Ultra-low sidelobe pulse compression waveform and matched filter method, system and medium

Abstract

The present invention provides a method for ultra-low sidelobe pulse compression waveforms and matched filters, comprising: substituting bandwidth and pulse width into a linear function and a tangent function, then combining them to obtain the derivative of the phase function of a nonlinear frequency modulation signal; obtaining an amplitude window of a function of power spectral density and signal phase, and substituting the derivative of the phase function into the amplitude window; obtaining a linear factor and introducing it into the derivative of the phase function; discretizing the derivative of the phase function into a sequence, and obtaining a discrete phase sequence through numerical calculation; discretizing the amplitude window into amplitude modulation, and combining it with the discrete phase sequence to obtain the desired signal; performing pulse compression on the signal to obtain a result; performing a conjugate transposition and then inverting the signal to obtain a matched filter; traversing parameters to search for parameters corresponding to a main-to-sidelobe ratio of less than 80dB; canceling the amplitude modulation when transmitting the signal, and improving the matched filter. The present invention solves the problem of excessively high sidelobes affecting range resolution after pulse compression.

Description

Technical Field

[0001] The present invention relates to the technical field of sidelobe pulse compression, and in particular to a method, system and medium for ultra-low sidelobe pulse compression waveform and matched filter. Background Art

[0002] Pulse compression was proposed to address the conflict between range and spatial resolution faced by traditional single-frequency pulse radars. To achieve compression, a compression network is placed at the receiver that is "conjugate matched" to the transmitted signal. When the signal passes through the matched filter, the stronger the signal frequency, the greater the filter's amplification factor; the weaker the signal frequency, the smaller the filter's amplification factor, thereby concentrating the signal in the time domain. Pulse compression techniques can be broadly categorized into linear frequency modulation (LFM), phase coding, and nonlinear frequency modulation. LFM signals are easy to generate using hardware or various techniques, but after matched filtering, the main-to-sidelobe ratio can reach as high as 13.2dB. When detecting multiple targets, the sidelobes of strong targets' echoes can overwhelm weaker signals, compromising their detection. In some weather radar systems, because the ground can reflect clutter as high as -55dB, the normalized sidelobe level must be below -60dB to measure precipitation.

[0003] While linear frequency modulation and phase-coded signals are easy to generate using hardware or various techniques, windowing or other processing can only slightly suppress their sidelobes after pulse compression, inevitably leading to a loss in signal-to-noise ratio. While nonlinear frequency modulation signals are difficult to generate and lack a fixed expression, their advantage lies in their ability to achieve very low sidelobes even after pulse compression without windowing. Traditional windowing can improve the main-to-sidelobe ratio, but at the expense of significant peak loss. Designing signals using continuous nonlinear frequency modulation functions, while offering better performance, inevitably results in a certain loss in signal-to-noise ratio and a broadening of the mainlobe. Summary of the Invention

[0004] The present invention provides a method, system and medium for ultra-low sidelobe pulse compression waveform and matched filter, which solves the problem that the sidelobe after pulse compression is too high and affects the distance resolution.

[0005] A first aspect of the present specification discloses an ultra-low sidelobe pulse compression waveform and a method for matching a filter, comprising:

[0006] S1. Obtain bandwidth B and pulse width T;

[0007] S2. Substituting the bandwidth B and pulse width T into the linear function and the tangent function, the derivative of the phase function of the nonlinear frequency modulation signal is obtained by combining them.

[0008]

[0009] Among them, α and γ are adjustable parameters; π is the circumference of a circle; t represents time;

[0010] S3. Obtain the function amplitude window a(t) of the power spectral density and signal phase, and substitute the derivative φ′(t) of the phase function to obtain:

[0011]

[0012] exp{·} represents an exponential function with the natural constant e as the base;

[0013] S4. Obtain the linear factor β and introduce it into the derivative of the phase function φ′(t), so that the derivative of the phase function becomes φm ′ (t):

[0014] φ m ′(t)=βφ′(t);

[0015] S5. Discretize φ′(t) into a sequence φ′(n), and obtain the discrete phase sequence φ by numerical calculation m (n);

[0016]

[0017] ∑ represents summation;

[0018] s6. Discretize the amplitude window a(t) into a(n) and combine it with the discrete phase sequence φ m (n) to obtain the desired signal s(n);

[0019] s(n)=a(n)exp[jφ m (n)];

[0020] S7. Pulse compression is performed on s(n) to obtain the result y(n); conjugate transpose and inversion are performed on s(n) to obtain the matched filter h(n);

[0021] y(n)=s(n)*h(n);

[0022]

[0023] Among them, * represents convolution, indicates conjugation;

[0024] S8. Traverse the parameters α, γ, and β and search for the parameters α, γ, and β corresponding to y(n) having a main-sidelobe ratio lower than 80 dB to update y(n);

[0025] s9. When transmitting the signal s(n), the amplitude modulation a(n) is canceled, that is, the signal s(n) is changed to And change the matched filter h(n) to

[0026]

[0027]

[0028] in, Expressed as inverse Fourier transform, Y(ω), They are y(n), Fourier transform of

[0029] use as the transmit waveform, and use as a matched filter.

[0030] In some embodiments of this specification, the linear function in S2 is:

[0031] In some embodiments of this specification, the tangent function in S2 is:

[0032] A second aspect of this specification discloses a system of ultra-low sidelobe pulse compression waveform and matched filter, comprising:

[0033] A first acquisition module is used to obtain bandwidth B and pulse width T;

[0034] A combination module is used to substitute the bandwidth B and the pulse width T into the linear function and the tangent function, and then combine them to obtain the derivative φ′(t) of the phase function of the nonlinear frequency modulation signal;

[0035]

[0036] The second acquisition module is used to obtain the function amplitude window a(t) of the power spectrum density and signal phase, and substitute the derivative φ′(t) of the phase function to obtain:

[0037]

[0038] The third acquisition module is used to obtain the linear factor β and introduce it into the derivative φ′(t) of the phase function, so that the derivative of the phase function becomes φ m ′(t):

[0039] φ m ′(t)=βφ′(t);

[0040] The first discrete module is used to discretize φ′(t) into a sequence φ′(n) and obtain the discrete phase sequence φ by numerical calculation. m (n);

[0041]

[0042] The second discretization module is used to discretize the amplitude window a(t) into a(n) and jointly discrete the phase sequence φ m (n) to obtain the desired signal s(n);

[0043] s(n)=a(n)exp[jφ m (n)];

[0044] The pulse compression and conjugation module is used to perform pulse compression on s(n) to obtain the result y(n); conjugate transpose and then invert s(n) to obtain the matched filter h(n);

[0045] y(n)=s(n)*h(n);

[0046]

[0047] Among them, * represents convolution, indicates conjugation;

[0048] The traversal module is used to traverse the parameters α, γ, and β, and search for the parameters α, γ, and β corresponding to y(n) having a main-sidelobe ratio lower than 80dB, so as to update y(n);

[0049] The transmitting and matching module is used to cancel the amplitude modulation a(n) when transmitting the signal s(n), that is, to change the signal s(n) to And change the matched filter h(n) to

[0050]

[0051]

[0052] in, Expressed as inverse Fourier transform, Y(ω), They are y(n), Fourier transform of

[0053] use as the transmit waveform, and use as a matched filter.

[0054] The third aspect of this specification discloses a computer-readable storage medium, which stores computer instructions. When a computer reads the computer instructions, the computer executes the method of ultra-low sidelobe pulse compression waveform and matching filter as described in any one of the above.

[0055] The embodiments of this specification can achieve at least the following beneficial effects:

[0056] The present invention can obtain a signal that has a very low main-to-sidelobe ratio and has little effect on pulse width and signal loss; the linear factor β is introduced to balance the bandwidth expansion brought by the designed waveform, reduce the influence of signal broadening, and solve the problem that the sidelobe is too high after pulse compression and affects the distance resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. 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 any creative work.

[0058] Figure 1 Schematic diagram of the ultra-low sidelobe pulse compression waveform and matched filter method involved in the present invention.

[0059] Figure 2 Schematic diagram of the NLFM signal frequency function / frequency modulation function / phase function / window function based on amplitude window weighting involved in the present invention.

[0060] Figure 3 Schematic diagram of the waveform of the NLFM signal with amplitude window involved in the present invention.

[0061] Figure 4 FIG. 4 is a schematic diagram of the pulse compression result of the NLFM signal with an amplitude window added in the present invention.

[0062] Figure 5 It is a schematic diagram of the pulse compression result involved in the present invention.

[0063] Figure 6 Schematic diagram of the NLFM signal waveform of the de-amplification window involved in the present invention.

[0064] Figure 7 Schematic diagram of the equivalent matched filter involved in the present invention.

[0065] Figure 8 Schematic diagram of pulse compression involving a de-amplification window and an equivalent matched filter in the present invention. DETAILED DESCRIPTION

[0066] Hereinafter, only certain exemplary embodiments are briefly described. As will be appreciated by those skilled in the art, the described embodiments may be modified in various ways without departing from the spirit or scope of the embodiments of the present invention. Therefore, the drawings and description are to be regarded as illustrative in nature and not restrictive.

[0067] The disclosure below provides many different embodiments or examples for implementing different structures of the embodiments of the present invention. In order to simplify the disclosure of the embodiments of the present invention, the components and configurations of specific examples are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. In addition, the embodiments of the present invention may repeat reference numerals and / or reference letters in different examples. Such repetition is for the purpose of simplicity and clarity and does not in itself indicate the relationship between the various embodiments and / or configurations discussed.

[0068] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0069] like Figure 1 As shown, the first aspect of this specification discloses an ultra-low sidelobe pulse compression waveform and a matched filter method, including:

[0070] S1. Obtain bandwidth B and pulse width T based on system requirements.

[0071] S2. Substituting the bandwidth B and pulse width T into the linear function and the tangent function, the derivative of the phase function of the nonlinear frequency modulation signal is obtained by combining them.

[0072]

[0073] Among them, α and γ are adjustable parameters; π is the circumference of a circle; and t represents time.

[0074] S3. Obtain the function amplitude window a(t) of the power spectral density and signal phase, and substitute the derivative φ′(t) of the phase function to obtain:

[0075]

[0076] S4. Obtain the linear factor β and introduce it into the derivative of the phase function φ′(t), so that the derivative of the phase function becomes φ m ′(t):

[0077] φ m ′(t)=βφ′(t);

[0078] Selecting appropriate parameters α and γ to design the amplitude window and phase function yields a waveform with low sidelobes after pulse compression. However, its mainlobe broadening is significantly greater than that of a linear frequency modulation signal, which also affects range resolution. This signal design essentially trades mainlobe broadening for sidelobe performance. To minimize the impact of signal broadening, a linear factor β is introduced to balance the bandwidth expansion brought about by the designed waveform.

[0079] S5. Discretize φ′(t) into a sequence φ′(n), and obtain the discrete phase sequence φ by numerical calculation m(n);

[0080]

[0081] S6. Discretize the amplitude window a(t) into a(n) and combine it with the discrete phase sequence φ m (n) to obtain the desired signal s(n);

[0082] s(n)=a(n)exp[jφ m (n)];

[0083] s7. Perform pulse compression on s(n) to obtain the result y(n); perform conjugate transposition and then inversion on s(n) to obtain the matched filter h(n);

[0084] y(n)=s(n)*h(n);

[0085]

[0086] Among them, * represents convolution, indicates conjugation;

[0087] S8. Traverse the parameters α, γ, and β and search for the parameters α, γ, and β corresponding to y(n) having a main-sidelobe ratio lower than 80 dB to update y(n);

[0088] Adjusting α can change the slope and shape of the FM curve, and adjusting γ can change the scale of the tangent curve;

[0089] S9. When transmitting the signal s(n), the amplitude modulation a(n) is canceled, that is, the signal s(n) is changed to And change the matched filter h(n) to

[0090]

[0091]

[0092] in, Expressed as inverse Fourier transform, Y(ω), They are y(n), Fourier transform of

[0093] use as the transmit waveform, and use As a matched filter, ultra-low sidelobes can be obtained.

[0094] Since the designed waveform has amplitude modulation a(n), it will bring burden to the transmitter during transmission, and amplitude distortion will occur after power amplification. Therefore, only the

[0095] In some embodiments of this specification, the linear function in S2 is:

[0096] In some embodiments of this specification, the tangent function in S2 is:

[0097] A second aspect of this specification discloses a system of ultra-low sidelobe pulse compression waveform and matched filter, comprising:

[0098] A first acquisition module is used to obtain bandwidth B and pulse width T;

[0099] A combination module is used to substitute the bandwidth B and the pulse width T into the linear function and the tangent function, and then combine them to obtain the derivative φ′(t) of the phase function of the nonlinear frequency modulation signal;

[0100]

[0101] The second acquisition module is used to obtain the function amplitude window a(t) of the power spectrum density and signal phase, and substitute the derivative φ′(t) of the phase function to obtain:

[0102]

[0103] The third acquisition module is used to obtain the linear factor β and introduce it into the derivative φ′(t) of the phase function, so that the derivative of the phase function becomes φ m ′(t):

[0104] φ m ′(t)=βφ′(t);

[0105] The first discrete module is used to discretize φ′(t) into a sequence φ′(n) and obtain the discrete phase sequence φ by numerical calculation. m (n);

[0106]

[0107] The second discretization module is used to discretize the amplitude window a(t) into a(n) and jointly discrete the phase sequence φ m (n) to obtain the desired signal s(n);

[0108] s(n)=a(n)exp[jφ m (n)];

[0109] The pulse compression and conjugation module is used to perform pulse compression on s(n) to obtain the result y(n); conjugate transpose and then invert s(n) to obtain the matched filter h(n);

[0110] y(n)=s(n)*h(n);

[0111]

[0112] Among them, * represents convolution, indicates conjugation;

[0113] The traversal module is used to traverse the parameters α, γ, and β, and search for the parameters α, γ, and β corresponding to y(n) having a main-sidelobe ratio lower than 80dB, so as to update y(n);

[0114] The transmitting and matching module is used to cancel the amplitude modulation a(n) when transmitting the signal s(n), that is, to change the signal s(n) to And change the matched filter h(n) to

[0115]

[0116]

[0117] in, Expressed as inverse Fourier transform, Y(ω), They are y(n), Fourier transform of

[0118] use as the transmit waveform, and use as a matched filter.

[0119] The third aspect of this specification discloses a computer-readable storage medium, which stores computer instructions. When a computer reads the computer instructions, the computer executes the method of ultra-low sidelobe pulse compression waveform and matching filter as described in any one of the above.

[0120] Set the simulation parameters as follows: T = 50 μs, B = 10 MHz, f s =4B, α=0.9, β=0.16, γ=1.37, by Figure 2 It can be seen that a(t) is very close to the rectangular window. Figure 3 The signal can be directly pulse compressed to obtain Figure 4 As a result, the main lobe ratio is better than 80dB, the peak loss is 2.4dB, and the main lobe width is 1.3μs. Reducing the signal main lobe width can be achieved by adjusting the parameter β. The other parameters mentioned above remain unchanged. Let β = 0.32, that is, the bandwidth is doubled. The simulation results are as follows Figure 5 As shown in the figure, the main lobe width is 0.75μs and the side lobes are better suppressed.

[0121] In practical applications, if Figure 3The signal is used as the waveform of the radar transmission signal. Since the operating point of the transmitter power amplifier is generally in the saturation or near saturation area, the amplitude will be seriously distorted after power amplification, and the amplitude window weighting will lose its effect. Therefore, it is necessary to remove the amplitude window of the transmission signal, such as Figure 6 As shown, the receiver then designs an equivalent matched filter as Figure 7 As shown, pulse compression is performed after receiving the echo. Figure 8 As shown, it can be seen that the same effect as adding an amplitude window to the transmitted signal is obtained.

[0122] The above embodiments are intended to illustrate the present invention, not to limit the present invention. Therefore, changes in illustrative values ​​or substitutions of equivalent components should still fall within the scope of the present invention.

[0123] From the above detailed description, it will be clear to those skilled in the art that the present invention can indeed achieve the aforementioned objectives and is in compliance with the provisions of the Patent Law.

[0124] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they become aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as covering the preferred embodiments and all changes and modifications that fall within the scope of the invention. The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

[0125] It should be noted that the above description of the relevant processes is for illustration and purpose only and does not limit the scope of application of this specification. For those skilled in the art, various modifications and changes can be made to the processes under the guidance of this specification. However, such modifications and changes are still within the scope of this specification.

[0126] The basic concepts have been described above. It will be apparent to those skilled in the art after reading this application that the above disclosures are merely illustrative and do not constitute limitations on this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and amendments to this application. Such modifications, improvements, and amendments are suggested in this application and remain within the spirit and scope of the exemplary embodiments of this application.

[0127] At the same time, this application uses specific terms to describe the embodiments of this application. For example, "one embodiment," "an embodiment," and / or "some embodiments" refer to a certain feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "one embodiment," "an embodiment," or "an alternative embodiment" mentioned twice or more in different places in this specification does not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application may be appropriately combined.

[0128] In addition, it will be understood by those skilled in the art that various aspects of the present application can be illustrated and described by a number of patentable categories or situations, including any new and useful combination of processes, machines, products or substances, or any new and useful improvements thereto. Therefore, various aspects of the present application can be implemented entirely by hardware, entirely by software (including firmware, resident software, microcode, etc.), or by a combination of hardware and software. The above hardware or software can all be referred to as "units", "modules" or "systems". In addition, various aspects of the present application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0129] The computer program code required for the operation of each part of the application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, Python, conventional procedural programming languages ​​such as C programming language, VisualBasic, Fortran2103, Perl, COBOL2102, PHP, ABAP, dynamic programming languages ​​such as Python, Ruby and Groovy or other programming languages. The program code can be run completely on the user's computer, or run on the user's computer as an independent software package, or run partly on the user's computer and partly on a remote computer, or run completely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer through any network form, such as a local area network (LAN) or a wide area network (WAN), or be connected to an external computer (such as by the Internet), or in a cloud computing environment, or used as a service such as software as a service (SaaS).

[0130] In addition, unless expressly stated in the claims, the order of the processing elements and sequences described in this application, the use of alphanumeric characters, or the use of other names are not intended to limit the order of the processes and methods of this application. Although the above disclosure discusses some embodiments of the invention that are currently considered useful through various examples, it should be understood that such details are only for illustrative purposes, and the attached claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that are consistent with the essence and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a pure software solution, for example, installation on an existing server or mobile device.

[0131] Similarly, it should be noted that in order to simplify the presentation of this disclosure and thereby facilitate understanding of one or more of the invention's embodiments, the foregoing descriptions of the embodiments of this disclosure sometimes combine multiple features into a single embodiment, figure, or description thereof. However, this approach should not be interpreted as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject matter of the invention may possess fewer features than the single embodiment described above.

Claims

1. Ultra-low sidelobe pulse compression waveform and matched filter method, characterized in that: include: S1. Obtain bandwidth B and pulse width T; S2. Substitute the bandwidth B and pulse width T into the linear function and tangent function, and combine them to obtain the derivative of the phase function of the nonlinear frequency modulation signal ; ； in, 、 is an adjustable parameter; is pi; Indicates time; S3. Obtain the function amplitude window of power spectrum density and signal phase , and the derivative of the phase function Substituting in: ； Where exp{·} represents the exponential function with the natural constant e as the base; S4. Obtaining linear factors , and introduce the derivative of the phase function , so that the derivative of the phase function becomes : ； S5. Discretize into a sequence , and the discrete phase sequence is obtained by numerical calculation ; ； in, Indicates summation; S6. Set the amplitude window Discretized into , and combined with discrete phase sequence Get the desired signal ; ； S7.Yes Do pulse compression and get the result ;right Perform conjugate transpose and then invert to get the matched filter ; ； ； Among them, * represents convolution, indicates conjugation; S8. Traversal parameters 、 、 , search out Parameters corresponding to a main-sidelobe ratio lower than 80dB 、 、 , to update ; S9. Transmit signal When the amplitude modulation Cancel, signal Change to ; and match the filter Change to ; ； ； in, Expressed as inverse Fourier transform, 、 They are 、 Fourier transform of use as the transmit waveform, and use as a matched filter.

2. The method of ultra-low sidelobe pulse compression waveform and matched filter according to claim 1, characterized in that: The linear function in S2 is: 。 3. The method of ultra-low sidelobe pulse compression waveform and matched filter according to claim 1, characterized in that: The tangent function in S2 is: 。 4. Ultra-low sidelobe pulse compression waveform and matched filter system, characterized in that: include: A first acquisition module is used to obtain bandwidth B and pulse width T; The combination module is used to substitute the bandwidth B and pulse width T into the linear function and the tangent function, and then combine them to obtain the derivative of the phase function of the nonlinear frequency modulation signal. ; ； in, 、 is an adjustable parameter; is pi; Indicates time; The second acquisition module is used to obtain the function amplitude window of power spectrum density and signal phase , and the derivative of the phase function Substituting in: ； The third acquisition module is used to obtain the linear factor , and introduce the derivative of the phase function , so that the derivative of the phase function becomes : ； The first discrete module is used to Discretize into a sequence , and the discrete phase sequence is obtained by numerical calculation ; ； The second discrete module is used to convert the amplitude window Discretized into , and combined with discrete phase sequence Get the desired signal ; ； Pulse compression and conjugation module for Do pulse compression and get the result ;right Perform conjugate transpose and then invert to get the matched filter ; ； ； Among them, * represents convolution, indicates conjugation; Traversal module, used to traverse parameters 、 、 , search out Parameters corresponding to a main-sidelobe ratio lower than 80dB 、 、 , to update ; Transmitting and matching module, used to transmit signals When the amplitude modulation Cancel, signal Change to ; and match the filter Change to ; ； ； in, Expressed as inverse Fourier transform, 、 They are 、 Fourier transform of use as the transmit waveform, and use as a matched filter.

5. A computer-readable storage medium, characterized in that The storage medium stores computer instructions. When a computer reads the computer instructions, the computer executes the method of ultra-low sidelobe pulse compression waveform and matched filter according to any one of claims 1 to 3.

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