Carrier phase estimation method and system

Abstract

The invention discloses a carrier phase estimation method and system, and the method comprises the following steps: obtaining a receiving signal, obtaining a first signal used for carrier phase estimation from the receiving signal, and enabling the number of symbols of the first signal to be N; initializing a phase set, wherein the number of phases in the phase set is B; obtaining first probability distribution, obtaining second probability distribution and third probability distribution according to the first probability distribution, obtaining fourth probability distribution according to the first probability distribution, the second probability distribution and the third probability distribution, and taking symbol indexes and phase indexes as independent variables for the first probability distribution, the second probability distribution and the third probability distribution; and obtaining an estimated phase according to the fourth probability distribution. Compared with a traditional method in a super-Nyquist system with strong inter-symbol crosstalk, the method has the advantage that the system performance is improved when the line width of a laser is relatively wide or the number of constellation points is relatively large. The method can be widely applied to optical communication systems.

Description

Technical Field

[0001] The present invention relates to the field of transmission impairment compensation in optical communication systems, and particularly to a carrier phase estimation method and system. Background Art

[0002] The electrical signal received by the receiver is output by a photodetector after the optical signal and the local oscillator light generated by the local oscillator laser are beat by an optical mixer. However, there are phase random jitters in both the laser at the transmitting end and the local oscillator laser at the receiving end, resulting in phase noise of the received electrical signal. Therefore, in order to improve the transmission performance of the system, the carrier phase recovery (CPR) algorithm is very important. Currently, many carrier phase estimation and compensation methods have been proposed in the academic and industrial fields. The blind phase search (BPS) algorithm is a commonly used CPR algorithm. However, this method has performance degradation when used for probabilistically shaped modulation signals and super Nyquist signals with inter-symbol interference (ISI), and there is a problem of phase cycle slips. Inserting pilots periodically in the signal as reference phases can suppress cycle slips. However, when there is severe ISI, such as in a super Nyquist system with a small compression ratio, the pilot symbols are affected by the previous and subsequent symbols, reducing the ability to suppress cycle slips. The CPR method based on Kalman filtering and KL divergence has good performance at a small linewidth, and can suppress cycle slips by presetting the phase initial value of the next data block based on the phase estimated from the previous data block. However, their linewidth tolerance is poor, and there is significant performance degradation in super Nyquist systems with strong inter-symbol interference. The principal component analysis method is relatively robust to inter-symbol interference, but there is still a certain degree of performance degradation, and the performance of this method depends severely on the constellation layout and the probabilities of its constellation points. Summary of the Invention

[0003] To solve at least one of the technical problems existing in the prior art to a certain extent, an object of the present invention is to provide a new high-performance carrier phase estimation method. This method first presets a phase range and discretizes the phase values within this range, then calculates the posterior probability of each phase being a discrete value at each moment, and then estimates the phase at each moment or the entire data block according to the posterior probability. This method solves the problem that the existing carrier phase recovery algorithms have performance degradation in super Nyquist systems with strong inter-symbol interference, when the laser linewidth is large and / or the modulation order is high.

[0004] The first technical solution adopted by the present invention is as follows:

[0005] A carrier phase estimation method, comprising the following steps:

[0006] Obtain a received signal, and obtain a first signal for carrier phase estimation from the received signal, where the number of symbols of the first signal is N;

[0007] Initialize a set of phases, where the number of phases in the set of phases is B;

[0008] Obtain a first probability distribution, obtain a second probability distribution and a third probability distribution according to the first probability distribution, and obtain a fourth probability distribution according to the first probability distribution, the second probability distribution and the third probability distribution; wherein the first to fourth probability distributions are functions of a symbol index and a phase index;

[0009] Obtain an estimated phase according to the fourth probability distribution.

[0010] The present invention can perform a block processing on a received signal, and the first signal is a data block obtained by performing block processing on the received signal. Estimate the phases at different symbol positions (or different times) in this data block according to the first signal, or when it is assumed that the phases within the entire data block are basically unchanged, estimate the common phase of this data block. The possible values of the phase are discrete, that is, a set with a preset number of phases B, and the estimated phase is an element in the set of phases. Among them, the mathematical symbols N and B are only for convenience of expression, and should not be regarded as a limitation of the present invention. Other mathematical symbols can also be used to represent the symbol length and the number of phases.

[0011] The core of the present invention is to estimate the phase by calculating the fourth probability distribution, where the fourth probability distribution is a function of a symbol index and a phase index. In one embodiment, the fourth probability distribution has N×B elements, but specifically represented as a two-dimensional distribution of N×B or B×N, or a one-dimensional distribution, or other representation methods are not limited. This probability distribution represents the probability that the phase is each value in the set of phases at each symbol position on the premise of knowing the first signal. Optionally, the probability in the fourth probability distribution can also represent other meanings. In addition, although the fourth probability distribution is a function of a symbol index and a phase index, it is not limited to traversing all N symbol indexes or B phase indexes. For example, when it is assumed that adjacent two symbol positions have the same estimated phase, the symbol index only needs to include odd indexes or even indexes, and the fourth probability distribution has N / 2×B elements, or still let the fourth probability distribution have N×B elements, but the probabilities on adjacent two symbol indexes under the same phase index are the same.

[0012] The fourth probability distribution is obtained from the first probability distribution, the second probability distribution and the third probability distribution. The second probability distribution and the third probability distribution are obtained by combining the first probability distribution with relevant operations.

[0013] Further, the step of obtaining the first signal from the received signal includes the step of dividing the received signal into blocks.

[0014] The carrier phase estimation method proposed by the present invention adopts a block processing method, divides the received signal into signal blocks with the number of symbols being N, and performs phase estimation on each signal block using the proposed method. It should be noted that the present invention does not limit the first signal and the received signal to have the same sampling rate. For example, the sampling rate of the first signal can be half of the sampling rate of the received signal. In this embodiment, the received signal is divided into blocks, the number of symbols in each signal block is 2N, and then downsampling is performed to obtain the first signal with the number of symbols being N. Let the first signal be r = {r 0 , r 1 … r N-1}, where the subscript represents the symbol index, and the proposed method estimates the phase θ est,k , k = 0, 1… N - 1 at each symbol position, or approximately assumes that the phase change in the first signal is very small, so as to estimate the common phase θ est at all symbol positions in the first signal. Optionally, it can also be considered that every two symbols in the first signal have the same phase, so as to estimate the phase on every two symbols, and no specific limitation is made.

[0015] Furthermore, the initialization phase set includes:

[0016] Set the phase range, discretize the phase within the phase range, and obtain a phase set composed of B phase values.

[0017] Discretize the possible values of the phase. The initialization phase set is as follows: First, preset the range of possible values of the phase in the first signal, and then discretize the phase within the range to obtain a phase set composed of B phase values. One preset method is to obtain the estimated phase of the last symbol in the previous data block of the first signal, denoted as θ', set the phase range as θ total , centered on θ', and equally divide it into B discrete phases within the range of θ total , and the phase set is Θ = θ' + θ total ×{(-B / 2 + 1) / B, (-B / 2 + 2) / B, … × B / 2 / B}. By this method, the present invention does not need to use pilot symbols to eliminate cycle slips. Optionally, B phase values can also be divided unequally within θ total , and no specific limitation is made in the present invention.

[0018] Furthermore, the obtaining of the first probability distribution includes:

[0019] Obtain the set of all possible values of the transmitted signal {a 0 , a 1 … a M-1}, where M is the number of all possible values;

[0020] For a certain \(k\in\{0,1,\ldots,N - 1\}\), \(n\in\{0,1,\ldots,B - 1\}\), and \(i\in\{0,1,\ldots,M - 1\}\), obtain the probability of the received signal \(r\) given that the transmitted signal \(s\) at the \(k\)-th symbol is known to be \(a\) and the phase \(\theta\). Denote this probability as k where \(s\), \(\theta\), and \(r\) are respectively the transmitted signal, the phase, and the received signal at the \(k\)-th symbol, \(a\) is the \(i\)-th value in the set of all possible values of the transmitted signal, i and \(\theta\) is the \(n\)-th phase in the set of phases; k is the received signal \(r\) k under the condition of where \(s\) k and \(\theta\) k and \(r\) k are respectively the transmitted signal, the phase, and the received signal at the \(k\)-th symbol, \(a\) is the \(i\)-th value in the set of all possible values of the transmitted signal, i and \(\theta\) is the \(n\)-th phase in the set of phases; is the \(n\)-th phase in the set of phases;

[0021] According to the obtain the first probability distribution.

[0022] The present invention provides a method for obtaining the first probability distribution: Assume the first probability distribution is \(p(k,n)\), with a dimension of \(N\times B\), where \(k = 0,1,\ldots,N - 1\) and \(n = 0,1,\ldots,B - 1\) respectively represent the symbol index and the phase index. Here, \(p(k,n)\) is just a representation method and should not be considered as a limitation on the representation method of the first probability distribution. For example, optionally, the first probability distribution can also be represented as \(p(n,k)\), with a dimension of \(B\times N\). In addition, the symbols \(k\), \(n\), \(i\), \(s\), \(\theta\), \(r\), \(a\), \(M\), and so on are only for the convenience of expression and should not be considered as limitations on the present invention. 1 (k,n), with a dimension of \(N\times B\), where \(k = 0,1,\ldots,N - 1\) and \(n = 0,1,\ldots,B - 1\) respectively represent the symbol index and the phase index. Here, \(p\) 1 (k,n) is just a representation method and should not be considered as a limitation on the representation method of the first probability distribution. For example, optionally, the first probability distribution can also be represented as \(p\) 1 (n,k), with a dimension of \(B\times N\). In addition, the symbols \(k\), \(n\), \(i\), \(s\) k and \(\theta\) k and \(r\) k and \(a\) i and M and etc. are only for the convenience of expression and should not be considered as limitations on the present invention.

[0023] The first distribution probability can be obtained according to where one embodiment is where \(\Gamma\) k is the set of all possible values of the transmitted signal at the \(k\)-th symbol. It should be noted that in a super-Nyquist system, the set of possible values of the transmitted signal \(\{a\) 0 , \(a\) 1 \ldots a\) M-1 \} should be the set of values considering inter-symbol interference.

[0024] Furthermore, the steps of obtaining the second probability distribution or the third probability distribution from the first probability distribution include recursive steps.

[0025] Further, the step of obtaining the second probability distribution according to the first probability distribution includes:

[0026] For a certain n ∈ {0, 1, … B−1}, m ∈ {0, 1, … B−1}, k ∈ {1, 2, … N−1}, obtain the probability that the phase θ of the first probability distribution and the second probability distribution on the (k−1)-th symbol is, respectively set as p k-1 is of, and are respectively set as p 1 (k−1, m) and p 2 (k−1, m);

[0027] According to p 1 (k−1, m) and p 2 (k−1, m) to obtain p 2 (k, n);

[0028] Assign p 2 (k, n) as the probability that the phase θ of the second probability distribution on the k-th symbol is k is of.

[0029] The present invention provides a method for obtaining a second probability distribution according to a first probability, where n, m, k, θ k-1 , p 1 (k−1, m), p 2 (k−1, m) and p 2 (k, n) and other symbols are only for convenience of expression and cannot be regarded as a limitation of the present invention. Specifically, the second probability distribution p 2 (k, n) is obtained according to p 1 (k−1, m) and p 2 (k−1, m). One embodiment is where Θ is the set of the phases, is the probability that the phase θ on the k-th symbol is k-1 is under the condition that the phase θ on the (k−1)-th symbol is k is of. When k = 1, the initial value of p 2 (0, m) can be set to 1 / B or determined according to the index value of the estimated phase on the last symbol of the previous signal block in the phase set, and the present invention does not make specific limitations.

[0030] Further, the step of obtaining the third probability distribution according to the first probability distribution includes:

[0031] For a certain \(n\in\{0,1,\ldots,B - 1\}\), \(m\in\{0,1,\ldots,B - 1\}\), \(k\in\{0,1,\ldots,N - 2\}\), obtain the probabilities of the first probability distribution and the third probability distribution at the \((k + 1)\)-th symbol for the phase \(\theta\), denoted as \(p\) k+1 is (k + 1,m) and \(p\) 1 (k + 1,m); 3 (k + 1,m);

[0032] According to \(p\) 1 (k + 1,m) and \(p\) 3 (k + 1,m), obtain \(p\) 3 (k,n);

[0033] Assign \(p\) 3 (k,n) as the probability that the phase \(\theta\) k is for the third probability distribution at the \(k\)-th symbol.

[0034] The present invention provides a method for obtaining the third probability distribution according to the first probability, where \(n\), \(m\), \(k\), \(\theta\) k+1 , p 1 (k + 1,m), \(p\) 3 (k + 1,m) and \(p\) 3 (k,n) and other symbols are only for the convenience of expression and should not be regarded as a limitation to the present invention. Specifically, the third probability distribution \(p\) 3 (k,n) is obtained according to \(p\) 1 (k + 1,m) and \(p\) 3 (k + 1,m). One embodiment is where \(\Theta\) is the set of said phases, is the probability that the phase \(\theta\) k is for the \((k + 1)\)-th symbol given that the phase \(\theta\) k+1 is for the \(k\)-th symbol. When \(k = N - 2\), the initial value of \(p\) 3 (N - 1,n) can be set to \(1 / B\) or \(p\) 2 (N - 1,n), and the present invention does not make a specific limitation.

[0035] Furthermore, in the step of obtaining the second probability distribution or the third probability distribution according to the first probability distribution, it includes:

[0036] For a certain \(k\in\{0,1,\ldots,N - 2\}\), \(n\in\{0,1,\ldots,B - 1\}\), \(m\in\{0,1,\ldots,B - 1\}\), obtain the probability that the phase \(\theta\) k is for the \((k + 1)\)-th symbol given that the phase \(\theta\) k+1 is The probability.

[0037] Specifically, in the step of obtaining the second probability distribution or the third probability distribution, the probability distribution

[0038]

[0039] Further, obtaining the fourth probability distribution according to the first probability distribution, the second probability distribution and the third probability distribution includes:

[0040] For a certain k ∈ {0, 1, … N - 1} and n ∈ {0, 1, … B - 1}, multiply the probabilities of the phase θ k being at the k-th symbol in the first probability distribution, the second probability distribution and the third probability distribution, and assign the product value as the probability of the phase θ k being at the k-th symbol in the fourth probability distribution.

[0041] The present invention provides a method for obtaining the fourth probability distribution. Assume that the first to fourth probability distributions are p 1 (k, n), p 2 (k, n), p 3 (k, n), p 4 (k, n), all with dimensions of N × B, where k = 0, 1, … N - 1 and n = 0, 1, … B - 1 represent the symbol index and the phase index respectively. The fourth probability distribution can be obtained in the following way: p 4 (k, n) = p 1 (k, n) × p 2 (k, n) × p 3 (k, n).

[0042] Further, obtaining the estimated phase according to the fourth probability distribution includes:

[0043] For a certain symbol index, find the maximum value of the probabilities corresponding to all phase indices at this symbol index in the fourth probability distribution, and assign the phase corresponding to the maximum value as the estimated phase value at this symbol index, or;

[0044] For a certain phase index, obtain the probability of the fifth probability distribution at this phase index according to the probabilities corresponding to all symbol indices at this phase index in the fourth probability distribution, where the obtained fifth probability distribution takes the phase index as the independent variable, then obtain the maximum value in the fifth probability distribution, and assign the phase corresponding to the maximum value as the estimated phase value at all symbol indices in the first signal.

[0045] Obtaining the estimated phase according to the fourth probability distribution is divided into two cases: 1) estimating the phase values at the symbol positions corresponding to all symbol indices in the fourth probability distribution; 2) assuming that the phase values at all symbol positions in the first signal are the same, then estimating the common phase at all symbol positions in the first signal. The former can give more detailed phase information, while the second method is simpler. Which method to use can be determined according to actual needs.

[0046] For the convenience of description, assume that the fourth probability distribution is denoted as p 4 (k,n), with dimensions N×B, where k = 0, 1…N - 1 and n = 0, 1…B - 1 represent the symbol index and phase index respectively. Examples in these two cases are as follows:

[0047] In the first case, the phase estimated at each symbol position

[0048] In the second case, the phase estimated at all symbol positions in the first signal

[0049] Optionally, when the symbol index or phase index in the fourth probability distribution does not traverse all N symbol indices or B phase indices, only the symbol index k and phase index n included in the fourth probability distribution need to perform the above operations.

[0050] The second technical solution adopted by the present invention is:

[0051] A carrier phase estimation system, comprising:

[0052] A receiver for receiving an optical signal and converting the optical signal into an analog electrical signal;

[0053] An analog-to-digital converter for converting the received analog electrical signal into a digital signal;

[0054] Digital signal processing, where the digital signal processing includes a phase estimation module to implement the method described above

[0055] The beneficial effects of the present invention are: The present invention realizes a high-performance carrier phase estimation scheme, which can achieve more accurate carrier phase estimation in a super-Nyquist system with strong inter-symbol interference, when the laser linewidth is relatively wide or the number of constellation points is relatively large. Description of the Drawings

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following introduces the accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings in the following introduction are only for conveniently and clearly presenting some embodiments of the technical solutions in the present invention. For those skilled in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0057] Figure 1 It is a flowchart of the steps of a phase estimation in an embodiment of the present invention.

[0058] Figure 2 It is a flowchart of the steps of obtaining a second probability distribution and a third probability distribution according to a first probability distribution in an embodiment of the present invention.

[0059] Figure 3 It is a flowchart of the steps of obtaining an estimated phase value according to a fourth probability in an embodiment of the present invention.

[0060] Figure 4 It is a block diagram of an ultra-Nyquist system in an embodiment of the present invention.

[0061] Figure 5 It is a schematic diagram of a curve showing the performance of the phase estimation algorithm in an embodiment of the present invention varying with the compression ratio.

[0062] Figure 6 It is a schematic diagram of a curve showing the performance of the phase estimation algorithm in an embodiment of the present invention varying with the line width. Detailed Embodiments

[0063] The following details the embodiments of the present invention. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals throughout indicate the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as a limitation of the present invention. For the step numbers in the following embodiments, they are only set for convenience of explanation and do not limit the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0064] In the description of the present invention, it should be understood that for the orientation description, such as the orientation or positional relationship indicated by up, down, front, back, left, right, etc., is based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying 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 a limitation of the present invention.

[0065] In the description of the present invention, "several" means one or more, "multiple" means two or more, "greater than", "less than", "exceeding", etc. are understood not to include the recited number, and "above", "below", "within", etc. are understood to include the recited number. If there is a description of "first" and "second", it is only for the purpose of distinguishing technical features and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence relationship of the indicated technical features. In addition, "and / or" describes the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after.

[0066] In the description of the present invention, unless otherwise clearly defined, words such as "set", "install", "connect", etc. should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0067] Aiming at the problem that the performance of traditional carrier phase estimation algorithms degrades in a super-Nyquist system with strong inter-symbol interference when the laser linewidth is relatively wide and / or the number of constellation points is relatively large, the present invention proposes a high-performance carrier phase estimation method. This method estimates the phase at each moment or the entire data block by calculating the posterior probability of each possible value of the phase at each moment, and improves the estimation performance compared with the traditional method.

[0068] As Figure 1 shown, the present invention proposes a carrier phase estimation method based on the maximum a posteriori criterion. This method performs block processing on the received signal, first discretizes the possible values of the phase, and calculates the posterior probability of each discrete value of the phase at each symbol position / moment based on the first signal (i.e., the received signal after block processing), that is, the fourth probability distribution. The fourth probability distribution is obtained from the first probability distribution, the second probability distribution, and the third probability distribution, and the first probability distribution is also used in the calculation of the second and third probability distributions, and is calculated by means of forward or backward recursion. Finally, the phase estimation value at each moment or the entire data block is obtained by using the calculated fourth probability distribution.

[0069] Let the length of the received signal after block processing be N, and the received signal is defined as r = {r 0 , r 1 … r N-1}, where the subscript k = 0, 1… N - 1 represents the symbol index of the received signal and also physically represents the kth moment, and its corresponding transmitted signal is s = {s 0 , s 1 … s N-1}. It should be noted that in the super-Nyquist system, s = {s 0 , s1 …s N-1} should be the signal considering inter-symbol interference. For example, assume the transmitted symbol is c = {c 0 , c 1 … c N-1}, the length of inter-symbol interference for super-Nyquist shaping is 3, and the coefficients are h -1 , h 0 and h 1 , then s i = h -1 ·c i-1 + h 0 ·c i + h 1 ·c i+1 . In practice, the relationship between s and the original transmitted symbol c can be established by means of a look-up table. Define the phase at these N received symbol positions / times as θ = {θ 0 , θ 0 … θ N-1}, then the posterior probability of the phase θ k at the k-th moment based on the received sequence r is expressed as:

[0070]

[0071] In practice, the value of phase noise is continuous. However, for the implementation of the present invention, first, the set of possible values of the initial and discrete phases is determined. Specifically, first, a phase range is preset, and the continuous phases within the range are discretized to obtain B discrete phase values to form a phase set. The estimated phase value is an element in the phase set. In practice, the carrier phase noise caused by the laser follows a Wiener distribution with a mean of 0 and can be expressed as:

[0072] θ k = θ k-1 + Δθ k (2)

[0073] where Δθ k is the difference between the phase at the k-th moment and the phase at the k - 1-th moment (θ k and θ k-1 ). Δθ k follows a normal distribution:

[0074]

[0075] In formula (3), Δf is the laser linewidth and τ is the symbol period. The variance σ p 2It is proportional to the laser linewidth Δf. Since the carrier phase noise changes continuously over time, it can be considered that: 1) the phase noise variation of each symbol within a signal block of length N is within a certain range, and 2) the phase distribution range of the current signal block has the estimated phase of the last symbol of the previous signal block as the midpoint. Based on the above assumptions, the phase range is determined, and the phase values within the range are discretized to form the estimated phase set of the signal block.

[0076] Let the estimated phase of the last symbol of the previous signal block be θ’, and let the range of the phase interval be π / 4. Then the preset range is [θ’ - π / 8, θ’ + π / 8]. The interval is discretized into B equally spaced phases, and the estimated phase set of the current signal block is obtained according to the following formula

[0077]

[0078] In actual implementation, the preset range of the phase distribution interval can be adjusted according to the magnitude of the laser linewidth, or the phase can be discretized within the preset range in a non-uniform manner, which is not limited in the present invention. Considering the phases in the above phase set Θ, the posterior probability in formula (1) can be written as:

[0079]

[0080] The probability distribution in formula (5) is an embodiment of the fourth probability distribution described in the present invention. It takes the symbol index k and the phase index n as independent variables, where k = 0, 1, …, N - 1, n = 0, 1, …, B - 1. In addition, for a given received sequence r, the value of p(r) is a constant. Therefore, the fourth probability distribution can also be defined as Next, we calculate the probability distribution

[0081]

[0082] Define the first probability distribution The second probability distribution The third probability distribution where k ∈ [0, N - 1], n ∈ [0, B - 1], r <k represents the received sequence symbols with subscript indices less than k, and r >k represents the received sequence symbols with subscript indices greater than k. Then the fourth probability distribution can be represented by the product of the first probability distribution, the second probability distribution, and the third probability distribution:

[0083] p 4 (k,n) = p 1 (k,n)p 2 (k,n)p 3 (k,n) (6)

[0084] According to formula (6), to obtain the fourth probability distribution, the probabilities p 1 (k,n), p 2 (k,n) and p 3 (k,n) need to be calculated separately.

[0085] First, calculate the first probability distribution. p 1 (k,n) can be calculated according to the following formula:

[0086]

[0087] where Γ k is the set of all possible values of a i at the k-th moment, where M is the number of all possible values of s k . When p(s k =a i ) has the same value for all a i , the first probability distribution can be simplified to:

[0088]

[0089] However, in a probability shaping or super-Nyquist system, p(s k =a i ) has different values for different a i , so the formula (7) still needs to be used to calculate the first probability distribution. In an AWGN channel, let n k be the Gaussian white noise at the k-th moment, and the received symbol r k can be expressed as:

[0090]

[0091] Thus,

[0092]

[0093] where σ noise 2 is the noise variance. The first probability distribution can be calculated using formulas (10) and (7), or formulas (10) and (8). Next, calculate the second probability distribution. At time 0, initialize p 2 (0,n) as:

[0094] p 2 (0,n)=1 / B, n∈[0,B - 1] (11)

[0095] Optionally, the initial value can also be set as p 2 (0,B / 2 - 1)=1, and when n≠B / 2 - 1, p2 (0,n) = 0. Then for the second probability distribution p 2 (k,n) at the k-th moment, as Figure 2 shown in (a) below, it can be obtained according to p 1 (k - 1,m), p 2 (k - 1,m), and obtained as follows:

[0096]

[0097] Therefore, according to formula (12), the values of the second probability distribution at k = 1, 2... N - 1 moments can be obtained recursively.

[0098] Next, calculate the third probability distribution. At the (N - 1)-th moment, initialize p 3 (N - 1,n) as:

[0099] p 3 (N - 1,n) = 1 / B, n ∈ [0, B - 1] (13)

[0100] Optionally, the initial value can also be set as p 3 (N - 1,n) = p 2 (N - 1,n). For the third probability distribution p 3 (k,n) at the k-th moment, as Figure 2 shown in (b) below, it can be obtained according to p 1 (k + 1,m) and p 3 (k + 1,m), and obtained as follows:

[0101]

[0102] Therefore, according to formula (14), the values of the third probability distribution at k = N - 2, N - 1... 0 moments can be obtained recursively.

[0103] In the recursive formulas (12) and (14), calculating the second and third probability distributions also requires knowing the probability that the phase θ k at the k-th symbol is and the phase θ k+1 at the (k + 1)-th symbol is , where k = 0, 1... N - 2, n = 0, 1... B - 1, m = 0, 1... B - 1. This probability can be calculated as follows:

[0104]

[0105] After obtaining the fourth probability distribution, the first implementation method proposed by the present invention is: according to the obtained fourth probability distribution values, take the phase corresponding to the maximum value of the fourth probability at each symbol / time index as the estimated phase value at that time. At this time, there is an estimated phase value at each time within the signal block, denoted as

[0106]

[0107] The second implementation method proposed by the present invention is as Figure 3 shown: obtain the fifth probability distribution according to the obtained fourth probability distribution values, where the fifth probability distribution takes the phase index as the independent variable. At each phase, the value of the fifth probability distribution is the probability mean or the probability summation value of the fourth probability distribution at different time indices within the signal block:

[0108] p 5 (n) = ∑ k p 4 (k,n) (17)

[0109] Then take the phase corresponding to the maximum value of p 5 (n) as the estimated phase value of the entire signal block. At this time, the estimated phase values at each time within the signal block are the same, denoted as

[0110]

[0111] To verify the effectiveness of the present invention, a comparison is made through simulation. As Figure 4 shown is the block diagram of the super-Nyquist simulation system. In the simulation, the super-Nyquist signal adopts a truncated Gaussian spectrum, the modulation format is QPSK, the baud rate is 55 GBaud, and the optical signal-to-noise ratio is set to 18 dB. In the proposed method, B is set to 36, and the estimated phase values are obtained using formulas (16) and (18) respectively, defined as Example 1 and Example 2. In addition, we also use the blind phase estimation (BPS) algorithm and the principal component analysis (PCPE) algorithm to compare with the proposed phase estimation method. In the BPS algorithm, the discrete number of phases B = 36, and a pilot symbol is inserted into each data block to solve the cycle slip.

[0112] Figure 5 shows the system performance using different carrier estimation algorithms at different compression ratios with a laser linewidth of 100 kHz. The data block length N in each method is the optimized value. It can be seen from the figure that the method proposed by the present invention has a performance advantage over the traditional BPS and PCPE algorithms at a larger compression ratio, solving the problem of performance degradation of the traditional method in the super-Nyquist system. Figure 6The system bit error rate at a compression ratio of 0.9 and different laser line widths. The data block length N of all methods has been optimized. It can be seen that the proposed method shows better line width tolerance than the traditional BPS and PCPE, and Example 2 is better than Example 1.

[0113] The present invention also proposes a carrier phase estimation system, including: a receiver for receiving an optical signal and converting the optical signal into an analog electrical signal; an analog-to-digital converter for converting the received analog electrical signal into a digital signal; digital signal processing, and the digital signal processing includes a phase estimation module to implement the proposed phase estimation method.

[0114] In some alternative embodiments, the functions / operations mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the functions / operations involved, two consecutive blocks shown may actually be executed substantially simultaneously or the blocks can sometimes be executed in the reverse order. In addition, the embodiments presented and described in the flowcharts of the present invention are provided by way of example for the purpose of providing a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logical flows presented herein. Alternative embodiments are contemplated, where the order of various operations is changed and where sub-operations described as part of a larger operation are executed independently.

[0115] In addition, although the present invention has been described in the context of functional modules, it should be understood that, unless otherwise stated to the contrary, one or more of the functions and / or features described may be integrated in a single physical device and / or software module, or one or more functions and / or features may be implemented in separate physical devices or software modules. It can also be understood that a detailed discussion of the actual implementation of each module is not necessary for understanding the present invention. More precisely, considering the attributes, functions, and internal relationships of the various functional modules in the devices disclosed herein, the actual implementation of the modules will be understood within the ordinary skills of an engineer. Therefore, those skilled in the art can implement the present invention as set forth in the claims without undue experimentation. It can also be understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0116] If the above-mentioned functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs.

[0117] The logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a predefined sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in combination with an instruction execution system, apparatus, or device.

[0118] More specific examples (non-exhaustive list) of computer-readable media include the following: electrical connection parts (electronic devices) having one or more wirings, portable computer disk cartridges (magnetic devices), random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memories), optical fiber devices, and portable compact disc read-only memories (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or, if necessary, other suitable processing, and then storing it in a computer memory.

[0119] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0120] In the foregoing description of this specification, the descriptions referring to the terms "one embodiment / example", "another embodiment / example" or "certain embodiments / examples", etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0121] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the claims and their equivalents.

[0122] The above has specifically described the preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Those skilled in the art can also make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A carrier phase estimation method, characterized in that: The following steps are involved: Acquire a received signal, and acquire a first signal for carrier phase estimation from the received signal, wherein the number of symbols of the first signal is N; Initialize a phase set, wherein the number of phases in the phase set is B; Obtain a first probability distribution, obtain a second probability distribution and a third probability distribution according to the first probability distribution, and obtain a fourth probability distribution according to the first probability distribution, the second probability distribution and the third probability distribution; wherein the first to fourth probability distributions all use a symbol index and a phase index as independent variables; An estimated phase is obtained according to the fourth probability distribution.

2. A carrier phase estimation method according to claim 1, characterized in that: The step of acquiring the first signal from the received signal includes the step of dividing the received signal into blocks.

3. A carrier phase estimation method according to claim 1, characterized in that: The initialization phase set includes: A phase range is set, and the phase is discretized within the phase range to obtain B phase values ​​to form a phase set.

4. A carrier phase estimation method according to claim 1, characterized in that: The obtaining of the first probability distribution comprises: Get the set of all possible values ​​of the transmitted signal {a0,a1…a M-1 }, where M is the number of all possible values; For a certain k∈{0,1,…N-1},n∈{0,1,…B-1},i∈{0,1,…M-1}, obtain the known transmitted signal s on the kth symbol k for a i and phase θ k for The signal r is received under the condition k The probability of where s k ,θ k and r k are the transmitted signal, phase and received signal on the kth symbol, respectively, and a i is the ith value in the set of all possible values ​​of the transmitted signal, is the nth phase in the phase set; According to the The first probability distribution is obtained.

5. A carrier phase estimation method according to claim 1, characterized in that: The step of acquiring a second probability distribution according to the first probability distribution includes: For a certain n∈{0,1,…B-1}, m∈{0,1,…B-1}, k∈{1,2,…N-1}, obtain the phase θ of the first probability distribution and the second probability distribution on the k-1th symbol k-1 for The probabilities of are set as p1(k-1,m) and p2(k-1,m) respectively; Obtain p2(k,n) based on p1(k-1,m) and p2(k-1,m); Assign p2(k,n) to the second probability distribution at the kth symbol with phase θ k for probability.

6. A carrier phase estimation method according to claim 1, characterized in that: The step of obtaining a third probability distribution according to the first probability distribution includes: For a certain n∈{0,1,…B-1}, m∈{0,1,…B-1}, k∈{0,1,…N-2}, obtain the first probability distribution and the third probability distribution at the phase θ of the k+1th symbol k+1 for The probabilities of are set as p1(k+1,m) and p3(k+1,m) respectively; Obtain p3(k,n) from p1(k+1,m) and p3(k+1,m); Assign p3(k,n) to the phase θ of the third probability distribution on the kth symbol k for probability.

7. A carrier phase estimation method according to claim 1, characterized in that: The step of obtaining a second probability distribution or a third probability distribution according to the first probability distribution includes: For a certain k∈{0,1,…N-2},n∈{0,1,…B-1},m∈{0,1,…B-1}, get the phase θ at the kth symbol k for Under the condition that the phase θ is k+1 for probability.

8. A carrier phase estimation method according to claim 1, characterized in that: The obtaining a fourth probability distribution according to the first probability distribution, the second probability distribution and the third probability distribution comprises: For a certain k∈{0,1,…N-1}, n∈{0,1,…B-1}, the phase θ on the kth symbol in the first probability distribution, the second probability distribution and the third probability distribution is k for The probability of multiplying by , and assigning the product value to the phase θ on the kth symbol in the fourth probability distribution k for probability.

9. A carrier phase estimation method according to claim 1, characterized in that: The obtaining an estimated phase according to the fourth probability distribution comprises: For a certain symbol index, find the maximum value of the probabilities corresponding to all phase indexes on the symbol index in the fourth probability distribution, and assign the phase corresponding to the maximum value to the phase value estimated on the symbol index, or; For a certain phase index, the probability of the fifth probability distribution on the phase index is obtained based on the probability corresponding to all symbol indices on the phase index in the fourth probability distribution, wherein the obtained fifth probability distribution takes the phase index as the independent variable, and then the maximum value in the fifth probability distribution is obtained, and the phase corresponding to the maximum value is assigned to the estimated phase value on all symbol indices in the first signal.

10. A carrier phase estimation system, characterized in that: include: A receiver, used for receiving optical signals and converting the optical signals into analog electrical signals; An analog-to-digital converter, used for converting the received analog electrical signal into a digital signal; Digital signal processing, the digital signal processing comprising a phase estimation module to implement the method according to any one of claims 1-9.

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