CN108629125A - Subspace projection filter design based on rejecting outliers - Google Patents

Abstract

The present invention proposes to carry out signature analysis to sample covariance matrix, whether method that Gaussian Profile examine exceptional value is met, and the method using test statistics, the threshold value of characteristic value between interference and signal is adaptively found out in the case of unknown disturbances parameter, detection interference exceptional value inhibits to interfere in conjunction with subspace projection method.Its main thought is：Utilize the difference of interference and signal and noise characteristic, seek sample autocorrelation matrix, then feature decomposition is carried out, use the detection algorithm of Lilliefors test statistics, the adaptive threshold for finding out interference characteristic value realizes that sample data is mapped in non-interference subspace according to the orthogonality of the corresponding proper subspace of unlike signal, to inhibit to interfere, performance of filter is improved.The problem of eigenvalue magnitude itself for avoiding different subspace differs larger, and excessive interference characteristic value can make smaller interference characteristic value be erroneously interpreted as signal or noise subspace under threshold value, eliminates the influence of interference characteristic value size gap itself.

Description

Design of Subspace Projection Filter Based on Outlier Detection

technical field

The present invention relates to adaptive interference signal suppression processing in the field of communication, in particular to a subspace projection interference suppression method for eigenvalue detection, that is, to perform eigendecomposition on sample covariance, and to design an adaptive detection interference by using the difference in interference and signal and noise characteristics Eigenvalue method to suppress interference.

Background technique

The filter designed by subspace projection can eliminate the interference subspace and reduce the influence of interference. However, in the subspace projection method, an accurate judgment is required for the number of eigenvalues corresponding to the interference subspace. If the number of eigenvalues judged is less than the actual number, the interference suppression will not be complete, and the residual interference components will continue to deteriorate. communication performance. On the contrary, if the number of judged eigenvalues is greater than the actual number, the useful signal will be damaged, reducing the signal-to-noise ratio and communication performance. Therefore, it is necessary to analyze the eigenvalues of the interference subspace and classify the eigenvalues, so as to provide an adaptive subspace judgment method and identify the interference eigenvalues. The general literature believes that the interference eigenvalue is "much larger" than the signal and noise eigenvalues, thus ignoring the detailed discussion, but adopting a rough method, typically "a few percent (threshold) greater than the maximum eigenvalue" Some of the eigenvalues are interference eigenvalues". The traditional method of detecting interference eigenvalues based on the difference in interference amplitude is not conducive to successful detection of interference eigenvalues with large amplitude differences. That is, in practical applications, the eigenvalue amplitudes corresponding to different subspaces are quite different, and too large interference eigenvalues will make smaller interference eigenvalues below the threshold and be mistaken for signal or noise subspaces.

In view of the above problems, the present invention proposes a subspace projection filter based on outlier detection. That is, based on the characteristics and parameters of white noise, the interference eigenvalue detection is performed. The difference between the eigenvalue and the white noise eigenvalue is greater than a certain multiple of the standard deviation. , combined with the subspace projection method to suppress interference.

Contents of the invention

The present invention proposes a method for analyzing the characteristics of the sample covariance matrix, checking whether it conforms to the Gaussian distribution, and using the method of test statistics to adaptively obtain the threshold value of the characteristic value between the interference and the signal, and detect the interference abnormal value, and finally According to the orthogonality of the characteristic subspaces corresponding to different signals, the sample data is mapped to the non-interference subspace, thereby suppressing interference.

In order to achieve the above technical objectives, the present invention adopts the following technical solutions to achieve.

A subspace projection filter design method based on outlier detection, comprising the following steps:

Step 1, calculate the autocorrelation function of the received signal and arrange it as an autocorrelation matrix;

Step 2, performing eigenvalue decomposition on the estimated covariance matrix to obtain the eigenvalue matrix;

Step 3, take the absolute value of the eigenvalue elements of the eigenvalue matrix, and arrange them from small to large as the order statistic X, and use the detection algorithm of the Lilliefors test statistic as the observation data sample to find the adaptive threshold of the interference eigenvalue;

Step 4: After detecting the interference feature value set Σ _i according to the obtained adaptive threshold, determine its subspace U _i , then the signal and noise subspaces are the complement of U _i , and perform subspace projection to suppress interference.

Compared with the prior art, the present invention has the following advantages:

First, according to the characteristic that the interference characteristic value is "far greater" than the signal and noise characteristic value, the order statistic X of the data to be tested is introduced into samples one by one from small to large, and multiple inspections are carried out, and the corresponding test statistics are calculated and arranged as vector D. When disturbances are taken into account, the statistic D suddenly increases dramatically. The number of conforming samples in the data X to be tested can be considered as the sample number corresponding to the minimum value of the statistic D changing with the amount of test data, that is, the sample range corresponding to the sample number can be considered as the threshold. Those above this threshold are outliers. Avoid the large difference in the magnitude of the eigenvalues of different subspaces. Too large interference eigenvalues will make smaller interference eigenvalues below the threshold and be mistaken for signal or noise subspaces.

Second, the present invention adopts adaptive detection of interference eigenvalues, adaptively obtains the threshold of interference eigenvalues, overcomes the problem of unclear judgment on the number of interference subspaces, minimizes the damage of communication performance, and improves the performance of the filter .

Description of drawings

FIG. 1 is a flow chart of the subspace projection filter simulation method for outlier detection in the present invention.

Fig. 2 is a flow chart of obtaining an adaptive threshold for outlier detection in the present invention.

Fig. 3 is the eigenvalue distribution diagram of interference and signal.

Figure 4 is a graph showing the variation of Lilliefors test statistic with order statistic.

Fig. 5 is a graph showing bit error rate performance curves detected by the filter of the present invention and the conventional filter respectively.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and implementation methods.

With reference to Fig. 1, the subspace projection filter simulation method based on outlier detection of the present invention comprises the following steps: obtain the autocorrelation matrix for the received signal, adaptively obtain the interference eigenvalue threshold, determine the non-interference subspace, subspace projection suppression interference.

Firstly, the autocorrelation matrix is solved for the sample data, that is,

Then perform eigenvalue decomposition on the autocorrelation matrix, assuming that the eigenvalue decomposition is

The subscripts i, s, and n represent interference, signal, and white noise, respectively.

Figure 2 shows the flow of the detection algorithm based on the Lilliefors test statistic, which adopts the idea of statistical testing and uses order statistics to perform sequential calculations. Arrange the decomposed eigenvalues from small to large as an order statistic X, which is regarded as an observation data sample. Let the number of observation data samples (dimension) be L. Set the minimum number of noise samples l ₀ . Step 2 includes the following steps:

Step 2-1: Given l=l ₀ ,...,L, take the first l data of X as the test vector X _l . Compute the sample mean and standard deviation parameters

Step 2-2: Calculate the expected cumulative distribution function of the Gaussian distribution

Step 2-3: Calculate the sample cumulative distribution function

Step 2-4: Calculate the lth element of the statistic D, which is

Step 2-5: Find the minimum value of the statistic D and give its corresponding sample points

For X(l) where l<L _n is a noise sample, and X(l) where l>L _n is an interference sample, the noise variance is estimated to be σ _n , and the noise sample ratio is η=L _n /L. The reasonable range of setting l ₀ is relatively loose, for example, l ₀ /L=0.5 can meet the requirement, because generally speaking, the interference characteristic value is not too much.

Using the algorithm to analyze the eigenvalues of the estimated covariance matrix can accurately detect the eigenvalues caused by interference, because the eigenvalues from the noise itself will make the statistics continuously decrease, and the abnormal amplitude of the interference eigenvalues will cause lead to a sharp increase in statistics. When disturbances are taken into account, the statistic D suddenly increases dramatically. The number of conforming samples in the data X to be tested can be considered as the sample number corresponding to the minimum value of the statistic D changing with the amount of test data, and the sample amplitude corresponding to the sample number is the threshold of the interference characteristic value.

After detecting the interference eigenvalue set Σ _i , determine its subspace U _i , then the signal and noise subspaces are the complement of U _i . Based on this subspace for projection, the designed receiver is

Figure 3 shows the distribution of eigenvalues of the interference and signal. In the simulation, the dimension of the receiver weight vector is 256, the order of the estimated covariance matrix is 256, and the number of its eigenvalues, that is, the number of samples to be detected is 256. Among them, the eigenvalues are arranged from small to large, and it can be clearly seen from the figure that when no interference eigenvalues are detected, the eigenvalues of the signal are evenly distributed. When the eigenvalue of the interference is detected, the amplitude of the eigenvalue of the interference is relatively large compared with the eigenvalue of the signal, and the change is very obvious.

Figure 4 shows statistics using the Lilliefors test. With the addition of larger eigenvalues, the Lilliefors statistic changes sharply before and after the interference eigenvalues are included, which is consistent with the design idea of the algorithm.

Fig. 5 shows the bit error rate performance curve of detection after using the subspace projection of outlier detection designed in the present invention to simulate BPSK signal and interference, and suppressing interference. Set the carrier frequency to 76Hz, the sampling frequency to 256Hz, and the Monte Carlo times to 1000. The simulation results show that, compared with the traditional matched filter, the outlier detection-based subspace projection filter algorithm extracted by the present invention can adaptively detect the interference characteristic value, obtain the signal subspace, suppress the interference, and reduce the bit error rate.

Claims (6)

1. a subspace projection filter design method based on outlier detection, is characterized in that, comprises the following steps as: Step 1, calculate the autocorrelation function of the received signal and arrange it as an autocorrelation matrix; Step 2, performing eigenvalue decomposition on the estimated covariance matrix to obtain the eigenvalue matrix of the signal; Step 3, take the absolute value of the eigenvalue elements of the eigenvalue matrix, and arrange them from small to large as the order statistic X, and use the detection algorithm of the Lilliefors test statistic as the observation data sample to find the adaptive threshold of the interference eigenvalue; Step 4: After detecting the interference feature value set Σ _i according to the obtained adaptive threshold, determine its subspace U _i , then the signal and noise subspaces are the complement of U _i , and perform subspace projection to suppress interference. 2. a kind of subspace projection filter design method based on outlier detection as claimed in claim 1, is characterized in that, in step 1, sample signal is arranged autocorrelation matrix, 3. a kind of subspace projection filter design method based on outlier detection as claimed in claim 1, is characterized in that, carries out eigenvalue decomposition to autocorrelation matrix, namely The subscripts i, s, and n represent interference, signal, and white noise, respectively. 4. a kind of subspace projection filter design method based on outlier detection as claimed in claim 1, is characterized in that, uses the detection algorithm of Lilliefors test statistic, detects the threshold value of disturbing characteristic value, obtains disturbing characteristic value set After Σ _i , determine its subspace U _i , then the signal and noise subspaces are the complement of U _i . Projecting based on this subspace, 5. A kind of subspace projection filter design method based on outlier detection as claimed in claim 1, 4, it is characterized in that, the calculation of the threshold value of the interference feature value adopts the idea of statistical inspection, and uses the order statistic to carry out sequentially calculate. Arrange the decomposed eigenvalues from small to large as an order statistic X, which is regarded as an observation data sample. Let the number of observation data samples (dimension) be L. Set the minimum number of noise samples l ₀ , given l=l ₀ ,...,L, take the first l data of X as the test vector X _l , and calculate the lth element of the statistic D, which is 6. A kind of subspace projection filter design method based on outlier detection as claimed in claim 5, is characterized in that, calculates the average value of sample and standard deviation parameters Expected cumulative distribution function of Gaussian distribution and the sample cumulative distribution function Find the minimum value of the statistic D and give its corresponding sample points L ₀ ≤ l ≤ L. For X(l) where l<L _n is a noise sample, and X(l) where l>L _n is an interference sample, the noise variance is estimated to be σ _n , and the noise sample ratio is η=L _n /L.