Multi-channel signal receiving calibration method and device based on cross-spectrum method

Abstract

The invention discloses a multi-channel signal receiving calibration method and device based on a cross-spectrum method, and relates to the field of signal processing, and the method comprises the following steps: S1, configuring system parameters, and generating a test signal; s2, performing frequency domain transformation on the test signal; s3, performing cross spectrum analysis on the test signal; s4, performing time delay extraction on the test signal; s5, performing compensation calibration; and S6, experimental verification. According to the multi-channel signal receiving calibration method and device based on the cross-spectrum method, by optimizing a cross-spectrum calculation process, introducing high-resolution time delay estimation and improving a phase compensation mechanism, the problems existing in the prior art are effectively solved, time delay and amplitude inconsistency between channels are accurately estimated and corrected, and the accuracy of calibration is improved. The problems that the calibration precision is limited due to high calculation complexity and poor real-time performance of a traditional method, the time delay estimation performance is reduced in a low signal-to-noise ratio environment, and the requirements of a modern multi-channel system for high synchronism and low delay cannot be met are solved.

Description

Technical Field

[0001] This invention relates to the field of signal processing, and in particular to a multi-channel signal receiving calibration method and apparatus based on the cross-spectral method. Background Technology

[0002] In multi-channel RF receiving systems, inter-channel consistency calibration is a critical factor in ensuring system performance. Due to factors such as manufacturing process deviations, temperature variations, component aging, and differences in transmission paths, inconsistencies in time delay and amplitude response are inevitable among the receiving channels. Unlike random noise, this type of channel mismatch has deterministic system characteristics, and its impact depends on the signal bandwidth, the number of channels, and the system operating environment. Especially in broadband multi-channel applications, this mismatch can lead to decreased signal coherence, severely affecting the performance of core functions such as beamforming, directional positioning, and signal detection.

[0003] In modern phased array radar, massive MIMO communication, and sonar detection systems, high-precision synchronous calibration of multi-channel received signals is of paramount importance. Channel consistency, as a fundamental guarantee of system performance, directly determines the accuracy of spatial spectrum estimation, beam pointing accuracy, and signal processing gain. By accurately calibrating the time delay and phase deviation between channels, the system's angular resolution, anti-jamming capability, and target detection probability can be effectively improved, thereby enhancing overall combat effectiveness.

[0004] From the perspective of signal processing implementation, multi-channel calibration technology mainly relies on methods such as cross-correlation analysis, frequency domain equalization, or adaptive filtering. In the literature "Dang Haohuai, Chen Juntao. A fast adaptive wideband multi-channel phase compensation method [J]. Information Research, 2022, 48(03)", a fast adaptive phase compensation method based on FPGA control is proposed. It uses an internal frequency synthesizer to scan in steps (2-18GHz, 20MHz step) and calculates the compensation value in real time. Although it shortens the full-band calibration time to 56 milliseconds, which is significantly better than the software method, this "ergodic" calibration strategy still requires sequential measurement and calculation of a large number of discrete frequency points. When the number of system channels increases and the bandwidth expands, more intensive frequency sampling and more complex compensation networks are required to ensure calibration accuracy. This will lead to an exponential increase in hardware resource consumption and computational complexity. In the literature "Ming Wenhua. Implementation of a channel equalization method in a wideband digital array radar [J]. Information Technology and Informatization, 2022(08)", a wideband channel equalization engineering implementation method based on frequency domain least squares fitting is proposed. This method obtains the channel frequency response by combining internal / external field correction and uses the weighted least squares method to solve for the FIR equalization filter coefficients. Simulation and field measurements show that it can effectively correct inter-channel amplitude and phase errors and improve beamforming performance. However, the core algorithm of this method involves solving canonical equations, and its calculation process includes large matrix multiplication, conjugate transpose, and highly complex inversion operations. As the number of system channels increases and the bandwidth expands, the computational load will increase dramatically, making it difficult to meet the low-latency requirements of real-time calibration and dynamic tracking of multi-channel signals in modern electronic systems.

[0005] Furthermore, while traditional cross-correlation-based time delay estimation methods are simple in principle, their performance degrades significantly in low signal-to-noise ratio environments, and their accuracy for fractional time delay estimation is limited. Although cross-spectral calibration techniques theoretically offer higher time delay estimation accuracy, they still face challenges in practical engineering implementation, including high computational complexity, poor real-time performance, and sensitivity to initial phase. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-channel signal receiving calibration method and apparatus based on the cross-spectrum method, thereby solving the problems mentioned in the background art.

[0007] To achieve the above objectives, this invention provides a multi-channel signal reception calibration method based on the cross-spectrum method, comprising the following steps: S1. Generate test signals: Configure system parameters and generate test signals by simulating the actual environment; S2. Perform cross-spectral analysis on the test signal: calculate the cross-power spectral density and extract amplitude and phase information; S3. Perform cross-spectral calculation on the test signal: Perform cross-spectral analysis by calculating the cross power spectral density; S4. Time delay extraction of test signal: Peak detection and time delay calculation of cross power spectral density; S5. Compensation Calibration: Generate channel compensation parameters based on relative time delay to perform phase and time delay compensation on multi-channel signals; S6. Conduct experimental verification using indicators.

[0008] Preferably, the system parameters in S1 include sampling frequency, signal bandwidth, and pulse width.

[0009] Preferably, the specific steps of S1 are as follows: S11. Generate the linear frequency modulation test signal LFM; S12. Introduce inter-channel time delay deviation and simulate the time delay of LFM by frequency domain phase rotation; S13. Add Gaussian white noise to simulate the actual environment and generate a test signal.

[0010] Preferably, the specific steps of S2 are as follows: S21. Perform FFT on the reference calibration signal and the time delay signal respectively; S22. The zero frequency is moved to the center of the spectrum by using the spectrum rearrangement operation function fftshift to center the spectrum.

[0011] Preferably, the specific formula for the FFT in S21 is as follows: ; ; in, For relative time delay, Let f be the complex representation of the signal in the frequency domain, where f is the frequency variable. Here, t is the original signal, e is the base of the natural logarithm, and j is the imaginary unit. Pi This introduces the complex representation of the signal in the frequency domain after channel delay.

[0012] Preferably, the specific steps of S3 are as follows: S31. Calculate the cross-power spectral density of the reference calibration signal and the time-delay signal. The formula for calculating the cross-power spectral density is as follows: ; in, This represents the cross-power spectral density of the signals from the two received channels in the frequency domain. Let X be the conjugate form of the complex number X. Let X(f) be the complex conjugate representation of the signal X(f) in the frequency domain; S32. Perform a Fourier transform on the cross-power spectral density to extract the amplitude and phase information of the cross-power spectrum, and perform cross-spectral analysis. The specific formula for the Fourier transform is as follows: ; in, The peak position represents the signal delay, that is, the time difference between the signal transmission between the two receiving channels. This is calculated... The difference between the peak positions is used to obtain the time difference between the two received signals, which is then used for time delay calibration.

[0013] Preferably, the specific steps of S4 are as follows: S41. Perform a high-resolution FFT on the cross-power spectrum and center the time domain using fftshift; S42. Perform peak detection and time delay calculation on the cross-power spectral density.

[0014] Preferably, the specific steps of S42 are as follows: S421. Locate the peak position of the cross-correlation function, and locate the time delay position by detecting the peak position; S422. Calculate the delay range based on the delay location; S423. Calculate the precise time delay value using the frequency domain-time domain mapping relationship, and map the peak position to the time delay value; S424. Output the delay value in microseconds.

[0015] Preferably, the specific steps of S5 are as follows: S51. Generate corresponding channel compensation parameters based on the delay value. The channel compensation parameters include phase and delay compensation. S52. By applying phase and time delay compensation to the channel signals, the reference calibration signal and the time delay signal are time-delay calibrated so that the compensated multi-channel signals are aligned on the time axis.

[0016] An apparatus for a multi-channel signal reception calibration method based on the cross-spectrum method, comprising: The cross-spectrum estimation and parameter extraction module is used to generate linear frequency modulation test signals, perform frequency domain transformation and cross power spectrum calculation on multi-channel signals, and accurately estimate the relative time delay and amplitude difference between channels. The calibration coefficients are applied to the signal output module to generate frequency domain compensation coefficients, perform real-time calibration on the original time-delay signal, and output high-precision synchronous multi-channel signals.

[0017] Therefore, the present invention employs the above-mentioned multi-channel signal receiving calibration method and apparatus based on the cross-spectrum method, which has the following beneficial effects: (1) This invention employs cross-spectral analysis and time delay extraction to achieve a high-precision phase compensation mechanism, enabling time delay estimation and real-time correction, effectively improving the consistency of multi-channel systems. Based on phase decoupling and frequency-domain linear phase rotation using cross-power spectrum, the relative time delay and amplitude deviation between channels can be accurately extracted. Furthermore, by dynamically adjusting the compensation coefficient, the problem of decreased time delay estimation accuracy and inability to meet the high synchronization requirements of broadband systems under low signal-to-noise ratio conditions, as addressed by traditional methods, is solved. Combining cross-spectral calculation and phase decoupling in the code implementation, this method significantly reduces beamforming errors and signal distortion while ensuring calibration accuracy.

[0018] (2) This invention adopts a pure digital signal processing flow. By optimizing the cross-spectrum calculation and peak detection algorithms, it avoids the complex matrix operations and inversion operations in traditional calibration techniques. It has low computational complexity, low resource consumption, and is easy to implement in real time on embedded platforms such as FPGA or DSP. The FFT transformation and frequency domain compensation in the code only involve basic operations and do not rely on external hardware calibration equipment, which enables the method to quickly adapt to the system requirements of different channel numbers and bandwidths.

[0019] (3) This invention combines cross-spectral analysis with adaptive compensation, and dynamically updates calibration parameters by tracking channel characteristic changes in real time, thus ensuring the long-term stability of the system. The calibration and compensation links work together, with cross-spectral analysis providing high-precision input and the compensation mechanism outputting a consistent signal, effectively improving the accuracy and adaptability of the multi-channel receiving system, especially suitable for applications with high real-time requirements such as phased array radar and large-scale MIMO.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is a detailed flowchart of an embodiment of a multi-channel signal receiving calibration method and apparatus based on the cross-spectrum method of the present invention; Figure 2 This is a complete flowchart of a multi-channel signal calibration technology according to an embodiment of a multi-channel signal receiving calibration method and apparatus based on the cross-spectrum method of the present invention; Figure 3 This is a time-domain waveform and frequency-domain amplitude spectrum of channel 1 in an embodiment of a multi-channel signal receiving calibration method and apparatus based on cross-spectrum method of the present invention. Figure 4 This is a time-domain waveform and frequency-domain amplitude spectrum of channel 2 in an embodiment of a multi-channel signal receiving calibration method and apparatus based on cross-spectrum method of the present invention. Figure 5 This is a comparison diagram of dual-channel signals from an embodiment of a multi-channel signal receiving calibration method and apparatus based on the cross-spectrum method of the present invention. Figure 6 This is a time-domain waveform of the correlation spectrum of an embodiment of a multi-channel signal receiving calibration method and apparatus based on cross-spectrum method of the present invention. Figure 7 This is a correlation spectrum-amplitude spectrum of an embodiment of a multi-channel signal receiving calibration method and apparatus based on cross-spectrum method of the present invention; Figure 8 This is a correlation spectrum-phase spectrum (unwinding) diagram of an embodiment of a multi-channel signal receiving calibration method and apparatus based on cross-spectrum method of the present invention; Figure 9 This is a delay estimation result diagram of an embodiment of a multi-channel signal receiving calibration method and apparatus based on the cross-spectrum method of the present invention. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0024] Example Please see Figures 1-9 This invention provides a multi-channel signal reception calibration method based on cross-spectrum analysis. This method is applied to multi-channel signal processing systems and includes cross-spectrum analysis, high-precision time delay estimation, and adaptive compensation. The principle is as follows: During multi-channel signal reception, the cross-power spectrum between channels is first calculated through cross-spectrum analysis to extract relative time delay and amplitude deviation characteristics. Then, the time delay value is accurately estimated using phase dewinding and frequency domain peak detection techniques. Finally, the adaptive compensation stage dynamically applies correction coefficients to eliminate inter-channel differences in real time. This technology achieves high-precision spatiotemporal alignment of multi-channel signals through pure digital signal processing. This method effectively balances calibration accuracy and real-time requirements, meeting the stringent requirements for multi-channel consistency in applications such as phased array systems and large-scale MIMO.

[0025] This embodiment calculates the time delay deviation between channels through cross-spectrum estimation and achieves accurate time delay measurement using frequency-to-time domain transformation. The calibration process mainly includes signal generation and parameter configuration, frequency domain transformation, cross-spectrum calculation, and time delay extraction. The specific steps are as follows: S1, Design signal generation and parameter configuration stage.

[0026] S11. Set system parameters: Configure key parameters such as sampling frequency, signal bandwidth, and pulse width.

[0027] S12, Generate test signal.

[0028] S121. Generate a linear frequency modulation test signal, represented by a complex baseband signal. The complex form facilitates subsequent frequency domain processing. ; in, This represents the complex baseband representation of the linear frequency modulated test signal in the time domain. t For time variables, and The in-phase and quadrature components of the linear frequency modulated signal are generated using the chirp function.

[0029] After the S122 and LFM signals are generated, the time delay of the analog channel signal is introduced.

[0030] By introducing inter-channel time delay deviation, time delay simulation is achieved through frequency domain phase rotation, as shown in the following formula: ; in, To introduce a time-domain representation of the signal after channel delay, The relative time delay between channels e is the base of the natural logarithm. For frequency coordinates, This represents the Fourier transform.

[0031] S123. Add Gaussian white noise to simulate the actual environment: ; in, To represent the signal with added noise in the time domain, s ( t This represents the original test signal without added noise in the time domain. n ( t () is a noise signal that meets the signal-to-noise ratio requirements.

[0032] S2, Design the frequency domain transformation stage.

[0033] S21. Perform cross-spectral calculation on the reference calibration signal and the time delay signal, and use Fast Fourier Transform (FFT) to accelerate frequency domain conversion and perform frequency domain analysis.

[0034] Set two primitives to receive signals Perform FFT on the signals from channel 1 and channel 2 respectively, and set the FFT length. The specific formula for FFT is as follows: ; in, X 1 represents the complex number representation of the first received channel signal in the frequency domain. X 2 represents the complex number representation of the second receiving channel signal in the frequency domain. s 1 represents the time-domain signal of the first receiving channel. s 2 represents the time-domain signal of the second receiving channel.

[0035] S22, Spectrum Centralization.

[0036] The zero frequency is shifted to the center of the spectrum using the fftshift operation, thus centering the spectrum. The specific formula is as follows: ; in, This is the function for spectrum rearrangement. This is the frequency domain representation of the first received channel signal after the fftshift operation. This is the frequency domain representation of the second received channel signal after the fftshift operation. Let be the complex representation of the first received channel signal in the frequency domain. This is the complex representation of the second receiving channel signal in the frequency domain.

[0037] S3. Design the cross-spectral calculation step.

[0038] S31. Calculate the cross power spectrum.

[0039] The specific formula for calculating the cross-power spectral density based on frequency domain signals is as follows: ; in, For cross power spectral density, This indicates the conjugate operation.

[0040] S32, Cross-spectral analysis.

[0041] The amplitude and phase information of the cross power spectrum are extracted, and cross-spectral analysis is performed.

[0042] The formula for calculating the amplitude spectrum is as follows: ; in, The amplitude spectrum of the cross power spectral density. Let be the cross-power spectral density function between signal x and signal y.

[0043] The amplitude spectrum is converted to a dB scale using the following formula: ; in, Let f be the decibel representation of the cross-power spectrum amplitude A(f). The amplitude spectrum of the cross-power spectral density; The phase spectrum is unwound, and the formula for calculating the phase spectrum is as follows: ; in, The phase spectrum is the cross-power spectrum. This is the phase extraction operator.

[0044] S4, Design delay extraction stage.

[0045] S41. Perform a high-resolution FFT on the cross-power spectrum and center it in the time domain using fftshift.

[0046] A high-resolution FFT is performed on the cross-power spectrum. The specific formula for the high-resolution FFT is as follows: ; in, The cross-correlation function is obtained from the cross-power spectrum via Fourier transform. This is the Fourier transform operator.

[0047] The time domain is centered using the fftshift (spectrum / time domain centering operation). The specific formula for fftshift is as follows: ; in, It is the amplitude sequence of the cross-correlation function.

[0048] S42. Perform peak detection and time delay calculation on the cross-power spectral density.

[0049] S421. Locate the peak position of the cross-correlation function, and determine the time delay position by detecting the peak position. The specific formula is as follows: ; in, This is the index value corresponding to the position of maximum amplitude in the cross-correlation function. The operator for finding the extreme value of the corresponding independent variable. This is the time-domain representation of the cross-correlation function after the fftshift operation.

[0050] Peak detection is achieved by analyzing the cross-correlation function. The amplitude values ​​are iterated and compared to determine the peak index corresponding to the maximum value. Since the FFT shift is applied, zero latency corresponds to the position fftlen / 2. Therefore, the actual latency index is: ; in, For index variables in the sequence, This is the length parameter of the Fast Fourier Transform.

[0051] S422. After obtaining the peak index position in step S421, determine the number of time delay sampling points based on the difference between the peak index and the spectrum center position: ; Based on sampling frequency Fs Convert the number of sampling points into time delay: ; because If the transform length is fftlen, then the maximum measurable time delay range corresponding to the cross-correlation function is: ; in, This represents the search range with time delay.

[0052] S423. Calculate the mapping from the peak position to the precise time delay value using the frequency-time domain mapping relationship: ; in This refers to the number of discrete sampling points used when performing a Fast Fourier Transform.

[0053] In this embodiment, the delay value is output in microseconds: ; in, Inter-channel delay estimation results expressed in microseconds This represents the relative time delay variable between channels.

[0054] The time delay value is input as a compensation parameter into the subsequent compensation and calibration process.

[0055] S5, Compensation Calibration Steps After obtaining the relative time delays between the multi-channel signals, corresponding channel compensation parameters are generated based on the relative time delays. Phase and time delay compensations are then applied to each received channel signal to align the compensated multi-channel signals on the time axis, achieving synchronous calibration of the multi-channel signals. Specifically: Obtain the relative time delay value between channels Then, calculate the corresponding number of delayed sampling points based on the sampling frequency Fs: A phase compensation function is constructed using frequency domain compensation: in For the frequency variable, the compensation function is multiplied by the frequency domain signal of the corresponding channel: The compensated time-domain signal is then obtained through inverse fast Fourier transform, thereby achieving accurate time delay compensation.

[0056] This embodiment uses the obtained time delay value to perform time delay calibration on the reference calibration signal and the time delay signal. It uses frequency domain transformation to adjust the phase of the signal to achieve time delay calibration, and finally outputs the calibrated signal.

[0057] S6. Experimental verification.

[0058] Please see Figures 3-9 The method in this embodiment is used to design and verify a multi-channel signal reception calibration method.

[0059] This embodiment implements and verifies the method for multi-channel signal calibration based on cross-correlation spectrum using the following metrics: (1) Complex sampling frequency of the signal ; (2) The transmitted signal is a linear frequency modulated signal with a pulse width of 40μs and a bandwidth of 80MHz; (3) Simulate the multi-channel time delay characteristics, perform calibration processing, and calculate the cross-correlation spectrum.

[0060] Through this invention, we have successfully calculated the time delay between two channel signals, and can generate a calibrated final output signal. For example... Figures 3-9 As shown, the evolution and key characteristics of the signal throughout the entire processing flow are clearly illustrated: Figure 3 The time-domain waveform and spectral characteristics of the channel 1 reference calibration signal are shown. This signal demonstrates the modulation characteristics of a linear frequency modulated signal in the time domain. The real and imaginary parts correspond to the in-phase (I) and quadrature (Q) components of the signal, providing an ideal excitation source for subsequent channel signal characteristic analysis and calibration. Figure 4 The time-domain waveform and spectral characteristics of the delayed signal in channel 2 are shown. It can be seen that a time delay has been introduced into this signal. Figure 5 The comparison between the channel 1 signal and the channel 2 signal is shown. Channel 1 is the reference calibration signal, which represents the time delay signal, while the channel 2 signal introduces a time delay, which can intuitively show the waveform offset caused by the time delay. Figure 6The real part (blue solid line) and imaginary part (red solid line) of the cross power spectrum (frequency domain) are shown to verify whether the cross spectrum calculation is correct and whether the frequency domain correlation is significant. Figure 7 The correlation spectrum-amplitude spectrum is displayed, which allows for a clearer observation of correlation changes within the frequency band. Figure 8 The diagram shows the correlation spectrum-phase spectrum (unwinding). Unwinding eliminates phase jumps and makes the phase continuous. This diagram is a key input for time delay extraction and is used to check the quality of the phase data. Figure 9 The delay estimation results are shown, with the delay value (1.51 ns in this example) directly output at the peak position, thereby generating the final calibrated output signal.

[0061] The present invention also provides an apparatus for a multi-channel signal reception calibration method based on the cross-spectrum method, comprising: The cross-spectrum estimation and parameter extraction module is used to generate linear frequency modulation test signals, perform frequency domain transformation and cross power spectrum calculation on multi-channel signals, and accurately estimate the relative time delay and amplitude difference between channels. The calibration coefficients are applied to the signal output module to generate frequency domain compensation coefficients, perform real-time calibration on the original time-delay signal, and output high-precision synchronous multi-channel signals.

[0062] The device achieves consistency calibration of multi-channel signals in two stages: the first stage is cross-spectrum estimation and parameter extraction, which generates a linear frequency modulated test signal and introduces channel delay deviations, performs frequency domain transformation and cross-power spectrum calculation on the multi-channel signals, and accurately estimates the relative delay and amplitude differences between channels based on peak detection and phase analysis; the second stage is calibration coefficient application and signal output, which first generates frequency domain compensation coefficients based on the estimated parameters, and then performs real-time calibration on the original time-delay signal through phase adjustment, finally outputting a high-precision synchronized multi-channel signal.

[0063] Therefore, the present invention adopts the above-mentioned multi-channel signal receiving calibration method and device based on cross-spectrum method. It addresses the technical bottlenecks of the prior art by accurately estimating and correcting the time delay and amplitude inconsistency between channels through high-precision cross-spectrum analysis and real-time phase compensation. It solves the problems of traditional methods, which have limited calibration accuracy due to high computational complexity and poor real-time performance, as well as the performance degradation of time delay estimation under low signal-to-noise ratio environment, and cannot meet the requirements of modern multi-channel systems for high synchronization and low delay.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-channel signal receiving calibration method based on cross-spectrum method, characterized in that, Includes the following steps: S1. Generate test signals: Configure system parameters and generate test signals by simulating the actual environment; S2. Perform frequency domain transformation on the test signal: including Fast Fourier Transform (FFT) and spectrum centering; S3. Perform cross-spectral analysis on the test signal: calculate the cross-power spectral density and extract amplitude and phase information; S4. Time delay extraction of test signal: Peak detection and time delay calculation of cross power spectral density to obtain the relative time delay between multi-channel signals; S5. Compensation Calibration: Generate channel compensation parameters based on relative time delay to perform phase and time delay compensation on multi-channel signals; S6. Conduct experimental verification using indicators.

2. The multi-channel signal receiving calibration method based on cross-spectrum method according to claim 1, characterized in that: The system parameters in S1 include sampling frequency, signal bandwidth, and pulse width.

3. The multi-channel signal receiving calibration method based on cross-spectrum method according to claim 1, characterized in that, The specific steps of S1 are as follows: S11. Generate the linear frequency modulation test signal LFM; S12. Introduce inter-channel time delay deviation and simulate the time delay of LFM by frequency domain phase rotation; S13. Add Gaussian white noise to simulate the actual environment and generate a test signal.

4. The multi-channel signal receiving calibration method based on cross-spectrum method according to claim 1, characterized in that, The specific steps of S2 are as follows: S21. Perform FFT on the reference calibration signal and the time delay signal respectively; S22. The zero frequency is moved to the center of the spectrum by using the spectrum rearrangement operation function fftshift to center the spectrum.

5. The multi-channel signal receiving calibration method based on cross-spectrum method according to claim 4, characterized in that, The specific formula for FFT in S21 is as follows: ； ； in, For relative time delay, Let f be the complex representation of the signal in the frequency domain, where f is the frequency variable. Here, t is the original signal, e is the base of the natural logarithm, and j is the imaginary unit. Pi This introduces the complex representation of the signal in the frequency domain after channel delay.

6. The multi-channel signal receiving calibration method based on cross-spectrum method according to claim 1, characterized in that, The specific steps of S3 are as follows: S31. Calculate the cross-power spectral density of the reference calibration signal and the time-delay signal. The formula for calculating the cross-power spectral density is as follows: ； in, This represents the cross-power spectral density of the signals from the two received channels in the frequency domain. Let X be the conjugate form of the complex number X. Let X(f) be the complex conjugate representation of the signal X(f) in the frequency domain; S32. Perform a Fourier transform on the cross-power spectral density to extract the amplitude and phase information of the cross-power spectrum, and perform cross-spectral analysis. The specific formula for the Fourier transform is as follows: ； in, The peak position represents the signal delay, that is, the time difference between the signal transmission between the two receiving channels. This is calculated... The difference between the peak positions is used to obtain the time difference between the two received signals, which is then used for time delay calibration.

7. The multi-channel signal receiving calibration method based on cross-spectrum method according to claim 1, characterized in that, The specific steps of S4 are as follows: S41. Perform a high-resolution FFT on the cross-power spectrum and center the time domain using fftshift; S42. Perform peak detection and time delay calculation on the cross-power spectral density.

8. A multi-channel signal receiving calibration method based on cross-spectrum method according to claim 7, characterized in that, The specific steps of S42 are as follows: S421. Locate the peak position of the cross-correlation function, and locate the time delay position by detecting the peak position; S422. Calculate the delay range based on the delay location; S423. Calculate the precise time delay value using the frequency domain-time domain mapping relationship, and map the peak position to the time delay value; S424. Output the delay value in microseconds.

9. A multi-channel signal receiving calibration method based on cross-spectrum method according to claim 8, characterized in that, The specific steps of S5 are as follows: S51. Generate corresponding channel compensation parameters based on the delay value. The channel compensation parameters include phase and delay compensation. S52. By applying phase and time delay compensation to the channel signals, the reference calibration signal and the time delay signal are time-delay calibrated so that the compensated multi-channel signals are aligned on the time axis.

10. An apparatus for applying the multi-channel signal receiving calibration method based on the cross-spectrum method according to any one of claims 1-9, characterized in that, include: The cross-spectrum estimation and parameter extraction module is used to generate linear frequency modulation test signals, perform frequency domain transformation and cross power spectrum calculation on multi-channel signals, and accurately estimate the relative time delay and amplitude difference between channels. The calibration coefficients are applied to the signal output module to generate frequency domain compensation coefficients, perform real-time calibration on the original time-delay signal, and output high-precision synchronous multi-channel signals.

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