V-OFDM secure transmission method, system and device based on dynamic feedback chaotic system and medium

Abstract

The invention discloses a V-OFDM secure transmission method, system and device based on a dynamic feedback chaotic system, and a medium, and the method comprises the steps: building a three-dimensional Lorenz chaotic mapping model based on a dynamic feedback factor, controlling the row-column transformation of an orthogonal DFT matrix, and carrying out the independent encryption of each vector block; the system, the equipment and the medium are used for realizing the method. According to the method disclosed by the invention, the vector block characteristic of the V-OFDM is fully utilized, and the dynamic row and column replacement of the DFT matrix is introduced, so that the encrypted constellation diagram is in a spherical disordered state and is difficult to crack by an eavesdropper, the resistance of a system to signal interception is greatly improved, the security of a physical layer is effectively enhanced, and the peak-to-average power ratio of the system is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a V-OFDM secure transmission method, system, equipment and medium based on a dynamic feedback chaotic system. Background Art

[0002] At present, vector orthogonal frequency division multiplexing (V-OFDM) technology is a generalized extension of orthogonal frequency division multiplexing (OFDM). By introducing the vector block processing mechanism, it can achieve efficient spectrum utilization while further improving the resistance to multipath interference and the flexible adaptation of signals. Compared with traditional OFDM, V-OFDM can flexibly adjust the size of vector blocks in different application scenarios to balance data rate, computational complexity and transmission reliability by splitting the large-scale fast Fourier transform (IFFT) operation into multiple small-scale vector IFFTs. However, V-OFDM systems still face several key technical challenges in practical applications: First, the high peak-to-average power ratio (PAPR) problem still exists. Due to the superposition effect of subcarriers in the vector block, the instantaneous power peak of the time domain signal may be higher, which will cause signal distortion, increase the nonlinear distortion of the amplifier, and reduce the transmission performance of the system; second, the existing physical layer security technology has not made further improvements on the vector block structure of V-OFDM to enhance the security of transmission.

[0003] Some existing technical solutions have attempted to improve the reduction of the peak-to-average ratio (PAPR) or physical layer security. In terms of reducing the peak-to-average ratio (PAPR), clipping and filtering technology reduces the PAPR by limiting the instantaneous power peak of the signal, but it will distort the original waveform of the signal, causing more serious distortion of the signal and resulting in a decrease in transmission quality. In addition, traditional security encryption technology relies on the upper-layer encryption algorithm, and the algorithm complexity is relatively high. At the same time, the symmetry after the constellation diagram is rotated and encrypted may still be exploited by eavesdroppers, and the risk of cracking is relatively high. Therefore, traditional technologies cannot effectively solve the dual needs of secure transmission of V-OFDM systems and reducing the peak-to-average ratio (PAPR).

[0004] Wuhan Qing (Wuhan Qing. Research on physical layer security algorithm based on OFDM system [D]. Jiangsu University of Science and Technology, 2018.) proposed a composite encryption scheme combining phase rotation, key matrix and artificial noise. The scheme encrypts the transmitted symbols through a dynamic diagonal key matrix and generates an artificial noise masking signal based on the OFDM system parameters. The scheme uses this method to reduce the PAPR by about 1.5dB while keeping the illegal demodulation bit error rate at 0.5.

[0005] Although the above research has made some progress in physical layer security or PAPR optimization, the solution based on the traditional OFDM framework is difficult to adapt to the vector block structure of V-OFDM and fails to effectively utilize its multi-dimensional characteristics for dynamic optimization. Therefore, the existing technology cannot effectively solve the dual needs of PAPR optimization and physical layer security in V-OFDM systems in dynamic environments. An innovative solution that can simultaneously solve PAPR optimization and physical layer security in V-OFDM systems is urgently needed. Summary of the invention

[0006] In order to overcome the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a V-OFDM secure transmission method, system, device and medium based on a dynamic feedback chaotic system, by constructing a three-dimensional Lorenz chaotic mapping model based on a dynamic feedback factor, controlling the row and column transformation of the orthogonal DFT matrix, and adopting dynamic orthogonal DFT matrix encryption, PAPR is reduced, the problem that the traditional fixed matrix is ​​easily deduced and cracked is avoided, and the vector block characteristics of V-OFDM are fully utilized to effectively improve the physical layer security of the system. Through the isometric transformation of the dynamic orthogonal DFT matrix, each vector block is independently encrypted, so that the encrypted signal presents a spherical chaotic characteristic on the constellation diagram, making it difficult for eavesdroppers to crack. At the same time, the parameters of the three-dimensional Lorenz chaotic mapping model can be flexibly adjusted according to the communication environment, thereby enhancing the robustness and anti-interference ability of the system, and meeting the needs of high-security and low-latency scenarios such as 5G communication and the Internet of Things. Through the method of the present invention, more efficient secure communication can be achieved at a lower cost, providing reliable physical layer protection for the V-OFDM system. In addition, the method has low computational complexity, simple generation process, is suitable for real-time communication scenarios, and can significantly reduce hardware and energy consumption costs.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A V-OFDM secure transmission method based on a dynamic feedback chaotic system comprises the following steps:

[0009] Step 1: Introduce dynamic feedback factors into the classic three-dimensional Lorenz chaotic model, construct a three-dimensional Lorenz chaotic mapping model, and generate a chaotic key sequence x i ,y i and z i , the chaotic key sequence x i ,y i and z i Mapping to discrete space for quantization;

[0010] Step 2: In the encryption phase, the input data is grouped into M×L vectors to obtain an M×L matrix, and the index vector is used to permute the rows and columns of the M×L matrix;

[0011] Step 3: Decompose the standard DFT matrix into a set of orthogonal row vectors, and use the index vector to permute the rows and columns of the decomposed DFT matrix; multiply the M×L matrix after the row and column permutation with the DFT matrix after the row and column permutation to generate an M×L encrypted matrix;

[0012] Step 4: Perform inverse fast Fourier transform on the M×L encrypted matrix at L points per row to obtain the time domain signal s=[s 0 ,s 1 ,...,s L-1 ]; the time domain signal s = [s 0 ,s 1 ,...,s L-1 ] performs parallel-to-serial conversion and adds a cyclic prefix (CP) to generate a transmit signal

[0013] Step 5: Transmit the signal After being transmitted to the receiving end through the wireless channel, a received signal is generated; then the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as the transmitting end is performed to obtain the time domain received signal y=[y 0 ,y 1 ,...,y L-1 ]; Then, the time domain received signal y is subjected to a fast Fourier transform at L points in a row to obtain a frequency domain signal Y = [Y 0 ,Y 1 ,...,Y L-1 ];

[0014] Step 6: In the decryption stage, the frequency domain signal Y is inversely permuted in rows and columns using the same index vector as in step 2, and the DFT matrix decomposed in step 3 is inverted to obtain the DFT inverse matrix, and the same index vector as in step 3 is used to perform inverse permutation in rows and columns; the frequency domain signal Y after inverse permutation in rows and columns is multiplied by the DFT inverse matrix after inverse permutation in rows and columns to generate an M×L decryption matrix;

[0015] Step 7: Perform parallel-to-serial conversion and orthogonal phase shift keying inverse mapping demodulation on the M×L decryption matrix in turn, and output binary output data.

[0016] The expression of the three-dimensional Lorenz chaotic mapping model in step 1 is as follows:

[0017]

[0018] Where a is the Prandtl number, b is the Rayleigh number, c is the direction ratio, and the variables (x, y, z) represent the three dynamic variables of the system state, and a>0, b>0, c>0; ζ 0 represents the initial value of the dynamic feedback factor, ∈ represents the control parameter of the fluctuation amplitude of the dynamic feedback factor in the time domain, μ represents the feedback modulation parameter, ζ0 >0,∈>0,μ>0.

[0019] In step 1, the random initial value (x 0 ,y 0 ,z 0 ) is used as the seed key to input into the three-dimensional Lorenz chaotic mapping model, and the model parameters a, b, c, ζ are set. 0 ,∈,μ, iteratively generate three sets of chaotic key sequences x i ,y i and z i .

[0020] In step 1, the chaotic key sequence x i ,y i and z i The formula for quantification is as follows:

[0021]

[0022] In the formula, They represent the quantized chaotic key sequences respectively.

[0023] The process of performing M×L vector grouping on the input data in step 2 is as follows: first, the input data is a data block composed of a pseudo-random binary sequence, and the length of the data block is set to N; the data block is sequentially subjected to serial-to-parallel conversion and orthogonal phase shift keying mapping, and then the mapped data block is grouped in M×L, that is, divided into L vector blocks, each vector block contains M symbols, satisfying N=LM, and establishing an M×L matrix.

[0024] The index vector in step 2 is obtained by quantizing the chaotic key sequence D xi and D yi Sort by, that is, the chaotic key sequence D after quantization xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D x =[d 1 ,d 2 ,...,d M ]; Similarly, in the quantized chaotic key sequence D yi Randomly select a sequence of length L and sort it in ascending order to obtain the index vector D y =[d 1 ,d 2 ,…,d L ].

[0025] The index vector in step 3 is obtained by quantizing the chaotic key sequence D xi and D ziSort by, that is, the chaotic key sequence D after quantization xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D' x =[d 1 ,d 2 ,…,d M ]; From the chaotic key sequence D zi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D z =[d 1 ,d 2 ,…,d M ].

[0026] The present invention also provides a V-OFDM secure transmission system based on a dynamic feedback chaotic system, comprising:

[0027] Model building module: Introduce dynamic feedback factors into the classic three-dimensional Lorenz chaotic model, build a three-dimensional Lorenz chaotic mapping model, and generate a chaotic key sequence x i ,y i and z i , the chaotic key sequence x i ,y i and z i Mapping to discrete space for quantization;

[0028] Encryption module: In the encryption stage, the input data is grouped into M×L vectors to obtain an M×L matrix, and the index vector is used to permute the rows and columns of the M×L matrix; at the same time, the standard DFT matrix is ​​decomposed into a set of orthogonal row vectors, and the index vector is used to permute the rows and columns of the decomposed DFT matrix; the M×L matrix after the row and column permutation is multiplied with the DFT matrix after the row and column permutation to generate an M×L encryption matrix;

[0029] Transmission module: Perform inverse fast Fourier transform on the M×L encryption matrix at L points per row to obtain the time domain signal s=[s 0 ,s 1 ,...,s L-1 ]; the time domain signal s = [s 0 ,s 1 ,...,s L-1 ] performs parallel-to-serial conversion and adds a cyclic prefix (CP) to generate a transmit signal Then send a signal After being transmitted to the receiving end through the wireless channel, a received signal is generated; then the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as the transmitting end is performed to obtain the time domain received signal y=[y 0 ,y 1 ,...,y L-1]; Then, the time domain received signal y is subjected to a fast Fourier transform at L points in a row to obtain a frequency domain signal Y=[Y 0 ,Y 1 ,...,Y L-1 ];

[0030] Decryption module: perform inverse permutation of the frequency domain signal Y using the same index vector in the encryption module, and invert the DFT matrix decomposed in the encryption module to obtain the DFT inverse matrix, and perform inverse permutation of the rows and columns using the same index vector in step 3; multiply the frequency domain signal Y after inverse permutation of the rows and columns by the DFT inverse matrix after inverse permutation of the rows and columns to generate an M×L decryption matrix;

[0031] Output module: The M×L decryption matrix is ​​sequentially converted from parallel to serial and demodulated by orthogonal phase shift keying inverse mapping, and binary output data is output.

[0032] The present invention also provides a V-OFDM secure transmission device based on a dynamic feedback chaotic system, comprising:

[0033] Memory: a computer program for storing the above-mentioned V-OFDM secure transmission method based on dynamic feedback chaotic system, which is a computer-readable device;

[0034] Processor: used to implement the above-mentioned V-OFDM secure transmission method based on dynamic feedback chaotic system when executing the computer program.

[0035] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement the above-mentioned V-OFDM secure transmission method based on a dynamic feedback chaotic system.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] 1. This invention combines chaotic encryption technology with the V-OFDM system for the first time, and innovatively improves the security of the system through M×L matrix and orthogonal DFT matrix. This method can effectively cope with the security challenges of V-OFDM in high-dynamic environments, provides a solid foundation for the application of V-OFDM in future high-dynamic communication scenarios, and provides a theoretical basis and engineering reference for the research and implementation of subsequent security and reliability technologies.

[0038] 2. The present invention adopts an improved three-dimensional Lorenz chaotic system and significantly enhances the randomness and initial value sensitivity of the chaotic sequence by introducing a dynamic feedback factor, thereby generating a chaotic sequence with higher randomness and unpredictability.

[0039] 3. The present invention combines chaotic sequences to generate index vectors to dynamically permute rows and columns of input data, and introduces a randomized DFT matrix for encryption processing, which is easy to implement and makes the encrypted constellation diagram present a spherical chaotic state, greatly improving the system's resistance to signal interception and effectively enhancing the security of the physical layer.

[0040] 4. The traditional V-OFDM system has a high peak-to-average ratio (PAPR) problem due to the use of multi-carrier modulation, which easily causes the power amplifier to enter the nonlinear working area, thereby causing signal distortion and reduced energy efficiency. The present invention optimizes the energy distribution of the signal in the frequency domain by introducing dynamic row and column permutation of the DFT matrix, which can significantly reduce the instantaneous peak power and avoid out-of-band interference and nonlinear distortion. At the same time, the randomization of the DFT matrix by the chaotic index further increases the complexity of the signal spectrum, effectively preventing energy aggregation and the occurrence of fixed spectrum positions, thereby enhancing the transmission reliability of the system and solving the problem of signal quality degradation caused by excessively high PAPR in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The present invention is a flow chart of the V-OFDM secure transmission method based on dynamic feedback chaotic system.

[0042] Figure 2 This is a three-dimensional phase diagram of the chaotic model based on dynamic feedback factors of the present invention.

[0043] Figure 3 This is the xy plane singular factor attraction diagram of the present invention.

[0044] Figure 4 It is the yz plane singular factor attraction diagram of the present invention.

[0045] Figure 5 This is the xz plane singular factor attraction diagram of the present invention.

[0046] Figure 6 Performance comparison between the traditional Lorenz chaos model and the improved dynamic feedback factor Lorenz model.

[0047] Figure 7 It is the original constellation diagram of QPSK of the present invention.

[0048] Figure 8 This is the constellation diagram after QPSK encryption of the present invention.

[0049] Fig. 9 It is a comparison diagram of CCDF curves of PAPR before and after encryption of the present invention. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0051] The present invention realizes the construction of the whole process from encryption to decryption of the cooperative communication sender and the legitimate fairy tale receiver of the V-OFDM system through the combination of dynamic feedback factor chaotic system and DFT matrix. In the encryption stage, the initial value of the chaotic model is first used as the seed key shared between the legitimate sender and receiver, and then the index vector is obtained by quantization and sorting of the chaotic model to permute the rows and columns of the data after the V-OFDM vector grouping, and the orthogonal DFT matrix is ​​introduced to permute the rows and columns. Due to the randomness of the chaotic sequence, the multi-level encryption of the data matrix is ​​realized, which not only improves the security of the physical layer, but also effectively reduces the peak-to-average ratio of the system. In the decryption stage, the legitimate user receiver uses the shared seed key to realize the efficient restoration of the data, and accurately restores the original signal arrangement by performing the inverse permutation processing of the sender.

[0052] like Figure 1 As shown, a V-OFDM secure transmission method based on a dynamic feedback chaotic system specifically includes the following steps:

[0053] Step 1: Introduce dynamic feedback factors into the classic three-dimensional Lorenz chaos model to construct a three-dimensional Lorenz chaos mapping model; the introduction of dynamic feedback factors aims to make the system exhibit more complex chaotic attractors, higher Lyapunov exponents and stronger initial value sensitivity by real-time regulation of the dynamic changes of nonlinear terms; the expression of the classic three-dimensional Lorenz chaos model is:

[0054]

[0055] The expression of the three-dimensional Lorenz chaotic mapping model based on dynamic feedback factors is as follows:

[0056]

[0057] Where a is the Prandtl number, b is the Rayleigh number, c is the direction ratio, and the variables (x, y, z) represent the three dynamic variables of the system state, and a>0, b>0, c>0; ζ 0 represents the initial value of the dynamic feedback factor, ∈ represents the control parameter of the fluctuation amplitude of the dynamic feedback factor in the time domain, μ represents the feedback modulation parameter, ζ 0 >0,∈>0,μ>0. The introduction of dynamic feedback factors enables the system to present more complex dynamic characteristics in time changes. Reasonable setting of the range and form of these parameters can ensure that the system is always in a chaotic state.

[0058] In this embodiment, in order to verify the chaotic performance of the improved system, the system parameters a=10, b=25, c=8 / 3, ζ 0=1,∈=0.1,μ=0.1, we get Figure 2 , 3 , 4, and 5 show the three-dimensional phase diagram of the three-dimensional Lorenz hyperchaotic mapping and the strange attractor diagrams of each plane. The attractor trajectory of the three-dimensional Lorenz chaos mapping model in three-dimensional space can clearly observe the complex and regular motion trajectory of the system in three-dimensional space. The three-dimensional Lorenz chaos mapping model introduces dynamic feedback factors, making the attractor shape more complex than the classic three-dimensional Lorenz chaos model, showing significant chaotic characteristics.

[0059] like Figure 3 As shown in the projection trajectory on the xy plane, it can be seen that the trajectory presents a typical double helix structure, indicating that there is a complex alternating attraction between the two attractors of the system model. This structure reflects the instability and sensitive dependence of the system model on this plane. Figure 4 As shown in Figure 2, the trajectory in the yz plane shows the symmetry and periodicity of the attractor, accompanied by a complex spiral convergence structure, reflecting the chaotic dynamics of the system in different dimensions. Figure 5 As shown, in the trajectory of the xz plane, a complex symmetrical morphological structure can be seen, which confirms that the dynamic feedback factor enhances the chaotic characteristics of the system.

[0060] In order to further analyze the advantages of the three-dimensional Lorenz model based on dynamic feedback factor proposed in the present invention, the performance comparison of the classical three-dimensional Lorenz chaos model and the improved dynamic feedback factor Lorenz model in Lyapunov exponent calculation is shown in Figure 2. Figure 6 As shown. The blue curve represents the Lyapunov index of the classic three-dimensional Lorenz chaos model, with a maximum value of 1.4410 and a Rayleigh number b of 197. In contrast, the green curve represents the improved three-dimensional Lorenz chaos mapping model, with a maximum Lyapunov index of 5.7300 and a Rayleigh number b of 165. The maximum Lyapunov index is increased by 2.97 times the original, and it shows a higher Lyapunov index in multiple parameter ranges, indicating that its chaos is significantly enhanced. In the region of Rayleigh number b>300, the Lyapunov index of the classic three-dimensional Lorenz chaos model gradually stabilizes and always remains at a low level, indicating that the chaos of the system is weak. The improved three-dimensional Lorenz chaos mapping model shows significant volatility and a higher Lyapunov index in the same parameter range, indicating that it has more complex chaotic behavior. This improvement benefits from the introduction of dynamic feedback factors, which increases the system's sensitivity to initial conditions and orbital bifurcation characteristics, significantly improves the system's chaotic performance, while maintaining good randomness and complexity, verifying the effectiveness and feasibility of the improvement scheme.

[0061] Step 2: Generate the chaotic key sequence x based on the three-dimensional Lorenz chaotic mapping model i ,y i and z i ;

[0062] The random initial value (x 0 ,y 0 ,z 0 ) is input into the model as the seed key, and the parameters a, b, c, ζ of the three-dimensional Lorenz chaotic mapping model are set the same as in step 1 0 ,∈,μ, after a certain number of iterations, three sets of chaotic key sequences x are generated i ,y i and z i The three-dimensional Lorenz chaotic mapping model based on dynamic feedback factor is 0 ,y 0 ,z 0 ) The pseudo-randomness of sensitivity to small changes can provide high-intensity security for the V-OFDM secure transmission system;

[0063] Step 3: Substitute the continuous chaotic key sequence x in step 2 i ,y i and z i Mapped to discrete space for quantization; the quantization formula is as follows:

[0064]

[0065] In the formula, They represent the quantized chaotic key sequences respectively;

[0066] By three sets of chaotic key sequences x i ,y i and z i It is amplified, that is, multiplied by 1000, and then limited to the range of 0 to N through modulo operation; through this quantization process, the floating-point number sequence can be converted into a discrete sequence of integers with finite precision while maintaining its pseudo-randomness, which can be directly used as a matrix index.

[0067] Step 4: In the encryption stage, the input data is grouped into M×L vectors to obtain an M×L matrix, and the chaotic key sequence quantized in step 3 is sorted to obtain an index vector; the index vector is used to permute the rows and columns of the M×L matrix;

[0068] First, the input data of the transmitter input into the transmitting end of the V-OFDM secure transmission system is a data block composed of a pseudo-random binary sequence, and the length of the data block is set to N; the data block is sequentially subjected to serial-to-parallel conversion and quadrature phase shift keying (QPSK) mapping, and then the mapped data block is grouped into M×L groups, that is, divided into L vector blocks, each vector block contains M symbols, satisfying N=LM, and an M×L matrix is ​​established;

[0069] The lth vector block can be expressed as:

[0070] x l =x lM ,x lM+1 ,...,x lM+M-1 T ,l=0,1,...,L-1

[0071] In the formula, T represents transpose;

[0072] The expression of the M×L matrix is ​​as follows:

[0073]

[0074] Then, the chaotic key sequence D quantized in step 3 is xi Randomly select a sequence of length M from xi =[x 0 ,x 1 ,...,x M ], for sequence D xi =[x 0 ,x 1 ,...,x M ] are sorted in ascending order to obtain the index vector D x =[d 1 ,d 2 ,...,d M ]; using the index vector D x =[d 1 ,d 2 ,...,d M ] Rearrange the rows of the M×L matrix. The M×L matrix after row permutation is expressed as:

[0075] X′(i,:)=X(D x [i],:),i=1,2,...,M

[0076] The sorting formula is as follows:

[0077]

[0078] Where D x ,D y ,Dz Respectively represent the sorted index vectors;

[0079] The sort operation here returns the subscript index in ascending order. For example, if Then D x =[3,1,2,0]. This index mapping is to extend randomness to the permutation dimension, converting numerical randomness into permutation randomness, further disrupting the data order. The permutation result has a higher dimensional complexity, which is difficult to crack through frequency domain or time domain analysis, and has higher security.

[0080] Similarly, the M×L matrix X′ after row permutation is quantized into the chaotic key sequence D yi Randomly select a sequence of length L from the sequence D yi =[y 0 ,y 1 ,...,y L ], for sequence D yi =[y 0 ,y 1 ,...,y L ] are sorted in ascending order to obtain the index vector D y =[d 1 ,d 2 ,...,d L ]; using the index vector D y =[d 1 ,d 2 ,...,d L ] Rearrange the columns of the M×L matrix. The M×L matrix X after column permutation is expressed as:

[0081] X(:,j)=X′(:,D y [j]),j=1,2,...,L

[0082] The sort operation here returns the subscript index in ascending order. For example, if Then D x =[3,1,2,0]. This index mapping is to extend randomness to the permutation dimension, converting numerical randomness into permutation randomness, further disrupting the data order. The permutation result has a higher dimensional complexity, which is difficult to crack through frequency domain or time domain analysis, and has higher security.

[0083] Step 5: Decompose the standard DFT matrix into a set of orthogonal row vectors, and use the index vector to permute the rows and columns of the decomposed DFT matrix; replace the M×L matrix after the row and column permutation in step 4 with the DFT matrix F after the row and column permutation M×M Multiply to generate an M×L encrypted matrix;

[0084] In order to further enhance the security of the system and solve the problem of high peak-to-average ratio of V-OFDM as a multi-carrier system, an orthogonal DFT matrix is ​​introduced on the basis of the original M×L matrix transformation. The role of the DFT matrix in signal processing is very critical. Its orthogonal characteristics and spectrum expansion capabilities make the data distribution in the frequency domain more uniform, thereby reducing the peak power of the signal. This not only optimizes the physical layer transmission performance of the signal, but also provides a higher dimensional complexity for the encryption scheme. The expression of the standard DFT matrix is ​​as follows:

[0085]

[0086] Where m and n are the row and column indices of the DFT matrix, respectively, ranging from m, n = 1, 2, ..., N. After the standard DFT matrix is ​​expanded, its form is as follows:

[0087]

[0088] This matrix can be decomposed into a set of orthogonal row vectors Right now:

[0089]

[0090] Since the input data is grouped into an M×L matrix, to maintain the orthogonality of the DFT matrix, N is set to M. For the DFT matrix F M×M From the quantized chaotic key sequence D xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D' x =[d 1 ,d 2 ,…,d M ], the rows of the DFT matrix are rearranged, and the DFT matrix after row permutation is expressed as:

[0091] F′ MM (i,:)=F MM (D′ x [i],:),i=1,2,…,M

[0092] After completing the row permutation, the DFT matrix F′ after row permutation is also M×M (i,:) from the chaotic key sequence D zi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D z =[d 1 ,d 2 ,…,d M ], rearrange the DFT matrix, and the DFT matrix F after column permutation M×M It is expressed as:

[0093] FMM (:,j)=F MM (:,D z [j]),j=1,2,…,M

[0094] The above row and column permutation steps also complete the dynamic randomization of the DFT matrix.

[0095] The expression for generating the M×L encryption matrix is:

[0096] S=F M×M X

[0097] Step 6: Perform an inverse fast Fourier transform (IFFT) on the M×L encrypted matrix at L points per row to obtain a time domain signal s=[s 0 ,s 1 ,...,s L-1 ], to realize the modulation of data; the time domain signal s=[s 0 ,s 1 ,...,s L-1 ] performs parallel-to-serial conversion and adds a cyclic prefix (CP) to generate a transmit signal

[0098] The expression of the time domain signal is:

[0099]

[0100] Step 7: Transmitting the Signal After being transmitted to the receiving end through the wireless channel, a received signal is generated; then the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as the transmitting end is performed to obtain the time domain received signal y=[y 0 ,y 1 ,...,y L-1 ]; Then, the time domain received signal y is subjected to a fast Fourier transform (FFT) at L points in a row to obtain a frequency domain signal Y = [Y 0 ,Y 1 ,...,Y L-1 ];

[0101] The expression of the time domain received signal is:

[0102]

[0103] Where h is the impulse response of the channel, and w is the additive Gaussian white noise;

[0104] The expression of the frequency domain signal is:

[0105]

[0106] Step 8: In the decryption stage, the frequency domain signal Y is inversely permuted using the same index vector as in step 4, and the DFT matrix F decomposed in step 5 is M×M Inverse the DFT inverse matrix and use the same index vector as in step 5 to perform inverse permutation of rows and columns. Multiply the frequency domain signal Y after inverse permutation of rows and columns with the inverse DFT matrix after inverse permutation of rows and columns to generate an M×L decryption matrix.

[0107] In the decryption phase, only the legitimate user receiver and the cooperative communication sender share the same key sequence, so they can get the same index vector. First, the DFT matrix F M×M Inverse, since the matrix has orthogonality, the DFT matrix F M×M The inverse matrix of is obtained by conjugate transpose, and the expression is

[0108]

[0109] Where H represents the conjugate transpose.

[0110] Then perform the same inverse operation of the row-column permutation in step 5, that is, first perform the same column transformation on the DFT inverse matrix, and then perform the same row transformation on the DFT inverse matrix to obtain the DFT inverse matrix F after row-column inverse permutation. -1 .

[0111] Then, the frequency domain signal Y is decrypted, and the same key sequence and index vector are shared with the sender. The inverse operation of row-column permutation as in step 4 is performed, that is, the same column transformation is performed on the M×L matrix first, and then the row transformation is performed on the M×L matrix after the column transformation to obtain the M×L matrix X in the original arrangement order. 1 .

[0112] The M×L matrix X after the inverse permutation of rows and columns 1 The DFT inverse matrix F after row and column inverse permutation -1 Multiply them to complete the decryption process and generate a decryption signal as an M×L matrix, expressed as:

[0113] X 2 =F -1 X 1

[0114] Step 9: Perform parallel-to-serial conversion and quadrature phase shift keying (QPSK) inverse mapping demodulation on the M×L decryption matrix in turn to obtain correct binary output data.

[0115] For the legitimate user receiver, since they share the same seed key sequence with the sender, the receiver can decrypt the data through the above series of inverse operations and refer to Figure 7 , demodulate and obtain the correct quadrature phase shift keying (QPSK) constellation diagram;

[0116] For illegal receivers, it is difficult to know the same key sequence due to the enhanced chaotic characteristics of the chaotic model and the sensitivity of the initial value, making it difficult to perform the corresponding decryption operation. The initial conditions and parameters of the chaotic model are extremely sensitive to the output chaotic sequence, and even a slight change will lead to completely different results. Therefore, even if the illegal receiver obtains the encrypted data, it cannot accurately restore the corresponding key sequence, and thus cannot restore the encrypted data. Figure 8 , the demodulated constellation diagram presents a spherical chaotic state, with noise-like characteristics, making it difficult to demodulate the correct data information.

[0117] refer to Fig. 9 Compared with the peak-to-average ratio of the traditional OFDM system (Wuhan Qing. Research on physical layer security algorithm based on OFDM system [D]. Jiangsu University of Science and Technology, 2018.), the peak-to-average ratio of the encrypted V-OFDM system of the present invention is reduced by 1.8dB. This is because the row-column permutation of the V-OFDM system and the addition of the DFT matrix after row-column permutation greatly disrupt the autocorrelation between symbols, thereby reducing the peak-to-average ratio of the system.

[0118] In summary, the above scheme provides a stable decryption process for legitimate user recipients through the complexity of the key and the high dependence on the initial conditions of the chaotic model, while for illegal user recipients, it increases the difficulty of cracking, thereby effectively ensuring the security of data transmission.

[0119] The present invention also provides a V-OFDM secure transmission system based on a dynamic feedback chaotic system, comprising:

[0120] Model building module: Introduce dynamic feedback factors into the classic three-dimensional Lorenz chaotic model, build a three-dimensional Lorenz chaotic mapping model, and generate a chaotic key sequence x i ,y i and z i , the chaotic key sequence x i ,y i and z i Mapping to discrete space for quantization;

[0121] Encryption module: In the encryption phase, the sender groups the input data into M×L vectors to obtain an M×L matrix, and uses the index vector to permute the rows and columns of the M×L matrix; at the same time, the standard DFT matrix is ​​decomposed into a set of orthogonal row vectors, and the index vector is used to permute the rows and columns of the decomposed DFT matrix; the M×L matrix after the row and column permutation is multiplied with the DFT matrix after the row and column permutation to generate an M×L encryption matrix;

[0122] Transmission module: Perform inverse fast Fourier transform on the M×L encryption matrix at L points per row to obtain the time domain signal s=[s 0 ,s 1 ,...,s L-1 ]; the time domain signal s = [s 0 ,s 1 ,...,s L-1 ] performs parallel-to-serial conversion and adds a cyclic prefix (CP) to generate a transmit signal Then send a signal After being transmitted to the receiving end through the wireless channel, a received signal is generated; then the cyclic prefix (CP) of the received signal is removed, and the same M×L grouping operation as the transmitting end is performed to obtain the time domain received signal y=[y 0 ,y 1 ,...,y L-1 ]; Then, the time domain received signal y is subjected to a fast Fourier transform at L points in a row to obtain a frequency domain signal Y=[Y 0 ,Y 1 ,...,Y L-1 ];

[0123] Decryption module: perform inverse permutation of the frequency domain signal Y using the same index vector in the encryption module, and invert the DFT matrix decomposed in the encryption module to obtain the DFT inverse matrix, and perform inverse permutation of the rows and columns using the same index vector in step 3; multiply the frequency domain signal Y after inverse permutation of the rows and columns by the DFT inverse matrix after inverse permutation of the rows and columns to generate an M×L decryption matrix;

[0124] Output module: The M×L decryption matrix is ​​sequentially converted from parallel to serial and demodulated by orthogonal phase shift keying inverse mapping, and binary output data is output.

[0125] The present invention also provides a V-OFDM secure transmission device based on a dynamic feedback chaotic system, comprising:

[0126] Memory: a computer program for storing the above-mentioned V-OFDM secure transmission method based on dynamic feedback chaotic system, which is a computer-readable device;

[0127] Processor: used to implement the above-mentioned V-OFDM secure transmission method based on dynamic feedback chaotic system when executing the computer program.

[0128] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement the above-mentioned V-OFDM secure transmission method based on a dynamic feedback chaotic system.

Claims

1. A V-OFDM secure transmission method based on a dynamic feedback chaotic system, characterized in that: The steps include: Step 1: Introduce dynamic feedback factors into the classic three-dimensional Lorenz chaotic model, construct a three-dimensional Lorenz chaotic mapping model, and generate a chaotic key sequence x i ,y i and z i , the chaotic key sequence x i ,y i and z i Mapping to discrete space for quantization; Step 2: In the encryption phase, the input data is grouped into M×L vectors to obtain an M×L matrix, and the index vector is used to permute the rows and columns of the M×L matrix; Step 3: Decompose the standard DFT matrix into a set of orthogonal row vectors, and use the index vector to permute the rows and columns of the decomposed DFT matrix; multiply the M×L matrix after the row and column permutation with the DFT matrix after the row and column permutation to generate an M×L encrypted matrix; Step 4: Perform inverse fast Fourier transform on the M×L encrypted matrix at L points per row to obtain the time domain signal s=[s0,s1,...,s L-1 ]; the time domain signal s=[s0,s1,...,s L-1 ] performs parallel-to-serial conversion and adds a cyclic prefix (CP) to generate a transmit signal Step 5: Transmit the signal The received signal is then transmitted to the receiving end through a wireless channel. The cyclic prefix (CP) of the received signal is then removed, and the same M×L grouping operation as the transmitting end is performed to obtain the time domain received signal y=[y0,y1,...,y L-1 ]; then the time domain received signal y is subjected to a fast Fourier transform at L points in a row to obtain a frequency domain signal Y = [Y0, Y1, ..., Y L-1 ]; Step 6: In the decryption stage, the frequency domain signal Y is inversely permuted in rows and columns using the same index vector as in step 2, and the DFT matrix decomposed in step 3 is inverted to obtain the DFT inverse matrix, and the same index vector as in step 3 is used to perform inverse permutation in rows and columns; the frequency domain signal Y after inverse permutation in rows and columns is multiplied by the DFT inverse matrix after inverse permutation in rows and columns to generate an M×L decryption matrix; Step 7: Perform parallel-to-serial conversion and orthogonal phase shift keying inverse mapping demodulation on the M×L decryption matrix in turn, and output binary output data.

2. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that: The expression of the three-dimensional Lorenz chaotic mapping model in step 1 is as follows: Where a is the Prandtl number, b is the Rayleigh number, c is the direction ratio, the variables (x, y, z) represent the three dynamic variables of the system state, and a>0, b>0, c>0; ζ0 represents the initial value of the dynamic feedback factor, ∈ represents the control parameter of the fluctuation amplitude of the dynamic feedback factor in the time domain, μ represents the feedback modulation parameter, ζ0>0,∈>0,μ>0.

3. A V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1 or 2, characterized in that: In step 1, the random initial value (x0, y0, z0) shared by the cooperative communication sender and the legitimate user receiver is input into the three-dimensional Lorenz chaotic mapping model as the seed key, and the model parameters a, b, c, ζ0, ∈, μ are set to iteratively generate three sets of chaotic key sequences x i ,y i and z i .

4. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that: In step 1, the chaotic key sequence x i ,y i and z i The formula for quantification is as follows: In the formula, They represent the quantized chaotic key sequences respectively.

5. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that: The process of performing M×L vector grouping on the input data in step 2 is as follows: first, the input data is a data block composed of a pseudo-random binary sequence, and the length of the data block is set to N; the data block is sequentially subjected to serial-to-parallel conversion and orthogonal phase shift keying mapping, and then the mapped data block is grouped in M×L, that is, divided into L vector blocks, each vector block contains M symbols, satisfying N=LM, and establishing an M×L matrix.

6. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that: The index vector in step 2 is obtained by quantizing the chaotic key sequence D xi and D yi Sort by, that is, the chaotic key sequence D after quantization xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D x =[d1,d2,...,d M ]; Similarly, in the quantized chaotic key sequence D yi Randomly select a sequence of length L and sort it in ascending order to obtain the index vector D y =[d1,d2,...,d L ].

7. The V-OFDM secure transmission method based on a dynamic feedback chaotic system according to claim 1, characterized in that: The index vector in step 3 is obtained by quantizing the chaotic key sequence D xi and D zi Sort by, that is, the chaotic key sequence D after quantization xi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D' x =[d1,d2,...,d M ]; From the chaotic key sequence D zi Randomly select a sequence of length M and sort it in ascending order to obtain the index vector D z =[d1,d2,...,d M ].

8. A V-OFDM secure transmission system based on a dynamic feedback chaotic system according to any one of claims 1 to 7, characterized in that: include: Model building module: Introduce dynamic feedback factors into the classic three-dimensional Lorenz chaotic model, build a three-dimensional Lorenz chaotic mapping model, and generate a chaotic key sequence x i ,y i and z i , the chaotic key sequence x i ,y i and z i Mapping to discrete space for quantization; Encryption module: In the encryption stage, the input data is grouped into M×L vectors to obtain an M×L matrix, and the index vector is used to permute the rows and columns of the M×L matrix; at the same time, the standard DFT matrix is ​​decomposed into a set of orthogonal row vectors, and the index vector is used to permute the rows and columns of the decomposed DFT matrix; the M×L matrix after the row and column permutation is multiplied with the DFT matrix after the row and column permutation to generate an M×L encryption matrix; Transmission module: Perform inverse fast Fourier transform on the M×L encryption matrix at L points per row to obtain the time domain signal s=[s0,s1,...,s L-1 ]; the time domain signal s=[s0,s1,...,s L-1 ] performs parallel-to-serial conversion and adds a cyclic prefix (CP) to generate a transmit signal Then send a signal The received signal is then transmitted to the receiving end through a wireless channel. The cyclic prefix (CP) of the received signal is then removed, and the same M×L grouping operation as the transmitting end is performed to obtain the time domain received signal y=[y0,y1,...,y L-1 ]; then the time domain received signal y is subjected to a fast Fourier transform at L points in a row to obtain a frequency domain signal Y = [Y0, Y1, ..., Y L-1 ]; Decryption module: perform inverse permutation of the frequency domain signal Y using the same index vector in the encryption module, and invert the DFT matrix decomposed in the encryption module to obtain the DFT inverse matrix, and perform inverse permutation of the rows and columns using the same index vector in step 3; multiply the frequency domain signal Y after inverse permutation of the rows and columns by the DFT inverse matrix after inverse permutation of the rows and columns to generate an M×L decryption matrix; Output module: The M×L decryption matrix is ​​sequentially converted from parallel to serial and demodulated by orthogonal phase shift keying inverse mapping, and binary output data is output.

9. A V-OFDM secure transmission device based on a dynamic feedback chaotic system, characterized in that: include: Memory: a computer program storing a V-OFDM secure transmission method based on a dynamic feedback chaotic system as described in any one of claims 1 to 7, which is a computer-readable device; Processor: used to implement the V-OFDM secure transmission method based on dynamic feedback chaotic system as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement a V-OFDM secure transmission method based on a dynamic feedback chaotic system as described in any one of claims 1 to 7.

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