CN103746699B - Signal reconstruction method based on rotation matrix error estimation for alternative sampling system - Google Patents
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Abstract
The invention discloses a signal reconstruction method based on rotation matrix error estimation for an alternative sampling system. The method comprises the following steps: I, initial parameter setting; II, training sample construction: transforming sample sequences of M A/D (Analog to Digital) conversion chips in the same time interval t to a frequency domain by means of fast Fourier transform to obtain M training samples, wherein the M training samples construct a training sample set; III, time base error estimation: selection of dual frequency points for error estimation, covariance matrix estimation, feature decomposition, extraction of a large feature value and a corresponding feature vector thereof and time base error estimation; IV, gain error estimation; V, gain error compensation; VI, weight vector reconstruction; VII, signal reconstruction in a frequency domain; VIII, inverse fast Fourier transform. The method disclosed by the invention is simple in steps, reasonable in design, convenient to implement and good in application effect, and the problems of complex error estimating process, large calculation amount, large signal error after reconstruction and the like existing in the conventional signal reconstruction method for a parallel alternative sampling system can be solved effectively.
Description
Technical Field
The invention relates to a signal reconstruction method of an alternate sampling system, in particular to a signal reconstruction method of the alternate sampling system based on rotation matrix error estimation.
Background
With the continuous expansion of the application range of digital signal processing technology, the frequency bandwidth (bandwidth for short) range of signals to be processed is also larger and larger. From the aspect of signal bandwidth, signals can be classified into narrowband signals, wideband signals and ultra wideband signals. The narrow-band signal is sampled by a single ADC conversion chip under most conditions, so that the aim of high precision can be fulfilled; on the premise of meeting the sampling theorem, the broadband signal can be sampled by a single high-rate ADC conversion chip generally, but the broadband signal has lower precision, cannot be sampled with high precision, cannot meet the use requirement of a large dynamic range, and has higher hardware cost of a circuit; for the ultra-wideband signal, on the premise of meeting the sampling theorem, the sampling is difficult to be carried out by using a single ADC conversion chip under the existing conditions.
Therefore, for wideband signals and ultra-wideband signals (the signal bandwidth is from tens of megabytes to hundreds of megabytes or even gigabytes), the single ADC conversion chip is difficult to achieve high-precision sampling and reconstruction of signals on the premise that the sampling theorem is satisfied or is not satisfied. If a multi-channel sampling system is formed by using a plurality of low-speed and high-precision ADC conversion chips by using a theory and a method for processing digital signals, high-precision sampling of the signals and real-time reconstruction of the signals can be realized under certain conditions. According to the basic theory of signal processing, for a sampling system with M channels, the lowest undistorted sampling frequency of each ADC conversion chip required by the system is 1/M of that of sampling by adopting a single ADC conversion chip, and along with the requirement on the sampling rate of the ADC conversion chip, the contradiction between the signal bandwidth and the sampling rate is greatly improved. In the practical use process, on one hand, the multichannel sampling system can improve the maximum signal bandwidth allowed to be input by the system to be M times of that of a single ADC conversion chip when the sampling rate of the ADC conversion chip is kept unchanged; on the other hand, when the maximum signal bandwidth allowed to be input by the system is kept unchanged, the input signal can be sampled by adopting a low-rate and high-precision ADC conversion chip, the purpose of reconstructing a high-speed and high-precision sampling sequence of the signal by using M low-rate and high-precision sampling sequences is achieved, and the contradiction between the sampling rate and the sampling precision is solved. Modern signal processing systems for radar, communication and the like generally require that signals received by an antenna are directly digitized and then processed. For wideband signals, this requires a high conversion rate of the ADC conversion chip, however, for each doubling of the sampling rate, the quantization precision is approximately reduced by one bit, resulting in a dynamic range reduction of about 6 dB; but also the stability of the sampling clock will decrease with increasing sampling rate, which will aggravate aperture jitter and thus decrease the signal-to-noise ratio, and the cost will increase dramatically.
The parallel alternate sampling technology, namely the front end utilizes a plurality of ADC conversion chips to perform parallel successive sampling, and the rear end performs serial multiplexing, can effectively solve the contradiction between the sampling rate and the signal bandwidth as well as between the sampling rate and the sampling precision. However, since it relies on an exact fit between the channels, there is more systematic error than single channel sampling. Firstly, the gains and offsets among ADC conversion chips of all channels are difficult to be strictly consistent; secondly, the sampling clock phase between the parallel channels cannot be accurately controlled (time base bias) under the prior art conditions. Therefore, multi-channel system errors will cause non-linear distortion of the sampled waveform, reducing system performance.
Aiming at the problems, a large number of documents propose different system error estimation methods, such as a signal spectrum analysis method, a correlation method, a parameter model method, a blind estimation method and the like, but most of the signal spectrum analysis method, the correlation method and the parameter model method require a known excitation signal with pure frequency spectrum as a correction source, the estimation process is complex, and the error parameter needs to be corrected again after being changed; however, although the blind estimation method does not need a special excitation signal, it needs multiple iterations and is not easy to converge, and the calculation amount is large.
In 2009, "electronic article" 37(10):2298-2301, "an adaptive non-uniform comprehensive calibration method in parallel sampling" published by tianshurin, panhuaqing and Wangzhiji, and in 2010 "electronic measurement and instrumentation article" 24(1):34-38, "a time-based non-uniform signal adaptive reconstruction method in parallel alternate sampling" published by panhuaqing, tianshurin, leaf 33411, etc., propose methods for respectively iterating time-based errors, gain errors and offset errors by converting mismatching error estimation into a multidimensional nonlinear optimization problem by using an adaptive control technology and using a minimum error criterion. However, since the method does not consider the influence of noise, the estimation accuracy will be reduced under the condition of low signal-to-noise ratio, and in addition, a local minimum point is easy to be trapped in the iteration process. In the document of parallel alternate sampling system error estimation based on subspace projection published by malun, lao gui and ludan in the 09 th year 2012, a parallel alternate sampling system error estimation method based on subspace projection is provided, in which after fourier transform processing is respectively performed on sampling data of each channel (due to the fact that a low-rate ADC conversion chip is adopted to sample broadband signals, spectrum aliasing is generated on the sampling data of a single channel), multi-channel frequency domain sampling output is regarded as array output, and a channel mismatch error is estimated by using orthogonal characteristics of a frequency domain linear phase vector corresponding to multi-channel time delay and a noise subspace obtained by the sampling data. However, since iteration is needed in the error estimation process, the method also has the difficulties of large calculation amount and easy falling into local minimum points.
In summary, the currently adopted parallel alternate sampling technology is not mature and perfect, and the existing parallel alternate sampling system error estimation methods have the defects and disadvantages of complex estimation process, multiple iterations, difficult convergence, large calculation amount, easy falling into local minimum points and the like to different degrees. Correspondingly, the signal reconstruction method based on the existing parallel alternate sampling system error estimation method also has the problems of simple method steps, large calculated amount, poor use effect, large error of the reconstructed signal and the like.
Disclosure of Invention
The invention aims to solve the technical problems in the prior art, and provides an alternative sampling system signal reconstruction method based on rotation matrix error estimation, which has the advantages of simple steps, reasonable design, convenient implementation and good use effect, and can effectively solve the problems of complex error estimation process, large calculated amount, large signal error after reconstruction and the like in the existing parallel alternative sampling system signal reconstruction method.
In order to solve the technical problems, the invention adopts the technical scheme that: a method for reconstructing a signal of an alternate sampling system based on rotation matrix error estimation is characterized by comprising the following steps:
step one, initial parameter input and setting: inputting the sampling frequency f of M, M A/D conversion chips adopted in a parallel alternative sampling system needing error estimation through a parameter input unitsAnd the bandwidth bps of the sampled wideband signal s (t); the parameter input unit is connected with the data processor;
step two, training sample construction, namely firstly taking sampling sequences of M A/D conversion chips in the same time period t, wherein each sampling sequence of the A/D conversion chip comprises n sampling signals, and n is t × fs(ii) a Performing fast Fourier transform on the sampling sequences of the M A/D conversion chips to a frequency domain, and correspondingly obtaining M training samples;
the M training samples are respectively training samples of M sampling channels of the parallel alternate sampling system, and the M training samples form a training sample set;
step three, time base error estimation: estimating the time base error of the parallel alternate sampling system by adopting a data processor and utilizing the training sample set constructed in the second step, wherein the process is as follows:
step 301, selecting a double frequency point for error estimation: from [ -fs/2,fs/2]In the method, two values f are randomly selected1And f2As a pair of frequency points for error estimation, where f1＞f2And Δ f ═ f1-f2；
Step 302, covariance matrix estimation: finding a frequency value f from the set of training samples1Forming a training sample A by the sample data, and finding out a frequency value f from the training sample set2Forming a training sample B by the sample data; then, covariance matrixes R of the training samples A and B are respectively calculatedaAnd Rb；
Step 303, feature decomposition: for covariance matrix RaAnd RbRespectively performing characteristic decomposition to obtain Ra＝Ua∑a(Ua)HAnd Rb＝Ub∑b(Ub)H(ii) a Wherein,and it is composed of M eigenvectorsA matrix of formations;and which is represented by M eigenvaluesIs a diagonal matrix of diagonal elements, and M eigenvaluesArranging from big to small;and it is composed of M eigenvectorsA matrix of formations;and which is represented by M featuresValue ofIs a diagonal matrix of diagonal elements, and M eigenvaluesArranging from big to small; h represents matrix conjugate transpose operation;
step 304, extracting the large characteristic value and the corresponding characteristic vector: from step 303, M eigenvaluesIn the method, the first 2I +1 large eigenvalues are extractedAnd its corresponding 2I +1 eigenvectorsReuse formulaFor 2I +1 eigenvectorsRespectively deforming to obtain 2I +1 vectorsWherein j is a positive integer and j is 1, …,2I + 1; at the same time, from step 303, M eigenvaluesIn the method, the first 2I +1 large eigenvalues are extractedAnd its corresponding 2I +1 eigenvectorsWherein,
step 305, time base error estimation: according to the formulaObtaining the time delay error vector of the parallel alternative sampling systemWherein ∠ represents a phase angle, τ ═ 0,1/Mfs,…(M-1)/Mfs]T；WhereinFor the 2I +1 eigenvectors extracted in step 304The sum of (1);for 2I +1 vectors in step 304The sum of (1); time base errors for the M sampling channels; i is a positive integer and I ═ 1, …,2I + 1;
step four, gain error estimation: using a data processor and based on the delay error vector obtained in step threeGain error for the parallel alternate sampling systemThe difference is estimated as follows:
step 401, time base error compensation: using the delay error vector of the parallel alternative sampling system obtained in step threeFor ideal frequency domain steering vector pi' (f) performing compensation to obtain a time-base error-compensated frequency-domain steering vector pi(f) Wherein I is a positive integer and I ═ 1, …,2I + 1;
step 402, utilizing formula Di＝diag{pi(f) F, the frequency domain steering vector p after the time base error compensation in the step 401 is correctedi(f) Deforming to obtain vector Di；
Step 403, according to the formulaSolving a matrix W;
in the formula,orWhereinFor the 2I +1 eigenvectors extracted in step 304Form a matrix and for the 2I +1 eigenvectors extracted in step 304Form a matrix and
step 404, feature decomposition: performing characteristic decomposition on the matrix W, and taking out the characteristic vector G which is corresponding to the maximum characteristic value as [1, G%2,…,gM]T；
Step 405, gain error estimation: according to the formulaDeriving a gain error vector for the parallel alternate sampling systemWherein1,g1,…,gM-1Gain errors of the M sampling channels respectively;
step five, gain error compensation: using a data processor and using the gain error vector of the parallel alternate sampling system derived in step 405The frequency domain steering vector p after the time base error compensation in step 402i(f) Compensating to obtain a frequency domain steering vector p after gain error compensationi"(f), wherein i is a positive integerAnd I is 1, …,2I + 1;
step six, weight vector reconstruction: using a data processor and in accordance withCalculating to obtain a weight vector wi(f) (ii) a Wherein, r (f) is a covariance matrix of a training sample composed of all sample data with frequency value f in the training sample set, where f [ -f [ ]s/2,fs/2]；
Step seven, signal reconstruction in the frequency domain: using a data processor and according to a formulaThe signals to be reconstructed are sampled by the parallel alternate sampling systemReconstructing to obtain a reconstructed signal S in the frequency domaini(f)；
The signal to be reconstructed comprises sampling sequences of M A/D conversion chips in the same time period TAnd it is recorded asWhereinWherein M is the number of M of the a/D conversion chips and M is 0,1, …, M-1; in the formula,to reconstruct the signalA signal obtained by performing a fast Fourier transform to a frequency domain, and
step eight, fast Fourier inverse transformation: performing inverse fast Fourier transform on the reconstructed signal in the frequency domain obtained in the step seven by adopting a data processor to obtain a reconstructed signal S (n); wherein S (n) ═ S0(n),S1(n),…,SM-1(n)]TAnd the reconstructed signal S (n) comprises a sampling sequence S of the M reconstructed A/D conversion chipsm(n)。
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: when the weight vector is reconstructed in the sixth step, the process is as follows:
step 601, wi(0) And (3) calculating: according to the formulaCalculate to obtain wi(0) (ii) a Wherein wi(0) Weight vector when f is 0, pi"(0) is the frequency domain steering vector p after the gain error compensation in the fifth stepiA frequency domain steering vector when f obtained in ═ 0; r (0) is a covariance matrix of a training sample formed by all sample data with the frequency value of 0 in the training sample set;
step 602, weight vector wi(f) And (3) calculating: according to the formula wi(f)＝B(f)·wi(0) Calculating to obtain wi(f) (ii) a In the formula,
the signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: after the time base error estimation is completed in step 305, obtaining a delay error vector of the parallel alternate sampling system, and then entering step 306;
step 306, returning to step 301, and repeating from [ -fs/2,fs/2]Two values are randomly selected as a pair of frequency points for error estimation, and then the error estimation is carried outObtaining a time delay error vector of the parallel alternative sampling system according to the method from the step 302 to the step 305;
307, repeating the step 306 one or more times to obtain one or more time delay error vectors of the parallel alternate sampling system;
308, averaging a plurality of delay error vectors obtained under the current condition to obtain a delay error vector of the parallel alternate sampling system
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: in the second step, n is 100-1000.
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: and in the second step, when sampling sequences of M A/D conversion chips in a time period t are taken, selecting by adopting a sliding window method.
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: in the first step, the parallel alternate sampling system comprises a plurality of A/D conversion chips, a plurality of delay control modules for respectively controlling the sampling time of the A/D conversion chips, a plurality of data processing units for respectively carrying out Fourier transform processing on signals sampled by the A/D conversion chips, a multiplexer which is respectively connected with the data processing units and outputs the signals processed by the data processing units in a data array form, and a data processor connected with the multiplexer, the plurality of delay control modules are respectively connected with the plurality of A/D conversion chips, the plurality of A/D conversion chips are respectively connected with the plurality of data processing units, and the plurality of delay control modules are controlled by a data processor and are connected with the data processor.
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: the parallel alternate sampling system also comprises a plurality of gain control modules which are respectively connected with the A/D conversion chips, and the gain control modules are respectively connected between the A/D conversion chips and the data processing units; the gain control module is an amplifier or an attenuator; and the gain control modules are controlled by a data processor and are connected with the data processor.
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: estimating the time delay error vector of the parallel alternate sampling system in the third stepThe data processor then derives a delay error vector from the estimateAnd respectively controlling the plurality of delay control modules.
The signal reconstruction method of the alternating sampling system based on the rotation matrix error estimation is characterized in that: estimating the gain error vector of the parallel alternative sampling system in the fourth stepThe data processor then derives a gain error vector from the estimateAnd respectively controlling the gain control modules.
Compared with the prior art, the invention has the following advantages:
1. the time base error estimation method is simple, reasonable in design and convenient to implement, and the time base error is estimated independently of the gain error, so that the influence of the uncertain quantity of the gain error on the time base error estimation precision is avoided.
2. The time base error estimation and gain error estimation method is simple, iteration is not needed, and high-precision estimation can be directly carried out on the time base error and the gain error. In addition, the time base error and the gain error are separated and are respectively estimated, so that iteration is not needed, the calculated amount is reduced, the estimation precision can be improved, and the local minimum point is avoided. Because the frequency domain linear phase vectors of two frequency channels in the parallel alternate sampling system only differ by one diagonal matrix (namely, the rotation matrix C, wherein the parameters in the rotation matrix C are consistent with the parameters in the rotation matrix B, the difference is only that the rotation matrix C is the diagonal matrix, and one vector of the rotation matrix B, namely B is another representation form of the rotation matrix C), and the rotation matrix is mainly determined by the time base error, based on the characteristics and the corresponding relation between the frequency domain linear phase vectors and the signal subspace, the invention can directly estimate the time base error and the gain error without iteration, and is stable to the residual offset error and the noise.
3. The estimation precision of the time base error and the gain error is high, and the deviation of the estimated time base error is about the same as the deviation of the estimated time base error on the premise of the same signal to noise ratioThe estimation precision is improved by 2 times compared with the existing self-adaptive method. In order to improve the sampling precision of the parallel alternate sampling system, the time delay error vector of the parallel alternate sampling system is estimatedThe data processor can then derive a delay error vector from the estimateRespectively controlling the plurality of delay control modules; and, estimating a gain error vector of the parallel alternate sampling systemThe data processor can then derive a gain error vector from the estimateAnd respectively controlling the gain control modules. Therefore, the method can effectively overcome the defects and shortcomings of the existing parallel alternate sampling system error estimation method that the estimation process is complex, multiple iterations are needed, convergence is not easy, the calculated amount is large, and the local minimum point is easy to fall into in different degrees.
4. The signal reconstruction method is simple, the calculated amount is small, the realization is convenient, the error of the reconstructed signal is small, and the problems of simple method steps, large calculated amount, poor using effect, large error of the reconstructed signal and the like existing in the signal reconstruction method of the existing parallel alternate sampling system can be effectively solved.
In conclusion, the method has the advantages of simple steps, reasonable design, convenience in implementation and good use effect, and can effectively solve the problems of complex error estimation process, large calculated amount, large error of the reconstructed signal and the like in the conventional parallel alternate sampling system signal reconstruction method.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
Fig. 1 is a schematic block diagram of a parallel alternate sampling system according to the present invention.
FIG. 2 is a block diagram of a method of the present invention.
Fig. 3 is a schematic diagram of a variation curve of the gain error estimation accuracy with the change of the signal-to-noise ratio according to the present invention.
Fig. 4 is a schematic diagram of a variation curve of the time-base error estimation accuracy with the change of the signal-to-noise ratio according to the present invention.
Description of reference numerals:
1-A/D conversion chip; 2-a delay control module; 3-a data processing unit;
4-a multiplexer; 5-a parameter input unit; 6-a data processor;
and 7, a gain control module.
Detailed Description
Fig. 2 shows a method for reconstructing a signal of an alternate sampling system based on rotation matrix error estimation, which includes the following steps:
step one, initial parameter input and setting: inputting the sampling frequency f of M, M A/D conversion chips 1 adopted in the parallel alternative sampling system needing error estimation through a parameter input unit 5sAnd the bandwidth bps of the sampled wideband signal s (t). The parameter input unit 5 is connected to a data processor 6.
Wherein M is a positive integer and M is not less than 3.
Step two, training sample construction, namely firstly taking sampling sequences of M A/D conversion chips 1 in the same time period t, wherein each sampling sequence of the A/D conversion chip 1 comprises n sampling signals, and n is t × fs(ii) a And performing fast Fourier transform on the sampling sequences of the M A/D conversion chips 1 to a frequency domain, and correspondingly obtaining M training samples.
The M training samples are respectively training samples of M sampling channels of the parallel alternate sampling system, and the M training samples form a training sample set.
In this embodiment, each of the M training samples includes n sample data.
In this embodiment, n in the second step is 100 to 1000.
In actual use, the value of n can be adjusted correspondingly according to specific requirements.
Step three, time base error estimation: estimating the time base error of the parallel alternate sampling system by adopting the data processor 6 and utilizing the training sample set constructed in the second step, wherein the process is as follows:
step 301, selecting a double frequency point for error estimation: from [ -fs/2,fs/2]In the method, two values f are randomly selected1And f2As a pair of frequency points for error estimation, where f1＞f2And Δ f ═ f1-f2。
Step 302, covariance matrix estimation: finding a frequency value f from the set of training samples1Forming a training sample A by the sample data, and finding out a frequency value f from the training sample set2Forming a training sample B by the sample data; then, covariance matrixes R of the training samples A and B are respectively calculatedaAnd Rb。
In this embodiment, when the sampling sequences of M a/D conversion chips 1 in a time period t are taken in step two, a sliding window method is used to select the sampling sequences, and a sample covariance matrix of sample data sampled by the sliding window method is used to select a covariance matrix RaAnd RbAnd (6) estimating. In actual sample construction, specifically referring to the estimation method of the selected sample and the covariance matrix by the sliding window method described in the document entitled "multichannel low-rate sampling method for wideband radar signal" by malun, li-zheng, and linguisng, published in the document "system engineering and electronics technology" 2007, 09, the covariance matrices R of the training sample a and the training sample B are calculatedaAnd Rb。
Step 303, feature decomposition: for covariance matrix RaAnd RbRespectively performing characteristic decomposition to obtain Ra＝Ua∑a(Ua)HAnd Rb＝Ub∑b(Ub)H(ii) a Wherein,and it is composed of M eigenvectorsA matrix of formations;and which is represented by M eigenvaluesIs a diagonal matrix of diagonal elements, and M eigenvaluesArranging from big to small;and it is composed of M eigenvectorsA matrix of formations;and which is represented by M eigenvaluesIs a diagonal matrix of diagonal elements, and M eigenvaluesArranging from big to small; h denotes a matrix conjugate transpose operation.
Step 304, extracting the large characteristic value and the corresponding characteristic vector: from step 303, M eigenvaluesIn the method, the first 2I +1 large eigenvalues are extractedAnd its corresponding 2I +1 eigenvectorsReuse formulaFor 2I +1 eigenvectorsRespectively deforming to obtain 2I +1 vectorsWherein j is a positive integer and j is 1, …,2I + 1; at the same time, from step 303, M eigenvaluesIn the method, the first 2I +1 large eigenvalues are extractedAnd its corresponding 2I +1 eigenvectorsWherein,where 2I is the number of spectral aliasing.
Step 305, time base error estimation: according to the formulaObtaining the time delay error vector of the parallel alternative sampling systemWherein ∠ represents a phase angle, τ ═ 0,1/Mfs,…(M-1)/Mfs]T；WhereinFor the 2I +1 eigenvectors extracted in step 304The sum of (1);for 2I +1 vectors in step 304The sum of (1); time base error for M sampling channels. I is a positive integer and I is 1, …,2I + 1.
In this embodiment, in step 303Wherein C is a rotation matrix and 2I +1 large eigenvaluesThe subspace spanned by the corresponding feature vectors is the signal subspace,2I +1 large eigenvaluesSubspace spanned by corresponding eigenvectors, i.e. signal subspace, formulaRepresenting the rotational relationship of the two signal subspaces.
Wherein,since the parameters inside C and B are the same, the difference is only that C is a diagonal matrix and B is a vector, so B is another expression form of the rotation matrix C.
Step four, gain error estimation: using a data processor 6 and based on the delay error vector obtained in step threeEstimating the gain error of the parallel alternate sampling system by the following process:
step 401, time base error compensation: using the delay error vector of the parallel alternative sampling system obtained in step threeFor ideal frequency domain steering vector pi' (f) performing compensation to obtain a time-base error-compensated frequency-domain steering vector pi(f) Wherein I is a positive integer and I is 1, …,2I + 1.
Step 402, utilizing formula Di＝diag{pi(f) F, the frequency domain steering vector p after the time base error compensation in the step 401 is correctedi(f) Deforming to obtain vector Di。
Step 403, according to the formulaThe matrix W is obtained.
In the formula,orWhereinFor the 2I +1 eigenvectors extracted in step 304Form a matrix and for the 2I +1 eigenvectors extracted in step 304Form a matrix and
step 404, feature decomposition: performing characteristic decomposition on the matrix W, and taking out the characteristic vector G which is corresponding to the maximum characteristic value as [1, G%2,…,gM]T。
Step 405, gain error estimation: according to the formulaDeriving a gain error vector for the parallel alternate sampling systemWherein1,g1,…,gM-1The gain errors of the M sampling channels, respectively.
In this embodiment, after the time base error estimation in step 305 is completed, a delay error vector of the parallel alternate sampling system is obtained, and then step 306 is further performed;
step 306, returning to step 301, and repeating from [ -fs/2,fs/2]Two values are randomly selected as a pair of frequency points for error estimation, and a delay error vector of the parallel alternate sampling system is obtained according to the method from step 302 to step 305.
Step 307, repeating step 306 one or more times, and obtaining one or more delay error vectors of the parallel alternate sampling system.
308, averaging a plurality of delay error vectors obtained under the current condition to obtain a delay error vector of the parallel alternate sampling system
Thus, after the steps 306 to 308, the estimation accuracy of the delay error can be further improved, and the time base error is respectively estimated and averaged by repeating the step 306 to select a plurality of frequency points to obtain the delay error vectorAnd estimating the gain error based on the averaged delay error vectorAnd (6) estimating.
In this embodiment, the number of times of repeating step 306 in step 307 is 2 to 10 times.
In step 401, when time base error compensation is performed, the delay error vector of the parallel alternate sampling system obtained in step 308 is usedTime base error compensation is performed.
Step five, gain error compensation: using a data processor 6 and using the gain error vector of the parallel alternate sampling system derived in step 405The frequency domain steering vector p after the time base error compensation in step 402i(f) Compensating to obtain a frequency domain steering vector p after gain error compensationi"(f), wherein I is a positive integer and I is 1, …,2I + 1.
Step six, weight vector reconstruction: using a data processor 6 and in accordance withCalculating to obtain a weight vector wi(f) (ii) a Wherein, r (f) is a covariance matrix of a training sample composed of all sample data with frequency value f in the training sample set, where f [ -f [ ]s/2,fs/2]。
In this embodiment, when estimating the covariance matrix R (f), the method and the covariance matrix RaAnd RbThe method of making the estimation is the same.
Step seven, signal reconstruction in the frequency domain: using a data processor 6 and according to a formulaThe signals to be reconstructed are sampled by the parallel alternate sampling systemReconstructing to obtain a reconstructed signal S in the frequency domaini(f)。
The signal to be reconstructed comprises sampling sequences of M A/D conversion chips 1 in the same time period TAnd it is recorded asWhereinWherein M is the number of M a/D conversion chips 1 and M is 0,1, …, M-1; in the formula,to reconstruct the signalA signal obtained by performing a fast Fourier transform to a frequency domain, and
step eight, fast Fourier inverse transformation: performing inverse fast fourier transform on the reconstructed signal in the frequency domain obtained in the step seven by using a data processor 6 to obtain a reconstructed signal s (n); wherein S (n) ═ S0(n),S1(n),…,SM-1(n)]TAnd the reconstructed signal S (n) comprises the reconstructed sampling sequence S of M A/D conversion chips 1m(n)。
In this embodiment, as shown in fig. 1, in the first step, the parallel alternate sampling system includes a plurality of a/D conversion chips 1, a plurality of delay control modules 2 for respectively controlling sampling times of the a/D conversion chips 1, a plurality of data processing units 3 for respectively performing fourier transform processing on signals sampled by the a/D conversion chips 1, a multiplexer 4 connected to the plurality of data processing units 3 and outputting signals processed by the plurality of data processing units 3 in a data array form, and a data processor 6 connected to the multiplexer 4, the plurality of delay control modules 2 are respectively connected to the plurality of a/D conversion chips 1, the plurality of a/D conversion chips 1 are respectively connected to the plurality of data processing units 3, the plurality of delay control modules 2 are controlled by the data processor 6, and the plurality of delay control modules 2 are each controlled by a number of the plurality of delay control modules 2 Connected according to a processor 6. The sampling frequencies of the a/D conversion chips 1 are all the same.
In this embodiment, to improve the sampling precision of the parallel and alternate sampling system, the delay error vector of the parallel and alternate sampling system is estimated in step threeThe data processor 6 then derives a delay error vector from the estimateAnd respectively controlling the plurality of delay control modules 2.
Meanwhile, the parallel alternate sampling system further comprises a plurality of gain control modules 7 respectively connected with the plurality of a/D conversion chips 1, and the plurality of gain control modules 7 are respectively connected between the plurality of a/D conversion chips 1 and the plurality of data processing units 3. The gain control module 7 is an amplifier or an attenuator.
In this embodiment, the gain error vector of the parallel alternate sampling system is estimated in step fourThe data processor 6 then derives a gain error vector from the estimateThe gain control modules 7 are controlled individually.
In conclusion, when the error estimation is carried out by adopting the method, the time base error and the gain error can be directly estimated with high precision without iteration. In addition, the time base error and the gain error are separated and are respectively estimated, so that iteration is not needed, the calculated amount is reduced, the estimation precision can be improved, and the local minimum point is avoided. And because the time base error is estimated independently of the gain error, the influence of the uncertain quantity of the gain error on the estimation precision of the time base error is avoided.
When the weight vector is reconstructed in the sixth step, the [ -f ] needs to be estimated one by ones/2,fs/2]The covariance matrix r (f) of each frequency point is inverted, and thus the calculation amount is very large.
In this embodiment, when the weight vector is reconstructed in step six, the process is as follows:
step 601, wi(0) And (3) calculating: according to the formulaCalculate to obtain wi(0) (ii) a Wherein wi(0) Weight vector when f is 0, pi"(0) is the frequency domain steering vector p after the gain error compensation in the fifth stepiA frequency domain steering vector when f obtained in ═ 0; and R (0) is a covariance matrix of a training sample formed by all sample data with the frequency value of 0 in the training sample set.
Step 602, weight vector wi(f) And (3) calculating: according to the formula wi(f)＝B(f)·wi(0) Calculating to obtain wi(f) (ii) a In the formula,
since the high-precision time delay error vector of the parallel alternate sampling system is estimated in the third stepThus can directly obtainThen, only the weight vector w when f is 0 needs to be estimatedi(0) I.e. directly obtaining [ -f [)s/2,fs/2]The weight vectors of other frequency points in the vector. That is, only one covariance moment will need to be calculatedThe whole spectrum reconstruction of the parallel alternate sampling system can be completed by arraying and solving the inverse of the matrix, so that the calculation amount is greatly reduced, and the inherent relation of the amplitude and the phase of the extracted spectrum is kept.
For comparing the estimation accuracy of the error estimation method adopted by the invention, the estimation accuracy of the gain ARMSE (namely, the gain error) and the time base ARMSE (namely, the time base error) obtained after 100 times of experiments are averaged under the conditions of different signal-to-noise ratios (SNR) shown in FIG. 3 and FIG. 4 is detailed, and it can be seen from FIG. 3 and FIG. 4 that the estimation accuracy of the error estimation method adopted by the invention is almost the same as that of the adaptive control method under the condition that the signal-to-noise ratio is greater than 20 dB; but when the signal-to-noise ratio is less than 15dB, the error estimation method adopted by the invention shows better robustness.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (9)
1. A method for reconstructing a signal of an alternate sampling system based on rotation matrix error estimation is characterized by comprising the following steps:
step one, initial parameter input and setting: inputting the sampling frequency f of M, M A/D conversion chips (1) adopted in a parallel alternative sampling system needing error estimation through a parameter input unit (5)sAnd the bandwidth bps of the sampled wideband signal s (t); the parameter input unit (5) is connected with the data processor (6);
step two, training sample construction:firstly, sampling sequences of M A/D conversion chips (1) in the same time period t are obtained, wherein the sampling sequence of each A/D conversion chip (1) comprises n sampling signals, and n is t × fs(ii) a Performing fast Fourier transform on the sampling sequences of the M A/D conversion chips (1) to a frequency domain, and correspondingly obtaining M training samples;
the M training samples are respectively training samples of M sampling channels of the parallel alternate sampling system, and the M training samples form a training sample set;
step three, time base error estimation: estimating the time base error of the parallel alternate sampling system by adopting a data processor (6) and utilizing the training sample set constructed in the second step, wherein the process is as follows:
step 301, selecting a double frequency point for error estimation: from [ -fs/2,fs/2]In the method, two values f are randomly selected1And f2As a pair of frequency points for error estimation, where f1＞f2And Δ f ═ f1-f2；
Step 302, covariance matrix estimation: finding a frequency value f from the set of training samples1Forming a training sample A by the sample data, and finding out a frequency value f from the training sample set2Forming a training sample B by the sample data; then, covariance matrixes R of the training samples A and B are respectively calculatedaAnd Rb；
Step 303, feature decomposition: for covariance matrix RaAnd RbRespectively performing characteristic decomposition to obtain Ra＝Ua∑a(Ua)HAnd Rb＝Ub∑b(Ub)H(ii) a Wherein,and it is composed of M eigenvectorsA matrix of formations;and which is represented by M eigenvaluesIs a diagonal matrix of diagonal elements, and M eigenvaluesArranging from big to small;and it is composed of M eigenvectorsA matrix of formations;and which is represented by M eigenvaluesIs a diagonal matrix of diagonal elements, and M eigenvaluesArranging from big to small; h represents matrix conjugate transpose operation;
step 304, extracting the large characteristic value and the corresponding characteristic vector: from step 303, M eigenvaluesIn the method, the first 2I +1 large eigenvalues are extractedAnd its corresponding 2I +1 eigenvectorsReuse formulaFor 2I +1 eigenvectorsRespectively deforming to obtain 2I +1 vectorsWherein j is a positive integer and j is 1, …,2I + 1; at the same time, from step 303, M eigenvaluesIn the method, the first 2I +1 large eigenvalues are extractedAnd its corresponding 2I +1 eigenvectorsWherein,
step 305, time base error estimation: according to the formulaObtaining the time delay error vector of the parallel alternative sampling systemWherein ∠ represents a phase angle, τ ═ 0,1/Mfs,…(M-1)/Mfs]T；WhereinFor the 2I extracted in step 304+1 feature vectorsThe sum of (1);for 2I +1 vectors in step 304The sum of (1); time base errors for the M sampling channels; i is a positive integer and I ═ 1, …,2I + 1;
step four, gain error estimation: using a data processor (6) and based on the delay error vector obtained in step threeEstimating the gain error of the parallel alternate sampling system by the following process:
step 401, time base error compensation: using the delay error vector of the parallel alternative sampling system obtained in step threeTo ideal frequency domain steering vector p'i(f) Compensating to obtain a time base error compensated frequency domain steering vector pi(f) Wherein I is a positive integer and I ═ 1, …,2I + 1;
step 402, utilizing formula Di＝diag{pi(f) F, the frequency domain steering vector p after the time base error compensation in the step 401 is correctedi(f) Deforming to obtain vector Di；
Step 403, according to the formulaSolving a matrix W;
in the formula,orWhereinFor the 2I +1 eigenvectors extracted in step 304Form a matrix and for the 2I +1 eigenvectors extracted in step 304Form a matrix and
step 404, feature decomposition: performing characteristic decomposition on the matrix W, and taking out the characteristic vector G which is corresponding to the maximum characteristic value as [1, G%2,…,gM]T；
Step 405, gain error estimation: according to the formulaDeriving a gain error vector for the parallel alternate sampling systemWherein1,g1,…,gM-1Gain errors of the M sampling channels respectively;
step five, gain error compensation: using a data processor (6) and using the gain error vector of the parallel alternate sampling system derived in step 405The frequency domain steering vector p after the time base error compensation in step 402i(f) Compensating to obtain a frequency domain steering vector p after gain error compensationi"(f), wherein I is a positive integer and I ═ 1, …,2I + 1;
step six, weight vector reconstruction: using a data processor (6) and based onCalculating to obtain a weight vector wi(f) (ii) a Wherein, r (f) is a covariance matrix of a training sample composed of all sample data with frequency value f in the training sample set, where f [ -f [ ]s/2,fs/2]；
Step seven, signal reconstruction in the frequency domain: using a data processor (6) and according to a formulaThe signals to be reconstructed are sampled by the parallel alternate sampling systemReconstructing to obtain a reconstructed signal S in the frequency domaini(f)；
The signal to be reconstructed comprises sampling sequences of M A/D conversion chips (1) in the same time period TAnd it is recorded asWhereinWherein M is the number of M A/D conversion chips (1) and M is 0,1, …, M-1; in the formula,to reconstruct the signalA signal obtained by performing a fast Fourier transform to a frequency domain, and
step eight, fast Fourier inverse transformation: performing inverse fast Fourier transform on the reconstructed signal in the frequency domain obtained in the step seven by adopting a data processor (6) to obtain a reconstructed signal S (n); wherein S (n) ═ S0(n),S1(n),…,SM-1(n)]TAnd the reconstructed signal S (n) comprises a reconstructed sampling sequence S of M A/D conversion chips (1)m(n)。
2. The method of rotation matrix error estimation based signal reconstruction for an interleaved sampling system according to claim 1, wherein: when the weight vector is reconstructed in the sixth step, the process is as follows:
step 601, wi(0) And (3) calculating: according to the formulaCalculate to obtain wi(0) (ii) a Wherein wi(0) Weight vector when f is 0, pi"(0) is the frequency domain steering vector p after the gain error compensation in the fifth stepiA frequency domain steering vector when f obtained in ═ 0; r (0) is a covariance matrix of a training sample formed by all sample data with the frequency value of 0 in the training sample set;
step 602, weight vector wi(f) And (3) calculating: according to the formula wi(f)＝B(f)·wi(0) Calculating to obtain wi(f) (ii) a In the formula,
3. method for signal reconstruction of an alternatively sampled system based on a rotation matrix error estimation according to claim 1 or 2, characterized in that: after the time base error estimation is completed in step 305, obtaining a delay error vector of the parallel alternate sampling system, and then entering step 306;
step 306, returning to step 301, and repeating from [ -fs/2,fs/2]Randomly selecting two numerical values as a pair of frequency points for error estimation, and obtaining a time delay error vector of the parallel alternate sampling system according to the method from step 302 to step 305;
307, repeating the step 306 one or more times to obtain one or more time delay error vectors of the parallel alternate sampling system;
308, averaging a plurality of delay error vectors obtained under the current condition to obtain a delay error vector of the parallel alternate sampling system
4. Method for signal reconstruction of an alternatively sampled system based on a rotation matrix error estimation according to claim 1 or 2, characterized in that: in the second step, n is 100-1000.
5. Method for signal reconstruction of an alternatively sampled system based on a rotation matrix error estimation according to claim 1 or 2, characterized in that: and in the second step, when sampling sequences of M A/D conversion chips (1) in a time period t are taken, selecting by adopting a sliding window method.
6. Method for signal reconstruction of an alternatively sampled system based on a rotation matrix error estimation according to claim 1 or 2, characterized in that: in the first step, the parallel alternate sampling system comprises a plurality of A/D conversion chips (1), a plurality of delay control modules (2) for respectively controlling the sampling time of the A/D conversion chips (1), a plurality of data processing units (3) for respectively carrying out Fourier transform processing on the signals sampled by the A/D conversion chips (1), a multiplexer (4) which is respectively connected with the data processing units (3) and outputs the signals processed by the data processing units (3) in a data array form, and a data processor (6) connected with the multiplexer (4), wherein the delay control modules (2) are respectively connected with the A/D conversion chips (1), the A/D conversion chips (1) are respectively connected with the data processing units (3), the delay control modules (2) are controlled by a data processor (6) and are connected with the data processor (6).
7. The method of rotation matrix error estimation based signal reconstruction for an interleaved sampling system according to claim 6, wherein: the parallel alternate sampling system also comprises a plurality of gain control modules (7) which are respectively connected with the A/D conversion chips (1), and the gain control modules (7) are respectively connected between the A/D conversion chips (1) and the data processing units (3); the gain control module (7) is an amplifier or an attenuator; the gain control modules (7) are controlled by a data processor (6) and are connected with the data processor (6).
8. The method of rotation matrix error estimation based signal reconstruction for an interleaved sampling system according to claim 6, wherein: estimating the time delay error vector of the parallel alternate sampling system in the third stepThe data processor (6) then derives a delay error vector from the estimateAnd respectively controlling the plurality of delay control modules (2).
9. The method of rotation matrix error estimation based signal reconstruction for an interleaved sampling system according to claim 7, wherein: estimating the gain error vector of the parallel alternative sampling system in the fourth stepThe data processor (6) then derives a gain error vector from the estimateAnd controlling the gain control modules (7) respectively.
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