High-dimensional signal encryption transmission method based on nonlinear adaptive modulation

Abstract

The invention discloses a high-dimensional signal encryption transmission method based on nonlinear adaptive modulation, which comprises the following steps of: sensing a channel state: acquiring channel noise and nonlinear distortion data, and calculating a covariance function cov (n (t)) and a transmission matrix H (t); chaotic parameter generation: generating a dynamic chaotic parameter set based on the covariance function cov (n (t)), and constructing a modulation sub-matrix A d (t); constructing a modulation matrix: generating a high-dimensional dynamic modulation matrix M (t) through tensor product operation; signal encryption mapping: mapping an original signal S raw into an encrypted signal S enc (t), and adding a noise masking item; anti-interference transmission: optimizing a target function through an APSO algorithm, and dynamically adjusting M (t) to counteract channel distortion; and decryption and restoration: the receiving end decrypts the ciphertext through the M (t) 1 inverse matrix to restore the original signal S raw. Through combination of the dynamic chaos parameter and the high-dimensional modulation matrix, channel adaptive encryption transmission is realized, the anti-interference capability and security are improved, and the method is suitable for high-dimensional signal secret communication under a complex channel.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a method for high-dimensional signal encryption transmission based on nonlinear adaptive modulation. Background Technology

[0002] With the popularization of wireless communication technology and the increasing precision of eavesdropping methods, traditional signal transmission schemes based on linear modulation (such as PSK and QAM) face serious security risks: on the one hand, the signal characteristics of linear modulation are predictable, and eavesdroppers can restore the original information through spectrum analysis and signal modeling; on the other hand, fixed modulation parameters cannot adapt to the nonlinear disturbances of complex channels (such as multipath fading, electromagnetic interference, and nonlinear distortion), resulting in insufficient transmission robustness.

[0003] While some existing technologies have introduced chaotic systems to improve encryption complexity, they mostly employ low-dimensional chaotic models (such as two-dimensional Logistic mapping), which are vulnerable to attacks by chaotic synchronous cracking algorithms. Meanwhile, in traditional high-dimensional signal transmission schemes, the mapping relationship between signal dimension and modulation matrix lacks a dynamic adaptation mechanism, making it impossible to balance encryption strength and transmission efficiency. There is an urgent need for a high-dimensional adaptive encryption framework based on nonlinear dynamics, which can achieve real-time matching of modulation parameters, signal dimension, and channel state through complex mathematical modeling. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a high-dimensional signal encryption transmission method based on nonlinear adaptive modulation. By constructing a high-dimensional dynamic modulation matrix and an adaptive generation mechanism for chaotic parameters, the method solves the problems of low security and insufficient robustness of fixed parameters in traditional linear modulation.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a high-dimensional signal encryption transmission method based on nonlinear adaptive modulation, comprising the following steps: Step 1: Channel state awareness: Collect channel noise and nonlinear distortion data using a signal detector, and calculate the covariance function. With transmission matrix ; Step 2: Generate chaotic parameters: based on the covariance function in Step 1. Generate a dynamic chaotic parameter set and construct a modulation submatrix. ; Step 3: Construct the modulation matrix and generate a high-dimensional dynamic modulation matrix through tensor product operations. ; Step 4, Signal Encryption Mapping: This involves mapping the original signal... Mapped to encrypted signals Add a noise masking option; Step 5, implement anti-interference transmission: dynamically adjust the objective function of the formula through the APSO algorithm optimization. To compensate for channel distortion; Step Six: Decrypt and Restore: The receiving end uses... The inverse of the modulation matrix is ​​used to decrypt the ciphertext and restore the original signal. .

[0006] As a further improvement of the present invention, the specific method for generating the dynamic chaotic parameter set in step two is to use the following formula: Here, a D-dimensional (D≥3) Lorentz chaotic system is defined, generating a set of modulation parameters that dynamically changes with time t. ,in Let d be the time derivative of the chaotic variable. For channel noise excitation term, This is a nonlinear disturbance compensation term; This is the proportionality coefficient. Rayleigh number, The attenuation coefficient is... , For high-dimensional expansion coefficients, all parameters satisfy... , Let be any chaotic parameter. For the adaptation coefficient, Let be the covariance function of the channel noise.

[0007] As a further improvement of the present invention, in step three, a high-dimensional dynamic modulation matrix is ​​generated through tensor product operation. The specific method is to generate it using the following formula: in, For tensor product operations, Let d be the N-order modulation submatrix corresponding to the d-th chaotic variable. For submatrix elements, Let d be the d-th chaotic variable. For dynamic angular frequency, This is the initial phase.

[0008] As a further improvement of the present invention, the signal encryption mapping in step four is achieved by the following formula: Among them, the original high-dimensional signal is defined. To encrypted signal The mapping, where For vectorized mapping operators, For the optimal fit matrix, This is a Gaussian noise masking term; For matrix vectorization operations, The dimensionality of the original signal and the modulation space is adapted through least squares optimization. satisfy Gaussian distribution, mean 0, variance It dynamically adjusts according to channel noise.

[0009] As a further improvement of the present invention, the specific method for optimizing the objective function of the formula using the APSO algorithm in step five is achieved by the following formula: Among them, the anti-interference optimization objective of encrypted transmission is defined. The modulation matrix is ​​iteratively optimized using the APSO algorithm. ,in For the receiving end to decrypt the signal, For channel transmission matrix, This is a nonlinear distortion metric function. , This is the regularization coefficient.

[0010] The beneficial effects of this invention are that it achieves a dual improvement in signal encryption strength and transmission robustness through a high-dimensional dynamic modulation matrix and an adaptive generation mechanism for chaotic parameters. The dynamic parameters are generated using a D≥3 dimensional Lorentz chaotic system, which presents a higher difficulty in cracking compared to traditional two-dimensional chaotic models. Real-time optimization of the modulation matrix using the APSO algorithm can dynamically offset channel nonlinear distortion, solving the problem that fixed parameters cannot adapt to complex channel environments. Furthermore, by driving the evolution of chaotic parameters through the channel noise covariance function, the encryption system becomes adaptive, achieving real-time matching between encryption strength and channel state. Therefore, the method of this invention: Encryption security: Based on the randomness of high-dimensional chaotic systems and the exponential dimension of tensor product matrices, eavesdroppers face the dual challenges of "chaotic trajectory cracking + high-dimensional matrix inversion", theoretically making it unbreakable; Anti-interference capability: By adaptively optimizing modulation parameters through the APSO algorithm, interference such as channel nonlinear distortion and multipath fading is effectively countered, and the transmission bit error rate is reduced; Compatibility: Supports raw signals of any dimension (audio, video, sensor data, etc.), and is compatible with existing communication equipment and transmission links without the need for hardware modification; Scalability: By adjusting the dimension D of the chaotic system and the order N of the modulation sub-matrix, it can be flexibly adapted to different transmission requirements. Detailed Implementation

[0011] The present invention will be further described in detail below with reference to the given embodiments.

[0012] This embodiment of a high-dimensional signal encryption transmission method based on nonlinear adaptive modulation includes the following steps: Step 1: Channel state awareness: Collect channel noise and nonlinear distortion data using a signal detector, and calculate the covariance function. With transmission matrix ; Step 2: Generate chaotic parameters: based on the covariance function in Step 1. Generate a dynamic chaotic parameter set and construct a modulation submatrix. ; Step 3: Construct the modulation matrix and generate a high-dimensional dynamic modulation matrix through tensor product operations. ; Step 4, Signal Encryption Mapping: This involves mapping the original signal... Mapped to encrypted signals Add a noise masking option; Step 5, implement anti-interference transmission: dynamically adjust the objective function of the formula through the APSO algorithm optimization. To compensate for channel distortion; Step Six: Decrypt and Restore: The receiving end uses... The inverse of the modulation matrix is ​​used to decrypt the ciphertext and restore the original signal. This method employs the following steps: Step 1 involves real-time channel state perception to provide a basis for subsequent parameter adjustments; Step 2 utilizes a high-dimensional chaotic system to generate dynamic parameters, addressing the vulnerability of traditional low-dimensional chaotic systems to manipulation; Step 3 constructs a high-dimensional modulation matrix to enhance signal spatial complexity; Step 4 incorporates a noise masking term to further strengthen anti-analysis capabilities; Step 5 utilizes an intelligent optimization algorithm to achieve channel adaptation, resolving the insufficient robustness of fixed parameters; and Step 6 employs inverse matrix decryption to ensure accurate reconstruction of the legitimate receiver. Overall, this method achieves synergistic optimization of security and transmission quality. In this embodiment, all the above steps are implemented using formulas to facilitate user implementation using a computer.

[0013] Furthermore, the specific method for generating the dynamic chaotic parameter set in step two is to use the parameter generation formula for a high-dimensional Lorentz chaotic system: Wherein: Define a D-dimensional (D≥3) Lorentz chaotic system, generating a set of modulation parameters that dynamically changes with time t. ,in Let d be the time derivative of the chaotic variable. For channel noise excitation term, This is a nonlinear disturbance compensation term.

[0014] This is the scaling factor (dynamic range [10,30]). The Rayleigh number (dynamic range [28, 100]). , where is the attenuation coefficient (dynamic range [2, 8 / 3]). , For high-dimensional expansion coefficients (dynamic range [5,20]), all parameters satisfy... ( Let be any chaotic parameter. For the adaptation coefficient, (where is the covariance function of the channel noise).

[0015] High-dimensional chaotic systems are sensitive to initial values ​​and exhibit parameter ergodicity, resulting in highly random modulation parameter sets. Eavesdroppers must simultaneously decipher the evolution trajectories of D chaotic variables, significantly increasing encryption complexity. Compared to traditional fixed-parameter chaotic systems, this dynamic generation method causes the statistical properties of the encrypted signal to change dynamically with the channel state, increasing the modeling difficulty for eavesdroppers; simultaneously, through… The parameter update mechanism achieves deep coupling between chaotic parameters and channel noise, further enhancing the system's anti-hacking capability.

[0016] Furthermore, in step three, a high-dimensional dynamic modulation matrix is ​​generated through tensor product operations. Tensor product modulation matrix construction formula Wherein: Constructing an N^D dimension dynamic modulation matrix ,in For tensor product operations, Let d be the N-order modulation submatrix corresponding to the d-th chaotic variable. For submatrix elements, Let d be the d-th chaotic variable. For dynamic angular frequency, This is the initial phase.

[0017] Tensor product operations cause the dimension of the modulation matrix to grow exponentially (e.g., when D=5 and N=4). The dimension is 4^5 = 1024, and the elements change in real time with the chaotic variable, satisfying the following conditions: ( (Using the Frobenius norm to ensure matrix energy normalization).

[0018] Spatial encryption of signals is achieved by using high-dimensional tensor product matrices, which forces eavesdroppers to crack the matrix inverse problem of exponential dimensions, thereby increasing the encryption strength.

[0019] The signal encryption mapping in step four is achieved through the following formula: Among them, the original high-dimensional signal is defined. (Dimension L×1) to encrypted signal A mapping of dimension N^D×1, where For vectorized mapping operators, For the optimal fit matrix, This is a Gaussian noise masking term.

[0020] Mapping logic: This is a matrix vectorization operation (stacking matrices column-wise into a vector). The dimensionality of the original signal and the modulation space is adapted through least squares optimization. satisfy (Gaussian distribution, mean 0, variance) (Dynamically adjusted according to channel noise).

[0021] Achieve high-dimensional encrypted mapping of original signals of arbitrary dimensions, further hide signal features through noise masking terms, and resist spectrum analysis attacks.

[0022] Furthermore, the specific method for optimizing the objective function of the formula using the APSO algorithm in step five is achieved by the following formula: Among them, the anti-interference optimization objective of encrypted transmission is defined. The modulation matrix is ​​iteratively optimized using the APSO algorithm. ,in For the receiving end to decrypt the signal, For channel transmission matrix, This is a nonlinear distortion metric function. , This is the regularization coefficient.

[0023] Optimization logic: The first term minimizes the deviation between the decrypted signal and the original signal; the second term limits the energy consumption of the modulation matrix. (For matrix trace operation); the third term suppresses channel nonlinear distortion (by amplifying the weights of strong nonlinear components through the cubic term).

[0024] By optimizing the transmission accuracy, energy consumption, and nonlinear resistance through multi-objective optimization, the original signal can be stably reproduced even in complex channels.

[0025] In summary, this invention provides a high-dimensional signal encryption transmission method based on nonlinear adaptive modulation. Through six steps—channel state perception, dynamic chaotic parameter generation, high-dimensional modulation matrix construction, signal encryption mapping, anti-interference transmission, and decryption—it solves the problems of traditional linear modulation signals being easily cracked and fixed parameters being unable to adapt to complex channels. It achieves a synergistic improvement in encryption strength and transmission robustness, providing an efficient and reliable technical solution for wireless communication security. This method is well-suited for: 1. Industrial control networks: Encrypted transmission of equipment control signals in scenarios such as intelligent manufacturing and power monitoring, resisting malicious industrial attacks; Deep-sea communication systems: High-security data transmission for deep-sea detectors and underwater robots, offsetting nonlinear interference from seawater channels; Wireless secure communication: Supporting wireless data transmission in fields such as finance, resisting spectrum eavesdropping and signal cracking attacks; Internet of Things (IoT) terminal communication: Enabling high-dimensional sensor data encryption transmission from massive IoT devices, ensuring communication privacy between devices; Satellite communication ground stations: Transmission of telemetry and control signals between ground stations, offsetting multipath fading and nonlinear distortion in atmospheric channels.

[0026] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for encrypted transmission of high-dimensional signals based on nonlinear adaptive modulation, characterized in that: Includes the following steps: Step 1: Channel state awareness: Collect channel noise and nonlinear distortion data using a signal detector, and calculate the covariance function. With transmission matrix ; Step 2: Generate chaotic parameters: based on the covariance function in Step 1. Generate a dynamic chaotic parameter set and construct a modulation submatrix. ; Step 3: Construct the modulation matrix and generate a high-dimensional dynamic modulation matrix through tensor product operations. ; Step 4, Signal Encryption Mapping: This involves mapping the original signal... Mapped to encrypted signals Add a noise masking option; Step 5, implement anti-interference transmission: dynamically adjust the objective function of the formula through the APSO algorithm optimization. To compensate for channel distortion; Step Six: Decrypt and Restore: The receiving end uses... The inverse of the modulation matrix is ​​used to decrypt the ciphertext and restore the original signal. .

2. The high-dimensional signal encryption transmission method based on nonlinear adaptive modulation according to claim 1, characterized in that: The specific method for generating the dynamic chaotic parameter set in step two is as follows: The parameter set is generated using the following formula: Here, a D-dimensional (D≥3) Lorentz chaotic system is defined, generating a set of modulation parameters that dynamically changes with time t. ,in Let d be the time derivative of the chaotic variable. For channel noise excitation term, This is a nonlinear disturbance compensation term; This is the proportionality coefficient. Rayleigh number, The attenuation coefficient is... , For high-dimensional expansion coefficients, all parameters satisfy... , Let be any chaotic parameter. For the fit coefficient, Let be the covariance function of the channel noise.

3. The high-dimensional signal encryption transmission method based on nonlinear adaptive modulation according to claim 1 or 2, characterized in that: In step three, a high-dimensional dynamic modulation matrix is ​​generated through tensor product operations. The specific method is to generate it using the following formula: in, For tensor product operations, Let d be the N-order modulation submatrix corresponding to the d-th chaotic variable. For submatrix elements, Let d be the d-th chaotic variable. For dynamic angular frequency, This is the initial phase.

4. The high-dimensional signal encryption transmission method based on nonlinear adaptive modulation according to claim 1 or 2, characterized in that: The signal encryption mapping in step four is achieved through the following formula: Among them, the original high-dimensional signal is defined. To encrypted signal The mapping, where For vectorized mapping operators, For the optimal fit matrix, This is a Gaussian noise masking term; For matrix vectorization operations, The dimensionality of the original signal and the modulation space is adapted through least squares optimization. satisfy Gaussian distribution, mean 0, variance It dynamically adjusts according to channel noise.

5. The high-dimensional signal encryption transmission method based on nonlinear adaptive modulation according to claim 1 or 2, characterized in that: The specific method for optimizing the objective function of the formula using the APSO algorithm in step five is achieved by the following formula: Among them, the anti-interference optimization objective of encrypted transmission is defined. The modulation matrix is ​​iteratively optimized using the APSO algorithm. ,in For the receiving end to decrypt the signal, For channel transmission matrix, This is a nonlinear distortion metric function. , is the regularization coefficient.

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