Three-dimensional space odd-order constellation design method based on index modulation
By optimizing the subcarrier index and symbol mode index using a three-dimensional chaotic system and index modulation technology, a three-dimensional odd-order 27QAM constellation was designed, which solved the data security problem of the PON system and achieved higher information transmission capacity and security.
Patent Information
- Application Number
- CN202511597034.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-04
- Publication Date
- 2026-02-06
AI Technical Summary
Existing PON systems have data security vulnerabilities, especially since the even-order signal structure is fixed and easily cracked by brute force, and existing encryption methods cannot effectively guarantee data security.
A three-dimensional odd-order constellation design method based on index modulation is adopted. The signal is perturbed in multiple dimensions by a three-dimensional chaotic system, and combined with three-dimensional spatial coding and index modulation technology, the subcarrier index and symbol mode index are optimized to form a 27QAM constellation design.
It achieves higher information transmission volume and data security, prevents brute-force attacks from unauthorized receivers, and improves the system's security performance.
Smart Images
Figure CN121485897A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of communications, and relates to optical transmission technology, specifically to a three-dimensional odd-order constellation design method based on index modulation. Background Technology
[0002] With the development of technologies such as 5G, virtual reality, and the metaverse, new demands are being placed on current communication systems. The increasing number of users and transmission traffic also exacerbates security issues and spectral efficiency problems under limited bandwidth. For current communication systems, fiber optic communication dominates due to its low cost and strong anti-interference capabilities. Passive Optical Networks (PONs) offer advantages such as wide bandwidth, low power consumption, and low cost, making them the primary technology used in access networks. PON technology has undergone numerous upgrades, including Time Division Multiplexing (TDM), Wavelength Division Multiplexing (WDM), and Code Division Multiplexing (CDM). Currently, Orthogonal Frequency Division Multiplexing (OFDM) PON is widely used and is considered the main direction for future access. Furthermore, in terms of coding and modulation techniques, researchers have conducted various studies to further improve the spectral efficiency of information transmission within existing bandwidths. Subcarrier indexing modulation (LCM) explores a new dimension for transmitting additional information. By selecting a certain number of silent subcarriers and utilizing their positions to transmit additional information, it achieves the transmission of additional data without increasing bandwidth. This increases data transmission volume while remaining compatible with current PON system architectures.
[0003] However, the architecture of PON systems also has certain security issues. The use of broadcast in the downlink of PON makes it vulnerable to unauthorized data eavesdropping. Furthermore, most communication schemes revolve around even-order signals or even powers of 2, resulting in a rigid and inflexible structure that is susceptible to brute-force attacks. These factors contribute to the increasing prominence of data security issues. To address these security vulnerabilities in data communication, commonly used encryption methods in communication systems include physical layer encryption and network layer encryption. Network layer encryption schemes are mostly implemented through various security protocols, but with the increasing volume of user data, key management becomes problematic, failing to effectively guarantee data security. Physical layer encryption, due to its lower cost and better security performance, is widely used, such as chaotic laser encryption, quantum key distribution, and chaotic encryption. However, chaotic laser encryption suffers from problems such as high bandwidth dependence, inability to meet the requirements of high-speed optical communication, and difficulty in synchronizing the transmitting and receiving ends. Quantum key distribution technology faces challenges such as slow key generation, technical limitations, and high cost, hindering its practical application. Summary of the Invention
[0004] Purpose of the Invention: Current 3D QAM constellation transmission schemes are mostly based on even-order signals or even powers of 2, resulting in rigid and inflexible structures that are vulnerable to brute-force attacks. Furthermore, most existing DSP transmission schemes suffer from security vulnerabilities. This invention provides a 3D odd-order constellation design method based on index modulation. It employs a 3D chaotic system to perform multi-dimensional perturbations on the signal's bits, subcarriers, and symbol points to improve transmission security. Simultaneously, by combining 3D spatial coding and index modulation techniques, additional information is transmitted by indexing the subcarriers. Furthermore, the patterns of the indexed subcarriers are indexed again, resulting in zero points on the 3D coordinate system, thus creating the constellation design effect. While transmitting more information, the invention also completes the design of a 27QAM constellation with odd-order signals in 3D space.
[0005] Technical Solution: To achieve the above objectives, this invention provides a three-dimensional odd-order constellation design method based on index modulation, comprising the following steps:
[0006] S1: The initial signal is XOR-encrypted at the bit level using a scrambled sequence generated by a three-dimensional chaotic system;
[0007] S2: Divide the XOR-encrypted signal into sub-blocks according to the number of bits;
[0008] S3: Use a three-dimensional chaotic system to scramble the subcarriers and symbol points after the sub-blocks are grouped to complete the basic encryption;
[0009] S4: Perform subcarrier indexing and symbol mode indexing sequentially on the basic encrypted signal to obtain a three-dimensional constellation diagram;
[0010] S5: The three-dimensional constellation diagram enters the optical fiber channel after passing through the OFDM system to obtain the received signal;
[0011] S6: The received signal is demodulated through the mode index to obtain the second symbol index bit. Then, the carrier index bit of the subcarrier index is recovered according to the mode. The symbol point and subcarrier are restored in sequence according to the scrambling sequence generated by the chaotic system. After sub-block recombination with the index bit matrix, the initial information is obtained by XOR recovery.
[0012] Furthermore, in step S1, the three-dimensional chaotic system employs a 3D chaotic model to achieve multi-layer encryption. The expression of the 3D chaotic model is as follows:
[0013]
[0014] Where X, Y, and Z are the first state variable, the second state variable, and the third state variable, respectively, and a, b, c, and d are the first system parameter, the second system parameter, the third system parameter, and the fourth system parameter, respectively.
[0015] Furthermore, in step S1, the initial data is a randomly generated binary data stream. After generating bit information, the initial data is XORed with a chaotic sequence X generated by X. The generation operation of the chaotic sequence X is as follows:
[0016]
[0017] Where mod(-) is the remainder function, floor(-) is the floor function, and X1 is the binarized sequence obtained by the 6th decimal place of the chaotic sequence, which is XORed with the randomly generated data.
[0018] Furthermore, the sub-block grouping in step S2 specifically includes:
[0019] First, the data transmission bits and index bits are separated. The index bits are further divided into subcarrier index bits and symbol index bits. These three parts of bits are then grouped again, with the data bits divided into 40 sub-blocks of 3 bits each. A 224 matrix, simultaneously dividing the subcarrier index bits into 3-bit sub-blocks of 40. A 32-bit matrix, with the sign index bits divided into 40 sub-blocks of 2 bits each. A matrix of 32 is used to facilitate subsequent indexing steps.
[0020] Furthermore, step S3 specifically includes:
[0021] The chaotic sequences generated using Y and Z from the chaotic sequence are used to scramble the subcarriers and symbol points of the signal, respectively, and then applied to the 40° of the transmitted signal. The specific operation for a 224 data matrix is as follows:
[0022]
[0023] First, sort the chaotic sequences Y and Z in ascending order and then generate matrices by reciprocal. Then, multiply these matrices with the original matrices to generate a scrambled square matrix with orders of subcarrier number and symbol number, respectively. Each row and column of the square matrix contains a 1, and the remaining elements are all marked as 0. Extract the positions of the 1s from the square matrices generated by Y and Z to generate two scrambled sequences. Here, mod(-) is the remainder function, and sort(-) is the ascending order sorting function.
[0024] Furthermore, the subcarrier indexing method in step S4 is as follows:
[0025] 40 after multi-dimensional encryption perturbation The 224 data matrix is divided into 1 Each group of 7 represents seven columns of subcarriers, for a total of 40. 32 groups, which correspond exactly to 40 in the subcarrier index. A 32 matrix is used; next, subcarrier indexing is performed, specifically by inserting a subcarrier into each group. Since each subcarrier index bit is 3 bits, it represents exactly eight cases. These eight cases are then mapped to the positions where empty subcarriers are inserted after there are already 7 columns of subcarriers in each group.
[0026] Furthermore, the method for symbol pattern indexing in step S4 is as follows:
[0027] The index subcarrier represents silence, meaning no information is transmitted; the coordinates are (0,0,0). (0,0,0) is split into two subcarrier columns. One column is determined by the subcarrier index and is designated as column i, while the other is designated as column 8-i+1. For the symbol mode index, the column with more zeros in the coordinates is used as the reference, where zero indicates that the data is not mapped to that coordinate position but is mapped sequentially. Since the symbol modes on the conjugate subcarriers in the group are complementary, this ensures that all data is mapped to the coordinate matrix. Furthermore, an additional 2 bits of symbol mode index are transmitted in each group. Finally, in each subcarrier group, an additional 3 bits of subcarrier index and 2 bits of symbol mode index are transmitted, allowing for the transmission of more information compared to non-indexed modulation.
[0028] Furthermore, the acquisition of the three-dimensional constellation diagram in step S4 includes:
[0029] Since the symbol pattern expands (0,0,0) to other cases, a series of new constellation points will be generated; at the same time, (0,0,0) continues to generate constellation points at the origin, and due to the cube design of the original 8QAM, the constellation points formed by the subsequent coordinates still belong to the original 8QAM constellation points and will not generate new constellation points, thus obtaining a three-dimensional constellation map.
[0030] Furthermore, in step S5, for the transmission of the three-dimensional constellation diagram, a fast inverse Fourier transform (IFFT) is first performed, with the row and column operations performed twice sequentially. After the IFFT, the frequency domain signal is converted into a time domain signal. To reduce inter-symbol interference, a cyclic prefix and suffix are added before and after the symbols. Then, the modulated parallel time domain signal is converted from parallel to serial to a serial signal for entry into the optical fiber channel. At the receiving end, the reverse operation is performed, and the received signal to be decrypted is obtained after serial-to-parallel conversion, removal of cyclic prefixes and suffixes, and Fourier transform.
[0031] Further, step S6 specifically includes:
[0032] A1: Index bit of the demodulation symbol mode, selected as 3. An 8-bit matrix is used for detection. The constellation points at the center of the six faces and the origin are demodulated by determining the face (symbol pattern) to which they belong, and the symbol index bits are recovered.
[0033] A2: Demodulate the subcarrier index bits based on the subcarrier position information where the symbol pattern is located;
[0034] A3: Following the scrambling sequence generated by the chaotic system, the symbol points and subcarriers are scrambled and restored sequentially. Then, after merging and recombining the sub-blocks with the index bit matrix, an XOR operation is performed to restore the initial information.
[0035] This invention differs from existing QAM modulation methods by employing indexed modulation technology to achieve a 27QAM constellation design in three-dimensional space. By optimizing subcarrier indexed modulation and performing symbol mode indexing after subcarrier indexing, more information can be transmitted. Furthermore, due to the characteristics of three-dimensional constellation coding, new constellation points are generated based on 8QAM, achieving odd-order constellation construction. In addition, a three-dimensional chaotic system is used to perform multi-dimensional perturbations on bits, subcarriers, and symbol points. For legitimate receivers, knowing the constellation modulation format and coding method, correct decryption and demodulation can be performed. For illegitimate receivers, not knowing the modulation format, brute-force cracking is difficult, thus ensuring the security of the transmitted signal.
[0036] Beneficial Effects: Compared with existing technologies, this invention cleverly optimizes subcarrier index modulation technology and combines it with the characteristics of three-dimensional constellation coding. After implementing subcarrier indexing, it performs silent symbol indexing again, achieving the transmission of more additional information compared to existing subcarrier index modulation. Simultaneously, it employs a unique constellation design, unlike existing constellation diagrams of different orders, realizing an odd-order constellation 3D in three-dimensional space. 3 The invention employs a 27QAM constellation design. Furthermore, the solution utilizes a three-dimensional chaotic encryption system to perturb the signal in multiple dimensions, effectively countering brute-force attacks from unauthorized receivers and synergistically enhancing the system's security performance. Attached Figure Description
[0037] Figure 1 This is a schematic flowchart of the method of the present invention;
[0038] Figure 2 A phase trajectory diagram of a three-dimensional chaotic system;
[0039] Figure 3 This is a schematic diagram of subcarrier indexing;
[0040] Figure 4 This is a schematic diagram of the original 8QAM constellation;
[0041] Figure 5 This is a schematic diagram illustrating the principle and process of symbolic pattern indexing.
[0042] Figure 6 Index the symbol pattern to the corresponding rule graph;
[0043] Figure 7 This is a 27QAM odd-order constellation diagram constructed after index modulation;
[0044] Figure 8 The 27QAM constellation diagram for the receiving end;
[0045] Figure 9 This is the 8QAM constellation diagram after index bit extraction. Detailed Implementation
[0046] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.
[0047] like Figure 1 As shown, this embodiment provides a three-dimensional odd-order constellation design method based on index modulation, including the following steps:
[0048] S1: The initial signal is XOR-encrypted at the bit level using a scrambled sequence generated by a three-dimensional chaotic system;
[0049] The three-dimensional chaotic system uses a 3D chaotic model to achieve multi-layer encryption. The expression of the 3D chaotic model is as follows:
[0050]
[0051] Where X, Y, and Z are the first, second, and third state variables, respectively, and a, b, c, and d are the first, second, third, and fourth system parameters, respectively. In this embodiment, when a = -0.6, b = 3, c = -10, and d = -0.3, the system is a chaotic system. In this embodiment, the initial values X0, Y0, and Z0 of the 3D chaotic model are set to (0, 0, 0). The partial differential equations can be solved using the Runge-Kutta method, and the phase diagram of the obtained chaotic model is shown below. Figure 2 As shown. From Figure 2 It can be observed that the value ranges of the three chaotic sequences in this model are (-6.6, 6.6), (-10.2, 10.2), and (-2.8, 2.8).
[0052] The initial data is a randomly generated binary data stream. After generating 33280 bits of information, the initial data is bitwise XORed with a chaotic sequence X generated by the first state variable X. The generation operation of the chaotic sequence X is as follows:
[0053]
[0054] Where mod(-) is the remainder function, floor(-) is the floor function, and X1 is the binarized sequence obtained by the 6th decimal place of the chaotic sequence, which is XORed with the randomly generated data.
[0055] S2: Divide the XOR-encrypted signal into sub-blocks according to the number of bits;
[0056] In this embodiment, the data transmission bits and index bits are first separated, resulting in 26,880 data bits and 6,400 index bits. The 6,400 index bits are further divided into 3,840 subcarrier index bits and 2,560 symbol index bits. These three parts of bits are then grouped again, with the data bits divided into 40 sub-blocks of 3 bits each. A 224 matrix, simultaneously dividing the subcarrier index bits into 3-bit sub-blocks of 40. A 32-bit matrix, with the sign index bits divided into 40 sub-blocks of 2 bits each. A matrix of 32 is used to facilitate subsequent indexing steps.
[0057] S3: Use a three-dimensional chaotic system to scramble the subcarriers and symbol points after the sub-blocks are grouped to complete the basic encryption;
[0058] The chaotic sequences generated using Y and Z from the chaotic sequence are used to scramble the subcarriers and symbol points of the signal, respectively, and then applied to the 40° of the transmitted signal. The specific operation for a 224 data matrix is as follows:
[0059]
[0060] First, sort the chaotic sequences Y and Z in ascending order and then generate matrices by reciprocal. Then, multiply these matrices with the original matrices to generate a scrambled square matrix with orders of subcarrier number and symbol number, respectively. Each row and column of the square matrix contains a 1, and the remaining elements are all marked as 0. Extract the positions of the 1s from the square matrices generated by Y and Z to generate two scrambled sequences. Here, mod(-) is the remainder function, and sort(-) is the ascending order sorting function.
[0061] S4: Perform subcarrier indexing and symbol mode indexing sequentially on the basic encrypted signal to obtain a three-dimensional constellation diagram;
[0062] Subcarrier index:
[0063] like Figure 3 As shown, 40 after multi-dimensional encryption perturbation The 224 data matrix is divided into 1 Each group of 7 represents seven columns of subcarriers, for a total of 40. 32 groups, which correspond exactly to 40 in the subcarrier index. A 32-bit matrix is used; next, subcarrier indexing is performed by inserting a subcarrier into each group. Since each subcarrier index bit is 3 bits, it represents eight possible cases. These eight cases are then mapped to the positions where a new subcarrier is inserted after 7 columns of subcarriers in each group. For example, when the index bit is 001, it corresponds to inserting a new subcarrier at position 2, resulting in 1. The subcarrier group consists of 8 subcarriers, and the inserted subcarriers contain no information. However, their positions allow for the transmission of an additional 3 bits of information. After subcarrier indexing, it is found that the 7 columns of subcarriers in each group become 8 columns of subcarriers, meaning the data matrix becomes 40. 256.
[0064] Symbol pattern index:
[0065] Then, a 3D mapping is performed. Due to the characteristics of 3D constellation encoding, each point in the data matrix representing a constellation is represented as 3D coordinates (x, y, z) after 3-bit mapping, i.e., 40. A matrix of 256 becomes 120 after mapping. A matrix of size 256. Each cell is now divided into three rows and one column, with the three rows representing the coordinates of each dimension. To construct a three-dimensional constellation diagram, this embodiment uses the classic 8QAM three-dimensional space for mapping, where the minimum Euclidean distance is 2. The 8QAM constellation diagram is shown below. Figure 4 As shown.
[0066] According to existing subcarrier indexing, the indexed subcarrier represents silence and does not transmit any information, i.e., the coordinates are (0,0,0). Other data is normally mapped to eight points, thus only generating a new point at the origin. This invention, however, additionally applies symbolic mode indexing, such as... Figure 5 As shown, the same eight columns of subcarriers are grouped together. In this embodiment, (0,0,0) is split into two columns of subcarriers. One column is determined by the subcarrier index and is denoted as the i-th column. The other column is specified as the (8-i+1)-th subcarrier. For the symbol pattern index, this embodiment uses the column with more 0s in the coordinates as the reference and specifies four cases, as detailed below. Figure 6 As shown in the diagram. 0 indicates that the data is not mapped to that coordinate position, but rather mapped sequentially. Since the symbol modes on the conjugate subcarriers in the group are complementary, this ensures that all data is mapped to the coordinate matrix. In addition, an extra 2 bits of symbol mode index bits are transmitted in each group. Finally, in each subcarrier group, an extra 3 bits of subcarrier index bits and 2 bits of symbol mode index bits are transmitted, allowing for the transmission of more information compared to non-indexed modulation.
[0067] Obtaining a 3D constellation chart:
[0068] It was found that because the symbol pattern expands (0,0,0) to other cases, a series of new constellation points are generated. For example, (0,0,x) will generate new constellation points on the z-axis, that is, new constellation points will appear at the center of the top and bottom faces of the 8QAM cube. In other words, two 0s will generate new constellation points at the center of the six faces of the cube. Meanwhile, the coordinates mapped on its complementary conjugate subcarriers contain only one 0, indicating that new constellation points appear at the midpoints of the 12 edges of the cube. Simultaneously, (0,0,0) continues to generate constellation points at the origin, and due to the original 8QAM cube design, the constellation points formed by the subsequent coordinates still belong to the original 8QAM constellation points and will not generate new constellation points. Thus, a constellation diagram of 8+12+6+1=27 is obtained, as detailed below. Figure 7 As shown, and it is 3 3 The odd-order three-dimensional spatial constellation diagram of 3, compared with the existing even-order QAM modulation, makes the signal under this modulation unknown to illegal receivers and difficult to crack by brute force.
[0069] S5: The three-dimensional constellation diagram enters the optical fiber channel after passing through the OFDM system to obtain the received signal;
[0070] For the transmission of the three-dimensional constellation diagram, an Inverse Fast Fourier Transform (IFFT) is first performed, with the row and column operations performed twice sequentially. After the IFFT, the frequency domain signal is converted into a time domain signal. To reduce inter-symbol interference, cyclic prefixes and suffixes are added before and after the symbols. Then, the modulated parallel time domain signal is converted from parallel to serial to a serial signal before entering the optical fiber channel. At the receiving end, the reverse operation is performed, and the received signal to be decrypted is obtained after serial-to-parallel conversion, removal of cyclic prefixes and suffixes, and Fourier transform.
[0071] S6: Signal Reception and Demodulation: The constellation diagram obtained after completing the above operations is as follows: Figure 8 As shown, this is a masked 27QAM signal. The received signal is demodulated using the mode index to obtain the symbol index bits for the second time. Then, the carrier index bits of the subcarrier index are recovered according to the mode. The resulting constellation diagram is as follows. Figure 9 The 8QAM signal shown is then processed according to the scrambling sequence generated by the chaotic system, sequentially restoring the symbol points and subcarriers. After sub-block recombination with the index bit matrix, an XOR operation is performed to recover the initial information.
[0072] In this embodiment, step S6 specifically includes:
[0073] A1: Index bit of the demodulation symbol mode, selected as 3. An 8-bit matrix is used for detection. The constellation points at the center of the six faces and the origin are demodulated by determining the face (symbol pattern) to which they belong, and the symbol index bits are recovered.
[0074] A2: Demodulate the subcarrier index bits based on the subcarrier position information where the symbol pattern is located; at this point, 120 is obtained. A data matrix of 256, then according to 3 Grouping 8 into sets, compressing all zero elements, and then shifting to the next coordinate, we can recover 120. A 224 matrix, with all coordinate information derived from the original 8QAM constellation, was used to recover the information. Then, demodulation was performed, reducing each sub-block to 3 bits of 40. 224 data matrix;
[0075] A3: Following the scrambling sequence generated by the chaotic system, the symbol points and subcarriers are scrambled and restored sequentially. Then, after merging and recombining the sub-blocks with the index bit matrix, an XOR operation is performed to restore the initial information.
[0076] For unauthorized receivers, the correct information cannot be extracted because they are unaware of the indexing rules, modulation format, and encryption method. The method of this invention not only ensures signal security through multiple encryptions but also provides a certain gain in the overall signal transmission performance (including anti-interference performance, bit error rate, and receiver sensitivity gain under the same conditions) under optimized indexing rules.
Claims
1. A method for designing odd-order constellations in three-dimensional space based on index modulation, characterized in that, Includes the following steps: S1: The initial signal is XOR-encrypted at the bit level using a scrambled sequence generated by a three-dimensional chaotic system; S2: Divide the XOR-encrypted signal into sub-blocks according to the number of bits; S3: Use a three-dimensional chaotic system to scramble the subcarriers and symbol points after the sub-blocks are grouped to complete the basic encryption; S4: Perform subcarrier indexing and symbol mode indexing sequentially on the basic encrypted signal to obtain a three-dimensional constellation diagram; S5: The three-dimensional constellation diagram enters the optical fiber channel after passing through the OFDM system to obtain the received signal; S6: The received signal is demodulated through the mode index to obtain the second symbol index bit. Then, the carrier index bit of the subcarrier index is recovered according to the mode. The symbol point and subcarrier are restored in sequence according to the scrambling sequence generated by the chaotic system. After sub-block recombination with the index bit matrix, the initial information is obtained by XOR recovery.
2. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 1, characterized in that, In step S1, the three-dimensional chaotic system uses a 3D chaotic model to achieve multi-layer encryption. The expression of the 3D chaotic model is as follows: ； Where X, Y, and Z are the first state variable, the second state variable, and the third state variable, respectively, and a, b, c, and d are the first system parameter, the second system parameter, the third system parameter, and the fourth system parameter, respectively.
3. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 2, characterized in that, In step S1, the initial data is a randomly generated binary data stream. After generating bit information, the initial data is bit-XORed using a chaotic sequence X generated by the first state variable X. The generation operation of the chaotic sequence X is as follows: ； Where mod(-) is the remainder function, floor(-) is the floor function, and X1 is the binarized sequence obtained by the 6th decimal place of the chaotic sequence, which is XORed with the randomly generated data.
4. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 3, characterized in that, The sub-block grouping in step S2 specifically includes: First, the data transmission bits and index bits are separated. The index bits are further divided into subcarrier index bits and symbol index bits. These three parts of bits are then grouped again, with the data bits divided into 40 sub-blocks of 3 bits each. A 224 matrix, simultaneously dividing the subcarrier index bits into 3-bit sub-blocks of 40. A 32-bit matrix, with the sign index bits divided into 40 sub-blocks of 2 bits each. A 32-dimensional matrix.
5. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 4, characterized in that, Step S3 specifically includes: The chaotic sequences generated using Y and Z from the chaotic sequence are used to scramble the subcarriers and symbol points of the signal, respectively, and then applied to the 40° of the transmitted signal. The specific operation for a 224 data matrix is as follows: ； First, sort the chaotic sequences Y and Z in ascending order and then generate matrices by reciprocal. Then, multiply these matrices with the original matrices to generate a scrambled square matrix with orders of subcarrier number and symbol number, respectively. Each row and column of the square matrix contains a 1, and the remaining elements are all marked as 0. Extract the positions of the 1s from the square matrices generated by Y and Z to generate two scrambled sequences. Here, mod(-) is the remainder function, and sort(-) is the ascending order sorting function.
6. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 5, characterized in that, The subcarrier indexing method in step S4 is as follows: 40 after multi-dimensional encryption perturbation The 224 data matrix is divided into 1 Each group of 7 represents seven columns of subcarriers, for a total of 40. 32 groups, which correspond exactly to 40 in the subcarrier index. A 32 matrix is used; next, subcarrier indexing is performed, specifically by inserting a subcarrier into each group. Since each subcarrier index bit is 3 bits, it represents exactly eight cases. These eight cases are then mapped to the positions where empty subcarriers are inserted after there are already 7 columns of subcarriers in each group.
7. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 6, characterized in that, The method for symbol pattern indexing in step S4 is as follows: The index subcarrier represents silence and no information is transmitted, i.e., the coordinates are (0,0,0). (0,0,0) is split into two columns of subcarriers, one of which is determined by the subcarrier index and denoted as the i-th column, and the other is specified as the (8-i+1)-th column of the subcarrier. For the symbol mode index, the column with more 0s in the coordinates is used as the reference, where 0 indicates that it is not mapped to the position of that coordinate, but is mapped to the next position. Since the symbol modes on the conjugate subcarriers in the group are complementary, this ensures that all data is mapped to the coordinate matrix. On this basis, an additional 2 bits of symbol mode index bits are transmitted in each group. Finally, in each group of subcarriers, an additional 3 bits of subcarrier index bits and 2 bits of symbol mode index bits are transmitted.
8. The method for designing a three-dimensional odd-order constellation based on index modulation according to claim 7, characterized in that, The acquisition of the three-dimensional constellation diagram in step S4 includes: Since the symbol pattern expands (0,0,0) to other cases, a series of new constellation points will be generated; at the same time, (0,0,0) continues to generate constellation points at the origin, and due to the cube design of the original 8QAM, the constellation points formed by the subsequent coordinates still belong to the original 8QAM constellation points and will not generate new constellation points, thus obtaining a three-dimensional constellation map.
9. A three-dimensional odd-order constellation design method based on index modulation according to claim 8, characterized in that, In step S5, for the transmission of the three-dimensional constellation diagram, a fast inverse Fourier transform (IFFT) is first performed, with the row and column operations performed twice sequentially. After the IFFT, the frequency domain signal is converted into a time domain signal. To reduce inter-symbol interference, a cyclic prefix and suffix are added before and after the symbols. Then, the modulated parallel time domain signal is converted from parallel to serial to a serial signal and enters the optical fiber channel. At the receiving end, the reverse operation is performed, and the received signal to be decrypted is obtained after serial-to-parallel conversion, removal of cyclic prefixes and suffixes, and Fourier transform.
10. A method for designing a three-dimensional odd-order constellation based on index modulation according to claim 9, characterized in that, Step S6 specifically includes: A1: Index bit of the demodulation symbol mode, selected as 3. An 8-dimensional matrix is used for detection. The constellation points at the center of the six faces and the origin are demodulated by determining the face to which they belong, and the symbol index bits are recovered. A2: Demodulate the subcarrier index bits based on the subcarrier position information where the symbol pattern is located; A3: Following the scrambling sequence generated by the chaotic system, the symbol points and subcarriers are scrambled and restored sequentially. Then, after merging and recombining the sub-blocks with the index bit matrix, an XOR operation is performed to restore the initial information.