equalizer input block, i=1, 2,...,K.

[0071] The equalizer tap coefficients are adaptively updated using the decision-directed least mean square (DD-LMS) algorithm. The specific calculation formula is as follows:

[0072] W xx (m+1)=W xx (m)+μe x (m)X i (n) * #(9)

[0073] W xy (m+1)=W xy (m)+μe x (m)Y i (n) * #(10)

[0074] W yx (m+1)=W yx (m)+μe y (m)X i (n) * #(11)

[0075] W yy (m+1)=W yy (m)+μ ey (m)Y i (n) * #(12)

[0076] Where W xx(m) indicates that the input in the mth iteration is the X polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the X polarization. W xx (m+1) indicates that in the m+1th iteration, the input is the X polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the X polarization. W xy (m) represents the filter coefficient of the filter whose input is the X polarization component and whose output is the output signal component on the Y polarization in the mth iteration, W xy (m+1) indicates the filter coefficient of the filter whose input is the X polarization component and whose output is the output signal component on the Y polarization in the m+1th iteration, W yx (m) represents the filter coefficient of the filter whose input is the Y polarization component and whose output is the output signal component on the X polarization in the mth iteration, W yx (m+1) indicates the filter coefficient of the filter whose input is the Y polarization component and whose output is the output signal component on the X polarization in the m+1th iteration, W yy (m) indicates that the input in the mth iteration is the Y polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the Y polarization. W yy (m+1) indicates that in the m+1th iteration, the input is the Y polarization component, and the output is the filter coefficient of the filter of the output signal component on the Y polarization, μ indicates the equalizer tap update step size, the superscript * indicates taking the conjugate, i=1, 2, ...K, and the equalizer tap update error signal is given by the following formula:

[0077]

[0078] where e x (m) represents the equalizer tap update error signal in the equalized signal sequence stream x(n), e y (m) represents the equalizer tap update error signal in another equalized signal sequence stream y(n), f x (m) represents the tap coefficient of the first-stage phase estimator in the equalized signal sequence x(n), and f y (m) represents the tap coefficient of the first-stage phase estimator in the other signal sequence stream y(n) to be equalized, s x (m) represents the tap coefficient of the second-stage phase estimator in the equalized signal sequence x(n), s y (m) represents the tap coefficient of the second-stage phase estimator in the other signal sequence stream y(n) to be equalized, d x (m) represents the training sequence or decision symbol in the signal sequence stream x(n) to be equalized, d y(m) represents the training sequence or decision symbol in the other signal sequence stream y(n) to be equalized. In the calculation process of the equalizer tap update error signal, the fast-changing phase fluctuation is removed, and the equalizer only tracks the slow-changing damage. Its output is respectively rotated by the two-stage phase estimator. and Therefore, the final output approaches d x，y (m).

[0079] Among them, the adaptive update method of the tap coefficients of the first-stage phase estimator is given by the following formula:

[0080]

[0081] e fx (m) = d x (m)-u x (m)#(17)

[0082] e fy (m) = d y (m)-u y (m)#(18)

[0083] where μ f represents the tap update step size of the first-stage phase estimator, f x (m+1) represents the tap coefficient of the first-stage phase estimator in the updated equalized signal sequence stream x(n), f y (m+1) represents the tap coefficient of the first-stage phase estimator in the updated signal sequence stream y(n) to be equalized, e fx (m) represents the tap update error signal of the first-stage phase estimator in the equalized signal sequence stream x(n), e fy (m) represents the tap update error signal of the first-stage phase estimator in another equalized signal sequence stream y(n), u x (m) = r x (m)f x (m) represents the output of the first-stage phase estimator in the equalized signal sequence x(n), u y (m) = r y (m)f y (m) represents the output of the first-stage phase estimator in another signal sequence stream y(n) to be equalized, the superscript * represents the conjugate, and ε represents a very small positive offset value.

[0084] Among them, the adaptive update method of the tap coefficients of the second-stage phase estimator is given by the following formula:

[0085]

[0086] e sx(m) = d x (m)-v x (m)#(21)

[0087] e sy (m) = d y (m)-v y (m)#(22)

[0088] where μ s represents the tap update step size of the second-stage phase estimator, s x (m+1) represents the tap coefficient of the second-stage phase estimator in the updated equalized signal sequence stream x(n), s y (m+1) represents the tap coefficient of the second-stage phase estimator in the updated signal sequence stream y(n) to be equalized, e sx (m) represents the tap update error signal of the second-stage phase estimator in the equalized signal sequence stream x(n), e sy (m) represents the tap update error signal of the second-stage phase estimator in another equalized signal sequence stream y(n), v x (m) = u x (m)s x (m) represents the output of the second-stage phase estimator in a signal sequence stream x(n) to be equalized, v y (m) = u y (m)s y (m) represents the output of the second-stage phase estimator in another signal sequence stream y(n) to be equalized, the superscript * represents the conjugate, and ε represents a very small positive offset value.

[0089] The phase difference θ(m) between the input and output of the first-stage phase estimator can be used to calculate the carrier frequency offset value Δf in the input block signal of the equalizer:

[0090] θ(m)=arg{U x，y (m)R x，y (m) *}#(twenty three)

[0091]

[0092] Among them U x，y represents the output u of the first-stage phase estimator x，y The Fourier transform of x，y Represents the equalizer output r x，y The Fourier transform of k θ represents the slope of a series of phase differences θ(m) obtained by linear regression, Indicates the symbol rate.

[0093] After obtaining the carrier frequency offset value, the equalizer input is compensated in the form of blocks in the tracking phase, and the current equalizer input block X is compensated. i (n), the compensation shall be in the following form:

[0094] X i (n) · ΔF#(25)

[0095]

[0096] The symbol · represents vector dot product, ΔF represents a vector of length N, and e represents a natural constant.

[0097] The invention discloses a high-tolerance equalization method for carrier phase disturbance under fractional oversampling, which can equalize a coherent optical channel and recover the carrier phase under fractional oversampling. By introducing a block compensation module in the tracking stage, the carrier frequency offset compensation is performed on the input block signal of the equalizer, which effectively improves the stability of the equalization, and improves the accuracy of phase estimation and the filtering stability.

[0098] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0099] The invention provides a high-tolerance equalization method for carrier phase disturbance under fractional oversampling, which mainly involves the signal processing process at the receiving end of the polarization multiplexing system, with an emphasis on equalization and carrier phase recovery under fractional oversampling. In the invention, the inherent delay caused by fractional oversampling is compensated by FDF, and the signal is divided into blocks through BDM, and the input of the equalizer is switched to the block of the next branch every T time. Then, the signal is equalized by the equalizer, and the two-stage phase estimator performs phase estimation on the equalizer output, and the tap coefficients of each part are jointly updated by the DD-LMS algorithm using the training sequence or the decision symbol.

[0100] A dual-polarization 16QAM system with a receiving end sampling rate of 5 / 4 times the symbol rate is taken as an example to illustrate a high-tolerance equalization method for carrier phase disturbance under fractional oversampling provided by the present invention.

[0101] The present invention provides a high tolerance equalization method for carrier phase disturbance under fractional oversampling to equalize and recover the carrier phase of a dual-polarization 16QAM signal sampled at 5 / 4 symbol rate. The specific implementation process is as follows: Figure 1 As shown:

[0102] (1) The signal sample rate is 5 / 4T, so each polarization state branch is further divided into four branches.

[0103] (2) The tap coefficients of each FDF are calculated according to the given formula (1), where the first FDF has an integer delay and each subsequent FDF is delayed by -1 / 4 compared to the previous one.

[0104] (3) The delayed signal is subjected to block shaping processing through BDM. For the same branch, the block is divided every five samples.

[0105] (4) In the training mode, the equalizer tap coefficients are initialized to all zeros, the single-tap phase estimator coefficients are initialized to one, and the training sequence is transmitted and the equalizer and phase estimator are jointly adaptively updated using the DD-LMS algorithm. The phase difference between the input and output of the first-stage phase estimator is calculated during the training process, and the slope is obtained by linear regression for frequency offset estimation.

[0106] (5) In tracking mode, the frequency offset compensation is performed on the equalizer input in block form. Symbol decision is performed after equalization and carrier phase recovery. The DD-LMS algorithm is used to jointly adaptively update the equalizer and phase estimator with the decision symbol as a reference, thereby achieving carrier phase tracking.

[0107] like Figure 2 As shown in the figure, in an experimental model of coherent optical communication, first, the binary sequence data with a sequence length of 262144 bits is converted from serial to parallel by the DSP at the transmitting end to obtain four parallel channels, which are input into the dual-polarization IQ modulator to obtain x- and y-polarized 16QAM signals and coupled multiplexed. ECL represents the external cavity laser. Next, the polarization multiplexed signal is sent to an optical fiber link with a transmission distance of 100 km and a central wavelength of 1550 nm for transmission. The optical fiber loss (0.2 dB / km) is compensated by the EDFA optical fiber amplifier.

[0108] At the receiving end, the optical signal is filtered through a bandpass filter; then, the coherent receiver receives the optical signal and the ADC samples it at a rate of 256G Sa / s; next, the electrical signal after photoelectric conversion is processed by a series of digital signal processing algorithms, including downsampling to 5 / 4 times the symbol rate, orthogonal normalization, dispersion compensation, equalization and carrier recovery, BER (bit error rate) calculation, and frequency deviation is introduced through the frequency difference between the local oscillator light source and the transmitting light source, and the phase noise is characterized by the light source linewidth.

[0109] Among them, the equalization and carrier recovery adopt the following three schemes for performance comparison, namely:

[0110] (1) LMS solution: First, frequency offset is compensated through frequency offset estimation (FOE), and then fractional oversampling LMS equalizer is used for equalization to ensure that the equalizer can work properly. After that, phase recovery is performed through blind phase search algorithm (BPS).

[0111] (2) CMA scheme: First use the fractional oversampling CMA equalizer for equalization, and then complete the carrier phase recovery through frequency offset estimation (FOE) and blind phase search algorithm (BPS).

[0112] (3) Solution of the present invention: Using a high-tolerance equalization method for carrier phase disturbance under fractional oversampling provided by the present invention (i.e. Figure 2 DD-LMS solution mentioned in (

[0113] The performance curves of BER versus optical signal-to-noise ratio (OSNR) for the above three schemes under 2x sampling and 1.25x sampling are shown in the figure below: Figure 3 As shown, the simulation data contains a 100 MHz frequency offset, and the line width of the lasers at the transmitting end and the receiving end are both 100 KHz. It can be seen that when the sampling rate is reduced to 1.25 times the symbol rate, the method of the present invention hardly shows any performance degradation.

[0114] The Q parameter performance curves of the above three schemes when different residual frequency offsets are artificially set are as follows: Figure 4 As shown, the simulation data OSNR is 25dB and the laser line width is 100k Hz. It can be seen that the LMS scheme is most sensitive to residual frequency deviation, so extremely accurate a priori frequency deviation estimation is required to ensure equalization performance; in the CMA scheme, the CMA performance is independent of the carrier phase, but when the residual frequency deviation reaches 20MHz, it exceeds the BPS phase compensation range, so the performance is degraded; the method of the present invention has the best residual frequency deviation tolerance, the equalization performance is independent of the frequency deviation, and even if the frequency deviation estimation in the scheme causes residual frequency deviation due to errors, the residual frequency deviation can be compensated by the phase estimator.

[0115] The performance curves of the Q parameters in the above three schemes as a function of the laser line width are as follows: Figure 5 As shown, the simulation data OSNR is 25dB, and the frequency deviation is 100MHz. It can be seen that the method of the present invention has the best phase noise tolerance. When the laser line width is up to 1MHz, the performance of the LMS scheme decreases by more than 1.4dB compared with the line width of 0, the performance of the CMA scheme decreases by about 0.75dB, and the performance of the method of the present invention decreases by only 0.43dB.

[0116] The invention provides a high-tolerance equalization method for carrier phase disturbance under fractional oversampling, which is an equalizer structure suitable for non-integer oversampling and having a two-stage phase estimator and a tap adaptive update method thereof. Compared with the existing T / 2 interval LMS / CMA equalizer, the invention introduces a fractional delay filter (Fractional Delay Filters, FDF) and a two-stage single-tap phase estimator in the equalizer structure, introduces a fractional delay filter before the equalizer to eliminate the inherent delay caused by non-integer oversampling, and the equalizer works at a fractional interval greater than T / 2. A two-stage single-tap phase estimator is introduced after the equalizer for phase estimation and compensation, and the taps of the equalizer and the phase estimator are jointly adaptively updated using DD-LMS to eliminate the influence of carrier phase disturbance on equalization. The invention can achieve equalization under fractional oversampling, and is not affected by carrier phase disturbance and polarization singularity problems, and significantly improves filtering accuracy and stability. Therefore, the invention provides a high-tolerance equalization method for carrier phase disturbance under fractional oversampling, which has important application prospects in the field of coherent optical communication.

[0117] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A high tolerance equalization method for carrier phase disturbance under fractional oversampling, characterized in that: The following steps are involved: The input signal is sequentially delayed by a fractional delay filter and processed by a block delay module to obtain an output block; the input signal is equalized by an equalizer; the equalizer output is sequentially phase rotated by a two-stage phase estimator; a training sequence or a decision symbol is used as a reference signal, and a joint adaptive update of the equalizer tap and the two-stage phase estimator tap is performed based on a decision-guided least mean square algorithm.

2. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 1, characterized in that: The input signals are two signal sequence streams x(n) and y(n) to be equalized. The two signal sequences to be equalized are copied and input into K multi-phase branches respectively. Each branch contains a fractional delay filter and a block delay module. The sample rate is M / KT, M / K represents the fractional oversampling factor, M represents the numerator of the fractional oversampling factor, K represents the denominator of the fractional oversampling factor, 1 / KT represents the block rate, 1 / T represents the symbol rate, that is, the working rate of the equalizer, and the equalizer input is switched between the output blocks of each branch at a rate of 1 / T.

3. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 1, characterized in that: For the i-th FDF, its k-th tap coefficient H i (k) is calculated as: Where j represents the parameter in the factorial process, L Denotes the FDF tap length, D i represents the expected delay of the i-th FDF, which is calculated as: in Indicates rounding down; The outputs of the two equalized signal sequence streams x(n) and y(n) after the i-th FDF delay and the i-th BDM block in the i-th branch are: in It represents the output of the signal sequence stream x(n) to be equalized after the i-th FDF delay in the i-th branch. represents the output of the signal sequence stream y(n) to be equalized after the ith FDF delay in the ith branch, X i (n) represents the output of the signal sequence stream x(n) to be equalized after the i-th FDF delay and the i-th BDM block in the i-th branch, Y i (n) represents the output of the signal sequence stream y(n) to be equalized after the i-th FDF delay and the i-th BDM block, n′=(n-1)M+i, n represents the index of the BDM output block, n′ represents the index of the sequence inside the block, N represents the tap length of the equalizer, [·] T represents the matrix transpose, H i (j) represents the j-th tap coefficient of the i-th FDF.

4. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 1, characterized in that: The equalizer outputs are: r x (m)=X i (n)W xx (m)+Y i (n)W yx (m)#(7) r y (m)=X i (n)W xy (m)+Y i (n)W yy (m)#(8) where r x (m) represents the output of the signal sequence stream x(n) to be equalized after delay, block division and equalization, r y (m) represents the output of the signal sequence stream y(n) to be equalized after delay, block division and equalization, W pq|p，q∈{x,y} Represents a vector composed of N equalizer tap coefficients, m = (n-1)K+i, m represents the index of the equalizer output sequence, n represents the index of the equalizer input block, i = 1, 2, ..., K.

5. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 1, characterized in that: The equalizer tap coefficients are adaptively updated using a decision-guided least mean square algorithm, and the calculation formula is as follows: W xx (m+1)=W xx (m)+μe x (m)X i (n) * #(9) W xy (m+1)=W xy (m)+μe x (m)Y i (n) * #(10) W yx (m+1)=W yx (m)+μe y (m)X i (n) * #(11) W yy (m+1)=W yy (m)+μe y (m)Y i (n) * #(12) Where W xx (m) indicates that the input in the mth iteration is the X polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the X polarization. W xx (m+1) indicates that in the m+1th iteration, the input is the X polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the X polarization. W xy (m) represents the filter coefficient of the filter whose input is the X polarization component and whose output is the output signal component on the Y polarization in the mth iteration, W xy (m+1) indicates the filter coefficient of the filter whose input is the X polarization component and whose output is the output signal component on the Y polarization in the m+1th iteration, W yx (m) represents the filter coefficient of the filter whose input is the Y polarization component and whose output is the output signal component on the X polarization in the mth iteration, W yx (m+1) indicates the filter coefficient of the filter whose input is the Y polarization component and whose output is the output signal component on the X polarization in the m+1th iteration, W yy (m) indicates that the input in the mth iteration is the Y polarization component, and the output is the filter coefficient of the filter that outputs the signal component on the Y polarization. W yy (m+1) indicates that in the m+1th iteration, the input is the Y polarization component, and the output is the filter coefficient of the filter of the output signal component on the Y polarization, μ indicates the equalizer tap update step size, the superscript * indicates taking the conjugate, i=1,2,...K, and the equalizer tap update error signal is given by the following formula: where e x (m) represents the equalizer tap update error signal in the equalized signal sequence stream x(n), e y (m) represents the equalizer tap update error signal in another equalized signal sequence stream y(n), f x (m) represents the tap coefficient of the first-stage phase estimator in one channel of the signal sequence stream x(n) to be equalized, fy(m) represents the tap coefficient of the first-stage phase estimator in another channel of the signal sequence stream y(n) to be equalized, s x (m) represents the tap coefficient of the second-stage phase estimator in the equalized signal sequence x(n), s y (m) represents the tap coefficient of the second-stage phase estimator in the other signal sequence stream y(n) to be equalized, d x (m) represents a training sequence or decision symbol in a signal sequence stream x(n) to be equalized, and dy(m) represents a training sequence or decision symbol in another signal sequence stream y(n) to be equalized.

6. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 1, characterized in that: The adaptive update method of the tap coefficients of the first-stage phase estimator in the two-stage phase estimator taps is given by the following formula: where μ f represents the tap update step size of the first-stage phase estimator, f x (m+1) represents the tap coefficient of the first-stage phase estimator in the updated equalized signal sequence stream x(n), f y (m+1) represents the tap coefficient of the first-stage phase estimator in the updated signal sequence stream y(n) to be equalized, e fx (m) represents the tap update error signal of the first-stage phase estimator in the equalized signal sequence stream x(n), e fy (m) represents the tap update error signal of the first-stage phase estimator in another equalized signal sequence stream y(n), u x (m) = r x (m)f x (m) represents the output of the first-stage phase estimator in the equalized signal sequence x(n), u y (m) = r y (m)f y (m) represents the output of the first-stage phase estimator in another signal sequence stream y(n) to be equalized, the superscript * represents the conjugate, and ε represents a very small positive offset value; The adaptive update method of the tap coefficients of the second-stage phase estimator in the two-stage phase estimator taps is given by the following formula: where μ s represents the tap update step size of the second-stage phase estimator, s x (m+1) represents the tap coefficient of the second-stage phase estimator in the updated equalized signal sequence stream x(n), s y (m+1) represents the tap coefficient of the second-stage phase estimator in the updated signal sequence stream y(n) to be equalized, e sx (m) represents the tap update error signal of the second-stage phase estimator in the equalized signal sequence stream x(n), e sy (m) represents the tap update error signal of the second-stage phase estimator in another equalized signal sequence stream y(n), v x (m) = u x (m)s x (m) represents the output of the second-stage phase estimator in a signal sequence stream x(n) to be equalized, v y (m) = u y (m)s y (m) represents the output of the second-stage phase estimator in another signal sequence stream y(n) to be equalized, the superscript * represents the conjugate, and ε represents a very small positive offset value.

7. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 6, characterized in that: The carrier frequency offset value △f in the input block signal of the equalizer is calculated using the phase difference θ(m) between the input and output of the first-stage phase estimator: θ(m)6g{U x，y (m)R x，y (m) * }#(23) Among them U x，y represents the output u of the first-stage phase estimator x，y The Fourier transform of x，y Represents the equalizer output r x，y The Fourier transform of k θ represents the slope of a series of phase differences θ(m) obtained by linear regression, Indicates the symbol rate.

8. The carrier phase disturbance high tolerance equalization method applicable to fractional oversampling according to claim 1, characterized in that: In tracking mode, a block compensation module is used to compensate the carrier frequency offset of the input block signal of the equalizer. The compensation form is as follows: X i (n)·△F#(25) Wherein the symbol · represents vector dot product, ΔF represents a vector of length N, e represents a natural constant, and Δf represents a carrier frequency offset value in the input block signal of the equalizer.

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