Sparse frequency waveform design method and device based on high bit rate and low distance resolution

Abstract

The application discloses a sparse frequency waveform design method and equipment based on high-bit rate and low distance resolution, and the method comprises the following steps: obtaining a phase encoding signal to be processed; calculating the spectrum of N p frequency components of the phase encoding signal to be processed, obtaining N p spectra; respectively performing pulse compression on the N p spectra, and respectively obtaining N p pulse compression values; performing pulse compression processing on a reference signal, and obtaining a pulse compression value of the reference signal; the encoding length of the reference signal is less than the encoding length of the phase encoding signal to be processed; determining an expected pulse compression main lobe value based on the encoding length relationship between the reference signal and the phase encoding signal to be processed and the pulse compression value of the reference signal; constructing an optimization objective function according to the N p pulse compression values, the expected pulse compression main lobe value, the N p spectra and a preset weight; and solving the optimization objective function to obtain a sparse frequency signal. The application can overcome the defects of easy generation of same-frequency narrowband interference and low degree of freedom of a full-band radar.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a sparse frequency waveform design method and apparatus based on high bit rate and low range resolution. Background Technology

[0002] In existing technologies, full-band radar achieves high-precision target detection and tracking by transmitting signals covering a wide frequency band. By transmitting wide-band pulse signals, a receiving array receives echo signals reflecting multiple frequencies from the target. The received signals undergo preprocessing, filtering, and digitization to extract the target's position information.

[0003] However, full-band radar is susceptible to interference from narrowband signals at the same frequency. When interference signals are mixed into the echo signals, they can seriously affect the radar's target detection and tracking performance. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention provides a sparse frequency waveform design method and apparatus based on high bit rate and low distance resolution.

[0005] The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a sparse frequency waveform design method based on high bit rate and low distance resolution, comprising:

[0007] Acquire the phase-encoded signal to be processed;

[0008] Calculate N of the phase-encoded signal to be processed p The spectrum of each frequency component is obtained to get N. p N spectrums; where N p It is 2 to the power of M, where M is a preset positive integer;

[0009] For the N p Each spectrum is pulse-compressed to obtain N. p Individual pulse pressure values;

[0010] The reference signal is subjected to pulse compression processing to obtain the pulse compression value of the reference signal; the encoding length of the reference signal is less than the encoding length of the phase-coded signal to be processed;

[0011] Based on the coding length relationship between the reference signal and the phase-coded signal to be processed, and the pulse compression value of the reference signal, the desired pulse compression main lobe value is determined;

[0012] According to the N p The pulse pressure value, the desired pulse compression main lobe value, and the N pGiven a spectrum and preset weights, construct an optimization objective function;

[0013] The sparse frequency signal is obtained by solving the optimization objective function.

[0014] The present invention also provides a sparse frequency waveform design device based on high bit rate and low distance resolution, comprising:

[0015] The acquisition module is used to acquire the phase-encoded signal to be processed;

[0016] The component calculation module is used to calculate the N of the phase-encoded signal to be processed. p The spectrum of each frequency component is obtained to get N. p N spectrums; where N p It is 2 raised to the power of M, where M is a positive integer;

[0017] Compression processing module, used for the N p Each spectrum is pulse-compressed to obtain N. p A pulse compression value is obtained by performing pulse compression processing on the reference signal; the encoding length of the reference signal is less than that of the phase-coded signal to be processed.

[0018] The desired pulse compression main lobe value determination module is used to determine the desired pulse compression main lobe value based on the coding length relationship between the reference signal and the phase-coded signal to be processed, and the pulse compression value of the reference signal.

[0019] The function constructor module is used to construct the function based on the N. p The pulse pressure value, the desired pulse compression main lobe value, and the N p Given a spectrum and preset weights, construct an optimization objective function;

[0020] The solution module is used to solve the optimization objective function to obtain the sparse frequency signal.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] This invention optimizes the waveform by pulse compression of each frequency component of the waveform, using pulse compression sidelobes and spectral sidelobes as objective functions, and solving the objective functions. The optimized sparse spectral waveform can form notches within the interference band to suppress interference, which not only reduces the impact of enemy interference, but also improves the radar's ability to detect low-detectability targets. It overcomes the shortcomings of existing full-band radars that are prone to narrowband interference at the same frequency. Furthermore, it can make the radar system occupy less spectral bandwidth when transmitting signals, thus improving spectral utilization efficiency.

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a sparse frequency waveform design method based on high bit rate and low distance resolution provided in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the spectrum of an exemplary sparse frequency signal provided in an embodiment of the present invention;

[0026] Figure 3(a) is the first schematic diagram of the expected and actual pulse compression waveforms of each frequency component provided in the embodiment of the present invention;

[0027] Figure 3(b) is the first schematic diagram of the sparse frequency waveform pulse compression provided in the embodiment of the present invention;

[0028] Figure 3(c) is a first schematic diagram of an exemplary sparse frequency waveform spectrum provided in an embodiment of the present invention;

[0029] Figure 3(d) is a first schematic diagram of an exemplary sparse frequency waveform spectrum (decibels) provided in an embodiment of the present invention;

[0030] Figure 4(a) is a second schematic diagram of the expected and actual pulse compression waveforms of each frequency component provided in the embodiment of the present invention;

[0031] Figure 4(b) is a second schematic diagram of the sparse frequency waveform pulse compression provided in an embodiment of the present invention;

[0032] Figure 4(c) is a second schematic diagram of an exemplary sparse frequency waveform spectrum provided in an embodiment of the present invention;

[0033] Figure 4(d) is a second schematic diagram of an exemplary sparse frequency waveform spectrum (decibels) provided in an embodiment of the present invention;

[0034] Figure 5(a) is a third schematic diagram of the expected and actual pulse compression waveforms of each frequency component provided in the embodiment of the present invention;

[0035] Figure 5(b) is a third schematic diagram of the sparse frequency waveform pulse compression provided in the embodiment of the present invention;

[0036] Figure 5(c) is a third schematic diagram of an exemplary sparse frequency waveform spectrum provided in an embodiment of the present invention;

[0037] Figure 5(d) is a third schematic diagram of an exemplary sparse frequency waveform spectrum (decibels) provided in an embodiment of the present invention. Detailed Implementation

[0038] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0039] Figure 1 This is a flowchart illustrating a sparse frequency waveform design method based on high bit rate and low distance resolution provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes:

[0040] S101. Obtain the phase-encoded signal to be processed.

[0041] S102. Calculate N of the phase-coded signal to be processed. p The spectrum of each frequency component is obtained to get N. p N spectrums; where N p It is 2 to the power of M, where M is a preset positive integer.

[0042] S103, N p Each spectrum is pulse-compressed to obtain N. p Individual pulse pressure values.

[0043] S104. Perform pulse compression processing on the reference signal to obtain the pulse compression value of the reference signal; the encoding length of the reference signal is less than the encoding length of the phase encoded signal to be processed.

[0044] S105. Based on the coding length relationship between the reference signal and the phase-coded signal to be processed, and the pulse compression value of the reference signal, determine the desired pulse compression main lobe value.

[0045] S106, According to N p Individual pulse pressure, expected pulse compression of the main lobe, N p Given a spectrum and preset weights, construct an optimization objective function.

[0046] S107. Solve the objective function to obtain the sparse frequency signal.

[0047] In this invention, S102 can be implemented through the following steps:

[0048] S1021. Divide the Fourier matrix F of the phase-encoded signal to be processed into N... p N block Fourier matrices; p Each block Fourier matrix represents the N of the Fourier matrix F. p There are frequency components in three different frequency ranges; where the frequency component in the first frequency range is the frequency component in the lowest frequency range, and the frequency component in the Nth frequency range is the frequency component in the lowest frequency range. p The frequency components within each frequency range are the frequency components of the highest frequency range.

[0049] For example, when the phase-encoded signal to be processed is At that time, the Fourier matrix F of the phase-encoded signal to be processed is N. s ×N s Dimension, where N s This represents the number of symbols in the phase-coded signal to be processed (i.e., the phase coding length), and the Fourier matrix F can be specifically expressed as: in,

[0050] Here, N p Preset values, for example, can be 2, 4, 8, etc. When N... p When the value of is determined, the Fourier matrix F can be divided into N. p Frequency components in different frequency ranges, thus corresponding to N p Each block Fourier matrix yields the F1 to F2. F1 to This represents the frequency components in F ranging from the lowest frequency range to the highest frequency range.

[0051] For example, the i-th block Fourier matrix F i The expression is: i is a positive integer, and the value of i ranges from 1 to N. p .

[0052] S1022, N p Each of the block Fourier matrices is multiplied by the phase-coded signal to be processed to obtain N. p Each spectrum.

[0053] For example, N p The vector s composed of the spectrum f Represented as: Wherein, the i-th spectrum s i The expression is: s i =F i s.

[0054] In this invention, after obtaining N p After one spectrum, N needs to be processed. p Each spectrum is pulse-compressed to obtain N. p pulse pressure value x1 to For example, the i-th pulse pressure value x i The expression is: Where p represents N s / 2×N s The inverse Fourier matrix of 2D, and,

[0055]

[0056] In this invention, the reference signal s ref It is also a phase-coded signal, with the reference signal s ref Primarily used to extract the main lobe shape of pulse compression; the encoding length N of the phase-coded signal to be processed. s It is the reference signal s ref Encoding length N ref m times, where m is a positive integer, i.e., N s =mN ref m is a preset value, and m is used to control the signal bandwidth. For the reference signal s... ref After pulse compression processing, the pulse compression value x of the reference signal is obtained. k,ref It can be represented as: in,(·) H J represents the conjugate transpose, k represents the distance shift, and J represents the distance shift. k It is a shift matrix.

[0057] In this invention, S105 is achieved through the following steps:

[0058] S1051. Perform linear interpolation on the pulse compression value of the reference signal to obtain N. s One reference pulse pressure value.

[0059] Here, after obtaining the pulse pressure value of the reference signal, linear interpolation is required to increase the pulse pressure value of the reference signal to N. s indivual.

[0060] S1052. Based on m, determine the desired pulse compression main lobe region.

[0061] Specifically, k = [-m, m] is taken as the desired pulse compression main lobe region.

[0062] S1053, N s Among the reference pulse pressure values, the reference pulse pressure value corresponding to the expected pulse compression main lobe region is used as the expected pulse compression main lobe value.

[0063] Specifically, the expected pulse compression main lobe value x Ref It is a vector consisting of the reference pulse pressure value corresponding to the expected pulse compression main lobe region.

[0064] This invention employs a high bit rate, low distance resolution waveform. That is, given a phase-coded signal pulse width and keeping the distance resolution constant, the degree of freedom is increased by increasing the symbol length of the phase-coded signal, thus overcoming the deficiency of low freedom in existing waveform optimization techniques.

[0065] In this invention, the preset weights include: the weighted value of the optimized component and N. pThe weighted value of a vector composed of several spectra; based on this, S106 above is implemented through the following steps:

[0066] S1061, Determine the desired pulse compression main lobe value and N respectively. p The difference between each pulse pressure value is N. p Individual pulse pressure difference value.

[0067] S1062, N p The total pulse pressure difference is obtained by summing the individual pulse pressure differences.

[0068] S1063, according to N p The weighted sum of the vectors composed of the spectra and N p A spectrum is used to determine the frequency-constrained optimization components.

[0069] Specifically, frequency-constrained optimization component y f The expression is: y f =w f ⊙s f ; where s f For the above N p A vector composed of several spectra, w f For N p The weighted value of a vector composed of spectral frequencies, where ⊙ represents the dot product.

[0070] S1064. Construct the optimization objective function based on the weighted values ​​of the optimization components, the frequency-constrained optimization components, and the total pulse pressure difference.

[0071] For example, the expression for optimizing the objective function J is as follows: Where ||.|| represents the L2 norm, x Ref x represents the desired pulse compression main lobe value. i N represents p The i-th pulse compression value in the pulse compression values, where w1 and w2 both represent the weighting values ​​of the optimized components, and S represents the phase-coded signal.

[0072] In this invention, S107 is achieved through the following steps:

[0073] S1071, Construct N s A matrix of size 1; where N is a 1×1 matrix; s The elements in the ×1 matrix are all random values ​​within the range [exp(j0), exp(j2π)).

[0074] S1072. Using the phase-coded signal as the independent variable of the objective function, based on N sGiven a 1×1 matrix, a preset maximum number of iterations, and a preset error threshold between optimal points, the Sequential Quadratic Programming (SQP) algorithm is used to iteratively calculate the objective function. The signal corresponding to the minimum value in the iteration results is selected as the sparse frequency signal.

[0075] Here, the constructed N s The ×1 matrix generates an initial phase-encoded signal for subsequent optimization, ensuring the signal possesses the required frequency characteristics. The specific function of the error threshold 'b' between optimal points is to control the accuracy and convergence conditions during the optimization process, balancing computational speed with result precision. It defines the acceptable error magnitude for the optimization algorithm when searching for the optimal solution. If the error is less than 'b', the optimization objective is considered achieved. Setting 'b' helps prevent the optimization algorithm from getting stuck in infinite loops or overcomputing. By defining a reasonable error threshold, the algorithm can stop computation when a sufficiently good solution is reached. The value of 'b' affects the convergence speed of the algorithm and the accuracy of the final solution. A larger 'b' can speed up convergence but may sacrifice some accuracy; a smaller 'b' can improve accuracy but may require longer computation time.

[0076] For example, Figure 2 Here is a schematic diagram of the spectrum of an exemplary sparse frequency signal, where f L f represents the lower limit of the radar signal frequency range. U f represents the upper limit of the radar signal frequency range. s This indicates the bandwidth of the radar signal.

[0077] This invention employs a high bit rate, low range resolution waveform. Specifically, given a phase-coded signal pulse width and maintaining constant range resolution, it increases the degree of freedom by increasing the symbol length of the phase-coded signal, overcoming the low degree of freedom inherent in existing waveform optimization techniques. This invention optimizes the waveform by pulse compression of each frequency component of the waveform, using pulse compression sidelobes and spectral sidelobes as objective functions, and solving these objective functions. The optimized sparse spectral waveform can form notches within the interference band to suppress interference, reducing the impact of enemy interference and improving the radar's detection capability for low-observable targets. This overcomes the limitation of existing full-band radars being prone to narrowband interference at the same frequency. Furthermore, it allows the radar system to occupy a smaller spectral bandwidth when transmitting signals, improving spectral efficiency.

[0078] The present invention also provides a sparse frequency waveform design device based on high bit rate and low distance resolution, comprising:

[0079] The acquisition module is used to acquire the phase-encoded signal to be processed;

[0080] The component calculation module is used to calculate the N component of the phase-encoded signal to be processed.p The spectrum of each frequency component is obtained to get N. p N spectrums; where N p It is 2 raised to the power of M, where M is a positive integer;

[0081] Compression processing module, used for N p Each spectrum is pulse-compressed to obtain N. p The pulse compression value is obtained by performing pulse compression processing on the reference signal; the encoding length of the reference signal is less than that of the phase-encoded signal to be processed.

[0082] The desired pulse compression main lobe value determination module is used to determine the desired pulse compression main lobe value based on the coding length relationship between the reference signal and the phase-coded signal to be processed, as well as the pulse compression value of the reference signal.

[0083] Function constructor module, used to determine N p Individual pulse pressure, expected pulse compression of the main lobe, N p Given a spectrum and preset weights, construct an optimization objective function;

[0084] The solver module is used to solve the objective function to obtain sparse frequency signals.

[0085] Here, the aforementioned device may be a software program installed in a computer device, which implements the aforementioned functions through the computer device.

[0086] The following simulation experiments further illustrate the technical effects of the present invention.

[0087] Assuming the radar transmitted waveform has a duration τ = 200µs and a sampling frequency f s =10.240MHz, signal center frequency f0=4MHz, symbol length N of transmitted signal s =τf s =2048, the signal frequency range is 1.44MHz to 6.56MHz. The used spectrum-optimized component weighting values ​​(i.e., w1 and w2 mentioned above) and pulse compression sidelobe weighting values ​​(i.e., w... f The ratio of ) is 0.7:0.3, and the optimization results of the double-peak sparse frequency waveform are as follows: Figures 3(a) to 3(d) , Figures 4(a) to 4(d) ,as well as Figures 5(a) to 5(d) As shown.

[0088] Specifically, Figures 3(a) to 3(d)The results show the optimized sparse spectrum waveform obtained by pulse compression of a 128-bit signal followed by eight linear interpolations to achieve the desired pulse-compressed main lobe. Figure 3(a) shows that the PSL of each frequency component waveform after pulse compression is approximately -27.5 dB, and Figure 3(b) shows that the PSL of the sparse frequency waveform as a whole after pulse compression is approximately -28 dB. Figures 3(c) to 3(d) It can be seen that the peak stopband level is approximately -23dB, and the spectral sparsity is improved compared to before the addition of frequency constraint optimization components. By adjusting the ratio of the weighting value of the spectral optimization components to the weighting value of the pulse compression sidelobe, a trade-off can be made between the low pulse compression sidelobe performance and the spectral sparsity performance of the sparse frequency waveform.

[0089] Figures 4(a) to 4(d) This demonstrates the waveform optimization result obtained by widening the desired pulse compression main lobe to 32 distance units, specifically by performing pulse compression followed by 16 linear interpolations on a 64-unit signal to achieve the desired pulse compression main lobe. Figures 4(a) to 4(b) It can be seen that the PSL of each frequency component waveform after pulse compression is approximately -18dB, and the PSL of the sparse frequency waveform after pulse compression is approximately -20dB; Figures 4(c) to 4(d) As shown, the frequency notch characteristics are improved compared to when the main lobe is not broadened, the frequency notch depth increases to -23dB, and the spectral sparsity is improved.

[0090] Figures 5(a) to 5(d) The diagram shows the waveform optimization results obtained by pulse compression of a 128-bit signal followed by four linear interpolations to achieve the desired pulse-compressed main lobe. Figure 5(a) shows that the PSL of each frequency component waveform after pulse compression is approximately -36 dB; Figure 5(b) shows that the PSL of the sparse frequency waveform as a whole after pulse compression is -38.5 dB; Figures 5(c) to 5(d) It can be seen that the frequency notch depth of the sparse frequency waveform increases to -27.5dB, and the spectral sparsity is improved, indicating that the sparse frequency waveform sacrifices some low pulse pressure sidelobe performance to obtain better spectral sparsity performance.

[0091] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0092] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0093] In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple instances. While different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce a good effect.

[0094] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A sparse frequency waveform design method based on high bit rate and low distance resolution, characterized in that, include: Acquire the phase-encoded signal to be processed; Calculate the phase-encoded signal to be processed The spectrum of each frequency component is obtained. One spectrum; among which 2 Power of 1 It is a preset positive integer; Regarding the Each spectrum is pulse-compressed to obtain... Individual pulse pressure values; The reference signal is pulse-compressed to obtain its pulse compression value; the encoding length of the reference signal is less than the encoding length of the phase-coded signal to be processed; the encoding length of the phase-coded signal to be processed is equal to the encoding length of the reference signal. times, It is a positive integer; Based on the coding length relationship between the reference signal and the phase-coded signal to be processed, and the pulse compression value of the reference signal, the desired pulse compression main lobe value is determined; According to the above The pulse pressure value, the expected pulse compression main lobe value, the Given a spectrum and preset weights, construct an optimization objective function; Solving the objective function yields a sparse frequency signal; The preset weights include: the weighted values ​​of the optimized components and the... The weighted value of a vector composed of several spectra; the value based on the... The pulse pressure value, the expected pulse compression main lobe value, the Given a spectrum and preset weights, construct an optimization objective function, including: Determine the desired pulse compression main lobe value and the... The difference between each pulse pressure value is obtained Individual pulse pressure difference value; Regarding the The total pulse pressure difference is obtained by summing the individual pulse pressure differences. According to the above The weighted value of the vector composed of the spectrum and the... One spectrum, determine the frequency constraint optimization components; Based on the weighted values ​​of the optimized components, the frequency-constrained optimized components, and the total pulse pressure difference, the optimization objective function is constructed, and the expression of the optimization objective function is as follows: ； in, This represents the optimization objective function. Describing the L2 norm, This represents the desired pulse compression main lobe value. Indicates the The first of the pulse pressure values pulse pressure value, It is a positive integer, and The value ranges from 1 to , This represents the frequency constraint optimization component. and Each represents a weighted value of the optimized component. This represents a phase-coded signal.

2. The sparse frequency waveform design method based on high bit rate and low distance resolution according to claim 1, characterized in that, The calculation of the phase-encoded signal to be processed The spectrum of each frequency component is obtained. The spectrum includes: The Fourier matrix of the phase-encoded signal to be processed Divided into A block Fourier matrix; the Each block Fourier matrix represents the Fourier matrix. of There are frequency components in three different frequency ranges; where the frequency component in the first frequency range is the frequency component in the lowest frequency range, and the frequency component in the second frequency range is the frequency component in the lowest frequency range. The frequency components within each frequency range are the frequency components of the highest frequency range; The Each block of Fourier matrices is multiplied by the phase-coded signal to be processed to obtain the... Each spectrum.

3. The sparse frequency waveform design method based on high bit rate and low distance resolution according to claim 2, characterized in that, No. A block Fourier matrix The expression is as follows: ； in, This indicates the number of symbols in the phase-coded signal to be processed. , It is a positive integer, and The value ranges from 1 to .

4. The sparse frequency waveform design method based on high bit rate and low distance resolution according to claim 1, characterized in that, The step of determining the desired pulse compression main lobe value based on the encoding length relationship between the reference signal and the phase-coded signal to be processed, and the pulse compression value of the reference signal, includes: Linear interpolation is performed on the pulse compression value of the reference signal to obtain... One reference pulse pressure value; According to the above Determine the desired pulse compression main lobe region; The Among the reference pulse pressure values, the reference pulse pressure value corresponding to the desired pulse compression main lobe region is used as the desired pulse compression main lobe value.

5. The sparse frequency waveform design method based on high bit rate and low distance resolution according to claim 4, characterized in that, The expression for the pulse compression value of the reference signal is: ,in, This represents the pulse compression value of the reference signal. This refers to the reference signal. This indicates the conjugate transpose. Indicates the number of displacements. It is a shift matrix. , ; According to the Determine the desired pulse compression main lobe region, including: Will This serves as the desired pulse compression main lobe region.

6. The sparse frequency waveform design method based on high bit rate and low distance resolution according to claim 1, characterized in that, Frequency-constrained optimization components The expression is as follows: ； in, For the The weighted value of a vector composed of several spectra. For the A vector composed of spectrums, This indicates dot product.

7. The sparse frequency waveform design method based on high bit rate and low distance resolution according to claim 1, characterized in that, Solving the objective function to obtain the sparse frequency signal includes: Build The matrix; wherein, the The elements in the matrix are all Random values ​​within; Using the phase-coded signal as the independent variable of the optimization objective function, according to the... The matrix, the preset maximum number of iterations, and the preset error threshold between the optimal points are used to iteratively calculate the optimization objective function using a sequential quadratic programming algorithm. The signal corresponding to the minimum value in the iteration results is selected as the sparse frequency signal.

8. A sparse frequency waveform design device based on high bit rate and low distance resolution, characterized in that, include: The acquisition module is used to acquire the phase-encoded signal to be processed; The component calculation module is used to calculate the phase-coded signal to be processed. The spectrum of each frequency component is obtained. One spectrum; among which 2 Power of 1 It is a positive integer; Compression processing module, used for the compression processing module Each spectrum is pulse-compressed to obtain... A pulse compression value is obtained by pulse compression processing of the reference signal; the encoding length of the reference signal is less than that of the phase-coded signal to be processed; the encoding length of the phase-coded signal to be processed is equal to the encoding length of the reference signal. times, It is a positive integer; The desired pulse compression main lobe value determination module is used to determine the desired pulse compression main lobe value based on the coding length relationship between the reference signal and the phase-coded signal to be processed, and the pulse compression value of the reference signal. The function constructor module is used to construct the function based on the stated function. The pulse pressure value, the expected pulse compression main lobe value, the Given a spectrum and preset weights, an optimization objective function is constructed; wherein, the preset weights include: the weighted values ​​of the optimization components and the... The weighted value of a vector composed of several spectra; the value based on the... The pulse pressure value, the expected pulse compression main lobe value, the Given a spectrum and preset weights, construct an optimization objective function, including: determining the expected pulse compression main lobe value and the... The difference between each pulse pressure value is obtained Individual pulse pressure difference value; for the aforementioned The total pulse pressure difference is obtained by summing the individual pulse pressure differences; according to the above... The weighted value of the vector composed of the spectrum and the... A spectrum is used to determine frequency-constrained optimization components; based on the weighted values ​​of the optimization components, the frequency-constrained optimization components, and the total pulse voltage difference, the optimization objective function is constructed, and the expression of the optimization objective function is: ,in, This represents the optimization objective function. Describing the L2 norm, This represents the desired pulse compression main lobe value. Indicates the The first of the pulse pressure values pulse pressure value, It is a positive integer, and The value ranges from 1 to , This represents the frequency constraint optimization component. and Each represents a weighted value of the optimized component. Indicates a phase-coded signal; The solution module is used to solve the optimization objective function to obtain the sparse frequency signal.

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