CN111355493A - Support set screening and reconstructing method for modulation broadband converter - Google Patents

Support set screening and reconstructing method for modulation broadband converter Download PDF

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CN111355493A
CN111355493A CN202010259795.3A CN202010259795A CN111355493A CN 111355493 A CN111355493 A CN 111355493A CN 202010259795 A CN202010259795 A CN 202010259795A CN 111355493 A CN111355493 A CN 111355493A
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张京超
乔立岩
张向鑫
彭喜元
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Harbin Institute of Technology
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Abstract

The invention discloses a support set screening and reconstructing method for a modulation broadband converter. Step 1: obtaining a signal matrix Z (f) to be shifted for modulating the broadband converter; step 2: calculating the inverse DTFT transformation Z [ n ] of the signal matrix Z (f) to be shifted]To obtain a new vector Z, of 2 norms of each row vectorL(ii) a And step 3: take out a new vector ZLFront L0Value L2L0+1, ordering from large to small to get vector Zz(ii) a Step 4; calculating a differential matrix Zz'; and 5: in the MATLAB picture scale, a differential matrix Z is drawnz' and finding a first slope line with a rising slope greater than the steep rise; step 6: the corresponding valid signal band is found. The invention aims to solve the problem that in practical application, even if a signal after the original signal spectrum is moved is reconstructed, the reconstructed signal-to-noise ratio is low because the current effective frequency band number cannot be obtained by the existing method.

Description

Support set screening and reconstructing method for modulation broadband converter
Technical Field
The invention relates to the technical field of signal sampling, in particular to a support set screening and reconstructing method for a modulation broadband converter.
Background
Compressed Sensing (CS) is a new signal sampling theory proposed in recent years, which indicates that for a sparse signal or a signal sparse in a certain transform domain, a measurement matrix unrelated to a transform basis can be used to project a source signal from a high-dimensional space to a low-dimensional space, and then the source signal can be reconstructed with high probability from a number of projections far smaller than the length of the signal by solving an optimization problem.
For a K sparse signal of length N:
Figure BDA0002438853810000011
where | supp (·) | represents the 0-norm of the signal, i.e., the number of signal values other than 0. Its m linear measurements can be found:
y＝Φx (2)
wherein:
Figure BDA0002438853810000012
is a measurement matrix, and m<<And N is added. With observation vector y and measurement matrix Φ, the source signal x can be reconstructed or approximated with an optimization problem in the 0-norm sense. This type of problem is also known as the Single Measurement Vector (SMV) problem.
Consider another type of Sparse Signal-a Multiband Sparse Signal (Sparse Multiband Signal), which is defined as follows:
1. the original signal x (t) is band limited;
2. the support of the fourier transform x (f) of the signal comprises N non-cross-connected frequency bands;
3. the width of each band is not greater than.
In the form shown in figure 1.
For multi-band sparse signal observation, the observation model can be described by using a Multiple Measurement Vectors (MMV) problem, which is defined as follows:
Y＝ΦX (3)
wherein
Figure BDA0002438853810000013
Is a measurement matrix, and m<<N。X∈RN×LIs a primary signalMatrix, each column vector representing one original signal Y ∈ Rm×LFor the observation matrix, each column is an observation vector. The purpose of the multiple observation vector problem is to achieve simultaneous recovery of the original signals by defining a suitable structure between the original signals.
At present, signal reconstruction methods for multi-observation vector problems are mainly extension methods of single-observation vector methods, such as a Simultaneous Orthogonal Matching Pursuit (SOMP) method, a synchronous Subspace approach (SSP), and the like, and still another method is to convert a multi-observation vector problem into a single-observation vector problem for solving, such as a rembo (reduction of MMV and boosting) method. However, these methods all require a known number of frequency bands for signal reconstruction, and in some practical applications, the number of currently active frequency bands generally changes over time, that is, the number of currently active frequency bands cannot be obtained when signal reconstruction is performed, and the above-mentioned methods cannot be applied in such cases.
Meanwhile, there are some reconstruction methods based on BPDN (base burst de-noise), which can directly reconstruct the original signal facing the signal itself, but for the modulation broadband converter, its schematic diagram is shown in fig. 2, the multiband signal enters the modulation broadband converter system and is received by m channels in parallel, m is a positive integer; each channel is modulated by a periodic sequence with the same period but different values, the purpose of the modulation is to shift the frequency spectrum, and the modulated signal is low-pass filtered to filter out the high-frequency part and leave the low-frequency part. Due to the low cut-off frequency of the low-pass filter, the bandwidth of the filtered signal is narrowed, so that the signal can be sampled at a low rate to obtain a series of global observation data of the signal. Then, low-speed sampling is carried out, and the sampling rate only needs to be larger than the width of the maximum low-pass filter frequency band, so that the sampling rate can be lower than the Nyquist frequency of the signal. And finally, recovering the original signal and the frequency spectrum thereof from the acquired data by utilizing the system sensing matrix obtained by calculation and a related signal reconstruction algorithm and through the mathematical relationship between the sensing matrix and the sampling information. Its model belongs to one of MMV models, after recovering sparse solution Z n by MMV
Figure BDA0002438853810000021
The applicant has proposed a blind reconstruction algorithm without knowing the number of carrier frequencies for SOMP in a greedy algorithm, which is object-oriented in an algorithm iteration process. However, in the conventional algorithm, when the sparse solution of the MMV is estimated by the BPDN algorithm, there is no suitable method for estimating the effective frequency band position in the sparse solution, which results in poor reconstruction performance of the signal. We propose a support set screening reconstruction method facing modulation broadband converter, which can solve the reconstruction problem of BPDN method when the carrier frequency number is unknown after algorithm iteration and before signal reconstruction.
Disclosure of Invention
The invention aims to solve the problem that in practical application of the existing method, even if a signal after original signal spectrum shifting is reconstructed, the reconstruction signal-to-noise ratio is low because the current effective frequency band number cannot be obtained, and thus a support set screening reconstruction method facing a modulation broadband converter is provided.
The invention is realized by the following technical scheme:
a support set screening reconstruction method for a modulation broadband converter comprises the following steps:
step 1: obtaining a signal matrix Z (f) to be shifted of the modulation broadband converter by using a classical algorithm;
step 2: calculating the inverse DTFT transformation Z [ n ] of the signal matrix Z (f) to be shifted obtained in the step 1]To obtain a new vector ZL；
And step 3: take out a new vector ZLFront L0Value L2L0+1, ordering from large to small to get vector Zz；
Step 4; calculate ZzOf the differential matrix Zz’；
And 5: in the normal MATLAB picture scale, Z is plottedzOf the differential matrix Zz' and finding a first inclined straight line with a rising slope larger than the steep rise, wherein the value in front of the inclined straight line is a noise frequency band which can be removed;
step 6: the corresponding valid signal band is found.
Further, in step 1, the relationship between the signal matrix z (f) to be moved and the original signal x (t) is
zi(f)＝X(f+(i-L0-1)fp),1≤i≤L
z(f)＝[z1(f)，...，zL(f)]T
Z[n]Is an inverse DTFT transformation of Z (f), Z [ n ]]Is a matrix of m x L, zi(f) There are a total of L cases, each being 1. ltoreq. i.ltoreq.L, all values, zL(f) Is that it represents the length of the vector L, fpIs the magnitude of each spectral shift.
Further, the new vector Z of step 2LIn order to realize the purpose,
ZL＝[||z1||2，...，||zi||2，…||zL||2]T
wherein, | | z1||2Is the 2 norm, | z, of the first column vector of the matrixi||2Is the 2 norm, | z, of the ith column vector of the matrixL||2Is the 2-norm of the lth column vector of the matrix.
Further, step 3 obtains Z by sequencing from large to smallz，
Figure BDA0002438853810000031
In the formula (I), the compound is shown in the specification,
Figure BDA0002438853810000032
is 2L0+1 means that the original vector of length L is split from the middle, left-right symmetric, and now only half of the symmetry.
Further, the differential matrix Z of step 4z' to (a) is,
Figure BDA0002438853810000044
in the formula, ZziIs ZzThe ith element of (1), Zzi+1Is ZzThe (i + 1) th element of (1).
Further, said step 6 finds the corresponding valid signal frequency band, assuming that the number is 2N, then
Figure BDA0002438853810000041
In the formula, λkFor the number of the found effective bands, the positions of the 2N effective bands are [ lambda ] respectively1,λk,…,λ2N]，
Figure BDA0002438853810000042
Is the location of the limited frequency band of the matrix,
Figure BDA0002438853810000043
is the process of the inverse shift of the spectrum.
The invention has the beneficial effects that:
compared with the traditional method for setting the threshold, the method has better effect on the noise with stable frequency domain, such as white Gaussian noise, because the energy of the noise can be very high, but if the frequency domain is stable, the difference value of the energy of the noise between different frequency bands is very small, and the method can be used for filtering out a pure noise frequency band. Secondly, threshold screening is set, and setting of the threshold is very difficult for blind reconstruction of the multi-band signal.
Drawings
FIG. 1 is a diagram of a prior art multi-band signal with 2 non-cross-linked frequency bands;
FIG. 2 is a schematic diagram of a modulated wideband converter;
FIG. 3 is Z for MATLAB generation at a signal-to-noise ratio of 10dBLThe length of the line graph is 195, and the number of effective frequency bands is 6;
FIG. 4 is Z for MATLAB generation at a signal-to-noise ratio of 10dBz' line drawings;
fig. 5 is a comparison graph of the reconstructed snr of the algorithm in combination with the SPGL1 algorithm and the SOMP algorithm, with the snr of the analog signal set to 10dB, and the number of channels set to m-20 to m-100, with 10 channels added each time.
FIG. 6 is a comparison graph of the signal-to-noise ratio of the original signal decreased from 25dB to-5 dB each time by 5dB when the number m of channels is 50, and the reconstructed signal-to-noise ratio of the algorithm combined with the SPGL1 algorithm and the SOMP algorithm is increased from the original signal-to-noise ratio.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
A support set screening reconstruction method for a modulation broadband converter comprises the following steps:
step 1: obtaining a signal matrix Z (f) to be shifted of the modulation broadband converter by using a classical algorithm, such as a signal reconstruction algorithm (SPG) and the like;
step 2: calculating the inverse DTFT transformation Z [ n ] of the signal matrix Z (f) to be shifted obtained in the step 1]To obtain a new vector Z, of 2 norms of each row vectorL；
And step 3: take out a new vector ZLFront L0Value L2L0+1, sequencing from large to small to give Zz；
Step 4; calculate ZzOf the differential matrix Zz’；
And 5: in the normal MATLAB picture scale, Z is plottedzOf the differential matrix Zz' and finding a first inclined straight line with a rising slope larger than the steep rise, wherein the value in front of the inclined straight line is a noise frequency band which can be removed;
step 6: the corresponding valid signal band is found.
Further, in step 1, the relationship between the signal matrix z (f) to be moved and the original signal x (t) is
zi(f)＝X(f+(i-L0-1)fp),1≤i≤L
z(f)＝[z1(f)，...，zL(f)]T
Z[n]Is an inverse DTFT transformation of Z (f), Z [ n ]]Is a matrix of m x L, zi(f) There are a total of L cases, each being 1. ltoreq. i.ltoreq.L, all values, zL(f) Is that it represents the length of the vector L, fpIs the magnitude of each spectral shift.
Further, the new vector Z of step 2LIn order to realize the purpose,
ZL＝[||z1||2，...，||zi||2，...||zL||2]T
wherein, | | z1||2Is the 2 norm, | z, of the first column vector of the matrixi||2Is the 2 norm, | z, of the ith column vector of the matrixL||2Is the 2-norm of the lth column vector of the matrix.
Further, the vectors Z are obtained by sequencing the step 3 from large to smallz，
Figure BDA0002438853810000051
Figure BDA0002438853810000061
In the formula (I), the compound is shown in the specification,
Figure BDA0002438853810000067
is 2L0+1 means that the original vector of length L is split from the middle, left-right symmetric, and now only half of the symmetry.
Further, the differential matrix Z of step 4z' to (a) is,
Figure BDA0002438853810000068
in the formula, ZziIs ZzThe ith element of (1), Zzi+1Is ZzThe (i + 1) th element of (1).
Further, said step 6 finds the corresponding valid signal frequency band, assuming that the number is 2N, then
Figure BDA0002438853810000062
In the formula, λkFor the number of the found effective bands, the positions of the 2N effective bands are [ lambda ] respectively1,λk,…,λ2N]，
Figure BDA0002438853810000063
Is the location of the limited frequency band of the matrix,
Figure BDA0002438853810000064
is the process of the inverse shift of the spectrum.
Example 2
The method of the present invention is compared with a conventional Simultaneous Orthogonal Matching Pursuit (SOMP) method by a specific simulation experiment, and the reconstruction probability of each method is calculated and compared.
The simulation experiment is carried out according to the following steps:
randomly generating a Gaussian distribution measurement matrix
Figure BDA0002438853810000065
Assuming the original signal satisfies
Figure BDA0002438853810000066
And suppose B is 50MHz, m is 40, e is 0.05, fNYQ＝10GHz，Ei、τi、fiRespectively representing the amplitude, delay and bandwidth of the signal d, Ei、τi、fiRandomly selecting, and assuming asThe number of previously active carrier frequencies is 3.
Secondly, obtaining an observation signal Y phi X through a formula II, reconstructing a support set of the signal by utilizing each reconstruction algorithm, and calculating the signal-to-noise ratio of the reconstructed signal;
and thirdly, running each reconstruction algorithm 1000 times, and calculating the reconstruction probability.
Drawing a variation curve of the signal-to-noise ratio along with the number of channels; the results of the experiments are shown in FIGS. 3-6, where FIG. 3 is the Z generated by MATLAB at a signal-to-noise ratio of 10dBLA line graph; FIG. 4 is Z for MATLAB generation at a signal-to-noise ratio of 10dBz' line drawings; fig. 5 and 6 are graphs comparing the signal-to-noise ratio curves of the present invention with those of the conventional synchronous orthogonal matching pursuit method.
As can be seen from fig. 3 to 6, the reconstruction performance of the method of the present invention is greatly improved compared to the SOMP method; and the method of the invention does not rely on the prior knowledge of the number of currently active frequency bands. The method is particularly suitable for occasions without knowing the number of carrier frequencies, such as the fields of radio communication, cognitive radio frequency spectrum sensing and the like.

Claims (6)

1. A support set screening reconstruction method for a modulation broadband converter is characterized by comprising the following steps:
step 1: obtaining a signal matrix Z (f) to be shifted of the modulation broadband converter by using a classical algorithm;
step 2: calculating the inverse DTFT transformation Z [ n ] of the signal matrix Z (f) to be shifted obtained in the step 1]To obtain a new vector Z, of 2 norms of each row vectorL；
And step 3: take out a new vector ZLFront L0Value L2L0+1, ordering from large to small to get vector Zz；
And 4, step 4: calculate ZzOf the differential matrix Zz’；
And 5: in the normal MATLAB picture scale, Z is plottedzOf the differential matrix Zz' and finding a first inclined straight line with a rising slope larger than the steep rise, wherein the value in front of the inclined straight line is a noise frequency band which can be removed;
step 6: the corresponding valid signal band is found.
2. The method as claimed in claim 1, wherein the step 1 is that the relationship between the signal matrix z (f) to be shifted and the original signal x (t) is
zi(f)＝X(f+(i-L0-1)fp),1≤i≤L
z(f)＝[z1(f)，...，zl(f)]T
Z[n]Is an inverse DTFT transformation of Z (f), Z [ n ]]Is a matrix of m x L, zi(f) There are a total of L cases, each being 1. ltoreq. i.ltoreq.L, all values, zL(f) Is that it represents the length of the vector L, fpIs the magnitude of each spectral shift.
3. The method for filtering and reconstructing support set of modulation-oriented wideband converter according to claim 1, wherein the new vector Z in step 2LIn order to realize the purpose,
ZL＝[||z1||2，...，||zi||2，…||zL||2]T
wherein, | | z1||2Is the 2 norm, | z, of the first column vector of the matrixi||2Is the 2 norm, | z, of the ith column vector of the matrixL||2Is the 2-norm of the lth column vector of the matrix.
4. The method for screening and reconstructing the support set of the modulation-oriented wideband converter according to claim 1, wherein the vector Z is obtained by sorting the step 3 from large to smallz，
Figure FDA0002438853800000011
Figure FDA0002438853800000012
In the formula (I), the compound is shown in the specification,
Figure FDA0002438853800000013
is 2L0+1 means that the original vector of length L is split from the middle, left-right symmetric, and now only half of the symmetry.
5. The support set screening reconstruction method for the modulation-oriented wideband converter as claimed in claim 1, wherein the differential matrix Z of step 4z' to (a) is,
Figure FDA0002438853800000021
in the formula, ZziIs ZzThe ith element of (1), Zzi+1Is ZzThe (i + 1) th element of (1).
6. The method as claimed in claim 1, wherein the step 6 finds the corresponding effective signal frequency bands, and assuming that the number of the effective signal frequency bands is 2N, the method further comprises the step of finding the corresponding effective signal frequency bands
Figure FDA0002438853800000022
In the formula, λkFor the number of the found effective bands, the positions of the 2N effective bands are [ lambda ] respectively1,λk,…,λ2N]，
Figure FDA0002438853800000023
Is the location of the limited frequency band of the matrix,
Figure FDA0002438853800000024
is the process of the inverse shift of the spectrum.
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