A method for improving the pulse compression performance of NLFM signals based on the first derivative of the phase function

Abstract

The present invention relates to a method for improving the pulse compression performance of an NLFM signal based on the first derivative of the phase function. Starting from the first derivative of the phase function, according to the S-shaped characteristic of the frequency function of the NLFM signal and the relationship between the frequency function and the phase function, a combination of a linear function and a tangent function is used to design the first derivative of the phase function of the NLFM signal, the frequency function is obtained, and the phase function is calculated by accumulating and summing the frequency function. Combining the relationship between the amplitude function of the NLFM signal and the second derivative of the phase function to solve the amplitude function. Finally, the spectrum of the NLFM signal is obtained. Experimental results show that this method can suppress the sidelobe level of the NLFM signal pulse compression result while solving the problems of excessive main lobe broadening and excessive SNR loss caused by the method of using mismatched windowing.

Description

Technical Field

[0001] The present invention belongs to the technical field of methods for improving the pulse compression performance of NLFM signals, and specifically relates to a method for improving the pulse compression performance of NLFM signals based on the design of the first derivative of the phase function. Background Art

[0002] The advantage of NLFM signals is that by directly designing the waveform of the transmitted signal, the influence of the weighting effect on the pulse compression performance of the signal is avoided. Currently, the commonly used methods for designing NLFM signal waveforms mainly include the window function weighting method and the continuous non-linear frequency modulation function method, etc.

[0003] Data shows that for the NLFM signal spectrum designed by the window function weighting method, while the sidelobe level in the pulse compression result decreases, the main lobe broadens too much. The continuous non-linear frequency modulation function method reduces the steps of designing the group delay function, but in the process of designing the frequency function, the successive approximation method is used multiple times and requires repeated calculations. Therefore, a large number of simulation experiments are inevitable, and the suppression of the sidelobes in the pulse compression result is mostly around -25dB to -35dB, and in some cases, it still cannot meet the actual requirements. Summary of the Invention

[0004] Technical Problems to be Solved

[0005] In order to avoid the deficiencies of the prior art, the present invention provides a method for improving the pulse compression performance of NLFM signals based on the design of the first derivative of the phase function, which is mainly used for designing the NLFM signal spectrum between the rectangular window and the ideal window function, aiming to suppress the sidelobe level of the signal pulse compression result while avoiding the problems of excessive main lobe broadening and excessive SNR loss caused by weighting.

[0006] Technical Solution

[0007] A method for improving the pulse compression performance of NLFM signals based on the design of the first derivative of the phase function, characterized by the following steps:

[0008] Step 1: Calculate the first derivative φ′(t) of the phase function;

[0009]

[0010] where T is the time width, B is the bandwidth, f s is the sampling rate, and both α and γ are control parameters to be designed. α controls the balance between tangent frequency modulation and linear frequency modulation, and γ controls the ratio of the tangent function to the linear function;

[0011] Step 2: Solve the frequency function f(t) according to the first derivative φ′(t) of the phase function obtained in Step 1:

[0012]

[0013] Step 3: Perform cumulative summation on the frequency function f(t) obtained in Step 2 to obtain the phase function φ(t):

[0014]

[0015] Step 4: Solve the second derivative φ″(t) of the phase function and calculate the amplitude function a(t) of the NLFM signal:

[0016]

[0017]

[0018] where S(φ′(t)) is the power spectral density function;

[0019] Step 5: Combine the phase function φ(t) and the amplitude function a(t) obtained in Step 3 and Step 4 respectively to calculate the time-domain expression of the NLFM signal;

[0020] s(t) = a(t)exp[jφ(t)]

[0021] Step 6: Perform matched pulse compression processing on the NLFM signal waveform, observe whether the first sidelobe level of the pulse compression result meets the requirements. If it does not meet the requirements, the values of the control parameters α and γ can be adjusted within the allowable range of main lobe broadening and SNR loss, and the above steps can be repeated until the first sidelobe level meets the system requirements.

[0022] A computer system, characterized in that it includes: one or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0023] A computer-readable storage medium, characterized in that it stores computer-executable instructions, and the instructions are used to implement the above method when executed.

[0024] Beneficial effects

[0025] The present invention proposes a method for designing the waveform of an NLFM signal by designing the first derivative of the phase function, thereby improving the pulse compression performance of the NLFM signal. This method first starts from the first derivative of the phase function. According to the S-shaped characteristic of the frequency function of the NLFM signal, by combining a linear function and a tangent function, relevant parameters for controlling the balance between tangent frequency modulation and linear frequency modulation and the ratio of the tangent function to the linear function are designed to obtain the first derivative of the phase function. Combining the relationship between the frequency function and the phase function, the frequency function is obtained, and the phase function is calculated by accumulating and summing the frequency function. Then, according to the relationship between the amplitude function of the NLFM signal and the second derivative of the phase function, the amplitude function is solved. Finally, the spectrum of the NLFM signal is obtained.

[0026] Experimental results show that by using the method for improving the pulse compression performance of the NLFM signal proposed by the present invention, the sidelobe level of the signal pulse compression result can be reduced to about -79 dB. At the same time, the problems of excessive main lobe broadening and excessive SNR loss are avoided, meeting the requirements of most practical engineering applications. Brief Description of the Drawings

[0027] The drawings are only for the purpose of illustrating specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference signs represent the same components.

[0028] Figure 1 It is a schematic diagram of the spectrum waveform of the Gaussian window used in the present invention;

[0029] Figure 2 It is a schematic diagram of the curve of the first derivative of the phase function of the NLFM signal designed by the present invention;

[0030] Figure 3 It is a schematic diagram of the curve of the frequency function of the NLFM signal designed by the present invention;

[0031] Figure 4 It is a schematic diagram of the curve of the phase function of the NLFM signal designed by the present invention;

[0032] Figure 5 It is a schematic diagram of the curve of the amplitude function of the NLFM signal designed by the present invention;

[0033] Figure 6 It is a schematic diagram of the time-domain waveform of the NLFM signal designed by the present invention;

[0034] Figure 7 It is a schematic diagram of the spectrum characteristics of the matched filter of the NLFM signal designed by the present invention;

[0035] Figure 8 It is a schematic diagram of the frequency-domain matched pulse compression waveform of the NLFM signal under the initial control parameters designed by the present invention;

[0036] Figure 9It is a schematic diagram of the frequency-domain matched pulse compression waveform of the NLFM signal under the optimized control parameters designed by the present invention. Specific embodiments

[0037] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0038] The objective of the present invention is to provide a method for improving the pulse compression performance of the NLFM signal based on the design of the first derivative of the phase function. This method has been applied in engineering experiments and has achieved obvious effects. The present invention starts from the first derivative of the phase function, and based on the S-shaped characteristic of the frequency function of the NLFM signal and the relationship between the frequency function and the phase function, a combination of a linear function and a tangent function is used to design the first derivative of the phase function of the NLFM signal, find the frequency function, and calculate the phase function by cumulative summation of the frequency function. Combining the relationship between the amplitude function of the NLFM signal and the second derivative of the phase function to solve the amplitude function. Finally, the spectrum of the NLFM signal is obtained. Experimental results show that this method can suppress the sidelobe level of the NLFM signal pulse compression result while solving the problems of excessive main lobe broadening and excessive SNR loss caused by the method of using mismatched windowing.

[0039] In the present invention, it is assumed that the spectrum of the NLFM signal is

[0040] s(t) = a(t)exp[jφ(t)] (1-1)

[0041] where a(t) is the signal amplitude function and φ(t) is the phase function. Taking the Fourier transform of the signal to obtain the corresponding frequency-domain expression:

[0042]

[0043] Since the phase function of the NLFM signal is a composite function, in order to obtain the relationship between a(t) and φ(t), it is assumed that a(t) changes slowly compared to φ(t). According to the phase stationary principle, it is assumed that the phase function φ(t) has a phase stationary point only at t = t0, then φ′(t0) = 0. At this time, the phase function φ(t) is Taylor-expanded at t = t0. For simplicity of calculation, only the first three terms are taken, and there is:

[0044]

[0045] Substituting Equation (1-3) into (1-2) gives:

[0046]

[0047] Combined with Poisson's formula:

[0048]

[0049] Then Equation (1-4) can be simplified to:

[0050]

[0051] Since the amplitude of the signal is the absolute value of S(ω), the expression of the amplitude function is:

[0052]

[0053] Then the power spectral density of the signal is:

[0054]

[0055] According to Equation (1-8), it can be seen that the power spectral density function is related to both the amplitude function a(t) and the phase function φ(t). Therefore, to solve the amplitude function, the expression of the power spectral density function must be given. Since the frequency-domain expressions of common ideal window functions are all composed of the sum of a series of cosine functions, the expression of the power spectral density function can be assumed as:

[0056]

[0057] Substituting Equation (1-9) into (1-8), the expression of the amplitude function can be obtained as:

[0058]

[0059] Assume that the window function selected in the design process is a Gaussian window, and its power spectral density function can be expressed as:

[0060]

[0061] Combined with Equation (1-10), it can be seen that the amplitude function a(t) is related to the second derivative φ″(t) of the phase function. Therefore, to determine the amplitude function, some information of the phase function must be known. By consulting the literature, the first derivative φ′(t) of the phase function can be designed. Based on the S-shaped characteristic of the frequency function of the NLFM signal, the design idea of φ′(t) is to combine a linear function with a tangent-linear function, that is:

[0062]

[0063] Among them, α and γ are control parameters that need to be designed. α controls the balance between tangent frequency modulation and linear frequency modulation, and γ controls the ratio of tangent function and linear function. Generally, the optimal values of α and γ can be determined through simulation experiments based on radar design parameters.

[0064] Based on the relationship between the phase function ′(t) and the frequency function f(t):

[0065]

[0066] The relationship between the frequency function f(t) and the first-order derivative φ′(t) of the phase function can be obtained as follows:

[0067]

[0068] The expression of the frequency function is:

[0069]

[0070] Through simulation experiments, it can be seen that when the value of α is small, the proportion of the linear function is large, causing the frequency function to become a linear frequency modulation function; when the value of γ is large, the frequency function is close to an S-shaped curve.

[0071] According to formula (1-12), the second-order derivative expression of the phase function can be obtained as follows:

[0072]

[0073] According to the phase lingering principle, the derivative of the phase function at the phase lingering point t0, φ′(t0)=0. According to formula (1-2), [-ωt+φ(t)]′=0, that is, ω=φ′(t). Substituting ω in formula (1-10) with φ′(t), the weighted amplitude function expression is obtained as follows:

[0074]

[0075] At this point, the amplitude function a(t) and the phase function φ(t) have been determined, and the time domain expression of the NLFM signal is:

[0076] s(t)=a(t)exp[jφ(t)] (1-18)

[0077] In order to enable those skilled in the art to better understand the present invention, the present invention is described in detail below in conjunction with specific embodiments.

[0078] Step 1: Given the radar design parameters: time width T, bandwidth B, sampling rate f s , the selected window function spectrum and the initial values of parameters α and γ. This experiment uses the Gaussian window spectrum, see Figure 1, the initial values are set to α = 0.5 and γ = 1.2. According to Equation (1-12), the first derivative φ′(t) of the phase function is calculated, see Figure 2 ;

[0079] Step 2, based on the first derivative φ′(t) of the phase function obtained in Step 1, and combining Equations (1-14) and (1-15), the frequency function f(t) is solved. The curve graph of the frequency function f(t) is shown in Figure 3 ;

[0080] Step 3, combining Equation (1-13), the frequency function f(t) obtained in Step 2 is accumulated and summed to obtain the phase function φ(t). The curve graph of the phase function φ(t) is shown in Figure 4 ;

[0081] Step 4, according to Equation (1-16), the second derivative φ″(t) of the phase function is solved, and then combining Equation (1-17), the amplitude function a(t) of the NLFM signal is calculated. The curve graph of the amplitude function a(t) is shown in Figure 5 ;

[0082] Step 5, combining the phase function φ(t) and the amplitude function a(t) obtained in Step 3 and Step 4 respectively, according to Equation (1-18), the time-domain expression of the NLFM signal is calculated. The time-domain waveform of the NLFM signal is shown in Figure 6 , and at the same time, the spectral characteristics of the matched filter of the NLFM signal are obtained, see Figure 7 ;

[0083] Step 6, perform matched pulse compression processing on the NLFM signal waveform, and observe whether the first sidelobe level of the pulse compression result meets the requirements. If it does not meet the requirements, the values of the control parameters α and γ can be adjusted within the allowable range of main lobe broadening and SNR loss, and repeat the above steps until the first sidelobe level meets the system requirements.

[0084] In the present invention, under the radar design parameters described above, the first sidelobe of the pulse compression result of the designed NLFM signal is approximately -33.75 dB, see Figure 8 ; When the parameters α and γ are set to α = 0.58 and γ = 1.48 respectively, see Table 1, the first sidelobe is reduced to -79 dB, and the main lobe broadening is within the allowable range, see Figure 9 . Therefore, the requirements of most practical projects are met.

[0085] Table 1 Explanation of Radar Design Parameters

[0086] Time width T Bandwidth B <![CDATA[Sampling rate f s > Window function α γ 40us 5MHz 20MHz Gaussian window 0.58 1.48

[0087] The pulse compression waveform can be obtained by performing matched pulse compression processing on the NLFM signal. The experimental results show that, by using the method for improving the pulse compression performance of the NLFM signal based on the first derivative of the phase function proposed in the present invention, the sidelobe level of the pulse compression result of the NLFM signal can be significantly reduced finally. The first sidelobe is only -79 dB, and at the same time, the main lobe broadening and SNR loss generated are both within an acceptable range.

[0088] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present invention.

Claims

1. A method for improving the pulse compression performance of NLFM signals based on the first derivative of the phase function, characterized in that The steps are as follows: Step 1: Calculate the first derivative φ′(t) of the phase function; Among them, T is the time width, B is the bandwidth, and f s is the sampling rate. Both α and γ are control parameters to be designed. α controls the balance between tangent frequency modulation and linear frequency modulation, and γ controls the ratio of the tangent function to the linear function; Step 2: Solve the frequency function f(t) according to the first derivative φ′(t) of the phase function obtained in Step 1: Step 3: Accumulate and sum the frequency function f(t) obtained in Step 2 to get the phase function φ(t): Step 4: Solve the second derivative φ″(t) of the phase function and calculate the amplitude function a(t) of the NLFM signal: where S(φ′(t)) is the power spectral density function; Step 5: Combine the phase function φ(t) and the amplitude function a(t) obtained in Step 3 and Step 4 respectively to calculate the time-domain expression of the NLFM signal; s(t) = a(t)exp[jφ(t)] Step 6: Perform matched pulse compression processing on the NLFM signal waveform, observe whether the first sidelobe level of the pulse compression result meets the requirements. If it does not meet the requirements, the values of the control parameters α and γ can be adjusted within the allowable range of main lobe broadening and SNR loss, and the above steps are repeated until the first sidelobe level meets the system requirements.

2. A computer system, characterized in that Including: One or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to claim 1.

3. A computer-readable storage medium, characterized in that Stored with computer-executable instructions, the instructions are used to implement the method according to claim 1 when executed.

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