A nonlinear sub-pulse carrier frequency design method based on broadband pulse train signals

Abstract

This invention discloses a method for designing nonlinear sub-pulse carrier frequencies based on broadband pulse train signals. Based on the pulse train signal model, this method introduces a skew sequence and frequency hopping coefficient. Based on the influence of the frequency hopping interval and modulation slope parameters on ambiguous sidelobes, a multi-objective optimization model is established. A design method for a specific carrier frequency hopping interval based on an ambiguity function is proposed to obtain the optimal carrier frequency variation step size. The modulation carrier frequency calculation rules are then improved to obtain nonlinear frequencies corresponding to different sub-pulses, thereby adjusting the signal's frequency domain structure. This invention significantly reduces the sidelobes of traditional broadband pulse train signals, effectively improving the signal's time-frequency resolution capability. This method expands the design approach for low-range ambiguous sidelobe waveforms, laying the foundation for high-resolution sonar detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of sonar, and in particular relates to a nonlinear sub-pulse carrier frequency design method based on a broadband pulse train signal. Background Art

[0002] The active sonar transmit waveform not only determines the signal processing method but also directly affects the system's range and radial velocity resolution, target parameter estimation accuracy, peak-to-sidelobe ratio, and interference suppression capabilities. Therefore, the transmit waveform plays a critical role in sonar systems, and designing the transmit waveform is an effective way to improve system performance. Pulse train signals, as comb-spectral signals, distribute their energy across multiple narrowband spectral segments, resulting in a broadband signal overall. They combine the advantages of both narrowband and broadband signals and are commonly used in shallow waters to suppress reverberation interference from low-speed targets. However, the repetitive pulse transmission method can result in excessively high range ambiguity sidelobes, leading to the problem that improving one signal performance characteristic can degrade others.

[0003] To achieve range sidelobe suppression, the characteristic that the signal's autocorrelation function and power spectrum form a Fourier transform pair is exploited to design a transmit waveform with a specific power spectrum structure, thereby obtaining a low-sidelobe signal. A specifically structured power spectrum can be achieved by modulating parameters such as the signal's amplitude and frequency. However, amplitude modulation limits the system's detection range, while frequency modulation, such as nonlinear frequency modulation (NFM), requires precise control of the modulation curve, making it more difficult to implement. Although nonuniform stepped frequency signals quantize the carrier frequency and reduce the complexity of designing NFM signals, randomly selecting the frequency modulation interval to disrupt the periodicity of the carrier frequency distribution and suppress grating lobes increases range sidelobes, thereby limiting signal resolution. Therefore, it is of great significance to seek a nonlinear sub-pulse carrier frequency design method based on FM pulse train signals that can eliminate grating lobes and suppress sidelobes to improve time-frequency resolution while still maintaining the ability to suppress reverberation interference from low-speed targets. Summary of the Invention

[0004] To overcome the shortcomings of the existing technology, the present invention provides a nonlinear sub-pulse carrier frequency design method based on broadband pulse train signals. Based on the pulse train signal model, the method introduces a skew sequence and a frequency hopping coefficient. A multi-objective optimization model is established based on the influence of the frequency hopping interval and modulation slope parameters on ambiguous sidelobes. A design method for a specific carrier frequency hopping interval based on an ambiguity function is proposed to obtain the optimal carrier frequency variation step size. The modulation carrier frequency calculation rules are then improved to obtain the nonlinear frequencies corresponding to different sub-pulses, thereby adjusting the signal's frequency domain structure. This method significantly reduces the sidelobes of traditional broadband pulse train signals, effectively improving the signal's time-frequency resolution capability. This method expands the design approach for low-range ambiguous sidelobe waveforms and lays the foundation for high-resolution sonar detection.

[0005] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0006] Step 1: Introduce the skew sequence and frequency hopping coefficient into the pulse train signal to construct a new signal model;

[0007] Step 2: Calculate the range ambiguity function of the signal according to the definition of the ambiguity function, and analyze the causes of side lobes and grating lobes;

[0008] Step 3: Establish an optimization function with the goal of sharpening the main lobe and suppressing fuzzy side lobes, propose a design method for the carrier frequency hopping interval based on the ambiguity function, and solve the optimal carrier frequency change step size;

[0009] Step 4: Improve the modulation carrier frequency calculation rules and design nonlinear frequencies corresponding to different sub-pulses.

[0010] Preferably, the step 1 is specifically:

[0011] Step 1-1: The pulse train signal is a signal model composed of multiple sub-pulses with the same duty cycle. Let T r is the pulse repetition interval, T p is the sub-pulse width, then the pulse train signal model x(t) is:

[0012]

[0013] Where n represents the nth sub-pulse, and n = 1, 2, ..., N, N is the number of sub-pulses, T represents the entire pulse duration, x n Represents the nth sub-pulse signal;

[0014] Step 1-2: When the sub-pulse signal is a linear frequency modulation signal, a frequency modulation pulse train signal is formed. The nth sub-pulse signal is expressed as:

[0015]

[0016] Where K = B p / T p Indicates the frequency modulation slope, B p is the sub-pulse bandwidth, f n is the carrier frequency of the sub-pulse, rect(.) represents the rectangular function;

[0017]

[0018] Where f0 is the center frequency of the signal, △f is the frequency jump step, and △f=B p , B represents the signal bandwidth;

[0019] Step 1-3: Introduce the tilt sequence {G n} and the frequency hopping coefficient {C n}, construct a new pulse train signal model, expressed as:

[0020]

[0021] in, K n =G n ·(B p / T p ).

[0022] x n Indicates the nth sub-pulse signal, which can be in different signal forms, such as linear frequency modulation signal (LFM signal) or hyperbolic frequency modulation signal (HFM signal)

[0023] Preferably, the step 2 is specifically as follows:

[0024] Step 2-1: The broadband ambiguity function expression of the signal is:

[0025]

[0026] Ψ(τ,s)=|χ(τ,s)| 2 (10)

[0027] Where τ is the target echo delay, s = (cv) / (c + v) is called the time scale or Doppler compression factor, c is the signal propagation speed in water, and v is the radial velocity of the target. When s = 1, we get Ψ(1,τ), which is called the range ambiguity function.

[0028] Step 2-2: Substitute the signal model of equation (8) into the definition of the broadband range ambiguity function to calculate the range ambiguity function of the signal.

[0029] The broadband ambiguity function is defined as:

[0030]

[0031] Where τ is the target echo delay, s = (cv) / (c + v) is called the time scale or Doppler compression factor, c is the signal propagation speed in water, and v is the radial velocity of the target, which is negative when moving towards each other. When s = 1, we get Ψ(τ, 1), which is called the range ambiguity function.

[0032] Substituting equation (8) into equation (11) and setting s = 1, we can obtain:

[0033]

[0034] The range ambiguity function is split into two products, R1(t) and R2(t). R1(t) represents the periodic grating lobe of the signal caused by a fixed frequency step, and R2(t) is the broadband frequency-shifted autocorrelation function of the complex envelope of a single pulse.

[0035] Preferably, the step 3 is specifically as follows:

[0036] Step 3-1: Main lobe area optimization goal: Minimize the main lobe area within the delay range:

[0037]

[0038] where Ω τ is the optimal time delay range for the main lobe area, D represents the optimized parameters △f and K of the FM pulse sequence n ;

[0039] Main-sidelobe ratio optimization goal: the width of the main lobe is kept within the set distance range or speed range, and the adjacent sidelobe levels are minimized in this area;

[0040] Step 3-2: Multiply the two results of the distance ambiguity function in decibel form:

[0041] Ψ dB (τ)=20log10[R1(τ)R2(τ)] (14)

[0042] Unify the form of objective function minimization, take the inverse of the difference between the main lobe and the side lobe, and establish the main-side lobe optimization objective function:

[0043]

[0044] In the multi-objective optimization problem, set the weight coefficient vector to w:

[0045]

[0046] Thus, the linear combination of the dual objective functions to be optimized is taken as the new objective function vector F. At this time:

[0047] F=w(F1,F2) (17)

[0048] Step 3-3: Waveform parameters under known frequency band overlap conditions:

[0049]

[0050] After the frequency hopping coefficient is introduced, the corresponding sub-pulse carrier frequency and bandwidth are expressed as:

[0051]

[0052] B p=|B-f0-(N-1)△f| (20)

[0053] The following relationship exists:

[0054]

[0055] Arranged:

[0056]

[0057] Assuming B≤f0, we can calculate:

[0058]

[0059] In summary, the overall optimization problem is modeled as a multi-objective optimization model under constraints as shown in Equation (23):

[0060]

[0061] Preferably, the step 4 is specifically as follows:

[0062] Considering the improvement of the Gaussian structure of the signal frequency domain, the calculation rule of the sub-pulse carrier frequency corresponding to the negative modulation slope position is rewritten, that is, f n Add B p ;

[0063] The nonlinear frequencies corresponding to different sub-pulses under the optimal carrier frequency change step are:

[0064]

[0065] By converting the nonlinear frequency design problem into a carrier frequency hopping step length solution problem, and combining it with the improved modulation carrier frequency calculation rule, the nonlinear frequencies corresponding to different sub-pulses can be calculated.

[0066] A computer program enables a computer to execute the above nonlinear sub-pulse carrier frequency design method.

[0067] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the above-mentioned nonlinear sub-pulse carrier frequency design method.

[0068] A computer-readable storage medium stores a computer program, which implements the above-mentioned nonlinear sub-pulse carrier frequency design method when executed by a processor.

[0069] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned nonlinear sub-pulse carrier frequency design method.

[0070] A computer program product, comprising a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and wherein the instructions, when executed by the at least one processor, implement the above-mentioned nonlinear sub-pulse carrier frequency design method.

[0071] The beneficial effects of the present invention are as follows:

[0072] (1) The present invention introduces a skewing sequence and a frequency hopping coefficient into the broadband pulse train to modulate the sub-pulse slope and carrier frequency, further improving the randomness of the waveform and increasing the freedom of waveform design, laying the foundation for effectively improving the waveform distance resolution performance.

[0073] (2) The present invention establishes a multi-objective optimization model based on the main lobe area and main-to-side lobe ratio constraints, proposes a design method for a special carrier frequency hopping interval based on an ambiguity function, obtains the optimal carrier frequency change step size, and then improves the modulation carrier frequency calculation rule, which can quickly calculate the nonlinear frequency corresponding to different sub-pulses through a simple formula.

[0074] (3) The nonlinear sub-pulse carrier frequency designed in the present invention makes the carrier frequency of the broadband pulse train signal show an "S"-shaped change. The waveform itself can suppress reverberation and improve the time-frequency resolution performance. In addition, due to the increase in the randomness of the waveform, the interference caused by forwarding after being intercepted by the enemy can be reduced, that is, the simultaneous suppression of environmental clutter and jammer interference can be achieved, providing favorable conditions for subsequent high-resolution detection and estimation of target parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 Flow chart of the method of the present invention.

[0076] Figure 2 It is the frequency domain diagram of the initial pulse train signal and the result diagram of the broadband range ambiguity function; Figure 2 (a) and Figure 2 (b) Frequency domain diagram and broadband range ambiguity diagram respectively.

[0077] Figure 3 The carrier frequency of the initial pulse train, the carrier frequency of the stepped frequency pulse train, the nonlinear carrier frequency result of the present invention and the nonlinear sub-pulse carrier frequency variation curves thereof in ascending order.

[0078] Figure 4 The pulse train waveform designed for the present invention, i.e., the frequency domain diagram of the nonlinear sub-pulse carrier frequency and the range ambiguity function diagram; Figure 4 (a) and Figure 4 (b) Frequency domain diagram and broadband range ambiguity diagram respectively. DETAILED DESCRIPTION

[0079] The present invention will be further described below with reference to the accompanying drawings and examples.

[0080] The basic idea of ​​the present invention is to introduce a modulation sequence and frequency hopping coefficient into the frequency modulated pulse train signal, analyze the causes of side lobes and grating lobes based on the closed-form expression of the distance ambiguity function, establish a multi-objective optimization model with the main lobe area and main-to-side lobe ratio constraints, and propose a design method for special carrier frequency hopping intervals based on the ambiguity function to obtain the optimal carrier frequency change step size; then adjust the signal frequency domain structure, improve the modulation carrier frequency calculation rules, and design nonlinear frequencies corresponding to different sub-pulses. Unlike the complexity of nonlinear frequency modulation signals using the stationary phase principle to solve the window function integral and the group delay inversion to obtain the frequency modulation curve, the method proposed in the present invention can quickly calculate the frequency using a simple formula, and the final carrier frequency law shows an "S"-shaped frequency modulation change.

[0081] The present invention mainly comprises the following steps:

[0082] (1) Introducing the skew sequence and frequency hopping coefficient into the pulse train signal to construct a new signal model;

[0083] (2) According to the definition of ambiguity function, calculate the range ambiguity function of the signal and analyze the causes of side lobes and grating lobes;

[0084] (3) An optimization function is established with the goal of sharpening the main lobe and suppressing the fuzzy side lobes. A design method for the carrier frequency hopping interval based on the ambiguity function is proposed to solve the optimal carrier frequency change step size.

[0085] (4) Improve the modulation carrier frequency calculation rules and design nonlinear frequencies corresponding to different sub-pulses.

[0086] The specific method of introducing the frequency hopping parameter in step (1) is:

[0087] Initial broadband pulse train signal:

[0088]

[0089] The skew adjustment sequence {G n} and the frequency hopping coefficient {C n}, used to modulate the sub-pulse slope and carrier frequency to construct a new signal model:

[0090]

[0091] in, K n =G n ·(B p / T p ).

[0092] The specific method for calculating the range ambiguity function of the signal and analyzing the influence of the waveform parameters in step (2) is: introduce the tilt adjustment sequence {G n} and the frequency hopping coefficient {C n Substituting the signal model of the 100-meter-high (100-meter) signal into the definition of the broadband ambiguity function, setting the scaling factor s = 1, and calculating Ψ(1,τ) to obtain the range ambiguity function. The result is then split into the product of two equations. The influence of waveform parameters on the range ambiguity function is then analyzed by region, laying the theoretical foundation for a design method for special carrier frequency hopping intervals based on the ambiguity function.

[0093] The specific method for solving the optimal jump step length in step (3) is: based on the theoretical analysis results of the distance ambiguity function, an optimization function is established with the goals of sharp main lobe and suppression of fuzzy side lobes. The two goals correspond to the single terms and product terms of the closed-form expression of the distance ambiguity function, respectively. Then, under the conditions that the main lobe area is minimized and the main lobe width remains constant within the time delay range, the adjacent side lobe levels are minimized in this area, characterizing the optimization goals of sharp main lobe and reducing fuzzy side lobes, and constructing a multi-objective joint optimization model. When solving the model, it is necessary to derive the constraints of the parameters to be optimized and convert them into an optimization problem under the constraints, thereby constructing a design model for the special carrier frequency jump interval based on the ambiguity function. Finally, within the constraints, the genetic algorithm is used to solve the optimal carrier frequency step length △f opt .

[0094] The specific method of improving the modulation carrier frequency calculation rule in step (4) is as follows: according to the "Wiener-Schinchin" theorem, the inverse Fourier transform of the Gaussian power spectrum can produce an autocorrelation function without side lobes. Therefore, combined with the optimal carrier frequency hopping step length obtained by solving, the signal frequency domain structure is adjusted, and the sub-pulse carrier frequency calculation rule corresponding to the negative modulation slope position is rewritten;

[0095] Design of nonlinear sub-pulse carrier frequency with optimal carrier frequency hopping step size

[0096]

[0097] In general, by converting the nonlinear frequency design problem into a special carrier frequency hopping step size solution problem, and combining it with the improved modulation carrier frequency calculation rules, the nonlinear frequency corresponding to different sub-pulses can be quickly calculated through a simple formula.

[0098] Example:

[0099] The flow chart of the method of the present invention is as follows Figure 1 The specific implementation method is as follows:

[0100] Step 1: Introduce the skew sequence and frequency hopping coefficient into the FM pulse train signal to construct a new signal model.

[0101] The pulse train waveform is a signal model composed of multiple sub-pulses with the same duty cycle. r is the pulse repetition interval, T p is the sub-pulse width, then the pulse train signal x(t) is:

[0102]

[0103] x n represents the nth sub-pulse signal, which can be in different signal forms, such as a linear frequency modulation signal (LFM signal) or a hyperbolic frequency modulation signal (HFM signal).

[0104] When the sub-pulse signal is a linear frequency modulation signal, it constitutes a frequency modulation pulse train signal, which is expressed as:

[0105]

[0106] Where N is the number of sub-pulses, K = B p / T p Indicates the frequency modulation slope, B p is the sub-pulse bandwidth, f n is the carrier frequency of the sub-pulse:

[0107]

[0108] Where f0 is the center frequency of the signal, △f is the frequency jump step, and △f=B p .

[0109] Due to the repetitive transmission of pulses, the spectrum of the signal is combed, resulting in the phenomenon of high-range fuzzy sidelobes. Direct windowing to suppress the sidelobes will widen the mainlobe, resulting in the problem that improving one performance of the signal will reduce other performances. In order to compensate for the design limitations, the tilt sequence {G n} and the frequency hopping coefficient {C n}, construct a new signal model, expressed as:

[0110]

[0111] in, K n =G n ·(B p / T p ).

[0112] Step 2: According to the definition of the ambiguity function, calculate the range ambiguity function of the signal and analyze the causes of side lobes and grating lobes.

[0113] The broadband ambiguity function expression of the signal is (positive expression):

[0114]

[0115] Ψ(τ,s)=|χ(τ,s)| 2 (10)

[0116] Where τ is the target echo delay, s = (cv) / (c + v) is called the time scale or Doppler compression factor, c is the signal propagation speed in water, and v is the radial velocity of the target. When s = 1, we obtain Ψ(1,τ), which is called the range ambiguity function.

[0117] Substituting the signal model of equation (8) into the definition formula and calculating the range ambiguity function, we get:

[0118]

[0119] Clearly, the range ambiguity function can be decomposed into two products: R1(t) and R2(t). R1(t) represents the signal's periodic grating lobes caused by a fixed frequency step size, and R2(t) is the broadband frequency-shifted autocorrelation function of the complex envelope of a single pulse. In this expression, the carrier frequency hopping step size and the modulation slope of the sub-pulse influence the overall performance of the ambiguity function. When the frequency increases linearly in a △f sequence, periodic grating lobes exist. When the frequency varies nonlinearly and randomly, the periodicity of the grating lobes is destroyed and suppressed, but high-range sidelobes appear, affecting the signal's range resolution. Therefore, based on this analysis, sidelobes can be significantly reduced by designing a specific carrier frequency step size.

[0120] Step 3: Establish an optimization function with the goal of sharpening the main lobe and suppressing the fuzzy side lobes, propose a design method for the special carrier frequency hopping interval based on the ambiguity function, and solve the optimal hopping step size.

[0121] The R2(t) term in Equation (11) can be used to constrain the width of the fuzzy mainlobe. The product term uses the mainlobe-to-sidelobe ratio to constrain the height of the distance fuzzy sidelobe. Therefore, a multi-objective joint optimization model is established based on the mainlobe area and mainlobe-to-sidelobe ratio constraints. A design method for the special carrier frequency hopping interval based on the ambiguity function is proposed to obtain the optimal carrier frequency hopping step size.

[0122] (1) Main lobe area optimization goal: Minimize the main lobe area within the delay range:

[0123]

[0124] where Ω τ The optimal delay range for the main lobe area. D represents the optimized parameters △f and K of the FM pulse sequence. n .

[0125] (2) Main-sidelobe ratio optimization goal: The width of the main lobe is kept within a certain distance range or speed range, and the adjacent sidelobe levels are minimized in this area.

[0126] Take the decibel form of the product of the two results of the distance ambiguity function:

[0127] Ψ dB (τ)=20log10[R1(τ)R2(τ)] (13)

[0128] At this point, the goal of minimizing the sidelobe level within the region of interest is transformed into maximizing the difference between the mainlobe peak and the sidelobe within the constraints. The form of the unified objective function minimization is taken as the inverse of the difference between the mainlobe and the sidelobe to establish the main-sidelobe optimization objective function;

[0129]

[0130] In the multi-objective optimization problem, set the weight coefficient vector to w:

[0131]

[0132] Thus, the linear combination of the dual objective functions to be optimized is taken as the new objective function vector F. At this time:

[0133] F=w(F1,F2) (16)

[0134] Unlike the completely consistent time-frequency structure of sub-pulses in a classic pulse train signal, the introduction of a skew sequence and frequency-hopping coefficients allows for the adjustment of the overlapping structure of sub-pulses across different frequency bands. In this case, solving a multi-objective joint optimization model requires deriving constraints on the parameters to be optimized. This involves constructing an optimization model for a specific carrier frequency hopping interval based on an ambiguity function under these constraints and solving the problem.

[0135] Waveform parameters under known frequency band overlap conditions:

[0136]

[0137] After the frequency hopping coefficient is introduced, the corresponding sub-pulse carrier frequency and bandwidth are expressed as:

[0138]

[0139] B p =|B-f0-(N-1)△f| (19)

[0140] Assuming the total signal bandwidth is B, the following relationship exists:

[0141]

[0142] Arranged:

[0143]

[0144] Assuming B≤f0, we can calculate:

[0145]

[0146] In summary, the overall optimization problem is modeled as a multi-objective optimization model under constraints as shown in Equation (23):

[0147]

[0148] Within the constraints, the genetic algorithm is used to solve the optimal carrier frequency hopping step size. The initial pulse train sequence parameters are set as bandwidth B0 = 10kHz, number of sub-pulses is 10, pulse duration T = 50ms, normalized frequency band range f = 10-20kHz, initial frequency hopping interval △f0 = B p =B0, the frequency domain result and the range ambiguity function result are as follows Figure 2 The genetic algorithm parameters are set as follows: the population is 100, the crossover probability is 0.7, the mutation probability is 0.1, and the algorithm iteration is more than 200 generations. The optimal carrier frequency change step size is calculated to be △f opt =277Hz.

[0149] Step 5: Improve the modulation carrier frequency calculation rules and design nonlinear frequencies corresponding to different sub-pulses.

[0150] The signal frequency domain structure is adjusted based on the optimal frequency hopping interval obtained. According to the Wiener-Schinchin theorem, the inverse Fourier transform of a signal's power spectrum is the signal's autocorrelation function. In theory, the inverse Fourier transform of a Gaussian power spectrum can produce an autocorrelation function without sidelobes. Therefore, considering the improvement of the Gaussian-like structure of the signal frequency domain, the calculation rules for the sub-pulse carrier frequency corresponding to the negative modulation slope position are rewritten.

[0151] The nonlinear frequencies corresponding to different sub-pulses under the optimal carrier frequency change step are:

[0152]

[0153] By converting the nonlinear frequency design problem into a special carrier frequency hopping step size solution problem, and combining it with the improved modulation carrier frequency calculation rule, the nonlinear frequency corresponding to different sub-pulses can be quickly calculated through a simple formula.

[0154] and Figure 2 The waveform parameters are set the same, the initial modulation pulse train carrier frequency, the step frequency pulse train carrier frequency and the nonlinear carrier frequency designed by the present invention are shown in the following figure: Figure 3As shown, the nonlinear frequencies are sorted and plotted in the red dotted part of the figure, and after curve fitting, they are shown as the light blue solid line in the figure. It can be seen that since the sub-pulses of the initial pulse train are exactly the same and the sub-pulse bandwidth is equal to the bandwidth of the entire signal, the carrier frequency is always at the center frequency point; the carrier frequency of the stepped frequency pulse train presents a linear change law. The algorithm designed by the present invention uses a simple formula to quickly calculate the nonlinear frequency of the corresponding sub-pulse, and the final frequency modulation change law presents an "S" shape. The waveform frequency domain result corresponding to this parameter is shown in the figure below. Figure 4 As shown in (a), the distance ambiguity function result is as follows Figure 4 As shown in (b), compared Figure 2 The frequency domain and range ambiguity function results for the initial pulse train signal shown in the figure show that the frequency domain structure of the modulated pulse train signal generated by the algorithm designed in this invention has been adjusted to exhibit a quasi-Gaussian shape. Under the same waveform parameters, the proposed method can significantly reduce the level of range ambiguity sidelobes and expand the area of ​​the blank area around the main lobe. A relatively ideal range ambiguity function is obtained through a simple formula, which is fast to calculate and easy to implement. It also eliminates periodic grating lobes while maintaining a sharp main lobe and good time-frequency resolution.

Claims

1. A nonlinear sub-pulse carrier frequency design method based on broadband pulse train signals, characterized in that: The steps include: Step 1: Introduce the skew sequence and frequency hopping coefficient into the pulse train signal to construct a new signal model; Step 1-1: The pulse train signal is a signal model composed of multiple sub-pulses with the same duty cycle. Let T r is the pulse repetition interval, T p is the sub-pulse width, then the pulse train signal model x(t) is: Where n represents the nth sub-pulse, and n = 1, 2, ..., N, N is the number of sub-pulses, T represents the entire pulse duration, x n Represents the nth sub-pulse signal; Step 1-2: When the sub-pulse signal is a linear frequency modulation signal, a frequency modulation pulse train signal is formed. The nth sub-pulse signal is expressed as: Where K = B p / T p Indicates the frequency modulation slope, B p is the sub-pulse bandwidth, f n is the carrier frequency of the sub-pulse, rect(.) represents the rectangular function; Where f0 is the center frequency of the signal, △f is the frequency jump step, and △f=B p , B represents the signal bandwidth; Step 1-3: Introduce the tilt sequence {G n } and the frequency hopping coefficient {C n }, construct a new pulse train signal model, expressed as: in, K n =G n ·(B p / T p ); Step 2: Calculate the range ambiguity function of the signal according to the definition of the ambiguity function, and analyze the causes of side lobes and grating lobes; Step 2-1: The broadband ambiguity function expression of the signal is: Ψ(τ,s)=|χ(τ,s)| 2 (10) Where τ is the target echo delay, s = (cv) / (c + v) is called the time scale or Doppler compression factor, c is the signal propagation speed in water, and v is the radial velocity of the target. When s = 1, we get Ψ(τ, 1), which is called the range ambiguity function. Step 2-2: Substitute the signal model of formula (8) into the definition of broadband range ambiguity function to calculate the range ambiguity function of the signal; The broadband ambiguity function is defined as: Where τ is the target echo delay, s = (cv) / (c + v) is called the time scale or Doppler compression factor, c is the signal propagation speed in water, and v is the radial velocity of the target, which is negative when moving towards each other. When s = 1, we get Ψ(τ, 1), which is called the range ambiguity function. Substituting equation (8) into equation (11) and setting s = 1, we can obtain: The range ambiguity function is split into two products, R1(τ) and R2(τ). R1(τ) represents the periodic grating lobe of the signal caused by the fixed frequency step, and R2(τ) is the broadband frequency-shifted autocorrelation function of the complex envelope of a single pulse. Step 3: Establish an optimization function with the goal of sharpening the main lobe and suppressing fuzzy side lobes, propose a design method for the carrier frequency hopping interval based on the ambiguity function, and solve the optimal carrier frequency change step size; Step 3-1: Main lobe area optimization goal: Minimize the main lobe area within the delay range: where Ω τ is the optimal time delay range for the main lobe area, D represents the optimized parameters △f and K of the FM pulse sequence n ; Main-sidelobe ratio optimization goal: the width of the main lobe is kept within the set distance range or speed range, and the adjacent sidelobe level is minimized within the set distance range or speed range; Step 3-2: Multiply the two results of the distance ambiguity function in decibel form: P dB (τ)=20log10[R1(τ)R2(τ)] (14) Unify the form of objective function minimization, take the inverse of the difference between the main lobe and the side lobe, and establish the main-side lobe optimization objective function: In the multi-objective optimization problem, set the weight coefficient vector to w: Thus, the linear combination of the dual objective functions to be optimized is taken as the new objective function vector F. At this time: F=w(F1,F2) (17) Step 3-3: Waveform parameters under known frequency band overlap conditions: After introducing the frequency hopping coefficient, the corresponding sub-pulse carrier frequency and bandwidth are expressed as: B p =|B-f0-(N-1)△f| (20) The following relationship exists: Arranged: Assuming B≤f0, we can calculate: In summary, the overall optimization problem is modeled as a multi-objective optimization model under constraints as shown in Equation (23): B p =|B-f0-(N-1)△f| (24); Step 4: Improve the modulation carrier frequency calculation rules and design nonlinear frequencies corresponding to different sub-pulses.

2. The method for designing nonlinear sub-pulse carrier frequency based on broadband pulse train signal according to claim 1, characterized in that: The step 4 is specifically as follows: Considering the improvement of the Gaussian structure of the signal frequency domain, the calculation rule of the sub-pulse carrier frequency corresponding to the negative modulation slope position is rewritten, that is, f n Add B p ; The nonlinear frequencies corresponding to different sub-pulses under the optimal carrier frequency change step are: By converting the nonlinear frequency design problem into a carrier frequency hopping step length solution problem, and combining it with the improved modulation carrier frequency calculation rule, the nonlinear frequencies corresponding to different sub-pulses can be calculated.

3. An electronic device, characterized in that: include: processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the method according to any one of claims 1 to 2.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 2 is implemented.

5. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes the method according to any one of claims 1 to 2.

6. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 2 is implemented.

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