Multi-factor adjustment phase function high main lobe and side lobe ratio nonlinear frequency modulation signal design method

Abstract

The invention belongs to the technical field of waveform design, and particularly relates to a multi-factor adjustment phase function high main lobe and side lobe ratio nonlinear frequency modulation signal design method. The method comprises the following steps: determining a signal parameter; introducing a sequence factor design sequence function according to the signal parameters; introducing a slope factor and an amplitude factor to design a phase function according to the sequence function, and adjusting the sequence factor, the slope factor and the amplitude factor of the phase function according to the criteria of adherence to constant modulus constraint, improvement of main and side lobe ratio after pulse compression and no undersampling to obtain a final phase function; and according to the final phase function, generating a nonlinear frequency modulation signal with a high main-side lobe ratio.

Description

Technical Field

[0001] The invention belongs to the field of waveform design (WD) technology, and in particular relates to a design method for a nonlinear frequency modulation signal with a high main-to-sidelobe ratio based on a multi-factor adjustment phase function. Background Art

[0002] Waveform is an important resource of radar system, and waveform design is a major driving force for radar to make active changes. Existing research has verified the advantages of waveform design in improving anti-interference ability and reducing sidelobe effects.

[0003] The main-to-sidelobe ratio is an important indicator of the signal, which determines the signal's ability to detect weak targets in a strong target environment. The key issue in radar waveform design is how to design a higher main-to-sidelobe ratio. Generally speaking, there are two approaches. One approach is to focus on the signal waveform and design a signal with a high main-to-sidelobe ratio; the other approach is to perform sidelobe suppression after matched filtering at the receiving end. Common sidelobe suppression methods include mismatch filtering, spectrum correction, and windowing at the receiving end. However, this processing method generally causes a loss in the signal-to-noise ratio (SNR); therefore, it is more appropriate to design a signal with a high main-to-sidelobe ratio.

[0004] In the middle of the last century, the definition of Linear Frequency Modulation (LFM) was proposed. Because of its simple signal form, easy generation and control, and convenient pulse compression, it is widely used in various radar systems. However, the main-sidelobe ratio of LFM signals can only reach about 13.2dB, which seriously limits the radar's multi-target detection performance. In 1959, Key, Fowle, and others proposed the concept of Non-Linear Frequency Modulation (NLFM). Non-Linear Frequency Modulation signals are insensitive to Doppler frequency, and the main-sidelobe ratio is much higher than that of LFM signals. Its changing modulation frequency makes the spectrum present the shape of a window function, so there is no need to perform frequency domain windowing. The pulse compression performance is equivalent to matching filtering and then frequency domain windowing of LFM signals. Non-Linear Frequency Modulation signals are also widely used because of their main-sidelobe ratio higher than that of LFM signals.

[0005] However, when traditional nonlinear frequency modulation signals are used in high-speed motion platforms, their main-to-sidelobe ratio still cannot meet the requirements. In order to improve the main-to-sidelobe ratio, researchers at home and abroad have been looking for ways to design and optimize NLFM waveforms. In 2015, Liu Ping and others further improved the design method of NLFM and proposed a NLFM signal design method based on window function weighting to improve the main-to-sidelobe ratio of nonlinear frequency modulation signals. Although the engineering implementation is difficult, thanks to the good sidelobe suppression capability, domestic and foreign researchers have invested more and more in NLFM signal design. In 2020, Zhang Yongwei of the Chinese Academy of Sciences used a weighted improved Chebyshev window to generate a low-sidelobe NLFM signal, and the main-to-sidelobe ratio can reach -41.05dB. This type of method is to optimize the window function, and then use the window function to calculate the phase function to generate the NLFM signal. The main-to-sidelobe ratio of the designed signal pulse after compression is still not high, and the design process is complicated, there are a lot of calculation errors, and the phase function does not have a display expression, which is difficult to meet engineering needs. Summary of the invention

[0006] In order to overcome the problems in the prior art, the present invention proposes a design method for a nonlinear frequency modulation signal with a high main-to-sidelobe ratio by adjusting a phase function with multiple factors.

[0007] The technical solution of the present invention to solve the above technical problems is as follows:

[0008] The present invention provides a method for designing a nonlinear frequency modulation signal with a high main-to-sidelobe ratio of a multi-factor phase adjustment function, comprising the following steps:

[0009] Step 1: Determine signal parameters;

[0010] Step 2: Introduce sequence factors according to signal parameters to design sequence functions;

[0011] Step 3: According to the sequence function, the slope factor and amplitude factor are introduced to design the phase function, and the sequence factor, slope factor and amplitude factor of the phase function are adjusted to obtain the final phase function based on the criteria of complying with the constant modulus constraint, improving the main-side lobe ratio after pulse compression and preventing undersampling;

[0012] Step 4: Generate a high main-to-sidelobe ratio nonlinear frequency modulation signal according to the final phase function.

[0013] Furthermore, in step 1, the signal parameters include the sampling rate f s , pulse width T, bandwidth B, number of signal points N and required main lobe to side lobe ratio, where N = f s *T.

[0014] Furthermore, in step 2, the sequence function is designed by introducing sequence factors according to the signal parameters, including:

[0015] Get sequence Generate initial sequence function based on sequence Where a is the sequence factor;

[0016] The normalized sequence function is:

[0017]

[0018] In the above formula, g is the normalized sequence function.

[0019] Furthermore, the step 3 includes:

[0020] According to the sequence function g, the initial phase function is generated by adjusting the slope by introducing the slope factor for:

[0021]

[0022] Normalize the initial phase function and introduce an amplitude factor to adjust the amplitude to obtain the phase function for:

[0023]

[0024] Among them, a is the sequence factor, b is the slope factor, and c is the amplitude factor;

[0025] By adjusting the values ​​of sequence factor a, slope factor b and amplitude factor c and plotting the phase function after multi-factor adjustment The real and imaginary parts of the generated nonlinear frequency modulation signal and the main lobe to side lobe ratio after pulse compression are used to determine the phase function. The final phase function is determined by determining whether the main-to-sidelobe ratio of the generated nonlinear frequency modulation signal is improved, whether the constant modulus constraint is complied with, and whether undersampling occurs.

[0026] Furthermore, in step 3, the final phase function is determined Whether the main-lobe to side-lobe ratio of the generated nonlinear frequency modulation signal is improved, whether the constant modulus constraint is followed, and whether undersampling occurs, specifically including:

[0027] Due to the combined adjustment of the three factors of sequence factor a, slope factor b and amplitude factor c, the main-side lobe ratio diagram after pulse compression is used to determine whether the main-side lobe ratio is improved and whether the main-side lobe ratio meets the use requirements;

[0028] If the main-to-sidelobe ratio does not rise to the usage requirement or even decreases, increase the slope factor b and adjust the sequence factor a and amplitude factor c;

[0029] Phase function after multi-factor adjustment The real and imaginary parts of the generated nonlinear frequency modulation signal can be used to determine whether undersampling occurs. That is, if there is obvious distortion on both sides of the image of the real and imaginary parts of the signal, it means that the amplitude of the phase function is too large and undersampling occurs. Otherwise, undersampling does not occur. At this time, the sequence factor a and the amplitude factor c should be appropriately reduced and the slope factor b should be adjusted.

[0030] Since no window function is used for filtering during pulse compression, it means that the constant modulus constraint is complied with.

[0031] Furthermore, in step 4, in the high main-to-sidelobe ratio nonlinear frequency modulation signal generated by the final phase function, the time series factor a=1.9952, the slope factor b=0.6017, and the amplitude factor c=155.47.

[0032] Furthermore, in step 4, the nonlinear frequency modulation signal generated by the final phase function is:

[0033]

[0034] Where n is the signal amplitude, which is 1.

[0035] Compared with the prior art, the present invention has the following technical effects:

[0036] The present invention proposes a design method for a nonlinear frequency modulation signal with a high main-sidelobe ratio based on a multi-factor adjustment phase function: determining signal parameters; introducing sequence factors according to the signal parameters to design a sequence function; introducing slope factors and amplitude factors according to the sequence function to design a phase function, and adjusting the sequence factor, slope factor and amplitude factor of the phase function to obtain a final phase function based on the criteria of complying with constant modulus constraints, improving the main-sidelobe ratio after pulse compression and not undersampling; generating a nonlinear frequency modulation signal with a high main-sidelobe ratio according to the final phase function. In addition, the present invention breaks away from the limitations of traditional nonlinear frequency modulation signal generation methods, and proposes a nonlinear frequency modulation signal generation method with a lower main-sidelobe ratio and an explicit expression for the phase function. The main-sidelobe ratio after pulse compression in the embodiment of the present invention can reach above -60dB. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 It is a schematic diagram of the overall structure of the system of the present invention;

[0039] Figure 2 It is a normalized sequence function diagram of the present invention;

[0040] Figure 3 is the real and imaginary part of the NLFM baseband signal;

[0041] Figure 4 This is the main lobe to side lobe ratio diagram after NLFM baseband signal pulse compression;

[0042] Figure 5 The sequence function diagram after adjusting multiple factors of the present invention;

[0043] Figure 6 A graph of the real and imaginary parts of the signal generated by the final phase function of the present invention;

[0044] Figure 7 This is a pulse output signal diagram of the present invention. DETAILED DESCRIPTION

[0045] In order to further explain the technical means and effects taken by the present invention to achieve the predetermined invention purpose, the specific implementation methods, structures, features and effects of the technical solutions proposed by the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments. The specific features, structures or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in the present invention have the same meaning as those commonly understood by technicians in the technical field of the present invention.

[0046] In order to solve the above problems and improve the main-to-sidelobe ratio of the NLFM signal after pulse compression, this embodiment proposes to improve the main-to-sidelobe ratio of the NLFM signal after pulse compression by adjusting the phase function by multiple factors, and compares this embodiment with the traditional nonlinear frequency modulation signal generated based on the stationary phase principle.

[0047] In one embodiment of the present invention, referring to Figure 1-Figure 7 , provides a design method for a nonlinear frequency modulation signal with a high main-to-sidelobe ratio based on a multi-factor adjustment phase function, comprising the following steps: Step 1: determining signal parameters, the signal parameters including sampling rate, pulse width, bandwidth and number of signal points; Step 2: designing a sequence function by introducing sequence factors according to the signal parameters; Step 3: designing a phase function by introducing slope factors and amplitude factors according to the sequence function, and adjusting the sequence factor, slope factor and amplitude factor of the phase function to obtain a final phase function based on the criteria of complying with constant modulus constraints, improving the main-to-sidelobe ratio after pulse compression and not undersampling; Step 4: generating a nonlinear frequency modulation signal with a high main-to-sidelobe ratio according to the final phase function.

[0048] The following is a detailed explanation of each of the above steps:

[0049] Step 1: Determine signal parameters, including sampling rate, pulse width, bandwidth and signal points;

[0050] In this embodiment, in step 1, signal parameters such as sampling rate, pulse width, bandwidth and number of signal points are determined according to the use requirements; NLFM signals can be applied to a variety of scenarios, and different signal performances are required for different use requirements, which in turn affects the signal parameters used when designing the signal. Determining signal parameters according to use requirements is a prerequisite for designing the required signal.

[0051] Based on this, the signal parameter sampling rate f is determined according to the usage requirements. s , pulse width T, bandwidth B, number of signal points N and required main lobe to side lobe ratio, where N = f s *T.

[0052] In a specific embodiment, it is assumed that the signal parameters are as shown in Table 1:

[0053] Table 1 Signal parameter names and values

[0054] Signal parameters Numeric Pulse Width T 100μs Bandwidth B 20MHz <![CDATA[Sampling rate f s > 100MHz Number of signal points N 10000 Required main-sidelobe ratio -60dB

[0055] Step 2: Introduce sequence factors according to signal parameters to design sequence functions;

[0056] Get sequence Generate initial sequence function based on sequence Where a is the sequence factor.

[0057] The normalized sequence function g is:

[0058]

[0059] In a specific embodiment, the sequence m = [-5000, -4999, ... 4998, 4999], assuming that the sequence factor a = 1 at this time, the image of the sequence function g is plotted, as shown in FIG. Figure 2 shown.

[0060] Step 3: According to the sequence function, the slope factor and amplitude factor are introduced to design the phase function, and the sequence factor, slope factor and amplitude factor of the phase function are adjusted to obtain the final phase function based on the criteria of complying with the constant modulus constraint, improving the main-to-sidelobe ratio after pulse compression and avoiding undersampling.

[0061] According to the sequence function g, the initial phase function is generated by adjusting the slope by introducing the slope factor for:

[0062]

[0063] Normalize the initial phase function and introduce an amplitude factor to adjust the amplitude to obtain the phase function for:

[0064]

[0065] Among them, a is the sequence factor, b is the slope factor, and c is the amplitude factor.

[0066] By adjusting the values ​​of sequence factor a, slope factor b and amplitude factor c and plotting the phase function after multi-factor adjustment The real and imaginary parts of the generated NLFM signal and the main lobe to side lobe ratio after pulse compression are used to determine the phase function. The final phase function is determined by determining whether the main-to-sidelobe ratio of the generated NLFM signal is improved, whether the constant modulus constraint is complied with, and whether undersampling occurs.

[0067] In a specific embodiment, this step may include the following sub-steps:

[0068] Step 31: Assuming that the slope factor b = 1 and the amplitude factor c = 1, plot the phase function at this time The real and imaginary parts of the generated NLFM signal and the main lobe to side lobe ratio after pulse compression are shown in Figure 2. Figure 3 and Figure 4 shown.

[0069] Step 32: Adjust the values ​​of sequence factor a, slope factor b, and amplitude factor c, and plot the phase function The real and imaginary parts of the generated nonlinear frequency modulation signal and the main lobe to side lobe ratio after pulse compression verify the final phase function Whether the generated nonlinear frequency modulation signal complies with the constant modulus constraint and whether the main-side lobe ratio is improved, otherwise further adjust the values ​​of the sequence factor a, slope factor b and amplitude factor c until the constant modulus constraint is complied with, undersampling does not occur and the main-side lobe ratio reaches -60dB, thereby determining the final phase function. The specific process is as follows:

[0070] Step 321: Comparative analysis of the phase function before and after multi-factor adjustment The main-sidelobe ratio diagram of the generated nonlinear FM signal after pulse compression can be used to determine whether the main-sidelobe ratio is improved and whether the main-sidelobe ratio meets the usage requirements. If the main-sidelobe ratio is not increased to -60dB or even decreases, the slope factor b should be appropriately increased and the sequence factor a and amplitude factor c should be adjusted in combination.

[0071] Step 322: Analyze the phase function after multi-factor adjustment The real and imaginary parts of the generated nonlinear frequency modulation signal can be used to determine whether undersampling occurs. That is, if the real and imaginary parts of the signal are obviously distorted on both sides, it means that the phase function amplitude is too large and undersampling occurs. Otherwise, undersampling does not occur. If the real and imaginary parts of the signal are too sparse, the sequence factor a and the amplitude factor c should be appropriately increased and the slope factor b should be adjusted. If undersampling occurs, the sequence factor a and the amplitude factor c should be appropriately reduced and the slope factor b should be adjusted.

[0072] Step 323: Since the window function is not used for filtering during pulse compression, it means that the constant modulus constraint is complied with at this time.

[0073] Step 324: By continuously adjusting the sequence factor a, slope factor b and amplitude factor c until the constant modulus constraint is satisfied, undersampling does not occur and the main-sidelobe ratio reaches -60 dB, the sequence factor a = 1.9952, the slope factor b = 0.6017, and the amplitude factor c = 155.47. The corresponding sequence function is as follows: Figure 5 As shown, the final phase function is:

[0074]

[0075] Step 4: Generate a high main-to-sidelobe ratio nonlinear frequency modulation signal according to the final phase function.

[0076] The final phase function generates the NLFM signal:

[0077]

[0078] Where n is the signal amplitude, which is usually 1.

[0079] Based on the designed NLFM signal, the real and imaginary parts of the designed NLFM signal and the main lobe to side lobe ratio after pulse compression are plotted, as shown in Figure 6 and Figure 7 shown.

[0080] In order to illustrate the effect of the method proposed in the present invention in improving the main-to-side lobe ratio, the present invention makes a horizontal comparison between the main-to-side lobe ratio and the existing research results. The comparison results are as follows:

[0081] The main-sidelobe ratio of the nonlinear frequency modulation signal after pulse compression is selected as a comparison factor, and the method proposed in the present invention is compared with the common methods: literature [1] (Y. Zhang, W. Wang, R. Wang, Y. Deng, G. Jin and Y. Long "A Novel NLFM Waveform With Low Sidelobes Based on Modified Chebyshev Window" in IEEE Geoscience and Remote Sensing Letters, vol. 17, no. 5, pp. 814-818, May 2020, doi: 10.1109 / LGRS.2019.2930817), literature [2] (Q. Xie, H. Zeng, Z. Mo and W. Li, "A Two-Step Optimization Framework for Low Sidelobe NLFM Waveform Using Fourier Series" in IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1-5, 2022, Art. no.4020905,doi:10.1109 / LGRS.2022.3141081.) and literature [3] (Qin Chunmiao, Meng Fanli, Zhai Hengfeng, et al. NLFM waveform design based on GASA algorithm and frequency modulation function [J]. Radar Science and Technology, 2019, 17(06):679-683+688.) are compared, and the main lobe to side lobe ratio is used as the evaluation index. In order to ensure the fairness of the comparison, the same bandwidth, pulse width, sampling rate and other parameters are used for the comparison, and the results are shown in Table 3.

[0082] Table 3 Comparison of the method of the present invention with other literature methods

[0083]

[0084] It can be seen that the method proposed in the present invention is superior to the existing high main-to-sidelobe ratio waveform design method.

[0085] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A method for designing a nonlinear frequency modulation signal with a high main-sidelobe ratio and a multi-factor phase adjustment function, characterized in that: The following steps are involved: Step 1: Determine signal parameters; Step 2: Introduce sequence factors according to signal parameters to design sequence functions; Step 3: According to the sequence function, the slope factor and amplitude factor are introduced to design the phase function, and the sequence factor, slope factor and amplitude factor of the phase function are adjusted to obtain the final phase function based on the criteria of complying with the constant modulus constraint, improving the main-side lobe ratio after pulse compression and preventing undersampling; Step 4: Generate a high main-to-sidelobe ratio nonlinear frequency modulation signal according to the final phase function.

2. The method for designing a nonlinear frequency modulation signal with a high main-sidelobe ratio and a multi-factor phase adjustment function according to claim 1, characterized in that: In step 1, the signal parameters include the sampling rate f s , pulse width T, bandwidth B, number of signal points N and required main lobe to side lobe ratio, where N = f s *T.

3. The method for designing a nonlinear frequency modulation signal with a high main-to-sidelobe ratio based on a multi-factor phase adjustment function according to claim 2, characterized in that: In the step 2, the sequence function is designed by introducing the sequence factor according to the signal parameter, including: Get sequence Generate initial sequence function based on sequence Where a is the sequence factor; The normalized sequence function is: In the above formula, g is the normalized sequence function.

4. The method for designing a nonlinear frequency modulation signal with a high main-sidelobe ratio and a multi-factor phase adjustment function according to claim 3, characterized in that: The step 3 includes: According to the sequence function g, the initial phase function is generated by adjusting the slope by introducing the slope factor for: Normalize the initial phase function and introduce an amplitude factor to adjust the amplitude to obtain the phase function for: Among them, a is the sequence factor, b is the slope factor, and c is the amplitude factor; By adjusting the values ​​of sequence factor a, slope factor b and amplitude factor c and plotting the phase function after multi-factor adjustment The real and imaginary parts of the generated nonlinear frequency modulation signal and the main lobe to side lobe ratio after pulse compression are used to determine the phase function. The final phase function is determined by determining whether the main-to-sidelobe ratio of the generated nonlinear frequency modulation signal is improved, whether the constant modulus constraint is complied with, and whether undersampling occurs.

5. The method for designing a nonlinear frequency modulation signal with a high main-sidelobe ratio and a multi-factor phase adjustment function according to claim 4, characterized in that: In step 3, the final phase function is determined Whether the main-lobe to side-lobe ratio of the generated nonlinear frequency modulation signal is improved, whether the constant modulus constraint is followed, and whether undersampling occurs, specifically including: Due to the combined adjustment of the three factors of sequence factor a, slope factor b and amplitude factor c, the main-side lobe ratio diagram after pulse compression is used to determine whether the main-side lobe ratio is improved and whether the main-side lobe ratio meets the use requirements; If the main-to-sidelobe ratio does not rise to the usage requirement or even decreases, increase the slope factor b and adjust the sequence factor a and amplitude factor c; Phase function after multi-factor adjustment The real and imaginary parts of the generated nonlinear frequency modulation signal can be used to determine whether undersampling occurs. That is, if there is obvious distortion on both sides of the image of the real and imaginary parts of the signal, it means that the amplitude of the phase function is too large and undersampling occurs. Otherwise, undersampling does not occur. At this time, the sequence factor a and the amplitude factor c should be appropriately reduced and the slope factor b should be adjusted. Since no window function is used for filtering during pulse compression, it means that the constant modulus constraint is complied with.

6. The method for designing a nonlinear frequency modulation signal with a high main-sidelobe ratio and a multi-factor phase adjustment function according to claim 4, characterized in that: In step 4, in the final phase function generating a nonlinear frequency modulation signal with a high main-to-sidelobe ratio, the time series factor a=1.9952, the slope factor b=0.6017, and the amplitude factor c=155.

47.

7. The method for designing a nonlinear frequency modulation signal with a high main-sidelobe ratio and a multi-factor phase adjustment function according to claim 4, characterized in that: In step 4, the nonlinear frequency modulation signal generated by the final phase function is: Where n is the signal amplitude, which is 1.

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