Phase modulation filtering method and device based on mutual matching and electronic equipment

By matching filtering two echo signals modulated by the same phase, the problem of degradation of radar target detection performance caused by passive phase modulation interference is solved, and effective suppression of phase modulation interference and improvement of radar target detection performance is achieved.

CN120178170APending Publication Date: 2025-06-20XIDIAN UNIV
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Patent Information

Application Number
CN202510204737.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-24
Publication Date
2025-06-20

AI Technical Summary

Technical Problem

Passive phase modulation interference makes it difficult for the radar system to separate the interference from the target echo signal, resulting in a degradation of radar target detection performance.

Method used

By obtaining two echo signals modulated by the same phase and matching filtering them as the other's reference signals, mutually matching phase modulation filtering is achieved.

Benefits of technology

Effectively suppress phase modulation interference, improve the pulse compression performance of the echo signal, thereby greatly improving the radar target detection performance.

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Abstract

The invention discloses a phase modulation filtering method and device based on mutual matching and electronic equipment. The method comprises the following steps: acquiring a first echo signal and a second echo signal; radar transmitting signals corresponding to the first echo signal and the second echo signal are linear frequency modulation signals, and the two radar transmitting signals are modulated by the same phase; and performing matched filtering on the reference signals of the first echo signal and the second echo signal which are mutually opposite to each other to realize mutually matched phase modulation filtering. According to the invention, the passive phase modulation interference is effectively suppressed, so that the pulse compression performance of the echo signal when the phase modulation interference exists is improved.
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Description

Technical Field

[0001] The present invention belongs to the field of radar interference suppression, and particularly relates to a mutual-matching based phase modulation filtering method, device and electronic equipment. Background Art

[0002] Matched filtering technology plays a core role in radar signal processing, mainly used to improve the signal-to-noise ratio of signals and optimize target detection performance. By matching the received signal with a known signal template, the matched filter can maximize the energy of the signal, significantly suppress noise, and enhance the detectability of weak signals. This enables the radar system to effectively identify targets in a complex electromagnetic environment. Matched filtering not only improves the sensitivity of signal processing but also plays a crucial role in scenarios such as target tracking, signal acquisition, and multipath propagation. Its simple implementation and high efficiency make matched filtering widely used in actual radar systems and it is one of the basic and core technologies in radar signal processing.

[0003] With the development of electromagnetic regulation technology, passive phase modulation interference can rapidly regulate the phase characteristics of target echoes, resulting in a decline in matched filtering performance and seriously affecting the radar target detection process. Different from traditional "additive" interferences such as intermittent sampling interference and smart noise interference, passive phase modulation interference multiplies with the target echo signal in the time domain and is essentially a "multiplicative" interference. Generally, for traditional interferences, radar countermeasure methods can utilize the differences between the interference and the target echo signal in time, frequency, space, and polarization feature domains for interference suppression. However, for phase modulation interference, it is difficult to separate the interference from the target echo signal in the above-mentioned domains, so traditional radar countermeasure methods are difficult to be directly applied to the suppression of phase modulation interference, leading to a serious decline in radar target detection performance under passive phase modulation interference conditions. Summary of the Invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a mutual-matching based phase modulation filtering method, device and electronic equipment.

[0005] The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] A mutual-matching based phase modulation filtering method includes:

[0007] Obtain a first echo signal and a second echo signal; the radar transmission signals corresponding to the first echo signal and the second echo signal are both linear frequency modulation signals, and the two radar transmission signals are subject to the same phase modulation;

[0008] Perform matched filtering with the first echo signal and the second echo signal as reference signals for each other to achieve mutual-matching based phase modulation filtering.

[0009] Optionally, the first echo signal and the second echo signal are used as reference signals for each other for matched filtering to achieve mutually matched phase modulation filtering, including:

[0010] Taking the first echo signal as a reference signal, conjugating the reference signal and then performing convolution with the second echo signal, and / or taking the second echo signal as a reference signal, conjugating the reference signal and then performing convolution with the first echo signal.

[0011] Optionally, the first echo signal and the second echo signal are dual-channel echo signals of a short baseline dual-channel radar system.

[0012] Optionally, the first echo signal and the second echo signal are respectively echoes of signals transmitted by different radars.

[0013] The present invention further provides a device for mutually matched phase modulation filtering, including:

[0014] An echo acquisition module, configured to acquire a first echo signal and a second echo signal; the radar transmission signals corresponding to the first echo signal and the second echo signal are both linear frequency modulation signals, and the two radar transmission signals are subject to the same phase modulation;

[0015] A phase modulation filtering module, configured to use the first echo signal and the second echo signal as reference signals for each other for matched filtering to achieve mutually matched phase modulation filtering.

[0016] Optionally, the phase modulation filtering module is specifically configured to: take the first echo signal as a reference signal, conjugate the reference signal and then perform convolution with the second echo signal, and / or take the second echo signal as a reference signal, conjugate the reference signal and then perform convolution with the first echo signal.

[0017] Optionally, the first echo signal and the second echo signal are dual-channel echo signals of a short baseline dual-channel radar system.

[0018] Optionally, the first echo signal and the second echo signal are respectively echoes of signals transmitted by different radars.

[0019] In a third aspect, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, where the processor, the communication interface, and the memory complete communication with each other through the communication bus;

[0020] The memory is used to store a computer program;

[0021] A processor, when executing a program stored in a memory, implements the steps of any one of the above-mentioned phase modulation filtering methods based on mutual matching.

[0022] The phase modulation filtering method based on mutual matching provided by the present invention realizes phase modulation filtering by performing matched filtering on two echo signals modulated by the same modulation, which helps to improve the pulse compression performance when there is phase modulation interference in the echo signal, thereby greatly improving the radar target detection performance.

[0023] The following will further elaborate on the present invention in conjunction with the accompanying drawings. Description of the Drawings

[0024] Figure 1 is a schematic flowchart of a phase modulation filtering method based on mutual matching provided by an embodiment of the present invention;

[0025] Figure 2 shows the comparison results of unmodulated, 1-bit phase period, and random modulation pulse compression in the simulation of the present invention;

[0026] Figure 3 shows the mutual matching result of 1-bit periodic phase modulation in the simulation of the present invention;

[0027] Figure 4 shows the mutual matching result of 1-bit random phase modulation in the simulation of the present invention;

[0028] Figure 5 shows the comparison results of unmodulated, 2-bit phase period, and random modulation pulse compression in the simulation of the present invention;

[0029] Figure 6 shows the mutual matching result of 2-bit periodic phase modulation in the simulation of the present invention;

[0030] Figure 7 shows the mutual matching result of 2-bit random phase modulation in the simulation of the present invention;

[0031] Figure 8 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. Detailed Embodiments

[0032] The following further describes the present invention in detail with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0033] In order to effectively suppress passive phase modulation interference and thus improve the pulse compression performance when there is phase modulation interference in the echo signal, an embodiment of the present invention provides a phase modulation filtering method based on mutual matching, as Figure 1 shown, the method includes the following steps:

[0034] S10. Obtain a first echo signal and a second echo signal; the radar transmission signals corresponding to the first echo signal and the second echo signal are both linear frequency modulation signals, and the two radar transmission signals are subject to the same phase modulation.

[0035] Here, the first echo signal and the second echo signal can be the dual-channel echo signals of a short baseline dual-channel system radar. Alternatively, the first echo signal and the second echo signal are respectively the echoes of signals transmitted by different radars.

[0036] In practice, the radar transmission signal is a linear frequency modulation signal. After the linear frequency modulation signal is transmitted into space through an antenna, it is modulated by passive phase modulation and then received by the radar receiving antenna. After the received signal is subjected to down-conversion and signal sampling processing, an echo signal is formed.

[0037] Among them, the coefficient of passive phase modulation can be:

[0038]

[0039] In formula (1), t represents time, rect(·) is a unit rectangular window function, T c represents the phase modulation period, K represents the number of modulation periods, j represents the imaginary unit, represents the discrete phase in the k-th modulation period. The discrete phase can be selected in [0, 2π]. Typically, the value of or

[0040]

[0041] Since the passive phase modulation interference has an approximately identical modulation response to incident electromagnetic waves within a certain carrier frequency range, and the smaller the carrier frequency difference between two incident electromagnetic waves, the more similar the phase modulation they receive. Assume that the radar transmission signals corresponding to two echo signals are both linear frequency modulation signals (LFM), and are respectively:

[0042]

[0043] Among them, f c1 and f c2 are respectively the carrier frequencies of the radar transmission signals corresponding to the two echo signals. The signal bandwidth is expressed as B = γT p , T p is the pulse width, and γ is the frequency modulation slope. Assume that Δf represents the carrier frequency difference. Considering the non-aliasing reception of two echoes affected by passive phase modulation, we generally have Δf = B + F c = f c1 - f c2 , When the carrier frequencies of the radar emission signals are close, since the phase modulations of the radar emission signals corresponding to the two echo signals are the same, the two echo signals can be respectively expressed as:

[0044]

[0045] Among them, s 1rr (t) represents the first target echo signal affected by passive phase modulation, s 2rr (t) represents the second target echo signal affected by passive phase modulation, n1(t) and n2(t) are independent complex Gaussian white noises, t0 represents the time delay caused by the relative position between the radar and the target, R represents the relative position distance between the radar and the target, and c is the speed of light.

[0046] S20. Use the first echo signal and the second echo signal as the reference signals for each other to perform matched filtering, so as to achieve the filtering of mutually matched phase modulation.

[0047] Generally, in radar signal processing, for the target echo signal s(t - t0) and the reference signal h(t), the matched filtering process in the time domain is defined as:

[0048]

[0049] Among them, y(t) is the signal after matched filtering, u is the integration variable, s * (u - t) is the conjugate of s(t - t0).

[0050] It can be seen from Equation (6) that when t = t0, the output result is the largest, that is, y(t0) obtains the maximum value, which is expressed as:

[0051]

[0052] It can be seen from the above Equation (7) that the maximum value of the matched filtering is the integral result of the multiplication of the emission signal and its conjugate, which can be considered as the energy of the emission signal.

[0053] As shown in the above Equations (4) and (5), the phase modulation coefficients in the two echo signals are in a multiplicative relationship with the target echo. This indicates that at the signal level, the phase modulation changes the structure of the radar emission signal, making it difficult for interference suppression means to play a role. On the other hand, according to the time-domain convolution principle, the matched filtering result at the target delay point is the integral of the product of the radar echo signal and the reference signal. For a signal with good autocorrelation characteristics, that is, a linear frequency modulation signal, this process can be considered as the conjugate multiplication of two linear frequency modulation signals in the time domain. Therefore, for two linear frequency modulation signals affected by the same phase modulation, the modulation can be filtered out by using the time-domain conjugate multiplication method.

[0054] Specifically, in order to effectively suppress phase modulation interference, in the embodiments of the present invention, two echo signals that are subject to the same phase modulation are subjected to conjugate product processing in the time domain, that is, one of the echo signals is first subjected to conjugate processing, and the echo signal after conjugate processing is convolved with the other echo signal in the time domain to achieve the so-called matched filtering processing.

[0055] Specifically, the first echo signal is used as a reference signal, and after taking the conjugate of the reference signal, it is convolved with the second echo signal, and / or the second echo signal is used as a reference signal, and after taking the conjugate of the reference signal, it is convolved with the first echo signal.

[0056] Exemplarily, assuming that the conjugate of s r2 (t) is taken as the reference signal, the result of directly performing matched filtering on the two echo signals is expressed as:

[0057]

[0058] Wherein,

[0059]

[0060] Wherein, is the conjugate of s 2rr (t), is the conjugate of n2(t), and τ is the integration variable.

[0061] In equations (8) and (9), y r1 (t) is the result of traditional matched filtering, and y r2 (t) + y r3 (t) + y r4 (t) is the cross term. Due to the existence of noise, the cross term will form an effect similar to the background noise in the matched filtering result and does not affect the effect of interference filtering. At the target delay t0, y r1 (t0) is expressed as:

[0062]

[0063] Wherein, E represents the energy of the transmitted signal.

[0064] It can be seen from the above equation (13) that the phase modulation filtering method based on mutual matching can obtain the maximum output energy at the target position delay, thereby realizing phase modulation filtering at the target position, improving the energy accumulation effect after pulse compression processing, and effectively restoring the pulse compression processing gain.

[0065] To prove the effectiveness of the present invention, the following simulation comparison experiments are used for further illustration.

[0066] (1) Simulation conditions:

[0067] Pure software simulation is adopted, and the experimental platform is Matlab R2021b.

[0068] The radar transmitting signal adopts the linear frequency modulation (LFM) signal transmitted by a dual-baseline radar, and the parameters are as shown in Table 1 below:

[0069] Table 1 Simulation Parameters

[0070]

[0071] (2) Simulation Results and Analysis

[0072] Using the parameters in Table 1 to generate the echo signals of the dual-baseline phase modulation radar, that is, generating the first echo signal and the second echo signal, and using the method of this embodiment of the present invention to filter out the phase modulation interference, the experimental results are as follows:

[0073] Figure 1 Shows the pulse compression results without phase modulation, 1-bit period, and random phase modulation. The horizontal axis is the discrete points in the radar range direction, and the vertical axis is the amplitude of the echo signal after filtering out the phase modulation. The same applies hereinafter. Figures 2 to 7 Same hereinafter. It can be seen from Figure 1 the results that due to the periodic variation law of the periodic phase modulation, the pulse compression result shows two false peaks, and due to the randomness of the random phase modulation, the pulse compression result shows an effect similar to the background noise.

[0074] Figure 2 Shows the 1-bit periodic phase modulation pulse compression and the corresponding cross-matching results. The results show that the cross-matching method suppresses the false targets generated by the periodic phase modulation and forms a high energy accumulation at the position of the real target.

[0075] Figure 3 Shows the 1-bit random phase modulation pulse compression and the corresponding cross-matching results. It can be seen from the results that at the target position, the cross-matching method effectively improves the target energy accumulation; at other positions, the cross-matching method has a small integrated energy.

[0076] Figure 4 Shows the pulse compression results without phase modulation, 2-bit period, and random phase modulation. Compared with the 1-bit periodic phase modulation, the 2-bit modulation generates false targets with asymmetric positions and energies.

[0077] Figure 5 Shows the 2-bit periodic phase modulation pulse compression and the corresponding cross-matching results. Similarly, the results show that the cross-matching method can form a high energy accumulation at the position of the real target and suppress false targets.

[0078] Figure 6The 2-bit random phase modulation pulse compression and the corresponding cross-matching results are shown. It can be seen from the results that at the target position, the cross-matching method effectively improves the energy accumulation by canceling the phase modulation; at other positions, the cross-matching method also has a small integral energy.

[0079] The above simulation experiment results prove the reliability and effectiveness of the present invention.

[0080] In summary, compared with the conventional modulation filtering method which is more suitable for the scenario where the target echo and the modulation signal are linearly related, the phase modulation filtering method based on cross-matching provided by the embodiments of the present invention realizes phase modulation filtering by performing matched filtering on two echo signals modulated by the same modulation, realizes the filtering of the target echo and the modulation phase under non-linear conditions, helps to improve the pulse compression performance when there is phase modulation interference in the echo signal, and thus greatly improves the radar target detection performance.

[0081] The method provided by the embodiments of the present invention can be applied to electronic devices. Specifically, the electronic device can be: a desktop computer, a portable computer, a server, or a radar, etc. There is no limitation here.

[0082] Based on the same inventive concept, the embodiments of the present invention also provide a phase modulation filtering device based on cross-matching, including: an echo acquisition module and a phase modulation filtering module.

[0083] The echo acquisition module is used to acquire a first echo signal and a second echo signal; the radar transmission signals corresponding to the first echo signal and the second echo signal are both linear frequency modulation signals, and the two radar transmission signals are modulated by the same phase modulation.

[0084] The phase modulation filtering module is used to perform matched filtering on the first echo signal and the second echo signal with each other as the reference signal of the other, to realize cross-matched phase modulation filtering.

[0085] Optionally, the phase modulation filtering module is specifically used for: taking the first echo signal as the reference signal, conjugating the reference signal and then performing convolution with the second echo signal, and / or taking the second echo signal as the reference signal, conjugating the reference signal and then performing convolution with the first echo signal.

[0086] Optionally, the first echo signal and the second echo signal are the dual-channel echo signals of a short baseline dual-channel system radar, or the first echo signal and the second echo signal are respectively the echo signals of signals transmitted by different radars.

[0087] The present invention also provides an electronic device, such as Figure 8As shown in the figure, it includes a processor 801, a communication interface 802, a memory 803, and a communication bus 804. Among them, the processor 801, the communication interface 802, and the memory 803 communicate with each other through the communication bus 804;

[0088] The memory 803 is used to store computer programs;

[0089] When the processor 801 is used to execute the computer programs stored on the memory 803, it implements the steps of any of the above-mentioned phase modulation filtering methods based on mutual matching.

[0090] The communication bus mentioned in the above electronic device can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, only a thick line is used to represent it in the figure, but it does not mean that there is only one bus or one type of bus.

[0091] The communication interface is used for communication between the above electronic device and other devices.

[0092] The memory may include a Random Access Memory (RAM), or may also include a Non-Volatile Memory (NVM), such as at least one disk memory. Optionally, the memory may also be at least one storage device located far from the aforementioned processor.

[0093] The above-mentioned processor may be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it may also be a Digital Signal Processing (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0094] It should be noted that for the apparatus / electronic device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and for the relevant parts, please refer to the partial description of the method embodiment.

[0095] It should be noted that the terms "first", "second", etc. are used to distinguish similar objects and do not necessarily describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0096] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0097] Although the present invention has been described in connection with various embodiments herein, however, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the accompanying drawings and the disclosure. In the description of the present invention, the term "including" does not exclude other components or steps, the term "one" or "a" does not exclude a plurality of cases, and the meaning of "a plurality" is two or more, unless otherwise specifically defined. In addition, certain measures are described in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0098] It should be noted that the devices, electronic devices, and storage media of the embodiments of the present invention are respectively devices and electronic devices applying the above-mentioned method of mutual-matching phase modulation filtering. Then all embodiments of the above-mentioned method of mutual-matching phase modulation filtering are applicable to the devices and electronic devices, and can achieve the same or similar beneficial effects.

[0099] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, an apparatus (device), or a computer program product. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects, which are collectively referred to herein as "modules" or "systems". Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) that contain computer-usable program code. The computer program is stored / distributed in a suitable medium, provided together with other hardware or as part of the hardware, and can also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

[0100] The present invention is described with reference to the flowcharts and / or block diagrams of the methods and apparatuses of the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0101] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device that implements the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0102] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0103] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A phase modulation filtering method based on mutual matching, characterized in that: include: Acquire a first echo signal and a second echo signal; the radar transmission signals corresponding to the first echo signal and the second echo signal are both linear frequency modulation signals, and the two radar transmission signals are subjected to the same phase modulation; The first echo signal and the second echo signal are used as reference signals for each other to perform matched filtering to achieve mutually matched phase modulation filtering.

2. The phase modulation filtering method based on mutual matching according to claim 1, characterized in that: The step of performing matched filtering on the first echo signal and the second echo signal as reference signals of each other to achieve mutually matched phase modulation filtering includes: The first echo signal is used as a reference signal, and conjugated with the reference signal before convolution with the second echo signal; and / or the second echo signal is used as a reference signal, and conjugated with the reference signal before convolution with the first echo signal.

3. The phase modulation filtering method based on mutual matching according to claim 1, characterized in that: The first echo signal and the second echo signal are dual-channel echo signals of a short-baseline dual-channel radar.

4. The phase modulation filtering method based on mutual matching according to claim 1, characterized in that: The first echo signal and the second echo signal are echoes of signals emitted by different radars respectively.

5. A phase modulation filtering device based on mutual matching, characterized in that: include: an echo acquisition module, used for acquiring a first echo signal and a second echo signal; the radar transmission signals corresponding to the first echo signal and the second echo signal are both linear frequency modulation signals, and the two radar transmission signals are subjected to the same phase modulation; The phase modulation filtering module is used to perform matched filtering on the first echo signal and the second echo signal, using them as reference signals for each other, to achieve mutually matched phase modulation filtering.

6. The phase modulation filtering device based on mutual matching according to claim 5, characterized in that: The phase modulation filtering module is specifically used to: use the first echo signal as a reference signal, conjugate the reference signal and then convolve it with the second echo signal, and / or use the second echo signal as a reference signal, conjugate the reference signal and then convolve it with the first echo signal.

7. The phase modulation filtering device based on mutual matching according to claim 5, characterized in that: The first echo signal and the second echo signal are dual-channel echo signals of a short-baseline dual-channel radar.

8. The phase modulation filtering device based on mutual matching according to claim 5, characterized in that: The first echo signal and the second echo signal are echoes of signals emitted by different radars respectively.

9. An electronic device, characterized in that: It includes a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor is used to implement the steps of the phase modulation filtering method based on mutual matching according to any one of claims 1 to 4 when executing a computer program stored in a memory.