A four-dimensional 4nqam constellation shaping method and system

Abstract

The application discloses a four-dimensional 4nQAM constellation shaping method and system, and belongs to the technical field of constellation shaping. The method comprises the following steps: taking a coordinate origin as a square center, according to a preset constellation point priority, expanding a to-be-shaped constellation point in a concentric square from an inner layer to an outer layer in progression to obtain a two-dimensional geometric shaping constellation; mapping the two two-dimensional geometric shaping constellations to a four-dimensional space in a quadrature manner to generate a four-dimensional geometric shaping constellation; initializing and layering the four-dimensional geometric shaping constellation to obtain independent bit streams of layers of the constellation; inputting the independent bit streams into a distribution matcher of a corresponding layer to perform probability distribution matching, and obtaining a constellation symbol index sequence of the layer; layering and mapping the constellation symbol index sequence according to different Hamming weights, and performing quadrant fusion with the four-dimensional geometric shaping constellation to obtain a four-dimensional probability shaping constellation. The application not only realizes flexible construction of a 4n-order constellation, but also can adaptively adjust a constellation structure according to different application requirements.

Description

Technical Field

[0001] This invention relates to the field of constellation shaping technology, and in particular to a four-dimensional 4nQAM constellation shaping method and system. Background Technology

[0002] While traditional modulation methods can meet some basic requirements, with the increasing complexity of application scenarios, especially in environments with high-speed data transmission and high noise interference, optimizing modulation formats and signal design has become a key direction for improving the performance of communication systems. Signal shaping has become a key technology due to its role in improving spectral efficiency, and it includes geometric shaping (GS) and probabilistic shaping (PS).

[0003] Geometric shaping optimizes signal distribution by adjusting the spatial positions of constellation points, thereby improving transmission efficiency. Traditional geometric shaping primarily focuses on quadrature amplitude modulation (QAM) signals, a choice made due to its ease of hardware implementation and computational complexity. However, the channel capacity for long-distance transmission is limited by nonlinear impairments. Non-quadrature QAM signal distributions lack more flexible geometric distributions, cannot better align with channel characteristics, and cannot achieve higher information transmission efficiency under the same bandwidth conditions. High-dimensional geometric shaping, however, goes beyond the two-dimensional in-phase / quadrature (I / Q) plane, extending constellation points to a higher-dimensional space, thus providing greater freedom in the distribution of constellation points. Furthermore, researchers are now exploring the integration of geometric shaping and probabilistic shaping to further optimize transmission.

[0004] Probabilistic shaping has been extensively studied due to its shaping gain and ability to achieve adaptive rates. Distribution matching (DM) is a key module in PS implementation, transforming a uniform input bit sequence into an output symbol sequence with a target distribution. A popular DM algorithm is Constant Composition Distribution Matcher (CCDM), where the probability distribution of each amplitude is fixed for all output sequences. The shaping gain of CCDM depends primarily on the block length; the longer the block length, the greater the shaping gain. Arithmetic coding is widely used as a method for implementing CCDM. Arithmetic coding has a serial implementation structure, which can lead to large latency for long block lengths. Furthermore, the implementation complexity tends to increase rapidly with increasing block length. Previous research has explored the design concept of constellation points for non-uniform signal probability distributions. Utilizing the unequal-length coding characteristics of prefix codes, non-uniform signals can be designed into Gaussian-like distributions through coding or certain rules, proving to be a simple and reliable method. This method not only reduces the average bit rate and narrows the gap with the Shannon limit but also achieves better bit error rate performance. This type of pattern has low complexity, and the mapping from symbols to constellation points can be easily performed using lookup tables. However, its high computational complexity and strong sequential processing limit its scalability in higher-order constellations. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a 4nQAM constellation shaping method and system. It not only breaks through the limitation that the order of QAM constellations is limited to powers of 2, realizing the flexible construction of 4n-order constellations, but also adaptively adjusts the constellation structure according to different application requirements, effectively improving energy efficiency and noise resistance.

[0006] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0007] On one hand, the present invention provides a four-dimensional 4nQAM constellation shaping method, comprising:

[0008] With the origin of the coordinate system as the center of the square, the constellation points to be shaped are expanded from the inner layer to the outer layer in concentric squares according to the preset constellation point priority, to obtain a two-dimensional geometric constellation; wherein, the number of constellation points in each quadrant of each layer is less than the number of layers.

[0009] The two-dimensional geometric constellation is copied to generate two two-dimensional geometric constellations. The two two-dimensional geometric constellations are then mapped orthogonally to four-dimensional space to generate a four-dimensional geometric constellation.

[0010] The four-dimensional geometrically shaped constellation is initialized and layered to obtain independent bitstreams for each layer of the constellation;

[0011] The independent bitstreams are input into the distribution matcher of the corresponding layer for probability distribution matching to obtain the constellation symbol index sequence of that layer.

[0012] Based on the Hamming weight-based hierarchical mapping mechanism, the constellation symbol index sequence is hierarchically mapped according to different Hamming weights to obtain the mapped constellation points;

[0013] The mapped constellation points are fused with the four-dimensional geometric integer constellation in quadrants to obtain the four-dimensional probabilistic integer constellation.

[0014] Optionally, with the origin of the coordinate system as the center of a square, and according to a preset constellation point priority, the constellation points to be shaped are expanded from the innermost layer to the outermost layer of concentric squares to obtain a two-dimensional geometrically shaped constellation, including:

[0015] In the first quadrant, the constellation points to be shaped are sequentially expanded to S1, S2, S3, S4, S5, S6, S7, S8, S9, and S1. 10 S k S m-1 S m This yields a two-dimensional geometrically shaped constellation in the first quadrant;

[0016] In other quadrants, two-dimensional geometric constellations in the corresponding quadrants are obtained by symmetrically mapping the two-dimensional geometric constellations in the first quadrant; the two-dimensional geometric constellations are symmetrically distributed about the quadrant bisectors.

[0017] Where S1 represents the first quadrant bisector; S2 represents the second quadrant closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S3 represents the second quadrant closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; S4 represents the third quadrant bisector; S5 represents the third quadrant closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S6 represents the third quadrant closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; S7 represents the fourth quadrant closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S8 represents the fourth quadrant closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; S9 represents the fourth quadrant second closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S 10 This indicates that the fourth layer is the second closest to the quadrant bisector and lies between the quadrant bisector and the vertical axis; S k S indicates the quadrant bisector or the quadrant closest to the bisector and located between the quadrant bisector and the horizontal axis; m-1 This indicates that the last layer is furthest from the quadrant bisector and lies between the quadrant bisector and the horizontal axis; S m This indicates that the last layer is the furthest from the quadrant bisector and lies between the quadrant bisector and the vertical axis.

[0018] Optionally, two two-dimensional geometrically shaped constellations are orthogonally mapped to four-dimensional space to generate a four-dimensional geometrically shaped constellation, including:

[0019] Two two-dimensional constellation points are obtained by selecting constellation points from two two-dimensional geometric integer constellations;

[0020] Based on the preset quadrant mapping mechanism, the bit symbol combination method of two two-dimensional constellation points and their quadrant positions in four-dimensional space are determined to obtain the four-dimensional constellation points.

[0021] Generate a four-dimensional geometric integer constellation based on four-dimensional constellation points.

[0022] Optionally, based on a preset quadrant mapping mechanism, the bit symbol combination method and quadrant position of the two two-dimensional constellation points are determined to obtain the four-dimensional constellation points, including:

[0023] According to the preset quadrant mapping mechanism, one two-dimensional constellation point is used to form the first two dimensions of the four-dimensional constellation point, and the other two-dimensional constellation point is used to form the last two dimensions of the four-dimensional constellation point. The two two-dimensional constellation points are orthogonal in a geometric sense. The quadrant position of the four-dimensional constellation point in four-dimensional space is determined to obtain the four-dimensional constellation point.

[0024] The preset quadrant mapping mechanism controls the combination of four-dimensional constellation points in four-dimensional space to form a symmetrical geometric arrangement through unified symbols.

[0025] Optionally, the independent bitstreams are input into the distribution matcher of the corresponding layer for probability distribution matching to obtain the constellation symbol index sequence of that layer, including:

[0026] Based on the constellation symbol table and target probability distribution of the layer where the independent bitstream is located, the parameters of the independent bitstream are customized to obtain the constellation symbol index sequence of that layer.

[0027] Optionally, before mapping the constellation symbol index sequence hierarchically according to different Hamming weights based on the Hamming weight-based hierarchical mapping mechanism, the method further includes:

[0028] The constellation symbol index sequences of each layer are ordered and integrated by the symbol combiner to generate a complete constellation symbol sequence.

[0029] Optionally, based on a Hamming weight-based hierarchical mapping mechanism, the constellation symbol index sequence is hierarchically mapped according to different Hamming weights to obtain mapped constellation points, including:

[0030] Using the independent bitstreams of each constellation layer as driving bits, the Hamming weight layer where each constellation symbol in the constellation symbol index sequence is located is determined.

[0031] Select the codewords corresponding to the constellation symbols in the constellation symbol index sequence from the codeword set of the Hamming weight layer to obtain the mapped constellation points;

[0032] In the constellation symbol index sequence, each position corresponds to a constellation symbol, and each constellation symbol corresponds to a codeword of a bit combination.

[0033] Optionally, the Hamming weight layer is divided into levels based on the number of non-zero elements in the codeword;

[0034] The number of non-zero elements in the codewords of the first Hamming weight layer is 0, the number of non-zero elements in the codewords of the second Hamming weight layer is 1, the number of non-zero elements in the codewords of the third Hamming weight layer is 2, and the number of non-zero elements in the codewords of the fourth Hamming weight layer is 3 or 4.

[0035] Optionally, the codeword set in the first Hamming weight layer is {0000};

[0036] The codeword set in the second Hamming weight layer is {0001}, {0010}, {0100}, {1000};

[0037] The codeword set in the third Hamming weight layer is {0011}, {0101}, {1001}, {0110}, {1010}, {1100};

[0038] The codeword set in the fourth Hamming weight layer is {0111}, {1011}, {1101}, {1110}, and {1111}.

[0039] Secondly, the present invention provides a four-dimensional 4nQAM constellation shaping system, comprising:

[0040] The two-dimensional geometric shaping module is used to: expand the constellation points to be shaped from the inner layer to the outer layer in concentric squares according to the preset constellation point priority, with the origin of the coordinate system as the center of the square, to obtain a two-dimensional geometrically shaped constellation; wherein, the number of constellation points in each quadrant of each layer is less than the number of layers.

[0041] The four-dimensional geometric shaping module is used to: copy the two-dimensional geometric shaping constellation to generate two two-dimensional geometric shaping constellations, and map the two two-dimensional geometric shaping constellations to four-dimensional space in an orthogonal manner to generate a four-dimensional geometric shaping constellation;

[0042] The bitstream generation module is used to: initialize and layer the four-dimensional geometrically shaped constellation to obtain independent bitstreams for each layer of the constellation;

[0043] The constellation sequence generation module is used to: input independent bitstreams into the distribution matcher of the corresponding layer for probability distribution matching, and obtain the constellation symbol index sequence of that layer;

[0044] The hierarchical mapping module is used to: map the constellation symbol index sequence according to different Hamming weights based on the Hamming weight-based hierarchical mapping mechanism to obtain the mapped constellation points;

[0045] The probability shaping module is used to: fuse the mapped constellation points with the four-dimensional geometrically shaped constellation in quadrants to obtain a four-dimensional probability shaping constellation.

[0046] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0047] This invention not only overcomes the limitation of QAM constellation order being restricted to powers of 2 by using a high-dimensional topology method, enabling flexible construction of 4n-order constellations, but also optimizes the spatial distribution of constellation points, improves the minimum Euclidean distance, and reduces the bit error rate. Through the Hamming weight hierarchical probabilistic shaping method, the constellation structure can be adaptively adjusted according to different application requirements, effectively improving energy efficiency and noise immunity. At the same time, it reduces hardware complexity, improves constellation scalability and spectral efficiency of the communication system, and has broad application prospects. Attached Figure Description

[0048] Figure 1 The diagram shown is a flowchart of one embodiment of the four-dimensional 4nQAM constellation shaping method of the present invention;

[0049] Figure 2 The diagram shown is a structural schematic of the two-dimensional geometrically shaped constellation of the present invention in one embodiment;

[0050] Figure 3 The diagram shown is a schematic representation of the constellation point priority principle in one embodiment of the present invention.

[0051] Figure 4 The diagram shown is a schematic representation of the principle of symmetric mapping in one embodiment of the present invention.

[0052] Figure 5 The diagram shown is a schematic representation of the principle of the layered extended constellation points of the present invention in one embodiment.

[0053] Figure 6 The diagram shown illustrates the construction principle of the four-dimensional geometrically shaped constellation in one embodiment of the present invention.

[0054] Figure 7 The diagram shown is a structural schematic of the four-dimensional geometrically shaped constellation of the present invention in one embodiment;

[0055] Figure 8 The diagram shown is a structural schematic of the four-dimensional geometrically shaped constellation of the present invention in a second embodiment.

[0056] Figure 9 The diagram shown is a structural schematic of the four-dimensional geometrically shaped constellation of the present invention in a third embodiment;

[0057] Figure 10 The diagram shown is a structural schematic of the four-dimensional geometrically shaped constellation of the present invention in the fourth embodiment.

[0058] Figure 11 The diagram shown is a flowchart of the probability shaping of the present invention in one embodiment;

[0059] Figure 12 The diagram shown is a flowchart of one embodiment of the hierarchical mapping mechanism based on Hamming weights of the present invention.

[0060] Figure 13 The diagram shown is a flowchart of another embodiment of the hierarchical mapping mechanism based on Hamming weights of the present invention.

[0061] Figure 14 The diagram shown is a comparison of the bit error rates of 4nQAM constellations of the same dimension but different orders in one embodiment of the present invention.

[0062] Figure 15 The diagram shown is a two-dimensional 16QAM constellation diagram of the receiver in one embodiment of the present invention;

[0063] Figure 16 The diagram shown is a two-dimensional 24QAM constellation diagram of the receiver in one embodiment of the present invention;

[0064] Figure 17 The diagram shown is a two-dimensional 40QAM constellation diagram of the receiver in one embodiment of the present invention;

[0065] Figure 18 The diagram shown is a comparative illustration of the normalized generalized mutual information of 4nQAM constellations of the same dimension but different orders in one embodiment of the present invention.

[0066] Figure 19 The diagram shown is a comparison of the bit error rates of the 4nQAM constellation in different dimensions in one embodiment of the present invention.

[0067] Figure 20 The diagram shown is a comparative illustration of the bit error rate of the four-dimensional 12QAM constellation with different probabilities of shaping in one embodiment of the present invention. Detailed Implementation

[0068] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0069] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0070] Example 1

[0071] like Figure 1 As shown in the figure, this embodiment introduces a four-dimensional 4nQAM constellation shaping method, including the following steps:

[0072] Step 1: Quadrant-based 4nQAM constellation geometry shaping, specifically:

[0073] Using the origin of the coordinate system as the center of a square, and according to a preset priority of constellation points, the constellation points to be shaped are progressively expanded from the innermost layer to the outermost layer in concentric squares to obtain a two-dimensional geometrically shaped constellation. This two-dimensional geometrically shaped constellation is defined as an M-layer structure, where the number of constellation points in each quadrant of each layer is less than the number of layers; that is, the i-th layer can accommodate at most i constellation points in each quadrant. Figure 2 As shown.

[0074] By progressively expanding from the inner layer to the outer layer, the number of constellation points can be gradually increased, with each increment being 4 points. This supports the design of arbitrary 4n-order Quadrature Amplitude Modulation (QAM). This hierarchical structure not only simplifies the constellation construction process but also lays the foundation for subsequent optimization and performance improvement.

[0075] Regarding the spatial distribution of constellation points, a quadrant modulation mechanism is adopted. First, the constellation points are constructed in the first quadrant, and then projected to the other three quadrants through symmetrical mapping. 00 represents the first quadrant, 01 represents the second quadrant, 11 represents the third quadrant, and 10 represents the fourth quadrant. Figure 4 As shown, this method fully utilizes the symmetry of two-dimensional space to achieve a balanced distribution of constellation points on the complex plane, greatly optimizing the minimum Euclidean distance of the constellation and effectively reducing the bit error rate. 00, 01, 11, and 10 are collectively referred to as "quadrant bits." Its core logic utilizes the geometric symmetry of the two-dimensional complex plane to rapidly generate a complete constellation distribution by transforming pre-constructed reference constellation points in the first quadrant. (Refer to...) Figure 4The coordinate layout is as follows: 00 represents the first quadrant, which serves as the reference region for the initial construction of all constellation points; 01 represents the second quadrant, which is obtained by horizontally flipping and mapping the points in the first quadrant along the imaginary axis (vertical axis); 11 represents the third quadrant, which is obtained by centrally symmetric mapping and transformation of the points in the first quadrant along the origin; and 10 represents the fourth quadrant, which is generated by vertically flipping and mapping the points in the first quadrant along the real axis (horizontal axis). This quadrant reuse mechanism not only greatly simplifies the construction process and demapping computation of high-order constellations, but also ensures that the constellation points are evenly and symmetrically distributed across the entire complex plane. By maximizing the minimum Euclidean distance between constellation points, it effectively improves the system's noise resistance in complex channel environments and reduces the bit error rate.

[0076] During the construction of each layer, a preset constellation point priority is introduced to indicate the priority placement of new points during expansion. This maximizes the minimum distance between constellation points when expanding to higher-order constellations, further improving noise resistance. Figure 3 As shown, in the first quadrant, the constellation points to be shaped are sequentially extended to S1, S2, S3, S4, S5, S6, S7, S8, S9, and S1. 10 S k S m-1 S m This yields a two-dimensional geometrically shaped constellation in the first quadrant;

[0077] In other quadrants, by performing a symmetrical mapping on the two-dimensional geometrically shaped constellations in the first quadrant, we obtain the two-dimensional geometrically shaped constellations in the corresponding quadrants; the two-dimensional geometrically shaped constellations are symmetrically distributed about the quadrant bisectors;

[0078] Where S1 represents the first quadrant bisector; S2 represents the second quadrant closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S3 represents the second quadrant closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; S4 represents the third quadrant bisector; S5 represents the third quadrant closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S6 represents the third quadrant closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; S7 represents the fourth quadrant closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S8 represents the fourth quadrant closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; S9 represents the fourth quadrant second closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; S 10 This indicates that the fourth layer is the second closest to the quadrant bisector and lies between the quadrant bisector and the vertical axis; S k S indicates the quadrant bisector or the quadrant closest to the bisector and located between the quadrant bisector and the horizontal axis; m-1 This indicates that the last layer is furthest from the quadrant bisector and lies between the quadrant bisector and the horizontal axis; Sm This indicates that the last layer is the furthest from the quadrant bisector and lies between the quadrant bisector and the vertical axis.

[0079] In the construction of the two-dimensional geometric constellation in the first quadrant, the constellation points follow a progressive principle of concentric squares from the inside out. The priority allocation of constellation points in each layer is strictly based on their distance from the quadrant bisector and their symmetry. Specifically, the first layer contains only S1, which is precisely located on the quadrant bisector and serves as the geometric core starting point of the entire constellation structure. Moving to the second layer, since this layer can accommodate a maximum of two points within a single quadrant, S2 and S3 are arranged on either side of the quadrant bisector and in symmetrical positions closest to it. S2 is located below the quadrant bisector and close to the horizontal axis, while S3 is located above the quadrant bisector and close to the vertical axis. The construction logic of the third layer reverts to the quadrant bisector priority. First, the center point S4 on the quadrant bisector is determined, and then S5 and S6 are extended to both sides. These two points correspond to the symmetrical positions in this layer that are closest to the quadrant bisector and respectively biased towards the horizontal and vertical axes. The largest fourth layer follows a gradient distribution pattern from the inside out. S7 and S8, as the symmetrical points closest to the quadrant bisectors of this layer, are distributed close to the horizontal and vertical axes, respectively; while S9 and S... 10 This represents the second closest extension point of the layer to the bisector, distributed in directions close to the horizontal and vertical axes. Its physical location is closest to the edge of the coordinate axis within the same layer, thus completing the layer's full coverage from the center to the axis. Other outer layers follow the same pattern. In this embodiment, the two-dimensional geometric shaping constellation is an M-layer structure.

[0080] If the last layer is an odd number of layers, then in the outermost layer, the first constellation point lies on the quadrant bisector, i.e., S. k The other constellation points are located in the following order: closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; second closest to the quadrant bisector and located between the quadrant bisector and the horizontal axis; second closest to the quadrant bisector and located between the quadrant bisector and the vertical axis; ...; and farthest from the quadrant bisector and located between the quadrant bisector and the horizontal axis, i.e., S. m-1 The region furthest from the quadrant bisector and located between the quadrant bisector and the vertical axis, i.e., S... m ;

[0081] If the last layer is an even number of layers, then in the outermost layer, the first constellation point is located closest to the quadrant bisector and between the quadrant bisector and the horizontal axis, i.e., S. k The second constellation point is located closest to the quadrant bisector and lies between the quadrant bisector and the vertical axis, i.e., S. k+1The other constellation points are located, in order, the second closest to the quadrant bisector and between the quadrant bisector and the horizontal axis, the second closest to the quadrant bisector and between the quadrant bisector and the vertical axis, ..., and the farthest from the quadrant bisector and between the quadrant bisector and the horizontal axis, i.e., S. m-1 The region furthest from the quadrant bisector and located between the quadrant bisector and the vertical axis, i.e., S... m ;

[0082] This arrangement method, based on hierarchy and distance gradient, ensures that when constellations of order 4n are flexibly added or removed, the constellation points can always maintain the maximum minimum Euclidean distance.

[0083] Based on two-dimensional geometrically shaped constellations, this embodiment can flexibly increase or decrease the number of constellation points in units of 4, enabling the design of non-standard QAM constellations such as 2D 8QAM, 2D 12QAM, 2D 16QAM, 2D 20QAM, 2D 24QAM, 2D 28QAM, 2D 32QAM, 2D 36QAM, and 2D 40QAM, and is not limited to powers of 2 such as 4, 16, and 64. Figure 5 As shown.

[0084] Taking 2D 8QAM as an example, the four newly added points are preferentially placed at specific positions in the second layer, namely positions S2. While maintaining the overall average power, the constellation structure achieves a better Euclidean distance distribution. For 2D 12QAM, one point is added sequentially in each quadrant based on the 2D 8QAM, preferentially placed at a specific position in the second layer, namely position S3, and so on. The specific strategy can be flexibly selected according to the performance requirements of the target application. This method greatly improves the controllability of constellation order and spectral efficiency, providing theoretical and technical support for communication systems to adaptively select the optimal modulation scheme based on actual channel conditions.

[0085] A high-dimensional extension of the 4nQAM constellation was achieved through quadrant multiplexing and bit grouping. For example... Figure 6 As shown, taking four-dimensional (4D) 12QAM as an example, two two-dimensional 12QAM constellations are generated by copying the two-dimensional 12QAM constellation. The two two-dimensional 12QAM constellations are then orthogonally mapped onto four-dimensional space to form a three-dimensional four-dimensional 12QAM constellation structure, as shown below. Figures 7 to 10 As shown.

[0086] The two 2D 12QAM constellations are considered to be located in two independent 2D orthogonal subspaces. The constellation points in the first 2D constellation are responsible for forming the first two dimensions P of the four-dimensional vector. n,1 (x1, y1), the constellation points in the second two-dimensional constellation are responsible for forming the last two dimensions P of the four-dimensional vector. n,2(x2, y2), since these two subspaces are geometrically orthogonal, there is no projection or interference between them, and they can naturally combine to form a four-dimensional constellation point (P). n,1 ,P n,2 ), that is, (x1, y1, x2, y2). This orthogonal mapping method allows the two-dimensional constellation to be directly expanded in four-dimensional space, that is, any four-dimensional constellation point is composed of two sets of two-dimensional constellation points.

[0087] To maintain the symmetry and minimum Euclidean distance structure of the constellations in four-dimensional space, the system introduces a quadrant mapping mechanism when mapping two-dimensional constellations to four-dimensional space. Through unified sign control, it ensures that the quadrants to which the four-dimensional vectors belong are structurally systematically distributed, so that the combination of two-dimensional constellations in four-dimensional space still maintains a symmetrical and balanced geometric arrangement, that is:

[0088] Figure 6 The bit encoding method in the code is represented by quadrant bits Q. n With plane bit P n,1 (x1,y1),P n,2 The joint control mechanism of (x2, y2) uses quadrant bits to determine the bit symbol combination of the four-dimensional constellation point (x1, y1, x2, y2). Through conjugate control of the four-dimensional symbols, it ensures that the output constellation point falls within a specific quadrant in four-dimensional space, maintaining a strictly four-dimensional symmetrical structure for the overall constellation. Two planar bits select specific constellation points within two two-dimensional 12QAM constellations: P n,1 Determine the hierarchy and symbol index of constellation points in one of the two-dimensional planes, P n,2 The positions of constellation points in another two-dimensional plane are determined in the same way;

[0089] First, the symbol direction is generated based on the quadrant bits, and the amplitude and layer position are determined based on the planar bits. The combination of these two results in the final four-dimensional constellation points. In other words, the encoding process first uses the planar bits to select specific points of two two-dimensional constellations, and then uses the quadrant bits to uniformly determine the sign and quadrant of the four-dimensional vector. This achieves a complete mapping from the bit sequence to four-dimensional coordinates, making the encoding and demapping processes of the four-dimensional 4nQAM constellation both structured and highly reversible.

[0090] Ultimately, by orthogonally superimposing two two-dimensional constellations and reusing quadrant symmetry, a three-dimensional four-dimensional 4nQAM constellation structure is formed, achieving higher-dimensional point set construction and distance gain than two-dimensional constellations. The constellation mapping and demodulation process only needs to be designed for a single quadrant bit sequence to complete the efficient mapping of high-dimensional space. This high-dimensional mapping mechanism further improves the system capacity and resistance to multipath fading.

[0091] like Figures 7 to 10The diagram illustrates the projection of a four-dimensional constellation (x1, y1, x2, y2) into different three-dimensional subspaces. The key difference lies in the different combinations of the observation dimensions: Figure 7 and Figure 8 The focus is on demonstrating the mutual constraints between the first two-dimensional plane (x1, y1) and the components x2 and y2 of the second two-dimensional plane, reflecting the joint control of quadrant bits on bit symbol combinations and the specific linear mapping structure formed in four-dimensional space; while Figure 9 and Figure 10 The focus is on demonstrating the distribution of the second complete two-dimensional plane (x2, y2) at a specific level of the first plane component x1 or y1. This intuitively verifies the geometric orthogonal mapping characteristics of the two two-dimensional subspaces and their preservation of symmetric and balanced arrangement structures during the combination process. Through the comprehensive comparison of these four projection angles, it is not only proven that the four-dimensional 4nQAM constellation achieves a higher degree of freedom in point set construction than the two-dimensional constellation, but also verifies the technical advantages of this mapping mechanism in maintaining the constellation's structure and reversibility.

[0092] In summary, the high-dimensional topological 4nQAM geometric shaping based on quadrant multiplexing fully utilizes spatial symmetry and the principle of hierarchical progression, which not only significantly improves the scalability and energy efficiency of constellation structures, but also provides strong theoretical and methodological support for flexible modulation in future next-generation high-spectral-efficiency and adaptive broadband communication systems.

[0093] Step 2: Four-dimensional 4nQAM constellation probability shaping based on a four-dimensional multilayer parallel distributed matcher, specifically:

[0094] To adapt to the non-standard geometric structure of the four-dimensional 4nQAM constellation, a probabilistic shaping based on the four-dimensional multi-layer parallel distribution matcher (MPDM) is further proposed. This architecture not only breaks through the performance and complexity bottleneck of the traditional single constant composition distribution matcher (CCDM) under large alphabets and complex constellations, but also achieves innovative breakthroughs in algorithm mechanism and hardware feasibility.

[0095] Taking the first quadrant of the four-dimensional 40QAM constellation as an example, the four-dimensional multi-level parallel distributed matcher includes the initialization distributed matcher DM0, the hierarchical demultiplexer (DEMUX), and the multi-level parallel distributed matchers DM1~DM2. M Key modules such as the symbol combiner and the Hamming weight-based mapper, etc. Figure 11 As shown.

[0096] First, the initialization distribution matcher DM0 receives a four-dimensional geometrically shaped constellation as allocation bits (L bits). Based on the target probability distribution, it performs initial grouping and probability adaptation on the input allocation bit stream, outputting the bit streams required for each constellation layer (L1, L2, L3, L4, ...). The initialization distribution matcher DM0 not only serves as the entry point and global scheduling unit for the distribution matching process but also implements pre-optimization of the distribution constraints.

[0097] Then, the hierarchical demultiplexer further subdivides the bit streams required for each constellation layer output by the initialization distribution matcher DM0 into independent bit streams for different constellation layers, laying the foundation for subsequent multi-layer distribution matching processing. The hierarchical demultiplexer adopts a dynamic allocation strategy, which can adaptively adjust the number of bits allocated to each layer according to the target probability distribution, thereby achieving flexible probability precision control.

[0098] The core innovation of the system lies in the multi-layer parallel distributed matcher DM1~DM M In this design, each distribution matcher is independently responsible for the probability shaping of its corresponding constellation layer. Based on the constellation symbol table and target probability distribution of its layer, it maps the required bit stream of each constellation layer into a constellation symbol index sequence within the layer.

[0099] For example, the distributed matcher DM1 is responsible for the L1 layer (1 point per quadrant), the distributed matcher DM2 corresponds to the L2 layer (2 points per quadrant), and so on, up to the outer layer; each distributed matcher customizes its parameters according to the constellation symbol table and target probability distribution of its layer, and the input bit rate also increases with the layer, with the inner layer near the center of the constellation having a lower bit rate and the outer layer having a higher bit rate.

[0100] This architecture allows all distributed matchers to run in full parallel, greatly improving the overall system throughput and significantly reducing the complexity and storage requirements of each distributed matcher. Furthermore, differentiated distributed matching strategies are designed for the characteristics of each constellation layer, achieving flexible adaptation and optimal efficiency.

[0101] Secondly, the symbol combiner integrates the constellation symbol index sequences of each layer output by each distribution matcher in an orderly manner to generate a complete constellation symbol sequence.

[0102] Then, the mapper is a hierarchical mapping mechanism based on Hamming weights, such as... Figure 12 As shown, taking four-dimensional 40QAM as an example, this mechanism maps the complete constellation symbol sequence in layers according to different Hamming weights to obtain mapped constellation points. It achieves precise coordination between the probability distribution of constellation points and the geometric structure, greatly improving the flexibility of probabilistic shaping and the scientific rigor of constellation mapping.

[0103] like Figure 12As shown, the four-dimensional 40QAM constellation is divided into four layers (L1 to L4). The number of constellation points in each layer corresponds one-to-one with the Hamming weight of the codeword allowed in that layer. That is, the layer of Hamming weight is divided according to the number of non-zero elements in the codeword. The number of non-zero elements in the codeword is 0 in the first Hamming weight layer, 1 in the second Hamming weight layer, 2 in the third Hamming weight layer, and 3 or 4 in the fourth Hamming weight layer.

[0104] The codeword set in the first Hamming heavyweight layer is {0000}, corresponding to layer L1, and the number of codewords in the codeword set is... The codeword set in the second Hamming heavyweight layer is {0001}, {0010}, {0100}, and {1000}, corresponding to the L2 layer. The number of codewords in the codeword set is... The codeword set in the third Hamming heavyweight layer is {0011}, {0101}, {1001}, {0110}, {1010}, and {1100}, corresponding to layer L3. The number of codewords in the codeword set is... The codeword set in the fourth Hamming heavyweight layer is {0111}, {1011}, {1101}, {1110}, and {1111}, corresponding to layer L4. The number of codewords in the codeword set is... .

[0105] Using the independent bitstreams of each constellation layer as driving bits, the Hamming weight layer where each constellation symbol in the complete constellation symbol sequence is located is determined.

[0106] The codewords corresponding to the constellation symbols in the constellation symbol index sequence are selected from the codeword set of the Hamming weight layer to obtain the mapped constellation points. In the constellation diagram, the constellation points can be arranged in a certain order to form a constellation index sequence. In the constellation symbol index sequence, each position corresponds to a constellation symbol, and each constellation symbol corresponds to a codeword of a bit combination. The codewords at each position are set according to the actual situation. This hierarchical structure not only matches the constellation geometry but also provides a highly controllable grouping basis for the design of the distributed matcher.

[0107] Multiple distributed matchers (DM1, DM2, DM3, DM4) corresponding to codeword sets in different Hamming weight layers will generate candidate symbol indices belonging to their respective layers at the same constellation point. Since each layer processes input bits independently, at any given constellation point, multiple outputs from multiple distributed matchers exist simultaneously. However, the communication link can only transmit one valid constellation point per symbol period. Therefore, a decision-making and selection mechanism is necessary to merge these parallel-generated symbol candidates into a single output sequence, i.e., the Hamming weight-based layered mapping mechanism.

[0108] After the initial demultiplexing of the input bits is completed, the initialization distribution matcher generates an independent bit stream to indicate the symbol level. This independent bit stream serves as the driving bit, which determines the Hamming weight level to which the current symbol should fall, thus specifying which distribution matcher's output should be used as the valid symbol. Based on the level indicated by the driving bit, only the constellation symbol corresponding to that level is selected from the output streams of multiple distribution matchers, while the outputs of the other distribution matchers are directly ignored at that symbol position. Through this mechanism, the originally parallel multi-channel symbol stream is compressed into a continuous, layer-ordered single-channel symbol sequence.

[0109] like Figure 13 The figure shows Figure 12 The specific processing flow of the DM3 corresponding selection process is as follows: First, the Hamming weight layer where the current constellation symbol is located is determined based on the driving bits, and the codeword set corresponding to that Hamming weight layer is accessed accordingly. , where 'a' represents the Hamming weight layer where the constellation symbol determined by the driving bits resides. After determining the Hamming weight layer, based on the codeword 'pos' at the corresponding position of the constellation symbol in the constellation symbol index sequence, from the codeword set... The codeword C(pos,a) corresponding to the given position is selected. This process enables dynamic selection between codeword sets at different levels, ensuring that only one final valid codeword is generated for each constellation symbol's corresponding position. Figure 13 The example demonstrates how, when the driving bit indicates Hamming weight layer a, the codewords are sequentially extracted from the set of codes. The codeword that matches the set C(pos,a) is selected as the final output. For example, codeword A is 0011, codeword B is 0101, and codeword C is 0110. This structure ensures the determinism and reversibility of the symbol selection process, so that the continuity of the symbol sequence and the correct hierarchical mapping relationship can still be maintained under the condition of multi-level distribution matching.

[0110] Finally, the mapped constellation points are fused with the four-dimensional geometrically shaped constellation to obtain the four-dimensional probabilistically shaped constellation. The four-dimensional geometrically shaped constellation determines which quadrant a constellation point is ultimately located in. Since all constellation points in the four-dimensional 4nQAM are designed in the first quadrant and then mirrored sequentially to the second, third, and fourth quadrants according to the symmetry of the complex plane, the hierarchical index output by the mapper alone cannot determine the final complex plane position of a point. It is necessary to rely on the four-dimensional geometrically shaped constellation, i.e., a set of quadrant-driving bits (Q bits), to determine the sign position (i.e., the quadrant selection of the sign) of the constellation point. Therefore, the Q bits determine which quadrant a constellation point is in or which 4D quadrant combination it belongs to (two quadrant-related bits are required in the 4D extension), while each distribution matcher is responsible for the hierarchical and positional probabilistic shaping within the same quadrant.

[0111] In the process of constellation probabilistic shaping, the input four-dimensional geometrically shaped constellation is initialized and decomposed, and then assigned to distribution matchers (DM1~DM4). Each distribution matcher generates a constellation symbol index sequence based on the number of points in its layer. Through a hierarchical mapping mechanism based on Hamming weight, a dedicated constant composition distribution matching code is performed to output a four-dimensional probabilistically shaped constellation, thus realizing probabilistic shaping. This fully utilizes the natural hierarchical decision characteristics of Hamming weight, allowing bit combinations of different probabilities to naturally cluster in different energy layers, thereby effectively improving the efficiency of probabilistic shaping and the controllability of constellation point distribution.

[0112] During the demapping stage, the receiver first obtains the constellation point index based on the minimum Euclidean distance decision, then looks up the corresponding 4-bit codeword. By calculating the Hamming weight of the codeword, the layer to which it belongs can be quickly determined, and the original distribution-matching bitstream can be reconstructed based on the intra-layer mapping relationship. This mechanism possesses high duality and algorithmic simplicity throughout the mapping-demapping process, effectively improving decoding accuracy and implementation efficiency.

[0113] Step 3: Obtain the 4nQAM sculpted constellation, specifically:

[0114] The 4nQAM four-dimensional integer constellation is the four-dimensional probabilistic integer constellation obtained in step two.

[0115] Example 2

[0116] Based on Example 1, this example presents an experimental case study of a four-dimensional 4nQAM constellation shaping method:

[0117] To verify the effectiveness of the proposed quadrant multiplexing-based four-dimensional 4nQAM geometric shaping, a series of simulation experiments were conducted. The main evaluations included the bit error rate performance, mutual information characteristics, and performance gains of high-dimensional extensions of 4nQAM constellations of different dimensions and orders.

[0118] like Figure 14 As shown, the bit error rate performance of QAM constellations of the same dimension but different orders, such as 2D 12QAM, 2D 16QAM, 2D 20QAM, 2D 24QAM and 2D 40QAM, was first compared. Figure 14The data shows the trend of Bit Error Ratio (BER) decreasing as Signal Noise Ratio (SNR) increases. When the SNR is low (0-5dB range), the BER is high for all modulation schemes. As the SNR increases to the 10dB-15dB range, the BER decreases significantly and eventually approaches zero at around 15dB and above. It can be seen that lower-order QAM (such as 2D 12QAM) has a lower BER under the same SNR conditions, while higher-order QAM (such as 2D 40QAM) performs relatively poorly in low SNR environments, but can provide higher data transmission rates. Figure 15 The constellation diagram clearly shows the receiver constellation of the two-dimensional 16QAM constellation. Figure 16 The receiver constellation diagram of the two-dimensional 24QAM constellation. Figure 17 The receiver constellation diagram of the two-dimensional 40QAM constellation in the figure verifies that the proposed concentric hierarchical structure design can achieve a uniform distribution of constellation points and effectively optimize the minimum Euclidean distance.

[0119] Figure 18 The figure illustrates the relationship between Normalized Generalized Mutual Information (NGMI) and SNR for 4nQAM constellations of different orders with the same dimension. It compares five modulation schemes: 2D 12QAM, 2D 16QAM, 2D 20QAM, 2D 24QAM, and 2D 40QAM. It can be observed that as SNR increases, the NGMI value of all modulation schemes shows an upward trend, eventually approaching 1 in the high SNR region (approximately 15dB-20dB). Lower-order QAMs (such as 2D 12QAM and 2D 16QAM) exhibit higher NGMI values ​​in low SNR environments (0-5dB), indicating that they can provide more reliable information transmission in noisy channels. In contrast, higher-order QAMs (such as 2D 40QAM) have lower NGMI values ​​in the low SNR region, but the differences in NGMI among various modulation schemes gradually decrease as SNR increases to approximately 12dB-15dB.

[0120] Figure 19This paper presents the relationship between the bit error rate (BER) performance curves of traditional two-dimensional and four-dimensional QAM modulation schemes and SNR. Four modulation schemes are compared: two-dimensional 12QAM, two-dimensional 24QAM, four-dimensional 12QAM, and four-dimensional 24QAM. The graphs show that the BER of all modulation schemes decreases with increasing SNR. In the low SNR region (0-5dB), two-dimensional 24QAM exhibits the highest BER. In the medium SNR region (5dB-10dB), four-dimensional modulation schemes (four-dimensional 12QAM and four-dimensional 24QAM) begin to show advantages, exhibiting lower BERs than their corresponding two-dimensional counterparts. In particular, four-dimensional 12QAM performs best across most of the SNR range. When the SNR reaches approximately 12dB or higher, the BER of all modulation schemes approaches zero. This result demonstrates that four-dimensional QAM modulation provides better noise immunity than traditional two-dimensional QAM at the same modulation order, especially under medium channel conditions. This is significant for communication systems that need to improve transmission reliability within limited bandwidth, showcasing the potential of multi-dimensional modulation technology in enhancing communication performance.

[0121] Furthermore, Figure 20 The bit error rate (BER) performance of four-dimensional 12QAM under different probability shaping degrees λ (0.2~1) is shown. As can be observed from the figure, the BER performance of four-dimensional 12QAM exhibits a gradual improvement with increasing probability shaping degree. When λ=0.2, the system exhibits a high BER, while as λ gradually increases to 1, the BER curve shifts significantly to the left, indicating that a lower BER can be obtained under the same signal-to-noise ratio (SNR). This result verifies the effectiveness of the probability shaping scheme based on a four-dimensional multilayer parallel distributed matcher, demonstrating that fine control of system performance can be achieved by adjusting the degree of probability shaping. Especially in the high SNR region, the BER curves of four-dimensional 12QAM with different probability shaping degrees show significant performance differences, providing theoretical support for dynamically adjusting probability shaping parameters according to channel quality in practical applications.

[0122] Based on the above experimental results, this embodiment achieves flexible constellation order adjustment. Each constellation order exhibits excellent bit error rate performance and capacity characteristics. The high-dimensional expansion scheme effectively improves the system's noise immunity. The introduction of probability shaping based on a four-dimensional multilayer parallel distributed matcher further optimizes the system performance, providing a new solution for high-reliability communication.

[0123] Furthermore, the performance differences of constellations of different orders under different signal-to-noise ratio conditions provide a rich selection space for the design of adaptive modulation systems, which has important practical value. These simulation results fully verify the theoretical correctness and practical effectiveness of the proposed design scheme, laying a solid foundation for the development of modulation technology for the next generation of high-efficiency and high-reliability communication systems.

[0124] Example 3

[0125] This embodiment introduces a four-dimensional 4nQAM constellation shaping system, including:

[0126] The two-dimensional geometric shaping module is used to: expand the constellation points to be shaped from the inner layer to the outer layer in concentric squares according to the preset constellation point priority, with the origin of the coordinate system as the center of the square, to obtain a two-dimensional geometrically shaped constellation; wherein, the number of constellation points in each quadrant of each layer is less than the number of layers.

[0127] The four-dimensional geometric shaping module is used to: map two two-dimensional geometric shaping constellations orthogonally to four-dimensional space to generate a four-dimensional geometric shaping constellation;

[0128] The bitstream generation module is used to: initialize and layer the four-dimensional geometrically shaped constellation to obtain independent bitstreams for each layer of the constellation;

[0129] The constellation sequence generation module is used to: input independent bitstreams into the distribution matcher of the corresponding layer for probability distribution matching, and obtain the constellation symbol index sequence of that layer;

[0130] The hierarchical mapping module is used to: map the constellation symbol index sequence according to different Hamming weights based on the Hamming weight-based hierarchical mapping mechanism to obtain the mapped constellation points;

[0131] The probability shaping module is used to: fuse the mapped constellation points with the four-dimensional geometrically shaped constellation in quadrants to obtain a four-dimensional probability shaping constellation.

[0132] The specific functions of each module described above are explained in the relevant content of the method in Embodiment 1, and will not be repeated here.

[0133] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0134] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0135] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0136] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0137] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A four-dimensional, 4nQAM constellation shaping method, characterized by, The method comprises the following steps: A two-dimensional geometric shaping constellation is obtained by expanding the to-be-shaped constellation points according to concentric squares from the inner layer to the outer layer according to a preset constellation point priority, taking the coordinate origin as the center of the square, wherein the number of constellation points in each quadrant of each layer is lower than the layer number; Two two-dimensional geometric shaping constellations are generated by copying the two-dimensional geometric shaping constellation, and the two two-dimensional geometric shaping constellations are mapped to a four-dimensional space in a quadrature manner to generate a four-dimensional geometric shaping constellation; The four-dimensional geometric shaping constellation is initialized and layered to obtain independent bit streams of each layer constellation; The independent bit streams are input into the distribution matcher of the corresponding layer for probability distribution matching to obtain the constellation symbol index sequence of the layer; According to a hierarchical mapping mechanism based on Hamming weight, the constellation symbol index sequence is hierarchically mapped according to different Hamming weights to obtain a mapped constellation point; The mapped constellation point is fused with the four-dimensional geometric shaping constellation in the quadrant to obtain a four-dimensional probability shaping constellation; A two-dimensional geometric shaping constellation is obtained by expanding the to-be-shaped constellation points according to concentric squares from the inner layer to the outer layer according to a preset constellation point priority, taking the coordinate origin as the center of the square, wherein the number of constellation points in each quadrant of each layer is lower than the layer number; In the first quadrant, the constellation points to be shaped are sequentially expanded to S1, S2, S3, S4, S5, S6, S7, S8, S9, S 10 , …, S k , …, S m -1 , S m , to obtain a two-dimensional geometrically shaped constellation in the first quadrant; In other quadrants, the two-dimensional geometric shaping constellation in the first quadrant is symmetrically mapped to obtain the two-dimensional geometric shaping constellation in the corresponding quadrant; the two-dimensional geometric shaping constellation is symmetrically distributed about the quadrant bisector; S1 represents the first layer on the quadrant bisector; S2 represents the second layer closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S3 represents the second layer closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S4 represents the third layer on the quadrant bisector; S5 represents the third layer closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S6 represents the third layer closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S7 represents the fourth layer closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S8 represents the fourth layer closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S9 represents the fourth layer second closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S 10 represents the fourth layer second closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S k represents the last layer on the quadrant bisector or closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S m-1 represents the last layer farthest from the quadrant bisector and between the quadrant bisector and the horizontal axis; S m represents the last layer farthest from the quadrant bisector and between the quadrant bisector and the vertical axis.

2. The four-dimensional, 4nQAM constellation shaping method of claim 1, wherein, Two two-dimensional geometric shaping constellations are generated by copying the two-dimensional geometric shaping constellation, and the two two-dimensional geometric shaping constellations are mapped to a four-dimensional space in a quadrature manner to generate a four-dimensional geometric shaping constellation, comprising: Two two-dimensional constellation points are selected from the two two-dimensional geometric shaping constellations to obtain two two-dimensional constellation points; According to a preset quadrant mapping mechanism, the bit symbol combination mode of the two two-dimensional constellation points and the quadrant position in the four-dimensional space are determined to obtain a four-dimensional constellation point; A four-dimensional geometric shaping constellation is generated according to the four-dimensional constellation point.

3. The four-dimensional, 4nQAM constellation shaping method of claim 2, wherein, According to a preset quadrant mapping mechanism, the bit symbol combination mode of the two two-dimensional constellation points and the quadrant position in the four-dimensional space are determined to obtain a four-dimensional constellation point, comprising: According to the preset quadrant mapping mechanism, one of the two two-dimensional constellation points constitutes the first two dimensions of the four-dimensional constellation point, and the other two-dimensional constellation point constitutes the last two dimensions of the four-dimensional constellation point, and the two two-dimensional constellation points are orthogonal in a geometric sense, and the quadrant position of the four-dimensional constellation point in the four-dimensional space is determined to obtain the four-dimensional constellation point; The preset quadrant mapping mechanism controls the combination of the four-dimensional constellation point in the four-dimensional space to be a symmetric geometric arrangement through uniform symbols.

4. The four-dimensional, 4nQAM constellation shaping method of claim 1, wherein, The independent bit streams are input into the distribution matcher of the corresponding layer for probability distribution matching to obtain the constellation symbol index sequence of the layer, comprising: The independent bit stream is parameterized according to the constellation symbol table and the target probability distribution of the layer where the independent bit stream is located to obtain the constellation symbol index sequence of the layer.

5. The four-dimensional 4nQAM constellation shaping method of claim 1, wherein, Before the constellation symbol index sequence is hierarchically mapped according to different Hamming weights according to the hierarchical mapping mechanism based on Hamming weight, the method further comprises the following steps: The constellation symbol index sequences of the layers are integrated in order by a symbol combiner to generate a complete constellation symbol sequence.

6. The four-dimensional 4nQAM constellation shaping method of claim 1, wherein, According to a hierarchical mapping mechanism based on Hamming weight, the constellation symbol index sequence is hierarchically mapped according to different Hamming weights to obtain a mapped constellation point, comprising: Each layer constellation independent bit stream is taken as a driving bit to determine the Hamming weight layer where each constellation symbol in the constellation symbol index sequence is located; The code word of the constellation symbol at the corresponding position of the constellation symbol index sequence is selected from the code word set of the Hamming weight layer to obtain the mapped constellation point; Wherein, each position in the constellation symbol index sequence corresponds to a constellation symbol, and each constellation symbol corresponds to a code word of a bit combination.

7. The four-dimensional, 4nQAM constellation shaping method of claim 6, wherein, The level of the Hamming weight layer is divided according to the number of non-zero elements in the code word; The number of non-zero elements in the code word in the first Hamming weight layer is 0, the number of non-zero elements in the code word in the second Hamming weight layer is 1, the number of non-zero elements in the code word in the third Hamming weight layer is 2, and the number of non-zero elements in the code word in the fourth Hamming weight layer is 3 or 4.

8. The four-dimensional 4nQAM constellation shaping method of claim 7, wherein, The code word set in the first Hamming weight layer is {0000}; The code word set in the second Hamming weight layer is {0001}, {0010}, {0100}, {1000}; The code word set in the third Hamming weight layer is {0011}, {0101}, {1001}, {0110}, {1010}, {1100}; The code word set in the fourth Hamming weight layer is {0111}, {1011}, {1101}, {1110}, {1111}.

9. A four-dimensional, 4nQAM constellation shaping system, characterized by, Comprising: A two-dimensional geometric shaping module is configured to: take the coordinate origin as the center of a square, and according to a preset constellation point priority, expand the to-be-shaped constellation points in a concentric square from an inner layer to an outer layer to obtain a two-dimensional geometric shaping constellation; wherein the number of constellation points in each quadrant of each layer is lower than the layer number; A four-dimensional geometric shaping module is configured to: copy the two-dimensional geometric shaping constellation to generate two two-dimensional geometric shaping constellations, map the two two-dimensional geometric shaping constellations to a four-dimensional space in a quadrature manner to generate a four-dimensional geometric shaping constellation; A bit stream generation module is configured to: initialize the four-dimensional geometric shaping constellation to obtain independent bit streams of each layer constellation; A constellation sequence generation module is configured to: input the independent bit streams into a distribution matcher of a corresponding layer to perform probability distribution matching to obtain a constellation symbol index sequence of the layer; A hierarchical mapping module is configured to: according to a hierarchical mapping mechanism based on Hamming weight, hierarchically map the constellation symbol index sequence according to different Hamming weights to obtain a mapped constellation point; A probability shaping module is configured to: perform quadrant fusion on the mapped constellation point and the four-dimensional geometric shaping constellation to obtain a four-dimensional probability shaping constellation. Take the coordinate origin as the center of a square, and according to a preset constellation point priority, expand the to-be-shaped constellation points in a concentric square from an inner layer to an outer layer to obtain a two-dimensional geometric shaping constellation, comprising: In the first quadrant, the constellation points to be shaped are sequentially extended to S1, S2, S3, S4, S5, S6, S7, S8, S9, S 10 , …, S k , …, S m -1 , S m , to obtain a two-dimensional geometrically shaped constellation in the first quadrant; In other quadrants, the two-dimensional geometric shaping constellation in the first quadrant is symmetrically mapped to obtain the two-dimensional geometric shaping constellation in the corresponding quadrant; the two-dimensional geometric shaping constellation is symmetrically distributed about the quadrant bisector; S1 represents the first layer on the quadrant bisector; S2 represents the second layer closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S3 represents the second layer closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S4 represents the third layer on the quadrant bisector; S5 represents the third layer closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S6 represents the third layer closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S7 represents the fourth layer closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S8 represents the fourth layer closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S9 represents the fourth layer second closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S 10 represents the fourth layer second closest to the quadrant bisector and between the quadrant bisector and the vertical axis; S k represents the last layer on the quadrant bisector or closest to the quadrant bisector and between the quadrant bisector and the horizontal axis; S m-1 represents the last layer farthest from the quadrant bisector and between the quadrant bisector and the horizontal axis; S m represents the last layer farthest from the quadrant bisector and between the quadrant bisector and the vertical axis.

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