A high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method

Abstract

The application discloses a high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method, and belongs to the technical field of communication. i The chaotic generator is used to generate a chaotic sequence p i at a transmitting end, a Kronecker product operation is performed on the chaotic sequence p and a full one sequence after symbolization processing to realize copying (P+1) times to generate a reference signal, different transmission coefficients are mapped to input information, a group of signals is designated as special signals according to the orthogonality of discrete sine variation, the special signals are mixed modulated with the rest of the signals by using the transmission coefficients, meanwhile, the positions of the special signals are shifted according to the transmission coefficients by combining index modulation technology, finally, the signals after shifting and the normalized reference signal are distributed to different carriers by using a multi-carrier technology.After the signals of the carriers are demodulated at a receiving end, the signals are denoised by using a piecewise average method, then the original input information is recovered by using correlation demodulation and corresponding mapping rules.The method has wide application potential in actual communication systems.

Description

Technical Field

[0001] This invention belongs to the field of communication technology and relates to a hybrid modulation multicarrier differential chaotic shift keying method. Background Technology

[0002] Chaos theory, one of the three major discoveries in 20th-century physics, has been deeply applied to fields such as topography, biology, economics, and communications. Especially in modern society with the rapid development of computer networks, network security has become a crucial issue for social life and national security. Chaotic signals, with their wide spectrum and noise-like characteristics, have led to the emergence of modern information security network architectures primarily characterized by chaotic secure communication. Chaotic secure communication, as an important application of chaos theory in the field of communications, has attracted widespread research interest from scholars. Proposed methods for chaotic secure communication include chaotic masking, chaotic keying, and chaotic modulation. Among these, chaotic keying, with its strong anti-interference capabilities and practical application value, has received considerable attention.

[0003] Early chaotic keying techniques were unable to address the robustness issue of coherent demodulation, leading current chaotic keying technologies to generally favor incoherent reception methods. Differential Chaos Shift Keying (DCSK) systems using incoherent reception employ a transmit-reference model, eliminating the need to transmit an additional reference signal during transmission. Instead, both the reference signal and the information-carrying signal are sent to the receiver simultaneously, avoiding channel estimation and significantly reducing system complexity. However, DCSK systems waste half of their time slots transmitting the reference signal, resulting in a low bit transmission rate. Furthermore, the use of time division multiple access (TDMA) in DCSK systems inevitably involves radio frequency (RF) delay lines, increasing implementation costs. To address these issues, researchers proposed the MC-DCSK (Multicarrier Differential Chaos Shift Keying) system. This system distributes information across different subcarriers for transmission, avoiding the use of RF delay lines. This improves transmission rate while reducing the impact of single-carrier error transmissions on overall system performance, thus enhancing system reliability. In 2001, Zbigniew Galias et al. proposed the quadrature chaos shiftkeying (QCSK) system. This system maps binary data information to one of the four quadrants of the complex plane using two orthogonal chaotic sequences, achieving a high transmission rate within the same bandwidth. However, with the continuous development of mobile communication technology and the increasing functionality of smartphones, the demand for high-speed data transmission is growing. Therefore, some researchers have turned their attention to index modulation technology. Index modulation technology introduces index bits and modulation bits to quickly retrieve the required information while ensuring the quality of transmitted data, thereby improving the transmission rate and reliability of the communication system.

[0004] To improve the transmission rate of the MC-DCSK system, this invention proposes a high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method that combines QCSK and index modulation techniques.

[0005] CN113595951 B discloses a differential chaotic phase shift keying (PSK) communication method and system based on hybrid indexes. This method addresses the problems of low spectral efficiency and energy efficiency, as well as slow data transmission rates, in existing differential chaotic PPSK communication schemes. The method includes a differential chaotic PPSK transmission signal modulation method based on hybrid indexes and a differential chaotic PPSK reception signal demodulation method based on hybrid indexes. The hybrid indexes are hybrid index bits, including carrier index bits and carrier number index bits. These carrier index bits and carrier number index bits are mixed to modulate the transmission signal. The combined modulation and demodulation under the hybrid indexes results in higher energy efficiency and spectral efficiency compared to a single differential chaotic PPSK communication method based on carrier index bits, comprehensively improving energy efficiency, spectral efficiency, and bit error rate performance.

[0006] The differences between this patent and the present invention are as follows: 1. The present invention mainly mixes DCSK modulation and QCSK modulation to introduce shift index bits. Simultaneously, due to the introduction of discrete orthogonal transformation, it can avoid internal signal interference and achieve a high transmission rate under the same bandwidth conditions. The patent, however, indexes the carrier side, requiring the exchange of spectrum resources for transmission rate. Furthermore, the patent only uses DCSK modulation. In short, under the same bandwidth, the transmission rate of the paper is lower than that of the present invention, meaning its spectral efficiency is lower. 2. The present invention employs segmented averaging noise reduction at the receiving end, which can reduce the variance of the system decision variable. The patent, however, does not employ noise reduction at the receiving end, resulting in lower bit error rate performance compared to the present invention. 3. The discrete orthogonal transformation used in the present invention can add multiple sets of signals, allowing the receiving end to transmit information from multiple sets of signals while avoiding internal signal interference. The Hilbert transform used in the patent cannot generate multiple sets of orthogonal signals; therefore, the energy efficiency of the patent is lower than that of the present invention. Summary of the Invention

[0007] This invention aims to solve the problems of the prior art. It proposes a high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method. The technical solution of this invention is as follows:

[0008] A high-speed shift hybrid modulation multicarrier differential chaotic shift keying method includes the following steps:

[0009] Step 1: Generate a reference signal using a chaos generator;

[0010] Step 2: Mix, modulate, and shift the reference signal to generate the data carrier signal;

[0011] Step 3: The reference signal and the data carrier signal are transmitted using a carrier wave;

[0012] Step 4: After the signal passes through the channel, carrier demodulation and information bit restoration are performed.

[0013] Furthermore, step 1 uses a chaos generator to generate a reference signal, specifically including:

[0014] The chaos generator at the transmitting end uses a second-order Chebyshev mapping to generate a chaotic signal p = [p1,…p] of sequence length R. R Then, the chaotic signal is symbolized to obtain x = [x1, ..., x]. R ], satisfying x i =sgn(p i ), where i = 1, ..., R, sgn(·) is the symbolic operation; x is a 1×(P+1) matrix of all 1s. Performing the Kronecker product operation yields Where "×" represents the multiplication operation, the specific expression is: ⊙ represents the Kronecker product operation, which replicates the signal (P+1) times; finally... After normalization, that is, by comparing with Perform the Hadamard product operation to obtain a reference signal y0 with length R(P+1).

[0015] Furthermore, step 2, the mixing and modulation of the reference signal specifically includes:

[0016] After serial-to-parallel conversion, the binary data information is divided into two parts: modulation bits and index bits. Bit κ1 is used as the modulation bit for mixed modulation, and bits κ2 = log2(P+1) are used as the index bits for shifting the signal after mixed modulation. Assume the interval time of the chaotic sequence is T. c That is The frame length is R(P+1)T c Then, it is mixed and modulated through u branches; assuming the branches here are U1,…,U u The signal after passing through the U1 branch is a special signal, in [0,RT] c Within a given time period, the switches in branch U1 are closed, meaning the signals interact with matrices U1, ..., U... u The elements from columns 1 to R are subjected to a Hadamard product to generate u sets of orthogonal signals, which are then modulated, with each set of signals carrying 1 bit of information; in [ΔRT] c ,(1+Δ)RT c During the time interval (Δ=1,…,P), the switch passing through branch U1 is opened, meaning the signal interacts with matrices U2,…,U respectively. u The Hadamard product operation of the elements in columns ΔR+1 to (1+Δ)R produces (u-1) sets of orthogonal signals. After modulation, each set of signals also carries 1 bit of information. Therefore, κ1 = (u-1)P + u; U1,…,U u Discrete Sine Transform Code and The expression for the Kronecker product, the discrete transform code, is as follows:

[0017]

[0018] in D s =[D s,1 ,…,D s,R ]and Performing the Kronecker product operation yields a U of length R(P+1). s ,Right now

[0019] After mapping, κ1 modulation bits can be used as c, a m,n ,b m,n This indicates that c represents the information carried by the special signal, and a... m,n ,b m,n The signals are respectively located in [(m-1)RT] c mRT c [Time period via U] 2n and U 2n+1 The information carried after the branch, where n = 1, ..., (u-1) / 2; m = 1, ..., P+1, has two different mapping relationships for the modulation bits:

[0020] (1) 0→-1, 1→+1, that is, c∈{+1,-1};

[0021] (2) Right now

[0022] Furthermore, the shifting step in step 2 specifically includes:

[0023] The signal is mixed and modulated to obtain a frame length of R(P+1)T c The signal, assuming κ2 index bits are κ, then by The shifting of the hybrid modulated signal determines the location containing the special signal, where B(·) is the binary-to-decimal conversion operation; assuming the signal is not shifted, the signal is represented as [y (1) ,y (2) ,…,y (P+1) ], where y (m) This represents a matrix of length R, where m = 1, ..., P+1, and the frame length is RT. c y (1) For a matrix containing a special signal; when y (1) Move backward 0×RT c Frame length, i.e., remains unchanged before and after the shift, when At that time, y (1) Move backward by 1×RTc The frame length, the shifted matrix y can be represented as: [y (2) ,y (1) ,…,y (P+1) ], At that time, y (1) Move backward by 2×RT c The frame length, the shifted matrix y can be represented as: [y (2) ,y (3) ,y (1) …,y (P+1) According to this pattern, when At that time, y (1) Move backward P×RT c The frame length, the shifted matrix y can be represented as: [y (2) ,…,y (P+1) ,y (1) ];y (m) The expression is:

[0024]

[0025] Where t1 is the signal in [0,RT] c The special signal of length R generated when passing through branch U1 within a time interval satisfies the following expression: t 2n and t 2n+1 This indicates that the signal is in [(m-1)RT] c mRT c [Time period passed through U respectively] 2n and U 2n+1 The signal of length R generated after the branch is expressed as:

[0026] Furthermore, step 3, which involves transmitting the reference signal and the data bearer signal using a carrier wave, specifically includes:

[0027] By combining multi-carrier technology, the data-carrying signal is extended to N channels, utilizing frequencies f1,…,f N The data carrier signal is transmitted using a subcarrier with frequency f0; assuming that the signal on the subcarrier with frequency q is shifted to obtain the data carrier signal y. q q = 1, ..., N, the signal of subcarrier f0 is y0, since y r It is a discrete signal, r = 0, ..., N, therefore first y r After digital-to-analog conversion and carrier modulation, the expression of the signal after digital-to-analog conversion is:

[0028]

[0029] Where y r,j Let y be the matrix r The j-th column element of (r = 0, ..., N), h(t) is a duration T. c The pulse signal, here the impulse response of the square-lifted cosine filter, has its energy normalized to 1; assume the interval between adjacent carriers satisfies (1+γ) / T c γ is the roll-off factor; therefore, the output expression of the transmitter is:

[0030]

[0031] Where, φ r Let represent the phase angle of the r-th subcarrier; since the total number of information bits transmitted by the system is N(κ1+κ2), the average bit energy of the system can be obtained from the above formula:

[0032]

[0033] Furthermore, after the signal in step 4 passes through the channel, it undergoes carrier demodulation and information bit restoration, specifically including:

[0034] Step 4.1: Signal via Channel: The signal s(t) in the AWGN channel is affected by additive white Gaussian noise n(t), which has a mean of 1 and a two-sided power spectral density of... The mathematical characteristics of the signal received at the receiving end are: r(t) = s(t) + n(t);

[0035] Step 4.2: Carrier Demodulation: After passing through the corresponding subcarrier, the signal r(t) is filtered by a matched filter, and then converted from analog to digital to obtain the recovered reference signal r0 and the data carrier signal r. q (q=1,…,N); r0 is the signal on a carrier wave with frequency f0, r q For a frequency of f q The signal on the carrier wave; analog-to-digital conversion to ideal sampling, with a sampling interval of jT. c (j=1,…,R(1+P)), in order to obtain the maximum output signal-to-noise ratio at each sampling time point, the matched filter here is matched with h(t); r q (q=1,…,N) is divided into (P+1) equal segments, i.e. in It is a matrix of dimension 1×R;

[0036] Step 4.3: Information Bit Reconstruction: To reduce the impact of noise, the recovered reference signal is now denoised using a piecewise averaging method to obtain a length of 1×R. In order to obtain the location of the special signal, Perform a Kronecker product operation with D1, then By performing correlation, we can obtain (P+1) correlation values. The expression is as follows:

[0037]

[0038] Where T is the transpose operation; taking the absolute value of (P+1) related values, i.e. Then, the maximum likelihood estimation yields the result that determines the location of the specific signal. Then to The index bits are obtained by performing a decimal-to-binary inverse mapping; to facilitate obtaining the corresponding modulation information bits, the shift detector... r q Perform reverse shift to obtain For example This means It contains a special signal, which is then inverted and shifted. Move forward by a length R, which is... In fact, let n (m) for The noise matrix in It can be represented as: Will After multiplying with the Hadamard code of the discrete sine transform, and then... The relevant decision criterion between the index bit and the modulation bit is as follows:

[0039]

[0040]

[0041] Where c q , For a frequency of f q On the subcarrier t1,t 2n ,t 2n+1 Corresponding modulation bits; c q , The modulation bits are recovered by inverse mapping of polarity.

[0042] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method as described in any one of the claims.

[0043] A non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method as described in any one of the claims.

[0044] A computer program product includes a computer program that, when executed by a processor, implements the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method as described in any one of the claims.

[0045] The advantages and beneficial effects of this invention are as follows:

[0046] This invention addresses the poor bit error rate performance and low transmission rate of multi-carrier differential chaotic shift keying (MC-DCSK) systems by proposing a high-speed shift-hybrid modulation method for MC-DCSK. This invention introduces index modulation technology, dividing binary data information into modulation bits and index bits. First, the transmitter uses Discrete Sine Transform (DST) to generate u mutually orthogonal signals, each carrying modulation bits. This increases the transmission rate while maintaining the same bandwidth and avoiding internal signal interference. Then, the orthogonal chaotic shift keying (QCSK) and differential chaotic shift keying (DCSK) modulation methods are combined, using the index bits to shift the signal, further improving the transmission rate. At the receiver, a segmented averaging method is used to reduce noise and improve the system's bit error rate performance.

[0047] 1. A hybrid modulation technique is employed, which simultaneously incorporates DCSK and QCSK modulation techniques. DCSK modulation maps binary data information to ±1, while QCSK modulation maps binary data information to... Furthermore, the special signal of this invention employs DCSK modulation, so the index bit can be obtained using maximum likelihood estimation after shifting the special signal. This allows the invention to improve the system's transmission rate under the same bandwidth conditions.

[0048] 2. Discrete orthogonal transformation is adopted. Discrete orthogonal transformation can generate multiple sets of orthogonal signals at the transmitting end. Since each set of signals carries modulation bits, it can ensure that more modulation bits can be transmitted in the same time slot, avoiding the waste of time slots in time division multiplexing. At the same time, it can also avoid the signal interference problem introduced during demodulation at the receiving end.

[0049] 3. Employing index modulation technology, this invention introduces index bits by changing the position of special signals, ensuring that the energy transmitted at the transmitting end remains constant within a given spectrum resource. Simultaneously, it can scramble the signal order, thereby improving system security.

[0050] 4. Segmented Averaging Noise Reduction: This invention reduces the variance of noise in the decision variable by segmenting and averaging the received signal, thus achieving noise reduction. As the number of replications increases, not only does the system's transmission rate increase, but its error rate performance also improves.

[0051] 5. The modulation scheme adopted in this invention maps the index bits of binary data information to decimal symbols, and then shifts the signal according to these symbols. This does not cause a change in the Euclidean distance of the system. Furthermore, the increase in index bits provides the system with more selectivity and flexibility, resulting in better bit error rate performance. This differs from the traditional MDCSK scheme, which, due to the increased number of input bits, introduces a smaller Euclidean distance during demodulation, leading to poorer bit error rate performance. Attached Figure Description

[0052] Figure 1 This is a preferred embodiment of the transmitter structure diagram provided by the present invention;

[0053] Figure 2 This is a schematic diagram of the (P+1) frame structure after the shifting of the present invention;

[0054] Figure 3 This is the power spectral density diagram of the transmitter of this invention;

[0055] Figure 4 This is a block diagram of the receiver of the present invention;

[0056] Figure 5 This invention involves a segmented averaging noise reduction process.

[0057] Figure 6 The present invention compares the simulated and theoretical values ​​of the system when u = 3, 5, and 7.

[0058] Figure 7 This invention differs from E b The relationship between u and system BER at / N0 value;

[0059] Figure 8 The present invention compares the simulated values ​​and theoretical values ​​of the system when N = 1, 2, 3;

[0060] Figure 9 The present invention compares the simulated and theoretical values ​​of the system when P = 1, 3, and 7.

[0061] Figure 10 Comparison of BER curves between the present invention and the MC-DCSK system when N=4, 10, 16;

[0062] Figure 11 This is a schematic diagram of a preferred embodiment of the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method provided by the present invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0064] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0065] The implementation of the present invention will now be described in detail with reference to the accompanying drawings. Figure 1 The diagram shows the structure of the transmitter. The chaos generator uses a second-order Chebyshev mapping to generate a chaotic signal p = [p1, ... p2] of length R. R The expression that satisfies this condition is:

[0066]

[0067] Then, the chaotic signal is symbolized to obtain x = [x1, ..., x]. R ], satisfying x i =sgn(p i ), where i = 1, ..., R, sgn(·) is the symbolic operation. Since x i The value of x can be either "+1" or "-1", therefore the relationship is: E(x) i ) = 0, var(x) i ) = 1, where E(·) is the expected value operation and var(·) is the variance operation. x is a 1×(P+1) matrix of all 1s. Performing the Kronecker product operation yields Where "×" represents the multiplication operation, the specific expression is: The ⊙ symbol represents the Kronecker product, which replicates the signal (P+1) times. Next... Through with The Hadamard product is performed to obtain the signal y0 on the reference subcarrier f0, which is essentially a normalization of the signal power for easier subsequent calculations. Simultaneously... The information subcarrier f is obtained by introducing discrete sine transform for hybrid modulation. q Signal y on (q=1,…,N) q Compared to traditional Walsh codes, the sequence length R does not need to satisfy R mod 2 = 0, where mod represents the modulo operation. The expression for the discrete sine transform is as follows:

[0068]

[0069] Where D w,v Let w be the w-th row and v-th column element of the discrete sine transform code group D, satisfying Take the u-row matrix D before D s =[D s,1 ,…,D s,R ](s=1,…,u) and Perform the Kronecker product operation to obtain U s ,Right now Then with U s After performing the Hadamard product, the mixture is modulated.

[0070] After serial-to-parallel conversion, the bit stream is divided into two parts: modulation bits and index bits, with the information subcarrier f. q On the sequence (q=1,…,N), there are κ1=(u-1)P+u modulation bits used for hybrid modulation, and κ2=log2(P+1) index bits used for shifting the signal after hybrid modulation. Assume the interval time of the chaotic sequence is T. c In order to introduce shift index bits, a special set of signals needs to be set as shift markers. Figure 1 This indicates that the special signal is generated by the U1 branch, in the range [0,RT]. c Within a given time period, when the switch in branch U1 is closed, the signal passes through U1, ..., U... u The u groups of orthogonal signals generated by the Hadamard product of columns 1 to R are mixed and modulated to carry u bits of information. In [ΔRT] c ,(1+Δ)RT c During the time interval (Δ=1,…,P), the switch is open, and the signal passes through U2,…,U u The Hadamard product of the elements in columns ΔR+1 to (1+Δ)R generates (u-1) sets of orthogonal signals carrying (u-1) bits of information. Next, the mixed-modulated signal is shifted, and the shifted signal is y. q .

[0071] Figure 2 This is a schematic diagram of the (P+1)th frame structure after shifting. The signal passes through the Uth frame. s The signal obtained after the branch is: If t is the Hadamard product, then s The element in the i-th column can be represented as: t s,i =D s,i x i (i = 1, ..., R). t1 is a special signal generated by the U1 branch, in f q On a carrier wave (q = 1, ..., N), t1 satisfies DCSK modulation, and the 1 bit of information it carries satisfies the mapping relationship: 0 → -1, 1 → +1, i.e., c q ∈{+1,-1}. t 2n and t 2n+1 (n=1,…,(u-1) / 2) satisfies QCSK modulation, and the 1 bit of information carried satisfies: That is, the signal is in [(m-1)RT c mRT c [During time intervals of m=1,…,P+1, U] 2n and U 2n+1 Information mapped after the branch Assuming the κ2 shift index bits are κ, then by The shifted signal after hybrid modulation determines the position containing t1, where B(·) is the binary-to-decimal conversion operation. For example... Figure 2 Assuming the signal is not shifted, the signal is represented as in This represents a matrix of length R, with a frame length of RT. c , Let be a matrix containing a specific signal t1. When Move backward 0×RT c Frame length, i.e., remains unchanged before and after the shift, when hour, Move backward by 1×RT c Frame length, shifted matrix y q It can be represented as: hour, Move backward by 2×RT c Frame length, shifted matrix y q It can be represented as: According to this pattern, when hour, Move backward P×RT c Frame length, shifted matrix y q It can be represented as: The expression is:

[0072]

[0073] The shifted signal and the signal on the reference carrier are converted to the output expression y by digital-to-analog (D / A) conversion. r (t)(r=0,…,N) is:

[0074]

[0075] Where h(t-jT) c y represents the impulse response generated by the pulse shaping filter, with energy normalized to 1. r,j For y on the r-th subcarrier after shifting r The j-th column element, r = 0, ..., N, j = 1, ..., R(1+P). Finally, the signal uses a center frequency of f. r For subcarrier transmission, to prevent signal interference between adjacent carriers, the spacing between adjacent carriers is assumed to satisfy (1+γ) / T. c γ is the roll-off factor. Therefore, the expression for the transmitter's output signal s(t) is:

[0076]

[0077] Where, φ r This represents the phase angle of the r-th subcarrier. The power spectral density diagram at its transmitter is shown below. Figure 3 .

[0078] Since the total number of information bits transmitted by the system is N(κ1+κ2), the average bit energy of the system can be obtained through equation (5):

[0079]

[0080] Figure 4 This is a block diagram of the receiver of the present invention. After the signal passes through the additive white Gaussian noise (AWGN) channel, the resulting signal is r(t). Signal r(t) passes through the corresponding subcarrier and is then filtered by a matched filter, followed by analog-to-digital conversion to obtain the recovered reference signal r0 and the data bearer signal r. q (q = 1, ..., N). r0 is the signal on a carrier wave with frequency f0, r q For a frequency of f q The signal on the carrier wave. Analog-to-digital conversion is performed for ideal sampling, with a sampling interval of jT. c (j=1,…,R(1+P)), where the matched filter is matched to h(t) to obtain the maximum output signal-to-noise ratio at each sampling time point. q (q=1,…,N) can be equally divided into (P+1) segments, i.e. in Given a 1×R matrix, we obtain a 1×R matrix by piecewise averaging and noise reduction on r0. It can be represented as:

[0081] Figure 5 This is a schematic diagram of segmented averaging for noise reduction. r0 is divided into (P+1) equal segments, and the elements of each segment are weighted and averaged. The element in the j-th column of r0 can be represented as r 0,j (j=1,…,R(1+P)), for example r 0,1 The corresponding element is r 0,pR+1 (p=1,…,P), the average of the corresponding (P+1) elements can be obtained. set up The noise in is n (0) n (0) The element in the i-th column is Therefore, after averaging the segments The expression for the element in the i-th column is: Then After performing the Hadamard product with D1, and then... Correlation summation, also known as piecewise summation, yields the correlation value. Its expression is:

[0082]

[0083] Where T is the transpose operation. This involves taking the absolute values ​​of (P+1) related values. The position that determines t1 is obtained through maximum likelihood estimation. Then The index bit is obtained by converting it to binary. To facilitate obtaining the corresponding modulation bit, the shift detector uses... r q Inverse shift obtained in For example, a matrix of dimension 1×R The signal matrix containing t1 is Will Moving forward by 1×R, which is the result after the shift, is... In fact, setting it as The noise matrix in the file, then It can be represented as: Then After multiplying with the DST code Hadamard, and then... The correlation is summed, and finally, the modulation bits are recovered by inverse mapping based on the polarity of the correlation values. Assume the position of t1 is located at... At this point, the correlation value after the piecewise summation operation is The correlation value at a non-t1 position can be expressed as Their expressions are as follows:

[0084]

[0085]

[0086] In equations (8) and (9) r0 is Gaussian white noise after noise reduction. and For r q Gaussian white noise in the image. When the index bit is incorrectly determined, it means that the noise intensity is too high, causing... Less than Therefore, the symbol error rate for index decision errors is:

[0087]

[0088] in and Pr{·} represents probability operations. for The cumulative distribution function, for The probability density function.

[0089] To demodulate the modulation bits, it is necessary to... After multiplying with the corresponding DST code Hadamard product, and then... Correlation summation, demodulation c in q At that time, it is necessary to After multiplying with D1 Hadamard, and then with Correlation summation, the result of which is because In and The demodulation is independent of each other, so here we only consider... For example. After multiplying with D2Hadamard, and then with The relevant summation can be used to make a judgment. Its expression is:

[0090]

[0091] Because it does not contain special signals The modulation and demodulation of the bits are also independent of each other, therefore, here we take... For example. After multiplying with D2Hadamard, and then with The relevant summation can be used to make a judgment. Its expression is:

[0092]

[0093] The bit error rate (BER) of the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method is analyzed and derived below using the Gaussian approximation method. Due to the good stability of the second-order Chebyshev mapping, it is used to generate chaotic sequences in the system simulation. The generated signal is symbolized and possesses the mathematical characteristic E(x) i ) = 0, var(x) i = 1. The mathematical characteristics satisfied by the discrete sinusoidal change are: When R is a constant value Δ1 and Δ2 can be calculated. Assume the noise level after noise reduction is n. (0) , For n (0) The elements in the i-th column, i = 1, ..., R, satisfy the following numerical characteristics: The noise n (m) The i-th element is The mathematical characteristics that are satisfied are Because n (0) and n (m) The carriers are independent of each other, and the demodulation between them is also independent. Based on the above conditions, according to the central limit theorem, equations (8), (9), (11), and (12) all approximately follow a Gaussian distribution. Taking their mean and variance, we can obtain:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] In equation (10) and They are represented as follows:

[0103]

[0104]

[0105] In equation (21), erf(·) is the error function, which satisfies In equation (22), exp(·) is an exponential function that satisfies exp(x)=e x .

[0106] The probability of demodulation error of the modulation bit in equations (8), (11), and (12) is:

[0107]

[0108]

[0109]

[0110] In equation (23), the complementary error function erfc(x) = 1 - erf(x) and in equations (24) and (25), the Q function...

[0111] When the shift index demodulation fails, r qAn inverse shift will result in an error. There are (2u-1) bits with an error probability of 0.5 in the κ1 bits, and the remaining bits have an error probability of P3. Therefore, the average bit error rate of the modulated bits can be expressed as:

[0112]

[0113] When the signal shift index demodulation is correct, the transmitter can be considered as having only modulated information bits, and its average bit error rate of the modulated bits is P. e , can be represented as:

[0114]

[0115] After considering the above factors, the probability of demodulation error in the modulated information bits is:

[0116] P mod =P e (1-P s )+P n P s (28)

[0117] The probability of an index bit error is related to P. s The satisfied relationship is:

[0118]

[0119] Therefore, the system's bit error rate expression is:

[0120]

[0121] Figure 6 This illustrates the changes in the theoretical bit error rate (BER) curve and the experimental simulation curve for a high-speed shift-modulated hybrid modulation multicarrier differential chaotic shift keying system with different values ​​of the number of orthogonal signal groups (u). As the signal-to-noise ratio (SNR) E... b As / N0 increases, the bit error rate (BER) decreases, and the theoretical and simulated values ​​are in good agreement, verifying the correctness of the formula derivation. The BER curve is highest when u = 3, but the changes are not significant when u = 5 and u = 7. To clearly see the differences in BER values ​​at different E... b The impact of u on BER under / N0 Figure 7 For high-speed shift hybrid modulation multicarrier differential chaotic shift keying systems in different E b The graph showing the change in BER (E / N0) with increasing u indicates that E b The larger / N0 is, the smaller the BER at this point, which is consistent with... Figure 6The conclusion is that, as u increases, BER first decreases and then increases. This is because, although increasing u increases the system's transmission rate and improves its performance, it also introduces more noise components. Figure 8 This section describes the changes in the theoretical bit error rate (BER) curve and the experimental simulation curve when the number of information subcarriers N is different. It can be seen that the theoretical and simulated values ​​are basically in agreement. When E... b When / N0 is constant, the larger the value of N, the smaller the BER of the high-speed shift hybrid modulation multicarrier differential chaotic shift keying system, and the E of N=1 and N=2 is also smaller. b The difference between / N0 and E is approximately 1 dB, and the difference between N=2 and N=3 is... b The / N0 difference is approximately 0.5dB. This is because the average bit energy of the system tends to a constant as the value of N increases, making the influence of N on BER smaller and smaller. Figure 9 This describes the changes in the theoretical bit error rate curve and the experimental simulation curve as P changes with the number of replications (P+1). It can be seen that at the same E... b Under the condition of / N0, BER increases with the increase of P. This is mainly because the receiver uses noise reduction processing. Increasing P will improve the noise reduction capability of the system, and the theoretical value basically matches the simulation value. Figure 10 It can be seen that, under the same conditions as the MC-DCSK system, the error rate performance of this invention is consistently superior to that of the MC-DCSK system. This is because this invention combines DCSK and QCSK modulation, utilizing the orthogonality of discrete sine transform to avoid internal signal interference, and further introduces index modulation technology, resulting in a transmission rate that is consistently better than that of the MC-DCSK system. This invention employs a segmented averaging method for noise reduction at the receiver, further improving the system's error rate performance.

[0122] This invention utilizes discrete sine transform at the transmitting end to generate u sets of orthogonal signals, avoiding internal signal interference. Then, binary data information is divided into index bits and modulation bits, mapped to different transmission coefficients. The mapped modulation bit transmission coefficients employ two modulation modes: DCSK modulation and QCSK modulation, ensuring increased transmission rate while maintaining bandwidth. This invention also incorporates indexing technology, shifting the hybrid modulated signal according to the transmission symbol of the mapped index bits, further enhancing the system's transmission rate. Finally, multi-carrier modulation distributes the signal across multiple carriers, increasing the system's anti-interference capability. At the receiving end, a segmented averaging method is used for noise reduction, improving the system's bit error rate performance. Through the derivation of the system's bit error rate and Monte Carlo simulation experiments, comparing the experimental results with the derived formulas shows that the simulated values ​​are in good agreement with the theoretical values, demonstrating superior bit error rate performance and broad application potential in practical communication systems.

[0123] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0124] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0125] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0126] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method, characterized in that, Includes the following steps: Step 1: Generate a reference signal using a chaos generator; Step 2: Mix, modulate, and shift the reference signal to generate the data carrier signal; Step 3: The reference signal and the data carrier signal are transmitted using a carrier wave; Step 4: After the signal passes through the channel, carrier demodulation and information bit restoration are performed; Step 1 uses a chaos generator to generate a reference signal, specifically including: The chaos generator at the transmitting end uses a second-order Chebyshev map to generate a chaotic signal with a sequence length of R. Then, the chaotic signal is symbolized to obtain... ,satisfy ,in , For symbolic operations; With dimension A matrix of all 1s Performing the Kronecker product operation yields ,in" " represents the multiplication operation, and the specific expression is: , To perform the Kronecker product operation and replicate the signal. Next; last After normalization, that is, by comparing with Performing the Hadamard product operation yields a length of Reference signal ; Step 2, specifically the mixing and modulation of the reference signal, includes: After binary data is converted from serial to parallel, it is divided into two parts: modulation bits and index bits. Bits are used as modulation bits for hybrid modulation. Bits are used as index bits for shifting the signal after hybrid modulation; assuming the interval time of the chaotic sequence is... That is The frame length is Then, it is mixed and modulated after passing through u branches; assuming that the branches here are ,through The signal after the branch is a special signal, in Within a time period, after When the branch switch is closed, the signal is respectively connected to the matrix. The elements from columns 1 to R are subjected to a Hadamard product to generate u sets of orthogonal signals, which are then modulated, with each set of signals carrying 1 bit of information; Within a time period, after The branch switch is open, meaning the signal is connected to the matrix respectively. of arrive The Hadamard product operation of column elements produces The signals are divided into groups of orthogonal signals, and after modulation, each group of signals also carries 1 bit of information. Therefore, here... ; Discrete Sine Transform Code and The expression for the Kronecker product, the discrete transform code, is as follows: in , ;Will and Performing the Kronecker product operation yields a length of of ,Right now ; After mapping, each modulation bit can be used express, Information carried by special signals The signals are respectively in Within a time period and The information carried by the branch, including ; There are two different mapping relationships for modulation bits, namely: (1) , ,Right now ; (2) , ,Right now .

2. The high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method according to claim 1, characterized in that, The shifting step in step 2 specifically includes: The signal is mixed and modulated to obtain a frame length of The signal, assuming The index bits are Then by The shifting of the hybrid modulated signal determines the location containing the special signal, where This is a binary to decimal conversion operation; assuming the signal is not shifted, the signal is represented as... ,in This represents a matrix of length R. Frame length is , For a matrix containing a special signal; when , Move backward Frame length, i.e., remains unchanged before and after the shift, when hour, Move backward Frame length, shifted matrix It can be represented as: , hour, Move backward Frame length, shifted matrix It can be represented as: According to this pattern, when hour, Move backward Frame length, shifted matrix It can be represented as: ; The expression is: in For the signal in Time passed The special signal of length R generated during branching satisfies the following expression: ; and Indicates the signal at Passing through the time respectively and The signal of length R generated after the branch is expressed as: , .

3. The high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method according to claim 1, characterized in that, Step 3, which involves transmitting the reference signal and the data carrier signal using a carrier wave, specifically includes: By combining multi-carrier technology, the data-carrying signal is extended to N channels, utilizing a frequency of Subcarrier transmission, with the reference signal utilizing a frequency of Subcarrier transmission; assuming the signal on the subcarrier with frequency q is shifted to obtain the data carrier signal. , , subcarrier The signal is ,because It is a discrete signal. Therefore, first After digital-to-analog conversion and carrier modulation, the expression of the signal after digital-to-analog conversion is: in For matrix The element in the j-th column, The duration is The pulse signal, here is the impulse response of a square-lifted cosine filter, with energy normalized to 1; assume the interval between adjacent carriers satisfies , The roll-off factor is used; therefore, the output expression of the transmitter is: in, This represents the phase angle of the r-th subcarrier; since the total number of information bits transmitted by the system is... Therefore, the average bit energy of the system can be obtained from the above formula: 。 4. The high-speed shift hybrid modulation multi-carrier differential chaotic shift keying method according to claim 1, characterized in that, The signal in step 4, after passing through the channel, undergoes carrier demodulation and information bit restoration, specifically including: Step 4.1: Signal via channel: signal Additive white Gaussian noise in AWGN channels The impact, It has a mean of 1 and a two-sided power spectral density of The mathematical characteristics; the signal received at the receiving end is: ; Step 4.2: Carrier Demodulation: Signal The corresponding subcarrier is followed by a matched filter, and then analog-to-digital conversion is performed to obtain the recovered reference signal. With data carrying signal ; For frequency Signal on carrier wave, For frequency The signal on the carrier wave; analog-to-digital conversion to ideal sampling, with a sampling interval of... To obtain the maximum output signal-to-noise ratio at each sampling time point, the matched filter here is... Matching; It is divided into (P+1) segments, i.e. ,in For dimension Matrix; Step 4.3: Information Bit Reconstruction: To reduce the impact of noise, the recovered reference signal is now denoised using a piecewise averaging method, resulting in a signal of length [length missing]. of In order to obtain the location of the special signal, and Perform the Kronecker product operation, then By performing related operations, we can obtain... Relevant values ; The expression is as follows: Where T is the transpose operation; Take the absolute value of each relevant value, that is Then, the maximum likelihood estimation yields the method that determines the location of the specific signal. Then to The index bits are obtained by performing a decimal-to-binary inverse mapping; to facilitate obtaining the corresponding modulation information bits, the shift detector... Will Perform reverse shift to obtain , This means It contains a special signal, which is then inverted and shifted. Move forward Length, that is In fact, assuming for The noise matrix in It can be represented as: ;Will After multiplying with the Hadamard code of the discrete sine transform, and then... The relevant decision criterion between the index bit and the modulation bit is as follows: in For frequency On the subcarrier middle The corresponding modulation bits; The modulation bits are recovered by inverse mapping of polarity.

5. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the program, it implements the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method as described in any one of claims 1 to 4.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method as described in any one of claims 1 to 4.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the high-speed shift hybrid modulation multicarrier differential chaotic shift keying method as described in any one of claims 1 to 4.

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