A carrier phase estimation method and system

Abstract

The application discloses a carrier phase estimation method and system, wherein the method comprises the following steps: acquiring a receiving signal, acquiring a first signal for carrier phase estimation from the receiving signal, wherein the number of symbols of the first signal is N; initializing a phase set, wherein the number of phases in the phase set is B; acquiring a first probability distribution, acquiring a second probability distribution and a third probability distribution according to the first probability distribution, and obtaining 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 take a symbol index and a phase index as independent variables; and acquiring an estimated phase according to the fourth probability distribution. Compared with a traditional method, the method improves system performance in an ultranewquist system with strong code interval crosstalk, when a laser linewidth is relatively wide or a constellation point number is relatively large. The application can be widely applied to an optical communication system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of transmission impairment compensation in optical communication systems, and in particular to a carrier phase estimation method and system. BACKGROUND

[0002] The electrical signal received by the receiver is output by the photodetector after the optical mixing of the optical signal and the local laser generated by the local laser. However, the phase of the laser at the transmitting end and the local laser at the receiving end both have random jitter, which causes phase noise of the received electrical signal. Therefore, to improve the transmission performance of the system, the carrier phase recovery (CPR) algorithm is very important. At present, many carrier phase estimation and compensation methods have been proposed by the academic and industrial communities. The blind phase search (BPS) algorithm is a commonly used CPR algorithm. However, this method has performance degradation when used for probability shaping modulation signals and super-Nyquist signals with inter-symbol interference (ISI), and has the problem of phase cycle slip. Periodic insertion of pilot signals as reference phases in the signal can suppress cycle slip. However, when there is severe ISI, such as in a super-Nyquist system with a small compression rate, the pilot symbols are affected by the previous and subsequent symbols, reducing the ability to suppress cycle slip. The CPR method based on Kalman filtering and KL divergence has good performance at small line widths, and can suppress cycle slip by presetting the initial phase of the next data block based on the phase estimated by the previous data block. However, they have poor line width tolerance, and have large performance degradation in super-Nyquist systems with strong inter-symbol interference. The principal component analysis method is relatively robust to inter-symbol interference, but still has some degree of performance degradation, and the performance of this method is heavily dependent on the constellation layout and the probability of the constellation points. SUMMARY

[0003] To at least partially solve one of the technical problems existing in the prior art, the purpose of the present application 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 the phase being each discrete value at each time, and then estimates the phase at each time or the entire data block based on the posterior probability. This method solves the problem of performance degradation of existing carrier phase recovery algorithms in super-Nyquist systems with strong inter-symbol interference, when the laser line width is large and / or the modulation order is high.

[0004] The first technical solution adopted by the present application is:

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

[0006] Obtaining a received signal, and obtaining a first signal for carrier phase estimation from the received signal, wherein the number of symbols of the first signal is N;

[0007] initialize a phase set, wherein the number of phases in the phase set 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 all take symbol index and phase index as independent variables;

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

[0010] The present application can adopt a block processing manner for the received signal, and the first signal is a data block obtained by block processing the received signal. The phase at different symbol positions (or different time instants) in the data block is estimated according to the first signal, or the common phase of the data block is estimated when it is assumed that the phase in the entire data block is basically unchanged. The possible values of the phase are discrete, that is, a preset phase set with B elements, and the estimated phase is an element in the phase set. Wherein, the mathematical symbols N and B are only for convenient expression, and should not be considered as a limitation of the present application. Other mathematical symbols can also be used to represent the symbol length and the number of phases.

[0011] The core of the present application is to estimate the phase by calculating the fourth probability distribution, wherein the fourth probability distribution takes symbol index and phase index as independent variables. In one embodiment, the fourth probability distribution has N×B elements, but the specific representation is a two-dimensional distribution of N×B or B×N, or a one-dimensional distribution, or other representation is not limited. The probability distribution represents the probability of the phase being each value in the phase set at each symbol position under 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 takes symbol index and phase index as independent variables, it does not require to traverse all N symbol indexes or B phase indexes. For example, when it is assumed that the 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 the fourth probability distribution still has N×B elements, but the probabilities of the same phase index at adjacent two symbol indexes are the same.

[0012] The fourth probability distribution is obtained by the first probability distribution, the second probability distribution and the third probability distribution. And the second probability distribution and the third probability distribution are obtained by combining the first probability distribution with the correlation operation.

[0013] Further, the step of obtaining the first signal from the received signal includes the step of block processing the received signal.

[0014] The carrier phase estimation method provided by the application adopts a block processing method, divides the received signal into signal blocks with a symbol number of N, and estimates the phase of each signal block by using the provided method. It should be noted that the application 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 signal blocks, each signal block has a symbol number of 2N, and then down-sampling is performed to obtain the first signal with a symbol number of N. Let the first signal be r={r0,r1…r N-1}, wherein the subscript represents the symbol index, the provided method estimates the phase θ est,k ,k=0,1…N-1 at each symbol position according to r, or it is approximately considered that the phase change in the first signal is small, so that the common phase θ est of all symbol positions in the first signal is estimated according to r. Optionally, it can also be considered that every two symbols in the first signal have the same phase, so that the phase of every two symbols is estimated, which is not limited in detail.

[0015] Further, the initialization of the phase set comprises:

[0016] Setting a phase range, discretizing the phase in the phase range to obtain B phase values to form a phase set.

[0017] Discretize the possible values of the phase. The initialization of the phase set is: first, preset the range of possible values of the phase in the first signal, then discretize the phase in the range to obtain B phase values to form a phase set. One of the preset methods is to obtain the estimated phase of the last symbol in the previous data block of the first signal, which is set as θ', and set the phase range as θ total . Divide B discrete phases equidistantly in the range of θ total centered on θ', and the phase set is Θ=θ'+θ total ×{(-B / 2+1) / B,(-B / 2+2) / B,…×B / 2 / B}. By this method, the application does not need to use pilot symbols to eliminate cycle slips. Alternatively, B phase values can be divided unequidistantly in θ total , which is not limited by the application.

[0018] Further, the acquisition of the first probability distribution comprises:

[0019] Acquire a set of all possible values of the transmitted signal {a0,a1…a M-1}, wherein M is the number of all possible values;

[0020] For a certain k∈{0,1,…N-1},n∈{0,1,…B-1},i∈{0,1,…M-1},obtain the probability of receiving signal r k for a i and phase θ k under the condition that the transmission signal s is known on the kth symbol, denoted as k where s k , θ k and r k are the transmission signal, phase and receiving signal on the kth symbol respectively, a i is the ith value in the set of all possible values of the transmission signal, is the nth phase in the set of phases;

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

[0022] The present application provides a method for obtaining the first probability distribution: assuming that the first probability distribution is p1(k,n), with the dimension of N×B, where k=0,1…N-1 and n=0,1…B-1 represent the symbol index and phase index respectively, here p1(k,n) is only a representation, and should not be considered as a limitation to the representation of the first probability distribution, for example, the first probability distribution can also be represented as p1(n,k), with the dimension of B×N. In addition, the symbols k, n, i, s k , θ k , r k , a i , M and the like are only for the convenience of description, and should not be considered as a limitation to the present application.

[0023] The first probability distribution can be obtained according to , and one embodiment is where Γ k is the set of all possible values of the transmission signal on the kth symbol. It should be noted that in the super-Nyquist system, the set of all possible values of the transmission signal {a0,a1…a M-1} should be the set of values considering the intersymbol interference.

[0024] Further, the step of obtaining the second probability distribution or the third probability distribution according to the first probability distribution includes a recursive step.

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

[0026] ​​​For any 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 at the (k-1)th symbol. k-1 for Let the probabilities be p1(k-1,m) and p2(k-1,m) respectively;

[0027] Given p1(k-1,m) and p2(k-1,m), obtain p2(k,n);

[0028] Assign p2(k,n) the phase θ of the second probability distribution on the k-th symbol. k for The probability of.

[0029] This invention provides a method for obtaining a second probability distribution based on a first probability, where n, m, k, θ k-1 , The symbols p1(k-1,m), p2(k-1,m), and p2(k,n) are used for convenience only and should not be considered as limitations on the present invention. Specifically, the second probability distribution p2(k,n) is obtained based on p1(k-1,m) and p2(k-1,m). One embodiment is as follows: Where Θ is the phase set. Given the phase θ at the (k-1)th symbol k-1 for Under the condition of phase θ on the kth symbol k for The probability. When k=1, the initial value of p2(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. This invention does not make specific limitations.

[0030] Furthermore, the step of obtaining the third probability distribution based on the first probability distribution includes:

[0031] For any n∈{0,1,…B-1}, m∈{0,1,…B-1}, k∈{0,1,…N-2}, obtain the phase θ of the first probability distribution and the third probability distribution at the (k+1)th symbol. k+1 for Let the probabilities be p1(k+1,m) and p3(k+1,m) respectively;

[0032] Given p1(k+1,m) and p3(k+1,m), obtain p3(k,n);

[0033] Assign p3(k,n) the phase θ of the third probability distribution on the k-th symbol. k for The probability of.

[0034] The application provides a method for obtaining a third probability distribution according to a first probability distribution, wherein n, m, k, θ k+1 , The symbols p1(k+1, m), p3(k+1, m) and p3(k, n) are only for convenience of expression, and cannot be regarded as a limitation to the application. Specifically, the third probability distribution p3(k, n) is obtained according to p1(k+1, m) and p3(k+1, m). One embodiment is wherein Θ is the phase set, is the probability that the phase θ k is known on the kth symbol, is the probability that the phase θ k+1 is on the k+1th symbol under the condition that the phase θ is known on the kth symbol. When k=N-2, the initial value of p3(N-1, n) can be set as 1 / B or p2(N-1, n), and the application does not make a specific limitation.

[0035] Further, the step of obtaining the second probability distribution or the third probability distribution according to the first probability distribution comprises:

[0036] For a certain k∈{0, 1, …N-2}, n∈{0, 1, …B-1}, m∈{0, 1, …B-1}, the probability that the phase θ k is known on the kth symbol, is the probability that the phase θ k+1 is on the k+1th symbol under the condition that the phase θ is known on the kth symbol.

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

[0038]

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

[0040] For a certain k∈{0, 1, …N-1}, n∈{0, 1, …B-1}, the probability that the phase θ k is on the kth symbol in the first probability distribution, the second probability distribution and the third probability distribution is multiplied, and the product value is assigned as the probability that the phase θ k is on the kth symbol in the fourth probability distribution.

[0041] ​​The application provides a method for obtaining a fourth probability distribution. Assuming that the first to fourth probability distributions are p1(k,n), p2(k,n), p3(k,n) and p4(k,n), and the dimensions are all NxB, wherein k=0, 1, …, N-1 and n=0, 1, …, B-1 represent symbol indexes and phase indexes respectively. The fourth probability distribution can be obtained by the following method: p4(k,n)=p1(k,n)×p2(k,n)×p3(k,n).

[0042] Further, the method comprises the following steps of:

[0043] For a certain symbol index, the maximum value of the probabilities corresponding to all phase indexes in the symbol index in the fourth probability distribution is found, and the phase corresponding to the maximum value is assigned as the estimated phase value in the symbol index, or

[0044] For a certain phase index, a fifth probability distribution in the phase index is obtained according to the probabilities corresponding to all symbol indexes in 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 as the estimated phase value in all symbol indexes in the first signal.

[0045] The method for obtaining the estimated phase according to the fourth probability distribution is divided into two cases: 1) the phase values in all symbol positions corresponding to the symbol indexes in the fourth probability distribution are estimated; and 2) the common phase in all symbol positions in the first signal is estimated by assuming that the phase values in all symbol positions in the first signal are the same. The former can give more detailed phase information, and the latter is simpler, and the specific method can be determined according to actual requirements.

[0046] For convenience of description, it is assumed that the fourth probability distribution is represented as p4(k,n), and the dimension is NxB, wherein k=0, 1, …, N-1 and n=0, 1, …, B-1 represent symbol indexes and phase indexes respectively, and the embodiments in the two cases are as follows:

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

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

[0049] Optionally, when the symbol indexes or the phase indexes in the fourth probability distribution do not traverse all N symbol indexes or B phase indexes, the above operations only need to be performed on the symbol indexes k and the phase indexes n contained in the fourth probability distribution.

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

[0051] A carrier phase estimation system comprises:

[0052] A receiver is configured to receive an optical signal and convert the optical signal into an analog electrical signal;

[0053] An analog-to-digital converter is configured to convert the received analog electrical signal into a digital signal;

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

[0055] The present application has the following advantages: the present application implements a high-performance carrier phase estimation scheme, which can achieve more accurate carrier phase estimation when the laser linewidth is wider or the constellation point number is larger in an over-Nyquist system with strong inter-symbol interference. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following introduces the drawings of the related technical solutions in the embodiments of the present application or the prior art. It should be understood that the drawings in the following introduction are only for the convenience of clearly describing part of the embodiments in the technical solutions of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0057] Figure 1 A step flow chart of a phase estimation in the embodiments of the present application.

[0058] Figure 2 A step flow chart of obtaining a second probability distribution and a third probability distribution according to a first probability distribution in the embodiments of the present application.

[0059] Figure 3 A step flow chart of obtaining an estimated phase value according to a fourth probability in the embodiments of the present application.

[0060] Figure 4 A block diagram of an over-Nyquist system in the embodiments of the present application.

[0061] Figure 5 A curve diagram showing the performance of the phase estimation algorithm in the embodiments of the present application changing with the compression rate.

[0062] Figure 6 A curve diagram showing the performance of the phase estimation algorithm in the embodiments of the present application changing with the linewidth. DETAILED DESCRIPTION

[0063] Embodiments of the present application are described below in detail with reference to the accompanying drawings, wherein the same or similar components or components having the same or similar functions are denoted by the same or similar reference numerals throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as a limitation on the present application. For the step numbers in the following embodiments, they are only set for the convenience of explanation, and the order between the steps is not limited in any way, and 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 application, it should be understood that the orientation description, such as the orientation or position relationship indicated by up, down, front, back, left, right, etc. is based on the orientation or position relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the device or component must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0065] In the description of the present application, one or more is meant by several, two or more is meant by multiple, greater than, less than, more than, etc. is understood to not include the number, above, below, etc. is understood to include the number. If the first, second is described, it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features or the order of indicated technical features. In addition, "and / or" describes the association relationship of the associated objects, which means that there can be three kinds of relationships, for example, A and / or B can represent: A exists alone, A and B exist together, and B exists alone. The character " / " generally represents an "or" relationship between the front and rear associated objects.

[0066] In the description of the present application, unless otherwise explicitly limited, the words such as setting, installing, connecting, etc. should be broadly understood, and those skilled in the art can reasonably determine the specific meaning of the above words in the present application in combination with the specific content of the technical solution.

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

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

[0069] Let the length of the blocked received signal be N, and the received signal be defined as r = {r0, r1…r N-1}, where the subscript k = 0, 1…N-1 represents the symbol index of the received signal, which also represents the kth time in physics, and the corresponding transmitted signal s = {s0, s1…s N-1}. It should be noted that in the super-Nyquist system, s = {s0, s1…s N-1} should be the signal considering the intersymbol interference. For example, let the transmitted symbol be c = {c0, c1…c N-1}, the intersymbol interference length of the super-Nyquist shaping be 3, and the coefficients be h -1 ,h0 and h1, then s i =h -1 ·c i-1 +h0·c i +h1·c i+1 . In practice, the relationship between s and the original transmitted symbol c can be established by looking up table. Define the phase at the N received symbol positions / times as θ = {θ0, θ0…θ N-1}, then the posterior probability of the phase θ k at the kth time based on the received sequence r is:

[0070]

[0071] In practice, the value of the phase noise is continuous, but in order to facilitate the implementation of the application, the initial and discrete phase value set is first discretized. Specifically, first, a phase range is preset, the continuous phase is discretized in the range, and B discrete phase values are obtained 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 satisfies the Wiener distribution with a mean of 0, which can be represented as:

[0072] θ k = θ k-1 + Δθ k (2)

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

[0074]

[0075] In formula (3), Δf is the laser linewidth, and τ is the symbol period. The variance σ p 2 is proportional to the laser linewidth Δf. Since the carrier phase noise varies continuously over time, it can be considered that: 1) the phase noise of each symbol in a signal block of length N varies within a certain interval, and 2) the phase distribution interval of the current signal block has the estimated phase of the last symbol of the previous signal block as the middle value. According to the above assumptions, the phase range is determined, and the phase values in the range are discretized as 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], and the interval is discretized into B phases at equal intervals. 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 size of the laser linewidth, or the phases can be discretized in the preset range in a non-equidistant manner, which is not limited by the present application. 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 application. It takes the symbol index k and the phase index n as independent variables, where k=0, 1, …, N-1, and n=0, 1, …, B-1. In addition, for a given received sequence r, the value of p(r) is constant, so the fourth probability distribution can also be defined as Next, we calculate the probability distribution

[0081]

[0082] The first probability distribution is defined as The second probability distribution is The third probability distribution is where k∈[0, N-1], n∈[0, B-1], and r<k r(k) denotes the received sequence symbol with subscript index less than k >k r(k) denotes the received sequence symbol with subscript index 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] p4(k,n) = pi(k,n) p2(k,n) p3(k,n) (6)

[0084] According to formula (6), to obtain the fourth probability distribution, the probabilities pi(k,n), p2(k,n) and p3(k,n) need to be calculated respectively.

[0085] First, the first probability distribution is calculated. pi(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 kth time 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 as:

[0088]

[0089] However, in a probability shaping or super-Nyquist system, p(s k = a i ) has different values for different a i , then 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 kth time, and the received symbol r k can be represented as:

[0090]

[0091] Thus, we have

[0092]

[0093] where σ noise 2 is the noise variance. The first probability distribution can be calculated by formula (10) and (7), or formula (10) and (8). Next, the second probability distribution is calculated. At the 0th time, initialize p2(0,n) as:

[0094] p2(0, n) = 1 / B, n e [0, B - 1] (11)

[0095] Alternatively, the initial value can be set as p2(0, B / 2 - 1) = 1, and p2(0, n) = 0 when n ≠ B / 2 - 1. Then, for the second probability distribution p2(k, n) at the kth moment, as shown in (a) of FIG. 2, it can be obtained according to p1(k - 1, m), p2(k - 1, m), and Figure 2

[0096] Therefore, the value of the second probability distribution at the k = 1, 2,..., N - 1 moment can be obtained by recursion according to formula (12).

[0097] Next, the third probability distribution is calculated. At the N - 1 moment, the initial value of p3(N - 1, n) is set as:

[0098] p3(N - 1, n) = 1 / B, n e [0, B - 1] (13)

[0099] Alternatively, the initial value can be set as p3(N - 1, n) = p2(N - 1, n). For the third probability distribution p3(k, n) at the kth moment, as shown in (b) of FIG. 2, it can be obtained according to p1(k + 1, m) and p3(k + 1, m) and

[0100] Figure 2

[0101]

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

[0103] In the recursive formulas (12) and (14), the calculation of the second and third probability distributions also needs to know the probability that the phase θ k is under the condition that the phase θ k+1 is at the k + 1th symbol, where k = 0, 1,..., N - 2, n = 0, 1,..., B - 1, and m = 0, 1,..., B - 1. This probability can be calculated in the following way:

[0104]

[0105] ​​​​​After obtaining the fourth probability distribution, the first implementation method proposed in this invention is as follows: Based on the obtained fourth probability distribution value, take the phase corresponding to the maximum fourth probability value under each symbol / time index as the estimated phase value for that time. At this time, there is an estimated phase value for each time step within the signal block, represented as...

[0106]

[0107] The second implementation method proposed in this invention is as follows: Figure 3 As shown: A fifth probability distribution is obtained based on the fourth probability distribution value, where the phase index is the independent variable. At each phase, the value of the fifth probability distribution is the mean or sum of the probabilities of the fourth probability distribution at different time indices within the signal block:

[0108] p5(n)=∑ k p4(k,n) (17)

[0109] Then, the phase corresponding to the value with the highest probability in p5(n) is taken as the estimated phase value for the entire signal block. At this point, the estimated phase value is the same at every moment within the signal block, represented as...

[0110]

[0111] To verify the effectiveness of this invention, a comparative simulation was conducted. For example... Figure 4 The diagram shows the block diagram of the super Nyquist simulation system. In the simulation, the super Nyquist signal uses 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 value is obtained using formulas (16) and (18), respectively, defined as Example 1 and Example 2. In addition, we also compare the proposed phase estimation method with the blind phase estimation (BPS) algorithm and the principal component analysis (PCPE) algorithm. In the BPS algorithm, the discrete phase number B = 36, and a pilot symbol is inserted for cycle slip resolution in each data block.

[0112] Figure 5 The system performance of different carrier estimation algorithms at various compression rates is demonstrated when the laser linewidth is 100kHz. The data block length N in each method is an optimized value. As shown in the figure, the method proposed in this invention has a performance advantage over traditional BPS and PCPE algorithms at higher compression rates, solving the performance degradation problem of traditional methods in super Nyquist systems. Figure 6 The system bit error rate is denoted by 0.9 for different laser linewidths. The data block length N of all methods has been optimized. It can be seen that the proposed method exhibits better linewidth tolerance than traditional BPS and PCPE, and Example 2 is superior to Example 1.

[0113] The present invention also proposes a carrier phase estimation system, comprising: 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; and digital signal processing, wherein 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 diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0115] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0116] If the aforementioned functions are implemented as 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 this invention, essentially, or the part that contributes to the prior art, or a portion of the 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 to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0117] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0118] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

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

[0120] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

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

[0122] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A carrier phase estimation method, characterized in that, Includes the following steps: Acquire the received signal, and obtain a first signal for carrier phase estimation from the received signal, wherein the number of symbols in the first signal is: N ; Initialize the phase set, wherein the number of phases in the phase set is B ; Obtain the first probability distribution; Based on the first probability distribution, the second probability distribution is obtained through forward recursion calculation; Based on the first probability distribution, the third probability distribution is obtained through backward recursive calculation; A fourth probability distribution is obtained based on the first probability distribution, the second probability distribution, and the third probability distribution; The estimated phase is obtained based on the fourth probability distribution; Among them, the first probability distribution, the second probability distribution, the third probability distribution and the fourth probability distribution all use the sign index and the phase index as independent variables; The first probability distribution is in the symbol index k and phase index n The probability characterizes the probability of the first time. k The phase on each symbol equals Receiving signals under the condition r k The probability of; The fourth probability distribution is in the symbol index k and phase index n The probability characterizes the probability of receiving the first signal in the second... k The phase on each symbol equals The probability of receiving the first signal and the second signal, or the probability of receiving the first signal and the second signal. k The phase on each symbol equals The joint probability; in , , The first in the phase set n Each phase, r k The first signal k Received signals on each symbol; The step of obtaining the fourth probability distribution based on the first probability distribution, the second probability distribution, and the third probability distribution includes: For a certain k {0, 1,… N -1}, n {0, 1,… B -1}, the first probability distribution, the second probability distribution, and the third probability distribution are in the symbol index. k and phase index n Multiply the probabilities and assign the product value to the symbol index of the fourth probability distribution. k and phase index is n The probability of.

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

3. The carrier phase estimation method according to claim 1, characterized in that, The initial phase set includes: Define a phase range, and discretize the phase within the phase range to obtain... B A phase set is composed of several phase values.

4. The carrier phase estimation method according to claim 1, characterized in that, Obtaining the first probability distribution includes: Get the set of all possible values ​​of the transmitted signal { a 0, a 1… a M-1 },in M 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 first k The transmitted signal is known on each symbol. s k for a i and phase θ k for Receiving signals under the condition r k The probability of is denoted as . p ( r k | s k= a i , θ k = ),in s k , θ k and r k They are respectively in the 1st k The transmitted signal, phase, and received signal on each symbol a i The first of the set of all possible values ​​of the transmitted signal i One value, The first in the phase set n One phase; According to the above p ( r k | s k= a i , θ k = The first probability distribution is obtained.

5. The carrier phase estimation method according to claim 1, characterized in that, The step of obtaining the second probability distribution based on 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 first probability distribution and the second probability distribution in the th... k -1 symbol phase θ k-1 for Let the probabilities be denoted as follows: p 1( k -1, m )and p 2( k -1, m ); according to p 1( k -1, m )and p 2( k -1, m )get p 2( k , n ); Will p 2( k , n The value is assigned to the second probability distribution at the . k Phase on each symbol θ k for The probability of.

6. The carrier phase estimation method according to claim 1, characterized in that, The step of obtaining the third probability distribution based on 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 in the th... k +1 symbol on phase θ k+1 for Let the probabilities be denoted as follows: p 1( k +1, m )and p 3( k+ 1, m ); according to p 1( k +1, m )and p 3( k+ 1, m )get p 3( k , n ); Will p 3( k , n Assigning a value to the third probability distribution at the ) k Phase on each symbol θ k for The probability of.

7. The carrier phase estimation method according to claim 1, characterized in that, The step of obtaining the second or third probability distribution based on the first probability distribution includes: For a certain k {0, 1,… N -2}, n {0, 1,… B -1}, m {0, 1,… B -1}, obtain the known position in the first place. k Phase on each symbol θ k for Under the condition of the first k +1 symbol on phase θ k+1 for The probability of.

8. The carrier phase estimation method according to claim 1, characterized in that, The step of obtaining the estimated phase based on the fourth probability distribution includes: For a given symbol index, find the maximum value of the probability corresponding to all phase indices at that symbol index in the fourth probability distribution, and assign the phase corresponding to the maximum value to the estimated phase value at that symbol index, or; For a given phase index, the probability of the fifth probability distribution on the phase index is obtained based on the probabilities corresponding to all symbol indices on the phase index in the fourth probability distribution. The obtained fifth probability distribution takes the phase index as the independent variable. Then, the maximum value in the fifth probability distribution is obtained, and the phase corresponding to the maximum value is assigned as the estimated phase value on all symbol indices in the first signal.

9. A carrier phase estimation system, characterized in that, include: A receiver is used to receive optical signals and convert them into analog electrical signals. An analog-to-digital converter is used to convert the received analog electrical signal into a digital signal; Digital signal processing, the digital signal processing including a phase estimation module, to implement the method of any one of claims 1-8.

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