FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method based on SVR-LWL

Abstract

The invention provides an FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method based on SVR-LWL, belongs to the technical field of amplitude-frequency error calibration, and solves the problems that the fitting precision of passband signals is reduced and the calibration effect is affected due to the fact that a traditional amplitude-frequency error calibration method is difficult to meet the actual application requirement. Comprising the following steps: step 1, pre-distortion processing is carried out on a target input signal of an FI-DAC system, ideal frequency division processing is carried out on the target input signal after pre-distortion processing by adopting a linear phase FIR digital filter, and a high-frequency sub-path signal and a low-frequency sub-path signal are obtained; 2, performing frequency mixing, filtering, analog-to-digital conversion and combination operation on the high-frequency sub-path signal and the low-frequency sub-path signal, and inputting the signals into an analog link to generate a broadband signal; and step 3, carrying out dynamic calibration on amplitude-frequency errors caused by nonlinear characteristics based on an amplitude-frequency error pre-equalizer in the analog link, generating a calibrated target signal waveform table, and outputting the calibrated target signal waveform table.

Description

Technical Field

[0001] The invention relates to a peak nonlinear amplitude-frequency error pre-calibration method of an FI-DAC system based on SVR-LWL, and belongs to the technical field of amplitude-frequency error calibration. Background Art

[0002] With the widespread application of arbitrary waveform generators (AWGs) in the field of high-frequency broadband signals, frequency interleaved DAC (FI-DAC) has gradually become a core technology for expanding the bandwidth capabilities of a single DAC. FI-DAC significantly improves the output range of broadband signals through high- and low-frequency division processing, but its non-ideal characteristics in the digital and analog domains will cause nonlinear errors in the amplitude-frequency response, especially in the overlapping area of ​​high- and low-frequency signals, showing dynamic amplitude-frequency fluctuations. This error not only reduces the flatness of the output signal, but also has an adverse effect on frequency consistency. Traditional amplitude-frequency error calibration methods, such as full-band calibration methods based on window function fitting or least squares optimization, have achieved some results in reducing the overall error, but have shown significant deficiencies in dealing with the complex dynamic characteristics of the overlapping band area. Specifically, the frequency fluctuations in the overlapping band area are large, and these methods are difficult to adapt effectively. In addition, in high-frequency signal processing, traditional methods are difficult to meet the actual application requirements due to their high computational complexity and limited real-time performance. Some methods also introduce too much attention in the stopband area, resulting in a decrease in the fitting accuracy of the passband signal, further affecting the calibration effect. Therefore, a calibration method is needed that can adapt to the dynamic characteristics of complex frequency bands, accurately deal with the nonlinear amplitude-frequency error in the FI-DAC overlap band area, and comprehensively improve the quality and consistency of the system output signal.

[0003] Support Vector Regression (SVR) is a regression method based on Support Vector Machine (SVM). Its core idea is to find a hyperplane in the feature space so that the sample points are as close to the hyperplane as possible and a certain error is allowed within the tolerance range.

[0004] Locally Weighted Learning (LWL) is a non-parametric learning method that gives greater weight to data points in the training set that are close to a new data point when predicting the new data point. The basic idea of ​​LWL is to build a model for each prediction task that is only sensitive to data near the current task.

[0005] The SVR-LWL joint algorithm combines the global optimization capability of SVR and the local optimization capability of LWL. The LWL module learns the local characteristics of each frequency point in the high-frequency analog signal band and the low-frequency analog signal band, and sets the interval band and fitting weight of the SVR model. SVR-LWL is used to design a nonlinear amplitude-frequency error pre-calibration module. Summary of the invention

[0006] In order to solve the problem that the traditional amplitude-frequency error calibration method is difficult to meet the actual application requirements, resulting in the decrease of the fitting accuracy of the passband signal and the influence of the calibration effect, the present invention proposes a FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method based on SVR-LWL, which specifically includes:

[0007] Step 1: Perform pre-distortion processing on the target input signal of the FI-DAC system, and use a linear phase FIR digital filter to perform ideal frequency division processing on the target input signal after pre-distortion preprocessing to obtain a high-frequency sub-path signal and a low-frequency sub-path signal;

[0008] Step 2: Mix, filter, perform analog-to-digital conversion and combine the high-frequency sub-path signal and the low-frequency sub-path signal to input into the analog link to generate a broadband signal;

[0009] Step 3: Based on the amplitude-frequency error pre-equalizer in the analog link, the amplitude-frequency error caused by the nonlinear characteristics is dynamically calibrated, and a calibrated target signal waveform table is generated and output.

[0010] Preferably, step 1 specifically includes:

[0011] Step 1.1: Set the frequency response Y of the target analog signal in (jΩ), where Ω is the continuous time frequency, in the digital domain, at the sampling rate f s The target analog signal is sampled to obtain a discrete time signal. The frequency response of a single cycle after sampling is X(e jω ), where ω is the discrete time frequency;

[0012] Step 1.2: Use a linear phase FIR digital filter to divide the signal frequency and set the frequency response of the target input signal to X(e jω ), the frequency response of the FIR digital filter is H LPF_div (e jω ), the frequency response expressions of the high-frequency sub-path signal and the low-frequency sub-path signal are:

[0013] X L_div (e jω )=X in (e jω )H LPF_div (e jω )

[0014]

[0015] In formula (1), X L_div (e jω ) is the frequency response of the low-frequency sub-path signal, X H_div (e jω ) is the frequency response of the high-frequency sub-path signal;

[0016] The expression of the frequency response of a single cycle after sampling is:

[0017]

[0018] Preferably, step 2 specifically includes:

[0019] Step 2.1: limiting the maximum output frequency of the high-frequency sub-path signal and the low-frequency sub-path signal to within the DAC sampling frequency, and performing M-fold downsampling processing on the high-frequency sub-path signal and the low-frequency sub-path signal;

[0020] Step 2.2: down-convert the high-frequency sub-channel signal after downsampling;

[0021] Step 2.3: DAC sampling extension of filtering out the low-frequency sub-path signal after down-sampling and the high-frequency sub-path signal after down-conversion processing by using an analog low-pass filter;

[0022] Step 2.4: Combine the low-frequency sub-signal and the high-frequency sub-signal after filtering and DAC sampling extension to obtain a low-frequency digital signal and a low-frequency digital signal. The low-frequency digital signal and the low-frequency digital signal are output through the DAC to output a high-frequency analog signal and a low-frequency analog signal. The zero-order hold characteristic H of the DAC DAC (jΩ), the high-frequency analog signal and the low-frequency analog signal are in the spectrum with the sampling rate f sm Performing cycle extension and performing error correction on high-frequency analog signals and low-frequency analog signals through an amplitude-frequency error pre-equalizer;

[0023] Step 2.5: The low-frequency analog signal is filtered through a low-pass filter LPF_L1 to remove redundant spectrum extension, thereby obtaining a low-frequency sub-channel baseband signal; the high-frequency analog signal is filtered through a low-pass filter LPF_H1 to remove redundant spectrum extension, thereby obtaining a high-frequency sub-channel baseband signal;

[0024] Step 2.6: Perform an up-conversion operation on the high-frequency sub-channel baseband signal, where the local oscillator frequency in the up-conversion operation is the same as the digital domain local oscillator setting, which is f LO , through the bandpass filters LPF_H2 and HPF_H3, the signal to be filtered is within the filter stopband range, and the image sideband signal, baseband leakage signal and local oscillator leakage signal are filtered out;

[0025] Step 2.7: Add the low-frequency sub-channel baseband signal and the high-frequency sub-channel baseband signal after the up-conversion operation through a combiner to output a broadband signal;

[0026] Step 2.8: With sampling rate f s Sampling is performed to obtain a discrete-time signal, which is compared with the input discrete-time signal after normalization to obtain the FI-DAC system loss;

[0027] The frequency response expression of the high-frequency sub-path signal after down-conversion processing is:

[0028]

[0029] The frequency response expressions of the downsampled high-frequency sub-path signal and the low-frequency sub-path signal are:

[0030]

[0031] In formula (4), X L_base (e jω ) is the frequency response of the low-frequency sub-channel signal after downsampling, X H_base (e jω ) is the frequency response of the high-frequency sub-path signal after downsampling;

[0032] The expressions of low-frequency sub-channel baseband signal and high-frequency sub-channel baseband signal are:

[0033]

[0034] In formula (5), Y L_DAC (jΩ) is the low-frequency sub-band signal, Y H_DAC (jΩ) is the high-frequency sub-channel baseband signal;

[0035] The expression of the high-frequency sub-channel baseband signal after up-conversion is:

[0036] Y H_LSB (jΩ)=Y H_DAC [j(Ω+2πf LO )]H LPF_H2 (jΩ)H HPF_H3 (jΩ)(6);

[0037] The expression of broadband signal is:

[0038] Y H_LSB (jΩ)=Y H_DAC [j(Ω+2πf LO )]H LPF_H2 (jΩ)H HPF_H3 (jΩ)(7);

[0039] The calculation formula of FI-DAC system loss is:

[0040]

[0041] Preferably, step 2.2 specifically includes:

[0042] Through the digital mixer, the high-frequency sub-channel signal after downsampling is moved to the baseband signal area, and the local oscillator signal frequency is set to ω LO The amplitude of the local oscillator sine wave signal of the high-frequency sub-path signal after downsampling is twice the frequency of the local oscillator signal. The high-frequency sub-path signal after downsampling is down-converted, and the image signal generated by the down-conversion process is placed in the stop band through the low-pass filter LPF_H0 to filter out the image sideband signal, and obtain the frequency response of the high-frequency sub-path signal after down-conversion.

[0043] Preferably, in step 3, the amplitude-frequency error pre-equalizer is composed of an SVR model and an LWL module, SVR is frequency-weighted support vector regression, and LWL is local weighted learning.

[0044] Preferably, step 3 specifically includes:

[0045] Step 3.1: In the analog link, a frequency weighting factor is introduced into the SVR model, and the high-frequency analog signal band and the low-frequency analog signal band are taken as the target frequency bands. According to the weights of the frequency points in the target frequency bands, the weight distribution of the correction target is precisely adjusted;

[0046] Step 3.2: The LWL module learns the local characteristics of each frequency point in the high-frequency analog signal band and the low-frequency analog signal band, performs deep learning on the overlapping band of the high-frequency analog signal and the low-frequency analog signal band, finds the nonlinear characteristics of the overlapping band and compensates for it, completes the optimization of the overlapping band, and performs a segmented precise feature fitting strategy on the high-frequency analog signal band to complete the optimization of the high-frequency analog signal band;

[0047] Step 3.3: Combine the SVR model and the LWL module to optimize the full frequency band of the high-frequency analog signal and the low-frequency analog signal to complete the dynamic calibration of the amplitude-frequency error.

[0048] Preferably, step 3.1 specifically includes:

[0049] The passband and overlap band of the high-frequency analog signal and the low-frequency analog signal band are given weights higher than the preset values ​​for precise adjustment, and the frequency points in the stopband area are processed by reducing the weights.

[0050] Preferably, in step 3.3, iterative optimization is performed using the SVR-LWL joint algorithm, specifically including:

[0051] Step 3.3.1: Use the currently collected high-frequency analog signal and low-frequency analog signal as training samples and perform standardized training;

[0052] Step 3.3.2: Set the interval band and fitting weight of the SVR model through the LWL algorithm;

[0053] Step 3.3.3: Fit the SVR model;

[0054] Step 3.3.4: Calculate the interval out-of-band loss of the fitted SVR model;

[0055] Step 3.3.5: Compare the interval out-of-band loss of the fitted SVR model with the current FI-DAC system loss;

[0056] Step 3.3.6: Repeat steps 3.3.1 to 3.3.5 until the parameter requirements are met or the maximum number of iterations is reached to obtain the optimal parameters of the FI-DAC system.

[0057] The beneficial effects of the present invention are:

[0058] 1. The present invention outperforms the traditional window function algorithm in overlapping frequency band fitting and can fit the target frequency response more accurately. The SVR-LWL algorithm of the present invention not only reduces the fitting error in the overlapping band, but also shows higher fitting ability in the dynamic amplitude-frequency error processing of the high-frequency sub-band.

[0059] 2. In the fitting performance analysis near the overlapping band frequency points, the SVR-LWL algorithm proposed in the present invention surpasses the traditional window function algorithm and can fit the target frequency response more accurately.

[0060] 3. The present invention solves the amplitude-frequency error problem caused by nonlinear characteristics in the FI-DAC system, especially the calibration requirements in the overlapping band of high and low frequency signals and the high frequency sub-band area. The present invention takes frequency weighting as the core and optimizes the amplitude-frequency response performance of the signal in the full frequency band through a refined frequency band calibration strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A flow chart of a method for pre-calibrating peak nonlinear amplitude-frequency error of a FI-DAC system based on SVR-LWL provided by the present invention;

[0062] Figure 2 A flowchart of the amplitude-frequency error pre-equalizer provided by the present invention;

[0063] Figure 3 Flow chart of the SVR-LWL joint algorithm provided by the present invention;

[0064] Figure 4This is a schematic diagram showing the comparison of the fitting performance of the SVR-LWL joint algorithm provided by the present invention, the BP algorithm and the traditional window function algorithm near the overlapping band frequency point. Figure 4 In the figure, (a) is a comparison of the predistorter fitting performance of SVR-LWL and BP algorithms in overlapping band 1, (b) is a comparison of the predistorter fitting performance of SVR-LWL and traditional window function algorithms in overlapping band 1, (c) is a comparison of the predistorter fitting performance of SVR-LWL and BP algorithms in overlapping band 2, (d) is a comparison of the predistorter fitting performance of SVR-LWL and traditional window function algorithms in overlapping band 2;

[0065] Figure 5 This is a schematic diagram comparing the flatness performance of the SVR-LWL joint algorithm provided by the present invention, the BP algorithm and the traditional window function algorithm after overlapping band correction. Figure 5 In the figure, (a) is a comparison of the correction performance of SVR-LWL and BP algorithms in overlap band 1, (b) is a comparison of the correction performance of SVR-LWL and traditional window function algorithms in overlap band 1, (c) is a comparison of the correction performance of SVR-LWL and BP algorithms in overlap band 2, and (d) is a comparison of the correction performance of SVR-LWL and traditional window function algorithms in overlap band 2. DETAILED DESCRIPTION

[0066] Specific implementation method 1: Combination Figure 1-3 To illustrate this embodiment, Figure 1 As shown, the steps of the FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method based on SVR-LWL described in this embodiment include:

[0067] S1: FI-DAC system error calculation;

[0068] S101: The digital domain process of the FI-DAC system includes ideal frequency division, down-conversion operation for high-frequency sub-channels, down-sampling and output of sub-channel signals, and assuming the frequency response Y of the target analog signal in (jΩ), where Ω is the continuous time frequency. In the digital domain, the sampling rate is f s Sampling is performed to obtain a discrete time signal. Without considering spectrum extension, the frequency response of a single cycle after sampling is expressed as X(e jω ), where ω is the discrete time frequency, and the frequency response of a single cycle after sampling satisfies:

[0069]

[0070] S102: To ensure the real-time performance of the output signal, this embodiment designs a linear phase FIR digital filter for signal frequency division. By using complementary window functions of the same order and the same cutoff frequency, the complementary frequency response can be achieved in an ideal situation. When the two divided signals are added together, the original target signal can be effectively restored to achieve the purpose of signal reconstruction. Assuming that the frequency response of the target input signal is X(e jω ), the frequency response of the N-order low-pass crossover filter is H LPF_div (e j ω ), by pre-distortion processing and frequency division processing of the signal, the frequency responses of the high-frequency sub-path signal and the low-frequency sub-path signal obtained by frequency division are:

[0071] X L_div (e jω )=X in (e jω )H LPF_div (e jω )

[0072]

[0073] In formula (2), X L_div (e jω ) is the frequency response of the low-frequency sub-path signal, X H_div (e jω ) is the frequency response of the high-frequency sub-path signal;

[0074] S103: In order to meet the bandwidth limitation of the DAC, its maximum output frequency should be within the DAC sampling rate limitation. In this implementation, a digital mixer is used to move the high-frequency signal to the baseband signal region. Assume that the local oscillator signal frequency is ω LO To prevent the single-sideband signal amplitude from being halved compared to the input signal amplitude, the input local oscillator sine wave signal amplitude is set to 2 times to compensate for the amplitude attenuation that may occur during the mixing process. The low-pass filter LPF_H0 is used to place the image signal in the stopband to effectively filter out the image sideband signal, and the signal frequency response after down-conversion is obtained as:

[0075]

[0076] S104: In order to meet the sampling rate requirements of the DAC, this embodiment then performs M-fold downsampling processing on the two sub-signals. By reasonably selecting the sampling multiple, aliasing errors can be effectively avoided, and the baseband signal can be simplified to a more easily processable form after downsampling:

[0077]

[0078] In formula (4), X L_base (ejω ) is the frequency response of the low-frequency sub-channel signal after downsampling, X H_base (e jω ) is the frequency response of the high-frequency sub-path signal after downsampling;

[0079] S105: The digital domain process of the FI-DAC system includes DAC sampling output, filtering out DAC sampling extension through a low-pass filter, then performing frequency conversion on the high-frequency sub-channel, and filtering out image sidebands and non-target signal leakage through a band-pass filter, and finally combining the two sub-channel signals for output. The digital signal passes through the DAC to output an analog signal, which is affected by the DAC's zero-order hold characteristic H. DAC (jΩ), the analog signal will be in the frequency spectrum with sampling rate f sm Perform period extension, and filter out the unnecessary spectrum extension through low-pass filters LPF_L1 and LPF_H1 to obtain the baseband signal;

[0080] The expressions of low-frequency sub-channel baseband signal and high-frequency sub-channel baseband signal are:

[0081]

[0082] In formula (5), Y L_DAC (jΩ) is the low-frequency sub-band signal, Y H_DAC (jΩ) is the high-frequency sub-channel baseband signal;

[0083] S106: The high-frequency sub-channel baseband signal is up-converted by a mixer, wherein the local oscillator frequency is the same as the digital domain local oscillator setting, which is f LO , through the bandpass filters LPF_H2 and HPF_H3, the signal to be filtered is within the filter stopband range, which can effectively filter out the image sideband signal, baseband leakage signal and local oscillator leakage signal;

[0084] The expression of the high-frequency sub-channel baseband signal after up-conversion is:

[0085] Y H_LSB (jΩ)=Y H_DAC [j(Ω+2πf LO )]H LPF_H2 (jΩ)H HPF_H3 (jΩ)(6);

[0086] S107: adding the two processed analog signals via a combiner to output a broadband signal;

[0087] The expression of broadband signal is:

[0088] Y H_LSB (jΩ)=Y H_DAC [j(Ω+2πf LO )]H LPF_H2(jΩ)H HPF_H3 (jΩ)(7);

[0089] S108: Perform system error analysis with sampling rate f s Sampling is performed to obtain a discrete-time signal, which is compared with the input discrete-time signal after normalization to obtain the system error performance;

[0090] The calculation formula of FI-DAC system loss is:

[0091]

[0092] The above formula only considers the ideal frequency response of each device. The amplitude-frequency error of the output signal originates from the non-ideal characteristics of the filter, especially the influence of the ripple effect in the filter passband on the signal amplitude. At the same time, the zero-order hold characteristic of the DAC will produce a certain amplitude attenuation on the high-frequency part of the target baseband signal, further affecting the amplitude-frequency response of the signal. The analog devices in the actual system will also introduce insertion loss. The gain of the device is not ideally flat within the operating frequency band, and will produce different losses with frequency changes, etc., which will affect the target signal.

[0093] In addition, analog devices also introduce additional signal components at non-target frequencies. DAC chips introduce signal components such as high-order harmonics and intermodulation distortion in actual work. Analog mixers introduce signal components such as intermodulation distortion and local oscillator leakage. In order to balance the energy of the two signals, the amplifier set in the high-frequency sub-path will introduce gain error, harmonic distortion and other signal components. The filter in the FI-DAC model can effectively filter out most of the non-target signals. The remaining non-target frequency components, such as system noise, have little effect on the frequency response of the output signal. In the combining link, the influence of the aliasing error caused by the addition of these frequency components with other sub-band signals on the amplitude-frequency error is not considered.

[0094] To address the above defects, this implementation introduces an amplitude-frequency error pre-equalizer in the analog domain to measure and correct the amplitude-frequency characteristics of the input signal at the target frequency, as shown below:

[0095] S2: Amplitude-frequency error pre-equalizer design method;

[0096] In digital signal processing, the design of FIR filters often starts from the frequency response of an ideal filter, and obtains its ideal impulse response h[n] through inverse Fourier transform, which is directly composed of the filter coefficients as the time domain representation of the filter. The order of the filter, N, directly determines the length of the filter and the number of its coefficients. Higher-order FIR filters can improve the accuracy of the frequency response by narrowing the transition band width, and effectively reduce sidelobes and frequency leakage, thereby optimizing the overall performance of the filter while maintaining highly precise control.

[0097] S201: Ideal transfer function for the target frequency response of any given discrete-time FIR filter It is converted into an ideal impulse response h by inverse Fourier transform d (n):

[0098]

[0099] In traditional FIR filter design, the ideal infinite impulse response is usually truncated to a finite length in the time domain. This direct truncation will cause the Gibbs phenomenon, resulting in oscillation, overshoot and ringing in the frequency response near the truncation point. In order to alleviate these adverse effects, various window function methods are widely used in FIR filter design to optimize the performance of the filter by smoothing the truncation edge. The window function is a function used in the time domain to control the side lobes and ripples introduced in the truncation process. It can be regarded as a weighted function defined on a finite time interval, which truncates or modulates the original signal to achieve a smooth transition of the frequency response, but also widens the main lobe and affects the sharpness of the edge response. In applications with high frequency selectivity, the performance of the filter is limited.

[0100] Common window function methods include Hanning window, Hamming window, Bartlett window, Blackman window, Chebyshev window and Kaiser window. Among them, Hanning window and Hamming window use smooth cosine form to reduce the jump at both ends of the window, thereby reducing spectrum leakage. Bartlett window uses linear form, its main lobe width is wider and the side lobe decays slowly, while Blackman window, by combining three cosine terms, further reduces the side lobe level. Chebyshev window optimizes the window function by minimizing the maximum side lobe outside the window, providing excellent side lobe suppression effect. Kaiser window adjusts parameters to balance the main lobe width and side lobe height, and is widely used in complex filter design that requires fine adjustment of stopband and passband performance.

[0101] Different window functions have a significant impact on the frequency response characteristics of the filter. If stopband suppression is the main consideration, considering the sidelobe suppression effect, the Chebyshev window or the Blackman window is the best choice. If it is necessary to balance the passband frequency resolution and sidelobe suppression, the Hanning window and the Hamming window can moderately suppress the sidelobes while ensuring the passband frequency resolution, which is suitable for a wide range of signal processing applications. In the process of fitting the FIR amplitude-frequency pre-calibration filter, the trade-off between frequency selectivity and passband frequency resolution is the most critical, and the Kaiser window has more advantages in parameter adjustment flexibility.

[0102] Window function method, using the window function ω[n] to intercept the ideal impulse response h d [n], obtain a transfer function H(e) of a realizable finite length unit impulse response FIR filter jω ), satisfying h[n]=h d[n]·ω[n]. At the same time, in order to avoid introducing additional phase errors during the pre-calibration of the FIR filter, the impulse response of the linear phase filter needs to ensure even symmetry.

[0103] Although the window function method is simple and easy to use, it may widen the transition band width while reducing the side lobes, while achieving extremely low side lobe levels and narrow main lobe widths. Its performance is often unsatisfactory for complex fitting targets. Higher-order FIR filters can effectively reduce side lobes and frequency leakage by narrowing the transition band and improving the accuracy of the frequency response. However, this also increases the computational requirements and may cause implementation difficulties in real-time processing systems.

[0104] Under the restriction of a certain order, when designing an FIR filter with a complex amplitude-frequency characteristic response, the coefficients of the filter are directly adjusted through numerical optimization technology to minimize the error between the expected frequency response and the actual frequency response, which can provide a more accurate fitting effect than the traditional window function method.

[0105] S202: For an N-order FIR filter, its length is N+1. To maintain the linear phase of the FIR, the impulse response h[n] of the filter must satisfy even symmetry. When the order N is an even integer, the corresponding length is an odd integer. A type I general filter without special zeros is made, and the coefficients are symmetric about N / 2, satisfying:

[0106] h(n)=h(Nn)(10);

[0107] The transfer function H(e) of the corresponding FIR filter jω )satisfy

[0108]

[0109] When the unit impulse response h(n) is a real number series, the filter frequency response can be converted into a combination of amplitude response and phase response:

[0110]

[0111] S203: The amplitude response of the filter can be further converted into the form of a Fourier series, where w(n) is the Fourier coefficient, and the specific h(n) value can be obtained by solving w(n).

[0112]

[0113] S204: for the known K discrete angular frequency points ω distributed in the 0-pi interval k =[ω1,ω2...ω K ], and its corresponding K-dimensional vector amplitude-frequency response H d (ω k), construct an overdetermined linear equation [w (N / 2+1)×1 ] T x(ω) (N / 2+1)×K +b=[y(ω) K×1 ] T . Where w n =w(n) is the weight sequence to be solved, b is the modified weight of w(0), y(ω) k =H d (ω k ) is the target amplitude-frequency response, x(ω) n,k =cos[(n-1)ω k ] Each column corresponds to the cosine value of each frequency point. Satisfying the equation:

[0114]

[0115] The amplitude-frequency error pre-equalizer of the present invention adopts a joint algorithm design based on frequency-weighted support vector regression (SVR) and local weighted learning (LWL), which solves the amplitude-frequency error problem caused by nonlinear characteristics in the FI-DAC system, especially the calibration requirements in the overlapping band of high- and low-frequency signals and high-frequency sub-band areas. The design is centered on frequency weighting and optimizes the amplitude-frequency response performance of the signal in the full frequency band through a refined frequency band calibration strategy.

[0116] S205: Figure 2 As shown in the figure, a frequency weighting factor is introduced into the support vector regression (SVR) model. According to the importance of the frequency point in the target frequency band, the weight distribution of the calibration target is precisely adjusted. For the passband and overlap band regions, these frequency bands have the most significant impact on the amplitude-frequency characteristics of the signal, so they are given higher weights to prioritize the optimization of the fitting accuracy; while for the frequency points in the stopband region, the interference of non-target frequencies on the model fitting is reduced by reducing the weights. This frequency weighting mechanism can not only improve the fitting effect of the passband signal, but also effectively control the impact of the stopband signal on the calibration result, avoiding the unnecessary increase of the model complexity.

[0117] S206: The local weighted learning (LWL) module further enhances the adaptability of the model. LWL optimizes the detailed characteristics of different frequency bands by learning the local characteristics of each frequency point, especially the complex error performance in the overlapping band and high-frequency sub-band area. In the overlapping band area, the dynamic error caused by the overlap of high and low frequency signals is more complex. LWL accurately captures its nonlinear characteristics and compensates for it by deep learning the local characteristics of this area. In addition, in the high-frequency sub-band, the dynamic fluctuations caused by the non-ideal characteristics of the analog link (such as uneven gain and mirror signal leakage) are more significant. The LWL module accurately adjusts the fitting strategy by dividing the frequency band to further improve the calibration accuracy.

[0118] S207: The joint SVR-LWL optimization strategy combines the frequency weighting mechanism with local weighted learning to optimize the calibration of the entire frequency band. Through the iterative optimization process of the joint algorithm, the error between the amplitude-frequency response of the target signal and the actual output is gradually reduced, ensuring that the calibrator can achieve efficient error compensation in complex frequency bands. The fitting accuracy within the passband range is significantly improved, and the stopband error is effectively suppressed, ensuring the overall performance of the calibrator. Compared with traditional calibration methods, this joint algorithm not only shows excellent fitting ability in the overlapping band and high-frequency sub-band area, but also significantly reduces excessive interference to non-target frequency bands, greatly improving the efficiency and accuracy of amplitude-frequency error calibration.

[0119] S20701: Figure 3 As shown, the currently collected high-frequency analog signal and low-frequency analog signal are used as training samples and standardized training is performed;

[0120] S20702: Set the interval band and fitting weight of the SVR model through the LWL algorithm;

[0121] S20703: Fit the SVR model;

[0122] S20704: Calculate the interval out-of-band loss of the fitted SVR model;

[0123] S20705: Compare the interval out-of-band loss of the fitted SVR model with the current FI-DAC system loss;

[0124] S20706: Repeat S20701-S20705 until the parameter requirements are met or the maximum number of iterations is reached, and the optimal parameters of the FI-DAC system are obtained.

[0125] Specific implementation method 2: Combination Figure 4 and Figure 5 This embodiment is described as follows. Figure 4 As shown, in order to verify the technical effect of the present invention, this embodiment was tested. The full-band fitting performance is shown in Table 1. From the fitting performance of the frequency response, the SVR-LWL algorithm performs better than other algorithms in the full frequency band and the overlapping band. In the full frequency band, the RMSE of the pre-calibrator designed by the SVR-LWL algorithm reaches 0.613e-3, which is further reduced than the 0.692e-3 of the BP algorithm. Compared with the Kaiser window and the Hamming window, the SVR-LWL has significant advantages in fitting accuracy and robustness. The data in the table clearly show that the SVR-LWL algorithm exhibits lower error and higher determination coefficient (R 2 This indicates that it has stronger frequency response consistency.

[0126] Table 1

[0127]

[0128] The fitting performance of the overlapping frequency band is shown in Table 2. In the fitting performance analysis of the overlapping frequency points (500MHz and 850MHz), the SVR-LWL algorithm shows a higher accuracy for the peak value of the amplitude-frequency error. For the 500MHz overlapping band position, the RMSE of the SVR-LWL algorithm is 0.213e-2, while the RMSE of the BP algorithm is 0.394e-2, which reflects a higher fitting accuracy. At the 850MHz overlapping band position, the SVR-LWL algorithm also surpasses the traditional window function algorithm and can fit the target frequency response more accurately. Combined with the specific data in the table, the SVR-LWL algorithm not only reduces the fitting error in the overlapping band, but also shows a higher fitting ability in the dynamic amplitude-frequency error processing of the high-frequency sub-band.

[0129] Table 2

[0130]

[0131] like Figure 4 (a) Figure 4 (b) Figure 4 (c) and Figure 4 As shown in (d), in the fitting performance analysis near the overlapping band frequency points (500MHz and 850MHz), the SVR-LWL algorithm shows a higher accuracy for the amplitude-frequency error peak. For the 500MHz overlapping band position, the RMSE of the SVR-LWL algorithm is 0.213e-2, while the RMSE of the BP algorithm is 0.394e-2, which reflects a higher fitting accuracy. At the 850MHz overlapping band position, the SVR-LWL algorithm also surpasses the traditional window function algorithm and can fit the target frequency response more accurately. Combined with the specific data in Tables 1 and 2, the SVR-LWL algorithm not only reduces the fitting error in the overlapping band, but also shows a higher fitting ability in the dynamic amplitude-frequency error processing of the high-frequency sub-band.

[0132] like Figure 5 (a) Figure 5 (b) Figure 5 (c) and Figure 5As shown in (d), after the pre-calibrator is integrated into the FI-DAC system, the amplitude-frequency response of the system is corrected and analyzed. From the flatness index of the output signal, the SVR-LWL algorithm significantly improves the full-band and overlap frequency response of the FI-DAC. Specifically, at the 500MHz and 850MHz overlap positions, the flatness of SVR-LWL is 0.031dB (maximum value) and -0.062dB (minimum value), respectively, which is close to the ideal value of 0dB. Compared with other algorithms, the SVR-LWL algorithm exhibits better flatness characteristics in the overlap band. Its corrected amplitude-frequency response is almost consistent with the target frequency response, while the traditional algorithm has significant deviations in the dynamic amplitude-frequency characteristics in these key areas.

[0133] The test results for full-band flatness are shown in Table 3. In the full-band range, the maximum flatness of the SVR-LWL algorithm is improved by 0.768dB, and the minimum flatness is improved by 1.57dB. These results show that the SVR-LWL algorithm can effectively correct the amplitude-frequency error of the FI-DAC and significantly improve the flatness and frequency consistency of the output signal.

[0134] Table 3

[0135]

[0136]

[0137] Through the analysis of the above experimental results, it can be seen that the amplitude-frequency error pre-calibrator based on the SVR-LWL algorithm is significantly better than the traditional algorithm in both fitting performance and correction performance. Especially in the nonlinear amplitude-frequency error processing of overlapping bands and high-frequency sub-bands, the SVR-LWL algorithm can better meet the high-frequency and broadband application requirements of the FI-DAC system with its high precision and efficiency.

[0138] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. The peak nonlinear amplitude-frequency error pre-calibration method of the FI-DAC system based on SVR-LWL is characterized by: The steps of the FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method based on SVR-LWL include: Step 1: Perform pre-distortion processing on the target input signal of the FI-DAC system, and use a linear phase FIR digital filter to perform ideal frequency division processing on the target input signal after pre-distortion preprocessing to obtain a high-frequency sub-path signal and a low-frequency sub-path signal; Step 2: Mix, filter, perform analog-to-digital conversion and combine the high-frequency sub-path signal and the low-frequency sub-path signal to input into the analog link to generate a broadband signal; Step 3: Based on the amplitude-frequency error pre-equalizer in the analog link, the amplitude-frequency error caused by the nonlinear characteristics is dynamically calibrated, and a calibrated target signal waveform table is generated and output.

2. The SVR-LWL-based FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Set the frequency response Y of the target analog signal in (jΩ), where Ω is the continuous time frequency, in the digital domain, at the sampling rate f s The target analog signal is sampled to obtain a discrete time signal. The frequency response of a single cycle after sampling is X(e jω ), where ω is the discrete time frequency; Step 1.2: Use a linear phase FIR digital filter to divide the signal frequency and set the frequency response of the target input signal to X(e jω ), the frequency response of the FIR digital filter is H LPF_div (e jω ), the frequency response expressions of the high-frequency sub-path signal and the low-frequency sub-path signal are: In formula (1), X L_div (e jω ) is the frequency response of the low-frequency sub-path signal, X H_div (e jω ) is the frequency response of the high-frequency sub-path signal; The expression of the frequency response of a single cycle after sampling is:

3. The FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method based on SVR-LWL according to claim 1, characterized in that: Step 2 specifically includes: Step 2.1: limiting the maximum output frequency of the high-frequency sub-path signal and the low-frequency sub-path signal to within the DAC sampling frequency, and performing M-fold downsampling processing on the high-frequency sub-path signal and the low-frequency sub-path signal; Step 2.2: down-convert the high-frequency sub-channel signal after downsampling; Step 2.3: DAC sampling extension of filtering out the low-frequency sub-path signal after down-sampling and the high-frequency sub-path signal after down-conversion processing by using an analog low-pass filter; Step 2.4: Combine the low-frequency sub-signal and the high-frequency sub-signal after filtering and DAC sampling extension to obtain a low-frequency digital signal and a low-frequency digital signal. The low-frequency digital signal and the low-frequency digital signal are output through the DAC to output a high-frequency analog signal and a low-frequency analog signal. The zero-order hold characteristic H of the DAC DAC (jΩ), the high-frequency analog signal and the low-frequency analog signal are in the spectrum with the sampling rate f sm Performing cycle extension and performing error correction on high-frequency analog signals and low-frequency analog signals through an amplitude-frequency error pre-equalizer; Step 2.5: The low-frequency analog signal is filtered through a low-pass filter LPF_L1 to remove redundant spectrum extension, thereby obtaining a low-frequency sub-channel baseband signal; the high-frequency analog signal is filtered through a low-pass filter LPF_H1 to remove redundant spectrum extension, thereby obtaining a high-frequency sub-channel baseband signal; Step 2.6: Perform an up-conversion operation on the high-frequency sub-channel baseband signal, where the local oscillator frequency in the up-conversion operation is the same as the digital domain local oscillator setting, which is f LO , through the bandpass filters LPF_H2 and HPF_H3, the signal to be filtered is within the filter stopband range, and the image sideband signal, baseband leakage signal and local oscillator leakage signal are filtered out; Step 2.7: Add the low-frequency sub-channel baseband signal and the high-frequency sub-channel baseband signal after the up-conversion operation through a combiner to output a broadband signal; Step 2.8: With sampling rate f s Sampling is performed to obtain a discrete-time signal, which is compared with the input discrete-time signal after normalization to obtain the FI-DAC system loss; The frequency response expression of the high-frequency sub-path signal after down-conversion processing is: The frequency response expressions of the downsampled high-frequency sub-path signal and the low-frequency sub-path signal are: In formula (4), X L_base (e jω ) is the frequency response of the low-frequency sub-channel signal after downsampling, X H_base (e jω ) is the frequency response of the high-frequency sub-path signal after downsampling; The expressions of low-frequency sub-channel baseband signal and high-frequency sub-channel baseband signal are: In formula (5), Y L_DAC (jΩ) is the low-frequency sub-band signal, Y H_DAC (jΩ) is the high-frequency sub-channel baseband signal; The expression of the high-frequency sub-channel baseband signal after up-conversion is: Y H_LSB (jΩ)=Y H_DAC [j(Ω+2πf LO )]H LPF_H2 (jΩ)H HPF_H3 (jΩ)(6); The expression of broadband signal is: Y H_LSB (jΩ)=Y H_DAC [j(Ω+2πf LO )]H LPF_H2 (jΩ)H HPF_H3 (jΩ)(7); The calculation formula of FI-DAC system loss is:

4. The SVR-LWL-based FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method according to claim 3, characterized in that: Step 2.2 specifically includes: Through the digital mixer, the high-frequency sub-channel signal after downsampling is moved to the baseband signal area, and the local oscillator signal frequency is set to ω LO The amplitude of the local oscillator sine wave signal of the high-frequency sub-path signal after downsampling is twice the frequency of the local oscillator signal. The high-frequency sub-path signal after downsampling is down-converted, and the image signal generated by the down-conversion process is placed in the stop band through the low-pass filter LPF_H0 to filter out the image sideband signal, and obtain the frequency response of the high-frequency sub-path signal after down-conversion.

5. The SVR-LWL-based FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method according to claim 1, characterized in that: In step 3, the amplitude-frequency error pre-equalizer is composed of an SVR model and an LWL module, where SVR stands for frequency-weighted support vector regression and LWL stands for local weighted learning.

6. The SVR-LWL-based FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: In the analog link, a frequency weighting factor is introduced into the SVR model, and the high-frequency analog signal band and the low-frequency analog signal band are taken as the target frequency bands. According to the weights of the frequency points in the target frequency bands, the weight distribution of the correction target is precisely adjusted; Step 3.2: The LWL module learns the local characteristics of each frequency point in the high-frequency analog signal band and the low-frequency analog signal band, performs deep learning on the overlapping band of the high-frequency analog signal and the low-frequency analog signal band, finds the nonlinear characteristics of the overlapping band and compensates for it, completes the optimization of the overlapping band, and performs a segmented precise feature fitting strategy on the high-frequency analog signal band to complete the optimization of the high-frequency analog signal band; Step 3.3: Combine the SVR model and the LWL module to optimize the full frequency band of the high-frequency analog signal and the low-frequency analog signal to complete the dynamic calibration of the amplitude-frequency error.

7. The SVR-LWL-based FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method according to claim 6, characterized in that: Step 3.1 specifically includes: The passband and overlap band of the high-frequency analog signal and the low-frequency analog signal band are given weights higher than the preset values ​​for precise adjustment, and the frequency points in the stopband area are processed by reducing the weights.

8. The SVR-LWL-based FI-DAC system peak nonlinear amplitude-frequency error pre-calibration method according to claim 6, characterized in that: In step 3.3, iterative optimization is performed using the SVR-LWL joint algorithm, specifically including: Step 3.3.1: Use the currently collected high-frequency analog signal and low-frequency analog signal as training samples and perform standardized training; Step 3.3.2: Set the interval band and fitting weight of the SVR model through the LWL algorithm; Step 3.3.3: Fit the SVR model; Step 3.3.4: Calculate the interval out-of-band loss of the fitted SVR model; Step 3.3.5: Compare the interval out-of-band loss of the fitted SVR model with the current FI-DAC system loss; Step 3.3.6: Repeat steps 3.3.1 to 3.3.5 until the parameter requirements are met or the maximum number of iterations is reached to obtain the optimal parameters of the FI-DAC system.

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