Low-sidelobe nonlinear frequency modulation waveform design method and device based on particle swarm optimization

Abstract

The invention provides a low-sidelobe nonlinear frequency modulation waveform design method and device based on a particle swarm algorithm, and the method comprises the steps: setting system parameters according to the requirements of a radar system, setting a particle swarm according to the system parameters, and setting particle swarm parameters; pulse compression of the continuous NLFM signals is completed, and a current particle adaptive value is obtained; updating the particle position vector of the ith particle in the pb by adopting the particle position with a relatively small adaptive value; according to particle positions corresponding to the particle optimal position matrix pb, continuous NLFM signals are generated, pulse compression is completed, a numerical value of a side lobe with the highest pulse pressure is obtained, and the particle position with the minimum adaptive value is selected as a particle swarm optimal position vector; updating the particle swarm; checking whether the maximum number of iterations is reached or not; and outputting the optimal position vector of the particle swarm, and obtaining a final low-sidelobe continuous NLFM waveform according to the optimal position vector of the particle swarm. According to the invention, the calculation overhead of the waveform design for searching parameters in the parameter space can be greatly reduced.

Description

Technical Field

[0001] The present application relates to the technical field of radar signal waveform design, and in particular to a method and device for designing a low-sidelobe nonlinear frequency modulation waveform based on a particle swarm algorithm. Background Art

[0002] Pulse compression (Pulse Compression) is an important processing technology of modern radar systems, which can enhance the signal-to-noise ratio of target signals. However, radar signals processed by traditional pulse compression technology usually have high side lobes, and there is a phenomenon that weak targets are obscured by the side lobes of strong targets. Low pulse compression side lobe technology can reduce the phenomenon that weak targets are obscured by the side lobes of strong targets, and improve the radar's weak target detection performance.

[0003] The continuous nonlinear frequency modulation (NLFM) waveform design method is a type of low sidelobe pulse compression technology. It achieves sidelobe energy cancellation during pulse compression by improving the frequency modulation function of the waveform, and then completes the low sidelobe pulse compression processing. In the document "An Improved Nonlinear Frequency Modulation Signal Design, Journal of Electronics, Vol. 37, No. 8, August 2009, pp. 1784-1788", He Xuehui, Tao Haihong and others proposed an improved nonlinear frequency modulation signal method based on the window function method, and obtained the pulse compression result of low sidelobe through multiple iterations; this method requires iteration during the pulse compression process, and its real-time performance is poor in engineering practice. In the document: Improved Ultra-low Range Sidelobe Pulse Compression Waveform Design, IET Electronics Letters, Vol. 40, No. 22, October, 2004, pp. 1448-1449, E. De Witte and HD Griffiths proposed a continuous NLFM signal waveform design algorithm. The algorithm is based on the segmented NLFM waveform design algorithm to improve the frequency modulation function. The waveform designed by the algorithm has a better sidelobe suppression capability. However, the traditional continuous NLFM waveform design method needs to find a parameter combination that meets the design requirements through a global search in a multi-parameter space, and then realize the waveform design. However, the computational overhead of the global search in the parameter space is large. Therefore, how to reduce the computational overhead of the continuous NLFM waveform design is a problem that needs to be solved. Summary of the invention

[0004] The present application provides a method and device for designing a low-sidelobe nonlinear frequency modulation waveform based on a particle swarm algorithm, which can be used to solve the technical problem of high computational overhead caused by global search for parameter combinations in a multi-parameter space in the prior art.

[0005] The present application provides a method for designing a low sidelobe nonlinear frequency modulation waveform based on a particle swarm algorithm, the method comprising:

[0006] Step 1: Set system parameters according to the requirements of the radar system, and set the particle swarm according to the system parameters, and set the particle swarm parameters; the system parameters include the sampling rate, pulse width and bandwidth of the signal;

[0007] Step 2: According to the continuous NLFM signal parameters C, τ and χ mapped by the current particle swarm position, complete the pulse compression of the continuous NLFM signal, and use the value of the highest sidelobe of the pulse compression result as the current particle adaptation value;

[0008] Step 3: Compare the current fitness value of the i-th particle with the particle position vector p b，i Compare the fitness values ​​of particles at corresponding positions, and use the particle position with the smaller fitness value to update p b The particle position vector p of the i-th particle in b，i ;

[0009] Step 4: According to the particle optimal position matrix p b The corresponding particle position is obtained based on the continuous NLFM signal parameters C, τ and χ obtained in the particle position and particle swarm 3D parameter space, and a continuous NLFM signal is generated, pulse compression is completed, and the value of the highest sidelobe of the pulse pressure is obtained. The value of the highest sidelobe of the pulse pressure obtained based on each particle position is used as the fitness value of each particle, and the particle position with the smallest fitness value is selected as the particle swarm optimal position vector g b ;

[0010] Step 5: According to the particle swarm learning factor, random number, p b , g b Update the velocity of the particle group and the current position of the particle group with the current particle group velocity;

[0011] Step 6: Check whether the number of iterations reaches the maximum value. If the number of iterations does not reach the maximum value, execute step 2; if the number of iterations reaches the maximum value, execute step 7;

[0012] Step 7: Output the particle swarm optimal position vector g b , and obtain the corresponding continuous NLFM signal waveform design parameters C, τ and χ according to the particle swarm optimal position vector and the particle swarm 3D parameter space, and get the final low sidelobe continuous NLFM waveform.

[0013] Further, the system parameters are set according to the requirements of the radar system, and the particle swarm is set according to the system parameters, and the particle swarm parameters are set; including:

[0014] Set the value range and step size of the three waveform parameters of the continuous nonlinear frequency modulation NLFM signal: the instantaneous frequency upper limit C, the frequency control parameter τ and the time control parameter χ; construct the particle swarm 3D parameter space according to the value range and step size of C, τ and χ, and encode the position and velocity vector of each particle in the particle swarm based on the parameter space; initialize the particle swarm parameters, set the particle swarm size M, and the particle swarm size is usually ≥10; set two learning factors c1 and c2, and the learning factors usually take the value interval of the closed interval [1,2]; set the maximum number of iterations of the algorithm; set the initial velocity of the i-th particle and initial position 1≤i≤M, initial velocity and initial speed are both constrained by the 3D parameter space of the particle swarm; set a random number.

[0015] Further, the pulse compression method is as follows:

[0016]

[0017] t′=T / 2-δ (2)

[0018]

[0019] g(t)=s(t)*[s H (t)h(t)] (6)

[0020] The frequency modulation function f of the continuous NLFM signal is generated according to expression (1), and the parameters in expression (1) are the linear frequency component time boundary t′, the nonlinear frequency component time parameter δ and the nonlinear frequency component frequency parameter Obtained by expressions (2)-(4) respectively, Kr is the frequency modulation slope;

[0021] In expressions (2)-(4), T is the pulse width, B represents the signal bandwidth, τ, χ and C are the frequency control parameter, time control parameter and the upper limit of the instantaneous frequency respectively; after obtaining f, the transmitted signal s(t) is obtained by expression (5); in equation (5), w(t) is the signal amplitude envelope function, which is a rectangular window function; the pulse compression processing process of the radar signal s(t) is shown in expression (6), where * represents convolution, h(t) is the window function, the superscript H represents the complex conjugate operation, and g(t) represents the pulse compression result.

[0022] Furthermore, the velocity of the i-th particle in the k-th iteration is and the position of the i-th particle at the k-th iteration Obtained through the following methods:

[0023]

[0024] in, is the velocity of the i-th particle in the k-th iteration; is the position of the i-th particle in the k-th iteration; is the velocity of particle i in the k-1th iteration; is the position of the i-th particle in the k-1th iteration.

[0025] Furthermore, the value range of the random number is a closed interval [0,1].

[0026] The present application also provides a low sidelobe nonlinear frequency modulation waveform design device based on a particle swarm algorithm, the device comprising:

[0027] The parameter determination module sets the system parameters according to the requirements of the radar system, and sets the particle swarm according to the system parameters, and sets the particle swarm parameters; the system parameters include the sampling rate, pulse width and bandwidth of the signal;

[0028] The pulse compression module is used to complete the pulse compression of the continuous NLFM signal according to the continuous NLFM signal parameters C, τ and χ mapped by the current particle group position, and use the value of the highest sidelobe of the pulse compression result as the current particle adaptation value;

[0029] Comparison module, used to compare the current fitness value of the i-th particle with the particle position vector p b，i Compare the fitness values ​​of particles at corresponding positions, and use the particle position with the smaller fitness value to update p b The particle position vector p of the i-th particle in b，i ;

[0030] The selection module is used to select the optimal position matrix p of the particle b The corresponding particle position is obtained based on the continuous NLFM signal parameters C, τ and χ obtained in the particle position and particle swarm 3D parameter space, and a continuous NLFM signal is generated, pulse compression is completed, and the value of the highest sidelobe of the pulse pressure is obtained. The value of the highest sidelobe of the pulse pressure obtained based on each particle position is used as the fitness value of each particle, and the particle position with the smallest fitness value is selected as the particle swarm optimal position vector g b ;

[0031] Update module, used to learn factors, random numbers, p according to the particle swarm b , g b Update the velocity of the particle group and the current position of the particle group with the current particle group velocity;

[0032] The judgment module is used to check whether the number of iterations has reached the maximum value. If the number of iterations has not reached the maximum value, the iteration continues; if the iteration reaches the maximum value, the output module is entered;

[0033] Output module, used to output the optimal position vector g of the particle swarmb , and obtain the corresponding continuous NLFM signal waveform design parameters C, τ and χ according to the particle swarm optimal position vector and the particle swarm 3D parameter space, and get the final low sidelobe continuous NLFM waveform.

[0034] Furthermore, the parameter determination module is specifically used for:

[0035] Set the value range and step size of the three waveform parameters of the continuous nonlinear frequency modulation NLFM signal: the instantaneous frequency upper limit C, the frequency control parameter τ and the time control parameter χ; construct the particle swarm 3D parameter space according to the value range and step size of C, τ and χ, and encode the position and velocity vector of each particle in the particle swarm based on the parameter space; initialize the particle swarm parameters, set the particle swarm size M, and the particle swarm size is usually ≥10; set two learning factors c1 and c2, and the learning factors usually take the value interval of the closed interval [1,2]; set the maximum number of iterations of the algorithm; set the initial velocity of the i-th particle and initial position 1≤i≤M, initial velocity and initial speed are both constrained by the 3D parameter space of the particle swarm; set a random number.

[0036] Furthermore, the pulse compression module is specifically used for:

[0037]

[0038] t′=T / 2-δ (2)

[0039]

[0040] g(t)=s(t)*[s H (t)h(t)] (6)

[0041] The frequency modulation function f of the continuous NLFM signal is generated according to expression (1), and the parameters in expression (1) are the linear frequency component time boundary t′, the nonlinear frequency component time parameter δ and the nonlinear frequency component frequency parameter Obtained by expressions (2)-(4) respectively, Kr is the frequency modulation slope;

[0042] In expressions (2)-(4), T is the pulse width, B represents the signal bandwidth, τ, χ and C are the frequency control parameter, time control parameter and the upper limit of the instantaneous frequency respectively; after obtaining f, the transmitted signal s(t) is obtained by expression (5); in equation (5), w(t) is the signal amplitude envelope function, which is a rectangular window function; the pulse compression processing process of the radar signal s(t) is shown in expression (6), where * represents convolution, h(t) is the window function, the superscript H represents the complex conjugate operation, and g(t) represents the pulse compression result.

[0043] Furthermore, the velocity of the i-th particle in the k-th iteration is and the position of the i-th particle at the k-th iteration Obtained through the following methods:

[0044]

[0045] in, is the velocity of the i-th particle in the k-th iteration; is the position of the i-th particle in the k-th iteration; is the velocity of particle i in the k-1th iteration; is the position of the i-th particle in the k-1th iteration.

[0046] Furthermore, the value range of the random number is a closed interval [0,1].

[0047] This application aims at the large amount of computational overhead caused by global search in traditional continuous NLFM waveform design, and optimizes the parameter search process by adopting particle swarm algorithm, reduces the number of parameter searches, and thus reduces the computational overhead of waveform design. The method provided in this application combines particle swarm algorithm with continuous nonlinear frequency modulation signal waveform design algorithm, and uses particle swarm algorithm to optimize the parameter selection process of continuous nonlinear frequency modulation signal waveform design, thereby reducing the number of parameter searches involved in waveform design, and then significantly reducing the computational overhead of continuous nonlinear frequency modulation waveform design. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flow chart of the method provided in an embodiment of the present application. DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0050] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0051] Step 1: First, set the system parameters according to the requirements of the radar system, and set the particle swarm according to the system parameters, and set the particle swarm parameters; the system parameters mainly include basic system parameters such as signal sampling rate, pulse width and bandwidth;

[0052] Set the value range and step size of the three waveform parameters of the continuous nonlinear frequency modulation NLFM signal: the instantaneous frequency upper bound C, the frequency control parameter τ, and the time control parameter χ; construct the particle swarm 3D parameter space according to the value range and step size of C, τ, and χ, and encode the position and velocity vector of each particle in the particle swarm based on the parameter space; initialize the particle swarm parameters, set the particle swarm size M, and the particle swarm size is usually ≥10; set two learning factors c1 and c2, and the learning factor usually takes a closed interval [1,2]; set the maximum number of iterations of the algorithm, and the maximum number of iterations is ≥50; set the initial velocity of the i-th particle and initial position 1≤i≤M, the initial velocity and initial speed are both constrained by the 3D parameter space of the particle swarm; set a random number, and the range of the random number is a closed interval [0,1];

[0053] Step 2: According to the continuous NLFM signal parameters C, τ and χ mapped by the current particle swarm position, complete the pulse compression of the continuous NLFM signal, and use the value of the highest sidelobe of the pulse compression result as the current particle adaptation value;

[0054] Specifically, based on expressions (1) to (6), the pulse compression of the continuous NLFM signal is completed, and the pulse compression method is as follows:

[0055]

[0056] t′=T / 2-δ (2)

[0057]

[0058] g(t)=s(t)*[s H (t)h(t)] (6)

[0059] The frequency modulation function f of the continuous NLFM signal is generated according to expression (1), and the parameters in expression (1) are the linear frequency component time boundary t′, the nonlinear frequency component time parameter δ and the nonlinear frequency component frequency parameter They are obtained by expressions (2)-(4) respectively, Kr is the frequency modulation slope; in expressions (2)-(4), T is the pulse width, B represents the signal bandwidth, τ, χ and C are the three waveform parameters of frequency control parameter, time control parameter and instantaneous frequency upper limit respectively; after obtaining f, the transmitted signal s(t) is obtained by expression (5); in formula (5), w(t) is the signal amplitude envelope function, which is a rectangular window function; the pulse compression processing process of radar signal s(t) is shown in expression (6), where * represents convolution, h(t) is the window function, the superscript H represents the complex conjugate operation, and g(t) represents the pulse compression result.

[0060] Step 3: Compare the current fitness value of the i-th particle with the particle position vector p b，i Compare the fitness values ​​of particles at corresponding positions, and use the particle position with the smaller fitness value to update p b The particle position vector p of the i-th particle in b，i .

[0061] Step 4: According to the particle optimal position matrix p b The corresponding particle position is obtained based on the continuous NLFM signal parameters C, τ and χ obtained in the particle position and particle swarm 3D parameter space, and a continuous NLFM signal is generated, pulse compression is completed, and the value of the highest sidelobe of the pulse pressure is obtained. The value of the highest sidelobe of the pulse pressure obtained based on each particle position is used as the fitness value of each particle, and the particle position with the smallest fitness value is selected as the particle swarm optimal position vector g b .

[0062] The method for generating a continuous NLFM signal, completing pulse compression, and obtaining the value of the highest sidelobe of the pulse pressure is consistent with that in step 2, that is, formulas (1)-(6) are used for processing, which will not be repeated here.

[0063] Step 5: According to the particle swarm learning factor, random number, p b , g b Update the velocity of the particle swarm and the current position of the particle swarm with the current particle swarm velocity.

[0064] Specifically, the velocity of the i-th particle in the k-th iteration is and the position of the i-th particle at the k-th iteration Obtained through the following methods:

[0065]

[0066] In the formula, the learning factors are two constants c1 and c2; the random number vectors R1 and R2 are random number vectors with values ​​between 0 and 1; the symbol Represents the dot product operation.

[0067] Step 6: Check whether the number of iterations reaches the maximum value. If the number of iterations does not reach the maximum value, execute step 2; if the number of iterations reaches the maximum value, execute step 7.

[0068] In each iteration, updating the particle swarm speed and current particle swarm position requires the use of particle swarm learning factor, random number, particle optimal position matrix, particle swarm optimal position vector and current particle swarm speed, where the value range of the random number is a closed interval [0,1].

[0069] Step 7: Output the particle swarm optimal position vector g b, and obtain the corresponding continuous NLFM signal waveform design parameters C, τ and χ according to the particle swarm optimal position vector and the particle swarm 3D parameter space, and get the final low sidelobe continuous NLFM waveform.

[0070] The present application also provides a low sidelobe nonlinear frequency modulation waveform design device based on a particle swarm algorithm. The present application provides a device for implementing the method provided in the present application, and the device includes:

[0071] The parameter determination module sets the system parameters according to the requirements of the radar system, and sets the particle swarm according to the system parameters, and sets the particle swarm parameters; the system parameters include the sampling rate, pulse width and bandwidth of the signal;

[0072] The pulse compression module is used to complete the pulse compression of the continuous NLFM signal according to the continuous NLFM signal parameters C, τ and χ mapped by the current particle group position, and use the value of the highest sidelobe of the pulse compression result as the current particle adaptation value;

[0073] Comparison module, used to compare the current fitness value of the i-th particle with the particle position vector p b，i Compare the fitness values ​​of particles at corresponding positions, and use the particle position with the smaller fitness value to update p b The particle position vector p of the i-th particle in b，i ;

[0074] The selection module is used to select the optimal position matrix p of the particle b The corresponding particle position is obtained based on the continuous NLFM signal parameters C, τ and χ obtained in the particle position and particle swarm 3D parameter space, and a continuous NLFM signal is generated, pulse compression is completed, and the value of the highest sidelobe of the pulse pressure is obtained. The value of the highest sidelobe of the pulse pressure obtained based on each particle position is used as the fitness value of each particle, and the particle position with the smallest fitness value is selected as the particle swarm optimal position vector g b ;

[0075] Update module, used to learn factors, random numbers, p according to the particle swarm b , g b Update the velocity of the particle group and the current position of the particle group with the current particle group velocity;

[0076] The judgment module is used to check whether the number of iterations has reached the maximum value. If the number of iterations has not reached the maximum value, the iteration continues; if the iteration reaches the maximum value, the output module is entered;

[0077] Output module, used to output the optimal position vector g of the particle swarm b , and obtain the corresponding continuous NLFM signal waveform design parameters C, τ and χ according to the particle swarm optimal position vector and the particle swarm 3D parameter space, and get the final low sidelobe continuous NLFM waveform.

[0078] Furthermore, the parameter determination module is specifically used for:

[0079] Set the value range and step size of the three waveform parameters of the continuous nonlinear frequency modulation NLFM signal: the instantaneous frequency upper limit C, the frequency control parameter τ and the time control parameter χ; construct the particle swarm 3D parameter space according to the value range and step size of C, τ and χ, and encode the position and velocity vector of each particle in the particle swarm based on the parameter space; initialize the particle swarm parameters, set the particle swarm size M, and the particle swarm size is usually ≥10; set two learning factors c1 and c2, and the learning factors usually take the value interval of the closed interval [1,2]; set the maximum number of iterations of the algorithm; set the initial velocity of the i-th particle and initial position 1≤i≤M, initial velocity and initial speed are both constrained by the 3D parameter space of the particle swarm; set a random number.

[0080] Furthermore, the pulse compression module is specifically used for:

[0081]

[0082] t′=T / 2-δ (2)

[0083]

[0084] g(t)=s(t)*[s H (t)h(t)] (6)

[0085] The frequency modulation function f of the continuous NLFM signal is generated according to expression (1), the parameters of the linear frequency component time boundary t′, the nonlinear frequency component time parameter δ and the nonlinear frequency component frequency parameter ζ in expression (1) are obtained by expressions (2)-(4) respectively, and Kr is the frequency modulation slope;

[0086] In expressions (2)-(4), T is the pulse width, B represents the signal bandwidth, τ, χ and C are the frequency control parameter, time control parameter and the upper limit of the instantaneous frequency respectively; after obtaining f, the transmitted signal s(t) is obtained by expression (5); in equation (5), w(t) is the signal amplitude envelope function, which is a rectangular window function; the pulse compression processing process of the radar signal s(t) is shown in expression (6), where * represents convolution, h(t) is the window function, the superscript H represents the complex conjugate operation, and g(t) represents the pulse compression result.

[0087] Furthermore, the velocity of the i-th particle in the k-th iteration is and the position of the i-th particle at the k-th iteration Obtained through the following methods:

[0088]

[0089] in, is the velocity of the i-th particle in the k-th iteration; is the position of the i-th particle in the k-th iteration; is the velocity of particle i in the k-1th iteration; is the position of the i-th particle in the k-1th iteration.

[0090] Furthermore, the value range of the random number is a closed interval [0,1].

[0091] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A low sidelobe nonlinear frequency modulation waveform design method based on particle swarm algorithm, characterized in that: The method comprises: Step 1: Set system parameters according to the requirements of the radar system, and set the particle swarm according to the system parameters, and set the particle swarm parameters; the system parameters include the sampling rate, pulse width and bandwidth of the signal; Step 2: According to the continuous NLFM signal parameters C, τ and χ mapped by the current particle swarm position, complete the pulse compression of the continuous NLFM signal, and use the value of the highest sidelobe of the pulse compression result as the current particle adaptation value; Step 3: Compare the current fitness value of the i-th particle with the particle position vector p b，i Compare the fitness values ​​of particles at corresponding positions, and use the particle position with the smaller fitness value to update p b The particle position vector p of the i-th particle in b，i ; Step 4: According to the particle optimal position matrix p b The corresponding particle position is obtained based on the continuous NLFM signal parameters C, τ and χ obtained in the particle position and particle swarm 3D parameter space, and a continuous NLFM signal is generated, pulse compression is completed, and the value of the highest sidelobe of the pulse pressure is obtained. The value of the highest sidelobe of the pulse pressure obtained based on each particle position is used as the fitness value of each particle, and the particle position with the smallest fitness value is selected as the particle swarm optimal position vector g b ; Step 5: According to the particle swarm learning factor, random number, p b , g b Update the velocity of the particle group and the current position of the particle group with the current particle group velocity; Step 6: Check whether the number of iterations reaches the maximum value. If the number of iterations does not reach the maximum value, execute step 2; if the number of iterations reaches the maximum value, execute step 7; Step 7: Output the particle swarm optimal position vector g b , and obtain the corresponding continuous NLFM signal waveform design parameters C, τ and χ according to the particle swarm optimal position vector and the particle swarm 3D parameter space, and get the final low sidelobe continuous NLFM waveform.

2. The method according to claim 1, characterized in that Set system parameters according to the requirements of the radar system, set the particle swarm according to the system parameters, and set the particle swarm parameters; including: Set the value range and step size of the three waveform parameters of the continuous nonlinear frequency modulation NLFM signal: the instantaneous frequency upper limit C, the frequency control parameter τ and the time control parameter χ; construct the particle swarm 3D parameter space according to the value range and step size of C, τ and χ, and encode the position and velocity vector of each particle in the particle swarm based on the parameter space; initialize the particle swarm parameters, set the particle swarm size M, and the particle swarm size is usually ≥10; set two learning factors c1 and c2, and the learning factors usually have a value range of a closed interval [1,2]; set the maximum number of iterations of the algorithm; set the initial velocity of the i-th particle and initial position 1≤i≤M, initial velocity and initial speed are both constrained by the 3D parameter space of the particle swarm; set a random number.

3. The method according to claim 1, characterized in that The pulse compression method is as follows: The frequency modulation function f of the continuous NLFM signal is generated according to expression (1), and the parameters in expression (1) are the linear frequency component time boundary t′, the nonlinear frequency component time parameter δ and the nonlinear frequency component frequency parameter Obtained by expressions (2)-(4) respectively, Kr is the frequency modulation slope; In expressions (2)-(4), T is the pulse width, B represents the signal bandwidth, τ, χ and C are the frequency control parameter, time control parameter and the upper limit of the instantaneous frequency respectively; after obtaining f, the transmitted signal s(t) is obtained by expression (5); in equation (5), w(t) is the signal amplitude envelope function, which is a rectangular window function; the pulse compression processing process of the radar signal s(t) is shown in expression (6), where * represents convolution, h(t) is the window function, the superscript H represents the complex conjugate operation, and g(t) represents the pulse compression result.

4. The method according to claim 1, characterized in that: The velocity of the i-th particle at the k-th iteration and the position of the i-th particle at the k-th iteration Obtained through the following methods: in, is the velocity of the i-th particle in the k-th iteration; is the position of the i-th particle in the k-th iteration; is the velocity of particle i in the k-1th iteration; is the position of the i-th particle in the k-1th iteration.

5. The method according to claim 1, characterized in that: The value range of random numbers is the closed interval [0,1].

6. A low sidelobe nonlinear frequency modulation waveform design device based on particle swarm algorithm, characterized in that: The device comprises: The parameter determination module sets the system parameters according to the requirements of the radar system, and sets the particle swarm according to the system parameters, and sets the particle swarm parameters; the system parameters include the sampling rate, pulse width and bandwidth of the signal; The pulse compression module is used to complete the pulse compression of the continuous NLFM signal according to the continuous NLFM signal parameters C, τ and χ mapped by the current particle group position, and use the value of the highest sidelobe of the pulse compression result as the current particle adaptation value; Comparison module, used to compare the current fitness value of the i-th particle with the particle position vector p b，i Compare the fitness values ​​of particles at corresponding positions, and use the particle position with the smaller fitness value to update p b The particle position vector p of the i-th particle in b，i ; The selection module is used to select the optimal position matrix p of the particle b The corresponding particle position is obtained based on the continuous NLFM signal parameters C, τ and χ obtained in the particle position and particle swarm 3D parameter space, and a continuous NLFM signal is generated, pulse compression is completed, and the value of the highest sidelobe of the pulse pressure is obtained. The value of the highest sidelobe of the pulse pressure obtained based on each particle position is used as the fitness value of each particle, and the particle position with the smallest fitness value is selected as the particle swarm optimal position vector g b ; Update module, used to learn factors, random numbers, p according to the particle swarm b , g b Update the velocity of the particle group and the current position of the particle group with the current particle group velocity; The judgment module is used to check whether the number of iterations has reached the maximum value. If the number of iterations has not reached the maximum value, the iteration continues; if the iteration reaches the maximum value, the output module is entered; Output module, used to output the optimal position vector g of the particle swarm b , and obtain the corresponding continuous NLFM signal waveform design parameters C, τ and χ according to the particle swarm optimal position vector and the particle swarm 3D parameter space, and get the final low sidelobe continuous NLFM waveform.

7. The method according to claim 6, characterized in that The parameter determination module is specifically used for: Set the value range and step size of the three waveform parameters of the continuous nonlinear frequency modulation NLFM signal: the instantaneous frequency upper limit C, the frequency control parameter τ and the time control parameter χ; construct the particle swarm 3D parameter space according to the value range and step size of C, τ and χ, and encode the position and velocity vector of each particle in the particle swarm based on the parameter space; initialize the particle swarm parameters, set the particle swarm size M, and the particle swarm size is usually ≥10; set two learning factors c1 and c2, and the learning factors usually have a value range of a closed interval [1,2]; set the maximum number of iterations of the algorithm; set the initial velocity of the i-th particle and initial position 1≤i≤M, initial velocity and initial speed are both constrained by the 3D parameter space of the particle swarm; set a random number.

8. The device according to claim 6, characterized in that The pulse compression module is specifically used for: The frequency modulation function f of the continuous NLFM signal is generated according to expression (1), and the parameters in expression (1) are the linear frequency component time boundary t′, the nonlinear frequency component time parameter δ and the nonlinear frequency component frequency parameter Obtained by expressions (2)-(4) respectively, Kr is the frequency modulation slope; In expressions (2)-(4), T is the pulse width, B represents the signal bandwidth, τ, χ and C are the frequency control parameter, time control parameter and the upper limit of the instantaneous frequency respectively; after obtaining f, the transmitted signal s(t) is obtained by expression (5); in equation (5), w(t) is the signal amplitude envelope function, which is a rectangular window function; the pulse compression processing process of the radar signal s(t) is shown in expression (6), where * represents convolution, h(t) is the window function, the superscript H represents the complex conjugate operation, and g(t) represents the pulse compression result.

9. The device according to claim 6, characterized in that The velocity of the i-th particle at the k-th iteration and the position of the i-th particle at the k-th iteration Obtained through the following methods: in, is the velocity of the i-th particle in the k-th iteration; is the position of the i-th particle in the k-th iteration; is the velocity of particle i in the k-1th iteration; is the position of the i-th particle in the k-1th iteration.

10. The device according to claim 6, characterized in that The value range of random numbers is the closed interval [0,1].

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