High dynamic displacement demodulation method for millimeter wave interference radar weak motion measurement

Abstract

The invention discloses a high-dynamic displacement demodulation method for millimeter wave interference radar weak motion measurement. In the prior art, the dynamic range of a working interval is not enough, and weak motion with low signal-to-noise and deep sub-wavelength motion amplitude at the same time cannot be accurately measured, i.e., the working interval cannot cover the measurement scene. According to the high dynamic displacement demodulation method provided by the invention, the zero mean Gaussian white noise in the signal can be compressed while the displacement track is amplified by four times, and the dynamic range of the radar detectable weak motion in two dimensions of motion amplitude and signal-to-noise ratio is expanded, so that accurate measurement of low signal-to-noise ratio and small displacement motion is realized; and expansion of the detectable minimum displacement amplitude and the minimum signal-to-noise ratio boundary of the millimeter wave interference radar is completed. The specific implementation steps are as follows: firstly, a mode of directly utilizing an IQ signal to perform displacement demodulation in the prior art is abandoned, and a fourth-order cumulant signal of the IQ signal is adopted to perform displacement demodulation; theoretical derivation proves that the fourth-order cumulant signal of the IQ signal suppresses the zero-mean Gaussian white noise and quadruple amplifies the motion trail, so that the measurement precision of the weak motion displacement is greatly improved. Simulation and experiments prove that compared with the existing demodulation technology, the high-dynamic displacement demodulation technology provided by the invention makes up the shortages of the existing millimeter wave interference radar in the aspects of low signal-to-noise ratio, small displacement and weak motion measurement, and is suitable for the application fields of high precision, high-dynamic displacement, high-dynamic signal-to-noise ratio and the like; and the detectable scene of the millimeter wave interference radar is expanded.

Description

Technical Field

[0001] This invention relates to the technology of high-precision radar detection of weak target motion, specifically a high dynamic displacement demodulation method for weak motion measurement using millimeter-wave interferometric radar. Background Technology

[0002] In recent years, thanks to the high sensitivity and inherent penetration capability of millimeter-wave interferometric radar, it has been widely used in motion detection applications, such as... Figure 1 As shown, these include cardiopulmonary monitoring, mechanical vibration measurement, and gesture-based human-computer interaction. These advantages enable millimeter-wave interferometric radar to achieve precise displacement detection from deep subwavelength to multi-wavelength scales, with accuracy down to the micrometer level. Furthermore, the non-contact, portable, and low-cost characteristics of interferometric radar give it significant advantages in scenarios involving weak motion sensing.

[0003] Most research on precise displacement measurement using millimeter-wave interferometric radar focuses on small displacement motions or cross-wavelength motions of macroscopic objects, such as bridge vibration detection and motor vibration. These objects have large radar cross-sections and high signal-to-noise ratios (SNR) in their echo signals. Figure 2 As shown in (c). Some related research focuses on detecting the large-amplitude movements of small targets (with small radar cross-sections) in complex environments, such as detecting the swinging of an M5 nut. Although the radar reflection signal power generated by such targets is small, the resulting phase modulation trajectory is very long, such as... Figure 2 As shown in (b). However, few studies have solved the problem as described. Figure 2 (a) illustrates the challenges of measuring the weak motion of a target with a small radar cross-section and a motion amplitude in the deep subwavelength range.

[0004] conform to Figure 2 (a) Motion measurement scenarios frequently occur in high-precision detection applications, such as detecting chip etching processes and the movement of nanofilm materials. However, traditional millimeter-wave interferometric radar technology and demodulation methods cannot accurately detect weak motion displacements in such scenarios because the arc length of the target motion is submerged by noise and is smaller than the trajectory detection error that the noise may cause. In other words, existing methods cannot cover the dynamic range of the signal-to-noise ratio and motion length working intervals. Figure 2(a) shows the weak target motion. The Differential Cross Multiplication (DACM) and Modified Differential Cross Multiplication (MDACM) methods effectively avoid phase discontinuity problems and provide high linearity demodulation performance, making the detection of large-amplitude motion possible. However, these two methods are very sensitive to errors in weak received signals, such as DC offset, channel mismatch, and noise. Because these two methods involve a large number of differential and integral calculations, significant errors are introduced, and they require a high minimum signal-to-noise ratio (SNR) of at least 30 dB for high accuracy. The arctangent-based (ATAN) method heavily relies on the phase unwinding equation to overcome the limitations of the (–π / 2, π / 2) and (–π, π) demodulation domains, resulting in insufficient dynamic range in cross-wavelength displacement scenarios and low efficiency when handling displacement detection with large amounts of phase unwinding. Some alternative methods based on approximating the motion trajectory using the chord length of the IQ arc have also been proposed, but these methods are more sensitive to noise. Figure 2 (a) It cannot work in scenario . Summary of the Invention

[0005] This invention addresses the insufficient dynamic range of existing millimeter-wave interferometric radar technology, which cannot cover low signal-to-noise ratio deep subwavelength motion measurement scenarios. It proposes a high-dynamic displacement demodulation method for weak motion measurement using millimeter-wave interferometric radar. Instead of directly using IQ signals for displacement demodulation, this method employs the fourth-order cumulant of the IQ signals to achieve displacement demodulation. This allows for four-fold amplification of the displacement trajectory while compressing zero-mean Gaussian white noise in the signal, achieving a level of performance comparable to... Figure 2 (d) achieves the effect of accurately measuring target displacement in low signal-to-noise ratio and small displacement motion scenarios. It can also accurately detect cross-scale displacement motion, ultimately realizing a high dynamic range operating range for millimeter-wave interferometric radar in both signal-to-noise ratio and motion amplitude dimensions. This expands the minimum displacement amplitude and minimum signal-to-noise ratio boundaries detectable by millimeter-wave interferometric radar, ultimately achieving precise displacement demodulation coverage for more practical measurement scenarios, including low signal-to-noise ratio and deep subwavelength displacement.

[0006] This invention is achieved through the following technical solution: This invention relates to a high-dynamic displacement demodulation method for measuring weak motion in millimeter-wave interferometric radar. Its key feature is that it abandons the existing method of directly using IQ signals for displacement demodulation, instead employing the fourth-order cumulant of the IQ signals to complete displacement demodulation. This method can amplify the displacement trajectory by four times while compressing zero-mean Gaussian white noise in the signal, achieving high-dynamic displacement demodulation of weak target motion in both displacement amplitude and signal-to-noise ratio dimensions. The specific implementation includes the following steps: Step 1: Obtain the raw IQ signal: The millimeter-wave interferometric radar emits radio frequency electromagnetic waves. When these waves strike the target surface, they backscatter, generating an echo signal. The motion information of the echo signal is also modulated into its phase. After signal amplification and down-conversion by the millimeter-wave interferometric radar receiver, the IQ signal is obtained. Step 2: Obtaining the standardized IQ signal: Due to static object reflections in the target's environment and the imperfections in the millimeter-wave interferometric radar hardware, there are radio frequency leakage and sub-mixing issues, resulting in a DC bias signal in the original IQ signal. This DC bias signal needs to be removed through circular fitting calibration to obtain the standardized IQ signal. Step 3: Obtain the fourth-order cumulant (FOC) signal: Perform complex summation on the obtained IQ signals to obtain a complex signal. Calculate and obtain the fourth-order cumulant signal form of the complex signal based on the expression for the fourth-order cumulant of a one-dimensional random variable. Step 4: Demodulation of displacement based on the differential and conjugate multiplication of the fourth-order cumulants: Calculate the differential and conjugate forms of the four-section cumulant signals respectively, and demodulate the displacement motion by multiplying the two.

[0007] The standardized IQ signal refers to an IQ signal with equal amplitude and a 90° phase difference. and .

[0008] The complex signal referred to is: .

[0009] The fourth-order cumulant, as mentioned above, refers to a series of quantities in probability theory and statistics that provide information similar to moments, representing a set of values ​​for a random signal. Cumulants are closely related to the moments of random variables. For complex signals composed of IQ signals, due to the superposition of noise, they can be considered as one-dimensional random signals. Therefore, their fourth-order cumulants can be calculated. Since the fourth-order and higher cumulants of zero-mean Gaussian white noise are zero, the suppression of the zero-mean Gaussian white noise superimposed on the IQ signal is achieved. (One-dimensional random signal) The expression for the four-section cumulative quantity is as follows: The aforementioned displacement demodulation based on the differential and conjugate multiplication of fourth-order cumulants refers to the following: by differentiating and multiplying the four-section cumulant signals, the target motion displacement contained in the phase of the fourth-order cumulant signal is linearly restored to the amplitude, thereby completing the accurate extraction of the target motion.

[0010] Technical effect This invention utilizes the relationship that the phase of the fourth-order cumulant of the IQ signal is four times that of the target's motion displacement, and the characteristic that the fourth-order cumulant of Gaussian white noise is zero, to simultaneously achieve a fourfold amplification of the trajectory of weak targets and a significant compression of additive noise. This greatly improves the dynamic operating range of millimeter-wave interferometric radar in both signal-to-noise ratio and motion amplitude dimensions, enabling precise displacement demodulation of weak motions with low signal-to-noise ratio and small displacement.

[0011] Compared with existing technologies, this invention overcomes the problem that millimeter-wave interferometric radar cannot accurately detect weak motions with low signal-to-noise ratio and small displacement. This invention abandons the existing technology of directly using IQ signals for displacement demodulation, and uses the fourth-order cumulant of IQ signals to complete displacement demodulation. This significantly compresses noise while amplifying the motion trajectory four times, greatly improving the measurement accuracy of weak motion displacement. It makes up for the shortcomings of existing millimeter-wave interferometric radar in measuring weak motions with low signal-to-noise ratio and small displacement, and is suitable for applications with high dynamic displacement and high dynamic signal-to-noise ratio, with a wider range of application prospects. Attached Figure Description

[0012] Figure 1 A schematic diagram illustrating the detection of weak target motion by millimeter-wave interferometric radar; Figure 2 A schematic diagram of the arc length of the trajectory of a weak target; Figure 3 A flowchart of a high dynamic demodulation method; Figure 4 A comparison chart of dynamic working ranges for small displacement motion scenarios; Figure 5 A comparison chart of dynamic working ranges for large displacement motion scenarios; Figure 6 Diagram showing the setup for an experiment using millimeter-wave interferometric radar to detect the motion of a pencil target. Figure 7 The results of a pencil weak motion measurement experiment using a 24 GHz millimeter-wave interferometric radar with the demodulation method of this invention are shown. Figure 8 The results are from an experiment measuring pencil motion across wavelengths using a 24 GHz millimeter-wave interferometric radar employing the demodulation method of this invention. Detailed Implementation

[0013] like Figure 1As shown, the millimeter-wave interferometric radar involved in this embodiment refers to a sensor system composed of a transmitter, a receiver, a baseband circuit, and a data acquisition system. The transmitter generates a continuous sinusoidal signal of a fixed frequency using a voltage-controlled oscillator, which is then amplified by a power amplifier and transmitted via a transmitting antenna. The receiver receives the signal reflected from the target via a receiving antenna and amplifies the signal using a low-noise amplifier. The amplified signal is then down-converted by mixing it with the transmitted signal in a mixer to obtain the baseband IQ signal. The baseband circuit further amplifies the baseband IQ signal using an operational amplifier before sending it to the data acquisition system to obtain the original IQ signal. and The original IQ signal is calibrated by circular fitting to obtain the standardized IQ signal.

[0014] The original IQ signal includes: , ,in: The original I signal, The original Q signal, The signal amplitude, The carrier wavelength of millimeter-wave interferometric radar, For the target's slight movement, The radial distance from the target to the radar. This is the DC bias in the original I signal. This is the DC bias in the echo Q signal. Additive noise in the original I signal, This is additive noise in the original Q signal. and It is usually defined as zero-mean Gaussian white noise that is independent of each other, i.e. , This represents the calculation of mathematical expectation. This is residual phase noise, which can be ignored during close-range detection.

[0015] The circle fitting calibration includes: using the original IQ signal and Satisfy the equation Solve the equation to find the center of the circle. and the radius of the circle It can be observed that the coordinates of the center of the circle are the DC bias values ​​of the original IQ signal, i.e. , The radius of the circle is the signal amplitude of the original IQ signal, i.e. Therefore, the coordinates of the center of the circle can be subtracted from the original IQ signal to correspond to the... and Then divide by the radius of the circle. This completes the normalization of the signal, thereby obtaining the standardized IQ signal. and ,in, , , , According to the linearity of Gaussian random variables, and It is still zero-mean Gaussian white noise that is independent of each other.

[0016] like Figure 3 As shown, this embodiment relates to a high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar. It extracts weak motion by utilizing the relationship between the fourth-order cumulant of the IQ signal and the motion displacement, including: 1) Calculate the complex signal of the IQ signal. : ,in, The phase of the complex signal; It is zero-mean complex Gaussian white noise, i.e. ; Defined as a deterministic signal, The sum of a deterministic signal and a random signal is still a random signal, therefore... It is a one-dimensional random signal.

[0017] 2) Calculate the square of the complex signal Mathematical expectation : 1) Bring in and expand Based on the probability and statistical properties of random variables, if a deterministic signal does not exhibit rapid time changes, then the expected value of that deterministic signal is equal to the signal itself. Similarly, the expected value of the product of a deterministic signal and a random signal is equal to the product of the expected values ​​of the deterministic signal and the random signal. 3) Calculate the fourth power of the complex signal Mathematical expectation : 1) Bring in and expand .

[0018] 4) Calculate the fourth-order cumulant signal : The calculations obtained in 3) and 4) and Substituting and simplifying, we get Since all odd-order moments of zero-mean Gaussian white noise are zero, and the cumulants of fourth order and above are also zero, therefore... The third moment is zero, that is... , The fourth-order cumulant is also zero, that is... ,so It can be further simplified to Based on the formulaic relationship between the fourth-order cumulant signal and the phase, we can conclude that: Zero-mean Gaussian white noise was removed, and the phase was amplified fourfold, meaning the trajectory of the weak motion signal was amplified fourfold. This changed the relationship between the motion signal trajectory and noise in the weak motion measurement scenario from its original state. Figure 2 (a) transformed into Figure 2 (d) That is, the motion is no longer drowned out by noise, thereby expanding the dynamic range and greatly improving the accuracy of millimeter-wave interferometric radar in measuring weak motion.

[0019] 5) Demodulation based on the differential and conjugate multiplication shift of fourth-order cumulants: ,in, It is the differential form of the fourth-order cumulant. This is the conjugate form of the four-section cumulative quantity. This expression also does not suffer from phase discontinuity issues; therefore, this method can also demodulate motion amplitude across wavelengths.

[0020] The phase discontinuity refers to the fact that when the length of the target displacement trajectory exceeds π or is not within the range of the first or fourth quadrant, the demodulated displacement signal will have discontinuities, which is called the phase discontinuity problem.

[0021] Through simulation experiments, such as Figure 4 and Figure 5 As shown, all simulations are based on a 24 GHz millimeter-wave interferometric radar with a sampling frequency of 10 kHz. The relative root mean square error (RRMSE) of motion measurement is compared between the high dynamic displacement demodulation method proposed in this invention and six existing demodulation methods under different signal-to-noise ratios and motion amplitudes. The working region of the demodulation method is defined as the region where the RRMSE remains below 1% (or −20 dB). Figure 4 To compare the working range of this invention with six existing demodulation methods within a simulated signal-to-noise ratio range of -10 dB to 60 dB, when the target motion amplitude scans from 12.5 μm (1 / 1000λ) to 3.125 mm (0.25λ), the following comparisons were made. Figure 4 (g) represents the working area obtained during motion demodulation simulation using the high dynamic displacement demodulation method proposed in this invention. Figure 4(a)-(f) show the working range obtained by existing demodulation methods when demodulating simulated motion. The high-dynamic displacement demodulation method exhibits a wider working range compared to traditional methods. Notably, even with an SNR of 35 dB and a displacement motion amplitude of 1 / 1000λ, the RRMSE of the motion recovered by the high-dynamic displacement demodulation method proposed in this invention remains below 10%, while existing demodulation methods require an SNR exceeding 50 dB to achieve similar performance. Moreover, existing demodulation methods rely on adjacent chord angle accumulation (ACAA) and polar coordinate chord accumulation (PCA) techniques that approximate the motion trajectory with chord length. Figure 7 The RRMSE of the recovered motion in (e) and (f) is greater than the actual motion itself, meaning that demodulation has completely failed because the short string length variation is masked by noise. According to Figure 4 The simulation results show that the demodulation method proposed in this invention covers the largest dynamic range in small displacement motion scenarios with a motion amplitude of less than 0.25λ, and achieves the highest measurement accuracy in low signal-to-noise ratio and small displacement motion tests. It fills the gap in existing demodulation methods that cannot accurately measure weak motion with low signal-to-noise ratio and small displacement, and effectively expands the working range of millimeter-wave interferometric radar when measuring weak motion.

[0022] Figure 5 To compare the working range of the high dynamic demodulation method proposed in this invention with that of six existing demodulation methods within the simulated signal-to-noise ratio range of -10 dB to 60 dB, when the target motion amplitude scans from 3.125 mm (0.25λ) 1 / 1000λ to 15.625 mm (1.25λ). Figure 5 The existing DAM and MDACM demodulation methods in (a) and (b) require an SNR of over 40 dB to enter the operating region with an RRMSE of <1%. When the original IQ signal SNR is 30 dB, the RRMSE of the displacement motion extracted by these two demodulation methods is approximately 10%. Figure 5 The arctangent demodulation method in (c) requires phase unwinding equations to solve the discontinuity problem, consuming a large amount of computational resources. Furthermore... Figure 5 The arctangent and arcsine demodulation methods in (c) and (d) require an SNR > 30 dB in their operating region. In contrast, Figure 5 (g) The high dynamic displacement demodulation method proposed in this invention still maintains the widest working range, requires an SNR of less than 18 dB, and the demodulated displacement motion within the working range has the lowest RRMSE (in Figure 5 (g) indicates the dark blue area, thus demonstrating the minimal requirements for the hardware link budget of millimeter-wave interferometric radar. Furthermore, the high-dynamic displacement demodulation method proposed in this invention does not suffer from phase discontinuity issues. Overall, Figure 4 and Figure 5The high dynamic displacement demodulation technique proposed in this invention provides the widest working range, alleviates the pressure on the hardware link budget of millimeter-wave interferometric radar, and exhibits superior performance in motion extraction, especially when detecting challenging targets with small displacement and low signal-to-noise ratio, demonstrating high dynamics, high robustness and high accuracy.

[0023] After specific experiments, the experimental setup is as follows: Figure 6 As shown, a pencil, as a weakly reflective target with a small radar cross-section, is fixed on a standard slide table (Zaber X-LDM060C-AE54D12). The slide table induces a sinusoidal motion of 0.5 Hz in the pencil. The motion amplitudes were 8 µm (2 / 3125λ @ 24 GHz) and 12.5 mm (λ @ 24 GHz), respectively, to verify the accuracy of the proposed high-dynamic displacement demodulation method in measuring weak motion and cross-wavelength motion under low SNR conditions. Other settings were as follows: the millimeter-wave interferometric radar emitted a continuous sinusoidal signal, and the frequency... GHz, carrier wavelength cm, distance between pencil and radar m, sampling frequency kHz.

[0024] Figure 7 The displacement demodulation results are shown when the probe pencil's motion amplitude is 8 µm (deep subwavelength motion). Among them, Figure 7 (a) shows the original IQ signal, indicating signal fluctuations caused by the target's motion, with the useful signal being overwhelmed by noise. Figure 7 (b)–(e) show the demodulation results of the existing demodulation method. Clearly, the traditional method failed to reconstruct the displacement waveform, verifying that the working region of the existing demodulation method cannot cover weak movements with low signal-to-noise ratio and small displacements, as demonstrated in the simulation results. In contrast, Figure 7 (f) shows the fourth-order cumulant signal, clearly displaying the periodic waveform formed by pencil motion modulation. Thanks to the high dynamic demodulation method proposed in this invention, zero-mean Gaussian white noise and phase distortion can be suppressed. Amplification is performed by four times. The motion trajectory demodulated using the proposed demodulation method is as follows: Figure 7 As shown in (g), the results are highly consistent with the actual motion (GT) of the pencil, with a root mean square error (RMSE) of only 1.03 µm, proving that the method can measure the displacement of weak motion with high precision.

[0025] Figure 8 The displacement demodulation results are shown when the probe pencil moves by an amplitude of 12.5 mm. Figure 8 (a) shows the original IQ signal waveform. Figure 8(b)–(g) present the experimental results of six existing demodulation methods. The ACAA demodulation method still fails to demodulate, and the PCA demodulation method can only barely measure the period of the pencil motion, but the recovered motion trajectory is severely distorted compared with the real motion, and the RMSE is as high as 3441.94 µm. Figure 8 (h) shows the motion waveform extracted by the high-dynamic displacement demodulation method proposed in this invention. The demodulation error RMSE is <0.5%, and the demodulation accuracy is an order of magnitude higher than that of existing DAM and MDACM demodulation methods. The demodulation method proposed in this invention achieves accurate motion trajectory reconstruction. Existing arctangent and arcsine methods also have demodulation errors RMSE of less than 0.5%, but the arctangent method requires the assistance of phase unwinding equations, and the arcsine demodulation method relies on arcsine operations; both are very computationally intensive. Therefore, in summary, the demodulation method proposed in this invention still has the widest dynamic range, the highest computational efficiency, and avoids the phase discontinuity problem.

[0026] To more comprehensively demonstrate the accuracy of the high dynamic demodulation method in extracting targets under different SNR conditions and displacement amplitude scenarios, multiple sets of experiments were conducted. Using... Figure 6 A small corner reflector (CR2) and a pencil were used as targets for testing under multiple sinusoidal motion amplitudes. The experimental results are summarized in Table I. Table I shows that, in all displacement amplitudes of the two targets measured, the RMSE of the motion trajectory reconstructed by the high-dynamic displacement demodulation method proposed in this invention is consistently better than the results obtained by existing demodulation methods, demonstrating the high dynamic and high-precision performance of the proposed method, which is applicable to various scenarios of millimeter-wave interferometric radar detection.

[0027] Table I: Displacement demodulation results for different motion amplitudes and detected targets Compared with existing technologies, this method performs fourth-order cumulant analysis on the IQ signal of millimeter-wave interferometric radar, overcoming the limitations of low demodulation accuracy or even demodulation failure when measuring weak motion. By suppressing noise and amplifying the target's motion trajectory by four times, this method expands the dynamic working range and displacement measurement accuracy of millimeter-wave interferometric radar, ultimately improving the detection capability of millimeter-wave interferometric radar for weak motion.

[0028] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A high-dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar, characterized in that, Abandoning the existing method of directly using IQ signals for displacement demodulation, this method employs the fourth-order cumulant of the IQ signals to complete displacement demodulation. This can amplify the displacement trajectory by four times while compressing zero-mean Gaussian white noise in the signal, achieving high dynamic displacement demodulation of weak target motion in both displacement amplitude and signal-to-noise ratio dimensions. The specific implementation includes the following steps: Step 1: Obtain the raw IQ signal: The millimeter-wave interferometric radar emits radio frequency electromagnetic waves. When these waves strike the target surface, they backscatter, generating an echo signal. The motion information of the echo signal is also modulated into its phase. After signal amplification and down-conversion by the millimeter-wave interferometric radar receiver, the IQ signal is obtained. Step 2: Obtaining the standardized IQ signal: Due to static object reflections in the target's environment and the imperfections in the millimeter-wave interferometric radar hardware, there are radio frequency leakage and sub-mixing issues, resulting in a DC bias signal in the original IQ signal. This DC bias signal needs to be removed through circular fitting calibration to obtain the standardized IQ signal. Step 3: Obtain the fourth-order cumulant (FOC) signal: Perform complex summation on the obtained IQ signals to obtain a complex signal. Calculate and obtain the fourth-order cumulant signal form of the complex signal based on the expression for the fourth-order cumulant of a one-dimensional random variable. Step 4: Demodulation of displacement based on the differential and conjugate multiplication of the fourth-order cumulants: Calculate the differential and conjugate forms of the four-section cumulant signals respectively, and demodulate the displacement motion by multiplying the two.

2. The high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar according to claim 1, characterized in that, The original IQ signal refers to: , ,in: The original I signal, The original Q signal, The signal amplitude, The carrier wavelength of millimeter-wave interferometric radar, For the target's slight movement, The radial distance from the target to the radar. This is the DC bias in the original I signal. This is the DC bias in the echo Q signal. This is additive noise in the original I signal. Additive noise in the original Q signal, and It is usually defined as zero-mean Gaussian white noise that is independent of each other, i.e. , This represents the calculation of mathematical expectation. This is residual phase noise, which can be ignored during close-range detection.

3. The high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar according to claim 1, characterized in that, The circle fitting calibration includes: using the original IQ signal and Satisfy the equation Solve the equation to obtain the coordinates of the center of the circle. and the radius of the circle It can be observed that the coordinates of the center of the circle are the DC bias values ​​of the original IQ signal, i.e. , The radius of the circle is the signal amplitude of the original IQ signal, i.e. Therefore, the coordinates of the center of the circle can be subtracted from the original IQ signal to correspond to the... and Then divide by the radius of the circle. This completes the normalization of the signal, thereby obtaining the standardized IQ signal. and ,in, , , , According to the linearity of Gaussian random variables, and It is still zero-mean Gaussian white noise that is independent of each other.

4. The high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar according to claim 1, characterized in that, The standardized IQ signals refer to I(n) and Q(n) signals with equal amplitude and a 90° phase difference.

5. The high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar according to claim 1, characterized in that, The complex signal referred to is: ,in, The phase of the complex signal; It is zero-mean complex Gaussian white noise, i.e. ; Defined as a deterministic signal, The sum of a deterministic signal and a random signal is still a random signal, therefore... It is a one-dimensional random signal.

6. The high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar according to claim 1, characterized in that, The fourth-order cumulant, as mentioned above, refers to a series of quantities in probability theory and statistics that provide information similar to moments, representing a set of values ​​for a random signal. Cumulants are closely related to the moments of random variables. For complex signals composed of IQ signals, due to the superposition of noise, they can be considered as one-dimensional random signals. Therefore, their fourth-order cumulants can be calculated. Since the fourth-order and higher cumulants of zero-mean Gaussian white noise are zero, the suppression of the zero-mean Gaussian white noise superimposed on the IQ signal is achieved. (One-dimensional random signal) The expression for the four-section cumulative quantity is as follows: It can be simplified to , Zero-mean complex Gaussian white noise The third moment, for The fourth-order cumulant, therefore , ,so It can be finally simplified to , Zero-mean Gaussian white noise was removed, and the phase was amplified fourfold, meaning the trajectory of the weak motion signal was amplified fourfold. The relationship between the motion signal trajectory and noise in the weak motion measurement scenario changed from Figure 2(a) to Figure 2(d), meaning the motion was no longer submerged by noise, thus expanding the dynamic range and greatly improving the accuracy of millimeter-wave interferometric radar in measuring weak motion.

7. The high dynamic displacement demodulation method for weak motion measurement in millimeter-wave interferometric radar according to claim 1, characterized in that, The aforementioned demodulation based on the differential and conjugate multiplication shift of fourth-order cumulants refers to: ,in, It is the differential form of the fourth-order cumulant. This is the conjugate form of the four-section cumulative quantity. This expression also does not suffer from phase discontinuity issues; therefore, this method can also demodulate motion amplitude across wavelengths.

8. The fourth-order cumulant-based differential and conjugate multiplication shift demodulation according to claim 7, characterized in that, The phase discontinuity refers to the fact that when the length of the target displacement trajectory exceeds π or is not within the range of the first or fourth quadrant, the demodulated displacement signal will have discontinuities, which is called the phase discontinuity problem.

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