A multi-dimensional constellation visualization method based on color and geometric shape markers

Abstract

The application discloses a multi-dimensional constellation visualization method based on color and geometric shape marking, and belongs to the technical field of communication, which comprises the following steps: collecting physical coordinates of three-dimensional constellation points; assigning a predefined color label to each three-dimensional constellation point under the condition that the minimum Euclidean distance is invariant; fusing a color dimension value corresponding to the color label with the physical coordinates of the three-dimensional constellation points, and adopting a subspace product decomposition mapping strategy to perform structure division to generate a physical coordinate set of four-dimensional constellation points; performing four-dimensional bit mapping through a Gray mapping algorithm and adding a predefined geometric shape label; fusing a geometric shape label value corresponding to the geometric shape label with the physical coordinates of the four-dimensional constellation points, and adopting the subspace product decomposition mapping strategy to perform structure division to generate a physical coordinate set of five-dimensional constellation points, and obtaining the five-dimensional constellation points through five-dimensional bit mapping through the Gray mapping algorithm.

Description

TECHNICAL FIELD

[0001] The application relates to a multi-dimensional constellation visualization method based on color and geometric shape marking, and belongs to the technical field of communication. BACKGROUND

[0002] In a traditional two-dimensional modulation constellation, symbol points are only distributed along two degrees of freedom of amplitude and phase, although the hardware implementation is mature and the processing complexity is low, when the constellation order increases, the constellation figure of merit (CFM) is reduced, which limits the system noise immunity performance and power efficiency. To overcome these bottlenecks, researchers have expanded the modulation constellation to three dimensions, by introducing additional degrees of freedom such as subcarriers or phase differences, so that the symbols have greater geometric compactness and higher minimum distance in three-dimensional space, thereby significantly reducing the bit error rate under the same bandwidth condition. However, even so, when the three-dimensional constellation gradually advances to a higher order, the complexity and signal processing burden still increase exponentially, making it difficult to meet the dual demands of high speed and high reliability of the next generation communication system. In order to further improve the dimension utilization rate, the academic circle once added color coding in the three-dimensional constellation projection diagram, mapping different symbol sets to different colors as a "fourth dimension" visual marker. This color marking not only can intuitively distinguish multiple groups of parameters or signal categories in scientific research display and teaching demonstration, but also to some extent helps engineers quickly identify performance differences.

[0003] However, the prior art has the technical problems of insufficient high-order constellation visualization distinction and high mapping complexity. As the number of constellation points or classification labels increases, the distinction capacity of a single color quickly reaches the upper limit, and the friendliness to colorblind or visually impaired users is insufficient, making it difficult to balance the readability and accessibility of high-dimensional visualization. At the same time, high-order constellations also face the problem of dramatic increase in mapping complexity in real systems: when the number of points is 64, 128 or even higher, the number of neighbors for each symbol increases dramatically, and it becomes almost impossible to maintain single-bit adjacency through Gray coding. SUMMARY

[0004] The purpose of the present application is to provide a multi-dimensional constellation visualization method based on color and geometric shape marking, which splits high-order constellations into low-order subspaces by using Gray coding, and marks four-dimensional constellations with predefined colors and five-dimensional constellations with geometric shapes, to solve the technical problems of insufficient high-order constellation visualization distinction and high mapping complexity in the prior art. With the help of five-dimensional expansion, the CFM value of the constellation is further improved, the power efficiency is enhanced, and the system bit error rate is reduced.

[0005] To solve the above technical problems, the present application is realized by adopting the following technical scheme:

[0006] The application provides a multi-dimensional constellation visualization method based on color and geometric shape marking, comprising:

[0007] collecting physical coordinates of three-dimensional constellation points;

[0008] assigning a predefined color label to each three-dimensional constellation point under the condition that the minimum Euclidean distance between three-dimensional constellation points is unchanged;

[0009] fusing the color dimension value corresponding to the color label and the physical coordinates of the three-dimensional constellation point, and adopting a subspace product decomposition mapping strategy to perform structure division to generate a physical coordinate set of four-dimensional constellation points;

[0010] performing four-dimensional bit mapping on the physical coordinate set of the four-dimensional constellation points through a Gray mapping algorithm to obtain four-dimensional constellation points;

[0011] attaching a predefined geometric shape label to the four-dimensional constellation points according to the subspace shape formed by the four-dimensional constellation points;

[0012] fusing the geometric shape label value corresponding to the geometric shape label and the physical coordinates of the four-dimensional constellation points, and adopting a subspace product decomposition mapping strategy to perform structure division to generate a physical coordinate set of five-dimensional constellation points;

[0013] performing five-dimensional bit mapping on the physical coordinate set of the five-dimensional constellation points through a Gray mapping algorithm to obtain five-dimensional constellation points;

[0014] wherein the distance between any two constellation points of different color dimensions or different geometric shape labels is not less than the minimum Euclidean distance, and the three-dimensional distance between any two points of the five-dimensional constellation is not less than the minimum Euclidean distance.

[0015] Further, the physical coordinates of the three-dimensional constellation points are collected, comprising:

[0016] receiving the physical coordinates of the three-dimensional constellation points through a preset interface;

[0017] wherein the minimum Euclidean distance between constellation points is 2, and the coordinate value rule of the three-dimensional constellation points with a cubic base constellation comprises:

[0018] for a three-dimensional constellation comprising 8 three-dimensional constellation points:

[0019] the coordinate value is taken from the set {−1, +1} to correspond to eight corner points in the three-dimensional space;

[0020] for a three-dimensional constellation comprising 16 three-dimensional constellation points:

[0021] on the structure of the three-dimensional constellation comprising 8 three-dimensional constellation points, 8 points with coordinates (±2.1547, ±2.1547, ±2.1547) are additionally added to form a 16-point layout;

[0022] For a three-dimensional constellation containing 32 three-dimensional constellation points:

[0023] On the structure of a three-dimensional constellation containing 8 three-dimensional constellation points, 24 points with coordinates (±3, ±1, ±1), (±1, ±3, ±1) and (±1, ±1, ±3) are additionally added to form a 32-point layout;

[0024] For a three-dimensional constellation containing 64 three-dimensional constellation points:

[0025] The coordinate values are taken from the set {−3,−1,+1,+3}, including 4³=64 three-element combinations to form a 64-point layout.

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

[0027] The present application effectively reduces the coupling interference between dimensions in multi-dimensional constellation design by superimposing color coding and geometric shape markers as independent dimensions onto three-dimensional constellation coordinates, combining subspace product decomposition mapping strategy and Gray mapping algorithm for low-order subspace splitting and mapping of high-order constellation, and improves the parallel decoding efficiency of the receiving end for multi-dimensional label features. At the same time, the improvement of the CFM value after five-dimensional expansion further optimizes the power allocation uniformity of the constellation points, so that the system realizes the cooperative optimization of the bit error rate and the spectral efficiency under high-order modulation while maintaining the low complexity Gray mapping design, solving the technical problems of insufficient visualization distinction of high-order constellation and high mapping complexity in the prior art. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 is a flowchart of a multi-dimensional constellation visualization method based on color and geometric shape markers provided by an embodiment of the present application;

[0029] Figure 2 is a schematic diagram of three-dimensional constellation coordinates based on a cubic as a basic unit for different orders provided by an embodiment of the present application;

[0030] Figure 3 is a process diagram of expanding a three-dimensional constellation to a five-dimensional constellation provided by an embodiment of the present application;

[0031] Figure 4 is a simulation process diagram provided by an embodiment of the present application;

[0032] Figure 5 is a signal-to-noise ratio performance comparison diagram of different dimension expansion schemes provided by an embodiment of the present application. DETAILED DESCRIPTION

[0033] The technical solutions of the present application will be described in detail below with reference to the drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application. In the case of no conflict, the technical features in the embodiments and the embodiments can be combined with each other.

[0034] Embodiment 1: In view of the technical problems that the existing high-order constellation has insufficient visualization distinction and excessively high mapping complexity, the existing technology is often limited to increasing the capacity by increasing the order in two-dimensional or three-dimensional space, which will cause the constellation points to be densely stacked and the demodulation difficulty to be greatly increased. Therefore, the present embodiment proposes an innovative multi-dimensional optimization strategy: the high-order constellation is disassembled into multiple low-order subsets, and the constellation structure is reconstructed by the subspace product combination mode of the multi-dimensional space, for example, 32x2 decomposition in four-dimensional space, 16x2x2 or 8x4x2 decomposition in five-dimensional space. This decomposition mode can not only keep the total number of constellation points unchanged, but also can convert the complex high-order mapping problem into simplified design in the low-order subspace, thereby significantly reducing the mapping algorithm complexity.

[0035] Further, in order to meet the needs of intuitive display and demodulation optimization of high-dimensional constellation, the present embodiment designs a general visualization scheme: breaking through the single-dimensional limitation of traditional color marking, constructing a multi-dimensional label system by superimposing color coding and geometric shape marking two independent visual variables. Among them, the color dimension is used to distinguish the subspace characteristics, and the geometric shape label is used to strengthen the constellation point category identification, and the two can work together to improve the readability and demodulation efficiency of the high-dimensional constellation.

[0036] As shown in Figure 1 , the present embodiment introduces a multi-dimensional constellation visualization method based on color coding and geometric shape superimposed marking, comprising:

[0037] Step 1: Collecting the physical coordinates of three-dimensional constellation points.

[0038] The present application collects the physical coordinates of three-dimensional constellation points to ensure the accuracy of the coordinate space definition, supports the fusion processing of color coding and geometric shape marking and high-order mapping optimization, and avoids the demodulation performance decline caused by the dimension expansion due to the initial coordinate error.

[0039] Step 2: Assigning a predefined color label to each three-dimensional constellation point under the condition that the minimum Euclidean distance between the three-dimensional constellation points is unchanged.

[0040] The application introduces a pre-defined color label as an independent marking dimension under the premise of maintaining the minimum Euclidean distance physical characteristics between three-dimensional constellation points, which not only improves the visual distinction of three-dimensional constellation points to solve the problem of insufficient visualization distinction of high-order constellations, but also avoids the decline of demodulation reliability caused by directly adjusting physical coordinates, thereby providing low-coupling marking support for subsequent four-dimensional fusion.

[0041] Step three: fusing the color dimension value corresponding to the color label with the physical coordinates of the three-dimensional constellation points, and adopting a subspace product decomposition mapping strategy to perform structure division to generate a physical coordinate set of the four-dimensional constellation points.

[0042] The application fuses the color dimension as an independent coordinate axis with the three-dimensional physical coordinates to construct a four-dimensional coordinate system, realizes visualization expansion from three-dimensional to four-dimensional, maintains the original physical distance characteristics, increases the information capacity, and provides a low-complexity subspace basis for subsequent Gray mapping through independent fusion of the color dimension, thereby simplifying the high-order mapping design.

[0043] Step four: performing four-dimensional bit mapping on the physical coordinate set of the four-dimensional constellation points through a Gray mapping algorithm to obtain a four-dimensional constellation point.

[0044] The application adopts a Gray mapping algorithm to perform bit mapping on the four-dimensional coordinates, significantly reduces the bit error probability of the receiving end during demodulation through the characteristic that only one bit is different between adjacent four-dimensional constellation points, maintains a low-complexity mapping design after four-dimensional expansion, and solves the problem of rising bit error rate caused by the increase of dimensions in traditional high-order mapping.

[0045] Step five: adding a pre-defined geometric shape label to the four-dimensional constellation points according to the subspace shape formed by the four-dimensional constellation points.

[0046] The application adds geometric shape labels such as circles and triangles based on the shape characteristics of the four-dimensional constellation, further strengthens the category identification of the four-dimensional constellation points through the geometric shape labels, breaks through the single-dimension limitation of traditional color marking, improves the readability of high-dimensional constellations, and avoids real-time calculation overhead through the pre-defined characteristics of geometric shapes, thereby providing efficient visual marking support for five-dimensional expansion.

[0047] Step six: fusing the geometric shape label value corresponding to the geometric shape label with the physical coordinates of the four-dimensional constellation points, and adopting a subspace product decomposition mapping strategy to perform structure division to generate a physical coordinate set of the five-dimensional constellation points.

[0048] This invention constructs a five-dimensional coordinate system by fusing geometric shape labels as independent coordinate axes with four-dimensional physical coordinates, thereby achieving a visualization extension from four-dimensional to five-dimensional and further improving information capacity. The independent fusion of geometric shape labels, combined with a subspace multiplication and integral decomposition mapping strategy such as 16×2×2 decomposition, decomposes the five-dimensional mapping into low-order subspace mappings, simplifying the complexity of high-order mappings while maintaining the low coupling characteristics between dimensions.

[0049] Step 7: The physical coordinate set of the five-dimensional constellation points is mapped to five-dimensional bits using the Gray mapping algorithm to obtain the five-dimensional constellation points.

[0050] This invention employs the Gray mapping algorithm to perform bit mapping on five-dimensional coordinates. By leveraging the characteristic that there is only a 1-bit difference between adjacent five-dimensional constellation points, the probability of bit misjudgment during demodulation at the receiver is further reduced. Combined with the improvement of CFM value after five-dimensional expansion, the power distribution uniformity of constellation points is optimized. While maintaining a low-complexity mapping design, the invention achieves synergistic optimization of bit error rate and spectral efficiency under high-order modulation, solving the demodulation performance bottleneck problem caused by dimensional coupling in traditional high-order constellations.

[0051] Among them, the distance between any two constellation points of labels with different color dimensions or different geometric shapes is not less than the minimum Euclidean distance, and the three-dimensional distance between any two points of the five-dimensional constellation is not less than the minimum Euclidean distance.

[0052] In this invention, the constraint that the distance between any two constellation points of different color dimensions or different geometric shapes is not less than the minimum Euclidean distance is achieved through a dimension-independent labeling and subspace multiplication decomposition mapping strategy. This ensures that the introduction of additional dimensions does not destroy the minimum Euclidean distance characteristic of the original physical coordinates, thus guaranteeing the reliability of decomposition.

[0053] Example 2: Based on the same inventive concept as Example 1, this example introduces a multi-dimensional constellation visualization method based on color coding and geometric shape overlay markings, including:

[0054] Step 1: Collect the physical coordinates of the three-dimensional constellation points.

[0055] This embodiment receives the physical coordinates of three-dimensional constellation points through a preset interface. Taking a cube as the basic unit of the constellation as an example, the three-dimensional constellations containing 8, 16, 32, and 64 three-dimensional constellation points are named Cube-8, Cube-16, Cube-32, and Cube-64, respectively. The three-dimensional coordinates of Cube-8, Cube-16, Cube-32, and Cube-64 are as follows: Figure 2 As shown, where, Figure 2 In this context, (a) represents Cube-8. Figure 2 In this context, (b) represents Cube-16.Figure 2 In this example, (c) represents Cube-32, and the minimum Euclidean distance among the constellation points is 2 by default.

[0056] Among them, the minimum Euclidean distance between constellation points is 2, and the coordinate rules for the three-dimensional constellation points with a cube as the base constellation include:

[0057] For a three-dimensional constellation containing 8 three-dimensional constellation points:

[0058] The coordinate values ​​are taken from the set {−1,+1}, which correspond to the eight corner points in three-dimensional space.

[0059] For a three-dimensional constellation containing 16 three-dimensional constellation points:

[0060] On the structure of a three-dimensional constellation containing eight three-dimensional constellation points, an additional eight points with coordinates (±2.1547,±2.1547,±2.1547) are added to form a 16-point layout;

[0061] For a three-dimensional constellation containing 32 three-dimensional constellation points:

[0062] On the structure of a three-dimensional constellation containing 8 three-dimensional constellation points, an additional 24 points with coordinates (±3,±1,±1), (±1,±3,±1), and (±1,±1,±3) are added to form a 32-point layout;

[0063] For a three-dimensional constellation containing 64 three-dimensional constellation points:

[0064] The coordinate values ​​are taken from the set {−3,−1,+1,+3}, which includes 4³=64 triplet combinations to form a 64-point layout.

[0065] In this embodiment, the physical coordinates of the three-dimensional constellation points are represented as follows:

[0066] ;

[0067] In the formula, Represents the physical coordinates of points in a three-dimensional constellation. Indicates the first The x-coordinates of three-dimensional constellation points Indicates the first The ordinates of three-dimensional constellation points Indicates the first The vertical coordinates of a three-dimensional constellation point This represents the total number of points in a three-dimensional constellation.

[0068] Step 2: Assign a predefined color label to each three-dimensional constellation point while keeping the minimum Euclidean distance between the three-dimensional constellation points constant.

[0069] In this embodiment, the set of values ​​for the color dimension corresponding to the color label is represented as follows:

[0070] ;

[0071] In the formula, This represents the set of possible values ​​for the color dimension corresponding to the color label. Indicates the first The color dimension value corresponding to each color label This indicates the total number of color tags.

[0072] Step 3: Merge the color dimension values ​​corresponding to the color labels with the physical coordinates of the three-dimensional constellation points, and use the subspace multiplication and integral decomposition mapping strategy to perform structural partitioning to generate a set of physical coordinates of the four-dimensional constellation points.

[0073] Step 4: The physical coordinate set of the four-dimensional constellation points is mapped to four-dimensional bits using the Gray mapping algorithm to obtain the four-dimensional constellation points.

[0074] Step 5: Based on the subspace shape formed by the four-dimensional constellation points, attach predefined geometric shape labels to the four-dimensional constellation points.

[0075] In this embodiment, the set of values ​​for the geometric shape label corresponding to the geometric shape label is represented as follows:

[0076] ;

[0077] In the formula, This represents the set of possible values ​​for the geometric shape label corresponding to the geometric shape label. Indicates the first The geometric shape label value corresponding to each geometric shape label. This indicates the total number of geometric shape labels.

[0078] Step 6: Merge the geometric shape label values ​​corresponding to the geometric shape labels with the physical coordinates of the four-dimensional constellation points, and use the subspace multiplication integral solution mapping strategy to divide the structure and generate a set of physical coordinates of the five-dimensional constellation points.

[0079] In this embodiment, the physical coordinates of the five-dimensional constellation points are represented as follows:

[0080] ;

[0081] In the formula, Represents the physical coordinates of a point in a five-dimensional constellation.

[0082] Step 7: The physical coordinate set of the five-dimensional constellation points is mapped to five-dimensional bits using the Gray mapping algorithm to obtain the five-dimensional constellation points.

[0083] In this embodiment, after the constellation dimensions represented by the color labels and shape labels are superimposed, multiple labels can be intuitively distinguished in the 3D projection map. Since points within the same color label and the same geometric label completely coincide with the 3D constellation, the 3D distance between any two points in its 5D constellation is not less than the minimum Euclidean distance; while the distance between any two constellation points with different color dimensions or different geometric shape labels is not less than the minimum Euclidean distance, expressed as:

[0084] ;

[0085] In the formula, Indicates the first The color dimension value corresponding to each color label Indicates the first The color dimension value corresponding to each color label This is a logical judgment symbol, representing "any". Indicates the minimum Euclidean distance. Indicates the first The geometric shape label value corresponding to each geometric shape label. Indicates the first The geometric shape label value corresponding to each geometric shape label.

[0086] In this embodiment, the three-dimensional distance between any two points of the five-dimensional constellation is not less than the minimum Euclidean distance, expressed as:

[0087] ;

[0088] In the formula, Indicates the first The x-coordinates of three-dimensional constellation points Indicates the first The ordinates of three-dimensional constellation points Indicates the first The vertical coordinates of a three-dimensional constellation point Indicates the first The x-coordinates of three-dimensional constellation points Indicates the first The ordinates of three-dimensional constellation points Indicates the first The vertical coordinates of three-dimensional constellation points.

[0089] In summary, the combined use of color and shape labels not only maintains the minimum Euclidean distance characteristic of three-dimensional constellations, but also visually achieves clear differentiation of multiple classification labels with more than four dimensions.

[0090] like Figure 3 As shown, where Figure 3 (a) in the diagram represents the constellation whose color dimension has been expanded. Figure 3(b) in (a) represents a constellation with shape dimension expansion, Figure 3 (c) in (b) represents a constellation with color dimension and shape dimension joint expansion, based on the three-dimensional base constellation Cube-8 containing 8 constellation points, by introducing color label C and geometric shape label H, a five-dimensional constellation can be constructed and named 5D-Cube, and the specific expansion method is:

[0091] The color label C takes 4 equally spaced values {−3,−1,1,3}, and the interval between adjacent values is 2, and the geometric label H takes 2 equally spaced values {−1,1}, and the interval between adjacent values is also 2, forming 64 five-dimensional constellation points, i.e. three-dimensional base constellation point number × color label level number × geometric label level number = 8 × 4 × 2 = 64.

[0092] Since the minimum Euclidean distance of the three-dimensional constellation Cube-8 is 2, and the numerical interval between any two adjacent levels of the additional dimensions color label C and geometric shape label H is not less than 2, therefore, after introducing the color label C and the geometric shape label H, the total Euclidean distance between any two points in the high-dimensional space, i.e. four-dimensional or five-dimensional, still satisfies the constraint that it is not less than 2, specifically:

[0093] When two three-dimensional constellation points completely coincide in three-dimensional coordinate level but have different color values, the additional distance caused by the difference in color label is 2, such as the interval between C=−3 and C=−1;

[0094] When two three-dimensional constellation points completely coincide in three-dimensional coordinate level and have the same color value, but have different shape values, the additional distance caused by the difference in geometric label is 2, such as the interval between H=−1 and H=1;

[0095] If there is a difference in any dimension of the three-dimensional coordinates, color values, and shape values between two points, the total distance will be calculated by the square root of the sum of the squares of the differences in each dimension, and the minimum value is still 2 when there is only a single dimension difference.

[0096] This numerical allocation scheme not only strictly satisfies the minimum distance constraint in the geometric layer, but also ensures the reliability of the demodulation, and realizes the intuitive and visual distinction of high-dimensional constellations through the value of the color label C and the value of the geometric shape, solving the problem of insufficient visual distinction of traditional high-order constellations.

[0097] Similarly, if a three-dimensional base constellation Cube-16 containing 16 constellation points is taken as the base constellation, only 4 color labels are introduced in the fourth dimension, and a 16*4=64-point four-dimensional constellation named 4D-Cube is obtained; if 2 color labels are introduced in the fourth dimension and 2 geometric labels are introduced in the fifth dimension, a 16*2*2=64-point five-dimensional constellation named 5D-Cube is obtained. If a three-dimensional base constellation Cube-32 containing 32 constellation points is taken as the base constellation, only 2 color labels are introduced in the fourth dimension, and a 32*2=64-point four-dimensional constellation named 4D-Cube is obtained.

[0098] In the process of performing four-dimensional bit mapping on the physical coordinate set of the four-dimensional constellation points through the Gray mapping algorithm and performing five-dimensional bit mapping on the physical coordinate set of the five-dimensional constellation points through the Gray mapping algorithm, when the constellation order increases, the constellation gain index decreases, wherein the constellation gain index is represented as:

[0099] ;

[0100] In the formula, E represents the constellation gain index, dmin represents the minimum Euclidean distance, P represents the normalized average power of each two dimensions of the constellation, Ei represents the average Euclidean power of the Euclidean energy of the coordinate vector of the i-th constellation point, N represents the total number of three-dimensional constellation points, and D represents the constellation dimension.

[0101] The CFM values of the constellations are calculated and shown in Table 1.

[0102] Table 1: CFM values of different constellations

[0103]

[0104] In this embodiment, the three-dimensional constellation points are defined in a three-dimensional coordinate space, and the coordinate values of each three-dimensional constellation point remain unchanged. A three-bit binary Gray code {000, 001, 010, 011, 100, 101, 110, 111} is used as a label to encode the coordinates of the three-dimensional constellation points. The four-dimensional constellation points are composed of the coordinates of the three-dimensional constellation points and color labels, and a two-bit binary Gray code {00, 01, 11, 10} is used to encode the color labels. The five-dimensional constellation points are composed of the coordinates of the three-dimensional constellation points, color labels, and geometric shape labels, and a one-bit binary Gray code {0, 1} is used to encode the geometric shape labels. ​​​​​​​​​

[0105] Three-dimensional constellation points use three-bit Gray code {000, 001, 010, 011, 100, 101, 110, 111} for encoding, ensuring that any adjacent points are only one bit different in geometry. On this basis, four-dimensional constellation points use two-bit Gray sequence {00, 01, 11, 10} for encoding, so that symbols that only switch in the fourth dimension also maintain a single-bit difference. Five-dimensional constellation points use one-bit Gray code {0, 1} for encoding, distinguishing between two geometric shapes. Thus, the bit encoding between each dimension strictly satisfies the Gray property, thereby helping to reduce the bit error rate caused by adjacent point misjudgment and improve the overall robustness of the system. Table 2 lists the 64 constellation points in the 5D-Cube constellation and their corresponding 6-bit Gray code mapping relationship. The mapping uses Gray mapping. Table 3 lists the Gray code mapping relationship of the 4D-Cube(8x4) constellation formed by copying the three-dimensional Cube-8 along the fourth dimension four times, i.e., the "8x4" structure, a total of 32 points. Table 4 lists the Gray code mapping relationship of the 5D-Cube(8x4x2) constellation formed by copying the four-dimensional 4D-Cube(8x4) along the fifth dimension twice, i.e., the "8x4x2" structure, a total of 64 points.

[0106] Table 2: Gray code mapping corresponding to three-dimensional constellation Cube-8 coordinates

[0107]

[0108] Table 3: Gray code mapping corresponding to four-dimensional constellation 4D-Cube(8x4) coordinates

[0109]

[0110] Table 4: Gray code mapping corresponding to five-dimensional constellation 5D-Cube(8x4x2) coordinates

[0111]

[0112] This embodiment is to verify the performance advantages of the multi-dimensional expansion and mapping optimization scheme. Simulations were performed in MATLAB software, as shown in Figure 4 , including a sending end, a receiving end, and a channel module. The sending end completes the input of the bit stream, the mapping of the constellation points, and the modulation. The receiving end demodulates and demaps the received signal. AWGN noise is introduced in the channel to simulate the bit error rate performance of the communication system under different signal-to-noise ratios.

[0113] The signal-to-noise ratio curves of different dimensional expansion schemes under the same signal-to-noise ratio are as follows Figure 5As shown, the embodiment is uniformly expressed as (A x B x C) to represent the multi-dimensional expansion structure of the constellation, wherein A is a basic point number, and B and C are respectively a replication multiple in the 4th dimension and the 5th dimension. It can be seen that the basic constellation Cube-64 has the maximum bit error rate, the curves of the four-dimensional constellations 4D-Cube(32 x 2) and 4D-Cube(16 x 4) introduced with color labels are obviously lower than that of the basic constellation Cube-64, which indicates that the single-dimensional expansion introduced with the color label can bring significant performance improvement, and the curves of the five-dimensional constellations 5D-Cube(16 x 2 x 2) and 5D-Cube(8 x 4 x 2) introduced with the geometric shape label are further lowered than those of the four-dimensional constellations introduced with the color label, especially the 5D-Cube(8 x 4 x 2) maintains the optimal bit error rate level, so it can be known that the joint expansion constellation dimension introduced with the color label and the geometric shape label and the subspace product decomposition mapping strategy can effectively reduce the bit error rate on the basis of preserving the original three-dimensional minimum Euclidean distance, thereby verifying the superiority of the multi-dimensional constellation scheme of the embodiment.

[0114] In summary of the above embodiment, the color coding and the geometric shape label are superimposed on the constellation coordinates as independent dimensions, the high-order constellation is split into low-order subspaces in combination with the Gray mapping, the coupling interference between the dimensions in the multi-dimensional constellation design is effectively reduced, and the parallel decoding efficiency of the multi-dimensional label features at the receiving end is improved; meanwhile, the CFM value after the five-dimensional expansion is improved, the power distribution uniformity of the constellation points is further optimized, the bit error rate and the spectral efficiency under the high-order modulation are cooperatively optimized while the low-complexity Gray mapping design is maintained, and the technical problems of insufficient visual distinction degree of the high-order constellation and excessively high mapping complexity in the prior art are solved.

[0115] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0116] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks.

[0117] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks.

[0118] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks.

[0119] The embodiments of the present application described above are merely intended to illustrate the principles of the present application, and the present application is not limited to the above-described embodiments, and the above-described embodiments are merely illustrative, but not restrictive, and those skilled in the art can make many forms under the guidance of the present application without departing from the purpose of the present application and the scope of the claims, and these are all within the protection of the present application.

Claims

1. A method for visualizing multi-dimensional star constellations based on color and geometric shape markers, characterized in that, The method comprises the following steps: collecting physical coordinates of three-dimensional constellation points; assigning a predefined color label to each three-dimensional constellation point while keeping the minimum Euclidean distance between the three-dimensional constellation points unchanged; fusing the color dimension value corresponding to the color label with the physical coordinates of the three-dimensional constellation points, and performing structural division by using a subspace product decomposition mapping strategy to generate a set of physical coordinates of four-dimensional constellation points; performing four-dimensional bit mapping on the set of physical coordinates of the four-dimensional constellation points by using a Gray mapping algorithm to obtain four-dimensional constellation points; applying a predefined geometric shape label to the four-dimensional constellation points according to the shape of the subspace formed by the four-dimensional constellation points; fusing the geometric shape label value corresponding to the geometric shape label with the physical coordinates of the four-dimensional constellation points, and performing structural division by using a subspace product decomposition mapping strategy to generate a set of physical coordinates of five-dimensional constellation points; performing five-dimensional bit mapping on the set of physical coordinates of the five-dimensional constellation points by using a Gray mapping algorithm to obtain five-dimensional constellation points; wherein the distance between any two constellation points of different color dimensions or different geometric shape labels is not less than the minimum Euclidean distance, and the three-dimensional distance between any two points of the five-dimensional constellation is not less than the minimum Euclidean distance.

2. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 1, wherein, The method for collecting physical coordinates of three-dimensional constellation points comprises the following steps: receiving physical coordinates of three-dimensional constellation points through a preset interface; wherein the minimum Euclidean distance between constellation points is 2, and the coordinate value rules of the three-dimensional constellation points with a cubic base constellation include: for a three-dimensional constellation containing 8 three-dimensional constellation points: the coordinate values are taken from the set {−1, +1} to correspond to eight corner points in three-dimensional space, respectively; for a three-dimensional constellation containing 16 three-dimensional constellation points: on the structure of the three-dimensional constellation containing 8 three-dimensional constellation points, 8 points with coordinates (±2.1547, ±2.1547, ±2.1547) are additionally added to form a 16-point layout; for a three-dimensional constellation containing 32 three-dimensional constellation points: on the structure of the three-dimensional constellation containing 8 three-dimensional constellation points, 24 points with coordinates (±3, ±1, ±1), (±1, ±3, ±1), and (±1, ±1, ±3) are additionally added to form a 32-point layout; for a three-dimensional constellation containing 64 three-dimensional constellation points: the coordinate values are taken from the set {−3, −1, +1, +3}, including 4³ = 64 three-element combinations to form a 64-point layout.

3. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 1, wherein, The physical coordinates of the three-dimensional constellation points are represented as: ； wherein denotes the physical coordinates of a three-dimensional constellation point, denotes the horizontal coordinate of the th three-dimensional constellation point, denotes the vertical coordinate of the th three-dimensional constellation point, denotes the vertical coordinate of the th three-dimensional constellation point, denotes the total number of three-dimensional constellation points.

4. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 3, wherein, the value set of the color dimension value corresponding to the color label is represented as: ； In the formula, a value set of color dimension values corresponding to the color label, a color dimension value corresponding to the i-th color label, a color dimension value corresponding to the i-th color label, a total number of color labels.

5. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 4, wherein, the value set of the geometric shape label value corresponding to the geometric shape label is represented as: ； In the formula, denotes a value set of the geometric shape label value corresponding to the geometric shape label, denotes the geometric shape label value corresponding to the geometric shape label, denotes the geometric shape label value corresponding to the geometric shape label, denotes the total number of geometric shape labels.

6. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 5, wherein, the physical coordinates of the five-dimensional constellation points are represented as: ； wherein denotes the physical coordinates of the five-dimensional constellation point.

7. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 1, wherein, the distance between any two constellation points of different color dimensions or different geometric shape labels is not less than the minimum Euclidean distance, represented as: ； In the formula, represents the color dimension value corresponding to the color label, represents the color dimension value corresponding to the color label, is a logical judgment symbol, representing "arbitrary", represents the minimum Euclidean distance, represents the geometric shape label value corresponding to the geometric shape label, represents the geometric shape label value corresponding to the geometric shape label.

8. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 7, wherein, the three-dimensional distance between any two points of the five-dimensional constellation is not less than the minimum Euclidean distance, represented as: ； wherein represents the abscissa of the th three-dimensional constellation point, represents the ordinate of the th three-dimensional constellation point, represents the z-coordinate of the th three-dimensional constellation point, represents the abscissa of the th three-dimensional constellation point, represents the ordinate of the th three-dimensional constellation point, represents the z-coordinate of the th three-dimensional constellation point.

9. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 1, wherein, in the process of performing four-dimensional bit mapping on the set of physical coordinates of the four-dimensional constellation points by using a Gray mapping algorithm and performing five-dimensional bit mapping on the set of physical coordinates of the five-dimensional constellation points by using a Gray mapping algorithm to obtain five-dimensional constellation points, when the constellation order increases, the constellation gain index decreases, wherein the constellation gain index is represented as: ； wherein denotes the constellation gain exponent, denotes the minimum Euclidean distance, denotes the normalized average power per two dimensions of the constellation, denotes the Euclidean energy of the coordinate vector of the i-th constellation point denotes the average Euclidean power of the coordinate vector of the i-th constellation point, denotes the total number of three-dimensional constellation points, denotes the constellation dimension.

10. The color and geometric shape marker based multi-dimensional constellation visualization method of claim 1, wherein, The three-dimensional constellation points are defined in a three-dimensional coordinate space, and the coordinate values of each three-dimensional constellation point remain unchanged, and a three-bit binary Gray code {000, 001, 010, 011, 100, 101, 110, 111} is used as a label to encode the coordinates of the three-dimensional constellation points; The four-dimensional constellation points are composed of the coordinates of the three-dimensional constellation points and color labels, and a two-bit binary Gray code {00, 01, 11, 10} is used to encode the color labels; The five-dimensional constellation points are composed of the coordinates of the three-dimensional constellation points, color labels and geometric shape labels, and a one-bit binary Gray code {0, 1} is used to encode the geometric shape labels.

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