CN-121984826-A - Three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping

CN121984826ACN 121984826 ACN121984826 ACN 121984826ACN-121984826-A

Abstract

The invention discloses a three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping, which belongs to the technical field of communication and comprises the steps of calculating radial distances of constellation point coordinates, carrying out hierarchical division to obtain radial energy hierarchical sets, calculating effective connectivity of constellation points through identifying main neighbors and secondary neighbors, carrying out folding times distribution based on hierarchical scale factors to obtain folding times and non-uniform probability distribution of each constellation point, constructing probability-geometric joint weighting side weights based on geometric distances among constellation points to obtain a weighted neighborhood matrix, and establishing a global mapping cost function according to the weighted neighborhood matrix and bit tag Hamming distance to obtain an optimal bit mapping relation for three-dimensional constellation shaping.

Inventors

WANG CHEN
REN JIANXIN
CHEN SHUAIDONG
ZHAO JIANYE
SONG XIUMIN
ZHAO LILONG
SUN TINGTING

Assignees

盐城工业职业技术学院
南京信息工程大学

Dates

Publication Date: 20260505
Application Date: 20260310

Claims (10)

1. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping is characterized by comprising the following steps of: calculating radial distances of constellation point coordinates of the three-dimensional constellation, and carrying out hierarchical division to obtain a radial energy hierarchical set; Identifying a primary neighbor and a secondary neighbor based on the radial energy hierarchy set, and calculating the effective connectivity of constellation points; According to the effective connectivity of the constellation points, carrying out folding times distribution based on the hierarchical scale factors to obtain folding times of each constellation point; carrying out probability normalization processing according to the folding times of each constellation point to obtain non-uniform probability distribution; constructing probability-geometric joint weighting side weights according to the non-uniform probability distribution and the geometric distance between constellation points to obtain a weighting neighborhood matrix; establishing a global mapping cost function according to the weighted neighborhood matrix and the bit tag Hamming distance; according to the global mapping cost function, carrying out bit mapping search by adopting an optimization algorithm to obtain an optimal bit mapping relation; and carrying out three-dimensional constellation shaping based on the optimal bit mapping relation.
2. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping according to claim 1, wherein calculating radial distances of constellation point coordinates of a three-dimensional constellation and performing hierarchical division to obtain a radial energy hierarchy set comprises: acquiring a geometric coordinate set of a three-dimensional modulation constellation; Radial distance calculation is carried out based on the geometric coordinate set, and a model value of each constellation point is obtained; Performing hierarchical division according to the modulus value of each constellation point, and dividing all constellation points into a plurality of radial energy hierarchies to obtain a radial energy hierarchy set; each constellation point only belongs to one radial energy level, and the union of all radial energy levels is a whole constellation point set; the modulus of the constellation point is expressed as: ; In the formula, Represent the first Individual constellation points Is used for the control of the (c), Representing a two-norm operation for calculating the Euclidean distance from the constellation point coordinates to the origin of coordinates; The set of radial energy levels is expressed as: ; In the formula, Representing the 1 st radial energy level, being the innermost region, Representing the 2 nd radial energy level, Represent the first The radial energy level is the outermost region.
3. The method for three-dimensional constellation shaping based on regional probability folding and weighted neighborhood mapping of claim 2 wherein identifying primary neighbors and secondary neighbors based on a set of radial energy levels and calculating the effective connectivity of constellation points comprises: Based on the radial energy level set, judging the radial energy level to which the constellation point belongs; for each constellation point, according to the radial energy level to which the constellation point belongs, defining the constellation point adjacent to the constellation point and located in the inner layer area as a main neighbor, and defining the constellation point adjacent to the constellation point and located in the outer layer area as a secondary neighbor; when the distance between any two constellation points is smaller than or equal to a preset adjacency judging threshold value, judging that the two constellation points are adjacent; And calculating the effective connectivity of the constellation points according to the number of the main neighbors and the number of the secondary neighbors of each constellation point.
4. A three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping according to claim 3, characterized in that the distance between the two constellation points is expressed as: ; In the formula, Represent the first Individual constellation points And (d) Individual constellation points A distance therebetween; the number of primary neighbors is expressed as: ; In the formula, Represent the first The number of primary neighbors with each constellation point adjacent to the inner region, Representing a preset adjacency determination threshold value, Represent the first The radial energy levels to which the individual constellation points belong, Represent the first Radial energy levels to which the constellation points belong; the number of secondary neighbors is expressed as: ; In the formula, Represent the first The number of secondary neighbors with each constellation point adjacent to the more outer region; the effective connectivity of the constellation points is expressed as: ; In the formula, Represent the first The effective connectivity of the individual constellation points, And the weighting coefficient representing the number of the secondary neighbors is used for reflecting the difference of the contribution degree of the primary neighbors and the secondary neighbors to the local connectivity.
5. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping as in claim 4 wherein performing folding times distribution based on hierarchical scale factors according to the effective connectivity of constellation points to obtain folding times of each constellation point comprises: setting level scale factors corresponding to each radial energy level; Wherein the hierarchical scale factor of the inner region is greater than the hierarchical scale factor of the outer region, expressed as: ; In the formula, Represents the level scale factor corresponding to the 1 st radial energy level, which is the level scale factor of the innermost region, Representing the level scale factor corresponding to the 2 nd radial energy level, Represent the first The corresponding level scale factors of the radial energy levels are the level scale factors of the outermost layer area; according to the effective connectivity of the constellation points, calculating based on the level scale factors corresponding to the radial energy levels to which each constellation point belongs, so as to obtain the folding times of each constellation point; The folding times of the constellation points are expressed as follows: ; In the formula, Represent the first The number of folds of the individual constellation points, Represent the first The level scale factors corresponding to the radial energy levels, Represent the first The radial energy levels ⌊ - ⌋ represent a downward rounding.
6. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping of claim 5 wherein performing probability normalization processing according to the folding times of each constellation point to obtain a non-uniform probability distribution comprises: Calculating the sum of folding times of all constellation points to obtain the global folding total; determining the emission probability of each constellation point according to the ratio of the folding times of each constellation point to the total global folding amount, and obtaining non-uniform probability distribution; The global fold total is expressed as: ; In the formula, Representing the total amount of global folding, Representing the number of constellation points; The non-uniform probability distribution is expressed as: ; In the formula, Represent the first Non-uniform probability distribution of individual constellation points.
7. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping of claim 6 wherein constructing probability-geometry joint weighting side weights based on non-uniform probability distribution and geometric distance between constellation points to obtain a weighted neighborhood matrix comprises: For any two constellation points, calculating probability weight items according to non-uniform probability distribution, and calculating geometric distance attenuation factors based on geometric distances between the constellation points, multiplying the probability weight items by the geometric distance attenuation factors to obtain probability-geometric joint weighting edge weights between the two constellation points, forming a weighting neighborhood matrix by the probability-geometric joint weighting edge weights between every two constellation points, wherein the probability-geometric joint weighting edge weights are expressed as: ; In the formula, Represent the first Constellation points and the first Probability-geometric joint weighting side weights between individual constellation points, Represent the first A non-uniform probability distribution of the individual constellation points, Represent the first Constellation points and the first Geometric distance attenuation factors between the constellation points; The geometric distance attenuation factor is expressed as: ; In the formula, Represent the first Constellation points and the first The geometric distance between the individual constellation points attenuates the factor, Represents an exponential function based on a natural constant e, Representing the minimum euclidean distance of the three-dimensional constellation.
8. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping of claim 7 wherein establishing a global mapping cost function based on a weighted neighborhood matrix and bit tag hamming distance comprises: Distributing a bit label for each constellation point, and calculating the Hamming distance between any two constellation point bit labels; multiplying each probability-geometry joint weighting side weight in the weighting neighborhood matrix with the Hamming distance between the corresponding two constellation point bit labels, and summing all constellation point pairs to obtain a global mapping cost function; The global mapping cost function is expressed as: ; In the formula, The cost function of the global map is represented, Represent the first Constellation points and the first Hamming distances between the individual constellation point bit labels.
9. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping according to claim 8, wherein performing a bit map search by using an optimization algorithm according to a global map cost function to obtain an optimal bit map relationship comprises: Initializing bit tag sequences of all constellation points, and setting initial temperature and annealing parameters of a simulated annealing algorithm; In the iterative optimization process, randomly exchanging bit labels of a preset number of constellation points to generate a new bit label sequence, and calculating a global mapping cost function value corresponding to the new bit label sequence; judging whether to accept the new bit tag sequence according to a Metropolis criterion; if so, updating the new bit tag sequence into the current bit tag sequence; if not, keeping the current bit tag sequence unchanged; gradually reducing the temperature according to a preset annealing strategy, repeating iteration until convergence conditions are met, and outputting an optimal bit mapping relation for minimizing the global mapping cost function.
10. The three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping of claim 9 wherein performing three-dimensional constellation shaping based on optimal bit mapping relationships comprises: And distributing corresponding bit labels to each constellation point in the three-dimensional constellation according to the optimal bit mapping relation to obtain the shaped three-dimensional constellation.

Description

Three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping Technical Field The invention relates to a three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping, and belongs to the technical field of communication. Background As optical and wireless communication systems evolve towards higher transmission rates and spectral efficiency, higher order modulation techniques have become a core component of modern communication systems, carrying more information within a limited bandwidth by increasing bit-level modulation efficiency. However, the continuous increase of modulation order and dimension results in more complex constellation structure, reduced minimum euclidean distance between constellation points, obviously enhanced sensitivity of the system to noise, nonlinear distortion and implementation error, and higher requirements on constellation design and signal processing methods. Especially in a multidimensional modulation scene, the spatial distribution of constellation points is more dense, and the matching relation between the geometric structure and the signal processing strategy has an important influence on the system performance. In order to cope with the challenge, researchers have proposed various constellation shaping and optimizing methods, including means such as geometric shaping, probability distribution and bit mapping optimization, by adjusting the geometric positions of constellation points or distributing non-uniform probabilities to non-uniform constellation points, the power efficiency and error code performance can be improved to a certain extent, and meanwhile, reasonably designing the bit mapping is helpful to reduce inter-symbol interference and error bit diffusion effects. However, the existing method mostly considers probability distribution and mapping design as mutually independent processing processes from a single point of view, and fails to fully consider inherent correlations among constellation structural characteristics, probability distribution characteristics and mapping rules. In a three-dimensional modulation constellation, the distribution of constellation points in space generally has obvious geometric hierarchy and neighborhood relation characteristics, and different constellation points have differences in the aspects of space position, adjacent quantity, geometric connectivity and the like. Most of the existing probability shaping methods are based on "energy criteria", such as maxwell-boltzmann distribution, i.e. probability is allocated only according to euclidean distance from a constellation point to an origin, and default that constellation points of the same energy level have the same transmission characteristics. This assumption may apply in regular two-dimensional QAM constellations, but in three-dimensional irregular constellations, such as regular dodecahedron, stacked spheres, etc., there are often significant differences in local geometry topologies, such as number of neighbors, connection tightness, even at the same radial distance, i.e. constellation points of the same energy. If the topology difference is ignored and the same probability is forcibly distributed, the constellation points with denser neighborhoods and more error-prone neighborhoods bear too high transmission probability, so that the local error risk is unbalanced, and the anti-noise potential of the constellation cannot be fully exploited. On the other hand, under the condition that the probability is unevenly distributed, the occurrence frequency of the constellation points is changed, and the error bit propagation characteristic and the neighborhood structure characteristic are also changed. If a bit mapping strategy designed based on uniform probability assumption is still adopted, the weight difference of different constellation points in probability distribution is difficult to reflect, so that potential gain caused by non-uniform probability distribution is weakened, and even new performance bottlenecks are introduced in some cases. Aiming at the problems, the invention provides a solution which can consider the local topological difference of the constellation points of the same layer and realize the joint optimization of probability distribution and bit mapping. Disclosure of Invention The invention aims to provide a three-dimensional constellation shaping method based on regional probability folding and weighted neighborhood mapping, which is used for generating nonuniform probability distribution adaptive to a geometric structure by combining a radial energy level of constellation points with a local topological structure, and constructing a global cost function of probability-geometric joint weighting to optimize a bit mapping relation so as to solve the problems of unbalanced error code risk caused by neglecting local topological difference of constell