A cascaded chaotic sequence mapping method and system for a frequency hopping communication system

Abstract

The application discloses a kind of cascade type chaotic sequence mapping method and system for frequency hopping communication system, method includes: setting the iteration parameter of first level chaotic sequence and second level chaotic sequence;The iteration parameter includes Prandtl number, Rayleigh number, direction ratio, fractal parameter and iteration initial value;First level chaotic sequence and second level chaotic sequence under two different initial value iterations are generated by first level chaotic model and second level chaotic model;Each iteration value generated by first level chaotic sequence is used as the initial value required for second level chaotic model iteration to carry out cascade, to generate cascade variable-parameter chaotic sequence;The time sequence of cascade variable-parameter chaotic sequence is scrambled, the sequence after scrambling is carried out hash transformation, then compression mapping is carried out, to generate processed chaotic sequence;Wide interval processing is carried out to the processed chaotic sequence to generate wide interval frequency hopping sequence.The application enhances the anti-interference of chaotic frequency hopping sequence.

Description

Technical Field

[0001] This invention relates to the field of image processing and communication technology, and in particular to a cascaded chaotic sequence mapping method and system for frequency hopping communication systems. Background Technology

[0002] To enhance the anti-jamming capabilities of information transmission, frequency-hopping communication emerged in military communications. Frequency-hopping communication involves the frequency of the information carrier changing according to a specific pattern, i.e., periodic hopping. This is achieved by utilizing an existing pseudo-random sequence, allowing the transmitter to send specific carrier signals at specific times; that is, the carrier change is controlled by the pseudo-random sequence. This pseudo-random sequence is also called a frequency-hopping sequence in frequency-hopping communication.

[0003] Chaos is a common natural phenomenon. Chaos theory belongs to the field of nonlinear science, and the only things that can produce chaotic motion are nonlinear chaotic systems. Typical chaotic systems include logistic regression equations, Lorenz chaotic systems, and chaotic systems based on tenter sequences. In spread spectrum systems, the initial condition sensitivity, correlation, and aperiodicity of chaos perfectly match the requirements of pseudo-random sequences. Therefore, chaotic systems are often used to generate chaotic pseudo-random sequences. Excellent initial condition sensitivity allows chaotic systems to generate a theoretically infinite number of qualified pseudo-random sequences, greatly increasing the number of code users. Good correlation makes them well-suited for use as frequency-hopping sequences in frequency-hopping systems. Aperiodicity improves the anti-interference capability of frequency-hopping systems, making the pattern of frequency-hopping difficult to predict.

[0004] The method for generating arbitrary-interval chaotic frequency-hopping sequences described in invention patent CN111786699A employs a single mapping method, resulting in low complexity. The pseudo-random sequence generator design method based on a generalized third-order Fibonacci chaotic system described in invention patent CN109495240A cascades a Fibonacci model and a Logistic model to generate a generalized third-order Fibonacci chaotic system model, but the interfering party can still reversibly map and iterate back to the original sequence. This invention utilizes the mutual constraints of different chaotic systems and further performs hash transformation on the generated chaotic sequence to enhance its resilience, thereby improving its confidentiality. Summary of the Invention

[0005] The main objective of this invention is to overcome the aforementioned deficiencies in the prior art and propose a cascaded chaotic sequence mapping method and system for frequency hopping communication systems. This method combines two chaotic systems to generate a cascaded variable-parameter chaotic sequence, further scrambles the timing of the generated sequence, and completes inverse mapping protection through hash transformation and wide-interval processing after obtaining the target generation matrix, thereby generating an anti-interference frequency hopping sequence.

[0006] The present invention adopts the following technical solution:

[0007] On the one hand, a cascaded chaotic sequence mapping method for frequency hopping communication systems includes:

[0008] S101, Set the iteration parameters for the first-level chaotic sequence and the second-level chaotic sequence; the iteration parameters include Prandtl number, Rayleigh number, direction ratio, fractal parameter and initial iteration value;

[0009] S102, using a first-level chaotic model and a second-level chaotic model to generate two different initial value iterations of first-level chaotic sequences and second-level chaotic sequences;

[0010] S103, each iteration value generated by the first-level chaotic sequence is used as the initial value required for the iteration of the second-level chaotic model to be cascaded, generating a cascaded variable-parameter chaotic sequence;

[0011] S104, the cascaded variable parameter chaotic sequence is temporally scrambled, the scrambled sequence is hashed, and then compressed and mapped to generate the processed chaotic sequence;

[0012] S105, perform wide-interval processing on the processed chaotic sequence to generate a wide-interval frequency hopping sequence.

[0013] Preferably, the chaotic sequence in S101 is a floating-point number with a value range of (0, 1), and the fractal parameter has a value range of (1, 4).

[0014] Preferably, the first-level chaotic sequence includes a Logistic sequence, a Lorenz sequence, a Tent sequence, or a Gold sequence; the second-level chaotic sequence includes a Logistic sequence, a Lorenz sequence, a Tent sequence, or a Gold sequence.

[0015] Preferably, in S103, the cascaded front and back ends have no sequential order.

[0016] Preferably, the timing scrambling in S104 includes the following steps:

[0017] a) Generate a one-dimensional vector S = {s} from the first-order chaotic mapping. 11 s 12 s 13 , ..., s 1n}, obtain n random sequence values;

[0018] b) Normalize this S to the interval (0, 1) to obtain vector A = {a 11 a 12 a 13 , ..., a 1n};

[0019] c) For each vector value in A, perform a second-level chaotic iteration to generate n sets of chaotic sequences, as follows:

[0020]

[0021] Where m is the truncated length of the sequence generated by the second-level chaotic single-level mapping; the first element of each vector is the real value of the sequence generated by the first-level chaotic mapping iteration;

[0022] d) Concatenate the tail element of each vector group with the first element of the next vector group to obtain the chaotic matrix, as follows:

[0023] Q = [A1A2A3…A] n ]

[0024] The sequence length of the first-level mapping is n, the sequence length of the second-level mapping is m, and the length of the final generated chaotic sequence is set to L. Then the total number of sequences that can be generated is (m*n)mod L.

[0025] e) Interleave the generated chaotic matrix, i.e., set up a fixed-length register, read each element of matrix Q row by row and output column by column to generate a one-dimensional vector:

[0026] W={a 11 a 21 …a n1 a 12 …a n2 …a nm}

[0027] f) Rearrange the one-dimensional vector into a matrix B of dimension t×L. Assuming that the length L of the final truncated sequence is less than the length n of the first-level chaotic single-level mapping, the expression for matrix B is as follows:

[0028]

[0029] Thus, we obtain t sets of cascaded binary chaotic sequences of length L, each of which is a row vector of matrix B.

[0030] Preferably, the hash transformation in S104 uses the middle square method, including the following steps:

[0031] a) Take the square of the real value of the cascaded binary chaotic sequence;

[0032] b) Through the quantization function y tl =sgn(a tl -0.5) Perform fixed-point transformation on the sequence in the cascaded binary chaotic sequence generated by matrix B; where a tl Let y represent the elements in matrix B. tlThis represents the value after hard-decision on each element of the chaotic sequence;

[0033] c) Set up a window of bit length i and slide it l times; let the distance between the tail of the window and the head of the next sliding window be the sliding distance r, that is, the distance of each slide is r+i, then i*l+(l-1)r≤L must be satisfied.

[0034] d) A frequency hopping pattern is obtained through the above sliding process, which includes l frequency points. Different sets of sequences generated by different initial values ​​can produce different frequency hopping patterns.

[0035] Preferably, the wide-spacing processing in S105 includes the following steps:

[0036] a) Remove the d frequency slots in the middle of the frequency hopping band, and the remaining frequency bands on both sides have the same number of frequency slots, which are denoted as F1 and F2 respectively;

[0037] b) If the current frequency point is within F1 / F2, the next frequency point will be increased to the corresponding position of F2 / F1.

[0038] On the other hand, a cascaded chaotic sequence mapping system for frequency hopping communication systems includes:

[0039] The first-level mapping module is used to generate a first-level chaotic sequence through the first-level mapping.

[0040] The second-level mapping module is used to generate a second-level chaotic sequence through the second-level mapping.

[0041] The chaotic sequence generation module is used to cascade each iteration value generated by the first-level chaotic sequence as the initial value required for the iteration of the second-level chaotic model, thereby generating a cascaded variable-parameter chaotic sequence.

[0042] The chaotic sequence processing module is used to scramble the time sequence of the cascaded variable parameter chaotic sequence, perform hash transformation on the scrambled sequence, and then perform compression mapping to generate the processed chaotic sequence.

[0043] The wide-interval processing module is used to perform wide-interval processing on the processed chaotic sequence to generate a wide-interval frequency hopping sequence.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] This invention uses a two-dimensional iteration between a first-level chaotic model and a second-level chaotic model to generate a chaotic matrix with chaotic characteristics in the sequence values. Then, the matrix is ​​scrambled using a rearrangement algorithm to obtain several sets of chaotic sequences. The sequences are compressed and mapped using the mid-square method in hash transformation to obtain hash addresses, which are then mapped to frequency points in frequency hopping communication. Finally, wide-interval processing is applied to each set of frequency points to enhance the anti-interference capability of the chaotic frequency hopping sequences. Attached Figure Description

[0046] Figure 1 This is a flowchart of a cascaded chaotic sequence mapping method for frequency hopping communication systems according to an embodiment of the present invention;

[0047] Figure 2 This is a chaotic attractor diagram of the Lorenz model in an embodiment of the present invention;

[0048] Figure 3 This is a chaotic attractor diagram of the xy phase plane mapping of the Lorenz model in an embodiment of the present invention;

[0049] Figure 4 This is a chaotic attractor diagram of the xz phase plane mapping of the Lorenz model in an embodiment of the present invention.

[0050] Figure 5 This is a chaotic attractor diagram of the yz phase plane mapping of the Lorenz model in an embodiment of the present invention;

[0051] Figure 6 This is a probability density curve of the Logistic system according to an embodiment of the present invention;

[0052] Figure 7 This is a schematic diagram of a hash mapping based on a sliding window according to an embodiment of the present invention;

[0053] Figure 8 This is a diagram showing the autocorrelation characteristics of the frequency hopping sequence in an embodiment of the present invention.

[0054] Figure 9 This is a cross-correlation diagram of the frequency hopping sequences according to an embodiment of the present invention;

[0055] Figure 10 This is a diagram illustrating the frequency uniformity effect of an embodiment of the present invention.

[0056] Figure 11 This is an initial value sensitivity diagram of the Logistic mapping in an embodiment of the present invention;

[0057] Figure 12 This is a graph showing the relationship between the mean square value of the autocorrelation sidelobe of the frequency hopping sequence and the truncation length (the truncation length is less than 1000) in an embodiment of the present invention.

[0058] Figure 13This is a graph showing the relationship between the mean square value of the autocorrelation sidelobe of the frequency hopping sequence and the truncation length (the truncation length exceeds 1000) in an embodiment of the present invention.

[0059] Figure 14 This is a graph showing the relationship between the balance of the frequency hopping sequence and the truncated length in an embodiment of the present invention.

[0060] Figure 15 This is a diagram illustrating the traversal characteristics of the frequency hopping sequence in an embodiment of the present invention.

[0061] Figure 16 This is a structural block diagram of a cascaded chaotic sequence mapping system for frequency hopping communication systems according to an embodiment of the present invention. Detailed Implementation

[0062] The present invention will be further illustrated below with reference to 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. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0063] See Figure 1 As shown, on one hand, a cascaded chaotic sequence mapping method for frequency hopping communication systems includes:

[0064] S101, Set the iteration parameters for the first-level chaotic sequence and the second-level chaotic sequence; the iteration parameters include Prandtl number, Rayleigh number, direction ratio, fractal parameter and initial iteration value;

[0065] S102, using a first-level chaotic model and a second-level chaotic model to generate two different initial value iterations of first-level chaotic sequences and second-level chaotic sequences;

[0066] S103, each iteration value generated by the first-level chaotic sequence is used as the initial value required for the iteration of the second-level chaotic model to be cascaded, generating a cascaded variable-parameter chaotic sequence;

[0067] S104, the cascaded variable parameter chaotic sequence is temporally scrambled, the scrambled sequence is hashed, and then compressed and mapped to generate the processed chaotic sequence;

[0068] S105, perform wide-interval processing on the processed chaotic sequence to generate a wide-interval frequency hopping sequence.

[0069] The perturbation mechanism of the variable-parameter Logistic chaotic system is to perturb the iterative parameters through another uncorrelated chaotic system, which can further reduce the possibility of parameter estimation. By artificially restricting the domain values ​​of the Lorenz mapping and the Logistic mapping to the same range, the cascaded mappings generate a novel cascaded variable-parameter chaotic sequence to improve the system complexity. In this embodiment, the Lorenz chaos with good ergodicity is taken as the first-level chaos, which allows for dynamic global updates of the initial state of the next level. The Logistic chaotic mapping with better chaotic characteristics is taken as the second-level output, and the real values ​​generated by the first-level chaotic mapping are transformed to serve as the parameters of the second-level chaotic system. After generating a frequency hopping sequence that approximates the chaotic characteristics, some hash address values ​​are obtained through hash mapping, and the corresponding frequency points are indexed based on these addresses. Different combinations of frequency point sets are set so that each frequency point set generates a different frequency hopping pattern, further optimizing the anti-interference of the frequency hopping pattern.

[0070] Specifically, in this embodiment, the method includes the following steps:

[0071] 1) Lorenz mapping steps

[0072] The function of the chaotic dynamic cascade mapping system is to generate the required chaotic sequence, ensuring that the frequency-hopping sequence has randomness, uniformity, and good correlation. This step utilizes the Lorenz map to generate a sequence S = {s} with chaotic properties. 11 ,s 12 ,s 13 ,…,s 1n Then, each sequence value is passed to the next level of the model for iteration, generating a chaotic matrix. This process is a two-dimensional iterative process; the Lorenz mapping generates a column vector, i.e., S = {s}. 11 ,s 12 ,s 13 ,…,s 1n The Logistic model generates n row vectors, each of which is a chaotic sequence generated iteratively from the elements of S. The row vectors of the chaotic matrix are successively shortened and concatenated end-to-end to form a single row vector, which is the generated cascaded chaotic sequence.

[0073] The first-level chaotic mapping used in the algorithm is the Lorenz 3D mapping, whose expression is as follows:

[0074]

[0075] The three system parameters are: Prandtl number α, Rayleigh number γ, and direction ratio β. When α = 10 and γ = 28, At this point, the maximum Lyapunov exponent of the Lorenz system is approximately 2.12. As the number of iterations increases, the system eventually moves towards a chaotic state. The complexity of a chaotic system can be described by observing the motion of the chaotic attractor. Figures 2 to 5 The Lorenz 3D model and its three cross-sections show chaotic attractor diagrams. It can be seen that the chaotic system has complex motion characteristics, and the chaotic sequence of any term generated has better randomness.

[0076] 2) Logistic mapping steps

[0077] The second-level chaotic mapping is a Logistic mapping, expressed as follows:

[0078] x n+1 =r*x n *(1-x n )

[0079] Where 1 ≤ r ≤ 4, and r is the fractal parameter. Different values ​​of the fractal parameter and their initial values ​​will affect the degree of chaos in the system, mainly reflected in the convergence and traversal at certain state points. When the Logistic mapping reaches a chaotic state, the mean of the generated sequence is 0.5, and its probability density distribution function is...

[0080]

[0081] probability distribution curves as follows Figure 6 As shown. Based on the probability density function, an ideal Logistic chaotic sequence is equivalent to white noise with a mean of 0.5, and can be considered an ideal random sequence, thus making it well-suited for use as a frequency-hopping code in frequency-hopping communication systems. We take the fractal parameter r = 4 to achieve a fully mapped state for the chaotic system.

[0082] 3) Matrix rearrangement steps

[0083] First, a one-dimensional vector S = {s} is generated by the first-order Lorenz mapping. 11 ,s 12 ,s 13 ,…,s 1n}, obtain n random sequence values. Then, normalize these S to the interval (0,1) to obtain the vector A = {a 11 ,a 12 ,a 13 ,…,a 1n The second-level Logistic mapping iterates through the n sequence values ​​of P as the initial state, generating n sets of chaotic sequences, which can be represented as one-dimensional vector groups.

[0084]

[0085] Where m is the truncated length of the sequence generated by the single-level Logistic mapping. The first element of each vector group is the real value of the sequence generated by the first-level Lorenz mapping iteration. Then, the last element of each vector group is concatenated with the first element of the next vector group to obtain the chaotic matrix Q = [A1A2A3…A…]. n Since the sequence length of the first-level mapping is n and the sequence length of the second-level mapping is m, if the length of the final generated chaotic sequence is set to L, then the total number of sequences t that can be generated is:

[0086] t = (m*n) mod L

[0087] Considering the limitations of hardware precision, the system cannot fully achieve a chaotic state, and the iterative values ​​may exhibit periodic cycles with a low probability. To avoid this, the generated chaotic matrix is ​​interleaved. Specifically, a fixed-length register is used to read each element of matrix Q row by row and output column by column, generating a one-dimensional vector W.

[0088] W={a 11 a 21 …a n1 a 12 …a n2 …a nm}

[0089] The value of the sequence number t allows for tail-pruning of the vector, and the one-dimensional vector W is rearranged into a matrix B of dimension t×L. Assuming that the final truncated sequence length L is less than the length n of the Lorenz single-level mapping, then the expression for matrix B is as follows:

[0090]

[0091] After the above processing, t sets of cascaded binary chaotic sequences of length L will be obtained.

[0092] 4) Hash transformation based on sliding window

[0093] The hash transformation method first takes the square of the real value of the sequence, and then performs binary quantization. Since the traversal interval of the second-level mapping is between (0, 1), median quantization is used to perform binary quantization on each group of chaotic sequences. That is, the median of the traversal interval is taken as the quantization decision threshold, and the quantization function y is set. tl as follows:

[0094] y tl =sgn(a tl -0.5)

[0095] Among them, a tl Let y represent the elements in matrix B. tlThis represents the value after hard-decision on each element in the chaotic sequence.

[0096] Based on the available space, the middle n bits of the square number are selected as the hash address. This method works by amplifying the differences through squaring; the middle bits of the square value are related to every bit of the number, thus reducing the likelihood of hash function collisions for different keys, resulting in more uniform hash addresses. This addresses the frequency hopping table containing the frequency key, sending the mapped frequency to the frequency synthesizer to complete frequency hopping and de-hopping. Sequence transformations include squaring and sliding window selection, with the structure as follows: Figure 7 As shown.

[0097] For the mid-square method, the real values ​​of the sequence are first squared. Then, a sliding window mode is used, i.e., a window of length i is set, and l bit-skipping operations are performed. Let the distance between the last bit of the window and the first bit of the next sliding window be the sliding distance r, i.e., the distance of each slide is r+i. Then, the following condition must be met:

[0098] i*l+(l-1)r≤L

[0099] The above equation holds true if and only if the header of the initial window is the first bit of the binary chaotic sequence. A Lorenz chaotic sequence generated by an initial value iteration of the first-level mapping can be processed by sliding hashing to obtain a frequency hopping pattern, which includes l frequency points. Different sets of sequences generated by different initial value iterations can obtain different frequency hopping patterns.

[0100] 5) Wide-interval processing

[0101] Because address collisions can occur during the hashing process, meaning a frequency point appears consecutively in several time slots, we apply a wide-interval processing to the final frequency hopping pattern. We remove the middle d frequency slots of the frequency hopping band F, leaving the remaining bands on either side as F1 and F2, which have the same number of slots. If the current hop frequency is within F1, the next hop is forced to F2, and the next hop is forced back to F1, thus constructing the wide-interval frequency hopping sequence.

[0102] In summary, this invention designs a highly secure chaotic frequency-hopping sequence. Through two-dimensional iteration using the Lorenz and Logistic models, a chaotic matrix with chaotic sequence values ​​is generated. Then, a rearrangement algorithm is applied to scramble the matrix to obtain several sets of chaotic sequences, which are used to generate different frequency-hopping patterns. The sequence is compressed and mapped using the mid-square method in hash transformation to obtain hash addresses, which are then mapped to frequency points in frequency-hopping communication. Finally, wide-interval processing is applied to each frequency point set to increase the uncertainty of the hopping frequency points and optimize the system's anti-interference performance.

[0103] The effects of this invention will be described below from six aspects: correlation, sequence uniformity, initial value sensitivity, side lobe mean square value of the correlation function, balance, and sequence traversal effect.

[0104] i. Correlation

[0105] The frequency hopping sequences generated by this invention have good correlation; see [link to related document]. Figure 8 and Figure 9 As shown, the main differences are: the normalized autocorrelation function exhibits near-ideal peak characteristics, with values ​​close to the mean in other regions. The normalized cross-correlation function also tends towards an ideal state. When chaotic sequences are applied to spread spectrum communication, the better the autocorrelation, the lower the bit error rate. The cross-correlation of chaotic sequences affects the system's ability to resist multiple access interference between users; the better the cross-correlation, the stronger the anti-interference capability.

[0106] ii. Sequence uniformity

[0107] The frequency points obtained by mapping the frequency hopping sequence proposed in this method are uniformly distributed. Figure 10 It consists of 1280 frequency points generated from the frequency hopping sequence. The frequency points are evenly distributed in the 1st to 16th indices, and each fluctuates around 80 times.

[0108] iii. Initial value sensitivity

[0109] The Logistic mapping is located in the second part of the cascaded system, and its initial values ​​are provided by the previous stage, namely the Lorenz model, which exhibits high randomness and ergodicity. Different initial values ​​can be set to verify the initial value sensitivity of the Logistic chaotic sequence. Using initial values ​​of 0.35700 and 0.35701, and substituting them into the mapping, the first 100 sequence values ​​are extracted respectively. See [link / reference]. Figure 11 As shown, chaotic sequences exhibit strong initial value sensitivity.

[0110] iv. Mean square value of sidelobes of the correlation function

[0111] As the truncation length increases, the mean square values ​​of the autocorrelation and cross-correlation sidelobes of the chaotic sequence gradually decrease. Before the truncation length is less than 1000, the decrease in the mean square values ​​of the autocorrelation and cross-correlation sidelobes with increasing sequence length is relatively steep; after the truncation length exceeds 1000, the decreasing trend of the mean square values ​​of the autocorrelation and cross-correlation sidelobes with increasing sequence length slows down significantly, eventually leveling off. See the results below. Figure 12 and Figure 13 As shown.

[0112] v. balance

[0113] When the sequence length is small, the equilibrium value of the chaotic sequence exhibits large oscillations and is extremely unstable. As the number of iterations increases, the sequence balance gradually stabilizes and eventually approaches the ideal value of 0. See the results below. Figure 14 As shown.

[0114] vi. Sequence traversal effect

[0115] The frequency hopping sequence proposed in this method eventually traverses the entire (0, 1) interval. Due to the wide-interval processing, the highest and lowest thresholds of the sequence are selected as 0.1 and 0.9, respectively. See [link to traversal results] for details. Figure 15 As shown.

[0116] See Figure 16 As shown, according to another aspect of the present invention, this embodiment provides a cascaded chaotic sequence mapping system for frequency hopping communication systems, comprising:

[0117] The first-level mapping module 1601 is used to generate a first-level chaotic sequence through the first-level mapping;

[0118] The second-level mapping module 1602 is used to generate a second-level chaotic sequence through the second-level mapping;

[0119] The chaotic sequence generation module 1603 is used to cascade each iteration value generated by the first-level chaotic sequence as the initial value required for the iteration of the second-level chaotic model to generate a cascaded variable-parameter chaotic sequence.

[0120] The chaotic sequence processing module 1604 is used to scramble the cascaded variable parameter chaotic sequence in time, perform hash transformation on the scrambled sequence, and then perform compression mapping to generate the processed chaotic sequence.

[0121] The wide-interval processing module 1605 is used to perform wide-interval processing on the processed chaotic sequence to generate a wide-interval frequency hopping sequence.

[0122] This embodiment provides a specific implementation of a cascaded chaotic sequence mapping system for frequency hopping communication systems. The same cascaded chaotic sequence mapping method for frequency hopping communication systems will not be described again in this embodiment.

[0123] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A cascaded chaotic sequence mapping method for frequency hopping communication systems, characterized in that, include: S101, Set the iteration parameters for the first-level chaotic sequence and the second-level chaotic sequence; the iteration parameters include Prandtl number, Rayleigh number, direction ratio, fractal parameter and initial iteration value; S102, using a first-level chaotic model and a second-level chaotic model to generate two different initial value iterations of first-level chaotic sequences and second-level chaotic sequences; S103, each iteration value generated by the first-level chaotic sequence is used as the initial value required for the iteration of the second-level chaotic model to be cascaded, generating a cascaded variable-parameter chaotic sequence; S104, the cascaded variable parameter chaotic sequence is temporally scrambled, the scrambled sequence is hashed, and then compressed and mapped to generate the processed chaotic sequence; S105, Perform wide-interval processing on the processed chaotic sequence to generate a wide-interval frequency hopping sequence; The timing scrambling in S104 includes the following steps: a1) Generate a one-dimensional vector from the first-order chaotic mapping. Obtain n random sequence values; b1) Normalize this S to the interval (0,1) to obtain the vector. ; c1) For For each vector value in the dataset, a second-level chaotic iteration is performed to generate... A group of chaotic sequences is represented as follows: ； in, The truncated length of the sequence generated by the second-level chaotic single-level mapping; the first element of each vector is a real value of the sequence generated iteratively by the first-level chaotic mapping; d1) Concatenate the tail element of each vector group with the first element of the next vector group to obtain the chaotic matrix, as follows: ； The sequence length of the first-level mapping is The sequence length of the second-level mapping is Set the length of the final generated chaotic sequence to . The total number of sequences that can be generated is ; e1) Interleave the generated chaotic matrix, i.e., set a fixed-length register to interleave the matrix. Each element is read in row by row and output column by column, generating a one-dimensional vector: ； f1) rearranges the one-dimensional vector into a shape with dimension f1. matrix Assuming the final truncation sequence length Less than the length of the first-level chaotic single-level mapping Then the matrix The expression is as follows: ； Thus, t sets of cascaded binary chaotic sequences of length L are obtained, each of which is a row vector of matrix B; The hash transformation in S104 uses the middle-square method and includes the following steps: a2) Take the square of the real value of the cascaded binary chaotic sequence; b2) Through quantization function Fixed-point transformation is performed on the sequences in the cascaded binary chaotic sequence generated by matrix B; where, Representation matrix The elements in This represents the value after hard-decision on each element of the chaotic sequence; c2) Set a bit length as In the window, perform Each slide; the distance between the bottom of the window and the top of the window in the next slide is recorded as the slide distance. That is, the distance of each slide is Then it must satisfy ; d2) A frequency hopping pattern is obtained through the above sliding process, which includes the following number of frequency points: Different sets of sequences generated by different initial values ​​can produce different frequency hopping patterns. The wide-interval processing in S105 includes the following steps: a3) Remove the middle part of the frequency hopping band. Each frequency band has one slot, and the remaining frequency bands on both sides have the same number of slots, denoted as _____. and ; b3) If the current frequency point is in / If the frequency increases to [a specific value], then the next frequency point will be [a specific value]. / Corresponding position.

2. The cascaded chaotic sequence mapping method for frequency hopping communication systems according to claim 1, characterized in that, The chaotic sequence described in S101 is a floating-point number with a value range of (0, 1), and the fractal parameter has a value range of (1, 4).

3. The cascaded chaotic sequence mapping method for frequency hopping communication systems according to claim 1, characterized in that, The first-level chaotic sequence includes a Logistic sequence, a Lorenz sequence, a Tent sequence, or a Gold sequence; the second-level chaotic sequence includes a Logistic sequence, a Lorenz sequence, a Tent sequence, or a Gold sequence.

4. The cascaded chaotic sequence mapping method for frequency hopping communication systems according to claim 1, characterized in that, In S103, there is no order between the front and back ends of the cascade.

5. A cascaded chaotic sequence mapping system for frequency hopping communication systems, characterized in that, The method based on any one of claims 1 to 4 includes: The first-level mapping module is used to generate a first-level chaotic sequence through the first-level mapping. The second-level mapping module is used to generate a second-level chaotic sequence through the second-level mapping. The chaotic sequence generation module is used to cascade each iteration value generated by the first-level chaotic sequence as the initial value required for the iteration of the second-level chaotic model, thereby generating a cascaded variable-parameter chaotic sequence. The chaotic sequence processing module is used to scramble the time sequence of the cascaded variable parameter chaotic sequence, perform hash transformation on the scrambled sequence, and then perform compression mapping to generate the processed chaotic sequence. The wide-interval processing module is used to perform wide-interval processing on the processed chaotic sequence to generate a wide-interval frequency hopping sequence.

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