Data-driven background time mismatch calibration method and system without reference channel, terminal and storage medium

Abstract

The invention discloses a data-driven background time mismatch calibration method and system without a reference channel, a terminal and a storage medium. The method comprises the following steps: inputting an input signal into a multi-coset sampling system to obtain a sampling sequence containing time mismatch; performing cross-correlation calculation according to the sampling sequence to obtain a channel cross-correlation difference value; and iteratively updating a pseudo partial derivative parameter estimation value and a time mismatch estimation value by adopting a data-driven adaptive calibration method, and performing error compensation on the sampling sequence by adopting a time mismatch error compensation method based on Taylor approximation. According to the method, the time mismatch error is estimated by analyzing the statistical characteristics of the sampling sequence, system sampling does not need to be interrupted, and a reference channel which is coprime with the sampling rate of a target channel does not need to be introduced; a data-driven adaptive calibration algorithm is adopted to update a time mismatch estimated value, and fast convergence and high-precision calibration is realized only depending on real-time measured data and without depending on step length selection.

Description

Technical Field

[0001] The present invention relates to the technical field of time mismatch calibration, and particularly to a data-driven background time mismatch calibration method, system, terminal, and computer-readable storage medium without a reference channel. Background Art

[0002] Currently, the main sub-Nyquist sampling architectures mainly include: multi-coset sampling systems, random demodulator sampling systems, and modulated wideband converter sampling systems. Among them, the multi-coset sampling system utilizes the sparsity of broadband signals to sample and retain the key information of the signal at a sampling rate lower than the Nyquist sampling rate. In contrast, the multi-coset sampling system has significant advantages in terms of hardware implementation, energy efficiency, and algorithm complexity. However, process-voltage-temperature variations can cause mismatch problems between channels, generating spurious components in the output spectrum, thereby distorting the input signal and reducing the dynamic performance. Among them, the performance degradation caused by time mismatch is particularly serious. The calibration of time mismatch includes two steps: estimation and calibration. Background calibration does not require a reference signal and can quickly track the changes in mismatch errors without interrupting the continuous operation of the system. Therefore, for a sampling system that operates continuously for a long time, the background calibration method is a more ideal choice. However, existing background calibration methods usually need to introduce a reference channel with a relatively prime sampling rate to the target channel, which will introduce dynamic impedance interference and asynchronous sampling problems. Moreover, the speed and accuracy of existing adaptive iterative calibration methods are limited by the selection of the step size in the adaptive iterative algorithm, and there are limitations.

[0003] Therefore, the prior art still needs to be improved and developed. Summary of the Invention

[0004] The main purpose of the present invention is to provide a data-driven background time mismatch calibration method, system, terminal, and computer-readable storage medium without a reference channel, aiming to solve the problem that existing background time mismatch calibration methods usually need to introduce a reference channel and the speed and accuracy of adaptive iterative calibration are limited by the selection of the step size.

[0005] To achieve the above invention purpose, the present invention provides a data-driven background time mismatch calibration method without a reference channel, and the data-driven background time mismatch calibration method without a reference channel includes:

[0006] Obtain an input signal, and input the input signal into a plurality of sampling channels of a multi-coset sampling system for sampling to obtain a sampling sequence containing time mismatch output by each sampling channel;

[0007] Randomly set an initial time mismatch estimation value, and based on the initial time mismatch estimation value, perform preliminary time mismatch error compensation on the sampling sequence containing time mismatch by using a time mismatch error compensation method based on Taylor approximation;

[0008] Based on the initial time mismatch estimation value and the sampled sequence after preliminary time mismatch error compensation, perform cross-correlation calculation to obtain the channel cross-correlation difference, and determine whether the channel cross-correlation difference meets the error tolerance condition;

[0009] If not, adopt a data-driven adaptive calibration method to iteratively update the pseudo-partial derivative parameter estimation value and the time mismatch estimation value, and based on the updated time mismatch estimation value, adopt a time mismatch error compensation method based on Taylor approximation to perform time mismatch error compensation on the sampled sequence after preliminary time mismatch error compensation until the channel cross-correlation difference meets the error tolerance condition.

[0010] Optionally, the multi-coset sampling system is implemented by using p sampling channels in the time-interleaved analog-to-digital converters of L sampling channels, where p ≤ L, and the set consisting of p different integers randomly selected from {0, 1, …, L - 1} i is called the (L, p) sampling pattern, where c

[0011] The sampling rate of each sampling channel is where the offset of the i-th sampling channel is c i T s , and the sampling moment of the i-th sampling channel is Φ i (t) = (mL + c i )T s , where f s is the system sampling rate, T s is the sampling interval, and m is an arbitrary integer;

[0012] The obtaining of the input signal and inputting the input signal into multiple sampling channels of the multi-coset sampling system for sampling to obtain sampled sequences with time mismatch output by each sampling channel specifically includes:

[0013] Obtain the input signal, define the input signal as the continuous-time signal x(t), and the output of the i-th sampling channel in the multi-coset sampling system at the n-th sampling moment is:

[0014]

[0015] Define the time mismatch of the i-th sampling channel as Δt i , then in the case of time mismatch, the output of the i-th sampling channel at the n-th sampling moment is:

[0016]

[0017] where t represents time, yi [n] represents the sampling sequence without time mismatch output by the i-th sampling channel at the n-th sampling moment, and x(nT s ) is the value of the continuous-time signal x(t) at time nT s . Here, n is an integer, is the set of integers, δ[·] is the discrete-time impulse function, represents the sampling sequence with time mismatch output by the i-th sampling channel at the n-th sampling moment.

[0018] Optionally, according to the initial time mismatch estimation value, a preliminary time mismatch error compensation is performed on the sampling sequence with time mismatch by using a time mismatch error compensation method based on Taylor approximation, which specifically includes:

[0019] Taking the initial time mismatch estimation value corresponding to the i-th sampling channel as the time mismatch Δt i ;

[0020] Taking the sampling sequence with time mismatch output by the i-th sampling channel as the actual sampling sequence

[0021] Taking the sampling sequence after preliminary time mismatch error compensation corresponding to the i-th sampling channel as the ideal sampling sequence y i ;

[0022] Establishing an error term according to the time mismatch Δt i and the Taylor series expansion method, and subtracting the error term from the actual sampling sequence to obtain the ideal sampling sequence;

[0023]

[0024] where d is the order of the Taylor series, and d! represents the factorial of d, represents the d-th derivative of the actual sampling sequence .

[0025] Optionally, according to the initial time mismatch estimation value and the sampling sequence after preliminary time mismatch error compensation, a cross-correlation calculation is performed to obtain the cross-correlation difference between channels, and it is determined whether the cross-correlation difference between channels meets the error tolerance condition, which specifically includes:

[0026] Taking the initial time mismatch estimation value as the time mismatch Δt, and taking the sampling sequence after preliminary time mismatch error compensation as the sampling sequence output by the sampling channel to be estimated for time mismatch;

[0027] Taking the first sampling channel as the reference sampling channel, setting the time mismatch Δt1 of the first sampling channel to 0, and taking the second sampling channel as the sampling channel for which the time mismatch is to be estimated, setting the time mismatch Δt2 of the second sampling channel to Δt;

[0028] The time mismatch causes the sampling moments of the sampling channels to shift, changing the sampling interval from T s to T s ±ΔtT s . By performing cross-correlation calculation on the sampling sequences output by the first sampling channel and the second sampling channel, we obtain:

[0029]

[0030] where R(·) is the cross-correlation function, E(·) is the expected value, y1[·] represents the sampling sequence output by the first sampling channel, represents the sampling sequence output by the second sampling channel, and k is an integer, k = 1, …, n;

[0031] For ΔtT s , according to the first-order Taylor approximation principle, we have:

[0032] R(T s +ΔtT s ) = R(T s ) + ΔtT s ×R(T s );

[0033] R(T s -ΔtT s ) = R(T s ) - ΔtT s ×R′(T s );

[0034] where R′(·) is the derivative of the cross-correlation function R(·);

[0035] Performing a difference operation on the above formula to eliminate the R(T s ) term, we obtain the channel cross-correlation difference ∈:

[0036] ∈ = R(T s +ΔtT s ) - R(T s -ΔtT s ) = 2ΔtT s ×R(T s );

[0037] According to the channel cross-correlation difference, determine whether the relative error between the channel cross-correlation difference and the expected value of the channel cross-correlation difference is not greater than the set error tolerance;

[0038] If so, it indicates that there is no time mismatch in the sampling channel to be estimated for time mismatch;

[0039] If not, it indicates that there is a time mismatch in the sampling channel to be estimated for time mismatch.

[0040] Optionally, the data-driven adaptive calibration method is adopted to iteratively update the pseudo partial derivative parameter estimate and the time mismatch estimate, which specifically includes:

[0041] Define the time mismatch estimate of the i-th sampling channel in the k-th iteration as u i (k). In the k-th iteration, u i (k) and the channel cross-correlation difference ∈ i (k) of the i-th sampling channel in the k-th iteration have the following relationship:

[0042] ∈ i (k) = f(∈ i (k - 1), …, ∈ i (k - n ∈ ), u i (k), …, u i (k - n u ));

[0043] where f(·) is an unknown non-linear system, ∈ i (·) represents the channel cross-correlation difference of the i-th sampling channel, u i (·) represents the time mismatch estimate of the i-th sampling channel, and n ∈ represents the order of the historical channel cross-correlation difference relative to ∈ i (k), and n u represents the order of the historical time mismatch estimate relative to u i (k);

[0044] Assume that the partial derivative of the non-linear system with respect to u i (k) is continuous and the non-linear system satisfies the Lipschitz continuity condition. Then, for any k, there is:

[0045] Δ∈ i (k) = ∈ i (k) - ∈ i (k - 1);

[0046] Δu i (k) = u i (k) - u i (k - 1), Δu i (k) ≠ 0;

[0047] where Δ∈ i(·) represents the change in the channel cross-correlation difference between two adjacent iterations, Δu i (·) represents the change in the time mismatch estimate between two adjacent iterations;

[0048] For all iteration rounds k, there exists a pseudo partial derivative parameter φ i (k), and using the pseudo partial derivative parameter φ i (k) to transform ∈ i (k) into an equivalent dynamic linearization model:

[0049] Δ∈ i (k) = φ i (k)Δu i (k);

[0050] where φ i (k) represents the pseudo partial derivative parameter of the i-th sampling channel at the k-th iteration;

[0051] In order to estimate the pseudo partial derivative parameter φ i (k), a first criterion function is defined:

[0052]

[0053] where J(·) represents the first criterion function, represents the estimated value of the pseudo partial derivative parameter of the i-th sampling channel at the k-th iteration, represents the estimated value of the pseudo partial derivative parameter of the i-th sampling channel at the (k - 1)-th iteration, and μ is a weight factor used to avoid excessive changes;

[0054] Since the first criterion function is a convex function, solving gives:

[0055]

[0056] where η is a step constant used to control the update amplitude;

[0057] According to the calculation formula of , calculate and update the estimated value of the pseudo partial derivative parameter;

[0058] In order to accurately track the time-varying pseudo partial derivative parameter and ensure that Δu i (k) ≠ 0, reset the estimated value of the pseudo partial derivative parameter:

[0059] If or |Δu i (k - 1)| 2 ≤ ε or

[0060] Among them, φ i (0) is the initial value of the pseudo partial derivative parameter, ε is a positive constant used to reset , and sign(·) is the sign function;

[0061] In order to perform time mismatch error compensation on the sampling sequence according to u i (k), a second criterion function is defined:

[0062]

[0063] Among them, J′(·) represents the second criterion function, is the expected value of the channel cross-correlation difference of the i-th sampling channel, and λ is a weight factor used to limit the change rate of u i (k);

[0064] According to and Δu i (k) = u i (k) - u i (k - 1), it can be obtained that:

[0065]

[0066] Since the second criterion function is a convex function, solving obtains:

[0067]

[0068] Among them, ρ is a step constant used to control the update amplitude of u i (k);

[0069] According to the calculation formula of u i (k), calculate and update the time mismatch estimate value.

[0070] Optionally, according to the updated time mismatch estimate value, a time mismatch error compensation method based on Taylor approximation is used to perform time mismatch error compensation on the sampling sequence after preliminary time mismatch error compensation until the channel cross-correlation difference meets the error tolerance condition, specifically including:

[0071] Take the updated time mismatch estimate value corresponding to the i-th sampling channel as the time mismatch Δt i , and let Δt i = u i (k);

[0072] Take the sampling sequence after preliminary time mismatch error compensation corresponding to the i-th sampling channel as the actual sampling sequence

[0073] Take the sampled sequence after compensating the time mismatch error corresponding to the \(i\)-th sampling channel as the ideal sampled sequence \(y\). i ;

[0074] Based on the time mismatch \(\Delta t\) i and the Taylor series expansion method, establish an error term, and subtract the error term from the actual sampled sequence to obtain the ideal sampled sequence;

[0075]

[0076] Based on the updated time mismatch estimate value and the sampled sequence after time mismatch error compensation, perform cross-correlation calculation to obtain the channel cross-correlation difference \(\epsilon\) i (k);

[0077] Based on the channel cross-correlation difference \(\epsilon\) i (k), determine whether the relative error between the channel cross-correlation difference \(\epsilon\) i (k and the expected value of the channel cross-correlation difference is not greater than the set error tolerance value \(\sigma\), and determine whether the current iteration round \(k\) is greater than the maximum iteration number \(k\) max ;

[0078] If the channel cross-correlation difference \(\epsilon\) i (k) satisfies or the current iteration round \(k\) satisfies \(k > k\) max , then stop the iteration;

[0079] Otherwise, repeat the iteration to update the pseudo partial derivative parameter estimate value and the time mismatch estimate value until the channel cross-correlation difference satisfies the error tolerance condition or reaches the maximum iteration number;

[0080] When the condition for triggering the iteration stop is that \(\epsilon\) i (k) satisfies , return \(u\) i (k as the time mismatch calibration result;

[0081] When the condition for triggering the iteration stop is that \(k\) satisfies \(k > k\) max , return the time mismatch estimate value corresponding to the minimum element in the channel cross-correlation difference set \(\Gamma\) i as the time mismatch calibration result.

[0082] Optionally, the data-driven background time mismatch calibration method without a reference channel further includes:

[0083] Perform background time mismatch calibration on each of the multiple sampling channels of the multi-coset sampling system one by one;

[0084] The data-driven background time mismatch calibration method without a reference channel further includes:

[0085] For a sampling channel with sampling interval symmetry, directly perform cross-correlation calculation to obtain the cross-correlation difference between channels;

[0086] Based on the cross-correlation difference between channels, use a data-driven adaptive calibration method to calibrate the sampling channel with sampling interval symmetry, and obtain a calibrated sampling channel with sampling interval symmetry;

[0087] For a sampling channel without sampling interval symmetry, introduce the minimum number of additional sampling channels in layers. Based on the calibrated sampling channel with sampling interval symmetry, perform cross-correlation calculation and use a data-driven adaptive calibration method to calibrate the additional sampling channels, and obtain calibrated additional sampling channels;

[0088] Based on the calibrated additional sampling channels, perform cross-correlation calculation and use a data-driven adaptive calibration method to calibrate the sampling channel without sampling interval symmetry, and obtain a calibrated sampling channel without sampling interval symmetry.

[0089] To achieve the above invention purpose, the present invention also provides a data-driven background time mismatch calibration system without a reference channel. The data-driven background time mismatch calibration system without a reference channel includes:

[0090] Sampling module: used to obtain an input signal, input the input signal into a plurality of sampling channels of a multi-coset sampling system for sampling, and obtain sampling sequences containing time mismatch output by each sampling channel;

[0091] Preliminary estimation and compensation module: used to randomly set an initial time mismatch estimation value, and according to the initial time mismatch estimation value, use a time mismatch error compensation method based on Taylor approximation to perform preliminary time mismatch error compensation on the sampling sequence containing time mismatch;

[0092] Cross-correlation calculation module: used to perform cross-correlation calculation according to the initial time mismatch estimation value and the sampling sequence after preliminary time mismatch error compensation, obtain the cross-correlation difference between channels, and determine whether the cross-correlation difference between channels meets the error tolerance condition;

[0093] Adaptive calibration module: used to, if not, use a data-driven adaptive calibration method to iteratively update the pseudo partial derivative parameter estimation value and the time mismatch estimation value, and according to the updated time mismatch estimation value, use a time mismatch error compensation method based on Taylor approximation to perform time mismatch error compensation on the sampling sequence after preliminary time mismatch error compensation until the cross-correlation difference between channels meets the error tolerance condition.

[0094] To achieve the above-mentioned invention objectives, the present invention also provides a terminal, which includes: a memory, a processor, and a data-driven background time mismatch calibration program without reference channels stored on the memory and executable on the processor. When the data-driven background time mismatch calibration program without reference channels is executed by the processor, it realizes the steps of the data-driven background time mismatch calibration method without reference channels as described above.

[0095] To achieve the above-mentioned invention objectives, the present invention also provides a computer-readable storage medium, which stores a data-driven background time mismatch calibration program without reference channels. When the data-driven background time mismatch calibration program without reference channels is executed by a processor, it realizes the steps of the data-driven background time mismatch calibration method without reference channels as described above.

[0096] In the present invention, an input signal is obtained and input into multiple sampling channels of a multi-coset sampling system for sampling to obtain sampling sequences with time mismatch output from each sampling channel; an initial time mismatch estimate value is randomly set, and based on the initial time mismatch estimate value, a time mismatch error compensation method based on Taylor approximation is used to perform preliminary time mismatch error compensation on the sampling sequences with time mismatch; according to the initial time mismatch estimate value and the sampling sequences after preliminary time mismatch error compensation, cross-correlation calculation is performed to obtain channel cross-correlation differences, and it is determined whether the channel cross-correlation differences meet the error tolerance condition; if not, a data-driven adaptive calibration method is used to iteratively update the pseudo partial derivative parameter estimate value and the time mismatch estimate value, and based on the updated time mismatch estimate value, a time mismatch error compensation method based on Taylor approximation is used to perform time mismatch error compensation on the sampling sequences after preliminary time mismatch error compensation until the channel cross-correlation differences meet the error tolerance condition. The present invention estimates the time mismatch error by analyzing the statistical characteristics of the sampling sequences, without interrupting system sampling and without introducing a reference channel that is relatively prime to the sampling rate of the target channel, avoiding the dynamic impedance interference and asynchronous sampling problems in traditional background calibration methods; a data-driven iterative algorithm is used to update the time mismatch estimate value, which only depends on real-time measured data and does not depend on the selection of the step size. By establishing a local dynamic linearization data model based on time-varying pseudo partial derivative parameters and minimizing the calibration error through multiple iterations to search for the optimal time mismatch estimate value, fast convergence and high-precision calibration are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 is a flowchart of a preferred embodiment of the data-driven background time mismatch calibration method without reference channels of the present invention;

[0098] Figure 2 are a structural schematic diagram and a timing diagram of a multi-coset sampling system;

[0099] Figure 3 is a multi-coset sampling timing diagram with time mismatch;

[0100] Figure 4 is a waveform diagram showing the impact of time mismatch;

[0101] Figure 5 is a schematic diagram of the time mismatch estimation process for a multi-coset sampling system;

[0102] Figure 6 is a schematic diagram of the structure of a data-driven adaptive calibration method;

[0103] Figure 7 is a comparison chart of channel cross-correlation difference curves for various background calibration schemes;

[0104] Figure 8 is a performance comparison chart of various background calibration schemes under different signal-to-noise ratios;

[0105] Figure 9 is a structural diagram of a preferred embodiment of the data-driven background time mismatch calibration system of the present invention without a reference channel;

[0106] Figure 10 is a structural diagram of a preferred embodiment of the terminal of the present invention. Detailed implementation manners

[0107] To make the objectives, technical solutions and advantages of the present invention clearer and more definite, the following further describes the present invention in detail with reference to the accompanying drawings and by way of examples. It should be understood that the specific examples described herein are only used to explain the present invention and are not used to limit the present invention.

[0108] With the rapid progress of wireless communication technologies, society's demand for higher capacity, denser network coverage, and lower latency is increasing day by day. This trend will be even more significant in the 6G era. 6G networks not only need to support transmission bandwidths in the hundreds of megahertz or even terahertz range, but also need to meet the requirements of new application scenarios such as holographic communication, intelligent transportation, and remote healthcare. To achieve these goals, 6G networks will rely on a series of key technological innovations, including terahertz band communication, artificial intelligence-driven network optimization, and quantum communication. However, with the continuous expansion of bandwidth, challenges such as high-speed sampling and processing of broadband signals have become increasingly prominent. Broadband signal sampling can instantaneously capture wideband, high-dynamic electromagnetic spectrum signals, improve spectrum acquisition efficiency, and quickly extract valuable information, and is a necessary means for electromagnetic spectrum sensing.

[0109] Traditional Nyquist sampling requires the sampling rate to be at least twice the maximum bandwidth of the signal, making it difficult for high-speed sampling, large-capacity data storage, and real-time processing of broadband signals. Compressive sensing technology directly samples sparse or compressible signals at a sub-Nyquist rate and uses reconstruction algorithms to accurately recover the original signal, significantly reducing the requirements for storage, transmission, and processing hardware, and providing a new solution for real-time electromagnetic spectrum sensing.

[0110] Currently, the main sub-Nyquist sampling architectures mainly include: multi-coset sampling systems, random demodulator sampling systems, and modulated wideband converter sampling systems. The multi-coset sampling system utilizes the sparsity of broadband signals to sample and retain the key information of the signal at a rate lower than the Nyquist sampling rate. It achieves high-speed sampling of broadband signals through a multi-channel architecture, with each channel using the same sampling rate but different time offsets. Therefore, it can be implemented by using some channels of a time-interleaving analog-to-digital converter (TIADC), effectively reducing the hardware implementation cost. Among them, the TIADC sampling technology achieves high-speed Nyquist sampling through the parallel alternating operation of multiple low-sampling-rate analog-to-digital converters. The random demodulator sampling system multiplies the input signal by a pseudo-random sequence (modulation), and then samples at a low speed after low-pass filtering through an integrator. Random modulation "folds" the signal spectrum information into the low-frequency range to achieve sub-Nyquist sampling. However, it relies on the randomness of the pseudo-random sequence, has high requirements for the pseudo-random sequence, and the reconstruction algorithm is complex with a large computational overhead. The modulated wideband converter sampling system modulates and filters the signal through multiple channels. Each channel modulates the signal using a different pseudo-random sequence, and then performs low-pass filtering and low-speed sampling. Through multi-channel joint processing, the system can recover the spectrum information of the original signal. However, its hardware complexity is relatively high, requiring multiple channels, and the reconstruction algorithm is complex.

[0111] In contrast, the multi-coset sampling system has significant advantages in terms of hardware implementation, energy efficiency, and algorithm complexity. It does not need to rely on complex pseudo-random modulation or high-frequency filtering modules, has a simpler hardware structure and higher energy efficiency. At the same time, the multi-coset sampling system can be implemented by using some channels of the TIADC sampling system, with lower development difficulty and cost. The implementation of random demodulators and modulated wideband converters requires pseudo-random sequences operating at the Nyquist rate, with higher hardware complexity and computational overhead. In addition, the multi-coset sampling does not require complex spectrum folding or joint demodulation processing, and the signal reconstruction algorithm is simpler, especially suitable for real-time capture and processing scenarios of sparse broadband signals, and has more practical potential in 6G high-frequency band communication and dynamic spectrum sensing.

[0112] However, process-voltage-temperature variations can lead to inter-channel mismatch problems, generating spurious components in the output spectrum, distorting the input signal, and degrading the dynamic performance. Mismatch mainly includes three types, namely gain mismatch, offset mismatch, and timing mismatch. Many studies have analyzed the impact of channel mismatch problems on the spurious-free dynamic range (SFDR) and signal-to-noise and distortion ratio (SNDR) of multi-channel sampling systems, and the performance degradation caused by timing mismatch is particularly severe.

[0113] The calibration of timing mismatch consists of two steps: estimation and calibration. Depending on the estimation technique, it can be divided into foreground calibration and background calibration. Foreground calibration usually uses a known reference signal to calculate calibration parameters and requires interrupting the sampling process during calibration. Although it can achieve accurate mismatch estimation, it cannot track the dynamic changes of timing mismatch. Background calibration generally processes the output data of the system to extract error information while the system is operating normally. Compared with foreground calibration, background calibration does not require a reference signal and can quickly track the changes in mismatch errors without interrupting the continuous operation of the system. Therefore, for sampling systems that operate continuously for a long time, the background calibration method is a more ideal choice.

[0114] However, existing background calibration methods face some key limitations: they usually require a reference channel to estimate the timing mismatch error, but the requirement for relatively prime sampling rates between the reference channel and the target channel introduces dynamic impedance interference and asynchronous sampling problems, generating additional spurs and increasing system power consumption. At the same time, accurate timing mismatch estimation often requires multiple iterations to approach the accurate value. Adaptive iterative calibration methods can gradually correct the timing mismatch estimate by adjusting the update direction and amplitude of the calibration parameters for the next iteration based on the calibration error of the previous iteration, but the calibration speed and accuracy are limited by the choice of step size in the adaptive iterative algorithm, such as algorithms based on least-mean-squares (LMS) and variable-step-size least-mean-squares (VSSLMS). Among them, the LMS-based calibration scheme uses a fixed step size and cannot achieve both fast convergence and low steady-state error. The VSSLMS-based method improves the convergence speed by dynamically adjusting the step size but still depends on the choice of the initial step size.

[0115] To solve the above technical problems, the present invention provides a data-driven background time mismatch calibration method without a reference channel. An input signal is acquired and input into multiple sampling channels of a multi-coset sampling system for sampling to obtain sampling sequences containing time mismatch output by each sampling channel. An initial time mismatch estimate value is randomly set, and based on the initial time mismatch estimate value, a time mismatch error compensation method based on Taylor approximation is used to perform preliminary time mismatch error compensation on the sampling sequences containing time mismatch. Cross-correlation calculation is performed based on the initial time mismatch estimate value and the sampling sequences after preliminary time mismatch error compensation to obtain a channel cross-correlation difference value, and it is determined whether the channel cross-correlation difference value meets the error tolerance condition. If not, a data-driven adaptive calibration method is used to iteratively update the pseudo partial derivative parameter estimate value and the time mismatch estimate value, and based on the updated time mismatch estimate value, a time mismatch error compensation method based on Taylor approximation is used to perform time mismatch error compensation on the sampling sequences after preliminary time mismatch error compensation until the channel cross-correlation difference value meets the error tolerance condition. The present invention estimates the time mismatch error by analyzing the statistical characteristics of the sampling sequences, without interrupting system sampling and without introducing a reference channel that is relatively prime to the sampling rate of the target channel, avoiding the dynamic impedance interference and asynchronous sampling problems in traditional background calibration methods; uses a data-driven iterative algorithm to update the time mismatch estimate value, which only depends on real-time measured data and does not depend on the selection of the step size. By establishing a local dynamic linearization data model based on time-varying pseudo partial derivative parameters, the best time mismatch estimate value is searched by minimizing the calibration error through multiple iterations, thereby achieving fast convergence and high-precision calibration.

[0116] The following further describes the application content by describing the embodiments in conjunction with the accompanying drawings.

[0117] A preferred embodiment of the data-driven background time mismatch calibration method without a reference channel of the present invention is as Figure 1 shown, and specifically includes:

[0118] S1. Acquire an input signal, and input the input signal into multiple sampling channels of a multi-coset sampling system for sampling to obtain sampling sequences containing time mismatch output by each sampling channel.

[0119] In an implementation manner of this embodiment, the multi-coset sampling system is implemented by using p sampling channels in a time-interleaved analog-to-digital converter with L sampling channels, p ≤ L, and a set composed of p different integers randomly selected from {0, 1,..., L - 1} i is called an (L, p) sampling mode, where c

[0120] represents the i-th element in the set C, i = 1,..., p; where the offset of the \(i\)-th sampling channel is \(c\). i T s and the sampling time of the \(i\)-th sampling channel is \(\varPhi\). i (t) = (mL + c i )T s where \(f\) s is the system sampling rate, \(T\) s is the sampling interval, and \(m\) is an arbitrary integer;

[0121] The obtaining of the input signal, inputting the input signal into a plurality of sampling channels of a multi-coset sampling system for sampling, and obtaining sampling sequences with time mismatch output by each sampling channel specifically includes:

[0122] Obtaining an input signal, defining the input signal as a continuous-time signal \(x(t)\), and the output of the \(i\)-th sampling channel in the multi-coset sampling system at the \(n\)-th sampling time is:

[0123]

[0124] The problem of time mismatch will reduce the dynamic performance of the multi-coset sampling system. Figure 3 is the timing diagram of the multi-coset sampling system when there is time mismatch. Define the time mismatch of the \(i\)-th sampling channel as \(\Delta t\). i Then, in the case of time mismatch, the output of the \(i\)-th sampling channel at the \(n\)-th sampling time is:

[0125]

[0126] where \(t\) represents time, \(y\) i [n] represents the sampling sequence without time mismatch output by the \(i\)-th sampling channel at the \(n\)-th sampling time, \(x(nT\) s ) is the value of the continuous-time signal \(x(t)\) at time \(t = nT\). s n is an integer, is the set of integers, \(\delta[\cdot]\) is the discrete-time impulse function, represents the sampling sequence with time mismatch output by the \(i\)-th sampling channel at the \(n\)-th sampling time.

[0127] Specifically, the present invention analyzes based on the multi-coset sampling system in a wideband compressive sampling system. The multi-coset sampling technique is a periodic non-uniform sub-Nyquist sampling technique, which can be implemented through a multi-channel parallel sampling architecture, as Figure 2 shown, Figure 2 in which (a) is the structural schematic diagram of the multi-coset sampling system, Figure 2Among them, (b) is the timing diagram of the multi-coset sampling system. Compared with the TIADC sampling system with L channels, the multi-coset sampling system only needs p (p ≤ L) parallel sampling channels to implement. is the system sampling rate, T s is the Nyquist sampling time period interval of the input signal. The set composed of p different integers randomly selected from {0, 1, …, L - 1} is called the (L, p) sampling pattern. The average sampling rate of the multi-coset sampling system can be expressed as where is called the sub-Nyquist sampling rate, that is, the compression sampling rate, which represents the ratio of the actual number of sampling points to the Nyquist sampling points before compression, and reflects the sampling efficiency of the system.

[0128] S2. Randomly set the initial time mismatch estimation value, and according to the initial time mismatch estimation value, adopt a time mismatch error compensation method based on Taylor approximation to perform preliminary time mismatch error compensation on the sampling sequence containing time mismatch.

[0129] In an implementation manner of this embodiment, the step of performing preliminary time mismatch error compensation on the sampling sequence containing time mismatch by adopting a time mismatch error compensation method based on Taylor approximation according to the initial time mismatch estimation value specifically includes:

[0130] Take the initial time mismatch estimation value corresponding to the i-th sampling channel as the time mismatch Δt i ;

[0131] Take the sampling sequence containing time mismatch output by the i-th sampling channel as the actual sampling sequence

[0132] Take the sampling sequence after preliminary time mismatch error compensation corresponding to the i-th sampling channel as the ideal sampling sequence y i ;

[0133] According to the time mismatch Δt i Establish an error term with the Taylor series expansion method, and subtract the error term from the actual sampling sequence to obtain the ideal sampling sequence;

[0134]

[0135] where d is the order of the Taylor series, which is set to d = 3 in the present invention; d! represents the factorial of d, represents the actual sampling sequence of the d-th derivative.

[0136] Specifically, after obtaining the time mismatch estimation value (including the initially randomly set time mismatch estimation value and the time mismatch estimation value calculated in the adaptive iterative calibration algorithm) of the present invention, a compensation algorithm can be used to eliminate the output spectrum distortion. The present invention adopts a compensation method based on Taylor approximation: for the i-th sampling channel, first, an error term is established according to the time mismatch estimation value and the Taylor series expansion method, and then it is subtracted from the actual sampling sequence to obtain the ideal sampling sequence y i , that is, the compensation is completed. It can be seen from the above formula that the error between the actual sampling sequence and the ideal sampling sequence y i can be expressed as a polynomial containing the time mismatch Δt i , that is, the error term represents the error caused by the time mismatch Δt i . Among them, the Taylor series expansion is a method of approximating a function with a polynomial.

[0137] S3. Perform cross-correlation calculation based on the initially estimated time mismatch value and the sampling sequence after preliminary time mismatch error compensation to obtain the channel cross-correlation difference, and determine whether the channel cross-correlation difference meets the error tolerance condition.

[0138] In an implementation manner of this embodiment, the performing cross-correlation calculation based on the initially estimated time mismatch value and the sampling sequence after preliminary time mismatch error compensation to obtain the channel cross-correlation difference, and determining whether the channel cross-correlation difference meets the error tolerance condition specifically includes:

[0139] Take the initially estimated time mismatch value as the time mismatch Δt, and take the sampling sequence after preliminary time mismatch error compensation as the sampling sequence output by the sampling channel to be estimated for time mismatch;

[0140] Taking the first sampling channel as the reference sampling channel, setting the time mismatch Δt1 of the first sampling channel to 0, taking the second sampling channel as the sampling channel to be estimated for time mismatch, and setting the time mismatch Δt2 of the second sampling channel to Δt;

[0141] The time mismatch causes the sampling time of the sampling channel to shift, changing the sampling interval from T s to T s ±ΔtT s . By performing cross-correlation calculation on the sampling sequences output by the first sampling channel and the second sampling channel, we get:

[0142]

[0143] Among them, R(·) is the cross-correlation function, E(·) is the expected value, y1[·] represents the sampling sequence output by the first sampling channel, y2[·] represents the sampling sequence output by the second sampling channel, k is an integer, k = 1, …, n;

[0144] For a very small ΔtT s , according to the first-order Taylor approximation principle, we have:

[0145] R(T s +ΔtT s ) = R(T s ) + ΔtT s ×R′(T s );

[0146] R(T s -ΔtT s ) = R(T s ) - ΔtT s ×R′(T s );

[0147] Among them, R′(·) is the derivative of the cross-correlation function R(·);

[0148] Perform a difference operation on the above formula to eliminate the R(T s ) term, and obtain the channel cross-correlation difference ∈:

[0149] ∈ = R(T s +ΔtT s ) - R(T s -ΔtT s ) = 2ΔtT s ×R′(T s );

[0150] According to the channel cross-correlation difference, determine whether the relative error between the channel cross-correlation difference and the expected value of the channel cross-correlation difference is not greater than the set error tolerance;

[0151] If so, it means that there is no time mismatch in the sampling channel to be estimated for time mismatch;

[0152] If not, it means that there is a time mismatch in the sampling channel to be estimated for time mismatch.

[0153] Specifically, the present invention estimates the time mismatch error by analyzing the statistical characteristics of the channel sampling sequence, without interrupting the system sampling, and without introducing a reference channel that is relatively prime to the sampling rate of the target channel, avoiding the dynamic impedance interference and asynchronous sampling problems in the traditional background calibration method. Figure 4Shows the impact of time mismatch. Taking Channel 1, i.e., the first sampling channel, as the reference (Δt1 = 0), time mismatch estimation is performed on Channel 2, i.e., the second sampling channel (Δt2 = Δt). Time mismatch will cause an offset in the sampling moments of the channels, changing the sampling interval from T s to T s ±ΔtT s . By performing cross-correlation calculation on the sampling sequences output by the channels, the cross-correlation difference ∈ between the channels is obtained: ∈ = R(T s +ΔtT s ) - R(T s -ΔtT s ) = 2ΔtT s ×R′(T s ); This formula represents the proportional relationship between the time mismatch Δt and the cross-correlation difference ∈ between the channels. Based on this, without interrupting the system sampling and without introducing a reference channel that is relatively prime to the sampling rate of the target channel, the time mismatch can be detected according to the cross-correlation difference between the channels (detection means judging the existence of time mismatch. Specifically, if the time mismatch is very small or even close to 0, then the calculated cross-correlation difference between the channels will also be very small or even close to 0. Therefore, the existence of time mismatch can be judged according to the cross-correlation difference between the channels). However, when there is time mismatch, the term R′(T s is unknown, so the exact estimated value of the time mismatch cannot be accurately calculated. To solve this problem, an adaptive iterative calibration algorithm is usually used for multiple estimations and compensations until the above formula approaches zero. The specific process is described below.

[0154] In addition, a wideband compressive sampling system needs to construct a random measurement matrix to ensure that the original conditions of the signal are not lost under low-speed sampling conditions. The multi-coset sampling system is an important component for capturing wideband signals through multi-channel periodic non-uniform undersampling to avoid missing key frequencies that may occur in uniform low-speed sampling. Therefore, the sampling intervals between channels are often asymmetric. Since the calculation of the above cross-correlation difference between channels depends on the symmetry of the sampling time intervals between channels, the present invention innovatively proposes to achieve background calibration by hierarchically introducing the least number of additional sampling channels, effectively solving the calibration problem caused by non-uniform sampling in wideband compressive sampling. The specific process is described below.

[0155] S4. If not, then adopt the data-driven adaptive calibration method to iteratively update the estimated values of the pseudo-partial derivative parameters and the time mismatch estimation value, and according to the updated time mismatch estimation value, adopt the time mismatch error compensation method based on Taylor approximation to perform time mismatch error compensation on the sampling sequence after the preliminary time mismatch error compensation until the cross-correlation difference between the channels meets the error tolerance condition.

[0156] In an implementation of this embodiment, the data-driven adaptive calibration method is adopted to iteratively update the pseudo partial derivative parameter estimate and the time mismatch estimate, as Figure 6 shown, specifically including:

[0157] After the signal passes through multi-coset sampling, the sampled sequences of each channel containing time mismatch errors are obtained. It should be noted that in practical applications, since the initial time mismatch estimate is randomly set, the sampled sequence after preliminary time mismatch error compensation is also a sampled sequence containing time mismatch errors. In fact, before the time mismatch calibration is completed, that is, in all iteration rounds before the last iteration, the sampled sequence after time mismatch error compensation obtained can be understood as a sampled sequence containing time mismatch, that is, the actual sampled sequence. Define the time mismatch estimate of the i-th sampling channel in the k-th iteration as u i (k), and it is used as the calibration parameter in the error compensation algorithm; in the k-th iteration, the relationship between u i (k) and the cross-correlation difference ∈ i (k) of the i-th sampling channel in the k-th iteration can be described by the following general discrete-time system:

[0158] ∈ i (k) = f(∈ i (k - 1), …, ∈ i (k - n ∈ ), u i (k), …, u i (k - n u ));

[0159] where f(·) is an unknown nonlinear system, ∈ i (·) represents the cross-correlation difference of the i-th sampling channel, u i (·) represents the time mismatch estimate of the i-th sampling channel, n ∈ represents the order of the historical cross-correlation difference relative to ∈ i (k), n u represents the order of the historical time mismatch estimate relative to u i (k), and both are unknown orders;

[0160] The dynamic linearization of the nonlinear system is based on the following two assumptions:

[0161] Assumption 1: The partial derivative of the nonlinear system f(·) with respect to u i (k) is continuous;

[0162] Assumption 2: The nonlinear system satisfies the Lipschitz continuity condition, that is, for any k, there is |Δ∈ i (k)| ≤ b|Δu i(k)|, where b is a positive constant representing the maximum proportional relationship between Δ∈ i (k) and Δu i (k);

[0163] That is, assuming that the partial derivative of the non - linear system with respect to u i (k) is continuous and the non - linear system satisfies the Lipschitz continuity condition, then for any k, we have:

[0164] Δ∈ i (k)=∈ i (k)-∈ i (k - 1);

[0165] Δu i (k)=u i (k)-u i (k - 1), Δu i (k)≠0;

[0166] Where, Δ∈ i (·) represents the change in the cross - correlation difference of adjacent channels in two consecutive iterations, and Δu i (·) represents the change in the time mismatch estimate of adjacent channels in two consecutive iterations;

[0167] Considering the non - linear system and Assumptions 1 and 2, for all iteration rounds k, there exists a pseudo - partial derivative parameter (PPD) φ i (k) such that ∈ i (k) can be converted into the following equivalent dynamic linearization model, that is, using the pseudo - partial derivative parameter φ i (k) to convert ∈ i (k) into an equivalent dynamic linearization model:

[0168] Δ∈ i (k)=φ i (k)Δu i (k);

[0169] Where, φ i (k) represents the pseudo - partial derivative parameter of the i - th sampling channel at the k - th iteration;

[0170] Since the PPD parameter is unknown, in order to estimate the pseudo - partial derivative parameter φ i (k), a first criterion function is defined:

[0171]

[0172] Where, J(·) represents the first criterion function, Denotes the estimated value of the pseudo - partial - derivative parameter for the \(i\) - th sampling channel at the \(k\) - th iteration. Denotes the estimated value of the pseudo - partial - derivative parameter for the \(i\) - th sampling channel at the \((k - 1)\) - th iteration, and \(\mu\) is a weight factor used to avoid excessive changes, \(\mu>0\);

[0173] Since the first criterion function is a convex function, solving yields:

[0174]

[0175] where \(\eta\) is a step - size constant used to control the update amplitude;

[0176] According to the calculation formula of, calculate and update the estimated value of the pseudo - partial - derivative parameter;

[0177] To accurately track the time - varying pseudo - partial - derivative parameter (PPD vector) and ensure that \(\Delta u\) i (k)\(\neq0\), reset the estimated value of the pseudo - partial - derivative parameter:

[0178] If or \(\vert\Delta u\) i (k - 1)\(\vert\) 2 \(\leq\varepsilon\) or

[0179] where \(\varphi\) i (0) is the initial value of the pseudo - partial - derivative parameter, \(\varepsilon\) is a small positive constant used to reset and \(sign(\cdot)\) is the sign function; if the magnitude of \(\Delta u\) i (k - 1)\) or is too small, this reset scheme can enhance the tracking ability of the adaptive calibration scheme;

[0180] To minimize the channel cross - correlation difference, perform error compensation on the channel sampling sequence according to \(u\) i (k), and define the second criterion function:

[0181]

[0182] where \(J'(\cdot)\) represents the second criterion function, is the expected value of the channel cross - correlation difference of the \(i\) - th sampling channel, which is set to 0 in the experiment to minimize the channel cross - correlation difference, and \(\lambda\) is a weight factor used to limit the change rate of \(u\) i (k), \(\lambda>0\);

[0183] According to and \(\Delta u\) i (k)=u i(k)-u i (k - 1), we can obtain:

[0184]

[0185] Since the second criterion function is a convex function, solving we get:

[0186]

[0187] where ρ is the step constant used to control the update amplitude of u i (k);

[0188] According to the calculation formula of u i (k), calculate and update the time mismatch estimation value;

[0189] For the comparison of computational complexity, since the calibration scheme needs to calibrate p sampling channels one by one, its complexity mainly depends on the required number of iterations, that is, the computational complexity is O(p×N iter ), where O(·) represents the "big O notation" used to describe the time complexity of the algorithm, and N iter represents the number of iterations required for each channel during the calibration process.

[0190] In an implementation manner of this embodiment, based on the updated time mismatch estimation value, a time mismatch error compensation method based on Taylor approximation is used to perform time mismatch error compensation on the sampled sequence after preliminary time mismatch error compensation until the cross-channel correlation difference satisfies the error tolerance condition, which specifically includes:

[0191] Take the updated time mismatch estimation value corresponding to the i-th sampling channel as the time mismatch Δt i , and let Δt i = u i (k);

[0192] Take the sampled sequence after preliminary time mismatch error compensation corresponding to the i-th sampling channel as the actual sampled sequence

[0193] Take the sampled sequence after time mismatch error compensation corresponding to the i-th sampling channel as the ideal sampled sequence y i ;

[0194] Based on the time mismatch Δt i and the Taylor series expansion method, establish an error term, and subtract the error term from the actual sampled sequence to obtain the ideal sampled sequence;

[0195]

[0196] Perform cross-correlation calculation based on the updated time mismatch estimation value and the sampled sequence after time mismatch error compensation to obtain the channel cross-correlation difference ∈ i (k);

[0197] Based on the channel cross-correlation difference ∈ i (k), determine whether the relative error between the channel cross-correlation difference ∈ i (k) and the expected value of the channel cross-correlation difference is no greater than the set error tolerance value σ, and determine whether the current iteration round k is greater than the maximum number of iterations k max ;

[0198] If the channel cross-correlation difference ∈ i (k) satisfies or the current iteration round k satisfies k > k max , stop the iteration;

[0199] Otherwise, repeat the iteration to update the pseudo partial derivative parameter estimation value and the time mismatch estimation value until the channel cross-correlation difference satisfies the error tolerance condition or reaches the maximum number of iterations;

[0200] When the condition for triggering the iteration stop is ∈ i (k) satisfies , return u i (k) as the time mismatch calibration result;

[0201] When the condition for triggering the iteration stop is that k satisfies k > k max , return the time mismatch estimation value corresponding to the smallest element in the channel cross-correlation difference set Γ i as the time mismatch calibration result.

[0202] It should be noted that in practical applications, since the initial time mismatch estimation value is randomly set, the sampling sequence after preliminary time mismatch error compensation is also a sampling sequence containing time mismatch error. In fact, before the time mismatch calibration is completed, that is, in all iteration rounds before the last iteration, the sampling sequence obtained after time mismatch error compensation can be understood as a sampling sequence containing time mismatch, that is, the actual sampling sequence of the next iteration. Generally speaking, the sampling sequence before time mismatch error compensation in the current iteration round is the actual sampling sequence of the current iteration round, and the sampling sequence before time mismatch error compensation in the current iteration round is the sampling sequence after time mismatch error compensation in the previous iteration round (i.e., the ideal sampling sequence of the previous iteration round); the sampling sequence after time mismatch error compensation in the current iteration round is the ideal sampling sequence of the current iteration round, and the sampling sequence after time mismatch error compensation in the current iteration round is the sampling sequence before time mismatch error compensation in the next iteration round (i.e., the actual sampling sequence of the next iteration round). In addition, in practical applications, the initial time mismatch estimation value is usually randomly set twice. It can be understood that in adaptive iterative calibration, the time mismatch estimation values of the first iteration and the second iteration are randomly set. When the iteration round k is greater than 2, the time mismatch estimation value is calculated according to the pseudo partial derivative parameter estimation value.

[0203] As described above, the adaptive iterative calibration algorithm continuously estimates and compensates until the formula ∈ = R(T s +ΔtT s ) - R(T s -ΔtT s ) = 2ΔtT s ×R′(T s ) approaches zero. However, traditional adaptive iterative calibration methods (such as the schemes based on LMS and VSSLMS) rely on step size selection, which affects the convergence speed and accuracy. To address this deficiency, the present invention proposes: using a data-driven iterative algorithm (i.e., a data-driven adaptive calibration method) to update the time mismatch estimation value, which only depends on real-time measured data. By establishing a local dynamic linearization data model based on time-varying pseudo partial derivative parameters, the best time mismatch estimation value is searched by minimizing the calibration error (i.e., the relative error between the channel cross-correlation difference and its expected value) through multiple iterations, so as to achieve fast convergence and high-precision calibration. The overall scheme is as Figure 6 shown.

[0204] In an implementation manner of this embodiment, the data-driven background time mismatch calibration method without a reference channel further includes:

[0205] Performing background time mismatch calibration on each sampling channel of the multi-coset sampling system one by one;

[0206] The data-driven background time mismatch calibration method without a reference channel further includes:

[0207] For sampling channels with sampling interval symmetry, directly perform cross-correlation calculation to obtain the channel cross-correlation difference;

[0208] Based on the channel cross-correlation difference, use the data-driven adaptive calibration method to calibrate the sampling channels with sampling interval symmetry to obtain calibrated sampling channels with sampling interval symmetry;

[0209] For sampling channels without sampling interval symmetry, introduce the minimum number of additional sampling channels in layers. Based on the calibrated sampling channels with sampling interval symmetry, perform cross-correlation calculation and use the data-driven adaptive calibration method to calibrate the additional sampling channels to obtain calibrated additional sampling channels;

[0210] Based on the calibrated additional sampling channels, perform cross-correlation calculation and use the data-driven adaptive calibration method to calibrate the sampling channels without sampling interval symmetry to obtain calibrated sampling channels without sampling interval symmetry.

[0211] Specifically, since the calculation of the above channel cross-correlation difference depends on the symmetry of the sampling time intervals between channels, the present invention innovatively proposes to achieve background calibration by introducing the minimum number of additional sampling channels in layers, effectively solving the calibration problem brought by non-uniform sampling in wideband compressive sampling. Combining Figure 5 the example shown, the time mismatch estimation process of the multi-coset sampling system can be summarized as follows:

[0212] a) Initial estimation and calibration based on symmetry: Usually, channel 1 (c1 = 0) is used as a reference. The initial estimation and calibration will select a channel (such as Figure 5 channel 3 in, c3 = 4), whose sampling moment is located in the middle of two consecutive sampling moments of channel 1. Using the sampling sequence of channel 1, the channel cross-correlation difference can be calculated by a formula, and then time mismatch estimation and calibration are performed. Once the calibration is completed, the selected channel can assist in further calibrating other channels.

[0213] b) Introduce additional sampling channels as needed: For channels lacking sampling interval symmetry (such as channel 2 and channel 4), one or more additional sampling channels with the same sampling rate (such as Added channels) may need to be introduced. The time mismatch of these new channels can be estimated and calibrated through the sampling sequences of the calibrated channels (for example, the sampling sequences of channel 1 and channel 3 can estimate and calibrate the time mismatch of the Added channels). Once these additional channels are calibrated, they can assist in calibrating the time mismatch of the remaining channels.

[0214] c) Complete estimation and calibration: Using the sampling sequences of all calibrated channels, estimate and calibrate the time mismatch of the remaining channels, thereby completing the entire calibration process.

[0215] In summary, the present invention proposes a data-driven background time mismatch calibration method without a reference channel for time mismatch calibration of a broadband compressive sampling system. The specific implementation process includes: after the signal passes through the multi-coset sampling system, sampling sequences of each channel containing time mismatch errors are obtained. First, perform preliminary error compensation on it and calculate the cross-correlation difference between channels. Based on the relationship between time mismatch and the cross-correlation difference between channels, adopt a data-driven adaptive calibration scheme to establish an equivalent dynamic linearized data model through pseudo-partial derivative parameters, and iteratively track the estimated value of the time mismatch between channels. In each iteration, update the estimated value of the pseudo-partial derivative parameter and the estimated value of the time mismatch, and then based on the estimated value of the time mismatch, perform error compensation on the sampling sequence through an error compensation method based on Taylor approximation. Subsequently, recalculate the cross-correlation difference between channels. If it does not meet the expectation, the data-driven algorithm continues to iterate until the most suitable estimated value of the time mismatch is found. The present invention does not require interrupting the system sampling and does not require introducing a reference channel that is relatively prime to the sampling rate of the target channel; it does not depend on the selection of the step size and realizes fast convergence and high-precision calibration.

[0216] In another implementation manner of this embodiment, the iterative process of time mismatch calibration for each channel can be summarized as follows:

[0217] 1) Initial settings:

[0218] a) Preset the measurement data set: Preset the estimated value of the time mismatch for the i-th channel, and let U i ={u i (1), u i (2)}, that is, the estimated value of the time mismatch for the first iteration is u i (1), and the estimated value of the time mismatch for the second iteration is u i (2), where U i represents the set of estimated values of the time mismatch; preset the cross-correlation difference between channels, and let Γ i ={∈ i (1), ∈ i (2)}, that is, the cross-correlation difference between channels for the first iteration is ∈ i (1), and the cross-correlation difference between channels for the second iteration is ∈ i (2), where Γ i represents the set of cross-correlation differences between channels;

[0219] b) Preset the expected value of the cross-correlation difference between channels:

[0220] c) Preset the error tolerance: σ;

[0221] d) Preset a small positive constant: ε;

[0222] e) Preset the maximum number of iterations: k max ;

[0223] f) Preset the initial parameters: initial pseudo partial derivative φ i (0), step size constant η, step size constant ρ, weight factor μ, weight factor λ.

[0224] 2) Iteration process:

[0225] a) When k = 2, there exists

[0226] b) When k ≥ 3 and k < k max At this time, calculate the estimated value of the pseudo partial derivative parameter for the k-th iteration according to the following formula

[0227]

[0228] c) If or |Δu i (k - 1)| 2 ≤ ε or Then reset the estimated value of the pseudo partial derivative parameter for the k-th iteration Let Otherwise, do not reset

[0229] d) Calculate the time mismatch estimate value u i (k) for the k-th iteration according to the following formula:

[0230]

[0231] e) Based on u i (k), perform time mismatch error compensation for the k-th iteration according to the following formula to obtain the channel sampling sequence after error compensation:

[0232] where Δt i = u i (k);

[0233] f) Based on the channel sampling sequence, calculate the channel cross-correlation difference ∈ i (k) for the k-th iteration according to the following formula:

[0234] ∈ = R(T s + ΔtT s ) - R(T s - ΔtT s ) = 2ΔtTs ×R′(T s ), where Δt = u i (k);

[0235] g) Update the set of channel cross - correlation differences, i.e., Γ i ={Γ i , ∈ i (k)};

[0236] h) Update the set of time - mismatch estimates, i.e., U i ={U i , u i (k)};

[0237] i) If the channel cross - correlation difference ∈ i (k) satisfies or k satisfies k > k max , then stop the iteration; otherwise, repeat steps b) to h);

[0238] j) When the iteration stop is triggered for ∈ i (k) satisfying , return u i (k); when the iteration stop is triggered for k satisfying k > k max , return the time - mismatch estimate corresponding to the smallest element in the set of channel cross - correlation differences Γ i .

[0239] Compare the data - driven background calibration scheme proposed in the present invention with different background calibration schemes. The compression sampling rate of the multi - coset sampling system is set to α = p / L = 2 / 4, and the time mismatch is set to Δt = [0, 0.1]. The input signal is a dual - frequency sine signal x(t)=A·sin(2πf in = 0.27, 0.35]f s t)+n(t), where A and f in are the amplitude and the carrier frequency respectively, and n(t) is additive white Gaussian noise. As in shown in Figure 7 and Table 1, the step size μ of the LMS - based scheme and the initial step size μ initial of the VSSLMS - based scheme will affect the calibration speed and accuracy. For example, when μ = 0.005 and μ initial = 0.005, the calibration speed is slow; when μ = 0.5 and μ initial = 0.5, the larger step size will cause significant oscillations and more iterations are required to converge. In contrast, the data - driven background calibration scheme proposed in the present invention achieves faster convergence and higher accuracy, overcoming the limitations of step - size selection.

[0240] Table 1 Comparison of calibration performance in multi - coset sampling systems

[0241]

[0242] Furthermore, the present invention compares the performance of the proposed data-driven background calibration scheme with the background calibration schemes based on LMS and VSSLMS at different Signal-to-Noise Ratios (SNRs). The compression sampling rate of the multi-coset sampling system is set to α = p / L = 6 / 8, C = {0, 1, 2, 3, 4, 7}, and the time mismatch is set to Δt = [0, 0.04, 0.03, 0.05, 0.03, 0.02]. The input signal is a multi-frequency sine signal with a normalized frequency of f i = 0.14, 0.16, 0.18]. As Figure 8 shown, within the tested SNR range, the proposed data-driven background calibration scheme achieves a higher Signal-to-Noise Distortion Ratio (SNDR) compared to other background calibration schemes.

[0243] In summary, the present invention proposes a data-driven background calibration scheme without a reference channel for time mismatch calibration of a broadband compressive sampling system, with the following creative points:

[0244] 1) Background calibration architecture without a reference channel: Existing background calibration methods usually rely on a reference channel with a relatively prime sampling rate to the target channel, introducing dynamic impedance interference and causing asynchronous sampling problems. The present invention estimates the time mismatch by analyzing the statistical characteristics of the channel sampling sequences, without interrupting the system sampling and without introducing a reference channel with a relatively prime sampling rate to the target channel, thus completely avoiding the dynamic impedance interference and asynchronous sampling problems in traditional methods.

[0245] 2) Calculation of the cross-correlation difference between channels under non-uniform sampling: A broadband compressive sampling system needs to construct a random measurement matrix to ensure that the original conditions of the signal are not lost under low-speed sampling conditions. For example, a multi-coset sampling system captures the important components of a broadband signal through multi-channel periodic non-uniform undersampling to avoid missing key frequencies that may occur in uniform low-speed sampling. Therefore, the sampling intervals between channels are often asymmetric. However, the time mismatch estimation method based on calculating the cross-correlation difference between channels depends on the symmetry of the sampling time intervals between channels. Therefore, the present invention innovatively proposes to achieve background calibration by hierarchically introducing the least number of additional sampling channels, effectively solving the calibration problem brought about by non-uniform sampling in broadband compressive sampling.

[0246] 3) Fast-converging data-driven calibration method: The speed and accuracy of existing adaptive iterative calibration methods are often limited by the choice of step size in the adaptive iterative algorithm. The present invention uses a data-driven iterative algorithm to update the time mismatch estimate, relying only on real-time measured data. By establishing a local dynamic linearized data model based on time-varying pseudo partial derivative parameters and minimizing the calibration error through multiple iterations to search for the optimal time mismatch estimate, a fast and high-precision calibration effect is achieved.

[0247] In addition, based on the above-mentioned data-driven background time mismatch calibration method without a reference channel, the present invention also provides a data-driven background time mismatch calibration system without a reference channel. Among them, a preferred embodiment of the data-driven background time mismatch calibration system without a reference channel is as Figure 9 shown, and specifically includes:

[0248] Sampling module 01: Used to acquire an input signal, input the input signal into multiple sampling channels of a multi-coset sampling system for sampling, and obtain sampling sequences containing time mismatch output by each sampling channel;

[0249] Initial estimation and compensation module 02: Used to randomly set an initial time mismatch estimate value, and according to the initial time mismatch estimate value, use a time mismatch error compensation method based on Taylor approximation to perform preliminary time mismatch error compensation on the sampling sequence containing time mismatch;

[0250] Cross-correlation calculation module 03: Used to perform cross-correlation calculation according to the initial time mismatch estimate value and the sampling sequence after preliminary time mismatch error compensation, obtain the channel cross-correlation difference value, and determine whether the channel cross-correlation difference value meets the error tolerance condition;

[0251] Adaptive calibration module 04: Used if not, then use a data-driven adaptive calibration method to iteratively update the pseudo partial derivative parameter estimate value and the time mismatch estimate value, and according to the updated time mismatch estimate value, use a time mismatch error compensation method based on Taylor approximation to perform time mismatch error compensation on the sampling sequence after preliminary time mismatch error compensation until the channel cross-correlation difference value meets the error tolerance condition.

[0252] In addition, based on the above-mentioned data-driven background time mismatch calibration method and system without a reference channel, the present invention also correspondingly provides a terminal. Among them, a preferred embodiment of the terminal is as Figure 10 shown, and specifically includes a processor 10, a memory 20, and a display 30. Figure 10 Only some components of the terminal are shown, but it should be understood that it is not required to implement all the shown components, and more or fewer components can be alternatively implemented.

[0253] The memory 20 may be an internal storage unit of the terminal in some embodiments, such as the hard disk or memory of the terminal. The memory 20 may also be an external storage device of the terminal in some other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, and a Flash Card equipped on the terminal, etc. Further, the memory 20 may also include both the internal storage unit of the terminal and the external storage device. The memory 20 is used to store the application software installed on the terminal and various types of data, such as storing the program code of the terminal, etc. The memory 20 may also be used to temporarily store the data that has been output or will be output. In one embodiment, a data-driven background time mismatch calibration program 40 without a reference channel is stored on the memory 20, and the data-driven background time mismatch calibration program 40 without a reference channel can be executed by the processor 10, so as to implement the steps of the data-driven background time mismatch calibration method without a reference channel in the present application.

[0254] The processor 10 may be a Central Processing Unit (CPU), a microprocessor, or other data processing chips in some embodiments, and is used to run the program code stored in the memory 20 or process data, such as executing the data-driven background time mismatch calibration program 40 without a reference channel, etc.

[0255] The display 30 may be an LED display, a liquid crystal display, a touch liquid crystal display, and an OLED (Organic Light-Emitting Diode) toucher, etc. in some embodiments. The display 30 is used to display the information on the terminal and to display the visual user interface.

[0256] In one embodiment, when the processor 10 executes the data-driven background time mismatch calibration program 40 without a reference channel in the memory 20, the steps of the data-driven background time mismatch calibration method without a reference channel as described above are implemented.

[0257] The present invention also correspondingly provides a computer-readable storage medium. Among them, the computer-readable storage medium stores a data-driven background time mismatch calibration program without a reference channel. When the data-driven background time mismatch calibration program without a reference channel is executed by the processor, the steps of the data-driven background time mismatch calibration method without a reference channel as described above are implemented.

[0258] It should be noted that in this text, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or terminal including a series of elements not only includes those elements but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or terminal. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or terminal including such element.

[0259] Of course, those of ordinary skill in the art can understand that all or part of the processes of implementing the above-described method embodiments can be completed by instructing relevant hardware (such as a processor, a controller, etc.) through a computer program, and the program can be stored in a computer-readable storage medium readable by a computer. When the program is executed, it may include the processes of the above-described method embodiments. The computer-readable storage medium may be a memory, a magnetic disk, an optical disk, etc.

[0260] It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or transformations can be made according to the above description, and all such improvements and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A data-driven background time mismatch calibration method without a reference channel, characterized in that, The data-driven background time mismatch calibration method without a reference channel includes: Obtain an input signal, input the input signal into multiple sampling channels of a multi-coset sampling system for sampling, and obtain sampling sequences with time mismatch output by each sampling channel; Randomly set an initial time mismatch estimate value, and according to the initial time mismatch estimate value, use a time mismatch error compensation method based on Taylor approximation to perform preliminary time mismatch error compensation on the sampling sequences with time mismatch; Perform cross-correlation calculation based on the initial time mismatch estimate value and the sampling sequences after preliminary time mismatch error compensation, obtain a channel cross-correlation difference value, and determine whether the channel cross-correlation difference value meets the error tolerance condition; If not, then use a data-driven adaptive calibration method to iteratively update the pseudo partial derivative parameter estimate value and the time mismatch estimate value, and according to the updated time mismatch estimate value, use a time mismatch error compensation method based on Taylor approximation to perform time mismatch error compensation on the sampling sequences after preliminary time mismatch error compensation until the channel cross-correlation difference value meets the error tolerance condition.

2. The data-driven background time mismatch calibration method without a reference channel according to claim 1, wherein The multi-coset sampling system is implemented by using p sampling channels among the time-interleaved analog-to-digital converters of L sampling channels, where p ≤ L, and the set is composed of p different integers randomly selected from {0, 1, …, L−1} is called an (L, p) sampling pattern, where c i represents the i-th element in the set C, where i = 1, …, p; The sampling rate of each sampling channel is where the offset of the i-th sampling channel is c i T s , and the sampling time of the i-th sampling channel is Φ i (t) = (mL + c i )T s , where f s is the system sampling rate, T s is the sampling interval, and m is an arbitrary integer; The obtaining of the input signal, inputting the input signal into multiple sampling channels of a multi-coset sampling system for sampling, and obtaining sampling sequences with time mismatch output by each sampling channel specifically includes: Obtain an input signal, define the input signal as a continuous-time signal x(t), and the output of the i-th sampling channel in the multi-coset sampling system at the n-th sampling moment is: Define the time mismatch of the $i$-th sampling channel as $\Delta t$ i , then in the case of time mismatch, the output of the $i$-th sampling channel at the $n$-th sampling moment is: where t represents time, y i [n] represents the sampling sequence without time mismatch output by the i-th sampling channel at the n-th sampling moment, x(nT s ) is the value of the continuous-time signal x(t) at time nT s , n is an integer, is the set of integers, δ[·] is the discrete-time impulse function, represents the sampling sequence with time mismatch output by the i-th sampling channel at the n-th sampling moment.

3. The data-driven background time mismatch calibration method without a reference channel according to claim 2, wherein The performing of preliminary time mismatch error compensation on the sampling sequences with time mismatch according to the initial time mismatch estimate value by using a time mismatch error compensation method based on Taylor approximation specifically includes: Use the initial time mismatch estimate value corresponding to the i-th sampling channel as the time mismatch Δt i ; Take the sampling sequence containing time mismatch output by the i-th sampling channel as the actual sampling sequence Take the sampling sequence after compensating the preliminary time mismatch error corresponding to the i-th sampling channel as the ideal sampling sequence y i ; Based on the time mismatch Δt i establish an error term with the Taylor series expansion method, and subtract the error term from the actual sampling sequence to obtain the ideal sampling sequence; where d is the order of the Taylor series, and d! represents the factorial of d, represents the actual sampling sequence of the d-th derivative.

4. The data-driven background time mismatch calibration method without a reference channel according to claim 3, characterized in that The performing of cross-correlation calculation based on the initial time mismatch estimate value and the sampling sequences after preliminary time mismatch error compensation, obtaining a channel cross-correlation difference value, and determining whether the channel cross-correlation difference value meets the error tolerance condition specifically includes: Take the initial time mismatch estimate value as the time mismatch Δt, and take the sampling sequences after preliminary time mismatch error compensation as the sampling sequences output by the sampling channels to be estimated for time mismatch; Take the first sampling channel as the reference sampling channel, let the time mismatch Δt1 of the first sampling channel be 0, take the second sampling channel as the sampling channel to be estimated for time mismatch, and let the time mismatch Δt2 of the second sampling channel be Δt; Time mismatch causes the sampling moment of the sampling channel to shift, resulting in the sampling interval changing from T s to T s ±ΔtT s , and by performing cross-correlation calculation on the sampling sequences output by the first sampling channel and the second sampling channel, we obtain: where R(·) is the cross-correlation function, E(·) is the expected value, y1[·] represents the sampling sequence output by the first sampling channel, represents the sampling sequence output by the second sampling channel, k is an integer, k = 1, …, n; For ΔtT s , according to the first-order Taylor approximation principle, we have: R(T s +ΔtT s ) = R(T s ) + ΔtT s ×R′(T s ); R(T s -ΔtT s ) = R(T s ) - ΔtT s ×R′(T s ); where R′(·) is the derivative of the cross-correlation function R(·); Perform a difference operation on the above formula to eliminate the R(T s ) term, and obtain the channel cross-correlation difference ∈: ∈ = R(T s + ΔtT s ) - R(T s - ΔtT s ) = 2ΔtT s × R′(T s ); According to the channel cross-correlation difference value, determine whether the relative error between the channel cross-correlation difference value and the expected value of the channel cross-correlation difference value is not greater than the set error tolerance value; If so, it indicates that there is no time mismatch in the sampling channel to be estimated for time mismatch; If not, it indicates that there is time mismatch in the sampling channel to be estimated for time mismatch.

5. The data-driven background time mismatch calibration method without a reference channel according to claim 4, characterized in that The using of a data-driven adaptive calibration method to iteratively update the pseudo partial derivative parameter estimate value and the time mismatch estimate value specifically includes: Define the time mismatch estimation value of the i-th sampling channel at the k-th iteration as u i (k). In the k-th iteration, u i (k) and the channel cross-correlation difference ∈ i (k) of the i-th sampling channel at the k-th iteration have the following relationship: ∈ i (k) = f(∈ i (k - 1), …, ∈ i (k - n ∈) , u i (k), …, u i (k - n u )); where f(·) is an unknown nonlinear system, ∈ i (·) represents the cross-correlation difference of the i-th sampling channel, u i (·) represents the time mismatch estimation value of the i-th sampling channel, n ∈ represents with respect to ∈ i (k) the order of the historical cross-correlation difference of the channel, n u represents with respect to u i (k) the order of the historical time mismatch estimation value; Set the partial derivative of the non - linear system with respect to u i (k) to be continuous and the non - linear system to satisfy the Lipschitz continuity condition. Then, for any k, we have: Δ∈ i (k)=∈ i (k)-∈ i (k - 1); Δu i (k) = u i (k) - u i (k - 1), Δu i (k) ≠ 0; where, Δ ∈ i (·) represents the change in the channel cross-correlation difference between two adjacent iterations, Δu i (·) represents the change in the time mismatch estimate between two adjacent iterations; For all iteration rounds k, there exists a pseudo partial derivative parameter φ i (k), and the equivalent dynamic linearization model is obtained by using the pseudo partial derivative parameter φ i (k) to convert ∈ i (k): Δ∈ i (k) = φ i (k)Δu i (k); where φ i (k) represents the pseudo partial derivative parameter of the i-th sampling channel at the k-th iteration; In order to estimate the pseudo partial derivative parameter φ i (k), a first criterion function is defined: where, J(·) represents the first criterion function, represents the pseudo partial derivative parameter estimation value of the i-th sampling channel at the k-th iteration, represents the pseudo partial derivative parameter estimation value of the i-th sampling channel at the (k - 1)-th iteration, and μ is a weight factor used to avoid excessive changes; Since the first criterion function is a convex function, solving gives: where η is a step constant for controlling the update amplitude; According to the calculation formula, calculate and update the pseudo partial derivative parameter estimate value; To accurately track the time-varying pseudo partial derivative parameter and ensure that Δu i (k)≠0, reset the estimated value of the pseudo partial derivative parameter: If or |Δu i (k - 1)| 2 ≤ ε or i = 1, …, p; where, φ i (0) is the initial value of the pseudo partial derivative parameter, ε is a positive constant used to reset ; sign(·) is the sign function; In order to perform time mismatch error compensation on the sampled sequence according to u i (k), a second criterion function is defined: where J′(·) represents the second criterion function, is the expected value of the channel cross-correlation difference of the i-th sampling channel, and λ is the weight factor used to limit the change rate of u i (k); According to and Δu i (k) = u i (k) - u i (k - 1), it can be obtained that: Since the second criterion function is a convex function, solving yields: where ρ is the step constant for controlling the update amplitude of u i (k); According to the calculation formula of u i (k), calculate and update the time mismatch estimation value.

6. The data-driven background time mismatch calibration method without a reference channel according to claim 5, characterized in that According to the updated time mismatch estimation value, a time mismatch error compensation method based on Taylor approximation is used to perform time mismatch error compensation on the sampled sequence after the preliminary time mismatch error compensation until the channel cross-correlation difference meets the error tolerance condition. Specifically, it includes: Use the updated time mismatch estimation value corresponding to the i-th sampling channel as the time mismatch Δt i , let Δt i = u i (k); Use the sampling sequence after compensating the preliminary time mismatch error corresponding to the i-th sampling channel as the actual sampling sequence Take the sampling sequence after compensating the time mismatch error corresponding to the i-th sampling channel as the ideal sampling sequence y i ; Based on the time mismatch Δt i establish an error term with the Taylor series expansion method, and subtract the error term from the actual sampling sequence to obtain the ideal sampling sequence; Perform cross-correlation calculation based on the updated time mismatch estimation value and the sampled sequence after time mismatch error compensation to obtain the channel cross-correlation difference ∈ i (k); According to the cross-correlation difference value ∈ i (k) of the channels, determine whether the cross-correlation difference value ∈ i (k) of the channels and the expected value of the cross-correlation difference value of the channels have a relative error not greater than the set error tolerance value σ, and determine whether the current iteration round k is greater than the maximum number of iterations k max ; If the channel cross-correlation difference ∈ i (k) satisfies or the current iteration round k satisfies k > k max , then stop the iteration; Otherwise, repeat the iterative update of the pseudo-partial derivative parameter estimation value and the time mismatch estimation value until the channel cross-correlation difference meets the error tolerance condition or the maximum number of iterations is reached; When the condition for triggering iteration stop is ∈ i (k) satisfies return u i (k) as the time mismatch calibration result; When the condition for triggering the iteration stop is that k satisfies k > k max , return the time mismatch estimation value corresponding to the smallest element in the channel cross-correlation difference set Γ i as the time mismatch calibration result.

7. The data-driven background time mismatch calibration method without a reference channel according to claim 6, wherein The data-driven background time mismatch calibration method without a reference channel further includes: Performing background time mismatch calibration on multiple sampling channels of a multi-coset sampling system one by one; The data-driven background time mismatch calibration method without a reference channel further includes: For sampling channels with sampling interval symmetry, directly perform cross-correlation calculation to obtain the channel cross-correlation difference; Based on the channel cross-correlation difference, use a data-driven adaptive calibration method to calibrate the sampling channels with sampling interval symmetry to obtain calibrated sampling channels with sampling interval symmetry; For sampling channels without sampling interval symmetry, introduce the least number of additional sampling channels in layers. Based on the calibrated sampling channels with sampling interval symmetry, perform cross-correlation calculation and use a data-driven adaptive calibration method to calibrate the additional sampling channels to obtain calibrated additional sampling channels; Based on the calibrated additional sampling channels, perform cross-correlation calculation and use a data-driven adaptive calibration method to calibrate the sampling channels without sampling interval symmetry to obtain calibrated sampling channels without sampling interval symmetry.

8. A data-driven background time mismatch calibration system without a reference channel, characterized in that, The data-driven background time mismatch calibration system without a reference channel includes: Sampling module: used to acquire an input signal, input the input signal into multiple sampling channels of a multi-coset sampling system for sampling, and obtain sampled sequences containing time mismatch output by each sampling channel; Preliminary estimation and compensation module: used to randomly set an initial time mismatch estimation value, and according to the initial time mismatch estimation value, use a time mismatch error compensation method based on Taylor approximation to perform preliminary time mismatch error compensation on the sampled sequence containing time mismatch; Cross-correlation calculation module: used to perform cross-correlation calculation according to the initial time mismatch estimation value and the sampled sequence after preliminary time mismatch error compensation, obtain the channel cross-correlation difference, and determine whether the channel cross-correlation difference meets the error tolerance condition; Adaptive calibration module: used to, if not, use a data-driven adaptive calibration method to iteratively update the pseudo-partial derivative parameter estimation value and the time mismatch estimation value, and according to the updated time mismatch estimation value, use a time mismatch error compensation method based on Taylor approximation to perform time mismatch error compensation on the sampled sequence after preliminary time mismatch error compensation until the channel cross-correlation difference meets the error tolerance condition.

9. A terminal, characterized in that, The terminal includes: a memory, a processor, and a data-driven background time mismatch calibration program without reference channels stored on the memory and executable on the processor. When the data-driven background time mismatch calibration program without reference channels is executed by the processor, the steps of the data-driven background time mismatch calibration method without reference channels according to any one of claims 1-7 are implemented.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a data-driven background time mismatch calibration program without reference channels. When the data-driven background time mismatch calibration program without reference channels is executed by a processor, the steps of the data-driven background time mismatch calibration method without reference channels according to any one of claims 1-7 are implemented.

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