Pre-calibration method for peak nonlinearity amplitude-frequency error of fi-dac system based on svr-lwl

Abstract

The application 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 problem that a traditional amplitude-frequency error calibration method is difficult to meet actual application requirements, causes the fitting precision of a passband signal to be reduced, and influences calibration effect, and comprises the following steps: 1, pre-distortion processing is performed on a target input signal of an FI-DAC system, an ideal frequency division processing is performed on the target input signal after pre-distortion preprocessing by adopting a linear-phase FIR digital filter, and high-frequency sub-path signals and low-frequency sub-path signals are obtained; 2, the high-frequency sub-path signals and the low-frequency sub-path signals are subjected to mixing, filtering, analog-to-digital conversion and combining operation input analog link to generate a wideband signal; and 3, amplitude-frequency error caused by nonlinear characteristics is dynamically calibrated based on an amplitude-frequency error pre-equalizer in the analog link, a calibrated target signal waveform table is generated and output.

Description

Technical Field

[0001] This invention relates to a pre-calibration method for peak nonlinear amplitude-frequency error of FI-DAC system based on SVR-LWL, belonging to the field of amplitude-frequency error calibration technology. Background Technology

[0002] With the widespread application of arbitrary waveform generators (AWGs) in high-frequency broadband signal processing, frequency-interleaved DACs (FI-DACs) have gradually become a core technology for extending the bandwidth of single DACs. FI-DACs significantly improve the output range of broadband signals through high-low frequency division processing, but the non-ideal characteristics in their digital and analog domains lead to nonlinear errors in the amplitude-frequency response, especially exhibiting dynamic amplitude-frequency fluctuations in the overlapping regions of high and low frequency signals. This error not only reduces the flatness of the output signal but also adversely affects frequency consistency. Traditional amplitude-frequency error calibration methods, such as full-band calibration methods based on window function fitting or least-squares optimization, while effective in reducing overall errors, are significantly inadequate in dealing with the complex dynamic characteristics of overlapping regions. Specifically, the frequency fluctuations in overlapping regions are large, making these methods difficult to adapt effectively. Furthermore, traditional methods in high-frequency signal processing suffer from high computational complexity and limited real-time performance, making them unsuitable for practical applications. Some methods also introduce excessive attention in the stopband region, leading to a decrease in the fitting accuracy of the passband signal and further affecting the calibration effect. Therefore, a calibration method that can adapt to the dynamic characteristics of complex frequency bands is needed to accurately address the nonlinear amplitude-frequency error in the FI-DAC overlap band region 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 Machines (SVM). Its core idea is to find a hyperplane in the feature space such that sample points are located as close as possible to this hyperplane, while allowing for a certain amount of error within a tolerance range.

[0004] Locally Weighted Learning (LWL) is a nonparametric learning method that assigns greater weight to data points in the training set that are neighbors of the predicted data point when making predictions. The basic idea of ​​LWL is to build a model for each prediction task that is only sensitive to data in the vicinity of the current task.

[0005] The SVR-LWL joint algorithm combines the global optimization capabilities of SVR with the local optimization capabilities of LWL. The LWL module learns the local characteristics of each frequency point in both high-frequency and low-frequency analog signal bands, and sets the interval bands and fitting weights of the SVR model. An SVR-LWL module for nonlinear amplitude-frequency error pre-calibration is designed. Summary of the Invention

[0006] This invention addresses the problem that traditional amplitude-frequency error calibration methods fail to meet practical application requirements, leading to decreased passband signal fitting accuracy and affecting calibration results. Therefore, it proposes a pre-calibration method for peak nonlinear amplitude-frequency error in FI-DAC systems based on SVR-LWL, specifically including:

[0007] Step 1: Perform predistortion processing on the target input signal of the FI-DAC system. Use a linear phase FIR digital filter to perform ideal frequency division processing on the predistorted target input signal to obtain the high-frequency sub-channel signal and the low-frequency sub-channel signal.

[0008] Step 2: Mix, filter, convert analog to digital and combine the high-frequency and low-frequency signals and input them into the analog link to generate a broadband signal;

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

[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, and in the digital domain, it is expressed at a sampling rate f. s The target analog signal is sampled to obtain a discrete-time signal. The frequency response of a single period after sampling is X(e^(-1 / 2)). 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 as X(e^(-π / 2)). jω The frequency response of the FIR digital filter is H. LPF_div (e jω The expressions for the frequency response of the high-frequency sub-channel signal and the low-frequency sub-channel 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 X represents the frequency response of the low-frequency sub-channel signal. H_div (e jω () represents the frequency response of the high-frequency sub-channel signal;

[0016] The expression for the frequency response after sampling in a single period is:

[0017]

[0018] Preferably, step 2 specifically includes:

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

[0020] Step 2.2: Perform down-conversion processing on the downsampled high-frequency sub-channel signal;

[0021] Step 2.3: Use an analog low-pass filter to filter out the DAC sampling extension of the downsampled low-frequency sub-channel signal and the downconverted high-frequency sub-channel signal;

[0022] Step 2.4: Combine the low-frequency and high-frequency sub-channel signals after filtering and DAC sampling extension to obtain low-frequency digital signals and low-frequency analog signals. These low-frequency digital signals and low-frequency analog signals are then processed by the DAC to output high-frequency and low-frequency analog signals, respectively, subject to the DAC's zero-order hold characteristic H. DAC (jΩ), high-frequency analog signals and low-frequency analog signals are sampled at a frequency f in the spectrum. sm Periodic extension is performed, and error correction is applied to high-frequency and low-frequency analog signals using an amplitude-frequency error pre-equalizer.

[0023] Step 2.5: The low-frequency analog signal is filtered by a low-pass filter LPF_L1 to remove redundant spectral extensions, and the low-frequency sub-path baseband signal is obtained. The high-frequency analog signal is filtered by a low-pass filter LPF_H1 to remove redundant spectral extensions, and the high-frequency sub-path baseband signal is obtained.

[0024] Step 2.6: Perform up-conversion on the high-frequency sub-circuit baseband signal, wherein the local oscillator frequency in the up-conversion operation is set to the same as the digital domain local oscillator frequency, f. LO By using bandpass filters LPF_H2 and HPF_H3, the signal to be filtered is placed within the filter stopband range, thus filtering out the image sideband signal, baseband leakage signal, and local oscillator leakage signal.

[0025] Step 2.7: The low-frequency sub-circuit baseband signal and the high-frequency sub-circuit baseband signal after up-conversion are added together by a combiner to output a broadband signal;

[0026] Step 2.8: Using sampling rate f s The discrete-time signal is obtained by sampling, and then compared with the normalized input discrete-time signal to obtain the FI-DAC system loss.

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

[0028]

[0029] The frequency response expressions for the downsampled high-frequency sub-channel signal and low-frequency sub-channel signal are as follows:

[0030]

[0031] In formula (4), X L_base (e jω X represents the frequency response of the downsampled low-frequency sub-channel signal. H_base (e jω () represents the frequency response of the downsampled high-frequency sub-channel signal;

[0032] The expressions for the low-frequency sub-channel baseband signal and the high-frequency sub-channel baseband signal are as follows:

[0033]

[0034] In formula (5), Y L_DAC (jΩ) represents the low-frequency sub-path baseband signal, Y H_DAC (jΩ) represents the baseband signal of the high-frequency sub-path;

[0035] The expression for the baseband signal of the high-frequency sub-circuit 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 for a 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 formula for calculating the loss of the FI-DAC system is:

[0040]

[0041] Preferably, step 2.2 specifically includes:

[0042] The downsampled high-frequency sub-channel signal is shifted to the baseband signal region using a digital mixer, and the local oscillator signal frequency is set to ω. LO The amplitude of the local oscillator sine wave signal of the downsampled high-frequency sub-channel signal is twice the frequency of the local oscillator signal. The downsampled high-frequency sub-channel signal is downconverted, and the mirror signal generated by the downconversion is placed in the stopband by the low-pass filter LPF_H0 to filter out the mirror sideband signal, so as to obtain the frequency response of the downconverted high-frequency sub-channel signal.

[0043] Preferably, in step 3, the amplitude-frequency error pre-equalizer consists of an SVR model and an LWL module, where 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, introduce a frequency weighting factor into the SVR model, take the high-frequency analog signal band and the low-frequency analog signal band as the target frequency band, and adjust the weight distribution of the correction target precisely according to the weight of the frequency point in the target frequency band;

[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, learns the nonlinear characteristics of the overlapping band and compensates for them, completes the optimization of the overlapping band, and performs a segmented accurate 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 LWL module to optimize the entire frequency band of high-frequency analog signals and low-frequency analog signals, and complete the dynamic calibration of amplitude-frequency error.

[0048] Preferably, step 3.1 specifically includes:

[0049] For the passband and overlap band of high-frequency analog signals and low-frequency analog signals, weights higher than preset values ​​are assigned for precise adjustment, while for the frequency points in the stopband region, the weights are reduced.

[0050] Prioritized, step 3.3 involves iterative optimization using the SVR-LWL joint algorithm, specifically including:

[0051] Step 3.3.1: Use the currently acquired 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 weights of the SVR model using 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 loss of the current FI-DAC system;

[0056] Step 3.3.6: Repeat steps 3.3.1-3.3.5 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 this invention are:

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

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

[0060] 3. This invention solves the amplitude-frequency error problem caused by nonlinear characteristics in FI-DAC systems, especially the calibration requirements in the overlapping bands of high and low frequency signals and the high-frequency sub-band region. This invention takes frequency weighting as the core and optimizes the amplitude-frequency response performance of the signal across the entire frequency band through a refined frequency band calibration strategy. Attached Figure Description

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

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

[0063] Figure 3 A flowchart of the SVR-LWL joint algorithm provided by this invention;

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

[0065] Figure 5 This diagram illustrates a comparison of the flatness performance of the SVR-LWL joint algorithm, the BP algorithm, and the traditional window function algorithm after overlap band correction, as provided in this invention. Figure 5 In the figure, (a) is a comparison of the performance of SVR-LWL and BP algorithms in the correction of overlapping zone 1, (b) is a comparison of the performance of SVR-LWL and traditional window function algorithms in the correction of overlapping zone 1, (c) is a comparison of the performance of SVR-LWL and BP algorithms in the correction of overlapping zone 2, and (d) is a comparison of the performance of SVR-LWL and traditional window function algorithms in the correction of overlapping zone 2. Detailed Implementation

[0066] Specific implementation method one: Combining Figure 1-3 This implementation method is described as follows: Figure 1 As shown, the steps of the peak nonlinear amplitude-frequency error pre-calibration method for the FI-DAC system based on SVR-LWL described in this embodiment include:

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

[0068] S101: The digital domain flow of the FI-DAC system includes ideal frequency division, downconversion operation for high-frequency sub-channels, downsampling of the sub-channel signal output, and assumption of the frequency response Y of the target analog signal. in (jΩ), where Ω is the continuous-time frequency. In the digital domain, with a sampling rate f... s Discrete-time signals are obtained by sampling. Ignoring spectral extension, the frequency response of a single period after sampling is X(e^(-π / 2)). jω ), where ω is the discrete-time frequency, and the frequency response of a single period after sampling satisfies:

[0069]

[0070] S102: To ensure the real-time performance of the output signal, this implementation uses a linear-phase FIR digital filter for signal frequency division. By using complementary window functions of the same order and cutoff frequency, complementary frequency responses can be achieved under ideal conditions. When the two divided signals are added together, the original target signal can be effectively recovered, achieving the purpose of signal reconstruction. Assume the target input signal frequency response is X(e^(-1 / 2)). jω The frequency response of the Nth-order low-pass divider filter is H. LPF_div (e j ω By performing pre-distortion processing and frequency division on the signal, the frequency responses of the high-frequency sub-channel signal and the low-frequency sub-channel signal are obtained as follows:

[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 X represents the frequency response of the low-frequency sub-channel signal. H_div (e jω () represents the frequency response of the high-frequency sub-channel signal;

[0074] S103: To meet the bandwidth limitations of the DAC, its maximum output frequency should be within the DAC sampling rate limit. This implementation uses a digital mixer to shift the high-frequency signal to the baseband signal region. Assume the local oscillator signal frequency is ω. LO To avoid the single-sideband signal amplitude being halved compared to the input signal amplitude, the amplitude of the input local oscillator sine wave signal is set to twice the input amplitude to compensate for possible amplitude attenuation during mixing. The image signal is placed within the stopband by a low-pass filter LPF_H0 to effectively filter out the image sideband signal, resulting in the following signal frequency response after down-conversion:

[0075]

[0076] S104: To meet the sampling rate requirements of the DAC, this implementation then performs M-fold downsampling on the two sub-signals. By appropriately selecting the sampling factor, aliasing errors can be effectively avoided, and the baseband signal can be simplified into a more easily processed form after downsampling.

[0077]

[0078] In formula (4), X L_base (ejω X represents the frequency response of the downsampled low-frequency sub-channel signal. H_base (e jω () represents the frequency response of the downsampled high-frequency sub-channel signal;

[0079] S105: The digital domain flow of the FI-DAC system includes DAC sampling output, filtering out DAC sampling extension through a low-pass filter, then performing frequency conversion operation on the high-frequency sub-path, filtering out image sidebands and non-target signal leakage through a band-pass filter, and finally combining the two sub-path signals for output. The digital signal is then output as an analog signal by the DAC, subject to the DAC's zero-order hold characteristic H. DAC (jΩ), the analog signal will be displayed on the spectrum at a sampling rate f sm Periodic extension is performed, and unwanted spectral extension is filtered out by low-pass filters LPF_L1 and LPF_H1 respectively to obtain the baseband signal;

[0080] The expressions for the low-frequency sub-channel baseband signal and the high-frequency sub-channel baseband signal are as follows:

[0081]

[0082] In formula (5), Y L_DAC (jΩ) represents the low-frequency sub-path baseband signal, Y H_DAC (jΩ) represents the baseband signal of the high-frequency sub-path;

[0083] S106: The high-frequency sub-circuit baseband signal is up-converted by a mixer, where the local oscillator frequency is the same as the digital domain local oscillator frequency, f. LO By using bandpass filters LPF_H2 and HPF_H3 to place the signal to be filtered within the filter stopband range, the image sideband signal, baseband leakage signal and local oscillator leakage signal can be effectively filtered out.

[0084] The expression for the baseband signal of the high-frequency sub-circuit 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: Combines the two processed analog signals through a combiner to output a wideband signal;

[0087] The expression for a 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 systematic error analysis at sampling rate f s The discrete-time signal is obtained by sampling, and then compared with the normalized input discrete-time signal to obtain the system error performance.

[0090] The formula for calculating the loss of the FI-DAC system is:

[0091]

[0092] The above formulas only consider 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 ripple effect in the filter passband, which affects the signal amplitude. Simultaneously, the zero-order hold characteristic of the DAC will cause a certain amplitude attenuation in the high-frequency portion of the target baseband signal, further affecting the signal's amplitude-frequency response. In actual systems, analog devices also introduce insertion loss, and the device gain is not ideally flat within the operating frequency band, resulting in varying loss amounts with frequency, all of which affect the target signal.

[0093] Furthermore, analog devices introduce additional signal components at non-target frequencies. In actual operation, DAC chips introduce signal components such as high-order harmonics and intermodulation distortion, while analog mixers introduce signal components such as intermodulation distortion and local oscillator leakage. To balance the energy of the two signals, the amplifiers set in the high-frequency sub-circuit introduce signal components such as gain error and harmonic distortion. The filters in the FI-DAC model can effectively filter out most non-target signals. The remaining non-target frequency components, such as system noise, have little impact on the frequency response of the output signal. In the combining stage, the aliasing error caused by the addition of these frequency components to other sub-band signals is not considered to affect the amplitude-frequency error.

[0094] To address the aforementioned shortcomings, this embodiment 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: Design method for amplitude-frequency error pre-equalizer;

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

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

[0098]

[0099] In traditional FIR filter design, the ideal infinite impulse response is typically truncated to a finite length in the time domain. This direct truncation causes the Gibbs phenomenon, leading to oscillations, overshoot, and ringing in the frequency response near the truncation point. To mitigate these undesirable effects, various window function methods are widely used in FIR filter design to optimize filter performance by smoothing the truncation edges. A window function is a function used in the time domain to control the sidelobes and ripples introduced during the truncation process. It can be viewed as a weighting function defined over a finite time interval, truncating or modulating the original signal to achieve a smooth transition in the frequency response, but also widening the main lobe and affecting the sharpness of the edge response. This limits the filter's performance in applications with high frequency selectivity.

[0100] Common window function methods include the Hanning window, Hamming window, Bartlett window, Blackman window, Chebyshev window, and Kaiser window. The Hanning and Hamming windows use smooth cosine terms to reduce transitions at both ends of the window, thus reducing spectral leakage. The Bartlett window uses a linear form, resulting in a wide main lobe and slow side lobe attenuation. The Blackman window, by incorporating three cosine terms, further reduces sidelobe levels. The Chebyshev window optimizes the window function by minimizing the maximum sidelobe outside the window, providing excellent sidelobe suppression. The Kaiser window, by adjusting parameters to balance the main lobe width and sidelobe height, is widely used in complex filter designs requiring precise adjustments to stopband and passband performance.

[0101] Different window functions have a significant impact on the frequency response characteristics of a filter. If stopband suppression is the primary consideration, and sidelobe suppression is taken into account, the Chebyshev or Blackman window is the best choice. When a balance between passband frequency resolution and sidelobe suppression is required, the Hanning and Hamming windows can moderately suppress sidelobes while maintaining passband frequency resolution, making them suitable for a wide range of signal processing applications. In fitting an FIR amplitude-frequency pre-calibration filter, the trade-off between frequency selectivity and passband frequency resolution is most critical, and the Kaiser window offers greater flexibility in parameter adjustment.

[0102] The window function method uses a window function ω[n] to truncate the ideal impulse response h. d [n], to obtain the transfer function H(e^(n+1)) of a realizable finite-length unit impulse response FIR filter. jω ), satisfying h[n]=h d[n]·ω[n]. Meanwhile, during pre-calibration of the FIR filter, to avoid introducing additional phase errors, the impulse response of the linear phase filter needs to maintain even symmetry.

[0103] While the window function method is simple and easy to implement, it may widen the transition band while reducing sidelobes, achieving both extremely low sidelobe levels and a narrow main lobe width. For complex fitting targets, its performance is often unsatisfactory. Higher-order FIR filters improve the accuracy of the frequency response by narrowing the transition band, effectively reducing sidelobes and frequency leakage. However, this also increases computational requirements, potentially making implementation difficult in real-time processing systems.

[0104] Under certain order constraints, when designing FIR filters with complex amplitude-frequency response, numerical optimization techniques can be used to directly adjust the filter coefficients to minimize the error between the desired and actual frequency responses, providing a more accurate fitting effect than traditional window function methods.

[0105] S202: For an Nth-order FIR filter with a length of 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-purpose filter without special zeros is constructed, with coefficients 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 sequence, the filter frequency response can be converted into a combination of the amplitude response and the phase response:

[0110]

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

[0112]

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

[0114]

[0115] The amplitude-frequency error pre-equalizer of this invention employs a joint algorithm design based on frequency-weighted support vector regression (SVR) and local weighted learning (LWL) to solve the amplitude-frequency error problem caused by nonlinear characteristics in FI-DAC systems, especially addressing calibration requirements in the overlapping bands of high and low frequency signals and high-frequency sub-bands. This design, with frequency weighting as its core, optimizes the amplitude-frequency response performance of the signal across the entire frequency band through a refined frequency band calibration strategy.

[0116] S205: As Figure 2 As shown, a frequency weighting factor is introduced into the Support Vector Regression (SVR) model. Based on the importance of the frequency points in the target frequency band, the weight distribution of the calibration target is precisely adjusted. For the passband and overlapping 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 optimizing the fitting accuracy. For the frequency points in the stopband region, the interference of non-target frequencies on the model fitting is reduced by decreasing the weight. This frequency weighting mechanism can not only improve the fitting effect of the passband signal, but also effectively control the influence of the stopband signal on the calibration results, avoiding unnecessary increases in model complexity.

[0117] S206: The Locally Weighted Learning (LWL) module further enhances the model's adaptability. LWL learns the local characteristics of each frequency point and optimizes the detailed characteristics of different frequency bands. It has a significant enhancement effect on the complex error performance in the overlapping band and high-frequency sub-band regions. In the overlapping band region, the dynamic error caused by the overlap of high and low frequency signals is more complex. LWL accurately captures and compensates for its nonlinear characteristics by performing deep learning on the local characteristics of this region. In addition, in the high-frequency sub-band, the dynamic fluctuations caused by the non-ideal characteristics of the analog link (such as gain unevenness and image signal leakage) are more significant. The LWL module further improves the calibration accuracy by accurately adjusting the fitting strategy by frequency band.

[0118] S207: The joint SVR-LWL optimization strategy combines frequency weighting with local weighted learning to perform calibration optimization across the entire frequency band. Through the iterative optimization process of the joint algorithm, the error between the target signal's amplitude-frequency response and the actual output is gradually reduced, ensuring that the calibrator can achieve efficient error compensation in complex frequency bands. The fitting accuracy in the passband range is significantly improved, while the stopband error is effectively suppressed, guaranteeing the overall performance of the calibrator. Compared with traditional calibration methods, this joint algorithm not only demonstrates superior fitting ability in overlapping bands and high-frequency sub-band regions but also significantly reduces excessive interference to non-target frequency bands, resulting in a substantial improvement in the efficiency and accuracy of amplitude-frequency error calibration.

[0119] S20701: As Figure 3 As shown, the currently acquired 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 weights of the SVR model using 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 loss of the current FI-DAC system;

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

[0125] Specific Implementation Method Two: Combining Figure 4 and Figure 5 This embodiment will be described as follows: Figure 4 As shown in Table 1, to verify the technical effect of this invention, tests were conducted on this embodiment. The full-band fitting performance is shown in Table 1. From the perspective of frequency response fitting performance, the SVR-LWL algorithm outperforms other algorithms in both the full frequency band and overlapping bands. Within the full frequency band, the RMSE of the pre-calibrator designed with the SVR-LWL algorithm reaches 0.613e-3, further reducing it compared to the 0.692e-3 of the BP algorithm. Compared to the Kaiser window and Hamming window, SVR-LWL has significant advantages in both fitting accuracy and robustness. The data in the table clearly show that the SVR-LWL algorithm exhibits lower error and a higher coefficient of determination (R²) in full-band fitting. 2 The value is close to 1), which indicates that it has a stronger frequency response consistency.

[0126] Table 1

[0127]

[0128] Table 2 shows the fitting performance for the overlapping frequency bands. In the fitting performance analysis of the overlapping frequency points (500MHz and 850MHz), the SVR-LWL algorithm exhibits higher accuracy in detecting the peak amplitude-frequency error. For the 500MHz overlapping band, the RMSE of the SVR-LWL algorithm is 0.213e-2, while the RMSE of the BP algorithm is 0.394e-2, demonstrating higher fitting accuracy. At the 850MHz overlapping band, the SVR-LWL algorithm also surpasses the traditional window function algorithm, fitting the target frequency response more accurately. Combining the specific data in the table, the SVR-LWL algorithm not only reduces the fitting error in the overlapping bands but also demonstrates higher fitting ability in handling dynamic amplitude-frequency errors in high-frequency sub-bands.

[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 frequency points (500MHz and 850MHz), the SVR-LWL algorithm exhibits higher accuracy for the peak amplitude-frequency error. For the 500MHz overlapping band, the RMSE of the SVR-LWL algorithm is 0.213e-2, while the RMSE of the BP algorithm is 0.394e-2, demonstrating higher fitting accuracy. At the 850MHz overlapping band, the SVR-LWL algorithm also surpasses the traditional window function algorithm, fitting the target frequency response more accurately. Combining the specific data in Tables 1 and 2, the SVR-LWL algorithm not only reduces the fitting error in the overlapping band but also demonstrates higher fitting ability in handling the dynamic amplitude-frequency error 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 was integrated into the FI-DAC system, the system's amplitude-frequency response was corrected and analyzed. From the perspective of output signal flatness, the SVR-LWL algorithm significantly improved the full-band and overlapping band frequency response of the FI-DAC. Specifically, in the 500MHz and 850MHz overlapping bands, the flatness of SVR-LWL was 0.031dB (maximum) and -0.062dB (minimum), respectively, close to the ideal value of 0dB. Compared to other algorithms, the SVR-LWL algorithm exhibited better flatness characteristics in the overlapping band. Its corrected amplitude-frequency response almost matched the target frequency response, while traditional algorithms showed significant deviations in the dynamic amplitude-frequency characteristics of these key regions.

[0133] Table 3 shows the full-band flatness test results. Across the entire frequency range, the SVR-LWL algorithm improved the maximum flatness by 0.768 dB and the minimum flatness by 1.57 dB. These results demonstrate that the SVR-LWL algorithm can effectively correct the amplitude-frequency error of the FI-DAC, significantly improving the flatness and frequency consistency of the output signal.

[0134] Table 3

[0135]

[0136]

[0137] The experimental results above demonstrate that the amplitude-frequency error pre-calibrator based on the SVR-LWL algorithm significantly outperforms traditional algorithms in both fitting and correction performance. Particularly in the processing of nonlinear amplitude-frequency errors in overlapping bands and high-frequency subbands, the SVR-LWL algorithm, with its high accuracy and efficiency, better meets the high-frequency broadband application requirements of FI-DAC systems.

[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A pre-calibration method for peak nonlinear amplitude-frequency error of FI-DAC system based on SVR-LWL, characterized in that, The steps of the pre-calibration method for peak nonlinear amplitude-frequency error of the FI-DAC system based on SVR-LWL include: Step 1: Perform predistortion processing on the target input signal of the FI-DAC system. Use a linear phase FIR digital filter to perform ideal frequency division processing on the predistorted target input signal to obtain the high-frequency sub-channel signal and the low-frequency sub-channel signal. Step 2: Mix, filter, convert digital to analog and combine the high-frequency and low-frequency signals and input them into the analog link to generate a broadband signal; Step 3: Based on the amplitude-frequency error pre-equalizer in the analog link, dynamically calibrate the amplitude-frequency error caused by nonlinear characteristics, generate a calibrated target signal waveform table, and output it; In step 3, the amplitude-frequency error pre-equalizer consists of an SVR model and an LWL module. SVR is frequency-weighted support vector regression, and LWL is local weighted learning. Step 3 specifically includes: Step 3.1: In the analog link, introduce a frequency weighting factor into the SVR model, take the high-frequency analog signal band and the low-frequency analog signal band as the target frequency band, and adjust the weight distribution of the correction target precisely according to the weight of the frequency point in the target frequency band; 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, learns the nonlinear characteristics of the overlapping band and compensates for them, completes the optimization of the overlapping band, and performs a segmented accurate 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 LWL module to optimize the entire frequency band of high-frequency analog signals and low-frequency analog signals, and complete the dynamic calibration of amplitude-frequency error.

2. The method for pre-calibrating the peak nonlinear amplitude-frequency error of a FI-DAC system based on SVR-LWL according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Set the frequency response of the target analog signal ,in For continuous time frequency, in the digital domain, it is expressed as the sampling rate. The target analog signal is sampled to obtain a discrete-time signal. The frequency response of a single period after sampling is: ,in It is a 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 as follows. The frequency response of the FIR digital filter is The expressions for the frequency response of the high-frequency sub-channel signal and the low-frequency sub-channel signal are: （1）； In formula (1), For the frequency response of the low-frequency sub-channel signal, This refers to the frequency response of the high-frequency sub-channel signal; The expression for the frequency response after sampling in a single period is: （2）。 3. The method for pre-calibrating the peak nonlinear amplitude-frequency error of a FI-DAC system based on SVR-LWL according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Limit the maximum output frequency of the high-frequency sub-channel signal and the low-frequency sub-channel signal to within the DAC sampling frequency, and perform M-fold downsampling processing on the high-frequency sub-channel signal and the low-frequency sub-channel signal; Step 2.2: Perform down-conversion processing on the downsampled high-frequency sub-channel signal; Step 2.3: Use an analog low-pass filter to filter out the DAC sampling extension of the downsampled low-frequency sub-channel signal and the downconverted high-frequency sub-channel signal; Step 2.4: Combine the low-frequency and high-frequency sub-channel signals after filtering and DAC sampling extension to obtain low-frequency digital signals and low-frequency analog signals. These low-frequency digital signals and low-frequency analog signals are then passed through the DAC to output high-frequency and low-frequency analog signals, respectively, which are affected by the DAC's zero-order hold characteristic. High-frequency analog signals and low-frequency analog signals are displayed in the spectrum at a sampling rate. Periodic extension is performed, and error correction is applied to high-frequency and low-frequency analog signals using an amplitude-frequency error pre-equalizer. Step 2.5: The low-frequency analog signal is filtered by a low-pass filter LPF_L1 to remove redundant spectral extensions, and the low-frequency sub-path baseband signal is obtained. The high-frequency analog signal is filtered by a low-pass filter LPF_H1 to remove redundant spectral extensions, and the high-frequency sub-path baseband signal is obtained. Step 2.6: Perform up-conversion on the high-frequency sub-circuit baseband signal, wherein the local oscillator frequency in the up-conversion operation is set to be the same as the digital domain local oscillator frequency. By using bandpass filters LPF_H2 and HPF_H3, the signal to be filtered is placed within the filter stopband range, thus filtering out the image sideband signal, baseband leakage signal, and local oscillator leakage signal. Step 2.7: The low-frequency sub-circuit baseband signal and the high-frequency sub-circuit baseband signal after up-conversion are added together by a combiner to output a broadband signal; Step 2.8: Using the sampling rate The discrete-time signal is obtained by sampling, and then compared with the normalized input discrete-time signal to obtain the FI-DAC system loss. The expression for the frequency response of the high-frequency sub-channel signal after down-conversion is: （3）； The frequency response expressions for the downsampled high-frequency sub-channel signal and low-frequency sub-channel signal are as follows: （4）； In formula (4), This refers to the frequency response of the downsampled low-frequency sub-channel signal. This refers to the frequency response of the downsampled high-frequency sub-channel signal; The expressions for the low-frequency sub-channel baseband signal and the high-frequency sub-channel baseband signal are as follows: （5）； In formula (5), For low-frequency sub-circuit baseband signals, It is a high-frequency sub-circuit baseband signal; The expression for the baseband signal of the high-frequency sub-circuit after up-conversion is: （6）； The expression for a broadband signal is: （7）； The formula for calculating the loss of the FI-DAC system is: （8）。 4. The peak nonlinear amplitude-frequency error pre-calibration method for FI-DAC systems based on SVR-LWL according to claim 3, characterized in that, Step 2.2 specifically includes: The downsampled high-frequency sub-channel signal is shifted to the baseband signal region using a digital mixer, and the local oscillator signal frequency is set to [value missing]. The amplitude of the local oscillator sine wave signal of the downsampled high-frequency sub-channel signal is twice the frequency of the local oscillator signal. The downsampled high-frequency sub-channel signal is downconverted, and the mirror signal generated by the downconversion is placed in the stopband by the low-pass filter LPF_H0 to filter out the mirror sideband signal, so as to obtain the frequency response of the downconverted high-frequency sub-channel signal.

5. The peak nonlinear amplitude-frequency error pre-calibration method for FI-DAC systems based on SVR-LWL according to claim 1, characterized in that, Step 3.1 specifically includes: For the passband and overlap band of high-frequency analog signals and low-frequency analog signals, weights higher than preset values ​​are assigned for precise adjustment, while for the frequency points in the stopband region, the weights are reduced.

6. The method for pre-calibrating the peak nonlinear amplitude-frequency error of a FI-DAC system based on SVR-LWL according to claim 1, characterized in that, Step 3.3 involves iterative optimization using the SVR-LWL joint algorithm, specifically including: Step 3.3.1: Use the currently acquired 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 weights of the SVR model using 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 loss of the current FI-DAC system; Step 3.3.6: Repeat steps 3.3.1-3.3.5 until the parameter requirements are met or the maximum number of iterations is reached to obtain the optimal parameters of the FI-DAC system.

Images