A frequency offset estimation method for discrete spectrum modulation nonlinear frequency division multiplexing system

Abstract

The present invention discloses a frequency offset estimation method for a discrete spectrum modulation nonlinear frequency division multiplexing system, and relates to the technical field of optical fiber communication. Carrier frequency offset (CFO), or frequency offset (FO) for short, is a frequency offset caused by the mismatch between the center frequencies of a transmitting end laser and a local oscillator laser, which may cause transmission signal damage. The present invention first determines a rough range of frequency offset estimation based on the eigenvalue offset, then generates an ideal matching signal based on the nonlinear Fourier transform (NFT) theory and a training sequence (TS), and then constructs an optimization model for FO. Finally, a grid search method is used to solve the problem. The method of the present invention eliminates the constraint of the baud rate on the frequency offset estimation range, and has low computational complexity.

Description

Technical Field

[0001] The present invention relates to the field of optical fiber communication technology, and more particularly to a frequency offset estimation technology for a discrete spectrum modulation nonlinear frequency division multiplexing system. Background Art

[0002] Digital signal processing (DSP) has been widely used in coherent optical communication systems and can effectively compensate for many types of impairments, such as chromatic dispersion (CD), frequency offset (FO), polarization mode dispersion (PMD), etc. However, fiber nonlinearity remains the determining factor limiting the transmission capacity of optical communication systems. In order to suppress fiber nonlinearity in coherent optical communication systems, NFDM technology has been proposed by relevant scholars and has attracted widespread attention in recent years. Compared with traditional fiber nonlinearity suppression schemes that regard fiber nonlinearity as an unfavorable factor in the transmission system, NFDM technology regards fiber nonlinearity as an inherent property of the optical fiber communication system and designs transmission schemes based on the characteristics of the nonlinear optical fiber channel, thereby avoiding the adverse effects of fiber nonlinearity. In addition, compared with traditional nonlinear compensation methods, NFDM technology is very simple in compensating for fiber nonlinearity and dispersion.

[0003] Because the local oscillator laser at the receiving end is not frequency-locked with the transmitter laser in a coherent receiver, a frequency offset can occur in the received signal. Existing frequency offset estimation methods for discrete spectrum modulation (NFDM) coherent optical communication systems primarily include eigenvalue shift, M-th power estimation, pilot-based methods based on periodic sequences, and nonlinear frequency domain (NFD) compensation methods based on NFT theory and assisted by training sequences.

[0004] The eigenvalue shift method estimates the frequency offset by calculating the offset of the real part of the eigenvalue based on the frequency shift property of NFT. However, in actual optical fiber transmission, there are transmission impairments (such as optical fiber loss, amplified spontaneous emission noise, etc.) and it is not accurate enough. The frequency offset estimation range of the M-th power estimation method is limited to [-R s / 2m,+R s / 2m], where R s Indicates the baud rate, and m indicates the number of constellation points in the modulation format. Since the baud rate of the discrete spectrum modulated NFDM system is low in long-distance optical fiber transmission, this method is only applicable to situations where the frequency deviation is very small, which obviously does not meet the needs of practical applications. The pilot method based on periodic sequence requires a longer sequence to obtain better frequency deviation estimation accuracy, and the longer the required sequence, the greater the sacrifice in the spectrum efficiency of the NFDM system. Compared with the M-th power estimation method, the frequency deviation estimation range of the NFD method based on NFT theory and training sequence assistance can be extended to [-R s / 2,+R s / 2], compared with the pilot method based on periodic sequence, the NFD method can obtain better estimation accuracy under the same training sequence length. However, this method assumes that the bursts of TS in different time slots are interference-free and uses exp(4jλ 2 z) Perform channel equalization. In this case, the transmission rate (baud rate) of the discrete spectrum modulation (NFDM) system for long-distance transmission is usually not high, which limits the frequency offset estimation range of this method. Summary of the Invention

[0005] In view of the defects of the prior art, the present invention aims to propose an estimation method that can eliminate the constraints of the baud rate on the frequency offset estimation range and has low computational complexity.

[0006] To achieve the above object, the present invention provides a frequency offset estimation method for a discrete spectrum modulation nonlinear frequency division multiplexing system based on eigenvalue shift and signal matching.

[0007] Carrier frequency offset CFO, or frequency offset FO for short, is a frequency offset caused by the mismatch between the center frequency of the transmitting laser and the local oscillator laser, which will cause damage to the transmission signal. Compared with the pilot method based on periodic sequences, the method of the present invention can obtain better estimation accuracy under the same training sequence length, and is transparent to the modulation format. Compared with the NFD method, the method of the present invention can eliminate the constraint of the baud rate on the frequency offset estimation range, and has lower computational complexity. The frequency offset is introduced by the mismatch between the center frequency of the transmitting laser and the local oscillator laser. This processing method first determines the rough range of the frequency offset estimation based on the eigenvalue offset, and then generates an ideal matching signal based on the nonlinear Fourier transform NFT theory and the known training sequence TS, and then constructs an optimization model for FO. Finally, in the process of solving the optimization model, the grid search method is used to solve and obtain the frequency offset estimate.

[0008] In an optional embodiment, a frequency offset estimation method for a discrete spectrum modulation nonlinear frequency division multiplexing system includes:

[0009] The frequency offset introduced by the mismatch between the center frequencies of the transmitting laser and the local oscillator laser is first estimated based on the eigenvalue shift to determine a rough range. Then, an optimization model for FO is constructed based on the NFT theory and the known TS. Finally, a grid search algorithm is used to solve the problem to obtain the estimated frequency offset.

[0010] In an optional embodiment, the frequency offset estimation method for the discrete spectrum modulation nonlinear frequency division multiplexing system, wherein the method for determining a rough range of the frequency offset estimation based on the eigenvalue shift is as follows:

[0011] The frequency shift properties of NFT theory,

[0012]

[0013] Here q(t,z) represents the time domain signal, ω represents the frequency, and a(λ-ω,z) and b(λ-ω,z) represent the spectral coefficients of the nonlinear Fourier transform in the frequency domain.

[0014] According to the above properties, we can see that frequency deviation will cause the shift of eigenvalue. However, due to the existence of spontaneous emission noise (ASE) and fiber loss, this property can only be used to roughly locate the frequency deviation.

[0015] Δf e =E[Re(λ-ω)] / (-π*T0)=E[Re(λ-ω)] / (-π*T p / 2t max )

[0016] Here E represents the mean, Re represents the real part operation, λ represents the spectrum parameter of nonlinear Fourier transform, ω = -πΔfT0, Δf represents the real frequency deviation, T p Indicates the fixed width of the time window, t max =T p / (2T0), represents the dimensionless time parameter, and T0 represents the free parameter.

[0017] Therefore, the rough range of the frequency offset estimation is

[0018] [Δf e -ρ|Δf e |-δMHz, Δf e +ρ|Δf e |+δMHz]

[0019] Here, ρ and δ are parameters used to control the frequency offset estimation range.

[0020] In an optional embodiment, the frequency offset estimation method for a discrete spectrum modulation nonlinear frequency division multiplexing system is characterized by constructing an optimization model for FO based on NFT theory and known TS:

[0021] According to the transmission evolution property of NFT theory, the i-th ideal matching signal is generated as follows,

[0022]

[0023] Here a i (λ, 0), b i (λ, 0) represents the spectrum coefficient of the i-th ideal matching signal at the normalized distance z = 0, z is the normalized distance of transmission, Q i (t, z) represents the i-th ideal matching signal.

[0024] Then the following optimization model is constructed:

[0025]

[0026] here It represents the i-th signal after the receiver has made frequency offset estimation compensation and normalization. is the frequency offset estimator to be optimized, and m is the length of the training sequence.

[0027] In an optional embodiment, the frequency offset estimation method for a discrete spectrum modulation nonlinear frequency division multiplexing system is characterized by using a grid search algorithm to solve:

[0028] For the objective function , in the search range [Δf e -ρ|Δf e |-δMHz, Δf e +ρ|Δf e The grid search is performed within |+δMHz], with ρ=0.05, δ=70, and a step size of 0.5MHz to obtain the optimal frequency deviation. This is the value of the frequency offset estimate. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a comparison diagram of the errors of NFD and the method of the present invention in a single soliton transmission system at different frequency offset test points;

[0030] Figure 2 This is a comparison diagram of the errors of NFD and the method of the present invention in a double soliton transmission system at different frequency offset test points;

[0031] Figure 3 : This is a comparison diagram of the frequency offset estimation error between NFD and the method of the present invention under different training sequence lengths;

[0032] Figure 4 1 is a comparison chart of the running time of NFD and the method of the present invention under different training sequence lengths.

[0033] Specific implementation examples

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0035] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0036] The frequency offset introduced by the mismatch between the center frequencies of the transmitting laser and the local oscillator laser is first estimated based on the eigenvalue shift to determine a rough range. Then, an optimization model for FO is constructed based on the NFT theory and the known TS. Finally, a grid search algorithm is used to solve the problem to obtain the estimated frequency offset.

[0037] The rough range of frequency offset estimation based on eigenvalue shift is determined as follows:

[0038] The frequency shift properties of NFT theory,

[0039]

[0040] According to the above properties, it can be seen that frequency deviation will cause the shift of eigenvalue. However, due to the existence of spontaneous emission noise (ASE) and fiber loss, this property can only be used to roughly locate the frequency deviation.

[0041] Δf e =E[Re(λ-ω)] / (-π*T0)=E[Re(λ-ω)] / (-π*T p / 2t max ) (2)

[0042] Therefore, the rough range of the frequency offset estimation is

[0043] [Δf e -ρ1Δf e |-δMHz, Δf e +ρ|Δf e |+δMHz] (3)

[0044] Construct an optimization model for FO based on NFT theory and known TS:

[0045] According to the transmission evolution property of NFT theory, the i-th ideal matching signal is generated as follows,

[0046]

[0047] Then the following optimization model is constructed:

[0048]

[0049] Solve using a grid search algorithm:

[0050] For the objective function: , in the search range The grid search is performed with a step size of 0.5MHz to find the optimal This is the value of the frequency offset estimate.

[0051] Table 1. Parameters of different modulation schemes

[0052]

[0053] The single soliton NFDM transmission system with a baud rate of 2 Gbaud and the double soliton NFDM transmission system with a baud rate of 1 Gbaud are used for verification. The specific modulation scheme parameters are given in Table 1.

[0054] The designed TS is inserted in front of the transmission symbol sequence in the form of b coefficients. All transmission symbol sequences and TS are generated using nonlinear inverse Fourier transform (INFT) to generate time domain waveforms. Each fiber loop is 80 km long with non-zero dispersion shifted fiber (NZDSF) (α = 0.2 dB / km, β2 = -5.75 ps 2 / km, γ=1.31W -1 km -1 ) and is amplified by an erbium-doped fiber amplifier (EDFA). The fiber transmission process is simulated using a step-by-step Fourier algorithm with a step size of 1 km. The specific simulation results are given by Figure 1-4 Given, here the search range [Δf e -ρ|Δf e |-δMHz, Δf e +ρ|Δf e The parameters in |+δMHz] are taken as ρ=0.05 and σ=70.

[0055] Depend on Figure 1-2 It can be seen that under different frequency offset settings, the frequency offset estimation method of the present invention is applicable to both single-soliton and multi-soliton NFDM systems, and achieves high frequency offset estimation accuracy, reaching approximately 1 MHz at 32 TS. Compared to the NFD method, the frequency offset estimation range of this method is unaffected by the baud rate, making it more adaptable to frequency offset variations in actual transmission systems.

[0056] Depend on Figure 3 It can be seen that as the TS length increases, the frequency offset estimation error becomes smaller. Figure 4 It can be seen that compared with the NFD method, the computational complexity of the method of the present invention is lower.

[0057] It should be noted that the frequency offset estimation method provided in the embodiment of the present invention may also include more or fewer parts, which will not be described in detail here.

[0058] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for estimating frequency offset in a discrete spectrum modulation nonlinear frequency division multiplexing system, characterized in that: include: To address the frequency offset introduced by the mismatch between the center frequencies of the transmitting laser and the local oscillator laser, a rough range of the frequency offset estimate is first determined based on the eigenvalue shift. An optimization model for the frequency offset (FO) is then constructed based on the nonlinear Fourier transform (NFT) theory and the known training sequence (TS). Finally, a grid search algorithm is used to solve the problem and obtain the frequency offset estimate. The optimization model for FO based on the nonlinear Fourier transform NFT theory and the known training sequence TS includes: According to the transmission evolution property of NFT theory, the i-th ideal matching signal is generated as follows: Here a i (λ,0),b i (λ,0) represents the spectrum coefficient of the i-th ideal matching signal at the normalized distance z = 0, z is the normalized distance of transmission, Q i (t,z) represents the i-th ideal matching signal; Construct the following optimization model: here It represents the i-th signal after the receiver has made frequency offset estimation compensation and normalization. is the frequency offset estimator to be optimized, and m is the length of the training sequence.

2. The frequency offset estimation method for discrete spectrum modulation nonlinear frequency division multiplexing system according to claim 1, characterized in that: The coarse range of frequency offset estimation is determined based on the eigenvalue shift, First, the frequency offset is roughly located using the frequency shift property of NFT theory. Δf e =E[Re(λ-ω)] / (-π*T0)=E[Re(λ-ω)] / (-π*T p / 2t max ) Here E represents the mean, Re represents the real part operation, λ represents the spectrum parameter of nonlinear Fourier transform, ω=-πΔfT0, Δf represents the real frequency deviation, T p Indicates the fixed width of the time window, t max =T p / (2T0), represents the dimensionless time parameter, T0 represents the free parameter; Then, according to the coarse positioning frequency offset value Δf e , giving a rough range of estimates, [Δf e -ρ|Δf e |-δMHz,Δf e +ρ|Δf e |+δMHz] Here, ρ and δ are parameters used to control the frequency offset estimation range.

3. The frequency offset estimation method for discrete spectrum modulation nonlinear frequency division multiplexing system according to claim 2, characterized in that: The solution is obtained by using the grid search algorithm: For the objective function Perform grid search within a rough range to find the optimal frequency deviation This is the value of the frequency offset estimate

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