A frequency control array radar radio frequency stealth waveform design method

Abstract

The application discloses a frequency control array radar radio frequency stealth waveform design method, constructs an LFM-CPC-DCFC combined coding waveform of a frequency control array radar, uses a complementary binary phase code sequence to perform phase coding between sub-pulses, and combines a chaotic sequence generated by a chaotic mapping to perform discrete chaotic frequency coding between the sub-pulses, and finally modulates the generated baseband waveform to the carrier of each array element of the frequency control array for emission. The design method disclosed by the application can effectively reduce the autocorrelation peak sidelobe level of the emitted waveform and make the waveform have a "thumbtack type" ambiguity function, while increasing the complexity and pseudo-randomness of the waveform, so that the radio frequency stealth performance of the radiation waveform of the frequency control array radar can be improved.

Description

Technical Field

[0001] This invention relates to the field of radar waveform design technology, and in particular to a method for designing radio frequency stealth waveforms for frequency-controlled array radar. Background Technology

[0002] Passive detection systems, with their advantage of single-path ranging, have a maximum detection range far exceeding that of conventional radar systems. This poses a significant threat to radar and other radiation source equipment performing normal detection tasks on the battlefield. Modern radars have an increasing need to improve their radio frequency (RF) stealth capabilities.

[0003] RF stealth technology, also known as Low Probability of Interception (LPI) technology or active target signature reduction technology, refers to using various methods to minimize the radio frequency (RF) signal characteristics of radar, communication, and other electronic equipment mounted on airborne or vehicle-mounted platforms, making it difficult for enemy electronic reconnaissance systems to detect and locate the radiation source in a timely manner. RF stealth technology can significantly improve radar defense capabilities and increase the survivability of radar on the battlefield, and is currently a key research focus in the field of electronic warfare.

[0004] Radio frequency (RF) stealth waveform design, as an important branch of RF stealth technology, plays a crucial role in improving the RF stealth capabilities of radar and other radiation source devices. Currently, most research on RF stealth waveform design is based on phased arrays, while frequency-controlled arrays are essentially a special type of phased array that introduces an additional frequency offset to each element. Therefore, frequency-controlled arrays possess all the functional characteristics of phased arrays, but also have some advantages that phased arrays lack, making them particularly promising for applications in the field of RF stealth.

[0005] Linear Frequency Modulation (LFM) signals are simple and widely used LPI pulse compression signals. Although LFM signals can achieve a large time-bandwidth product through pulse compression techniques, they suffer from high sidelobe levels and range-Doppler coupling issues. Compared to LFM signals, coded signals can improve the versatility of the modulated signal. Phase-coded signals, due to their large bandwidth and periodic ambiguity function with low sidelobe levels, have strong anti-interference characteristics. However, phase-coded signals such as binary phase codes suffer from Doppler sensitivity and relatively high sidelobe levels. Frequency-coded signals can vary their frequency over a wide bandwidth, resulting in a larger equivalent bandwidth and effectively reducing the probability of non-cooperative receivers intercepting their waveforms. However, frequency-coded signals also suffer from high sidelobe levels, which necessitates some additional weighting processing when these waveforms are applied to matched filters. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a method for designing radio frequency stealth waveforms for frequency-controlled array radars, thereby reducing the probability that the radiation waveforms of frequency-controlled array radars can be detected by enemy passive detection systems.

[0007] A method for designing radio frequency stealth waveforms for frequency-controlled array radar includes the following steps:

[0008] Step S1: Generate the original frequency-coded sequence using Bernoulli mapping, wherein the Bernoulli mapping formula is:

[0009]

[0010] Where, x n Let α be the value of the nth chaotic sequence, and let α be the parameter of the Bernoulli mapping. After multiple iterations using the initial value x0 according to the mapping formula, a Bernoulli discrete chaotic sequence X is generated: X = {x1, x2, ...}, n = 0, 1, 2, ...;

[0011] Step S2: Perform uniform quantization on the Bernoulli discrete chaotic sequence X to generate a discrete chaotic frequency-coded codeword sequence, represented as: D DCFC ={d1,d2,…};

[0012] Step S3: Construct a pair of complementary phase-coded codeword sequences of length N using the basic code group and construction method of complementary codes, denoted as A = {a1, a2, ..., a...} N} and B = {b1,b2,…,b N};

[0013] Step S4: Divide a pulse evenly into N sub-pulses. Use the DCFC discrete chaotic frequency coding codeword sequence and the CPC complementary phase coding codeword sequence to perform frequency modulation and phase modulation between the sub-pulses respectively, generating a linear frequency modulation-complementary phase coding-discrete chaotic frequency coding (LFM-CPC-DCFC) joint coding modulation signal. Its M pulse signals can be represented as:

[0014]

[0015] In the formula, a m,n The complementary phase encoding of the (n+1)th sub-pulse in the (m+1)th pulse, where k is the modulation coefficient and τ m,n =nT LFM +mT r T LFM T is the sub-pulse width. r f is the pulse repetition period. m,n =D DCFC(m×N+n)·Δf is the encoding frequency of the (n+1)th sub-pulse in the (m+1)th pulse, Δf is the frequency interval, and rect(·) is the rectangular function, expressed as:

[0016]

[0017] Step S5: Modulate the linear frequency modulation-complementary phase coding-discrete chaotic frequency coding (LFM-CPC-DCFC) baseband signal onto the carrier of each element of the frequency control array;

[0018] Step S6: Verify the time-frequency domain distribution, autocorrelation function, and ambiguity function characteristics of the received echo signal to evaluate its radio frequency stealth performance.

[0019] Furthermore, step S1, discrete chaotic mapping, also includes the following sub-steps:

[0020] Step S11: Determine the initial value x0 of the Bernoulli chaotic map. Change the initial value x0 of the chaotic map in steps of 0.001 within the range of values. Select the initial value that minimizes the peak autocorrelation sidelobe level (PSLL) of the generated chaotic sequence as the optimal initial value of the chaotic map. The definition of the peak autocorrelation sidelobe level (PSLL) is:

[0021]

[0022] Where k is the index of each value point in the autocorrelation function; R(k) is the level of all sidelobes of the autocorrelation function except when k = 0;

[0023] Step S12: Using the determined optimal initial value x0, generate the Bernoulli chaotic sequence X = {x1, x2, ...} through iteration according to the Bernoulli mapping formula.

[0024] Furthermore, the uniform quantization process in step S2 also includes the following steps:

[0025] Step S21: Perform multi-valued quantization on the Bernoulli chaotic sequence X. Assume the range of values ​​in the chaotic sequence is between a and b, the number of quantization levels is N, and the quantization interval when using uniform quantization is: The endpoints of the quantization interval are:

[0026] m i = a + i × Δv i = 0, 1, ..., N;

[0027] Step S22: Quantize the output level d i The value is the left endpoint of the quantization interval minus 'a', then divided by the quantization interval, i.e.:

[0028]

[0029] The chaotic sequence X is quantized to generate a DCFC discrete chaotic frequency encoded codeword sequence: D DCFC ={d1,d2,…}.

[0030] Furthermore, step S3 also includes the following steps:

[0031] The length of the complementary binary phase code is set to the number of sub-pulses in a single pulse. Using a shorter base code group, a new complementary code sequence of a specified length is generated according to certain construction rules. A pair of CPC complementary phase-coded codeword sequences A and B of length N are constructed using a concatenation method. These two sequences are a positive code sequence and a complement code sequence, respectively, and their values ​​only contain +1 and -1. After the autocorrelation functions of the complementary binary phase codes are added, their sidelobe levels are completely canceled out, while the peak value at the main lobe is doubled.

[0032]

[0033] Among them, R A R is the autocorrelation function of the positive code sequence. B Let τ be the autocorrelation function of the two's complement sequence, and τ be the delay unit.

[0034] Furthermore, step S4 specifically includes the following sub-steps:

[0035] Step S41: Divide a complete pulse duration into N sub-pulses, where each sub-pulse transmits an LFM signal. The signal in a pulse can be represented as:

[0036]

[0037] Among them, T LFM Let be the sub-pulse width, k be the modulation coefficient, rect(.) be the rectangular function, and:

[0038]

[0039] Where T is the width of the rectangle;

[0040] Step S42: Utilize the DCFC discrete chaotic frequency encoded codeword sequence D DCFC ={d1,d2…} The LFM signal transmitted in each sub-pulse of step S41 is frequency modulated between sub-pulses to form a linear frequency modulation-discrete chaotic frequency-coded LFM-DCFC signal. Its time-domain expression in the M pulses is:

[0041]

[0042] Where τ m,n =nT LFM +mT rT r D is the pulse repetition period. DCFC (n) is the (n+1)th element in the DCFC codeword sequence, f m,n =D DCFC (m×N+n)·Δf is the encoding frequency of the (n+1)th sub-pulse in the (m+1)th pulse, and Δf is the frequency interval;

[0043] Step S43: Using the CPC complementary phase-coded codeword sequence, the linear frequency modulation-discrete chaotic frequency-coded (LFM-DCFC) signal is phase-coded and modulated between sub-pulses to obtain a joint LFM-CPC-DCFC coded and modulated signal, whose complex envelope time-domain expression in M ​​pulses is:

[0044]

[0045] Where, a m,n Let be the encoded phase of the (n+1)th sub-pulse in the (m+1)th pulse, and satisfy:

[0046] A(n) is the (n+1)th element of the positive code sequence in the CPC codeword sequence, and B(n) is the (n+1)th element of the complement code sequence in the CPC codeword sequence.

[0047] Furthermore, step S5 specifically includes:

[0048] If the frequency control array is a uniform linear array with M transmitting elements and an element spacing of d, then the carrier frequency of the m-th element is expressed as:

[0049] f m =f0+mΔf,m=0,1,…,M-1;

[0050] Where f0 and Δf are the carrier frequency and frequency offset, respectively;

[0051] The pulse signal emitted by the m-th array element can be represented as:

[0052] s m (t)=φ(t)·exp(j2πf m t), m=0,1,…,M-1.;

[0053] Where φ(t) is the baseband signal of the LFM-CPC-DCFC joint coded modulation signal;

[0054] If the transmission weight vector w T =[ω T,0 ,ω T,1 ,…,ω T,M-1 ]T ,in T This indicates the transpose operation; the synthesized signal at the far-field azimuth angle θ and distance r can be represented as:

[0055]

[0056] Wherein, the far-field azimuth angle θ is referenced to the antenna line-of-sight direction, the distance r is referenced to the first transmitting element, and τ m =r m / c represents the propagation delay of the signal from the m-th array element to the far-field point (θ, r), where c is the speed of light and r is the speed of light. m =r-mdsin(θ) is the distance from the m-th element to the far-field point.

[0057] Furthermore, in step S6, the time-frequency domain distribution utilizes short-time Fourier transform to perform time-frequency domain analysis on the radar waveform; the autocorrelation function represents the similarity between signals as a function of their time difference, and is a measure of signal similarity, with the formula:

[0058]

[0059] Where τ represents the time delay, f(τ) represents the signal waveform, * represents the convolution operation, and (·) * This indicates the conjugate operation.

[0060] Furthermore, the ambiguity function in step S6 describes the response of a finite-duration signal through a matched receiver, and its formula is:

[0061]

[0062] Where τ is the time delay, ξ is the Doppler frequency shift, u(t) is the signal waveform, and |·| is the modulus operation.

[0063] The beneficial effects of this invention are as follows: This invention proposes a method for designing radio frequency (RF) stealth waveforms for frequency-controlled array radar. It constructs a joint LFM-CPC-DCFC coded waveform for the RF-controlled array radar, uses complementary binary phase code sequences for phase coding between sub-pulses, and combines this with chaotic sequences generated by chaotic mapping for discrete chaotic frequency coding between sub-pulses. Finally, the resulting baseband waveform is modulated onto the carrier waves of each element of the RF-controlled array for transmission. This waveform design method effectively reduces the autocorrelation peak sidelobe level of the transmitted waveform and gives the waveform a "thumbtack-shaped" ambiguity function. Simultaneously, it increases the complexity and pseudo-randomness of the waveform, thereby improving the RF stealth performance of the RF-controlled array radar's radiated waveform. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating the LFM-CPC-DCFC signal generation process of a frequency-controlled array radar in an embodiment of the present invention.

[0065] Figure 2 This is a time-frequency distribution diagram of a single pulse of the frequency-controlled array radar LFM-CPC-DCFC signal in an embodiment of the present invention;

[0066] Figure 3 This is a graph of the autocorrelation function of the frequency-controlled array radar LFM signal in an embodiment of the present invention;

[0067] Figure 4 This is a graph of the autocorrelation function of the frequency-controlled array radar LFM-CPC-DCFC signal in an embodiment of the present invention;

[0068] Figure 5 This is a three-dimensional ambiguity function graph of the frequency-controlled array radar LFM signal in an embodiment of the present invention;

[0069] Figure 6 This is a three-dimensional ambiguity function diagram of the frequency-controlled array radar LFM-CPC-DCFC signal designed in an embodiment of the present invention. Detailed Implementation

[0070] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0071] This invention proposes a method for designing radio frequency stealth waveforms for frequency-controlled array radar. The waveform generation process is as follows: Figure 1 As shown, it includes the following steps:

[0072] S1. The original frequency-coded sequence is generated using the Bernoulli mapping. The Bernoulli mapping formula is:

[0073]

[0074] Where, x n Let x be the nth chaotic sequence value, and α be the parameter of the Bernoulli mapping. Using the initial value x0, the sequence after multiple iterations according to the mapping formula is: X = {x1, x2, ...}.

[0075] S2. Perform uniform quantization on the Bernoulli discrete chaotic sequence X generated in step S1 to generate a Discrete Chaos Frequency-Coding (DCFC) codeword sequence, represented as: D DCFC ={d1,d2,…}.

[0076] S3. Using the basic code group and construction method of complementary codes, generate a pair of complementary phase-coding (CPC) codeword sequences of length N, denoted as A = {a1, a2, ..., a...} N} and B = {b1,b2,…,b N}

[0077] S4. Divide a pulse evenly into N sub-pulses. Using the DCFC codeword sequence and CPC codeword sequence generated in steps S2 and S3, perform frequency modulation and phase modulation respectively between the sub-pulses to generate a Linear Frequency Modulation-Complementary Phase Coding-Discrete Chaos Frequency Coding (LFM-CPC-DCFC) signal. Its M pulse signals can be represented as:

[0078]

[0079] In the formula, a m,n The complementary phase encoding of the (n+1)th sub-pulse in the (m+1)th pulse, where k is the modulation coefficient and τ m,n =nT LFM +mT r T LFM T is the sub-pulse width. r f is the pulse repetition period. m,n =D DCFC (m×N+n)·Δf is the encoding frequency of the (n+1)th sub-pulse in the (m+1)th pulse, Δf is the frequency interval, and rect(·) is the rectangular function, expressed as:

[0080]

[0081] S5. Use frequency-controlled array radar to transmit modulated radio frequency stealth waveforms.

[0082] S6. Verify the time-frequency domain distribution, autocorrelation function, and ambiguity function characteristics of the received echo signal, and evaluate its radio frequency stealth performance.

[0083] In this embodiment, step S1 includes the following sub-steps:

[0084] S11. Determine the initial value x0 of the Bernoulli chaotic map. Since different initial values ​​lead to different autocorrelation properties in chaotic sequences, the initial value x0 of the chaotic map is changed in steps of 0.001 within its range. The initial value that minimizes the peak side-lobe level (PSLL) of the generated chaotic sequence is selected as the optimal initial value for the chaotic map. The PSLL is defined as follows:

[0085]

[0086] Where k is the index of each value point in the autocorrelation function; R(k) is the level of all sidelobes of the autocorrelation function except for k=0.

[0087] S12. Using the optimal initial value x0 determined in step S11, generate the Bernoulli chaotic sequence X = {x1, x2, ...} iteratively according to the Bernoulli mapping formula. The Bernoulli mapping formula is expressed as:

[0088]

[0089] Where, x n Let α be the value of the nth chaotic sequence, and let α be the parameter of the Bernoulli chaotic map, where n = 0, 1, 2, ...

[0090] In this embodiment, step S2 further includes:

[0091] The Bernoulli chaotic sequence X generated in step S1 is subjected to multi-value quantization. Assume the chaotic sequence values ​​range between a and b, the number of quantization levels is N, and the quantization interval for uniform quantization is:

[0092]

[0093] The endpoints of the quantization interval are:

[0094] m i =a+i×Δv i=0,1,…,N.

[0095] Quantization output level d i The value is the left endpoint of the quantization interval minus 'a', then divided by the quantization interval, i.e.:

[0096]

[0097] The chaotic sequence X is quantized to generate the DCFC codeword sequence D. DCFC ={d1,d2,…}.

[0098] In this embodiment, step S3 further includes:

[0099] The length of a complementary binary phase code is set to the number of sub-pulses in a single pulse. Complementary binary phase codes can generate new complementary code sequences of a specified length using shorter base code groups according to certain construction rules. Assume A = {a0, a1, ..., a...} N-1 B = {b0, b1, ..., b} N-1 Let} be a pair of complementary codes of length N, and the polynomial of the sequence is defined as A(x) = a0 + a1x + a2x 2 +…a N-1 x N-1New complementary code groups can be generated using the concatenation method. The generated new sequence is represented as E1(x) = A(x) + x. N B(x), E2(x)=A(x)-x N B(x), which form a pair of complementary codes of length 2N.

[0100] Using the aforementioned basic code group and construction method, a pair of CPC codeword sequences A and B of length N are generated. These two sequences are called the positive code sequence and the complement code sequence, respectively, and their values ​​only contain +1 and -1. After the autocorrelation functions of the complementary binary phase codes are added, their sidelobe levels are completely canceled out, while the peak value at the main lobe is doubled, that is:

[0101]

[0102] Where R A R is the autocorrelation function of the positive code sequence. B Let τ be the autocorrelation function of the two's complement sequence, and τ be the delay unit.

[0103] In this embodiment, step S4 includes the following sub-steps:

[0104] S41. Divide the duration of a complete pulse into N sub-pulses, where each sub-pulse transmits an LFM signal. The signal in a pulse can be represented as:

[0105]

[0106] Among them, T LFM Let be the sub-pulse width, k be the modulation coefficient, and rect(.) be the rectangular function.

[0107]

[0108] Where T is the width of the rectangle.

[0109] S42. Using the DCFC codeword sequence D obtained in step S2 DCFC ={d1,d2…} The signal generated in step S41 is frequency modulated between sub-pulses. The modulated signal is called a Linear Frequency Modulation-Discrete Chaos Frequency-coding (LFM-DCFC) signal, and its time-domain expression in M ​​pulses is:

[0110]

[0111] Where τ m,n =nT LFM +mT r T rD is the pulse repetition period. DCFC (n) is the (n+1)th element in the DCFC codeword sequence, f m,n =D DCFC (m×N+n)·Δf is the encoding frequency of the (n+1)th sub-pulse in the (m+1)th pulse, and Δf is the frequency interval.

[0112] S43. Using the CPC codeword sequence generated in step S3, the LFM-DCFC signal generated in step S42 is subjected to phase-coded modulation between sub-pulses to obtain the LFM-CPC-DCFC joint coded modulation signal, whose complex envelope time-domain expression in M ​​pulses is:

[0113]

[0114] Where, a m,n The encoded phase of the (n+1)th sub-pulse in the (m+1)th pulse satisfies:

[0115]

[0116] A(n) is the (n+1)th element of the positive code sequence in the CPC codeword sequence, and B(n) is the (n+1)th element of the complement code sequence in the CPC codeword sequence.

[0117] In this embodiment, step S5 further includes:

[0118] Assuming the frequency control array is a uniform linear array with M transmitting elements and an element spacing of d, the carrier frequency of the m-th element is expressed as:

[0119] f m =f0+mΔf,m=0,1,…,M-1;

[0120] Where f0 and Δf are the carrier frequency and frequency offset, respectively. Therefore, the pulse signal transmitted by the m-th element can be expressed as:

[0121] s m (t)=φ(t)·exp(j2πf m t), m=0,1,…,M-1.;

[0122] Where φ(t) is the LFM-CPC-DCFC joint coded baseband signal generated in step S4.

[0123] Assuming the transmission weight vector w T =[ω T,0 ,ω T,1 ,…,ω T,M-1 ] T ,in TThis indicates the transpose operation. The synthesized signal at the far-field azimuth angle θ (with reference to the antenna line of sight) and distance r (with reference to the first transmitting element) can be expressed as:

[0124]

[0125] Where, τ m =r m / c represents the propagation delay of the signal from the m-th array element to the far-field point (θ, r), where c is the speed of light and r is the speed of light. m =r-mdsin(θ) is the distance from the m-th element to the far-field point.

[0126] In this embodiment, step S6 further includes: analyzing the time-frequency domain distribution, autocorrelation function, and ambiguity function characteristics of the LFM-CPC-DCFC joint encoded waveform of the frequency control array radar to determine whether it meets the performance requirements of radio frequency stealth.

[0127] Time-frequency domain distribution: The invented radar waveform was analyzed in the time-frequency domain using the Short-Time Fourier Transform (STFT). STFT is a commonly used analysis tool in signal processing, used to transform signals from the time domain to the frequency domain. It is a variant of the Fourier Transform and can perform spectral analysis on non-stationary signals.

[0128] Autocorrelation function:

[0129]

[0130] The autocorrelation function is a function that expresses the similarity between signals with respect to their time difference; it is a measure of signal similarity. Here, τ represents the time delay, f(τ) represents the signal waveform, * represents the convolution operation, and (·) * This indicates the conjugate operation.

[0131] Fuzzy function:

[0132]

[0133] The ambiguity function describes the response of a signal of finite duration through a matched receiver and is often used as a tool to study different waveforms. Here, τ is the time delay, ξ is the Doppler frequency shift, u(t) is the signal waveform, and |·| is the modulus operation.

[0134] In this invention example, the time-frequency domain distribution, autocorrelation function graph, and fuzzy function graph of the LFM-CPC-DCFC joint coding waveform of the frequency control array radar are obtained by simulation, and the parameter settings are shown in Table 1.

[0135] In the specific implementation process, the software platform is the Matlab simulation experiment platform.

[0136] Table 1

[0137]

[0138]

[0139] The time-frequency domain distribution, autocorrelation function, and ambiguity function of the LFM-CPC-DCFC jointly coded waveform of the frequency-controlled array radar are shown below. Figure 2 , Figure 4 and Figure 6 As shown. By Figure 2 It can be seen that the LFM-CPC-DCFC joint coded waveform of the designed frequency-controlled array radar exhibits irregular frequency hopping in the time and frequency domains. (From...) Figure 3 It is known that the LFM signal of a frequency-controlled array radar has a high PSLL, which is detrimental to target detection; while the designed LFM-CPC-DCFC jointly coded waveform of the frequency-controlled array radar has an ultra-low PSLL of -33dB, such as Figure 4 As shown, this improves the low intercept performance of the waveform and the performance of target detection. (From...) Figure 5 It is known that the LFM signal of the frequency-controlled array radar suffers from range-Doppler coupling; and the designed LFM-CPC-DCFC joint encoded waveform of the frequency-controlled array radar has a "thumbtack-shaped" ambiguity function, such as... Figure 6 As shown, the problem of range-Doppler coupling has been solved.

[0140] The frequency-controlled array radar LFM-CPC-DCFC joint coding waveform designed in this invention utilizes complementary binary phase code sequences to perform complementary phase coding on the multi-subpulse LFM signal, and combines this with a chaotic sequence generated by chaotic mapping to perform discrete chaotic frequency coding. Finally, the generated baseband signal is modulated onto the frequency-controlled array elements. The designed waveform exhibits pseudo-random characteristics in the time-frequency domain, possesses ultra-low autocorrelation peak sidelobe levels, and a "thumbtack-shaped" ambiguity function, which can improve the radio frequency stealth performance of the frequency-controlled array radar.

[0141] The foregoing description and illustrations have shown and described the basic principles, main features, and advantages of this invention. Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for designing radio frequency stealth waveforms for frequency-controlled array radar, characterized in that, Includes the following steps: Step S1: Generate the original frequency-coded sequence using Bernoulli mapping, wherein the Bernoulli mapping formula is: Where, x n Let α be the value of the nth chaotic sequence, and let α be the parameter of the Bernoulli mapping. After multiple iterations using the initial value x0 according to the mapping formula, a Bernoulli discrete chaotic sequence X is generated: X = {x1, x2, ...}, n = 0, 1, 2, ...; Step S2: Perform uniform quantization on the Bernoulli discrete chaotic sequence X to generate a discrete chaotic frequency-coded codeword sequence, represented as: D DCFC ={d1,d2,…}; Step S3: Construct a pair of complementary phase-coded codeword sequences of length N using the basic code group and construction method of complementary codes, denoted as A = {a1, a2, ..., a...} N } and B = {b1,b2,…,b N }; Step S4: Divide a pulse evenly into N sub-pulses. Use the DCFC discrete chaotic frequency coding codeword sequence and the CPC complementary phase coding codeword sequence to perform frequency modulation and phase modulation between the sub-pulses respectively, generating a linear frequency modulation-complementary phase coding-discrete chaotic frequency coding (LFM-CPC-DCFC) joint coding modulation signal. Its M pulse signals can be represented as: In the formula, a m,n The complementary phase encoding of the (n+1)th sub-pulse in the (m+1)th pulse, where k is the modulation coefficient and τ m,n =nT LFM +mT r T LFM T is the sub-pulse width. r f is the pulse repetition period. m,n =D DCFC (m×N+n)·Δf is the encoding frequency of the (n+1)th sub-pulse in the (m+1)th pulse, Δf is the frequency interval, and rect(·) is the rectangular function, expressed as: Step S5: Modulate the linear frequency modulation-complementary phase coding-discrete chaotic frequency coding (LFM-CPC-DCFC) baseband signal onto the carrier of each element of the frequency control array; Step S6: Verify the time-frequency domain distribution, autocorrelation function, and ambiguity function characteristics of the received echo signal to evaluate its radio frequency stealth performance.

2. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 1, characterized in that, The discrete chaotic mapping step S1 further includes the following sub-steps: Step S11: Determine the initial value x0 of the Bernoulli chaotic map. Change the initial value x0 of the chaotic map in steps of 0.001 within the range of values. Select the initial value that minimizes the peak autocorrelation sidelobe level (PSLL) of the generated chaotic sequence as the optimal initial value of the chaotic map. The definition of the peak autocorrelation sidelobe level (PSLL) is: Where k is the index of each value point in the autocorrelation function; R(k) is the level of all sidelobes of the autocorrelation function except when k = 0; Step S12: Using the determined optimal initial value x0, generate the Bernoulli chaotic sequence X = {x1, x2, ...} through iteration according to the Bernoulli mapping formula.

3. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 2, characterized in that, The uniform quantization process in step S2 further includes the following steps: Step S21: Perform multi-valued quantization on the Bernoulli chaotic sequence X. Assume the range of values ​​in the chaotic sequence is between a and b, the number of quantization levels is N, and the quantization interval when using uniform quantization is: The endpoints of the quantization interval are: m i =a+i×Δv i=0,1,…,N; Step S22: Quantize the output level d i The value is the left endpoint of the quantization interval minus 'a', then divided by the quantization interval, i.e.: The chaotic sequence X is quantized to generate a DCFC discrete chaotic frequency encoded codeword sequence: D DCFC ={d1,d2,…}.

4. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 3, characterized in that, Step S3 further includes the following steps: The length of the complementary binary phase code is set to the number of sub-pulses in a single pulse. Using a shorter base code group, a new complementary code sequence of a specified length is generated according to certain construction rules. A pair of CPC complementary phase-coded codeword sequences A and B of length N are constructed using a concatenation method. These two sequences are a positive code sequence and a complement code sequence, respectively, and their values ​​only contain +1 and -1. After the autocorrelation functions of the complementary binary phase codes are added, their sidelobe levels are completely canceled out, while the peak value at the main lobe is doubled. Among them, R A R is the autocorrelation function of the positive code sequence. B Let τ be the autocorrelation function of the two's complement sequence, and τ be the delay unit.

5. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 4, characterized in that, Step S4 specifically includes the following sub-steps: Step S41: Divide a complete pulse duration into N sub-pulses, where each sub-pulse transmits an LFM signal. The signal in a pulse can be represented as: Among them, T LFM Let be the sub-pulse width, k be the modulation coefficient, rect(.) be the rectangular function, and: Where T is the width of the rectangle; Step S42: Utilize the DCFC discrete chaotic frequency encoded codeword sequence D DCFC ={d1,d2…} The LFM signal transmitted in each sub-pulse of step S41 is frequency modulated between sub-pulses to form a linear frequency modulation-discrete chaotic frequency-coded LFM-DCFC signal. Its time-domain expression in the M pulses is: Where τ m,n =nT LFM +mT r T r D is the pulse repetition period. DCFC (n) is the (n+1)th element in the DCFC codeword sequence, f m,n =D DCFC (m×N+n)·Δf is the encoding frequency of the (n+1)th sub-pulse in the (m+1)th pulse, and Δf is the frequency interval; Step S43: Using the CPC complementary phase-coded codeword sequence, the linear frequency modulation-discrete chaotic frequency-coded (LFM-DCFC) signal is phase-coded and modulated between sub-pulses to obtain a joint LFM-CPC-DCFC coded and modulated signal, whose complex envelope time-domain expression in M ​​pulses is: Where, a m,n Let be the encoded phase of the (n+1)th sub-pulse in the (m+1)th pulse, and satisfy: A(n) is the (n+1)th element of the positive code sequence in the CPC codeword sequence, and B(n) is the (n+1)th element of the complement code sequence in the CPC codeword sequence.

6. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 5, characterized in that, Step S5 specifically includes: If the frequency control array is a uniform linear array with M transmitting elements and an element spacing of d, then the carrier frequency of the m-th element is expressed as: f m =f0+mΔf,m=0,1,…,M-1; Where f0 and Δf are the carrier frequency and frequency offset, respectively; The pulse signal emitted by the m-th array element can be represented as: s m (t)=φ(t)·exp(j2πf m t),m=0,1,…,M-1.; Where φ(t) is the baseband signal of the LFM-CPC-DCFC joint coded modulation signal; If the transmission weight vector w T =[ω T,0 ,ω T,1 ,…,ω T,M-1 ] T ,in T This indicates the transpose operation; the synthesized signal at the far-field azimuth angle θ and distance r can be represented as: Wherein, the far-field azimuth angle θ is referenced to the antenna line-of-sight direction, the distance r is referenced to the first transmitting element, and τ m =r m / c represents the propagation delay of the signal from the m-th array element to the far-field point (θ, r), where c is the speed of light and r is the speed of light. m =r-mdsin(θ) is the distance from the m-th element to the far-field point.

7. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 6, characterized in that, Step S6, time-frequency domain distribution, utilizes short-time Fourier transform to perform time-frequency domain analysis on the radar waveform; the autocorrelation function represents the similarity between signals as a function of their time difference, and is a measure of signal similarity, with the formula: Where τ represents the time delay, f(τ) represents the signal waveform, * represents the convolution operation, and (·) * This indicates the conjugate operation.

8. The method for designing radio frequency stealth waveforms for a frequency-controlled array radar according to claim 6, characterized in that, The ambiguity function in step S6 describes the response of a finite-duration signal through a matched receiver, and its formula is: Where τ is the time delay, ξ is the Doppler frequency shift, u(t) is the signal waveform, and |·| is the modulus operation.

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