Nonlinear sub-pulse carrier frequency design method based on broadband pulse string signal

Abstract

The invention discloses a nonlinear sub-pulse carrier frequency design method based on a broadband pulse train signal, which comprises the following steps: on the basis of a pulse train signal model, introducing a skew adjustment sequence and a frequency hopping coefficient, and establishing a multi-objective optimization model according to the influence of a frequency hopping interval and a modulation slope parameter on a fuzzy sidelobe; a design method of a special carrier frequency hopping interval based on an ambiguity function is provided, an optimal carrier frequency change step length is obtained, then a modulation carrier frequency calculation rule is improved, nonlinear frequencies corresponding to different sub-pulses are obtained, and adjustment of a signal frequency domain structure is achieved. According to the method, the sidelobe of a traditional broadband pulse string signal is greatly reduced, the time-frequency resolution capability of the signal is effectively improved, the design thought of a low-distance fuzzy sidelobe waveform is expanded, and a foundation is laid for high-resolution detection of sonar.

Description

Technical Field

[0001] The 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 transmission waveform not only determines the signal processing method, but also directly affects the system's range resolution and radial velocity resolution, target parameter estimation accuracy, peak-to-sidelobe ratio, and interference suppression capability. Therefore, the transmission waveform plays a key role in the sonar system, and designing the transmission waveform is an effective way to improve system performance. As a comb spectrum signal, the pulse train signal has energy distributed in multiple narrowband spectrum segments, and the overall performance is a broadband signal, which has the advantages of both narrowband and broadband signals. It is usually used in shallow sea environments to suppress reverberation interference of low-speed targets, but the form of pulse repetition transmission will make the signal range fuzzy sidelobes too high, and there is a problem that improving one signal performance will reduce other performance.

[0003] In order to achieve range sidelobe suppression, the characteristics of the signal's autocorrelation function and power spectrum forming a Fourier transform pair are used to design a transmission waveform with a specific power spectrum structure, thereby obtaining a low sidelobe signal. The power spectrum of a specific structure can be achieved by modulating the signal's amplitude and frequency parameters, but amplitude modulation will limit the detection distance of the system, and frequency modulation, such as nonlinear frequency modulation signals, requires precise control of the modulation curve, which is difficult to achieve. Although the non-uniform step frequency signal quantizes the carrier frequency and reduces the complexity of designing a nonlinear frequency modulation signal, while randomly selecting the frequency modulation interval to destroy the periodicity of the carrier frequency distribution to suppress the grating lobe, it will increase the range sidelobe, thereby limiting the signal's resolution performance. Therefore, based on the frequency modulated pulse train signal, it is of great significance to seek a nonlinear sub-pulse carrier frequency design method that can eliminate the grating lobe to suppress the sidelobe to improve the time-frequency resolution performance, while still maintaining its ability to suppress the reverberation interference of low-speed targets. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a nonlinear sub-pulse carrier frequency design method based on broadband pulse train signals. On the basis of the pulse train signal model, the deflection sequence and frequency hopping coefficient are introduced, and a multi-objective optimization model is established according to the influence of the frequency hopping interval and the modulation slope parameter on the fuzzy sidelobe; a design method for a special carrier frequency hopping interval based on the ambiguity function is proposed to obtain the optimal carrier frequency change step length, and then the modulation carrier frequency calculation rule is improved to obtain the nonlinear frequency corresponding to different sub-pulses, so as to adjust the signal frequency domain structure. The present invention greatly reduces the side lobes of traditional broadband pulse train signals, effectively improves the signal time-frequency resolution capability, expands the design ideas of low-distance fuzzy sidelobe waveforms, and lays the foundation for high-resolution detection of sonar.

[0005] The technical solution adopted by the present invention to solve the technical problem is 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: 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;

[0008] Step 3: Establish an optimization function with the goal of sharp main lobe and suppressing fuzzy side lobes, propose a design method for carrier frequency hopping interval based on 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. Assume 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, and 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:

[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 propagation speed of the signal in water, and v is the radial velocity of the target; when s = 1, Ψ(1,τ) is obtained, 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 propagation speed of the signal in water, v is the radial velocity of the target, and it is negative when moving in opposite directions; when s = 1, Ψ(τ, 1) is obtained, 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, namely R1(t) and R2(t). R1(t) represents the periodic grating lobe of the signal caused by the fixed frequency step, and R2(t) is the broadband frequency shift autocorrelation function of the complex envelope of a single pulse.

[0035] Preferably, the step 3 is specifically:

[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 frequency modulation 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 level is 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 minimization of the objective function, 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 formula (23):

[0060]

[0061] Preferably, the step 4 is specifically:

[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 frequency corresponding to different sub-pulses under the optimal carrier frequency change step size is:

[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, the computer program product comprising a computer storage medium, the computer storage medium storing a computer program, the computer program comprising instructions executable by at least one processor, and the above-mentioned nonlinear sub-pulse carrier frequency design method is implemented when the instructions are executed by the at least one processor.

[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 a broadband pulse train to modulate the sub-pulse slope and carrier frequency, thereby further improving the randomness of the waveform and increasing the degree of freedom of waveform design, thus laying a foundation for effectively improving the distance resolution performance of the waveform.

[0073] (2) The present invention establishes a multi-objective optimization model based on the main lobe area and the 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. It can quickly calculate the nonlinear frequencies 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, it can reduce the interference caused by forwarding after being intercepted by the enemy, that is, it can achieve simultaneous suppression of environmental clutter and jammer interference, providing favorable conditions for subsequent high-resolution detection and estimation of target parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 The figure is a 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 It is the initial pulse train carrier frequency, the stepped frequency pulse train carrier frequency, the nonlinear carrier frequency result of the present invention and the nonlinear sub-pulse carrier frequency variation curve of the ascending rearrangement.

[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 distance 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 is further described below in conjunction with the accompanying drawings and embodiments.

[0080] The basic idea of ​​the present invention is to introduce the deflection sequence and frequency hopping coefficient into the frequency modulated pulse train signal, analyze the causes of the 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 the main-side lobe ratio constraints, and propose a design method for the special carrier frequency hopping interval based on the ambiguity function to obtain the optimal carrier frequency change step; then adjust the signal frequency domain structure, improve the modulation carrier frequency calculation rules, and design the nonlinear frequency corresponding to different sub-pulses. Different from the complexity of the nonlinear frequency modulation signal 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 by the present invention can quickly calculate the frequency with a simple formula, and the final carrier frequency law presents an "S" type 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 ambiguous 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 tilt 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 in step (2) and analyzing the influence of the waveform parameters is as follows: n} and the frequency hopping coefficient {C n The signal model of} is substituted into the definition of broadband ambiguity function, the scale factor s=1, and Ψ(1,τ) is calculated to obtain the range ambiguity function. The result is split into the product of two equations, and then the influence of waveform parameters on the range ambiguity function is analyzed by region, thus laying the theoretical foundation for proposing a design method for special carrier frequency hopping interval based on 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 sharp main lobe and the suppression of ambiguous side lobes as the goals. The two goals correspond to the single terms and product terms of the closed-form expression of the distance ambiguity function respectively. Then, within the time delay range, the main lobe area is minimized and the main lobe width is kept constant. The adjacent side lobe level is minimized in this area, characterizing the optimization goals of sharp main lobe and reducing ambiguous 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, so as to construct 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: according to the "Wiener-Schinchin" theorem, the inverse Fourier transform of the Gaussian power spectrum can produce an autocorrelation function without side lobes, so in combination with the optimal carrier frequency jump step length obtained by solving, the signal frequency domain structure is adjusted, and the sub-pulse carrier frequency calculation rule at the position corresponding to the negative modulation slope is rewritten;

[0095] Design of nonlinear sub-pulse carrier frequency under 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 rule, 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 frequency modulated 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 blurred sidelobes. Direct windowing to suppress the sidelobes will widen the main lobe, 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 the 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 propagation speed of the signal in water, and v is the radial velocity of the target. When s = 1, Ψ(1,τ) is obtained, which is called the range ambiguity function.

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

[0118]

[0119] Obviously, the distance ambiguity function can be decomposed into two products, namely R1(t) and R2(t). R1(t) represents the periodic grating lobe of the signal caused by the fixed frequency step, and R2(t) is the broadband frequency shift autocorrelation function of the complex envelope of a single pulse. In the expression, the carrier frequency jump step and the modulation slope of the sub-pulse affect the overall performance of the ambiguity function. When the frequency increases in a linear step-by-step manner of △f, there are periodic grating lobes. When the frequency changes nonlinearly and randomly, the periodicity of the grating lobes is destroyed and the grating lobes can be suppressed, but high-range side lobes will appear, affecting the distance resolution of the signal. Therefore, based on the analysis, the side lobes can be greatly reduced by designing a special carrier frequency step.

[0120] Step 3: Establish an optimization function with the goal of sharp main lobe and suppressing fuzzy side lobes, propose a design method for special carrier frequency hopping interval based on 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 main lobe. The product term uses the main-sidelobe ratio to constrain the height of the distance fuzzy sidelobe. Therefore, a multi-objective joint optimization model is established with the main lobe area and main-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 is the optimal delay range for the main lobe area. D represents the optimized parameters △f and K of the frequency modulation pulse sequence n .

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

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

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

[0128] At this time, the goal of minimizing the sidelobe level in the area of ​​interest is transformed into maximizing the difference between the main lobe peak and the side lobe within the constraints. Unify the form of minimizing the objective function, take the inverse of the difference between the main lobe and the side lobe, and establish the main-side lobe 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] Different from the completely consistent sub-pulse time-frequency structure of the classic pulse train signal, the introduction of the skew sequence and the frequency hopping coefficient can adjust the overlapping structure of different frequency bands of the sub-pulse. In this case, to solve the multi-objective joint optimization model, it is necessary to derive the constraints of the parameters to be optimized, that is, to construct an optimization model of the special carrier frequency hopping interval based on the ambiguity function under the constraints and solve it.

[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 formula (23):

[0147]

[0148] Within the constraints, the genetic algorithm is used to solve the optimal carrier frequency hopping step length. 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 distance ambiguity function result are as follows Figure 2 The genetic algorithm parameters are set as follows: the population item is 100, the crossover probability is 0.7, the mutation probability is 0.1, and the algorithm iteration exceeds 200 generations. The optimal carrier frequency change step length calculated is △f opt =277Hz.

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

[0150] Combined with the optimal frequency hopping interval obtained by the solution, the signal frequency domain structure is adjusted. According to the "Wiener-Schinchin" theorem, the inverse Fourier transform of a signal power spectrum is the autocorrelation function of the signal. In theory, the inverse Fourier transform of the Gaussian power spectrum can produce an autocorrelation function without side lobes. Therefore, considering the improvement of the Gaussian-like structure of the signal frequency domain, the calculation rules of the sub-pulse carrier frequency corresponding to the negative modulation slope position are rewritten;

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

[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, it is 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 step frequency pulse train presents a linear change law. The algorithm designed by the present invention can quickly calculate the nonlinear frequency of the corresponding sub-pulse with a simple formula, 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 Figure 4 As shown in (b), compared Figure 2 The frequency domain and range ambiguity function results of 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 by the present invention has been adjusted to present a Gaussian type. Under the same waveform parameters, the method proposed by the present invention can greatly reduce the level of the range ambiguity side lobe, expand the area of ​​the blank area around the main lobe, and obtain a more ideal range ambiguity function through a simple formula. The calculation speed is fast, easy to implement, and the periodic grating lobe is eliminated. At the same time, it has a sharp main lobe and maintains good time-frequency resolution.

Claims

1. A nonlinear sub-pulse carrier frequency design method based on a broadband pulse train signal, 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 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; Step 3: Establish an optimization function with the goal of sharp main lobe and suppressing fuzzy side lobes, propose a design method for carrier frequency hopping interval based on ambiguity function, and solve the optimal carrier frequency change step size; 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 1 is specifically as follows: Step 1-1: The pulse train signal is a signal model composed of multiple sub-pulses with the same duty cycle. Assume 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, and 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 ).

3. The method for designing nonlinear sub-pulse carrier frequency based on broadband pulse train signal according to claim 2, characterized in that: The step 2 is specifically as follows: 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 propagation speed of the signal in water, and v is the radial velocity of the target; when s = 1, Ψ(1,τ) is obtained, which is called the range ambiguity function; 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; 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 propagation speed of the signal in water, v is the radial velocity of the target, and it is negative when moving in opposite directions; when s = 1, Ψ(τ, 1) is obtained, 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, namely R1(t) and R2(t). R1(t) represents the periodic grating lobe of the signal caused by the fixed frequency step, and R2(t) is the broadband frequency shift autocorrelation function of the complex envelope of a single pulse.

4. The method for designing nonlinear sub-pulse carrier frequency based on broadband pulse train signal according to claim 3, characterized in that: The step 3 is specifically as follows: 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 frequency modulation 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 in this area; 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 minimization of the objective function, 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 the frequency hopping coefficient is introduced, 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 formula (23):

5. The method for designing nonlinear sub-pulse carrier frequency based on broadband pulse train signal according to claim 4, characterized in that: The step 4 is specifically as follows: Considering the improvement of the Gaussian-like 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 Plus B p ; The nonlinear frequency corresponding to different sub-pulses under the optimal carrier frequency change step size is: 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.

6. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 5.

7. 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 executes the method as claimed in any one of claims 1 to 5.

8. 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 5 is implemented.

9. 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 a method as claimed in any one of claims 1 to 5.

10. 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 5 is implemented.

Images