CN111355493B - Support set screening and reconstructing method for modulation broadband converter - Google Patents
Support set screening and reconstructing method for modulation broadband converter Download PDFInfo
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- H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
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Abstract
The invention discloses a support set screening reconstruction method for a modulation broadband converter. Step 1: obtaining a signal matrix Z (f) to be shifted of the modulation broadband converter; step 2: calculating inverse DTFT transform Z [ n ] of signal matrix Z (f) to be shifted]2 norms of the respective row vectors of (2) to obtain a new vector Z L The method comprises the steps of carrying out a first treatment on the surface of the Step 3: extracting new vector Z L Front L 0 Values, l=2l 0 +1, sorting from big to small to obtain vector Z z The method comprises the steps of carrying out a first treatment on the surface of the Step 4; calculating differential matrix Z z 'A'; step 5: in MATLAB picture scale, a differential matrix Z is drawn z ' and find a first rising slope greater than the steeply increasing slope; step 6: a corresponding effective signal band is found. The invention aims to solve the problem that in the practical application of the existing method, even if the signal with the original signal spectrum shifted is reconstructed, the reconstructed signal-to-noise ratio is low because the current effective frequency band number cannot be obtained.
Description
Technical Field
The invention relates to the technical field of signal sampling, in particular to a support set screening reconstruction method for a modulation broadband converter.
Background
Compressed sensing (Compressed Sensing, CS) is a completely new theory of signal sampling proposed in recent years, which indicates that for a sparse or sparse signal over a certain transform domain, a measurement matrix that is not related to the transform basis can be used to project the source signal from a high-dimensional space to a low-dimensional space, and then by solving an optimization problem, the source signal can be reconstructed with high probability from the number of projections that are much smaller than the signal length.
For a K sparse signal of length N:
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:
for measuring matrix, and m<<N. With the observation vector y and the measurement matrix Φ, the source signal x can be reconstructed or approximated with an optimization problem in the sense of a 0-norm. This type of problem is also known as a single observation vector (Single Measurement Vector, SMV) problem.
Consider another type of sparse signal, a multi-band sparse signal (Sparse Multiband Signal), defined as follows:
1. the original signal x (t) is band limited;
2. the support for the fourier transform X (f) of the signal contains N non-cross-linked frequency bands;
3. the width of each frequency band is not greater than.
In the form shown in figure 1.
For multi-band sparse signal observations, the observation model can be described by the multi-observation vector (Multiple Measurement Vectors, MMV) problem, defined as follows:
Y＝ΦX (3)
wherein the method comprises the steps of
For measuring matrix, and m<<N。X∈R N×L For the matrix of raw signals, each column vector represents one raw signal. Y εR m×L For an observation matrix, each column is an observation vector. The objective of the multi-observation vector problem is to achieve simultaneous restoration of original signals by defining the appropriate structure between the original signals.
The signal reconstruction method aiming at the multi-observation vector problem is mainly an expansion type method of a single-observation vector method, such as a synchronous orthogonal matching pursuit (Simultaneous Orthogonal Matching Pursuit, SOMP) method, a synchronous subspace method (Simultaneous Subspace Pursuit, SSP) method and the like, and the signal reconstruction method aiming at the multi-observation vector problem is also a method for solving the multi-observation vector problem by converting the multi-observation vector problem into the single-observation vector problem, 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 frequency bands currently active is generally time-varying, i.e. the number of currently active frequency bands cannot be obtained when signal reconstruction is performed, and the existing methods cannot be applied in such cases.
Meanwhile, some reconstruction methods based on BPDN (basic burst de-noise) exist, and the original signal can be directly reconstructed by facing the signal itself, but for a modulation broadband converter, the schematic diagram of the modulation broadband converter is shown in figure 2, a multiband signal enters the modulation broadband converter system and is received by m channels in parallel, and m is a positive integer; each channel is modulated by a periodic sequence with the same period but different values, the purpose of modulation is frequency spectrum shifting, and the modulated signals are subjected to low-pass filtering to filter out high-frequency parts and leave low-frequency parts. Because the cut-off frequency of the low-pass filter is low, the bandwidth of the filtered signal is narrowed, so that the signal can be sampled at a low rate to obtain global observation data of a series of signals. Then, the low-speed sampling is carried out, and the sampling rate is only required to be larger than the width of the frequency band of the maximum low-pass filter, so that the sampling rate can be lower than the Nyquist frequency of the signal. And finally, the original signals and the frequency spectrums thereof can be recovered from the acquired data by using a 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 the MMV is used for recovering thin fluffy Z [ n ]
The applicant has proposed a blind reconstruction algorithm without knowing the carrier frequency number for SOMP in a greedy algorithm, and its object-oriented algorithm iterative process. However, when the existing classical algorithm estimates the sparse solution of the MMV through the BPDN algorithm, no suitable method is available for estimating the effective frequency band position in the sparse solution, so that the reconstruction performance of the signal is poor. The support set screening and reconstructing method for the modulation broadband converter can solve the reconstruction problem of the BPDN method when the number of carrier frequencies is unknown after algorithm iteration and before signal reconstruction.
Disclosure of Invention
The invention aims to solve the problem that in the practical application of the existing method, even if the signal with the original signal spectrum shifted is reconstructed, the reconstructed signal-to-noise ratio is low because the current effective frequency band number cannot be obtained, thereby providing a support set screening reconstruction method for a modulation broadband converter.
The invention is realized by the following technical scheme:
a support set screening reconstruction method for a modulated broadband converter, the reconstruction method comprising the steps of:
step 1: obtaining a signal matrix Z (f) to be moved of the modulation broadband converter by using a classical algorithm;
step 2: calculating the inverse DTFT conversion Z [ n ] of the signal matrix Z (f) to be moved obtained in the step 1]Is used to obtain a new vector Z L ；
Step 3: extracting new vector Z L Front L 0 Values, l=2l 0 +1, sorting from big to small to obtain vector Z z ；
Step 4; calculation of Z z Is a differential matrix Z of (2) z ’；
Step 5: in the normal MATLAB picture scale, Z is plotted z Is a differential matrix Z of (2) z ' finding a first inclined straight line with the rising slope larger than the steep rise, wherein the value before the inclined straight line is a noise frequency band which can be removed;
step 6: a corresponding effective signal band is found.
Further, in the step 1, specifically, the relation between the signal matrix Z (f) to be shifted and the original signal x (t) is that
z i (f)＝X(f+(i-L 0 -1)f p ),1≤i≤L
z(f)＝[z 1 (f)，...，z L (f)] T
Z[n]Is the inverse DTFT transform of Z (f), Z [ n ]]Is a matrix of m x L, z i (f) In total L cases, all values in 1.ltoreq.i.ltoreq.L, z L (f) Is represented by a vector length L, f p Is the magnitude of each spectral shift of X (f).
Further, the new vector Z in the step 2 L In order to achieve this, the first and second,
Z L ＝[||z 1 || 2 ，...，||z i || 2 ，…||z L || 2 ] T
in the formula, ||z 1 || 2 Is the 2-norm, ||z, of the first column vector of the matrix i || 2 Is the 2-norm of the ith column vector of the matrix, ||z L || 2 Is the 2-norm of the L-th column vector of the matrix.
Further, the step 3 is to obtain Z from the order of big to small z ，
In the method, in the process of the invention,
l=2l of (2) 0 +1 means that the vector of original length L is separated from the middle and is symmetrical left and right, now taking only half of the symmetry.
Further, the differential matrix Z of the step 4 z The 'is' the number of the components,
wherein Z is zi Is Z z Is the ith element, Z zi+1 Is Z z I+1th element of (d).
Further, step 6 finds the corresponding effective signal band, assuming that the number is 2N
Wherein lambda is k The positions of the 2N effective bands are [ lambda ] for the number of the found effective band 1 ,λ k ,…,λ 2N ]，
Is the finite band position of the matrix, +.>
Is the spectrum reverse shifting process.
The beneficial effects of the invention are as follows:
compared with the traditional method for setting the threshold value, the method has better effect on noise with stable frequency domain, such as Gaussian white 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 proposed method can be used for filtering out the pure noise frequency band. Next, threshold screening is set, and setting of the threshold is very difficult for blind reconstruction of the multiband signal.
Drawings
Fig. 1 is a schematic diagram of a multi-band signal with 2 non-cross-connect bands in the background;
FIG. 2 is a schematic diagram of a modulation broadband converter;
FIG. 3 is a Z of MATLAB generation at a signal-to-noise ratio of 10dB L The length of the line diagram is 195, and the number of effective frequency bands is 6;
FIG. 4 is a Z of MATLAB generation at a signal-to-noise ratio of 10dB z ' line graph;
fig. 5 is a graph of the reconstructed snr of the SPGL1 algorithm and the SOMP algorithm combined with the fig. 5, where the snr of the analog signal is set to 10dB, the number of channels is set to m=20 to m=100, and 10 channels are added each time.
Fig. 6 is a graph showing the comparison of the reconstructed snr of the present algorithm combined with the SPGL1 algorithm and the SOMP algorithm to the increase in the original snr, when the number of channels m=50, where the snr of the original signal decreases from 25dB to-5 dB, each time by 5 dB.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
A support set screening reconstruction method for a modulated broadband converter, the reconstruction method comprising the steps of:
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 of SPG and the like;
step 2: calculating the inverse DTFT conversion Z [ n ] of the signal matrix Z (f) to be moved obtained in the step 1]2 norms of the respective row vectors of (2) to obtain a new vector Z L ；
Step 3: extracting new vector Z L Front L 0 Values, l=2l 0 +1, sorting from big to small to obtain Z z ；
Step 4; calculation of Z z Is a differential matrix Z of (2) z ’；
Step 5: in the normal MATLAB picture scale, Z is plotted z Is a differential matrix Z of (2) z ' finding a first inclined straight line with the rising slope larger than the steep rise, wherein the value before the inclined straight line is a noise frequency band which can be removed;
step 6: a corresponding effective signal band is found.
Further, in the step 1, specifically, the relation between the signal matrix Z (f) to be shifted and the original signal x (t) is that
z i (f)＝X(f+(i-L 0 -1)f p ),1≤i≤L
z(f)＝[z 1 (f)，...，z L (f)] T
Z[n]Is the inverse DTFT transform of Z (f), Z [ n ]]Is a matrix of m x L, z i (f) In total L cases, all values in 1.ltoreq.i.ltoreq.L, z L (f) Is represented by a vector length L, f p Is the magnitude of each spectral shift of X (f).
Further, the new vector Z in the step 2 L In order to achieve this, the first and second,
Z L ＝[||z 1 || 2 ，...，||z i || 2 ，...||z L || 2 ] T
in the formula, ||z 1 || 2 Is the 2-norm, ||z, of the first column vector of the matrix i || 2 Is the 2-norm of the ith column vector of the matrix, ||z L || 2 Is the 2-norm of the L-th column vector of the matrix.
Further, the step 3 is to sort from big to small to obtain a vector Z z ，
In the method, in the process of the invention,
l=2l of (2) 0 +1 means that the vector of original length L is separated from the middle and is symmetrical left and right, now taking only half of the symmetry.
Further, the differential matrix Z of the step 4 z The 'is' the number of the components,
wherein Z is zi Is Z z Is the ith element, Z zi+1 Is Z z I+1th element of (d).
Further, step 6 finds the corresponding effective signal band, assuming that the number is 2N
Wherein lambda is k The positions of the 2N effective bands are [ lambda ] for the number of the found effective band 1 ,λ k ,…,λ 2N ]，
Is the finite band position of the matrix, +.>
Is the spectrum reverse shifting process.
Example 2
The method is compared with the traditional synchronous orthogonal matching pursuit method (Simultaneous Orthogonal Matching Pursuit, SOMP) through specific simulation experiments, and the reconstruction probability of each method is calculated for comparison.
The simulation experiment is carried out according to the following steps:
1. randomly generating a Gaussian distribution measurement matrix
Assuming that the original signal satisfies
And assuming b=50 mhz, m=40, epsilon=0.05, f NYQ ＝10GHz，E i 、τ i 、f i Respectively represent the amplitude, delay and bandwidth of the signal d, E i 、τ i 、f i Randomly chosen and assuming the number of currently active carrier frequencies is 3.
2. Obtaining an observation signal Y=phi X through a formula II, reconstructing a support set of the signal by using each reconstruction algorithm, and calculating the signal-to-noise ratio of the reconstructed signal;
3. each reconstruction algorithm was run 1000 times and the reconstruction probabilities were calculated.
Drawing a change curve of signal-to-noise ratio along with the number of channels; the experimental results are shown in FIGS. 3 to 6, FIG. 3 is the Z generated by MATLAB at a signal to noise ratio of 10dB L A line graph; FIG. 4 is a Z of MATLAB generation at a signal-to-noise ratio of 10dB z ' line graph; fig. 5 and 6 are graphs comparing signal-to-noise ratio curves of the synchronous orthogonal matching pursuit method with those of the conventional synchronous orthogonal matching pursuit method after the present invention.
As can be seen from fig. 3 to 6, the reconstruction performance of the method of the present invention is greatly improved over that of the SOMP method; and the inventive method no longer relies on a priori knowledge of the number of frequency bands currently active. The method is particularly suitable for occasions without knowing the number of carrier frequencies, such as the fields of radio communication, cognitive radio spectrum sensing and the like.
Claims (4)
1. A modulation wideband converter oriented support set screening reconstruction method, characterized in that the reconstruction method comprises the following steps:
step 1: obtaining a signal matrix Z (f) to be moved of the modulation broadband converter by using a classical algorithm;
step 2: calculating the inverse DTFT conversion Z [ n ] of the signal matrix Z (f) to be moved obtained in the step 1]2 norms of the respective row vectors of (2) to obtain a new vector Z L ；
Step 3: extracting new vector Z L Front L 0 Values, l=2l 0 +1, sorting from big to small to obtain vector Z z ；
Step 4: calculation of Z z Is a differential matrix Z of (2) z ’；
Step 5: in the normal MATLAB picture scale, Z is plotted z Is a differential matrix Z of (2) z ' finding a first inclined straight line with the rising slope larger than the steep rise, wherein the value before the inclined straight line is a noise frequency band which can be removed;
step 6: finding a corresponding effective signal frequency band;
the step 1 is specifically that the relation between the signal matrix Z (f) to be shifted and the original signal X (f) is that
z i (f)＝X(f+(i-L 0 -1)f p ),1≤i≤L
z(f)＝[z i (f)，...，z L (f)] T
Z[n]Is a matrix of m x L, z i (f) In total L cases, all values in 1.ltoreq.i.ltoreq.L, z L (f) Is represented by a vector length L, f p The magnitude of each spectral shift of X (f);
the differential matrix Z of the step 4 z The 'is' the number of the components,
wherein Z is zi Is Z z Is the ith element, Z zi+1 Is Z z I+1th element of (d).
2. The method for filtering and reconstructing a support set for a modulated wideband converter of claim 1, wherein said step 2 new vector Z L In order to achieve this, the first and second,
Z L ＝[||z 1 || 2 ，...，||z i || 2 ，...||z L || 2 ] T
in the formula, ||z 1 || 2 Is the 2-norm, ||z, of the first column vector of the matrix i || 2 Is the 2-norm of the ith column vector of the matrix, ||z L || 2 Is the 2-norm of the L-th column vector of the matrix.
3. The method for filtering and reconstructing a support set for a modulated wideband converter of claim 1, wherein said step 3 is a step of sorting from large to small to obtain a vector Z z ，
In the method, in the process of the invention,
l=2l of (2) 0 +1 means that the vector of original length L is separated from the middle and is symmetrical left and right, now taking only half of the symmetry.
4. The method for filtering and reconstructing a support set for a modulated wideband converter of claim 1, wherein said step 6 finds the corresponding effective signal band, assuming a number of 2N
Wherein z [ n ]]Is the inverse DTFT transform of Z (f), lambda k The positions of the 2N effective bands are [ lambda ] for the number of the found effective band 1 ,λ k ,…,λ 2N ]，
Is the finite band position of the matrix, +.>
Is the spectrum reverse shifting process. />
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