CN107332566B - MWC-based support set rapid recovery method - Google Patents

Abstract

The invention provides a support set rapid recovery method based on MWC, and aims to solve the problem that time is consumed for constructing a CTF module and the recovery method in an MWC system. The method comprises the following steps: (1) matrix of measured values

According to the MWC undersampling system, the original signal is undersampled to obtain a measurement value matrix; (2) obtaining a new matrix of measurements

According to

The number of columns of the medium matrix and the number N of the prior knowledge sub-bands

Each column in the array is added to a matrix with only 2N columns

(ii) a (3) And recovering the original support set by utilizing an OMP algorithm. By the method, the recovery speed of constructing the CTF module and recovering the original support set is improved in the process of not reducing the reconstruction rate to a large extent.

Description

MWC-based support set rapid recovery method

Technical Field

The invention belongs to the technical field of intersection of blind spectrum signal processing and compressive sensing, and particularly discloses a support set fast recovery method based on an MWC system when the number of sub-bands is small.

Background

The Nyquist sampling theorem states that the original signal can only be perfectly restored if the sampling rate is greater than 2 times the maximum frequency of the signal, otherwise aliasing occurs. The current popular down-sampling techniques mainly comprise analog demodulation, periodic non-uniform sampling, digital down-conversion and the like, but the sampling bottleneck cannot be solved fundamentally by the techniques, and the bottleneck of twice the sampling rate of the traditional Nyquist sampling theorem is broken in the processing of sparse signals by the generation of a Compressed Sensing (CS) theory until 2006. At the beginning, the research focus is on the theoretical research of compressed sensing, namely the research of sensing recovery of a digital signal after Nyquist sampling, and the research of real analog domain Nyquist undersampling mainly includes a baronik team Random Demodulation (RD) compressed sampling model of Rice university and a modulation broadband Converter (MWC) model proposed by Eldar team of israel university. Random demodulation is suitable for multi-tone signals, frequency resolution of a full frequency band of 1Hz is subdivided into a plurality of frequencies, frequency components which are not 0 are found by a recovery algorithm, a modulation broadband converter is more common to a broadband sparse signal model, and the rear-end recovery is faster based on an analysis idea of frequency spectrum slicing.

The modulated broadband converter undersampling system is an undersampling system based on compressed sensing designed by Eldar in 2010 by Israeli, and is named as a modulated broadband converter (MWC) in Chinese. The MWC effectively undersamples the blind multiband sparse signal and can perfectly restore the original signal, so that the MWC can effectively reduce the sampling frequency of the non-cooperative broadband sparse signal, and the MWC has the unique advantage in full-band signal monitoring and detection. The MWC signal model is to perform segmented sensing on the broadband spectrum slice, so that the MWC can be completely applied to spectrum sensing. In the spectrum sensing of some signals, such as frequency modulated signal sensing, fast sensing is the primary objective, so it is necessary to study how to increase the recovery rate of MWC without greatly reducing the reconstruction rate.

The schematic block diagram of MWC is shown in FIG. 2, and the essence of MWC lies in that it uses the periodic pseudo-random signal in advance

Mixing with the original broadband sparse signal, moving the sub-bands in the broadband to the baseband, wherein the baseband contains the information of each sub-band, and filtering out the low-frequency signal by using a low-pass filter. Because no high-frequency component exists, uniform sampling can be completely realized by utilizing a commercial ADC device, the sampled information is a compressed sampling value, and the effective recovery of the support set can be realized by utilizing the recovery principle of compressed sensing.

In the recovery process of the MWC, the compressed sampling value of the analog domain needs to be input into a compressed sensing recovery algorithm to realize the recovery of the support set of the MWC, and the module is just used for realizing the recovery of the support set of the MWCIs Continuous to finite block (CTF). The principle analysis of MWC is mostly based on frequency domain analysis, because the idea of MWC is to slice the frequency domain and then find out the spectral slice that is not 0 for recovery. However, although the frequency domain-based analysis is adopted, the restoration is based on the time domain, because the frequency domain is infinite-dimensional, the CS model of the frequency domain is IMV (infinite Measurement vectors), and therefore, the frequency domain restoration cannot be realized, but the frequency domain restoration is not realized from the compressed sampling value of finite dimension

It is possible to recover the sample values of each spectral slice, which is the mmv (multiple Measurement vectors) theoretical model in MWC support set recovery. However, two places in the CTF recovery module are time-consuming, one is a process of solving the matrix V through the matrix Q, and the time-consuming process is performed because the eigenvalues of the matrix Q are decomposed, and the other is an MWC recovery algorithm (M-OMP), and because the sampling value matrix is multi-column, the recovery time is increased, and thus the recovery time can be reduced by starting from the two places. Fig. 3 is a time-consuming analysis diagram of the CTF module.

In the CTF module, firstly, the compressed sampling value obtained by the MWC undersampling system

Multiplication by

By conjugate transpose to obtain compressed sample values of m channels of MWC system

Matrix Q, then by

Taking a matrix V obtained by decomposing the characteristic value of Q as an observed value matrix, and further constructing a CS model

The support set of U can be found by using the M-OMP algorithm in CS, and finally, the support set is obtained by

The original signal is found. Because the measurement value matrixes are multiple columns, in the traditional CS model, the measurement value matrixes are all single columns, so that the inner product operation of V and C needs to be carried out for many times in the process of recovering the signals by utilizing the M-OMP algorithm, the recovery time can be prolonged by the measurement value matrixes with multiple columns, and if a method can be found, the column number of V can be reduced without losing the global information of the measurement value, the recovery time can be shortened on the premise of obtaining the approximate reconstruction rate.

Disclosure of Invention

The invention aims to provide a support set fast recovery method based on MWC aiming at the problem that the recovery time is too slow when a CTF module constructs a multi-column measurement value matrix, and the technical scheme is as follows:

the MWC-based support set fast recovery algorithm comprises the following steps:

the method comprises the following steps: obtaining a measurement value matrix through an MWC undersampling system

；

Step two: adding N columns in the matrix of measured values to a matrix of only 2N columns

；

Step three: and recovering the support set by using an M-OMP algorithm in the CS.

Drawings

Fig. 1 is a block diagram of a MWC-based support set fast recovery algorithm.

FIG. 2 is a schematic block diagram of an MWC.

FIG. 3 is a time-consuming analysis of the CTF module of the MWC.

FIG. 4 is a plot of support set recovery rate versus signal-to-noise ratio.

FIG. 5 is a graph of recovery time versus number of channels.

Fig. 6 is a graph of the support set recovery rate versus the signal-to-noise ratio and the number of channels.

Detailed Description

Fig. 1 is a flowchart of a MWC-based support set fast recovery method, and the specific embodiment of the present invention is divided into three steps, which are described below with reference to fig. 1:

the method comprises the following steps: FIG. 2 is a schematic block diagram of an MWC by converting an original signal having N sub-bands

Respectively input into m channels, and pseudo-random sequence

Mixing is performed to spread the spectrum information in the frequency band over the entire frequency band, and at this time, the entire spectrum information in the baseband is spread by a low-pass filter

Information in the baseband is filtered out, and because there is no high frequency component, the information can be equally spaced by the existing ADC sampler

Is sampled to obtain

Matrix of measurements of size

The expression is as follows;

step two: adding N columns of the measurement matrix to a matrix of only 2N columns instead of a matrix of other columns, e.g. when the number of subbands N =6, dividing N by 2N, rounding down to k, then at the measurement matrix

In the method, N columns are respectively decomposed into 2N k columns, and then k columns are added into one column to obtain a new measuring value matrix with 2N columns

The expression is as follows:

where m is the number of channels, N is the total number of bands containing the negative sub-bands,

. Thus, a new matrix of measured values less than the number of columns of the original matrix of measured values can be obtained

Corresponding compressed sensing

By this method, not only is the eigenvalue decomposition matrix Q eliminated, but the reduction in the number of columns of the matrix of measured values increases the rate of recovery

Step three: obtaining the MMV model

Thereafter, recovery is performed using the improved OMP algorithm

The supporting set of (2). The improved OMP algorithm comprises the following steps:

1) initialize: the iteration number t is 0, the residual error R is y, and the index set vector is [ ];

2) finding the index value with the maximum inner product value of the residual error R and the measurement matrix C

Will be

Is added to the vector of the index set,finding symmetric band index values at the same time

And adjacent spectral slice index values

And an

Corresponding adjacent spectral slice values

Adding the index set vector and the index set vector into the index set vector;

3) atomic coefficient updating by least square method

；

4) Updating residual errors

，t++；

5) Judging whether t meets an iteration condition, and if not, stopping iteration; otherwise, go back to step 2.

FIG. 4 is a graph showing the relationship between the SNR of-30 dB to 30dB and the recovery ratio of the original method and the new method when the number of sub-bands N is 6 and the number of channels m is 50.

Fig. 5 is a graph showing the relationship between the number of channels from 15 to 50 and the recovery time of the original method and the new method when the number of sub-bands N is 6 and the signal-to-noise ratio is 30 dB.

The simulation experiment of fig. 6 is a classic simulation diagram on the original text, and can simultaneously display the relationship among the number of channels, the signal-to-noise ratio, and the recovery rate, the horizontal axis represents the number of channels, the vertical axis represents the signal-to-noise ratio, the horizontal bar on the rightmost side represents the recovery rate, and the whiter the color is, the higher the recovery rate is.

Claims (1)

1. The MWC-based support set rapid recovery method is characterized by comprising the following steps:

the method comprises the following steps: obtaining a sampling value matrix through an MWC undersampling system

；

By mixing an original signal containing N sub-bands

Respectively input into m channels, and pseudo-random sequence

Mixing is performed to spread the spectrum information in the frequency band over the entire frequency band, and at this time, the entire spectrum information in the baseband is spread by a low-pass filter

Filtering out information in baseband, and using available ADC sampler to make equal interval

Is sampled to obtain

Matrix of measurements of size

The expression is as follows;

；

step two: matrix for adding N columns in sampling value matrix to 2N columns

；

Dividing N by 2N, rounding down to obtain k, and measuring the value matrix

In the method, N columns are respectively decomposed into 2N k columns, and then the k columns are added into one column to obtain a new measuring value matrix of 2N columns

The expression is as follows:

where m is the number of channels, N is the total number of bands containing the negative sub-bands,

；

step three: recovering a support set by using an improved OMP algorithm;

the improved OMP algorithm steps are as follows:

1) initialize: the iteration number t is 0, the residual error R is y, and the index set vector is [ ];

2) finding the index value with the maximum inner product value of the residual error R and the measurement matrix C

Will be

Adding to the index set vector, and finding symmetrical frequency band index value

And adjacent spectral slice index values

And an

Corresponding adjacent spectral slice values

Adding the index set vector and the index set vector into the index set vector;

3) atomic coefficient updating by least square method

；

4) Updating residual errors

，t++；

5) Judging whether t meets an iteration condition, and if not, stopping iteration; otherwise, go back to step 2).

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