CN111555819A

CN111555819A - Carrier phase estimation and compensation method and system

Info

Publication number: CN111555819A
Application number: CN202010323072.5A
Authority: CN
Inventors: 璧靛缓; 赵建
Original assignee: South China University of Technology SCUT
Current assignee: South China University of Technology SCUT
Priority date: 2020-04-22
Filing date: 2020-04-22
Publication date: 2020-08-18
Anticipated expiration: 2040-04-22
Also published as: CN111555819B

Abstract

The invention discloses a carrier phase estimation and compensation method and a carrier phase estimation and compensation system, wherein the method comprises the following steps: acquiring a received signal, and extracting a sample signal from the received signal; acquiring information of a first probability distribution of a target constellation diagram, and estimating a phase signal by combining the sample signal and the information of the first probability distribution; compensating the received signal according to the phase signal to obtain a compensated received signal; wherein, under the compensation of the phase signal, KL divergence information between the second probability distribution and the first probability distribution of the sample signal becomes smaller; the KL divergence information includes KL divergence and/or cross entropy. Compared with the traditional BPS, the invention has lower complexity, has better compensation performance compared with the existing Kalman filtering and principal component analysis, and can be widely applied to the field of communication.

Description

Carrier phase estimation and compensation method and system

Technical Field

The present invention relates to the field of communications, and in particular, to a method and a system for carrier phase estimation and compensation.

Background

Coherent detection and a high-level modulation mode based on constellation point probability shaping (PS for short) are important technologies for realizing future high-speed flexible optical communication systems. Estimation and compensation of carrier phase is an essential signal processing module in coherent optical communication systems. The problem is that phase jitter/offset of the modulated signal is caused by phase noise due to the linewidths of the transmitter and receiver lasers and/or residual frequency offset, and therefore phase estimation and compensation are required to recover the original signal. Currently, many methods for carrier phase estimation and compensation have been proposed in the academic and industrial fields. The conventional Viterbi-Viterbi (VV) algorithm is only applicable to Quadrature Phase Shift Keying (QPSK) modulation formats. Improved algorithms for VV include QPSK partitioning algorithms or VV algorithms implemented in high order QAM using some loop or loops of high order Quadrature Amplitude Modulation (QAM) constellation points. However, these improvements are either more complex or have reduced line width, residual frequency offset tolerance because fewer estimated samples can be used. These problems become particularly significant in probability shaped modulation, since the probability per turn of constellation points after shaping is variable and can be small, thus further reducing the number of estimation samples available. On the other hand, Blind Phase Searching (BPS) is a phase estimation method transparent to modulation formats and performs optimally if the searched phase values are sufficient. But this approach is highly complex. Therefore, researchers have proposed methods to reduce complexity, such as staging BPS or a combination of BPS and VV. Decision-aided maximum likelihood is another type of method. This type of approach also achieves good performance, but it has similar complexity as traditional BPS, preventing its application in real systems. Recently, researchers have proposed two methods, kalman filtering and principal component analysis, to balance performance and complexity. However, the principal component analysis method cannot be used for a modulation format of probability shaping, and the kalman filter has a smaller line width and residual frequency offset tolerance.

Disclosure of Invention

In order to solve one of the above technical problems, an object of the present invention is to provide a carrier phase estimation and compensation method and system for estimating and compensating carrier phase noise caused by transmitter and receiver line widths and/or residual frequency offsets.

The technical scheme adopted by the invention is as follows:

a carrier phase estimation and compensation method, comprising the steps of:

acquiring a received signal, and extracting a sample signal from the received signal;

acquiring information of a first probability distribution of a target constellation diagram, and estimating a phase signal by combining the sample signal and the information of the first probability distribution;

compensating the received signal according to the phase signal to obtain a compensated received signal;

wherein, under the compensation of the phase signal, KL divergence information between the second probability distribution and the first probability distribution of the sample signal becomes smaller;

the KL divergence information includes KL divergence and/or cross entropy.

The carrier phase estimation and compensation method has the following beneficial effects: the invention adopts KL divergence information to measure the matching degree between the probability distribution of the sample signal and the probability distribution of the constellation diagram, when the KL divergence information is smaller, namely the probability distribution of the sample signal is more matched with the probability distribution of the constellation diagram, the obtained phase value can more effectively compensate the received signal, and compared with the traditional BPS, the invention has lower complexity and better compensation performance compared with the existing Kalman filtering and principal component analysis. Wherein the phase signal is a phase value (defined as

) Or any data or signal or the like which can characterize the phase value, e.g. by

In the form of a characterized phase value. The KL divergence information includes KL divergence and/or cross entropy, and it should be noted that the KL divergence or cross entropy, in a broad sense, also includes any function that includes KL divergence or cross entropy and monotonically increases with KL divergence or cross entropy within a preset KL divergence or cross entropy range, such as a function that is multiplied by a constant or any one or combination of logarithms, exponents, etc. on the basis of KL divergence, or a function that is multiplied by a constant or any one or combination of logarithms, exponents, etc. on the basis of cross entropy. Wherein the information of the first probability distribution of the target constellation comprises at least one of a probability distribution function, any data or signal that may characterize the probability distribution function, a function that includes a probability distribution function, or any data or signal that may characterize a function that includes a probability distribution function. Wherein the function containing the probability distribution function is any one or more of partial derivative, integral, logarithm, exponential and the like on the basis of the probability distribution functionA combined function. Wherein the first probability distribution is obtained by establishing or by retrieving.

Further, the phase signal is obtained by searching, specifically:

dividing a preset phase range to obtain a plurality of phase values to form a phase set;

acquiring phase values from the phase set one by one, and compensating the sample signals by adopting the phase values;

calculating KL divergence information between the probability distribution of the compensated sample signal and the first probability distribution or a value of a first function containing the KL divergence information;

and acquiring a phase signal according to the phase value corresponding to the minimum KL divergence information.

Searching or trying possible phase values one by one in a certain range, compensating the sample signal by each phase value, calculating KL divergence information between the compensated sample signal and the probability distribution of the constellation diagram or the value of a first function containing the KL divergence information, and outputting the phase value with the minimum KL divergence information or any data or signal capable of representing the phase value. The first function containing the KL divergence information is any function containing KL divergence information and monotonically increasing or decreasing along with the KL divergence information within a preset KL divergence information range, for example, the KL divergence information is F, the first function is-F, and the largest-F corresponds to the smallest KL divergence information. In the present embodiment, the phase values in the phase set are discrete values, and the phase signal can be obtained quickly by calculating KL divergence information corresponding to each discrete value.

Further, the phase signal is obtained in an iterative manner, specifically:

s101, establishing an iteration relational expression and terminating an iteration condition;

s102, acquiring a previous phase signal, and combining the previous phase signal and the iterative relational expression to recur a next phase signal;

s103, when the fact that the iteration termination condition is met is determined, a final estimated phase signal is obtained according to the next phase signal which is pushed out, otherwise, the next phase signal which is pushed out is used as the previous phase signal to be fed back to the step S102, and the step S102 is continuously executed;

wherein the iterative relationship is such that, under compensation of a next phase signal of the sample signal, KL divergence information between the probability distribution of the sample signal and the first probability distribution is smaller than KL divergence information under previous phase compensation;

and the iteration termination condition is that the iteration frequency reaches a preset value or the KL divergence information between the probability distribution of the sample signal and the first probability distribution is smaller than a threshold value under the compensation of the next phase signal of the sample signal.

And obtaining the estimated signal through an iterative algorithm, wherein the target function of the algorithm is KL divergence information between the sample signal compensated by the estimated signal and the probability distribution of the constellation diagram or a first function containing the KL divergence information. Wherein the first function containing KL divergence information is any function containing KL divergence information and monotonically increasing or decreasing with KL divergence information within a preset range of KL divergence information. The iterative algorithm includes, but is not limited to, a gradient descent method, such as establishing an iterative relationship by partial derivation of KL divergence information or a first function containing KL divergence information, so that the KL divergence information is smaller after each iteration. Through an iterative mode, selection on discrete values is not needed, and therefore a more accurate phase signal is obtained.

Further, the convergence coefficient in the iterative algorithm is a variable convergence coefficient.

The convergence factor in the iterative algorithm is variable, including but not limited to, the convergence factor at each iteration is variable, and the convergence factor at different sample points in the sample signal is different.

Further, the phase signal is obtained in a hierarchical manner, specifically:

s201, presetting a stage number and an estimation method of each stage;

s202, acquiring a phase signal of a previous stage, and acquiring a phase signal of a next stage by combining an estimation method of the next stage;

s203, when the detected stage number reaches a preset value, obtaining a finally estimated phase signal according to the next-stage phase signal, otherwise feeding back the next-stage phase signal to S202 as the previous-stage phase signal, and continuing to execute the step S202;

wherein, the estimation method includes any one or more methods of a KL divergence information method, a BPS, a Kalman filtering method, a PCA or a VV method, the step S202 is executed twice or more, and at least one time, the step S202 is executed by adopting the KL divergence information method, so that under the compensation of the next phase signal of the sample signal in the step, the KL divergence information between the probability distribution of the sample signal and the first probability distribution is smaller than that under the compensation of the previous phase signal in the step.

The strategy of rough estimation and fine estimation is adopted, firstly, a rough estimation mode is adopted to obtain a phase signal of the previous stage, and a more accurate phase signal of the next stage is obtained by combining the phase signal of the previous stage and a preset method of the next stage, so that the operation efficiency is greatly improved. The preset method may be a conventional kalman filtering method or a VV method, or may be based on a KL divergence. Wherein, S202 can be executed repeatedly (twice or more), hierarchical searching is realized by executing step S202, and estimation accuracy is improved by continuously reducing the phase range at each stage, thereby better balancing estimation performance and complexity.

Further, the method comprises the step of cycle slip correction, such as:

under the narrow line width or the medium line width, correcting the phase signal by adopting a mode of comparing phase estimation values of adjacent data blocks;

under large line width, the phase signal is corrected by inserting pilot frequency symbols.

Wherein, the cycle slip correction is carried out on the estimated phase signal without adopting a grading mode; in a hierarchical manner, cycle slip correction is performed after any one or more stages of phase estimation. The correction methods include, but are not limited to, comparing the estimated phase signals of adjacent data blocks, inserting pilot symbols.

Further, the KL divergence information is approximated using an empirical average of the sample signal.

In calculating the KL divergence information, the first function containing the KL divergence information, the partial derivative of the KL divergence information, and the partial derivative of the first function containing the KL divergence information, an empirical mean approximation of the sample signal may be used.

Further, the information of the first probability distribution is a probability distribution function of a constellation diagram established by a lookup table or a function including the probability distribution function of the constellation diagram.

The function of the probability distribution function containing the constellation diagram comprises the probability distribution function and any one or a combination of partial derivatives, integrals, logarithms, exponents and the like on the basis of the probability distribution function.

Further, the probability distribution function of the constellation or the function containing the probability distribution function is an explicit function, and the information of the first probability distribution is a parameter of the explicit function or a discretized function value. Or the like, or, alternatively,

the probability distribution function of the constellation or a function comprising the probability distribution function is not an explicit function, and the information of the first probability distribution is a parameter characterizing the function or a discretized function value, which can be obtained by methods including, but not limited to, machine learning, artificial intelligence, or numerical computation.

Further, the probability distribution function of the target constellation includes the influence of any one or more noise sources other than phase noise, including but not limited to amplifier noise, receiver noise, nonlinear noise.

Further, the probability distribution function of the constellation map is decomposed into the sum of a plurality of sub probability distribution functions, and each sub probability distribution is the product of the occurrence probability of a certain constellation point at the transmitting end and the probability distribution of the constellation point at the receiving end; or the like, or, alternatively,

when the real part and the imaginary part of the constellation probability distribution are independent, the constellation probability distribution can be decomposed into a product of the real part probability distribution and the imaginary part probability distribution; or the like, or, alternatively,

a combination of the two above.

Further, the received signal is any one or a combination of multiple of a single carrier signal, a multi-carrier signal, QPSK, QAM, MPSK, offset QAM, a probability shaped signal, a geometric shaped signal, a polarization multiplexing signal, a wavelength division multiplexing signal, a multi-mode or multi-core optical fiber multiplexing signal after sampling.

Further, the sample signal is a sampling signal or a combination of several sampling signals in any dimension of time, subcarrier, polarization state, wavelength, multimode or multi-core fiber mode.

The other technical scheme adopted by the invention is as follows:

a carrier phase estimation and compensation system, comprising:

the device comprises a sample extraction module, a signal processing module and a signal processing module, wherein the sample extraction module is used for acquiring a received signal and extracting a sample signal from the received signal;

the phase estimation module is used for acquiring information of a first probability distribution of a target constellation diagram and estimating a phase signal by combining the sample signal and the information of the first probability distribution;

the phase compensation module is used for compensating the received signal according to the phase signal to obtain a compensated received signal;

the KL divergence information includes KL divergence and/or cross entropy.

The carrier phase estimation and compensation system has the following beneficial effects: the invention adopts KL divergence information to measure the matching degree between the probability distribution of the sample signal and the probability distribution of the constellation diagram, when the KL divergence information is smaller than a threshold value, namely the probability distribution of the sample signal is basically matched with the probability distribution of the constellation diagram, the obtained phase value can effectively compensate the received signal, and compared with the traditional BPS, the invention has lower complexity and better compensation performance compared with the existing Kalman filtering and principal component analysis.

Drawings

FIG. 1 is a flow chart of a phase estimation and compensation method in an embodiment;

FIG. 2 is a schematic flow chart of a phase estimation and compensation method including cycle slip correction according to an embodiment;

FIG. 3 is a schematic diagram of the constellation diagram distribution of probability shaping 16-QAM and the distribution of sampling samples when the phase of the sampling samples is π/12 in the example;

FIG. 4 is a schematic diagram of the constellation diagram distribution of probability shaping 16-QAM and the distribution of sampling samples when the phase of the sampling samples is 0 in the embodiment;

FIG. 5 is a schematic diagram of the constellation diagram distribution of probability shaping 16-QAM and the distribution of sampling samples when the phase of the sampling samples is-pi/12 in the embodiment;

FIG. 6 shows example F (w)_n) A graph diagram of variation with phase error;

FIG. 7 is a graphical illustration of standard deviation of phase estimates as a function of sample number;

FIG. 8 is a diagram illustrating a KL divergence information method based on search according to an embodiment;

FIG. 9 is a schematic diagram of an iteration-based KL divergence information method in an embodiment;

fig. 10 is information for establishing probability distribution of a target constellation using training data in an embodiment;

FIG. 11 is a phase estimation divided into two stages, the first stage using a sought KL divergence method for coarse estimation and the second stage using an iterative KL divergence method for fine estimation;

FIG. 12 is a phase estimation divided into two stages, the first stage using the KL divergence method of the search for coarse estimation, and the second stage using the same KL divergence method of the search for fine estimation;

FIG. 13 is a phase estimation divided into two stages, the first stage using a KL divergence method for coarse estimation and the second stage using a conventional Kalman filtering method for fine estimation

Fig. 14 is a schematic diagram of a coherent optical communication system employing the phase estimation and compensation method of the present embodiment;

fig. 15 is a block diagram of a carrier phase estimation and compensation system according to an embodiment.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.

In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, front, rear, left, right, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.

In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. If the first and second are described for the purpose of distinguishing technical features, they are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.

In the description of the present invention, unless otherwise explicitly limited, terms such as arrangement, installation, connection and the like should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.

The present embodiment provides a new phase estimation and compensation method. The method is transparent to modulation formats, including QPSK, QAM, Multiple PSK (MPSK), single carrier, multiple carrier, offset QAM, etc., and is particularly suitable for probability shaping modulation formats, including probability shaping single carrier, probability shaping multiple carrier, probability shaping offset QAM, etc.

In a communication system, due to the influence of the line widths of a transmitter and a receiver or residual frequency offsets, a time-varying phase difference exists between a received signal and a transmitted signal:

r_n＝exp(jφ_n)·s_n+_n(1)

where r is_n、s_nAnd phi_nRespectively, the received signal at time n, the transmitted signal, and the phase noise._nIs the noise at time n. The purpose of phase estimation and compensation is to obtain a phase

So that

The compensated signal is therefore:

because of phi in the real system_nIs slow compared to the transmission baud rate, so that sampled signals around time n can be used to estimate phi_n. Defining the sample for estimation as r_n＝[r_n-m+1,r_n-m+2…r_n+m]Here, 2m is the number of sample points.

In a first aspect, the present embodiment proposes an objective function, Kullback-Leibler (KL for short), for estimating carrier phase. With full compensation for phase noise, the Probability Distribution (PDF) of the sampled samples used for estimation should best match the desired signal constellation point probability distribution (including other noise besides phase noise). Suppose that

Has a probability distribution of

The desired probability distribution of constellation points (without phase noise but including other noise such as light amplification noise) is f (x, y), where x and y represent the x and y axes, or real and imaginary parts, of the constellation.

Is a phase variable. The KL divergence of the two probability distributions is:

where H (-) denotes the information entropy of the variable,

r {. and I {. denotes a real part and an imaginary part, respectively. Here two characteristics are utilized: 1.

is not dependent on the information entropy

(ii) a change; 2. the integral can be implemented by r_nAverage of the experience of (1). As described above, when

The probability distribution of the sampled samples used for estimation should best match the desired probability distribution of signal constellation points, i.e. the KL divergence in equation (3) should be minimized, when it is the desired value:

equation (4) indicates that minimizing the KL divergence can be degraded to minimize

And f (x, y). Alternatively, the estimated phase signal may be maximized by maximizing-F (w)_n) And (5) realizing.

In another aspect of this embodiment, the probability distribution f (x, y) needs to be known when implementing equation (4). f (x, y) may be obtained by training the communication system before transmitting data. Alternatively, optical communication systems usually employ maximum likelihood symbol detection or bit decoding based on soft-decision error correction codes, which also require f (x, y) information, and the obtained f (x, y) can also be used for phase estimation and compensation to avoid additional estimation of f (x, y). Alternatively, f (x, y) may also be obtained from a network monitoring system. Whether f (x, y) is established by itself or obtained externally and the source of acquisition is not limited herein.

In a specific implementation, if a constellation diagram has K constellation points, the coordinate of each constellation point in the constellation diagram and the probability distribution thereof are represented as a_iAnd p (a)_i) F (x, y) can be written as:

for example, in 16QAM and 64QAM, K is 16 and 64, respectively. For the probability shaped modulation format, p (a) in equation (5)_i) And is not equal to 1/K. As an aspect of one of the embodiments,

can be approximated as a 2-dimensional gaussian distribution:

a here_i,realAnd a_i,imagRespectively represent a_iReal and imaginary parts of (c).

And

are respectively at a_iThe variance of the noise on the real and imaginary parts of the signal, and their correlation coefficients.

Optionally, when a_iWhen the noise on the real and imaginary parts of (c) is uncorrelated, there are:

optionally, for rectangular QAMs (e.g., 16QAM,64QAM, etc.), there is p (a) whether or not probability shaping is included_i)＝p(a_i,real)p(a_i,imag) Thus f (x, y) can be written as:

the above description is merely exemplary, and the specific probability distribution function is determined according to the noise source of the system (the noise herein does not include phase noise), and is not limited herein.

In another aspect of this embodiment, the pair F (w) in equation (4)_n) The minimization of (c) can be accomplished in various implementations. One way is to search through a range of possible phases one by one and find the optimum, e.g. [0 π/2 in rectangular QAM]The phase of (A) is divided into N parts which are respectively [0, pi/(2N), 2 pi/(2N) … (N-1) pi/(2N)]Then calculate one by one when

When k is 0,1 … (N-1), F (w)_n) or-F (w)_n) A value of (a), wherein F (w) is caused_n) Minimum or-F (w)_n) The largest phase value is the estimated value. It is clear that the larger N, the higher the finesse, but also the higher the complexity, of the searched phase.

Optionally, the searching for the multiple phases may be performed in 2 stages, where the first stage coarse searching is performed in a larger phase range but with a lower searching precision, the estimated phase value is output to the next stage, and the second stage fine searching is performed to reduce the searching range but improve the searching precision based on the previous stage coarse searching result. This may reduce complexity.

Optionally, the search range of the phase is not limited to [0 pi/2 ], the number of search stages is not limited to 2, the search range of each stage is not specifically limited, but the search range of the previous stage is larger than the search range of the next stage, and the precision is lower than the precision of the next stage.

Optionally, the phase search method may be applied to various modulation formats, including MPSK, offset QAM, multi-carrier, single carrier, etc., the number of levels and the range and precision of each level of search may be adjusted according to a specific modulation mode, which is not limited herein.

In addition to searching and trying phases one by one within the range possible,F(w_n) Can also be done by iterative algorithms, one of which is described below:

w_n ^new＝w_n ^new/‖w_n ^new‖ (9-2)

here:

the initial value of the iteration at time n may be selected as the estimated output value at time n-1. Here, α is a convergence coefficient, and may be fixed or variable in application. Optionally, another iterative algorithm is:

w_n ^new＝w_n ^new/‖w_n ^new‖ (11-2)

angle (. circle.) here indicates the extraction Angle. As described above

Only the estimated samples r are needed for the update of (1)_iAnd an

And

the latter two can be implemented by building a look-up table.

Obtaining f (R { R } is needed for both the search method and the iterative method_i·w_n},I{r_i·w_n}) or Q (R { R }_i·w_n},I{r_i·w_n}). In practice, we first assign R { R }_i·w_nAnd l { r }_i·w_nQuantize, and then obtain f (R R) from the lookup table by the quantized value_i·w_n},I{r_i·w_n}) or Q (R { R }_i·w_n},I{r_i·w_n}) and then search or iteratively update the above method to find the optimized w_n。

Generally, phase estimates have a certain phase ambiguity, for example, rectangular QAM has a phase ambiguity of pi/2, while conventional BPS have a cycle slip problem of phase estimation, i.e., the estimated phase may be an integer multiple of pi/2 from the true phase difference. The KL divergence method based on searching has the same cycle slip problem as the traditional BPS; the KL divergence method based on iteration does not have the cycle slip problem described above in narrow and medium line widths. However, when the line width is large, the phase estimation values of adjacent data blocks may be very different, and the search method and the iterative method have the problem of cycle slip. Cycle slip can be corrected by comparing phase estimation values of adjacent data blocks under narrow line width and medium line width; at large line widths, it is possible to correct by inserting pilot symbols.

It should be noted that when the iterative algorithm is used, for narrow line width and medium line width, the optimization performance can be achieved by 1-2 iterations, the complexity is greatly reduced, and in addition, the iterative method has better robustness for estimation errors caused by small samples. However, the iterative method has a convergence problem in large linewidth, and has a linewidth tolerance damage compared with the search method. The above methods may be combined in use according to physical device characteristics.

The method is not limited to a single carrier, and can be used for single carrier signals, multi-carrier signals, wavelength division multiplexing signals, polarization multiplexing signals, and mode division multiplexing signals of multimode fiber/multi-core fiber. For example, when the same phase noise is present at the same time sampling point for both polarizations, the two polarizations can be jointly estimated and compensated; different subcarriers of a multicarrier signal at the same time also have approximately the same phase noise and can be jointly estimated and compensated simultaneously.

In addition, the method is not limited to modulation formats and can be used for MPSK, QPSK, QAM, probability shaping and geometric shaping. The specific parameters of the above method are also adjusted accordingly, for example, in offset QAM modulation, such as obtaining F (w) by searching_n) Is minimized

The search range of the first level is pi instead of pi/2 for rectangular QAM.

Finally, the above-described search method and iterative method may be combined. For example, the phase estimation can be divided into 2 stages, and the phase is roughly estimated by a searching method and then finely estimated by an iterative method. More generally, the method of the present embodiment may be combined with a conventional method, such as coarse estimation of the phase by a conventional BPS algorithm, and fine estimation by a KL-based iterative algorithm.

As shown in fig. 1, fig. 1 is a flow chart of a phase estimation and compensation method. The system firstly extracts an estimated sample from a received signal and combines a probability distribution f (x, y) to obtain w_n,estThen use w again_n,estThe multiplication compensates the phase noise of the received signal. Here, w is obtained_n,estIs such that_n,estThe compensated sample has the smallest KL divergence from f (x, y). From equation (4), minimizing the KL divergence is generally equivalent to minimizing the cross entropy. In actual practice, both KL divergence and cross entropy are given by r_nThe empirical mean approximation of (a):

referring to fig. 2, fig. 2 is a flow chart of a phase estimation and compensation method including cycle slip correction. The phase estimates all have a certain phase ambiguity, for example, rectangular QAM has a phase ambiguity of pi/2, which causes cycle slip problem, i.e. the estimated phase will be integral multiple of the true phase difference pi/2. Figure 2 presents a flow chart including cycle slip correction. Cycle slip can be corrected by comparing phase estimation values of adjacent data blocks under narrow line width and medium line width; at large line widths, it is possible to correct by inserting pilot symbols. It is noted that the proposed method has no cycle slip problem at narrow and medium line widths when using an iterative algorithm.

Referring to fig. 3-5, fig. 3 is a schematic diagram illustrating a constellation distribution of probability shaping 16-QAM and a distribution of sampling samples when the phase of the sampling samples is pi/12; fig. 4 is a schematic diagram of the constellation distribution of probability shaping 16-QAM and the distribution of sampling samples when the phase of the sampling samples is 0; FIG. 5 is a schematic diagram of the constellation distribution of probability shaping 16-QAM and the distribution of sampled samples when the phase of the sampled samples is-pi/12; in fig. 3-5, the diamonds represent the distribution of sample samples for phase estimation. As can be seen in fig. 3-5, when the phase rotation is 0, the distribution of the sampled samples is the best match to f (x, y), and the KL divergence can be used to measure the match between the probability distributions.

Referring to FIGS. 6-7, FIG. 6 shows F (w)_n) The curve as a function of phase error confirms that whatever probability shaping format is employed, the value of the KL divergence is minimal when the phase is correctly compensated. Fig. 7 shows a plot of the standard deviation of the phase estimate as a function of the number of samples. It can be seen that 20-30 samples can result in standard deviations below 0.02 rad. Furthermore, the standard deviation of the KL divergence estimate is the same as that of the conventional BPS, which is, however, highly complex. The modulation format in fig. 6 and 7 is probability shaped 16-QAM, and E represents the entropy of probability shaping.

Referring to FIG. 8, FIG. 8 is a KL divergence information method based on search. The information of the probability distribution of the constellation obtained is logf (x, y) will be 0 pi/2]The phase of (A) is divided into N parts which are respectively [0, pi/(2N), 2 pi/(2N) … (N-1) pi/(2N)]Then use one by one

k is 0,1 … (N-1) compensation r_nAnd calculating the corresponding F (w) using equation (4)_n) A value of (a), wherein F (w)_n) Log f (R { R) }_i·w_n},I{r_i·w_n}) may be given byObtained by obtaining the logf (x, y). Corresponding to the smallest F (w)_n) The phase value of (a) is the estimated phase signal. The phase ambiguity of the estimated phase signal is eliminated through cycle slip correction.

Referring to FIG. 9, FIG. 9 is a method based on iterative KL divergence information. In this example, the obtained information of the probability distribution of the target constellation is Q (x, y) in formula (10), and the iterative relationship is shown in formula (11). In this example, the maximum number of iterations is fixed, and the iterations are terminated when the number of iterations reaches a preset value. The iterative method in fig. 9 does not require cycle slip correction at small or medium linewidths.

Referring to fig. 10, fig. 10 shows information for establishing and reading a probability distribution of a constellation. Wherein, the information of the probability distribution of the established constellation diagram is Q (x, y) in formula (10). In this example, f (x, y) is the probability distribution in equation (6), and a can be obtained using the training data_i,real，a_i,imag，

And

these parameters are then used to build a look-up table of (x, y) → Q (x, y). In phase estimation, the iterative algorithm reads the value of Q (x, y) by (x, y), and then uses Q (x, y) for the calculation of the iterative relationship, equation (11). Fig. 10 is only an example, and the information of the probability distribution of the constellation diagram may also be the parameter a_i,real，a_i,imag，

And

rather than a built (x, y) → Q (x, y) look-up table. The phase estimation module is used for estimating the phase of the signal by extracting a_i,real，a_i,imag，

And

q (x, y) in equation (11) is calculated with equal parameters. This approach reduces the required memory but increases the computational load per iteration.

Referring to fig. 11-13, the phase estimation can be divided into two stages. FIG. 11 shows that the search-based KL divergence method can be used in combination with the iterative-based KL divergence method, with the first stage obtaining a more accurate estimate by searching for a coarse estimate of the phase value and the second stage obtaining a more accurate estimate by an iterative method. Fig. 12 shows that the KL divergence based search method can be used in combination with itself, the first stage by searching for a coarse estimated phase value, the second stage still obtaining a more accurate estimate by the search method. Fig. 13 shows that the proposed method can be used in combination with the conventional method, the first stage roughly estimating the phase value by the sought KL divergence method, and the second stage obtaining a more accurate estimate by the conventional kalman filtering method. Fig. 11-13 are shown as examples, the phase estimation can be divided into more than 2 stages in specific implementations, the combination method is not limited to that shown in fig. 11-13, and the position of the cycle slip correction is not limited to that after the compensation of the coarse estimation and the fine estimation, for example, the position can be placed after the coarse estimation and before the fine estimation, or after the fine estimation.

Referring to fig. 14, fig. 14 shows an example of a coherent optical communication system using the phase estimation and compensation method to compensate for laser linewidth and residual frequency offset. The received signal is transmitted from the input to the polarization demultiplexing and filtering, and passes through two lasers, the phase of the received signal at the moment has noise, if the noise is not removed, the decoding error rate can be provided in the decoding process, and even the decoding cannot be normally performed. After the method of the embodiment is used for compensating the received signal, the phase noise is eliminated, and the subsequent decoding quality is improved.

In summary, the carrier phase estimation and compensation method of the present embodiment is transparent to modulation formats, has lower complexity compared to the conventional BPS, and has better compensation performance compared to the conventional kalman filtering and principal component analysis. In addition, compared with BPS and principal component analysis, the KL estimation method based on the iterative algorithm has better robustness on cycle slip and estimation noise under small samples.

As shown in fig. 15, the present embodiment further provides a carrier phase estimation and compensation system, including:

the KL divergence information includes KL divergence and/or cross entropy.

The carrier phase estimation and compensation system of the embodiment can execute the carrier phase estimation and compensation method provided by the method embodiment of the invention, can execute any combination implementation steps of the method embodiment, and has corresponding functions and beneficial effects of the method.

It will be understood that all or some of the steps, systems of methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as is well known to those of ordinary skill in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by a computer. In addition, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media as known to those skilled in the art.

The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims

1. A method for carrier phase estimation and compensation, comprising the steps of:

the KL divergence information includes KL divergence and/or cross entropy.

2. The method of claim 1, wherein the phase signal is obtained by searching, specifically:

acquiring a phase signal according to a phase value corresponding to the minimum KL divergence information;

wherein the first function containing KL divergence information is any function containing KL divergence information and monotonically increasing or decreasing with KL divergence information within a preset range of KL divergence information.

3. The carrier phase estimation and compensation method according to claim 1, wherein the phase signal is obtained in an iterative manner, specifically:

4. A carrier phase estimation and compensation method as claimed in claim 3, wherein the convergence factor in the iterative algorithm is a variable convergence factor.

5. The carrier phase estimation and compensation method according to claim 1, wherein the phase signal is obtained in a hierarchical manner, specifically:

s201, presetting a stage number and an estimation method of each stage;

wherein, the estimation method includes any one or more methods of a KL divergence information method, a BPS, a kalman filtering method, a PCA or a VV method, the step S202 is performed twice or more, and at least one time of performing the step S202 adopts the KL divergence information method mentioned in claim 1, so that the KL divergence information between the probability distribution of the sample signal and the first probability distribution under the compensation of the next phase signal of the sample signal at this step is smaller than the KL divergence information under the compensation of the previous phase signal at this step.

6. The carrier phase estimation and compensation method of claim 1, further comprising a cycle slip correction step.

7. The method according to claim 1, wherein the KL divergence information is approximated by an empirical average of the sample signal.

8. The method of claim 1, wherein the information of the first probability distribution is a function of a probability distribution of a constellation diagram or a function including a probability distribution of a constellation diagram, which is established by a look-up table.

9. The carrier phase estimation and compensation method according to claim 1, wherein the received signal is any one or more of a sampled single carrier signal, a multi-carrier signal, QPSK, QAM, MPSK, offset QAM, a probability shaped signal, a geometry shaped signal, a polarization multiplexed signal, a wavelength division multiplexed signal, a multi-mode or multi-core fiber multiplexed signal.

10. A carrier phase estimation and compensation method as claimed in claim 1, wherein the sample signal is a sampled signal or a combination of several sampled signals in any dimension of time, sub-carrier, polarization, wavelength, multi-mode or multi-core fiber mode.

11. A carrier phase estimation and compensation system, comprising:

the KL divergence information includes KL divergence and/or cross entropy.