A constellation based on right tetragonal pyramid splicing and a shaping design method and system thereof

Abstract

The application discloses a constellation based on regular tetrahedron splicing and a shaping design method and system thereof, and belongs to the field of communication technologies; the method comprises the following steps: taking an origin O as a vertex, constructing four regular tetrahedrons to form a regular tetrahedron splicing structure; constructing symmetry points F, G, J, K and L of the origin O; offsetting the whole constellation to the x and y directions respectively, so that the geometric center of the constellation returns to the origin O; and optimizing the emission probability of constellation points according to the geometric positions of the constellation points in the constellation structure. Through optimization of the geometric structure of the constellation points, the constellation gain index is improved, the minimum Euclidean distance is increased, and thus the anti-interference capability is effectively improved; through overall translation of the constellation points, the average emission power is reduced, and the energy efficiency of the system is significantly improved; and in combination with the probability shaping technology, the usage probability distribution of the constellation points is optimized, the bit error rate is effectively reduced, and the transmission performance and the anti-interference capability of the communication system are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication, and particularly relates to a constellation based on positive four-pyramid splicing and a shaping design method and system thereof. BACKGROUND

[0002] With the continuous development of communication technology, especially in the field of optical communication and wireless communication, the demand for higher data rate and lower bit error rate is increasing. In order to realize efficient data transmission, constellation design becomes a key link in the modulation scheme. Due to the limitation of space utilization, the traditional two-dimensional constellation design is difficult to further improve the anti-noise performance and spectral efficiency, so three-dimensional and higher-dimensional constellation structures are gradually introduced into the communication system. Compared with two-dimensional constellation, three-dimensional constellation can utilize more spatial degrees of freedom, and improve the anti-interference ability and transmission performance of the system by reasonably distributing constellation points. However, the complexity of three-dimensional constellation design also increases the difficulty of design and optimization, especially in improving system gain and reducing bit error rate, there are still many challenges.

[0003] In constellation design, the minimum Euclidean distance is an important indicator to measure the anti-noise performance of the constellation, and a larger minimum Euclidean distance can effectively improve the anti-interference ability of the communication system and reduce the bit error rate. Although three-dimensional constellation can increase the spatial degrees of freedom, when the number of constellation points increases, the minimum Euclidean distance between points decreases, and the reliability of the system also decreases, resulting in that the constellation figure of merit (CFM) is still not high enough, which limits the further improvement of the performance of the communication system. Therefore, how to reasonably distribute the constellation points in three-dimensional space to increase the minimum Euclidean distance becomes the key to improving the performance of the communication system.

[0004] Geometric shaping (GS) is a method of optimizing the geometric position of constellation points to improve the performance of the constellation. Through geometric shaping, the minimum Euclidean distance can be increased, and the CFM can be improved. In the existing three-dimensional constellation design, although some have combined probabilistic shaping (PS) to optimize the distribution of constellation points, the overall effect is limited, and the CFM has not reached the ideal level. In addition, there is a lack of global optimization of the overall position of the constellation, resulting in that the system performance cannot achieve the optimal. SUMMARY

[0005] In view of the deficiencies of the prior art, the purpose of the present application is to provide a constellation based on positive four-pyramid splicing and a shaping design method and system thereof, which solves the problems in the prior art.

[0006] The purpose of the present application can be achieved by the following technical solutions:

[0007] A constellation shaping design method based on regular tetrahedron splicing, comprising the following steps:

[0008] With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure;

[0009] Symmetrical points F, G, J, K and L of the origin O are constructed;

[0010] The entire constellation is offset in x and y directions respectively, so that the geometric center of the constellation returns to the origin O;

[0011] According to the geometric positions of each constellation point in the constellation structure, the emission probability of the constellation point is optimized.

[0012] Further, in the four regular tetrahedrons, the bottom surface of the first regular tetrahedron is composed of vertices A1, B1, B2 and A2, and the length of the bottom surface and each waist is 2d; the bottom surface of the second regular tetrahedron is composed of vertices B1, B2, C2 and C1, and the length of the bottom surface and each waist is 2d; the bottom surface of the third regular tetrahedron is composed of vertices C1, C2, D2 and D1, and the length of the bottom surface and each waist is 2d; the bottom surface of the fourth regular tetrahedron is composed of vertices D1, D2, E2 and E1, and the length of the bottom surface and each waist is 2d.

[0013] Further, two pentagons A1B1C1D1E1 and A2B2C2D2E2 are formed in the regular tetrahedron splicing structure, and the vertical distance between the origin O and the two pentagons is d, and the distance between A1 and E1 and A2 and E2 is 2.1773d.

[0014] Further, the symmetrical point F is symmetrical to the origin O with respect to the pentagon A1B1C1D1E1, and the symmetrical point G is symmetrical to the origin O with respect to the pentagon A2B2C2D2E2; and the distance between the symmetrical points F and G and the origin O is 2d.

[0015] Further, the symmetrical point J is symmetrical to the origin O with respect to the quadrilateral A1E1E2A2, the symmetrical point K is symmetrical to the origin O with respect to the quadrilateral D1E1E2D2, and the symmetrical point L is symmetrical to the origin O with respect to the quadrilateral C1D1D2C2; and the distance between the origin O and the symmetrical points K and L is 2d.

[0016] Further, the entire constellation is offset by 0.2722d and -0.0481d in x and y directions respectively.

[0017] Further, the probability distribution of the constellation point is determined by the following formula:

[0018]

[0019] In the formula, P x(x) represents the probability distribution of constellation point x, v is a non-negative scaling factor used to adjust the constellation shaping degree and the information entropy of the modulation scheme, when v = 0, the probability distribution of the constellation point is uniform, and the information entropy reaches the maximum value, and when v > 0, the probability distribution gradually converges to the low information entropy direction; |x| 2 represents the power of the constellation point x; is a normalization factor used to ensure that the sum of all constellation point probabilities is 1; X is the set of all constellation points; x represents a constellation point in the current constellation; x' represents a constellation point in the constellation set X, used for normalization calculation.

[0020] A constellation shaping design system based on regular tetrahedron splicing, comprising:

[0021] A regular tetrahedron construction module: taking the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure;

[0022] A symmetry point construction module: symmetry points F, G, J, K and L of the origin O are constructed;

[0023] A constellation translation module: the entire constellation is offset in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O;

[0024] And a probability shaping module: the transmission probability of each constellation point in the constellation structure is optimized according to the geometric position of the constellation point.

[0025] A constellation based on regular tetrahedron splicing is designed by using the above-mentioned constellation shaping design method based on regular tetrahedron splicing.

[0026] A computer storage medium storing a readable program, when the program is run, the above-mentioned constellation shaping design method based on regular tetrahedron splicing can be executed.

[0027] The beneficial effects of the present application are:

[0028] 1、The present application optimizes the geometric structure of the constellation point, improves the constellation gain index, increases the minimum Euclidean distance, and effectively improves the anti-interference ability.

[0029] 2、By translating the constellation point as a whole, the average transmission power is reduced, and the energy efficiency of the system is significantly improved.

[0030] 3、Combined with the probability shaping technology, the probability distribution of the constellation point is optimized, the bit error rate is effectively reduced, and the transmission performance and anti-interference ability of the communication system are improved. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments or prior art description. Obviously, for those skilled in the art, based on these drawings, other drawings can also be obtained without any creative effort.

[0032] Figure 1 is a flow chart of a regular tetrahedron splicing constellation structure design of the present application;

[0033] Figure 2 is a mapping diagram of the regular tetrahedron splicing constellation of the present application. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be clearly and completely described in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative effort fall within the protection scope of the present application.

[0035] Embodiment 1

[0036] As shown in Figure 1 , a constellation design method based on regular tetrahedron splicing includes the following steps:

[0037] S1, constructing a regular tetrahedron splicing structure;

[0038] As shown in Figure 1 (a), four regular tetrahedrons are constructed with the origin O as the vertex, the bottom surface of the first regular tetrahedron is composed of the vertices A1, B1, B2 and A2, and the length of the bottom surface and each waist is 2d. Similarly, the other three regular tetrahedrons are also formed by different four vertices and the origin O, and the side surfaces are connected to each other to jointly form a regular tetrahedron splicing structure around the origin O. For the other three regular tetrahedrons, the structure is specifically:

[0039] The bottom surface of the second regular tetrahedron is composed of the vertices B1, B2, C2 and C1, and the length of the bottom surface and each waist is 2d; the bottom surface of the third regular tetrahedron is composed of the vertices C1, C2, D2 and D1, and the length of the bottom surface and each waist is 2d; and the bottom surface of the fourth regular tetrahedron is composed of the vertices D1, D2, E2 and E1, and the length of the bottom surface and each waist is 2d.

[0040] Through this geometric layout, two pentagons A1B1C1D1E1 and A2B2C2D2E2 are formed, which are not standard regular pentagons, the vertical distance between the origin O and the two pentagons is d, and the distance between A1 and E1 and the distance between A2 and E2 is 2.1773d.

[0041] S2, constructing the symmetry points F and G of the origin O;

[0042] As shown in (b) of FIG. 1, Figure 1 As shown in (b) of FIG. 1,

[0043] S3, constructing the symmetry points J, K, L of the O point;

[0044] As shown in (c) of FIG. 1, Figure 1 As shown in (c) of FIG. 1,

[0045] S4, offsetting the entire constellation by 0.2722d and -0.0481d in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O.

[0046] The geometric shaping design of the constellation is completed through S1-S4, and through the above geometric construction, the number of point pairs satisfying the minimum Euclidean distance is maximized, a total of 47 pairs, ensuring that the constellation points are uniformly distributed in the three-dimensional space, reducing the average power of the whole, thereby greatly improving the constellation gain index CFM.

[0047] The constellation gain index calculation formula is known as:

[0048]

[0049] Where d min is the minimum Euclidean distance between constellation points, P avg is the average power of the constellation points, and the calculation method is the average of the square of the distance of all constellation points from the origin.

[0050] It can be calculated that the CFM of the traditional three-dimensional constellation with a regular hexahedron as a primitive is 0.4726, the CFM of the regular quadrangular pyramid spliced constellation structure designed by the application before overall translation is 0.8981, and the CFM after translation is 0.9138. Compared with the traditional regular hexahedron primitive three-dimensional constellation, it is improved by 0.4412, which can greatly reduce the bit error rate of the communication system under the same power.

[0051] After the positions of the 16 constellation points are determined, the constellation points are mapped in the application, and the bits carrying digital information are mapped into 16 serial numbers, and one serial number contains 4 bits. Since there are more adjacent point pairs in the constellation designed by the application, the Hamming distance of any adjacent symbols that cannot be completely Gray mapped is 1, so the total Hamming distance of the system is minimized, and the total difference between adjacent bits of the whole system is minimized, so that the bit error rate is minimized under the same symbol error rate. The system of the application also adopts probability shaping, and the probability of the points in the constellation close to the origin is greater than that of the points far from the origin, so the priority is allocated according to the distance, and the Hamming distance of the central point is minimized in priority. The mapping rule is shown in Table 1 and Figure 2

[0052] Table 1: Coordinates of constellation points and mapping bits

[0053]

[0054] S5, according to the geometric positions of the constellation points in the constellation structure, the transmission probability of the constellation points is optimized to realize probability shaping of the constellation points;

[0055] After the geometric shaping of the three-dimensional constellation is completed, the transmission probability of the constellation points is further optimized by the probability shaping technology to reduce the bit error rate and improve the transmission performance of the system. Specifically, for each constellation point in the three-dimensional constellation structure, first, based on the geometric position of the constellation point in the three-dimensional space, the influence of the constellation point on the overall system performance is evaluated. In order to better improve the system energy efficiency and increase the communication reliability, the application selectively allocates higher transmission probability to the constellation points close to the origin, thereby effectively reducing the bit error rate.

[0056] The transmission probability distribution of the constellation points is determined by the following formula:

[0057]

[0058] where P x (x) represents the probability distribution of the constellation point x. v is a non-negative scaling factor used to adjust the constellation shaping degree and the information entropy of the modulation scheme. When v = 0, the probability distribution of the constellation point is uniform, and the information entropy reaches the maximum value. When v > 0, the probability distribution gradually converges to the low information entropy direction. |x| 2 represents the power of the constellation point x. is a normalization factor used to ensure that the sum of the probabilities of all constellation points is 1. X is the set of all constellation points. x represents a constellation point in the current constellation diagram. x' ∈ X represents a constellation point in the constellation point set X, which is used for normalization calculation.

[0059] The following table lists the information entropy and constellation gain index corresponding to different v values.

[0060] ​Table 2 Influence of different probability shaping parameters on constellation information entropy and gain index

[0061]

[0062] As can be seen from Table 2, through probability shaping, the transmission probability of constellation points is reasonably optimized, and compared with the constellation without probability shaping, the system after probability shaping has higher reliability and anti-interference ability. This optimization ensures that the system is closer to the Shannon limit under the same power condition, meeting the demand of modern optical communication and wireless communication systems for efficient and reliable data transmission.

[0063] Based on the similar inventive concept, the embodiment of the application also provides a computer storage medium, which stores a readable program, and when the program runs, the operation of the above-mentioned constellation shaping design method based on the splicing of regular tetrapods can be performed.

[0064] Based on the similar inventive concept, the embodiment of the application provides an electronic device, which comprises a processor, a memory, a communication interface and a communication bus, and the processor, the memory and the communication interface complete communication with each other through the communication bus.

[0065] The memory is used to store at least one executable instruction, and the executable instruction makes the processor perform the operation corresponding to the above-mentioned constellation shaping design method based on the splicing of regular tetrapods.

[0066] Based on the similar inventive concept, the embodiment of the application also provides a computer program product, which comprises computer instructions, and the computer instructions instruct a computing device to perform the operation corresponding to the above-mentioned constellation shaping design method based on the splicing of regular tetrapods.

[0067] Embodiment 2

[0068] In this embodiment, a constellation shaping design system based on the splicing of regular tetrapods is proposed, which specifically comprises:

[0069] A regular tetrapod construction module: taking the origin O as the vertex, four regular tetrapods are constructed to form a regular tetrapod splicing structure;

[0070] A symmetric point construction module: symmetric points F, G, J, K and L of the origin O are constructed;

[0071] A constellation translation module: the entire constellation is offset in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O;

[0072] And a probability shaping module: according to the geometric positions of the constellation points in the constellation structure, the transmission probability of the constellation points is optimized.

[0073] The method of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CDROM, RAM, floppy disk, hard disk or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded over a network and will be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a special-purpose processor or programmable or special-purpose hardware (such as an ASIC or FPGA). It will be understood that a computer, a processor, a microprocessor controller or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, a processor or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown here, the execution of the code converts the general-purpose computer into a special-purpose computer for executing the method shown here.

[0074] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention, and such changes and modifications fall within the scope of the invention as claimed.

Claims

1. A constellation shaping design method based on regular tetrahedron splicing, characterized in that: The following steps are involved: With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure; Construct the symmetrical points F, G, J, K and L about the origin O; Shift the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O; Optimize the transmission probability of constellation points based on the geometric position of each constellation point in the constellation structure; Among the four regular square pyramids, the base of the first regular square pyramid is composed of vertices A1, B1, B2 and A2, and the length of the side of the base and the length of each waist are both 2d; the base of the second regular square pyramid is composed of vertices B1, B2, C2 and C1, and the length of the side of the base and the length of each waist are both 2d; the base of the third regular square pyramid is composed of vertices C1, C2, D2 and D1, and the length of the side of the base and the length of each waist are both 2d; the base of the fourth regular square pyramid is composed of vertices D1, D2, E2 and E1, and the length of the side of the base and the length of each waist are both 2d; Two pentagons are formed in the regular tetrahedron splicing structure: A1B1C1D1E1 and A2B2C2D2E2. The vertical distances between the origin O and the two pentagons are both d, and the distances between A1 and E1 and between A2 and E2 are both 2.1773d. The symmetric point F is symmetric to the origin O about the pentagon A1B1C1D1E1, and the symmetric point G is symmetric to the origin O about the pentagon A2B2C2D2E2; and the distance between the symmetric points F and G and the origin O is 2d; The symmetric point J is symmetric to the origin O about quadrilateral A1E1E2A2, the symmetric point K is symmetric to the origin O about quadrilateral D1E1E2D2, and the symmetric point L is symmetric to the origin O about quadrilateral C1D1D2C2; and the distance between the origin O and the symmetric points K and L is 2d.

2. The constellation shaping design method based on regular quadrangular pyramid splicing according to claim 1, characterized in that: The entire constellation is offset by 0.2722d and -0.0481d in the x and y directions respectively.

3. The constellation shaping design method based on regular tetrahedron splicing according to claim 1, characterized in that: The probability distribution of constellation points is determined by the following formula: Where, P x (x) represents the probability distribution of constellation point x, v is a non-negative scaling factor used to adjust the degree of constellation shaping and the information entropy of the modulation scheme. When v = 0, the probability distribution of the constellation points is uniform and the information entropy reaches the maximum value. When v > 0, the probability distribution gradually converges to the direction of low information entropy; |x| 2 represents the power of constellation point x; is a normalization factor used to ensure that the sum of the probabilities of all constellation points is 1; X is the set of all constellation points; x represents a constellation point in the current constellation diagram; x′∈X represents a constellation point in the constellation point set X, which is used for normalization calculation.

4. A constellation shaping design system based on regular tetrahedron splicing, capable of executing the design method according to any one of claims 1 to 3, characterized in that: include: Regular tetrahedron building module: With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure; Symmetrical point construction module: construct the symmetrical points F, G, J, K and L of the origin O; Constellation translation module: shifts the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O; And, the probability shaping module: optimizes the transmission probability of the constellation points based on the geometric position of each constellation point in the constellation structure.

5. A constellation based on regular tetrahedron splicing, characterized in that: The constellation shaping design method based on splicing regular tetrahedrons as described in any one of claims 1 to 3 is adopted for design.

6. A computer storage medium storing a readable program, characterized in that: When the program is running, it can execute the constellation shaping design method based on regular tetrahedron splicing as described in any one of claims 1 to 3.

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