A real-time generation method of piecewise linear frequency modulation signal

Abstract

The present invention discloses a real-time generation method of a piecewise linear frequency modulation signal, the method comprising: determining the parameters of the piecewise linear frequency modulation signal according to system parameters, including signal bandwidth, signal pulse width, number of segments and peak sidelobe ratio PSLR; determining the power spectrum function of the piecewise linear frequency modulation signal according to the peak sidelobe ratio; integrating the power spectrum function to obtain a group delay function; then calculating the piecewise instantaneous frequency function of the piecewise linear frequency modulation signal according to the group delay function; integrating the piecewise instantaneous frequency function to obtain a phase function, and determining the time domain expression of the piecewise linear frequency modulation signal according to the phase function; generating a digital signal according to the time domain expression, and performing digital-to-analog conversion on the digital signal to obtain the piecewise linear frequency modulation signal. The method of the present invention can realize the real-time generation of the piecewise linear frequency modulation signal.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a real-time generation method of a piecewise linear frequency modulation (PLFM) signal. Background Art

[0002] Synthetic Aperture Radar (SAR) is one of the important technical means in the field of remote sensing. It is widely used in defense, environmental monitoring, natural resource survey and disaster monitoring with its advantages of all-day and all-weather. At present, LFM signal is the most commonly used transmitting waveform in SAR system, but the peak side lobe ratio (PSLR) of the autocorrelation function of LFM signal is very high, which is -13 decibels (dB), which will reduce the imaging performance of SAR system. In order to suppress the sidelobe height, weighted window function, filtering or optimization are usually used, but these methods will reduce the output signal to noise ratio (SNR). The autocorrelation function of nonlinear frequency modulation signal (NLFM) has a very low peak side lobe ratio (PSLR) and will not reduce the output SNR, but the current technical means can only obtain the discrete value of NLFM signal, which is difficult to promote in engineering.

[0003] Compared with NLFM signals, PLFM signals can also obtain very low PSLR by adjusting the linear frequency modulation component, and this process does not lose the output SNR. Through relevant experiments, PLFM signals can avoid 1-2dB loss of SNR, which is equivalent to saving 25% of antenna transmission power. For radar systems with limited energy, using PLFM signals as transmission waveforms can improve system performance.

[0004] The commonly used technical means at present is to obtain the discrete value of the signal through ground processing calculation, and then save the discrete value of the signal to the read-only memory (ROM) of the field-programmable gate array (FPGA). When in use, the discrete data saved in the ROM is read, digital-to-analog conversion is performed, and the PLFM signal is generated. However, this method requires the signal to be collected and saved before it can be called and converted to generate the PLFM signal. Due to the limited storage space of the ROM, this storage mode causes the PLFM signal to be only used for scientific experiments and cannot be promoted in engineering.

[0005] The peak sidelobe ratio of the autocorrelation function of the PLFM signal can be changed by adjusting the linear frequency modulation component, but it is difficult to quickly obtain a PLFM signal with low PSLR. Therefore, how to shorten the time of generating PLFM signals and realize real-time generation of PLFM signals is an urgent problem to be solved. Summary of the invention

[0006] In order to solve the above technical problem, the present invention provides a method for generating a segmented linear frequency modulation signal in real time.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A method for real-time generation of a piecewise linear frequency modulation signal comprises the following steps:

[0009] Step 101, determining the segmented linear frequency modulation signal parameters according to the system parameters, including signal bandwidth, signal pulse width, number of segments and peak sidelobe ratio PSLR;

[0010] Step 102, determining the power spectrum function of the piecewise linear frequency modulation signal according to the peak sidelobe ratio;

[0011] Step 103, integrating the power spectrum function to obtain a group delay function;

[0012] Step 104, calculating the piecewise instantaneous frequency function of the piecewise linear frequency modulation signal according to the signal parameters and the group delay function;

[0013] Step 105, integrating the segmented instantaneous frequency function to obtain a phase function, and determining a time domain expression of the segmented linear frequency modulation signal according to the phase function;

[0014] Step 106: Generate a digital signal according to the time domain expression, and perform digital-to-analog conversion on the digital signal to obtain a piecewise linear frequency modulation signal.

[0015] Furthermore, the step 102 includes:

[0016] Taking the peak sidelobe ratio PSLR as an index, searching for a window function with the same peak sidelobe ratio PSLR, and then taking the window function as an approximate power spectrum function of the piecewise linear frequency modulation signal;

[0017] The window function is a Hamming window, a raised cosine window, or a Taylor window.

[0018] Furthermore, when the window function is a Taylor window, the Taylor window is used as an approximate power spectrum function of the piecewise linear frequency modulation signal, which is expressed as:

[0019]

[0020] Where, f is the frequency axis, represents the Taylor coefficient, B and T represent the bandwidth and pulse width of the piecewise linear signal, η and They represent the sidelobe level and the number of equal-height sidelobes respectively, which are used to control the peak sidelobe ratio PSLR, and m is the calculation process quantity.

[0021] Furthermore, the step 103 includes:

[0022] By integrating the approximate power spectrum function corresponding to the window function, we can obtain the group delay function G(f) of the piecewise linear signal, which is expressed as:

[0023]

[0024] Where C is a constant, expressed as:

[0025]

[0026] Furthermore, when the window function is a Taylor window, its corresponding group delay function is expressed as:

[0027]

[0028] Furthermore, the step 104 includes:

[0029] The bandwidth B of the signal is evenly divided into N segments, where the starting point of the nth (n = 1, 2, ..., N) segment is B n , the end point is B n+1 , each segment length is B / N, and:

[0030]

[0031] This gives the bandwidth vector for:

[0032]

[0033] Then, the frequency segment vector is calculated according to the delay function in equation (2): The corresponding pulse width vector

[0034]

[0035] in:

[0036] T n =G(B n ) (8)

[0037] According to the pulse width vector and bandwidth vector Computes the piecewise linear frequency function of a piecewise linear frequency modulated signal, including:

[0038] First, calculate the modulation frequency K of each linear frequency function n for:

[0039]

[0040] Where n = 1, 2, ..., N;

[0041] Then the piecewise linear frequency function f(t) is obtained as:

[0042]

[0043] Among them, t is the time axis, Ω n =[T n ,T n+1 ),n=1,2,…,N.

[0044] Furthermore, the step 105 includes:

[0045] The phase function of the piecewise linear frequency modulation signal can be solved by the following formula:

[0046]

[0047] According to equations (10) and (11), the phase function is expressed as:

[0048]

[0049] in:

[0050] C1=0,C n+1 =C n +π(B n+1 +B n )(T n+1 -T n ),n=1,2,…,N-1 (13)

[0051] Finally, the time domain expression of the piecewise linear FM signal is:

[0052]

[0053] Where j is the imaginary unit and rect(x) represents the rectangular function, defined as:

[0054]

[0055] Further, the step 106 includes:

[0056] Determine signal parameters of the signal according to the system parameters, wherein the signal parameters include signal bandwidth, signal pulse width, number of segments N, peak sidelobe ratio PSLR, and system sampling rate F;

[0057] Divide the signal bandwidth evenly into N segments and obtain the bandwidth vector

[0058] Determine the power spectral density function according to the peak sidelobe ratio PSLR;

[0059] Determine the group delay function based on the power spectral density function;

[0060] Calculate the pulse width vector based on the group delay function

[0061] The time axis vector is calculated based on the signal pulse width and the system sampling rate:

[0062]

[0063] in, Indicates rounding down, t i =-T / 2+(i-1)T / I,i=1,2…,I;

[0064] The segmented instantaneous frequency vector is calculated according to the segmented instantaneous frequency function, which is:

[0065]

[0066] in:

[0067]

[0068] Integrate the segment instantaneous frequency vector to obtain the phase vector;

[0069] Determine the signal time domain discrete vector according to the phase vector;

[0070] Finally, the signal time domain discrete vector is converted into digital-to-analog format to obtain a piecewise linear frequency modulation signal.

[0071] Beneficial effects:

[0072] Traditional methods require interpolation when generating signals, which increases the computational complexity. The method of the present invention can avoid the interpolation process and only involves the calculation of basic functions such as sine, cosine, and linear functions, thereby reducing the computational complexity and facilitating the real-time generation of signals. The present invention greatly reduces the complexity of signal design and is a segmented linear frequency modulation signal suitable for real-time generation by FPGA. Furthermore, compared with LFM signals, it can save transmission power and reduce SNR loss, thereby improving system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 A schematic flow chart of a method for real-time generation of a piecewise linear frequency modulation signal according to an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of the structure of a real-time device for generating a piecewise linear frequency modulation signal according to an embodiment of the present invention;

[0075] Figure 3 A schematic diagram of a device structure based on FPGA hardware implementation according to an embodiment of the present invention;

[0076] Figure 4 A schematic diagram of a timing structure for generating a PLFM signal based on a SAR system according to an embodiment of the present invention;

[0077] Figure 5 is a time domain signal real part image of the PLFM signal of an embodiment of the present invention;

[0078] Figure 6 This is a time domain signal image after pulse compression according to an embodiment of the present invention. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended 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.

[0080] The present invention provides a real-time generation method for a piecewise linear frequency modulation signal, which initializes signal parameters according to requirements; determines a group delay function according to a set power spectrum density function; determines a bandwidth vector according to the number of segments and the bandwidth; determines a pulse width vector according to the group delay function and the bandwidth vector; determines an instantaneous frequency function according to the bandwidth vector and the pulse width vector; calculates an instantaneous frequency vector according to the instantaneous frequency function; integrates the instantaneous frequency vector to obtain a signal phase; and determines a discrete value of a time domain signal according to the signal phase.

[0081] like Figure 1 , Figure 2 As shown, a real-time generation method of a segmented linear frequency modulation signal of the present invention specifically comprises the following steps:

[0082] Step 101: Determine signal parameters of the segmented linear frequency modulation signal according to system parameters, including signal bandwidth, signal pulse width, number of segments, and peak sidelobe ratio PSLR.

[0083] Step 102: determine the power spectrum function of the piecewise linear frequency modulation signal according to the peak sidelobe ratio. Specifically, use the peak sidelobe ratio PSLR as an index to find a window function with the same PSLR, and then use the window function as the approximate power spectrum function of the piecewise linear frequency modulation signal.

[0084] The window function may include: Hamming window, raised cosine window and Taylor window. Taking Taylor window as an example, the Taylor window is used as the approximate power spectrum function of the piecewise linear frequency modulation signal, which is expressed as:

[0085]

[0086] Where, f is the frequency axis, represents the Taylor coefficient, B and T represent the bandwidth and pulse width of the piecewise linear signal, η and They represent the sidelobe level and the number of equal-height sidelobes respectively, which are used to control the peak sidelobe ratio PSLR, and m is the calculation process quantity.

[0087] Step 103: Integrate the approximate power spectrum function corresponding to the window function to obtain the group delay function G(f) of the piecewise linear signal, which is expressed as:

[0088]

[0089] Where C is a constant, expressed as:

[0090]

[0091] Taking the Taylor window as an example, its corresponding group delay function can be expressed as:

[0092]

[0093] Step 104, calculating the piecewise instantaneous frequency function of the piecewise linear frequency modulation signal according to the signal parameters and the group delay function, including:

[0094] First, divide the bandwidth B of the signal evenly into N segments, where the starting point of the nth (n=1, 2, ..., N) segment is B n , the end point is B n+1 , each segment length is B / N, and:

[0095]

[0096] This gives the bandwidth vector for:

[0097]

[0098] Then, the frequency segment vector is calculated according to the delay function in equation (2): The corresponding pulse width vector

[0099]

[0100] in:

[0101] T n =G(B n ) (8)

[0102] Further, according to the pulse width vector and bandwidth vector Calculate the piecewise linear frequency function of the piecewise linear frequency modulation signal. Specifically, first calculate the modulation frequency K of each linear frequency function n for:

[0103]

[0104] Then the piecewise linear frequency function f(t) can be obtained as:

[0105]

[0106] Among them, t is the time axis.

[0107] Step 105, integrating the segmented instantaneous frequency function to obtain a phase function, and determining a time domain expression of the segmented linear frequency modulation signal according to the phase function, including:

[0108] The phase function of the piecewise linear frequency modulation signal can be solved by the following formula:

[0109]

[0110] Further, according to equations (10) and (11), the phase function is expressed as:

[0111]

[0112] in:

[0113]

[0114] Finally, the time domain expression of the piecewise linear FM signal is:

[0115]

[0116] Where j is the imaginary unit and rect(x) represents the rectangular function, defined as:

[0117]

[0118] Step 106, generating a digital signal according to the time domain expression, and performing digital-to-analog conversion on the digital signal to obtain a piecewise linear frequency modulation signal, including:

[0119] Determine the signal parameters of the signal according to the system parameters: including signal bandwidth, signal pulse width, number of segments N, peak sidelobe ratio PSLR, sampling rate F; divide the signal bandwidth evenly into N segments to obtain the bandwidth vector

[0120] Determine the power spectral density function according to the peak sidelobe ratio PSLR;

[0121] Determine the group delay function based on the power spectral density function;

[0122] Calculate the pulse width vector based on the group delay function

[0123] The time axis vector is calculated based on the signal pulse width and the system sampling rate:

[0124]

[0125] in, Indicates rounding down, t i =-T / 2+(i-1)T / I,i=1,2…,I;

[0126] The segmented instantaneous frequency vector is calculated according to the segmented instantaneous frequency function, which is:

[0127]

[0128] in:

[0129]

[0130] Integrate the segment instantaneous frequency vector to obtain the phase vector;

[0131] Determine the signal time domain discrete vector according to the phase vector;

[0132] Finally, the signal time domain discrete vector is converted into digital-to-analog format to obtain a piecewise linear frequency modulation signal.

[0133] The present invention will be described in further detail below in conjunction with the embodiments.

[0134] like Figure 3 As shown, according to the input instruction, the signal bandwidth, pulse width and other parameters are initialized. Then, the group delay function is used to calculate each linear function. Further, the linear function is synthesized into an instantaneous frequency function. Then, the phase value of the signal is obtained by integration, and the discrete value of the signal in the time domain is determined. Finally, the digital-to-analog conversion is performed to obtain the signal output.

[0135] The embodiment of the present invention provides a timing structure for generating a PLFM signal based on a SAR system, such as Figure 4 As shown, including:

[0136] After receiving the input command transmitted by the upper computer at a certain moment, the signal parameters are initialized before the next pulse repetition time PRI starts; in order not to flush out the radar waveform data transmitted by the next PRI stored in the RAM of the FPGA, the calculation process starts with the end of the next PRI signal transmission window; the signal is calculated, and after the corresponding PLFM signal is calculated, the analog PLFM signal output corresponding to the signal transmission window of the next PRI is waited for.

[0137] The initialization parameters are: signal bandwidth 300Mhz, signal pulse width 20us, and number of segments 100. The -40dB Taylor window function is selected as the initial power spectrum density function, and the sampling rate of the system is 360MHz. The real part of the time domain signal of the generated PLFM signal is as follows: Figure 5 As shown, the pulse compression results are as follows Figure 6 The performance index results of PLFM signal and LFM signal are shown in the following table:

[0138]

[0139] It can be seen from the above description that the method provided by the present invention can greatly reduce the complexity of signal design and is a PLFM signal suitable for real-time generation by FPGA. Furthermore, compared with the LFM signal, it can save transmission power and reduce the signal-to-noise ratio loss, thereby improving system performance.

[0140] The above description is only an embodiment of the present invention and is not intended to limit the protection scope of the present invention. It is easy for those skilled in the art to understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for real-time generation of a piecewise linear frequency modulation signal, characterized in that: The steps include: Step 101, determining signal parameters of the segmented linear frequency modulation signal according to system parameters, including signal bandwidth, signal pulse width, number of segments and peak sidelobe ratio PSLR; Step 102, determining the power spectrum function of the piecewise linear frequency modulation signal according to the peak sidelobe ratio; Step 103, integrating the power spectrum function to obtain a group delay function, including: Integrate the approximate power spectrum function corresponding to the window function to obtain the group delay function of the piecewise linear frequency modulation signal , expressed as: (2) in, is a constant, expressed as: (3) Step 104, calculating the piecewise instantaneous frequency function of the piecewise linear frequency modulation signal according to the signal parameters and the group delay function, including: The bandwidth of the signal Divided evenly The starting point of the nth segment is , the end point is , n=1,2,…,N, the length of each segment is ,and: (5) This gives the bandwidth vector for: (6) Then, the frequency segment vector is calculated according to the delay function in equation (2): The corresponding pulse width vector : (7) in: (8) According to the pulse width vector and bandwidth vector Computes the piecewise linear frequency function of a piecewise linear frequency modulated signal, including: First, calculate the modulation frequency of each linear frequency function for: (9) Where n=1,2,…,N; Then we get the piecewise linear frequency function for: (10) in, For the time axis, ; Step 105, integrating the segmented instantaneous frequency function to obtain a phase function, and determining a time domain expression of the segmented linear frequency modulation signal according to the phase function; Step 106: Generate a digital signal according to the time domain expression, and perform digital-to-analog conversion on the digital signal to obtain a piecewise linear frequency modulation signal.

2. The method for real-time generation of a piecewise linear frequency modulation signal according to claim 1, characterized in that: The step 102 includes: Taking the peak sidelobe ratio PSLR as an index, searching for a window function with the same peak sidelobe ratio PSLR, and then taking the window function as an approximate power spectrum function of the piecewise linear frequency modulation signal; The window function is a Hamming window, a raised cosine window, or a Taylor window.

3. The method for real-time generation of a piecewise linear frequency modulation signal according to claim 2, characterized in that: When the window function is a Taylor window, the Taylor window is used as the approximate power spectrum function of the piecewise linear frequency modulation signal, which is expressed as: (1) in, is the frequency axis, represents the Taylor coefficient, and represents the bandwidth and pulse width of the piecewise linear signal, and They represent the sidelobe level and the number of equal-height sidelobes, respectively, to control the peak sidelobe ratio PSLR. To calculate the process quantity.

4. The method for real-time generation of a piecewise linear frequency modulation signal according to claim 1, characterized in that: When the window function is a Taylor window, the corresponding group delay function is expressed as: (4)。 5. The method for real-time generation of a piecewise linear frequency modulation signal according to claim 1, characterized in that: The step 105 comprises: The phase function of the piecewise linear frequency modulation signal is solved by the following formula: (11) According to equations (10) and (11), the phase function is expressed as: (12) in: (13) Finally, the time domain expression of the piecewise linear FM signal is: (14) Where j is the imaginary unit, represents the rectangular function, defined as: 。 6. The method for real-time generation of a piecewise linear frequency modulation signal according to claim 5, characterized in that: The step 106 includes: The signal parameters of the signal are determined according to the system parameters, and the signal parameters include signal bandwidth, signal pulse width, number of segments , Peak Sidelobe Ratio PSLR, System Sampling Rate ; Divide the signal bandwidth evenly Segment, get the bandwidth vector ; Determine the power spectral density function according to the peak sidelobe ratio PSLR; Determine the group delay function based on the power spectral density function; Calculate the pulse width vector based on the group delay function ; The time axis vector is calculated based on the signal pulse width and the system sampling rate: (15) in, , Indicates rounding down. ; The segmented instantaneous frequency vector is calculated according to the segmented instantaneous frequency function, which is: (16) in: (17) Integrate the segment instantaneous frequency vector to obtain the phase vector; Determine the signal time domain discrete vector according to the phase vector; Finally, the signal time domain discrete vector is converted into digital-to-analog format to obtain a piecewise linear frequency modulation signal.

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