A method of correction for a radio frequency mixer for a random demodulation system

Abstract

This invention relates to the field of compressed sensing signal processing technology, and more particularly to a correction method for an RF mixer in a random demodulation system, comprising the following steps: S1, acquiring observation sequences and auxiliary signals output from multiple RF mixers, calculating the cross-correlation peak value of the auxiliary signals, and obtaining an initial time delay reference; S2, initializing error parameters based on the initial time delay reference, performing a first-order Taylor expansion on the fractional delay model of the RF mixer, and generating a Taylor expansion matrix containing the error parameters. This invention can adaptively evaluate the clock synchronization status between nodes in a distributed system, achieve high signal-to-noise ratio restoration of broadband signals when clocks are highly aligned, and automatically switch to an envelope extraction process in the energy space when encountering severe clock drift, effectively avoiding the cancellation phenomenon caused by the direct superposition of multi-channel signals, and improving the reconstruction robustness of the distributed array in harsh environments.

Description

Technical Field

[0001] This invention relates to the field of compressed sensing signal processing technology, and in particular to a correction method for an RF mixer used in a random demodulation system. Background Technology

[0002] Distributed random demodulation array systems utilize multiple spatially dispersed radio frequency nodes working collaboratively. Each node mixes and compresses broadband target signals using local pseudo-random sequences, then aggregates its observation data at a fusion center for joint reconstruction. This effectively overcomes the physical bottleneck of single-node hardware sampling rate without relying on high-speed analog-to-digital converters. This architecture can acquire broadband spectrum information at a lower hardware cost and improve signal interception probability and reconstruction signal-to-noise ratio through spatial diversity of multiple nodes. It has broad application value in broadband signal interception, radio spectrum monitoring, cooperative electronic reconnaissance, and detection of small, slow targets.

[0003] Existing distributed broadband signal reconstruction methods typically rely on strict clock synchronization between nodes. However, in practical applications, due to the natural drift of physical oscillators and environmental interference, each node is prone to random phase jitter and time delay skew. In this case, direct signal synthesis can easily lead to multi-channel signal cancellation, making it difficult to ensure stable reconstruction of broadband signals when time synchronization is compromised. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a correction method for radio frequency mixers in random demodulation systems, aiming to improve the existing distributed broadband signal reconstruction methods, which usually rely on strict clock synchronization between nodes, but are limited by the natural drift of physical oscillators and environmental interference in practical applications.

[0005] This invention provides the following technical solution: a calibration method for an RF mixer in a random demodulation system, comprising the following steps:

[0006] S1. Collect the observation sequence and auxiliary signal output from multiple RF mixers, calculate the cross-correlation peak value of the auxiliary signal, and obtain the initial time delay reference;

[0007] S2. Based on the initial time delay reference, initialize the error parameters, perform a first-order Taylor expansion on the fractional delay model of the RF mixer, and generate a Taylor expansion matrix containing the error parameters.

[0008] S3. Multiply the Taylor expansion matrix with a preset sparse basis to construct a dynamic sensing matrix, and combine the observation sequence with the sparse regularization term to generate a joint cost function that couples the target signal and the error parameter.

[0009] S4. Alternately solve the joint cost function to extract the signal estimate of the target signal, and use the signal estimate as a reference to perform filtering recursion and update the error parameter;

[0010] S5. Substitute the updated error parameters into the dynamic sensing matrix, and perform coherent synthesis on the observation sequence based on the updated dynamic sensing matrix to reconstruct a broadband signal.

[0011] Preferably, in step S1, obtaining the initial time delay reference specifically includes the following steps:

[0012] The cross power spectrum is extracted by performing frequency domain conjugate multiplication on the auxiliary signals output from multiple RF mixers;

[0013] The cross-power spectrum is inversely transformed to obtain a cross-correlation sequence, and the position of the cross-correlation peak of the cross-correlation sequence is used as the integer sampling delay;

[0014] The phase of the cross-power spectrum is unwound, and a linear slope of the unwound phase as a function of frequency is fitted. The subsampling delay is calculated from the linear slope, and the sum of the integer sampling delay and the subsampling delay is used as the initial delay reference.

[0015] Preferably, in S2, generating the Taylor expansion matrix containing the error parameters specifically includes the following steps:

[0016] Construct the time-domain discrete matrix of the pseudo-random sequence used by the radio frequency mixer, and calculate the band-limited interpolation finite difference matrix of the pseudo-random sequence, using the band-limited interpolation finite difference matrix as the basis of the Jacobian matrix;

[0017] The error parameter is decoupled into an integer chip delay variable and a fractional delay variable;

[0018] Using the Jacobian matrix, the fractional delay variable is used as a linear combination coefficient and added to the time-domain discrete matrix corresponding to the integer chip delay variable to generate a Taylor expansion matrix.

[0019] Preferably, calculating the band-limited interpolation finite difference matrix of the pseudo-random sequence specifically includes the following steps:

[0020] Using a preset cutoff frequency as a band-limited constraint, a first-order derivative kernel function of the Dirichlet kernel is constructed, and a window function is applied to the derivative kernel function to truncate it, thereby obtaining a finite-length difference kernel;

[0021] The finite-length difference kernel is convolved with the time-domain discrete matrix along the time dimension to generate a band-limited interpolation finite difference matrix;

[0022] Calculate the truncated residual energy of the finite-length difference kernel. When the truncated residual energy is higher than a first preset threshold, add a second-order derivative kernel function to construct a second-order compensation term, and superimpose the second-order compensation term with the band-limited interpolation finite difference matrix.

[0023] Preferably, in step S3, generating the joint cost function of the coupled target signal and the error parameters specifically includes the following steps:

[0024] Calculate the residual terms between each observation sequence and the dynamic sensing matrix, input each residual term into the Huber loss function, and use the sum of the output results as the residual fidelity term;

[0025] The target signal is mapped to a continuous parameter space, an atomic norm is constructed as the sparse regularization term, and the atomic norm is multiplied by the regularization parameter to obtain the penalty term;

[0026] The residual fidelity term is added to the penalty term to output the joint cost function.

[0027] Preferably, inputting each of the residual terms into the Huber loss function specifically includes the following steps:

[0028] The median absolute deviation of the residual term is calculated for each RF mixer, and the product of the median absolute deviation and a preset multiple is used as the turning point threshold of the Huber loss function of the corresponding RF mixer.

[0029] A subset of radio frequency mixers is randomly selected from multiple radio frequency mixers. The error parameter is solved from the observation sequence of the subset. The number of radio frequency mixers whose residual terms outside the subset are lower than the inflection threshold is counted.

[0030] When the number is higher than the preset number, the subset and the RF mixers with residual terms lower than the turning point threshold are merged into a consensus set. The residual terms of the RF mixers outside the consensus set are removed, and the residual terms of the RF mixers within the consensus set constitute the residual fidelity term.

[0031] Preferably, in step S4, updating the error parameter specifically includes the following steps:

[0032] The joint cost function is decomposed using the alternating direction multiplier method, and the signal estimate is obtained by soft threshold shrinkage projection while keeping the error parameters fixed.

[0033] The estimated signal value is used as a reference observation and input into the extended Kalman filter;

[0034] In the extended Kalman filter, time updates are performed using a state-space model with clock drift, and measurement updates are performed using the reference observations, outputting error parameters.

[0035] Preferably, the time update using the state-space model with clock drift specifically includes the following steps:

[0036] The Allan variance corresponding to the clock drift is mapped to the process noise covariance of the state space model, and the state variables of the state space model include fixed time delay offset, frequency offset and phase noise walk term.

[0037] A zero-sum constraint is applied to the error parameter, and the error parameter of the preset anchor point RF mixer is fixed to zero.

[0038] After each round of output from the extended Kalman filter, a radio frequency mixer that did not participate in the current round of measurement update is reserved. The updated error parameters are used to predict the observation sequence of the corresponding radio frequency mixer. When the prediction residual is higher than the second preset threshold, the process falls back to the initial time delay reference and the alternating solution is re-executed.

[0039] Preferably, in S5, the step of performing coherent synthesis on the observed sequence based on the updated dynamic sensing matrix to reconstruct the broadband signal specifically includes the following steps:

[0040] Calculate the estimated variance of the error parameter in the filter recursive output;

[0041] When the estimated variance is lower than the preset coherence threshold, each observation sequence and the updated dynamic sensing matrix are concatenated row by row to form a joint observation equation and solve it in a unified manner, and coherent synthesis is performed.

[0042] When the estimated variance is higher than the preset coherence threshold, the power envelope of each observation sequence is extracted, and incoherent reconstruction is performed based on the envelope matrix to output a broadband signal.

[0043] The present invention has the following beneficial effects:

[0044] 1. This invention can adaptively evaluate the clock synchronization status between nodes in a distributed system, achieve high signal-to-noise ratio restoration of broadband signals when the clocks are highly aligned, and automatically switch to the envelope extraction process of energy space when encountering severe clock drift. This effectively avoids the cancellation phenomenon caused by the direct superposition of multi-channel signals and improves the reconfiguration robustness of the distributed array in harsh environments.

[0045] 2. In this invention, the complex physical timing skew is transformed into a linear combination of matrices with clear band-limited boundaries. The grid mismatch error caused by traditional discrete sampling is eliminated by dynamic compensation for high-frequency truncation error, providing a more accurate expansion space for parameter optimization and improving the system's accuracy in identifying minute time delays.

[0046] 3. In this invention, a piecewise loss function based on the statistical characteristics of the observation data itself is introduced, which can more accurately identify and isolate abnormal nodes affected by strong impulse interference, reduce the interference of local outliers on the global optimization objective, and ensure the convergence stability of multi-node collaborative processing under complex noise background. Attached Figure Description

[0047] Figure 1 This is a flowchart of a calibration method for an RF mixer in a random demodulation system proposed in this invention;

[0048] Figure 2 This is a schematic diagram of the alternating solution and filtering update process of the present invention;

[0049] Figure 3 This is a schematic diagram of the adaptive coherent and incoherent reconstruction process of the invention. Detailed Implementation

[0050] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention provides a correction method for an RF mixer in a random demodulation system, such as... Figures 1-3 As shown, it includes the following steps:

[0052] S1. Collect the observation sequence and auxiliary signal output from multiple RF mixers, calculate the cross-correlation peak value of the auxiliary signal, and obtain the initial time delay reference;

[0053] Furthermore, in S1, obtaining the initial time delay reference specifically includes the following steps:

[0054] The cross power spectrum is extracted by performing frequency domain conjugate multiplication on the auxiliary signals output from multiple RF mixers.

[0055] The cross-power spectrum is inversely transformed to obtain the cross-correlation sequence, and the position of the cross-correlation peak of the cross-correlation sequence is used as the integer sampling delay;

[0056] The phase of the cross-power spectrum is unwound, and the linear slope of the unwound phase as a function of frequency is fitted. The subsampling delay is calculated from the linear slope, and the sum of the integer sampling delay and the subsampling delay is used as the initial delay reference.

[0057] Specifically, in a distributed random demodulation system, the various RF mixers operate in parallel without sharing a physical clock. The discrete observation sequences of the outputs from multiple RF mixers, along with auxiliary signals obtained from the pre-mixing bypass, are acquired. Assume the system includes... The first RF mixer, the second The auxiliary signal output from each RF mixer is represented as a discrete-time sequence after analog-to-digital conversion. , in the formula The range of values ​​is to , This is the index of discrete sampling points, with a value range of [value range missing]. to Set the number of discrete sampling points for Set the physical sampling frequency of the auxiliary signal. for The corresponding physical sampling interval for Select the first Using an RF mixer as a reference, the auxiliary signal sequence output by it is set as the reference sequence. .

[0058] To obtain the initial relative time delays between the various RF mixers, the auxiliary signals output from multiple RF mixers are subjected to frequency-domain conjugate multiplication. To avoid time-domain aliasing caused by circular convolution, the discrete-time series... With reference sequence Tail-end zeroing extended to Points, set the number of expansion points for Perform the following steps on the zero-padding sequence: Point-wise discrete Fourier transform yields the frequency domain signal. With reference frequency domain signal , in the formula This is the index for discrete points in the frequency domain, with a value range of [value range missing]. to , The physical frequency corresponding to the discrete point in the frequency domain is calculated as follows: The first Frequency domain signal of an RF mixer Complex conjugate with reference frequency domain signal By multiplying each value point by point at the corresponding frequency points, the cross-power spectrum sequence is obtained. The calculation formula is as follows:

[0059] ;

[0060] In the formula, Represents the reference frequency domain signal The result of the complex conjugate operation.

[0061] For cross-power spectrum sequences implement The point-discrete inverse Fourier transform yields the cross-correlation sequence in the time domain. , in the formula This is the discrete-time index after the inverse transform, with a value range of [value range missing]. to Traverse and search cross-correlation sequences The global maximum value of the modulus is used as the location of the cross-correlation peak, and the discrete-time index corresponding to this maximum value is used to determine the location of the peak value. Utilizing the number of extended points Location of cross-correlation peak Execute direction mapping processing: when the cross-correlation peak is located Less than When the current delay is determined to be a positive delay, the relative point count is directly taken as the location of the cross-correlation peak. When the cross-correlation peak is located at Greater than or equal to When the current delay is determined to be negative, the relative points are converted to... Let the number of relative points after direction mapping be... , relative points With physical sampling interval Multiply to calculate the first... Integer sampling delay of each RF mixer relative to a reference. The calculation formula is as follows:

[0062] ;

[0063] Extracting cross-power spectrum sequence The phase angle within the effective signal frequency band yields the original phase sequence. The calculation formula is: , in the formula This represents the operator operation for extracting the principal value of the complex phase. The effective signal frequency band is set to... to Its corresponding frequency domain discrete point index The range of values ​​is to For the original phase sequence Perform phase unwinding processing to eliminate phase jumps exceeding twice pi, resulting in a continuous unwinding phase sequence. Using the obtained integer sampling delay The tilt of the unwound phase sequence is compensated, and a least-squares linear fitting model with angular frequency as the independent variable is constructed. The subsampling delay is obtained by inversely solving the linear slope of this fitting model. The calculation formula is as follows:

[0064] ;

[0065] The obtained integer sampling delay With subsampling delay Perform scalar addition to obtain the first... The total initial delay of each RF mixer relative to the reference reference The calculation formula is as follows:

[0066] ;

[0067] The total initial delay corresponding to each RF mixer in the system. The summaries form the initial time delay baseline, which is then used directly as the initial input value for subsequent parameter decoupling iteration steps.

[0068] This step combines bidirectional mapping of time-domain cross-correlation peaks with frequency-domain phase slope compensation fitting, achieving a coarse-to-fine relative time delay measurement under low sampling rate conditions, providing a high-precision initial iterative benchmark for subsequent decoupled updates of error parameters.

[0069] S2. Initialize the error parameters based on the initial time delay reference, perform a first-order Taylor expansion on the fractional delay model of the RF mixer, and generate a Taylor expansion matrix containing the error parameters.

[0070] Furthermore, in S2, generating the Taylor expansion matrix containing the error parameters specifically includes the following steps:

[0071] Construct the time-domain discrete matrix of the pseudo-random sequence used in the RF mixer, and calculate the band-limited interpolation finite difference matrix of the pseudo-random sequence, using the band-limited interpolation finite difference matrix as the basis of the Jacobian matrix.

[0072] The error parameter is decoupled into an integer chip delay variable and a fractional delay variable;

[0073] Using the Jacobian matrix, the fractional delay variables are used as linear combination coefficients and added to the time-domain discrete matrix of the corresponding integer chip delay variables to generate the Taylor expansion matrix.

[0074] Furthermore, calculating the band-limited interpolation finite difference matrix of the pseudo-random sequence specifically includes the following steps:

[0075] Using a preset cutoff frequency as a band-limited constraint, a first-order derivative kernel function of the Dirichlet kernel is constructed, and a window function is applied to truncate the derivative kernel function to obtain a finite-length difference kernel.

[0076] A finite-length difference kernel is convolved with a time-domain discrete matrix along the time dimension to generate a band-limited interpolation finite difference matrix;

[0077] Calculate the cutoff residual energy of the finite-length difference kernel. When the cutoff residual energy is higher than the first preset threshold, add a second-order derivative kernel function to construct a second-order compensation term, and then superimpose the second-order compensation term with the band-limited interpolation finite difference matrix.

[0078] Specifically, the total initial delay of each RF mixer output from the previous processing step is used as the iteration benchmark, and the... Error parameters of individual RF mixers Initialize to the corresponding total initial delay Obtain the physical chip period of the pseudo-random sequence in the RF mixer. ,set up for Continuous error parameters Decoupling to integer chip delay variables With score delay variable The calculation formula is as follows:

[0079] ;

[0080] ;

[0081] In the formula, This indicates the floor function. This represents the integer chip offset aligned to the discrete sampling grid. Represents the residual sub-chip time between the physical delay and the integer chip boundary, with a value range limited to... to Between. Extract the one-dimensional discrete chip sequence of the pseudo-random sequence under the reference time series, arrange it along the main diagonal, and construct a time-domain discrete diagonal matrix. And based on the integer chip delay variable Perform a cyclic shift along the time column of this diagonal matrix to obtain the time-domain discrete matrix of the corresponding integer chip delay variable. .

[0082] To calculate the band-limited interpolation finite difference matrix of a pseudo-random sequence, a preset cutoff frequency is used. Constructing the first derivative kernel function of the Dirichlet kernel for band-limited constraints Based on the physical passband characteristics of the hardware anti-aliasing filter, a preset cutoff frequency is set. for Set the cutoff radius. for The discrete-time expression for the first-order derivative kernel function is as follows:

[0083] ;

[0084] In the formula, This is a discrete tap index, with a value range of [value range missing]. to An integer that is not equal to zero, when When equal to zero Select a length of Hamming window as a window function By multiplying the first-order derivative kernel function by the window function point by point and then truncating it with the window function, a finite-length difference kernel is obtained. The calculation formula is as follows:

[0085] ;

[0086] Finite length difference kernel The time-domain discrete matrix of the corresponding integer chip delay variable Perform linear discrete convolution along the time dimension to generate a band-limited interpolation finite difference matrix. It is directly used as the basis of the Jacobian matrix in the expansion model.

[0087] Calculate the cut-off residual energy of a finite-length difference kernel during the window function cut-off process. The theoretical total energy of the untruncation ideal derivative kernel function is calculated based on Passevar's theorem. The cutoff residual energy is obtained by combining the finite-length difference kernel with discrete Riemannian calculus and approximation, and the calculation formula is as follows:

[0088] ;

[0089] Set the first preset threshold as When the residual energy is cut off When the value exceeds the first preset threshold, an additional second-order derivative kernel function is constructed to form the Dirichlet kernel. The formula is as follows:

[0090] ;

[0091] In the formula, when When equal to zero Applying the same Hamming window to the second-order derivative kernel function generates a second-order difference kernel. This second-order difference kernel is then compared with the time-domain discrete matrix. Convolution generates a second-order band-limited difference matrix. The initial fractional delay variable is taken. Half of it is used as a scalar and multiplied by the second-order band-limited difference matrix to construct a second-order compensation term. The second-order compensation term With band-limited interpolation finite difference matrix Superposition generates a modified Jacobian matrix that includes high-frequency energy compensation. When the residual energy is cut off When the value is not higher than the first preset threshold, the Jacobian matrix is ​​corrected. Keep as .

[0092] Using a defined modified Jacobian matrix Construct the final expanded representation. Delay the fractional variable. As linear combination coefficients, and the modified Jacobian matrix After multiplication, the time-domain discrete matrix of the corresponding integer chip delay variable is obtained. Add them together to generate a Taylor expansion matrix that includes the error parameters. The calculation formula is as follows:

[0093] ;

[0094] In the formula, the minus sign indicates that the sequence lag shift caused by the time delay is equivalent to a linear shift of the original discrete diagonal matrix along the negative gradient direction. All RF mixers in the system generate their own independent Taylor expansion matrices through this operation.

[0095] This step transforms the complex timing skew mapping of the hardware system into a linear combination of matrices with clearly defined band-limited physical boundaries. By using closed-derivative kernel-trunculated energy monitoring and adaptive second-order superposition, the model truncation error caused by high-frequency jumps is eliminated, providing a precise parameter expansion space for subsequent optimization.

[0096] S3. Multiply the Taylor expansion matrix with the preset sparse basis to construct the dynamic sensing matrix, and combine the observation sequence with the sparse regularization term to generate the joint cost function of the coupled target signal and error parameters.

[0097] Furthermore, in S3, generating the joint cost function of the coupled target signal and error parameters specifically includes the following steps:

[0098] Calculate the residual terms between each observation sequence and the dynamic sensing matrix, input each residual term into the Huber loss function, and use the sum of the output results as the residual fidelity term;

[0099] The target signal is mapped to a continuous parameter space, an atomic norm is constructed as a sparse regularization term, and the atomic norm is multiplied by the regularization parameter to obtain the penalty term.

[0100] Add the residual fidelity term and the penalty term to output the joint cost function.

[0101] Furthermore, inputting each residual term into the Huber loss function specifically includes the following steps:

[0102] The median absolute deviation of the residual term is calculated for each RF mixer, and the product of the median absolute deviation and a preset multiple is used as the turning point threshold of the Huber loss function for the corresponding RF mixer.

[0103] A subset of RF mixers is randomly selected from multiple RF mixers. The error parameters are solved from the observation sequence of the subset, and the number of RF mixers whose residual terms outside the subset are lower than the inflection threshold is counted.

[0104] When the number exceeds the preset number, the subset and the RF mixers with residual terms below the inflection threshold are merged into a consensus set. The residual terms of the RF mixers outside the consensus set are removed, and the residual terms of the RF mixers within the consensus set constitute the residual fidelity term.

[0105] Specifically, obtain the Taylor expansion matrix containing error parameters generated in the previous processing step. Set a preset sparse base. Given the discrete inverse Fourier transform matrix, combine it with the Taylor expansion matrix. Multiply to construct the first Dynamic sensing matrix corresponding to each RF mixer The target signal is defined as a column vector in the sparse frequency domain as follows: Using dynamic sensing matrix With target signal The product of these factors reconstructs the observed estimated sequence. The product of these factors... Observation sequences acquired by one radio frequency mixer Subtracting the observed estimated sequence from the calculated residual term column vector of the corresponding RF mixer yields the result. The calculation formula is as follows:

[0106] ;

[0107] To calculate the inflection threshold of the Huber loss function, the column vector of the residual terms is extracted for each RF mixer. The absolute values ​​of all scalar elements in the vector form the real modulus vector. Calculate the absolute deviation of the median of the modulus vector. The calculation formula is as follows:

[0108] ;

[0109] In the formula, This function retrieves the median of a sequence of real numbers. A preset multiplier is set. for This value maps to a three-standard-deviation confidence interval in robust statistics. The median absolute deviation... With preset multiple Multiplying these yields the inflection threshold of the corresponding Huber loss function for the RF mixer. Define the column vector of residual terms. The Middle scalar elements Huber loss function For piecewise mapping functions: when the absolute value of a scalar element... Less than or equal to the inflection threshold When, output When absolute value Greater than the turning point threshold When, output .

[0110] Assume the total number of RF mixers in the system is . A random sample of 100 RF mixers is taken from multiple RF mixers. A subset of RF mixers, set , in the formula This represents the floor function. A local sensing matrix is ​​constructed using the initial Taylor expansion matrix of the subset. The temporary target signal is reconstructed using an orthogonal matched pursuit algorithm. This temporary target signal is then substituted into the subset's observation equation, and the temporary error parameters of the subset are obtained using the first-order inverse least squares method. The residual terms of the remaining RF mixers outside the subset are reconstructed using the temporary target signal and the temporary error parameters, and the root mean square error of each residual term is calculated. Let the index of the RF mixers outside the subset be . The statistical root mean square error is lower than its corresponding inflection threshold. The number of RF mixers, when this number exceeds a preset number At that time, this subset is merged with the RF mixers whose root mean square error is below the inflection threshold into a consensus set. Remove consistent sets. Residual terms of the externally anomalous RF mixer. Consistent set. The residual term column vector elements of all RF mixers are input one by one into the Huber loss function, and all output results are summed to form the residual fidelity term. The calculation formula is as follows:

[0111] ;

[0112] In the formula, This is the index of the sampling points in the observation sequence, with a value range of... to , This represents the discrete sampling length of a single-path observation sequence.

[0113] To overcome the grid mismatch limitation caused by discrete sparse basis, the target signal is mapped to a parameter space constructed from continuous frequency parameters. The set of atoms in the continuous frequency domain is defined. ,in For continuous normalized frequency The corresponding guiding vector. The atomic norm is constructed using this set of atoms. As a sparse regularization term, its physical meaning is the sum of the absolute values ​​of the minimum atomic coefficients required to continuously reconstruct the target signal. The calculation formula is as follows:

[0114] ;

[0115] In the formula, Indicates the first A continuous frequency component that is activated. Let its corresponding expansion coefficients be... This indicates the flush operation. Set the regularization parameters. for The atomic norm With regularization parameters Multiplying yields a penalty term. The residual is then converted to a fidelity term. Added to the penalty term, the output is the coupled target signal. Joint cost function with error parameters The calculation formula is as follows:

[0116] ;

[0117] By introducing Huber loss that combines median absolute deviation with a subset-based consistency screening mechanism, mixer nodes that are clock-locked or subject to strong pulse interference are effectively isolated. Furthermore, the discrete reconstruction is extended to continuous space using atomic norms, providing a convex optimization objective model with resistance to outlier interference for subsequent alternating optimization.

[0118] S4. Alternately solve the joint cost function to extract the signal estimate of the target signal, and use the signal estimate as a reference to perform filtering recursion and update the error parameters;

[0119] Furthermore, in S4, updating the error parameters specifically includes the following steps:

[0120] The joint cost function is decomposed using the alternating direction multiplier method, and the signal estimate is obtained by soft threshold shrinkage projection under the premise of fixed error parameters.

[0121] The signal estimate is used as a reference observation and input into the extended Kalman filter;

[0122] In the extended Kalman filter, time updates are performed using a state-space model with clock drift, and measurement updates are performed using reference observations, outputting error parameters.

[0123] Furthermore, time updates using a state-space model with clock drift specifically include the following steps:

[0124] The Allan variance corresponding to clock drift is mapped to the process noise covariance of the state-space model. The state variables of the state-space model include fixed time delay offset, frequency offset and phase noise walk term.

[0125] Apply zero-sum constraints to the error parameters and fix the error parameters of the preset anchor point RF mixer to zero;

[0126] After each round of output from the extended Kalman filter, a radio frequency mixer that did not participate in the current round of measurement update is reserved. The observation sequence of the corresponding radio frequency mixer is predicted using the updated error parameters. When the prediction residual is higher than the second preset threshold, the process falls back to the initial time delay reference and the alternating solution is executed again.

[0127] Specifically, the joint cost function generated in the previous processing step is obtained, and it is solved alternately using the alternating direction multiplier method. An auxiliary variable vector with the same dimension as the target signal is introduced. and dual variable vector Transform the unconstrained joint cost function into one with equality constraints. augmented Lagrange function Set penalty factors It is a constant of 0.5. In the current iteration round... In this context, under the premise of fixing error parameters and other variables, the target signal is... Using gradient descent to find the augmented Lagrangian function with respect to The minimum value is updated to obtain the first value. Temporary signal of the wheel Then fix The atomic norm penalty term is transformed into a proximal mapping operation, and the auxiliary variable vector is solved by soft-threshold shrinkage projection. The update formula is as follows: , in the formula This represents the soft threshold operator. Given the regularization parameters determined in the previous processing step, this operator will reduce the amplitude to below the threshold. The continuous frequency components are forcibly set to zero, and the amplitudes of components above this threshold are linearly contracted. Finally, the gradient ascent update of the dual variable vector is performed, as shown in the formula: Repeat the iterations until the residuals converge, and then output the final auxiliary variable vector. As the signal estimate of the target signal in the sparse frequency domain .

[0128] Signal estimation As a reference observation, it is used to update the error parameters of the extended Kalman filter. A state-space model for clock drift is established, and the first... Each RF mixer operates at discrete filtering time steps. state vector A three-dimensional column vector The three elements of this state vector are, in order, the fixed time delay offset, the frequency offset, and the phase noise walk term. Define the state transition matrix. It is a third-order square matrix, and the elements in its first row are The second row of elements is The third row element is , in the formula The filtering time step is set to [value]. The time update formula for the state-space model is the prior state estimate. , in the formula This is the posterior state estimate for the previous filtering time step.

[0129] Obtain the nominal coefficients of the Allan variance of the local crystal oscillator of the system, including the white frequency modulation noise figure. With random walk frequency modulation noise figure Mapping the Allan variance to the process noise covariance matrix of the state-space model. ,set up It is a third-order main diagonal matrix. The first element on its main diagonal reflects the random spread of time delay, and is set to... The second element reflects the random walk of the frequency offset and is set to... The third element reflects independent phase noise and is set as a constant. The prior error covariance matrix is ​​calculated using the process noise covariance matrix. superscript in the formula This represents the matrix transpose operation. Let be the posterior error covariance matrix of the previous filtering time step.

[0130] Apply zero-sum constraints and anchor point constraints to the prior state estimate. The first... Each RF mixer is set as a preset anchor point RF mixer, forcing its prior state vector to be... All elements are fixed to zero. For the remaining working RF mixers within the consensus set determined in the previous processing step, calculate the arithmetic mean of the prior fixed delay offsets of all mixers, and uniformly subtract this arithmetic mean from the prior fixed delay offsets of each RF mixer for zero-mean projection, so that the sum of the corrected global delay offsets is strictly zero.

[0131] The process then proceeds to the measurement update stage of the extended Kalman filter. The Jacobian matrix of the observation equation at the prior state is calculated. The modified Jacobian matrix generated in the previous processing step is then... With preset sparse base Multiply by the signal estimate, then multiply by the signal estimate on the right. Then, by taking the negative sign, we obtain a one-dimensional column vector. This one-dimensional column vector is used as the observation Jacobian matrix. The first column is filled with zero elements, and the other two columns are filled with all zero elements to form the observation Jacobian matrix with dimensions matching the state vector. The observation noise variance matrix is ​​set as follows: Calculate the Kalman gain matrix The innovation vector is obtained by subtracting the actual observed sequence from the predicted state sequence. This innovation vector is then multiplied by the Kalman gain matrix and accumulated onto the prior state estimate to output the posterior state vector. Extracting the posterior state vector The fixed time delay offset in the time delay is used as the updated error parameter.

[0132] After all nodes have completed their outputs in each round of the extended Kalman filter, a cross-validation backoff mechanism is executed. One RF mixer that did not participate in the current round's measurement update is randomly selected from the consensus set as the validation node. The updated error parameters are substituted into the expanded model of the validation node to reconstruct the corresponding dynamic sensing matrix, and this dynamic sensing matrix is ​​then compared with the signal estimate. The predicted observation sequence of the RF mixer is multiplied. The squared L2 norm of the difference between the predicted observation sequence and the actual observation sequence at the verification node is calculated as the prediction residual. A second preset threshold is set. When the predicted residual exceeds the second preset threshold, it is determined that the current filtering state has diverged due to being trapped in a local minimum or encountering strong interference. At this point, all state update results of this round are discarded, the error parameters of all RF mixers are forcibly rolled back to the initial time delay reference, the prior error covariance matrix is ​​reset, and the iterative process is returned to the alternating solution step.

[0133] This step combines the alternating direction multiplier method with the extended Kalman filter incorporating the Allan variance model. It not only provides a rigorous variable splitting closed-form solution, but also achieves high-precision decoupling and updating of strongly coupled signals and nonlinear error parameters by using Jacobi matrix dimensionality reduction mapping and cross-validation mechanism, while ensuring that the global time base does not drift.

[0134] S5. Substitute the updated error parameters into the dynamic sensing matrix, and perform coherent synthesis on the observation sequence based on the updated dynamic sensing matrix to reconstruct the broadband signal.

[0135] Furthermore, in S5, the coherent synthesis of the observed sequence based on the updated dynamic sensing matrix to reconstruct the broadband signal specifically includes the following steps:

[0136] Calculate the estimated variance of the error parameters of the filter recursive output;

[0137] When the estimated variance is lower than the preset coherence threshold, each observation sequence and the updated dynamic sensing matrix are concatenated row by row to form a joint observation equation and solve it in a unified manner, and coherent synthesis is performed.

[0138] When the estimated variance is higher than the preset coherence threshold, the power envelope of each observation sequence is extracted, and incoherent reconstruction is performed based on the envelope matrix to output a broadband signal.

[0139] Specifically, the posterior state vector output from the extended Kalman filter measurement update stage in the previous processing step is extracted, and the fixed time delay offset in it is extracted as the updated error parameter. Update the error parameters Substitute the modified Taylor expansion matrix back into the Taylor expansion formula of the fractional delay model to generate the corrected Taylor expansion matrix, and then combine this corrected Taylor expansion matrix with the preset sparse basis. Multiply to calculate the first... Updated dynamic sensing matrix for each RF mixer Simultaneously, the posterior error covariance matrix of the extended Kalman filter, calculated synchronously during the measurement update phase, is obtained. The posterior error covariance matrix is ​​a diagonal matrix, and the first element on the diagonal represents the estimation uncertainty of the fixed time delay offset. This element is extracted as the estimated variance of the error parameter in the filter recursion output, denoted as . The formula is , in the formula Representation matrix No. Line number The elements of the column. Calculate the arithmetic mean of the estimated variances of all RF mixers currently involved in the update, and use this as the global estimated variance of the system. .

[0140] Set preset coherence threshold for This constant threshold maps to the physical boundary of time synchronization jitter at the sub-picosecond level. When the system's global estimation variance... When the value is below a preset coherence threshold, the distributed system is deemed to meet the high-precision phase alignment condition. This involves analyzing the observation sequences of all RF mixers within the consensus set. By connecting the first and last ends vertically, a joint observation sequence column vector is formed. Simultaneously update the dynamic sensing matrix corresponding to each RF mixer. Vertically stitched together along the row direction to form a joint dynamic sensing matrix. Based on the splicing results, a basis pursuit denoising algorithm is used to perform coherent synthesis and unified solution of the joint observation equation. The calculation formula is to find the target signal column vector to be solved. 1 norm The minimum solution that satisfies the tolerance constraint. , in the formula The first norm operation of a vector is represented. The squaring operation of the L2 norm of a vector is represented. The tolerance constant is set to . The target signal obtained by unified solution. Left-multiplying the pre-defined sparse base The reconstructed output is a high-resolution time-domain broadband signal.

[0141] When the global estimation variance of the system When the signal strength is above or equal to a preset coherence threshold, the system is deemed to have strong residual random phase jitter. Direct reconstruction would cause multi-channel signal cancellation, thus transitioning to a non-coherent processing flow. This involves observation sequences for each RF mixer. Applying a Hilbert transform yields orthogonal components. The sum of squares of corresponding elements in the original sequence and the orthogonal components is calculated, and the power envelope column vector of each observation sequence is directly extracted. . All extracted power envelope column vectors By connecting the first and last ends vertically, a joint envelope column vector is formed. For the updated dynamic sensing matrix Squaring the absolute values ​​of all elements in the matrix, we construct the amplitude sensing matrix in the pure energy space. Then, we vertically concatenate the amplitude sensing matrices of each mixer to form a joint energy sensing matrix. Based on the envelope vector and energy matrix, incoherent reconstruction is performed, constructing a non-negative least squares optimization problem, which is solved by minimizing the squared residual L2 norm. Solving for the energy envelope vector of a broadband signal The solution process imposes strict constraints on the energy envelope vector. All elements are greater than or equal to zero. The final output is the energy envelope vector obtained from the solution. As a broadband signal that is noncoherently reconstructed.

[0142] When clock synchronization accuracy is extremely high, joint matrix operations are used to restore the ultimate signal-to-noise ratio of broadband signals. Even when encountering severe clock drift, the basic interception of signals can still be guaranteed through rigorous envelope feature space dimensionality reduction, which significantly improves the reconfiguration robustness of distributed array systems in harsh electromagnetic environments.

[0143] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A calibration method for an RF mixer in a random demodulation system, characterized in that, Includes the following steps: S1. Collect the observation sequence and auxiliary signal output from multiple RF mixers, calculate the cross-correlation peak value of the auxiliary signal, and obtain the initial time delay reference; S2. Based on the initial time delay reference, initialize the error parameters, perform a first-order Taylor expansion on the fractional delay model of the RF mixer, and generate a Taylor expansion matrix containing the error parameters. S3. Multiply the Taylor expansion matrix with a preset sparse basis to construct a dynamic sensing matrix, and combine the observation sequence with the sparse regularization term to generate a joint cost function that couples the target signal and the error parameter. S4. Alternately solve the joint cost function to extract the signal estimate of the target signal, and use the signal estimate as a reference to perform filtering recursion and update the error parameter; S5. Substitute the updated error parameters into the dynamic sensing matrix, and perform coherent synthesis on the observation sequence based on the updated dynamic sensing matrix to reconstruct a broadband signal.

2. The calibration method for an RF mixer in a random demodulation system according to claim 1, characterized in that, In S1, obtaining the initial time delay reference specifically includes the following steps: The cross power spectrum is extracted by performing frequency domain conjugate multiplication on the auxiliary signals output from multiple RF mixers; The cross-power spectrum is inversely transformed to obtain a cross-correlation sequence, and the position of the cross-correlation peak of the cross-correlation sequence is used as the integer sampling delay; The phase of the cross-power spectrum is unwound, and a linear slope of the unwound phase as a function of frequency is fitted. The subsampling delay is calculated from the linear slope, and the sum of the integer sampling delay and the subsampling delay is used as the initial delay reference.

3. The calibration method for an RF mixer in a random demodulation system according to claim 1, characterized in that, In S2, generating the Taylor expansion matrix containing the error parameters specifically includes the following steps: Construct the time-domain discrete matrix of the pseudo-random sequence used by the radio frequency mixer, and calculate the band-limited interpolation finite difference matrix of the pseudo-random sequence, using the band-limited interpolation finite difference matrix as the basis of the Jacobian matrix; The error parameter is decoupled into an integer chip delay variable and a fractional delay variable; Using the Jacobian matrix, the fractional delay variable is used as a linear combination coefficient and added to the time-domain discrete matrix corresponding to the integer chip delay variable to generate a Taylor expansion matrix.

4. The calibration method for an RF mixer in a random demodulation system according to claim 3, characterized in that, The calculation of the band-limited interpolation finite difference matrix of the pseudo-random sequence specifically includes the following steps: Using a preset cutoff frequency as a band-limited constraint, a first-order derivative kernel function of the Dirichlet kernel is constructed, and a window function is applied to the derivative kernel function to truncate it, thereby obtaining a finite-length difference kernel; The finite-length difference kernel is convolved with the time-domain discrete matrix along the time dimension to generate a band-limited interpolation finite difference matrix; Calculate the truncated residual energy of the finite-length difference kernel. When the truncated residual energy is higher than a first preset threshold, add a second-order derivative kernel function to construct a second-order compensation term, and superimpose the second-order compensation term with the band-limited interpolation finite difference matrix.

5. The calibration method for an RF mixer in a random demodulation system according to claim 1, characterized in that, In S3, generating the joint cost function of the coupled target signal and the error parameters specifically includes the following steps: Calculate the residual terms between each observation sequence and the dynamic sensing matrix, input each residual term into the Huber loss function, and use the sum of the output results as the residual fidelity term; The target signal is mapped to a continuous parameter space, an atomic norm is constructed as the sparse regularization term, and the atomic norm is multiplied by the regularization parameter to obtain the penalty term; The residual fidelity term is added to the penalty term to output the joint cost function.

6. A calibration method for an RF mixer in a random demodulation system according to claim 5, characterized in that, The step of inputting each of the residual terms into the Huber loss function specifically includes the following steps: The median absolute deviation of the residual term is calculated for each RF mixer, and the product of the median absolute deviation and a preset multiple is used as the turning point threshold of the Huber loss function of the corresponding RF mixer. A subset of radio frequency mixers is randomly selected from multiple radio frequency mixers. The error parameter is solved from the observation sequence of the subset. The number of radio frequency mixers whose residual terms outside the subset are lower than the inflection threshold is counted. When the number is higher than the preset number, the subset and the RF mixers with residual terms lower than the turning point threshold are merged into a consensus set. The residual terms of the RF mixers outside the consensus set are removed, and the residual terms of the RF mixers within the consensus set constitute the residual fidelity term.

7. The calibration method for an RF mixer in a random demodulation system according to claim 1, characterized in that, In S4, updating the error parameter specifically includes the following steps: The joint cost function is decomposed using the alternating direction multiplier method, and the signal estimate is obtained by soft threshold shrinkage projection while keeping the error parameters fixed. The estimated signal value is used as a reference observation and input into the extended Kalman filter; In the extended Kalman filter, time updates are performed using a state-space model with clock drift, and measurement updates are performed using the reference observations, outputting error parameters.

8. A calibration method for an RF mixer in a random demodulation system according to claim 7, characterized in that, The time update using the state-space model with clock drift specifically includes the following steps: The Allan variance corresponding to the clock drift is mapped to the process noise covariance of the state space model, and the state variables of the state space model include fixed time delay offset, frequency offset and phase noise walk term. A zero-sum constraint is applied to the error parameter, and the error parameter of the preset anchor point RF mixer is fixed to zero; After each round of output from the extended Kalman filter, a radio frequency mixer that did not participate in the current round of measurement update is reserved. The updated error parameters are used to predict the observation sequence of the corresponding radio frequency mixer. When the prediction residual is higher than the second preset threshold, the process falls back to the initial time delay reference and the alternating solution is re-executed.

9. A calibration method for an RF mixer in a random demodulation system according to claim 1, characterized in that, In S5, the step of performing coherent synthesis on the observation sequence based on the updated dynamic sensing matrix to reconstruct the broadband signal specifically includes the following steps: Calculate the estimated variance of the error parameter in the filter recursive output; When the estimated variance is lower than the preset coherence threshold, each observation sequence and the updated dynamic sensing matrix are concatenated row by row to form a joint observation equation and solve it in a unified manner, and coherent synthesis is performed. When the estimated variance is higher than the preset coherence threshold, the power envelope of each observation sequence is extracted, and incoherent reconstruction is performed based on the envelope matrix to output a broadband signal.

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