A constellation graph geometry shaping method based on an improved GPO algorithm

Abstract

This invention relates to a constellation graph geometric shaping method based on an improved GPO algorithm, comprising the following steps: S101, initializing the constellation graph to be shaped under constraints, and mapping the constellation points using an optimized bit mapping method; S102, randomly selecting a constellation point S from the M constellation points of the initialized constellation graph. i ,i∈{1,2,…,M}, and move it slightly in the horizontal or vertical direction; S103, adjust the centroid of the remaining constellation points and scale the constellation points appropriately to satisfy the constraints; S104, find S by selecting the minimum calculated value of the analytical BER formula. i S105. Calculate the new positions of other constellation points; S106. Repeat the above steps until the BER performance improvement reaches saturation; S107. Output the optimized geometrically shaped constellation diagram. Compared with existing technologies, this invention has advantages such as reduced computational complexity and increased transmission capacity.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication system technology, and in particular to a constellation graph geometry shaping method based on an improved GPO algorithm. Background Technology

[0002] Currently, in high-speed coherent optical transmission systems, thanks to the development of high-speed digital-to-analog converters (DACs) and digital coherent receivers, higher-order quadrature amplitude modulation (QAM) formats (such as 16QAM and 64QAM) are applied to coherent optical communication to achieve high-capacity transmission. However, the communication capacity of these higher-order QAM signals is still far from the Shannon limit. Due to the limitations of signal-to-noise ratio (SNR) and fiber nonlinearity in optical communication links, shaping higher-order QAM formats to improve transmission capacity has become an important research topic.

[0003] To narrow the gap with the Shannon limit, two types of shaping schemes have been proposed to approximate channel capacity: geometric shaping and probabilistic shaping. Geometric shaping is highly promising due to its simplicity, low algorithm complexity, and minimal cost increase to actual hardware circuitry. The main algorithms for implementing geometric shaping include pairwise optimization (PPO), genetic algorithms, and neural network-based machine learning algorithms. Among these, the generalized pairwise optimization (GPO) algorithm, compared to other algorithms, has advantages such as low computational complexity and fast convergence speed, and has been applied in high-speed, long-distance coherent optical transmission systems to further improve communication capacity. The GPO algorithm optimizes a geometrically shaped constellation diagram with zero mean and constant average energy, given the constellation point bit mapping and SNR. During the optimization process, two constellation points are randomly selected sequentially and their positions are moved slightly, while keeping the positions of other constellation points fixed. However, during the movement of these two constellation points, it is necessary to maintain the overall constellation diagram's mean of zero and average energy constant; therefore, these two constellation points can only move within a calculated circle. In the GPO algorithm, optimizing each pair of constellation points requires calculating the equation of a circle, resulting in high computational complexity. Furthermore, for the M-QAM format, each optimization round requires traversing M×(M-1) / 2 pairs of points, and the computational complexity increases rapidly with the modulation order.

[0004] Therefore, how to reduce algorithm complexity and the complexity of constellation graph geometric reshaping optimization has become a technical problem that needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a constellation graph geometry shaping method based on an improved GPO algorithm.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A constellation graph geometry shaping method based on an improved GPO algorithm, comprising the following steps:

[0008] Step S101: Initialize the constellation diagram to be shaped under constraints, and map the constellation points using an optimized bit mapping method, then execute step S102.

[0009] Step S102: Randomly select one constellation point S from the M constellation points in the initialized constellation diagram. i ,i∈{1,2,…,M}, and move it slightly in the horizontal or vertical direction, and execute step S103;

[0010] Step S103: Adjust the centroid of the remaining constellation points and scale the constellation points to meet the constraints of step S101, and then execute step S104.

[0011] Step S104: Find S by selecting the minimum calculated value of the analytical BER formula. i To determine the new locations of other constellation points, proceed to step S105;

[0012] Step S105: Determine whether the BER performance has reached saturation. If not, proceed to step S102; if it has, proceed to step S106.

[0013] Step S106: Output the optimized geometrically shaped constellation diagram.

[0014] Furthermore, the constraints in step S101 are zero mean and constant average energy.

[0015] Furthermore, the expressions for the zero mean and constant average energy are as follows:

[0016]

[0017] Furthermore, the optimized bit mapping method in step S101 is specifically as follows: during bit mapping, the Euclidean distance between the current constellation point and its neighboring constellation points is calculated. The neighboring constellation point with the smallest Euclidean distance is most likely to be judged incorrectly. During bit mapping, the bit label of the neighboring constellation point with the smallest Euclidean distance is minimized to have the smallest difference from the bit label of the current constellation point.

[0018] Furthermore, the constellation point S in step S102 i It is a 2×1 vector composed of in-phase and quadrature components.

[0019] Furthermore, the adjustment of the centroid of the remaining constellation points in step S103 specifically involves adjusting the centroid of the remaining constellation points in the opposite direction to the selected constellation points until the constraint condition of zero mean is met.

[0020] Furthermore, the scaling of constellation points in step S103 specifically involves: simultaneously scaling all constellation points appropriately until the constraint condition of constant average energy is met.

[0021] Furthermore, the expression for the analytical BER formula in step S104 is as follows:

[0022]

[0023] In the formula, H(B) i B j ) represents two constellation points S i and S j Hamming distance between bit mappings, Q denotes the Gaussian function, ||S i -S j || represents the relationship between two constellation points S. i and S j Normalization, where N represents the noise variance calculated based on the set SNR value.

[0024] An electronic device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method as described in any of the preceding claims.

[0025] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any of the preceding claims.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] I. This invention utilizes an improved GPO algorithm to reduce the complexity of constellation diagram geometric shaping optimization, lower computational complexity, and increase signal transmission capacity, providing an effective solution for the practical application of geometric shaping in high-speed coherent optical communication systems.

[0028] Second, this invention proposes an optimized bit mapping method. When configuring the bit mapping of the initial constellation, it is impossible to apply the Gray mapping to the geometrically shaped QAM constellation graph. Therefore, this invention minimizes the difference between the bit label of the adjacent constellation point with the smallest Euclidean distance and the bit label of the current constellation point, thereby reducing the probability of judgment errors. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0030] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0031] Example

[0032] like Figure 1 As shown, a constellation graph geometry shaping method based on an improved GPO algorithm is described, and the method includes the following steps:

[0033] Step S101, consider the M-QAM symbol S i ,i∈{1,2,…,M} is a 2×1 vector composed of in-phase and quadrature components. It initializes the constellation diagram to be shaped under the constraints of zero mean and constant average energy, and uses an optimized bit mapping method to map the constellation points.

[0034] In this invention, when configuring the bit mapping of the initial constellation, it is impossible to apply Gray mapping to the geometrically shaped QAM constellation graph. Therefore, during bit mapping, the Euclidean distance between the current constellation point and its neighboring constellation points is calculated. The neighboring constellation point with the smallest Euclidean distance is most prone to error. During bit mapping, the goal is to minimize the difference between the bit label of the neighboring constellation point with the smallest Euclidean distance and the bit label of the current constellation point. For example, if the current constellation point coordinates are 1+1i, and it has four neighboring constellation points 1+2i, 3+1i, 1-1i, and -1+1i, the calculated neighboring constellation point with the smallest Euclidean distance to 1+1i is 1+2i. Therefore, during bit mapping, the goal is to minimize the difference between the bit label of 1+2i and the bit label of 1+1i.

[0035] The expressions for zero mean and constant average energy are:

[0036]

[0037] Step S102: Randomly select one constellation point S from the M constellation points in the initialized constellation diagram. i ,i∈{1,2,…,M}, and move it slightly in the horizontal or vertical direction.

[0038] Step S103: Adjust the centroid of the remaining constellation points in the opposite direction to the selected constellation point to satisfy the zero mean constraint, and simultaneously scale all constellation points to satisfy the constraint of constant average energy.

[0039] Step S104: Find S by selecting the minimum calculated value of the analytical BER formula. i New locations for other constellation points.

[0040] In this invention, the analytical BER formula is:

[0041]

[0042] Where H(B) i B j ) represents two constellation points S i and S j Hamming distance between bit mappings, Q denotes the Gaussian Q-function, ||S i -S j || represents the constellation point S i and S j Normalization, where N represents the noise variance calculated based on the set SNR (signal-to-noise ratio) value.

[0043] Step S105: Determine whether the BER performance has reached saturation. If not, proceed to step S102; if it has, proceed to step S106.

[0044] Step S106: Output the optimized geometrically shaped constellation diagram to reshape the high-order QAM format and improve transmission capacity.

[0045] The improved GPO algorithm proposed in this invention reduces the complexity of constellation graph geometric reshaping optimization. The improved GPO algorithm moves only one constellation point at a time during the optimization process, and moves all other constellation points as a whole, adjusting the centroid positions of the other constellation points to satisfy the zero-mean condition. Then, all constellation points are scaled as a whole to satisfy the condition of constant average energy. Thus, when moving constellation points, it is not necessary to solve the equation of the circle, and each optimization round only requires traversing the centroids of M pairs of single points and the remaining points. This improved GPO algorithm greatly simplifies computational complexity and provides an effective solution for the practical application of geometric reshaping in high-speed coherent optical communication systems.

[0046] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A constellation geometry shaping method based on an improved GPO algorithm, characterized in that, The method comprises the following steps: Step S101, initializing the constellation to be shaped under a constraint condition, and mapping the constellation points using an optimized bit mapping method, and performing step S102; Step S102, a constellation point is randomly selected from the M constellation points of the initialized constellation in sequence and slightly moves it in the horizontal or vertical direction, and step S103 is executed; Step S103, adjusting the centroid of the remaining constellation points, and scaling all the constellation points to meet the constraint condition of step S101, and performing step S104; Step S104, find the minimum value of the analytic BER formula by selecting the minimum calculation value, and execute step S105; S i and other constellation points, execute step S105; Step S105, judging whether the BER performance reaches saturation, if not, performing step S102, and if yes, performing step S106; Step S106, outputting the optimized geometrically shaped constellation; The optimized bit mapping method in step S101 is specifically: when bit mapping, the Euclidean distance of the current constellation point and its adjacent constellation points is calculated, wherein the adjacent constellation point with the minimum Euclidean distance is most likely to be misjudged, and when bit mapping, the bit label of the adjacent constellation point with the minimum Euclidean distance is made to differ from the bit label of the current constellation point by the least; The constraint condition in step S101 is zero mean and constant average energy; The adjustment of the centroid of the remaining constellation points in step S103 is specifically: adjusting the centroid of the remaining constellation points in the opposite direction of the selected constellation points until the constraint condition of zero mean is met; The expression of the analytic BER formula in step S104 is: wherein, represents the Hamming distance between the bit mappings of two constellation points S i and S j , Q represents a Gaussian function, represents the Hamming distance between the bit mappings of two constellation points S i and S j normalized, and N represents a noise variance calculated according to a set SNR value.

2. The constellation geometric shaping method based on the improved GPO algorithm according to claim 1, characterized in that, The expression for zero mean and constant average energy is:

3. The constellation geometric shaping method based on the improved GPO algorithm according to claim 1, characterized in that, The constellation point in step S102 S i is a 2x1 vector consisting of an in-phase component and a quadrature component.

4. The constellation geometric shaping method based on the improved GPO algorithm according to claim 1, characterized in that, The scaling of the constellation points in step S103 is specifically: simultaneously scaling all the constellation points appropriately until the constraint condition of constant average energy is met.

5. An electronic device comprising a memory and a processor, said memory having stored thereon a computer program, characterized in that, The processor executes the program to implement the method in any one of claims 1-4.

6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method in any one of claims 1-4.

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