CN104931937A - Submatrix-level orthogonal projection (OP) wave beam forming method based on covariance matrix normalization - Google Patents

Abstract

The invention discloses a submatrix-level OP wave beam forming method based on covariance matrix normalization. The method can be used to effectively inhibit interference, make a main lobe of a self-adaptive directional diagram conformal, reduce side lobes the self-adaptive directional diagram and obtain higher output SINR and convergence speed. The method comprises that submatrix-level reception signals are normalized, and a corresponding normalized sampling covariance matrix is calculated; the amount of interference signal sources is estimated by utilizing the MDL criterion, and further an interference subspace is obtained; and finally, the static weight vector is projected to an orthogonal complement space of the interference subspace to obtain a self-adaptive weight vector.

Description

Subarray Orthogonal Projection Beamforming Method Based on Covariance Matrix Normalization

technical field

The invention relates to the technical field of array signal processing, in particular to a subarray-level orthogonal projection beamforming method based on covariance matrix normalization.

Background technique

Array signal processing is an important branch in the field of signal processing, and it has been widely used in radar, sonar, communication, navigation, earthquake monitoring, speech signal processing, and biomedical engineering. Adaptive beamforming is an important research content in array signal processing. Its essence is to perform spatial filtering by adaptively weighting each array element, so as to achieve the purpose of enhancing desired signal, suppressing interference signal and weakening noise signal. Minimum Variance Distortionless Response (MVDR) is a commonly used algorithm, which suppresses interference by constraining the array gain to be 1 in the desired signal direction and minimizing the array output power. The covariance matrix inversion (SMI) algorithm is a commonly used method to realize the MVDR algorithm, but the output SINR (signal-to-interference-noise ratio) of this algorithm and the convergence speed of the adaptive pattern are slow at low snapshots.

In practical applications, considering hardware conditions and environmental factors, the number of sampling snapshots used to calculate adaptive weights is relatively small. In order to solve the problems caused by the SMI algorithm in the case of low snapshots, the Orthogonal Projection (OP) algorithm has been widely used. Its essence is to project the static weight vector to the orthogonal complement space of the interference subspace (ie, the noise subspace Space), and then get the adaptive weight vector. In this algorithm, the eigenvector corresponding to the small eigenvalue does not participate in the calculation of the adaptive weight vector, so under the condition of low snapshot, this algorithm can make the output SINR and the adaptive direction map converge to the optimal value quickly. However, when the OP algorithm is applied to the sub-array level, the uneven division of the sub-arrays will cause the noise output power of each sub-array to be unequal, which will affect the accuracy of the MDL criterion estimation, resulting in inaccurate estimated interference subspace, resulting in The main lobe of the adaptive pattern is deformed and the side lobe is increased, and the output SINR is severely reduced.

Contents of the invention

In view of this, the present invention provides a subarray-level orthogonal projection beamforming method based on covariance matrix normalization, which can effectively suppress interference and reduce the shape of the main lobe and side lobe of the adaptive pattern , and can obtain higher output SINR and faster convergence speed.

The subarray-level orthogonal projection beamforming method based on covariance matrix normalization of the present invention comprises the following steps:

Step 1. Normalize the subarray-level received signals, and calculate the normalized interference-plus-noise covariance matrix R _{sub_norm} : Among them, R _{in_sub} is the covariance matrix of the subarray level; T _L is the normalization matrix: Among them, L is the number of sub-arrays, $c_l=\left\{\begin{array}{cc}{\left(\underset{i=1}{\overset{N_0}{\Σ}}{w}_i^2\right)}^{1/2}& l=0\\ {\left(\underset{i=u}{\overset{Q}{\Σ}}{w}_i^2\right)}^{1/2}& l\&Greater\; Equal;1\end{array}\right.,$ w _i is the weighting coefficient of the i-th array element, U=N ₀ +N ₁ +…+N _l-1 -J ₀ -J ₁ -…-J _l-1 +1, Q=N ₀ +N ₁ + …+N _l -J ₀ -J ₁ -…-J _l-1 , N _i is the number of array elements contained in the i-th (0≤i≤L-1) sub-array, and J _i is the number of elements contained in the i-th (0≤i≤L-1) sub-array L-2) sub-arrays and the number of overlapping array elements of the i+1th sub-array; ( ) ^H represents complex conjugate transpose;

Step 2, use the MDL criterion to estimate the interference subspace:

Step 2.1, perform eigenvalue decomposition on the normalized interference-plus-noise covariance matrix R _{sub_norm} , obtain the eigenvalues and their corresponding eigenvectors, and arrange the eigenvalues from large to small;

Step 2.2, using the MDL criterion to estimate the number of interference signal sources as P, then the first P column vectors of the feature vector in step 2.1 form the interference subspace;

Step 3, using the interference subspace estimated in step 2, using the orthogonal projection adaptive beamforming method to solve the adaptive weight vector;

In step 4, the adaptive weight vector obtained in step 3 is used to perform weighting processing on the received echo data to obtain an adaptive beam.

Beneficial effect:

The present invention solves the problem of inaccurate interference subspace estimated by the traditional subarray-level orthogonal projection algorithm in the case of uneven division of subarrays and low sampling snapshots, resulting in interference that cannot be effectively suppressed, and the problem of adaptive pattern The problem of main lobe deformation and side lobe elevation can effectively complete subarray-level adaptive beamforming, adaptively form nulls in the interference direction, and keep the main lobe shape of the adaptive pattern while effectively suppressing interference and sidelobe reduction, the present invention has a higher output SINR after adaptive beamforming processing, and the output SINR has a faster convergence speed.

Description of drawings

Fig. 1 is the flow chart of the present invention.

Fig. 2 is a comparison diagram of the adaptive direction diagram between the method of the present invention and the method before improvement (when the number of snapshots is twice the number of sub-arrays).

Fig. 3 is a comparison diagram of the adaptive direction diagram between the method of the present invention and the method before improvement (when the number of snapshots is 10 times the number of sub-arrays).

Fig. 4 is a graph comparing the output SINR curve with the number of snapshots between the method of the present invention and the method before improvement.

Fig. 5 is a graph comparing the output SINR curves with beam pointing changes between the method of the present invention and the method before improvement.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and examples.

The present invention provides a subarray-level orthogonal projection beamforming method based on covariance matrix normalization. First, the subarray-level received signals are normalized, and the corresponding normalized sampling covariance matrix is calculated. ; Then use the MDL criterion to estimate the number of interference signal sources, and then obtain the interference subspace; finally, project the static weight vector to the orthogonal complement space of the interference subspace to obtain the adaptive weight vector. In the case of uneven division of sub-arrays and low sampling snapshots, the present invention can effectively suppress interference, reduce the shape of the main lobe and side lobes of the adaptive pattern, and obtain higher output SINR and Faster convergence speed. Flow process of the present invention is as shown in Figure 1, and concrete steps are as follows:

Step 1. Construct a normalized subarray-level covariance matrix

①Establishment of signal model

Assume a narrowband linear array with a total of N array elements, the array elements are isotropic, and P interference signals, all of which are far-field narrowband signals, assuming that the noise of each array element is a space-time white noise with independent power and equal power and The interfering signal and the noise are not correlated with each other. Then the signal model received by the array can be expressed as

X _in (t) = AS (t) + N (t) (1)

In the formula, A=[a(θ ₁ ), a(θ ₂ ),…a(θ _P )] is the array flow pattern matrix, a(θ _i )(i=1,2,…P) is the interference signal Steering vector, set the distance between the nth array element and the reference point as d _n (n=0,1,2,…,N-1), usually take the 0th array element as the reference point, at this time d ₀ =0 , λ is the wavelength, then θ _i (i=1,2,...P) is the incident angle of the interference signal, [·] ^T is the matrix transpose, S(t)=[S ₁ (t),S ₂ (t),...S _p ( t)] ^T , S _i (t) (i=1,2,…P) is the complex envelope of the i-th interference signal, N(t)=[n ₁ (t),n ₂ (t),… ,n _N (t)] is background white noise.

Thus, the array covariance matrix is obtained as

R _in ＝E{X _in (t)X _in ^H (t)} (2)

In the formula, E{·} represents the mathematical expectation, and (·) ^H represents the complex conjugate transpose.

In practical applications, according to the maximum likelihood estimation criterion, the array covariance matrix is estimated from the finite snapshot data X _in (t _i ), and we get

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula, X _in (t _i ) is the sampling value of the array at time i (i=1,2,...,K), and K is the number of sampling snapshots.

When processing at the sub-array level, the array is divided into L sub-arrays, and (L≥P+1), can be non-overlapping sub-arrays or overlapping sub-arrays, and the sub-array conversion matrix can be expressed as

T＝φ ₀ WT ₀ (4)

in Indicates the role of the phase shifter, assuming that the beam is directed in the same direction as the desired signal; W=diag(w _n ) _{n=0,1,…,N-1} , where w _n is the weighting coefficient of the nth array element, used for Suppress the side lobe level of the pattern; T ₀ is a matrix of N×L sub-arrays, and among all the elements in the lth (l=0,1,...,L-1) column, only the lth sub-array The value of the element corresponding to the array element number of is 1, and the rest are all 0 (in the case of non-overlapping sub-arrays, the column vectors of T ₀ are mutually orthogonal).

Then the sampling snapshot signal received at the sub-array level is

X _{in_sub} (t) = T ^H X _in (t) (5)

Then the covariance matrix of the subarray level is

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; T</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

②Normalization of the covariance matrix

First, the output of each sub-array is normalized, and the normalization is completed by the matrix T _L

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; g</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}}{\overset{\mathrm{<span\; class="notranslate">\; Q</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

U＝N ₀ +N ₁ +...+N _l-1 -J ₀ -J ₁ -...-J _l-1 +1

Q＝N ₀ +N ₁ +...+N _l -J ₀ -J ₁ -...-J _l-1

N _i is the number of array elements contained in the i-th (0≤i≤L-1) sub-array, and J _i is the overlapping array elements of the i-th (0≤i≤L-2) sub-array and the i+1-th sub-array number.

The normalized interference plus noise covariance matrix is

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Through normalization, the noise power of each sub-array is consistent, so that the MDL criterion can be applied.

Step 2. Estimate the interference subspace

Eigenvalue decomposition of the normalized covariance matrix R _{sub_norm}

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, λ _i (i=1,2,...,L) is the eigenvalue of the covariance matrix R _{sub_norm} , is the eigenvector corresponding to the eigenvalue λ _i , and λ _i is arranged from large to small

The MDL criterion is used to estimate the number of interference signal sources, and then the interference subspace is estimated.

The function of the MDL criterion is

$\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

in

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; \{</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{<span\; class="notranslate">\; \&Pi;</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}}}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

According to the MDL criterion, when the value of d changes, the value of d corresponding to the minimum value of formula (11) is the number P of interference signal sources, and the feature vector is selected The first P column vectors form the interference subspace U _s , namely It can be known from mathematical knowledge that the vector and vector a(θ ₁ ), a(θ ₂ ),…,a(θ _p ) form the same vector space, namely:

$\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \{</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Among them, span{ } represents the space formed by the vector, is the estimate of the interference subspace.

Step 3: Solve the adaptive weight vector of the improved algorithm

Using the interference subspace estimated in step 2, the adaptive weight vector of the improved algorithm is solved by using the orthogonal projection adaptive beamforming method.

Using the idea of the traditional orthogonal projection algorithm, the static weight vector w _{q_sub} is projected to the orthogonal complement space of the interference subspace U _s estimated in step 2, and the adaptive weight vector of the improved algorithm is obtained as

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; b</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

In the formula, I is an L×L-dimensional unit matrix, η is a constant, w _{q_sub} is a static weight vector, and each element is an L-dimensional column vector of 1, The effect of is to keep the gain in the main beam direction of the antenna unchanged.

Step 4: Perform adaptive beamforming on the received echoes

After getting the adaptive weight vector, the received echo data can be weighted:

^Y ＝WHX(t) (13)

In the formula, X(t) is the received echo signal, which effectively removes the interference and weakens the noise, and enhances the desired signal.

Since then, a sub-array-level orthogonal projection sub-adaptive beamforming method based on covariance matrix normalization has been completed to process the echo data.

In order to verify a subarray-level orthogonal projection adaptive beamforming method based on covariance matrix normalization proposed by the present invention, carry out the simulation of adaptive beam pattern and output signal-to-interference-noise ratio (SINR), and the simulation adopts narrowband Uniform linear array, the simulation parameters are shown in Table 1. Before the improvement, the algorithm uses the orthogonal projection (OP) algorithm to calculate the adaptive weight vector directly from the sub-array-level sampling snapshot signal.

Table 1 Simulation parameter settings

Fig. 2 and Fig. 3 are the comparison (simulation 1 time) of the self-adaptive beam pattern of the improved algorithm of the present invention and the improved algorithm, and the number of sampling snapshots is respectively 20 and 100, and the beam pointing angle is 0°, as can be seen, The main lobe of the adaptive beam pattern obtained by the improved algorithm is deformed and the side lobe level is seriously increased; the main lobe of the adaptive beam pattern obtained by the improved algorithm is conformal and the side lobe level is low, which is close to the static beam pattern , the performance is greatly improved than before.

Fig. 4 is under different sampling snapshot conditions, the expected signal angle is 0 °, the input signal-to-noise ratio is 0dB, other simulation conditions are the same as Fig. 2, the improved algorithm of the present invention and the output signal-to-interference-noise ratio (SINR) of the improved algorithm Compare. It can be seen from the simulation results that the output SINR of the improved algorithm is higher and the convergence is fast; while the output SINR of the improved algorithm is lower and the convergence is slower, and as the number of snapshots increases, the output SINR decreases, because the sampling The higher the number of snapshots, the lower the accuracy of the estimated interference subspace, and the interference cannot be effectively suppressed, resulting in a severe drop in the output SINR.

Figure 5 is a comparison of the improved algorithm of the present invention and the output signal-to-interference-noise ratio (SINR) of the improved algorithm at different beam pointing angles, the input signal-to-noise ratio is 0dB, and other simulation conditions are the same as in Figure 2, and it can be seen that the improved algorithm Can effectively suppress interference, and the output SINR is high.

It can be seen from FIG. 2 to FIG. 5 that the improved algorithm of the present invention can enhance the desired signal, has good anti-interference performance, and is a robust subarray-level adaptive beamforming algorithm.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (1)

1. A subarray level orthogonal projection beamforming method based on covariance matrix normalization, is characterized in that, comprises the steps: Step 1. Normalize the subarray-level received signals, and calculate the normalized interference-plus-noise covariance matrix R _{sub_norm} : Among them, R _{in_sub} is the covariance matrix of the subarray level; T _L is the normalization matrix: Among them, L is the number of sub-arrays, $c_l=\left\{\begin{array}{cc}{\left(\underset{i=1}{\overset{N_0}{\mathrm{\&Sigma;}}}{w}_i^2\right)}^{1/2}& l=0\\ {\left(\underset{i=u}{\overset{Q}{\mathrm{\&Sigma;}}}{w}_i^2\right)}^{1/2}& l\&Greater\; Equal;1\end{array}\right.,$ w _i is the weighting coefficient of the i-th array element, U=N ₀ +N ₁ +…+N _l-1 -J ₀ -J ₁ -…-J _l-1 +1, Q=N ₀ +N ₁ + …+N _l -J ₀ -J ₁ -…-J _l-1 , N _i is the number of array elements contained in the i-th (0≤i≤L-1) sub-array, and J _i is the number of elements contained in the i-th (0≤i≤L-1) sub-array L-2) sub-arrays and the number of overlapping array elements of the i+1th sub-array; ( ) ^H represents complex conjugate transpose; Step 2, use the MDL criterion to estimate the interference subspace: Step 2.1, perform eigenvalue decomposition on the normalized interference-plus-noise covariance matrix R _{sub_norm} , obtain the eigenvalues and their corresponding eigenvectors, and arrange the eigenvalues from large to small; Step 2.2, using the MDL criterion to estimate the number of interference signal sources as P, then the first P column vectors of the feature vector in step 2.1 form the interference subspace; Step 3, using the interference subspace estimated in step 2, using the orthogonal projection adaptive beamforming method to solve the adaptive weight vector; In step 4, the adaptive weight vector obtained in step 3 is used to perform weighting processing on the received echo data to obtain an adaptive beam.