Auxiliary common phase error compensation method based on projection thermodynamic diagram in coherent light OFDM (Orthogonal Frequency Division Multiplexing) system

Abstract

The invention relates to a public phase error compensation method based on projection thermodynamic diagram assistance (PHM) in a coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. According to the method, rotation and divergence three-dimensional projection thermodynamic diagram distribution characteristics, caused by phase noise, of signal points in a constellation diagram of a receiving end are analyzed, a convergence area is set with an original constellation point as the center for target optimization, and the optimal compensation phase is determined by counting the maximum number of the signal points in the convergence area. In combination with a staged test phase estimation strategy in a two-stage blind phase search (BPS) algorithm, the calculation complexity is reduced, and the compensation precision is improved at the same time. Simulation experiments show that compared with a traditional method, the method can effectively suppress common phase noise of various constellation diagrams in different shapes under 16-QAM modulation, the bit error rate performance is better under the same signal-to-noise ratio, and the spectrum utilization rate is remarkably improved.

Description

Technical Field

[0001] The method of the present invention belongs to the technical field of phase noise compensation in a Coherent Optical Orthogonal Frequency-Division Multiplexing (CO-OFDM) system, and relates to a common phase error compensation method assisted by a projection heatmap (PHM) in a CO-OFDM system. This method mainly optimizes the target by setting a convergence region with constellation points as the center points, and combines the phase compensation mechanism of the Blind Phase Search (BPS) algorithm to compensate the phase noise of the signal. Background Art

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology has become one of the core technologies in modern wireless communication and optical communication systems due to its high spectral efficiency and multipath fading resistance. With the evolution of optical fiber communication towards high speed and large capacity, the CO-OFDM system has emerged as the times require. CO-OFDM combines the spectral efficiency advantage of OFDM and the high sensitivity characteristic of coherent detection, significantly improving the system's tolerance to channel impairments such as dispersion and polarization mode dispersion, and at the same time supporting the application of high-order modulation formats, becoming an important solution for long-distance and high-capacity optical communication.

[0003] However, the performance of the CO-OFDM system highly depends on the phase stability of the local oscillator laser. In an actual system, the phase noise caused by the laser linewidth will introduce two types of key impairments: one is the common phase error (CPE) caused by the zero-order phase noise component, which is manifested as the overall rotation of the received constellation diagram; the other is the inter-carrier interference (ICI) caused by the non-zero-order phase noise component, resulting in the divergence of constellation points. Among them, the influence of CPE on the bit error rate of high-order modulation signals is particularly significant.

[0004] Existing phase noise compensation techniques can be divided into two categories: pilot-assisted algorithms and blind algorithms. Pilot-assisted algorithms estimate phase errors by inserting known pilot symbols, but they sacrifice spectral efficiency. Blind algorithms (such as blind phase search based on decision feedback, BPS) do not require pilots, but have limited compensation accuracy for high-dimensional modulation and their performance degrades sharply in the presence of ICI. In addition, another traditional blind algorithm is based on the statistical projection histogram of rectangular constellations, which is difficult to adapt to complex modulation formats. Therefore, how to design a blind phase noise compensation method that is applicable to multiple modulation formats and robust to CPE while ensuring spectral efficiency has become a key challenge for the practical application of CO-OFDM systems.

[0005] Aiming at the above technical pain points, the method of the present invention proposes a common phase error compensation method based on projection heat map assistance, aiming to break through the limitations of traditional methods and provide a high-precision and low-complexity phase noise suppression scheme for CO-OFDM systems. Summary of the Invention

[0006] In view of this, the purpose of the method of the present invention is to provide a projection heat map-assisted common phase error compensation method in a coherent optical OFDM system.

[0007] To achieve the above object, the method of the present invention provides the following technical method:

[0008] The phase noise compensation method based on projection heat map assistance mainly processes the signal constellation diagram at the receiving end of the system. After being affected by interference signals such as phase noise, the received signal points mainly show that all the signal points on the constellation diagram are rotated and diffused as a whole by a certain angle. In the three-dimensional projection heat map, it is roughly shown as multiple annular distribution structures, and there is a central aggregation phenomenon generated by the rotation of the original constellation points in these annular distribution structures. The CPE compensation method based on the projection heat map uses this characteristic to convert the CPE compensation problem into an optimization problem with the ideal constellation point as the convergence center. By constructing a dynamic phase compensation model, two optimization goals are achieved: (1) correcting the phase rotation deviation of the central aggregation feature; (2) guiding the divergent signal points to return to the theoretical convergence region. The optimization variable is the preset test phase. All the test phases are used for CPE phase compensation, and then the sum of the signal point numbers in the area near the convergence center is obtained through statistics. The test phase corresponding to the maximum value is the phase noise value that is best used for CPE compensation.

[0009] The beneficial effects of the method of the present invention are as follows:

[0010] From theory and computer simulations, it is known that the method of the present invention can handle the problem of the rotation of received signal points in most shaped constellation diagrams caused by CPE. Compared with the least squares (LS) algorithm proposed in the pilot-assisted algorithm in Ref. [1] "MOUSA-PASANDI M E, PLANT DV. Noniterative interpolation-based partial phase noise ICI mitigation for CO-OFDM transport systems [J]. IEEE Photonics Technology Letters, 2011, 23(21): 1594-1596.", the linearly processed and least squares (LLS) algorithm after linearly correlating the cyclic prefix in Ref. [2] "HONG X Z, HONG X J, HE S. Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system [J]. Optics Express, 2015, 23(4): 4691-4702.", and the CPE phase noise compensation algorithm based on projection histogram (PH) in Ref. [3] "LI Z X, LI Y, MAJ J, et al. Projection Histogram-Assisted Estimation of Common Phase Error in Coherent Optical OFDM Systems [J]. IEEE Photonics Journal, 2019, 11(3): 1-9.", the bit error rate performance has been improved to a certain extent. Among them, the PH algorithm can only handle the problem of the rotation of received signal points in rectangular constellation diagrams, while the method of the present invention can effectively suppress the common phase noise of various different shaped constellation diagrams and has good bit error rate performance. The whole method process does not require any additional pilot overhead, and greatly improves the spectrum utilization rate compared with the pilot-assisted algorithms, which is a blind phase noise compensation method with good performance. Therefore, in practical applications, the method of the present invention has high utilization value and practical significance for compensating the phase noise of CO-OFDM systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to make the objectives, technical solutions and beneficial effects of the method of the present invention clearer, the following drawings are provided to illustrate the method of the present invention:

[0012] Figure 1 This is the technical roadmap of the method of the present invention;

[0013] Figure 2 These are the constellation diagrams without phase compensation under rectangular, circular, and triangular 16QAM modulation;

[0014] Figure 3 These are the constellation diagrams with phase compensation under rectangular, circular, and triangular 16QAM modulation;

[0015] Figure 4 This is the comparison diagram of signal-to-noise ratio (SNR) - bit error rate (BER) of each method when the laser linewidth is 100 kHz under rectangular 16QAM;

[0016] Figure 5 This is the comparison diagram of signal-to-noise ratio (SNR) - bit error rate (BER) of each method when the laser linewidth is 100 kHz under circular 16QAM;

[0017] Figure 6 This is the comparison diagram of signal-to-noise ratio (SNR) - bit error rate (BER) of each method when the laser linewidth is 100 kHz under triangular 16QAM; Specific Embodiments

[0018] Hereinafter, the preferred embodiments of the method of the present invention will be described in detail with reference to the accompanying drawings.

[0019] 1. The method of the present invention is a projection heat map-assisted common phase error compensation method in a CO-OFDM system; the PHM method is mainly a solution proposed for the constellation rotation problem caused by CPE. This method analyzes the three-dimensional projection heat map distribution characteristics of the rotation and divergence of signal points in the received constellation diagram due to phase noise, sets a convergence region centered on the original constellation points for target optimization, determines the optimal compensation phase by maximizing the number of signal points in the convergence region, and combines the phased test phase estimation strategy in the two-stage blind phase search (BPS) algorithm to reduce the computational complexity and improve the compensation accuracy at the same time; specifically, it includes the following steps:

[0020] (1) The ideal prerequisite for achieving high-precision PHM methods is that only CPE phase noise exists. However, in actual CO-OFDM systems, CPE and ICI exist simultaneously, and even a small amount of ICI exists when the line width is small. For methods based on the PHM method type, the core is to compensate for phase noise by converging signal points near the original constellation center. The problem of constellation point divergence caused by a small amount of ICI will also cause data to deviate from the target convergence region (such as diverging to adjacent centers), resulting in decision errors and reducing the method performance. Therefore, it is necessary to perform a certain preprocessing on ICI before processing the PHM method. First, use the cyclic prefix (CP) information in the OFDM symbol to linearly process the tail information of the corresponding OFDM symbol at the transmitting end of the system, minimize the ICI power, eliminate the projection decision errors caused by constellation point divergence, and thus improve the estimation and compensation accuracy of the PHM method for phase noise. The process of linearly processing the CP is as shown in Equation (1):

[0021]

[0022] In the formula, y i,n and y i ' ,n respectively represent the symbol information of length n in the i-th OFDM symbol before and after linear processing; p n and q n are the combination coefficients between the tail information of the OFDM symbol and the CP of length g during the linear processing process; according to the Nyquist criterion, the relationship between the two satisfies Equation (2):

[0023] p n = 1 - q n , N - g < n < N - 1 (2)

[0024] (2) The phase noise compensation method based on PHM mainly processes the signal constellation diagram at the receiving end of the system. First, the time-domain received signal y of the k-th sampling point x i,k in the i-th OFDM symbol affected by phase noise i,k is expressed as Equation (3):

[0025]

[0026] Among them, h i,k and w i,k respectively represent the channel impulse response and additive white Gaussian noise (AWGN).

[0027] Then, use a small number of pilots to obtain a rough compensation signal y' i,k ;

[0028] The PHM method adopts the two-stage estimation method proposed in the BPS algorithm in the test phase selection stage to reduce complexity; by dividing the test phase estimation process into two stages, fewer test phases can be used to determine the phase error, thus reducing the complexity of the method; first, take M1 uniformly spaced phases between as the test phases for the first-stage estimation and obtain a roughly estimated phase value Then take M2 uniformly spaced test values In for precise estimation around.

[0029] The test phases of the two stages are as shown in Eqs. (4) and (5):

[0030]

[0031] Take as the CPE compensation value of the received signal x i,k , and obtain M1 signals after test phase compensation. The m-th compensated signal y i ' ,k (m) is expressed as Eq. (6):

[0032]

[0033] Then perform the second test phase division to obtain M2 test phases, and update the test phases to obtain the test phases of the second stage The optimal compensated phase noise value obtained after the second-stage phase compensation screening to obtain the finally compensated signal y i ” ,k As shown in Eq. (7):

[0034]

[0035] By dividing the test phase division process into two stages, it is possible to achieve the phase noise compensation effect of M1×M2 test phases with M1 + M2 test phases, greatly reducing the number of test phases used in the method, thus significantly reducing the method complexity.

[0036] (3) Determine the values of n1 and n2 by setting a convergence region with the constellation point as the center for target optimization. The optimization target is to statistically obtain the sum of the number of signals within the convergence region at the projection center for different test phases. The test phase corresponding to the maximum value is the optimal phase noise value for CPE compensation And The following is to obtain And Specific implementation steps:

[0037] In each OFDM symbol, after generating M1 signal constellation diagrams for these M1 test phases, first, respectively, count all the corresponding interfered signal points within a circular range centered at different noise-free constellation diagram coordinates (x1, y1), (x2, y2),... (x n ,y n ) with a radius of r, which is denoted as Then sum up the total number of these convergent center constellation points. The objective function of the first stage is as shown in Equation (8):

[0038]

[0039] where represents the sum of the constellation points near each convergent center at the test phase , and r represents the summation radius;

[0040] The larger the value, the better the corresponding test phase

[0041] , and the better the value for compensating CPE. Use this test phase for the optimal CPE phase noise estimation in the first stage; The selection process of the test phase in the second stage is the same as that of the test phase in the first stage; where the objective function

[0042]

[0043] (4) To reduce the computational complexity and operation time, when determining whether the interfered signal points are located in the convergence region of a certain original constellation point, simplify the distance operation between points, i.e., the power operation, to a comparison operation; the specific implementation steps are to change the original circular convergence region to the circumscribed square of the circle and use this as the new convergence region for the objective optimization of the test phase; obtain the new objective function as shown in Equation (10).

[0044]

[0045] 2. Combine the attached Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 to illustrate that in order to further illustrate the feasibility of the method of the present invention on constellation diagrams of various shapes and that there is also a relatively significant improvement in the performance of compensating the common phase noise of traditional rectangular constellation diagrams to a certain extent, an experiment is carried out below.

[0046] Experiment:

[0047] Table 1 Parameter settings used in simulation

[0048] Parameter Set size Number of subcarriers N 256 Cyclic prefix length 64 Baseband sampling frequency 20 GHz Modulation method Rectangle, circle, triangle 16QAM IFFT / FFT 256 Number of OFDM symbols 5000 Number of pilots 16 Channel AWGN

[0049] The parameters used in the experimental simulation are shown in Table 1.

[0050] Figure 2 and Figure 3 respectively show the comparison effects of constellation diagrams before and after phase compensation using the PHM method proposed by the method of the present invention. Under the experimental settings of a laser linewidth of 100 kHz and a signal-to-noise ratio of 15 dB, the comparison of the compensation effects for three typical constellation patterns (rectangular, circular, triangular) shows that: the PHM method proposed by the method of the present invention can process constellation diagrams of various different shapes. From Figure 2 it can be seen that the constellation points without phase compensation exhibit significant distribution characteristic differences, but there is a central aggregation phenomenon generated by the rotation of the original constellation points in all circular distribution structures. It should be noted that when the distribution density of the original constellation points is low, this rotational aggregation characteristic centered on the original points is more significant. The PHM method proposed by the method of the present invention precisely utilizes this characteristic to convert the CPE compensation problem into an optimization problem with an ideal constellation point as the convergence center.

[0051] Figure 4 , Figure 5 , Figure 6SNR-BER comparison diagrams of different phase noise suppression methods under different shaped constellation diagrams with a line width of 100 kHz under 16QAM modulation. The following four methods will be mentioned, namely, the PHM method proposed by the method of the present invention and the LS algorithm proposed in the pilot-assisted algorithm in the literature [1] "MOUSA-PASANDI M E, PLANT D V. Noniterative interpolation-based partial phase noise ICI mitigation for CO-OFDM transport systems [J]. IEEE Photonics Technology Letters, 2011, 23(21): 1594-1596.", the LLS algorithm that performs minimum mean square processing after linearly correlating the cyclic prefix in the literature [2] "HONG X Z, HONG X J, HE S. Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system [J]. Optics Express, 2015, 23(4): 4691-4702.", and the PH algorithm proposed in the CPE phase noise compensation algorithm based on the projection histogram in the literature [3] "LI Z X, LI Y, MAJ J, et al. Projection Histogram-Assisted Estimation of Common Phase Error in Coherent Optical OFDM Systems [J]. IEEE Photonics Journal, 2019, 11(3): 1-9.".

[0052] Figure 4 SNR-BER comparison diagrams of the PHM method proposed by the method of the present invention, the LS algorithm, the LLS algorithm, the PH algorithm, and the phase compensation on the rectangular 16QAM constellation diagram without the influence of phase noise. When the bit error rate is 10 -5 , the PHM method proposed by the method of the present invention has a performance improvement of approximately 0.15 dB compared to the LLS algorithm, approximately 0.3 dB compared to the PH algorithm, and approximately 0.36 dB compared to the LS algorithm.

[0053] Figure 5 SNR-BER comparison diagrams of the PHM method proposed by the method of the present invention, the LS algorithm, the LLS algorithm, and the phase compensation on the circular 16QAM constellation diagram without the influence of phase noise. When the bit error rate is 10 -5When the bit error rate is 10

[0054] Figure 6 This is the comparison diagram of SNR-BER after phase compensation on the triangular 16QAM constellation diagram for the PHM method proposed by the method of the present invention, the LS algorithm, the LLS algorithm, and without phase noise influence. When the bit error rate is 10 -5 When the bit error rate is 10

[0055] Among them, the LS algorithm improves the compensation accuracy at the expense of spectral efficiency, but its ability to suppress CPE is limited at high signal-to-noise ratios. The LLS algorithm is a phase noise compensation algorithm proposed based on the LS algorithm, which first performs linear processing on the CP and then performs the LS algorithm. The PH algorithm also uses the rotation and divergence of the constellation diagram to observe the phase noise compensation ability of CPE. However, due to its algorithm relying on the rotation characteristics of the constellation diagram, it is vulnerable to the influence brought by ICI and is limited by the algorithm principle to only act on rectangular constellations.

[0056] Based on the above simulation verification, since the method of the present invention is sensitive to phase noise in the CO-OFDM system and is easily affected, a method combining cyclic prefix linear processing and projection heat map assistance in the coherent optical OFDM system is proposed to suppress the influence of phase noise on the CO-OFDM system, improving the performance and spectral efficiency of the system.

[0057] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A method for compensating common phase error (CPE) based on projection heatmap-assisted (PHM) in a coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system; this method analyzes the distribution characteristics of the three-dimensional projection heatmap of the rotation and divergence of signal points in the received constellation diagram caused by phase noise, sets a convergence region centered on the original constellation points for target optimization, determines the optimal compensation phase by maximizing the number of signal points within the convergence region, and combines the phased test phase estimation strategy in the two-stage blind phase search (BPS) algorithm to reduce the computational complexity and improve the compensation accuracy at the same time; the specific steps of this method are as follows: (1) Before processing the PHM method, first linearly process the tail information of the corresponding OFDM symbol at the transmitting end of the system using the cyclic prefix (CP) information in the orthogonal frequency division multiplexing (OFDM) symbol to minimize the inter-carrier interference (ICI) power and eliminate the projection decision errors caused by the divergence of constellation points; the linear processing process of CP for correlation is as shown in Equation (1): where y i,n and y' i,n respectively represent the symbol information of length n in the i-th OFDM symbol before and after linear processing; p n and q n are the combination coefficients between the tail information of the OFDM symbol and the CP of length g during the linear processing; according to the Nyquist criterion, their relationship satisfies Equation (2): p n = 1 - q n , N - g < n < N - 1 (2) (2) The PHM-based phase noise compensation method mainly processes the signal constellation diagram at the receiving end of the system. First, the time-domain received signal y of the k-th sampling point x in the i-th OFDM symbol affected by phase noise is expressed as Equation (3): i,k i,k ​​ Among them, h i,k and w i,k represent the channel impulse response and the additive white Gaussian noise, respectively; Then, a rough compensation signal y' of the phase noise is obtained by using a small amount of pilots i,k ; The PHM method adopts the two-stage phase estimation method proposed in the BPS algorithm in the test phase selection stage; first, M1 uniformly spaced phases are taken between as the test phases for the first-stage estimation, and a roughly estimated phase value is obtained Then, M2 uniformly spaced test values are taken for precise estimation around ; The test phases for the two stages are as shown in Equations (4) and (5): Take as the received signal y at the receiving end i,k of the CPE compensation value, and obtain M1 signals after tested phase compensation. The m-th compensated signal y′ i,k (m) is expressed as Equation (6): Then, a second test phase division is performed to obtain M2 test phases, and the test phases are updated to obtain the test phases of the second stage. The optimal compensated phase noise value obtained after the phase compensation screening in the second stage The finally compensated signal y″ is obtained i,k As shown in Equation (7): (3) Determine the values of n1 and n2 by setting a convergence region centered on the constellation points for target optimization. The optimization target is to statistically obtain the sum of the signal point numbers within the convergence region at the projection center for different test phases. The test phase corresponding to the maximum value is the phase noise value best used for CPE compensation. and The following are the specific implementation steps for obtaining and : In each OFDM symbol, after generating M1 signal constellations for these M1 test phases, first, the number of all corresponding interfered signal points within a circular range centered at different noise-free constellation coordinates (x1, y1), (x2, y2),...(x n , y n ) with a radius of r is counted respectively, denoted as Then, the total number of these converged center constellation points is summed up. The objective function of the first stage is as shown in Equation (8): Among them represents the sum of neighboring constellation points at each convergence center during the test phase and r represents the summation radius; The larger the value, the better the corresponding test phase is, and the better the value for compensating CPE is; use this test phase for the best CPE phase noise estimation in the first stage; The second-stage test phase is selected in the same way as the first-stage test phase; the objective function of the second stage is as shown in Equation (9): (4) To reduce the computational complexity and operation time, when determining whether the interfered signal points are located in the convergence region of a certain original constellation point, the distance operation between points, that is, the power operation, is simplified to a comparison operation; the specific implementation step is to change the original circular convergence region to the circumscribed square of the circle, and use this as the new convergence region for target optimization of the test phase, and obtain the new objective function as shown in Equation (10):

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