CN103885045B - Based on the circulation associating Adaptive beamformer method of Subarray partition - Google Patents

Abstract

The invention discloses a cyclic joint adaptive beamforming method based on subarray division, which solves the problems of large demand for independent and identically distributed samples, high computational complexity, and poor filtering effect when the interference number is large when large-scale radar antenna array beamforming is performed. . The implementation steps of the present invention are: (1) sub-array division; (2) obtaining steering vector; (3) direct integral decomposition of steering vector; (4) establishing cost function; (5) solving weight vector; (6) beam forming. Compared with the beamforming method of the prior art, the present invention has the advantages of good interference suppression effect, less required samples, and fast iterative convergence. The present invention can be used for large-scale radar antenna arrays, small number of training samples and large number of interferences Radar beamforming for the case.

Description

Recurrent Joint Adaptive Beamforming Method Based on Subarray Partition

technical field

The invention belongs to the technical field of radar, and further relates to a cyclic joint adaptive beamforming method based on subarray division in the technical field of array signal processing. The invention can be used to solve the problem of beam forming under the condition of large scale of radar antenna array, few training samples and many interferences.

Background technique

In the past 50 years of development, array signal processing technology has been widely used in many military and national economic fields such as radar, communication, navigation, sonar, voice processing, and geological exploration. Especially in recent years, with the rapid development of wireless digital communication technology, the application of array signal processing technology in mobile communication system has aroused people's extensive attention and research interest, which further accelerated the development of this technology. Adaptive beamforming, also known as spatial adaptive filtering, is to suppress spatial interference and noise, enhance useful signals, and obtain desired output results by performing weighted addition processing on spatial array elements at the receiving end. The method of adaptively solving the optimal weight of the array element is called the beamforming method. Currently, the frequently used beamforming technique is the sampling matrix inversion method. This method establishes a cost function according to the minimum variance criterion with linear constraints (that is, under the condition that the expected signal direction gain is constant, the energy of the received data of the array element is minimized) and uses the Lagrange multiplier method to solve the filter weight vector, the array element The covariance matrix of the received data is estimated from multiple independent and identically distributed sampling data. Scientific research has shown that in order to make the sampling matrix inversion method perform optimally, the number of independent and identically distributed samples required should be greater than twice the dimension of the covariance matrix. In practical applications, the interference environment usually changes rapidly, and the available The number of independent and identically distributed samples is limited. In addition, the sampling matrix inversion method needs to invert the covariance matrix, which has high computational complexity. In order to improve the spatial resolution of the array and the ability to detect weak and small target signals, the number of elements of a modern large-scale phased array may reach hundreds, thousands or even tens of thousands. If the sampling matrix inversion method is adopted, not only the number of independent and identically distributed samples is required And the calculation complexity is huge, and the amount of equipment and storage required is also huge, which is impossible and unnecessary in engineering. Likewise, some other existing beamforming methods face similar issues when applied to large-scale arrays.

The patent "Digital Array Ultra-Low Sidelobe Adaptive Digital Beamforming Method" (patent application number: 201210002661, publication number: CN102608580A) filed by Hohai University discloses a digital array ultra-low sidelobe adaptive digital beamforming method. The method first estimates the interference direction, then constructs the interference auxiliary beam for spatial dimensionality reduction, and finally calculates the beamformer weights. This method has very good shape-preserving ability of ultra-low sidelobe beams, and the demand for training samples is small, but the method still has the disadvantage that it needs to estimate the interference direction in advance. When the number of interference is large, it is necessary to estimate multiple interference A large amount of calculation is required, and the dimensionality of the covariance matrix is still high after dimension reduction processing, the number of training samples required is large, and the filtering effect is not ideal. At this time, the performance of this method will be greatly reduced .

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and propose a cyclic joint adaptive beamforming method based on subarray division. This method can effectively reduce the demand for independent and identically distributed samples and reduce the computational complexity. At the same time, it can effectively suppress interference, thereby solving the beamforming problem of large-scale radar antenna arrays.

The realization idea of the present invention is: firstly, the radar antenna array is divided into a plurality of sub-arrays on average; Then, calculate the radar target signal steering vector, the outer layer antenna array steering vector and the inner layer antenna array steering vector; then, divide the radar target signal steering vector Carry out direct integral decomposition, and use the linear constraint minimum variance criterion to establish the cost function; finally, use the loop minimization method to solve the cost function, obtain the filter weight vector, and perform beamforming.

Concrete steps of the present invention are as follows:

(1) Subarray division:

For multiple radar antenna array elements, p array elements are selected as a sub-array according to the average component order of the number of array elements N, forming M=N/p sub-arrays, and the outer array composed of M sub-arrays and An antenna array composed of nested inner arrays composed of p array elements, where N represents the number of radar antenna array elements, p represents the number of array elements contained in the sub-array of the radar antenna array, and M represents the number of sub-arrays of the radar antenna array number.

(2) Obtain the steering vector:

Using the steering vector formula, the radar target signal steering vector, the outer antenna array steering vector and the inner antenna array steering vector are calculated respectively.

(3) Direct integral solution of steering vector:

The radar target signal steering vector is decomposed into the direct product of the outer antenna array steering vector and the inner antenna array steering vector.

(4) Establish a cost function:

According to the linear constraint minimum variance criterion, the cost function of the outer antenna array weight vector corresponding to the outer antenna array steering vector and the inner antenna array weight vector corresponding to the inner antenna array steering vector is established.

(5) Solve the weight vector:

(5a) According to the following formula, set the iteration initial value vector of the outer antenna array weight vector:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$

Among them, v ₀ represents the iterative initial value vector of the outer antenna array weight vector, a _m represents the steering vector of the outer antenna array, * represents the conjugate operation, ||·|| represents the two-norm operation;

(5b) Let ε be the stop iteration parameter, the value range of ε is 0<ε<<1, and << means far less than;

(5c) Calculate the iterative initial value vector of the inner layer antenna array weight vector according to the following formula:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}$

Among them, u ₀ represents the iterative initial value vector of the inner antenna array weight vector, R ₀ represents the sample estimation matrix of the covariance matrix of the received data covariance matrix of the inner antenna array, s ₀ represents the coefficient vector of the inner antenna array, H represents the conjugate rotation Set operation, (·) ^-1 means inverse operation;

(5d) Calculate the iteration vector of the weight vector of the outer antenna array according to the following formula:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$

Among them, v ₁ represents the iterative vector of the weight vector of the outer antenna array, R ₁ represents the sample estimation matrix of the covariance matrix of the received data of the outer antenna array, s ₁ represents the coefficient vector of the outer antenna array, and H represents the conjugate transposition operation , (·) ^-1 represents the inverse operation, ||·|| represents the two-norm operation;

(5e) Determine whether the difference v ₁ -v ₀ between the iterative vector v ₁ of the outer antenna array weight vector and the iterative initial value vector v ₀ of the outer antenna array weight vector satisfies the stop iteration condition of the following formula, if satisfied, The iteration is terminated, and the iteration vector of the outer antenna array weight vector is obtained as the outer antenna array weight vector, and the iterative initial value vector of the inner antenna array weight vector is used as the inner antenna array weight vector; if not satisfied, the outer antenna array weight The iterative vector v ₁ of the vector is used as the iterative initial value vector v ₀ of the new outer antenna array weight vector, and step (5c) is performed until the stop iteration condition is satisfied, and the iteration is terminated, and the iterative vector of the outer antenna array weight vector is obtained as the outer layer antenna array weight vector, the iteration initial value vector of the inner layer antenna array weight vector is used as the inner layer antenna array weight vector;

||v ₁ -v ₀ ||≤ε

Among them, v ₁ and v ₀ represent the iteration vector and the iteration initial value vector of the outer antenna array weight vector respectively, ε represents the stop iteration parameter, the value range of ε is 0< _ε <<1, and ||·|| Two-norm operation, << means far less than.

(6) Beamforming:

Do the direct product operation of the outer antenna array weight vector and the inner antenna array weight vector to obtain the filter weight vector, and use the filter weight vector to weight and sum the data vectors received by the radar to minimize the output power of the radar antenna array , form the main beam in the direction of the desired target, and complete the beamforming.

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

First, because the present invention adopts the method of sub-array division, the original radar antenna array is divided into the nested form of outer array and inner array, which overcomes the problem of large demand for independent and identically distributed samples in the prior art, making The invention has the advantages of effectively reducing the sample demand, and can still obtain excellent performance under the condition of small samples.

Second, because the present invention adopts sub-array division and cycle minimization methods, it overcomes the problem of high computational complexity in the prior art, so that the present invention can quickly obtain filter weight vectors, greatly reducing computational complexity, and is more conducive to Advantages of real-time processing.

Third, because the present invention adopts the method of cyclic minimization, the cyclic joint adaptive processing of the outer array and the inner array overcomes the problem of poor filtering effect in the prior art when the radar antenna array is large in scale and the number of interferences is large, making the present invention The obtained radar antenna array beam pattern has the advantages of lower side lobe and better beam shape keeping ability, and is more conducive to filtering.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is the iterative convergence curve figure that the present invention adopts cycle minimization method to obtain;

Fig. 3 is the curve diagram of the output signal-to-interference-noise ratio of the present invention and prior art sampling matrix inversion method with input signal-to-noise ratio;

Fig. 4 is the curve diagram of the output signal-to-interference-noise ratio of the present invention and prior art sampling matrix inversion method with the number of samples;

Fig. 5 is a beam pattern in the range of -90° to 90° of the filter weight vector obtained by the sampling matrix inversion method of the present invention and the prior art.

detailed description

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

With reference to Fig. 1, concrete implementation steps of the present invention are as follows:

Step 1, sub-array division.

For multiple radar antenna array elements, p array elements are selected as a sub-array according to the average component order of the number of array elements N, forming M=N/p sub-arrays, and the outer array composed of M sub-arrays and An antenna array composed of nested inner arrays composed of p array elements, where N represents the number of radar antenna array elements, p represents the number of array elements contained in the sub-array of the radar antenna array, and M represents the number of sub-arrays of the radar antenna array number.

Step 2, get the steering vector.

Using the steering vector formula, the radar target signal steering vector, the outer antenna array steering vector and the inner antenna array steering vector are calculated respectively.

The radar target signal steering vector formula is as follows:

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</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">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

Among them, a _n represents the steering vector of the radar target signal, j represents the imaginary number unit, d represents the distance between the radar antenna array elements, θ represents the direction of the radar target, sin represents the sinusoidal operation, λ represents the operating wavelength of the radar, and N represents the radar antenna element The number of , T represents the transpose operation.

The steering vector formula of the outer antenna array is as follows:

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;pd</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; pd</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</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">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; pd</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

Among them, a _m represents the steering vector of the outer antenna array, j represents the imaginary number unit, d represents the distance between the radar antenna array elements, θ represents the direction of the radar target, sin represents the sine operation, λ represents the working wavelength of the radar, and p represents the radar antenna array The number of array elements contained in the sub-array, M indicates the number of sub-arrays of the radar antenna array, and T indicates the transposition operation.

The steering vector formula of the inner antenna array is as follows:

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</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">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

Among them, a _p represents the steering vector of the inner antenna array, j represents the imaginary number unit, d represents the distance between the radar antenna array elements, θ represents the direction of the radar target, sin represents the sinusoidal operation, λ represents the operating wavelength of the radar, and p represents the radar antenna array The number of array elements contained in the sub-array, T represents the transpose operation.

Step 3, the direct integral solution of the steering vector.

The radar target signal steering vector is decomposed into the direct product of the outer antenna array steering vector and the inner antenna array steering vector.

According to the definition of direct product in matrix theory, the radar target signal steering vector a _n is directly decomposed into the direct product of the outer antenna array steering vector a _m and the inner antenna array steering vector a _p , to obtain Indicates direct product.

Step 4, establish the cost function.

According to the linear constraint minimum variance criterion (minimize the output power of the radar antenna array under the condition that the expected target signal direction gain is constant), the outer antenna array weight vector and the inner antenna array steering vector corresponding to the outer antenna array steering vector are established The cost function of the inner antenna array weight vector corresponding to the vector.

Assuming that the radar antenna array is a uniform linear array composed of N array elements, the distance between the array elements is half a wavelength, and there is one target signal and J interference signals in the space, the received data of the radar antenna array can be expressed as the following formula:

x(t)=As(t)+n(t)

Among them, x(t) represents the data vector received by the radar antenna array, A represents the N×(1+J)-dimensional matrix composed of the steering vector of the target signal and the interference signal, s(t) represents the magnitude vector of the received signal at time t, and n (t) represents the Gaussian white noise vector received at time t. After sampling the data received by the radar antenna array, the actual output sampled data vector of the radar antenna array is x _i (i=1,...,L), where L represents the number of samples.

According to the linear constraint minimum variance criterion, the cost function is established as follows:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

Among them, min represents the operation of minimizing the output power of the radar antenna array under the condition that the expected target signal direction gain is constant, f(u, v) represents the output power of the radar antenna array, u represents the weight vector of the inner antenna array, and v represents the outer layer antenna array weight vector, E represents the expectation operation, || · || represents the two-norm operation, * represents the conjugate operation, represents the direct product, H represents the conjugate transpose operation, x represents the radar antenna array sampling data vector, st represents the constraint operation, _{am represents the steering vector of the outer antenna array, and a p represents} the steering vector of the inner antenna array.

By arranging x into a data matrix X with p rows and M columns, the above formula can be transformed into the following cost function formula:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; Xv</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

Among them, min represents the operation of minimizing the output power of the radar antenna array under the condition that the expected target signal direction gain is constant, f(u, v) represents the output power of the radar antenna array, u represents the weight vector of the inner antenna array, and v represents the outer layer antenna array weight vector, E represents the expectation operation, ||·|| represents the two-norm operation, H represents the conjugate transpose operation, X represents the radar antenna array sampling data matrix, st represents the constraint operation, and a _p represents The steering vector of the inner antenna array, a _m represents the steering vector of the outer antenna array, and T represents the transpose operation.

Step 5, solve the weight vector.

Using the circular minimization method, the cost function is solved, and the weight vector of the outer antenna array and the weight vector of the inner antenna array are obtained.

The solution process is described in detail below.

Assuming that the weight vector v of the outer antenna array is known, the following formula is obtained by using the Lagrangian multiplier method:

$\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>$

Among them, u represents the weight vector of the inner antenna array, λ represents the Lagrangian multiplier, v represents the weight vector of the outer antenna array, Indicates the sample estimation matrix of the received data covariance matrix of the inner antenna array, L indicates the number of samples, X _i indicates the i-th radar antenna array sampling data matrix, a _p indicates the steering vector of the inner antenna array, a _m indicates the outer antenna Array steering vector.

make The weight vector of the inner layer antenna array can be obtained as:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}$

Among them, u represents the inner layer antenna array weight vector, Represents the coefficient vector of the inner antenna array, H represents the conjugate transpose operation, (·) ^-1 represents the inverse operation.

Assuming that the weight vector u of the inner antenna array is known, the Lagrangian multiplier method is used to obtain:

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>$

Among them, v represents the weight vector of the outer antenna array, γ represents the Lagrangian multiplier, u represents the weight vector of the inner antenna array, Represents the sample estimation matrix of the received data covariance matrix of the outer antenna array, * represents the conjugate operation, H represents the conjugate transpose operation, and T represents the transpose operation.

make The weight vector of the outer antenna array can be obtained as:

$\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}$

Among them, v represents the weight vector of the outer antenna array, A vector of coefficients representing the outer antenna array. Due to the scale ambiguity problem of the cost function, that is, for any non-zero constant The following relationship exists:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&PartialD;</span>}^{<span\; class="notranslate">\; *</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>{<span\; class="notranslate">\; \&PartialD;</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>$

In order to solve the problem of scale ambiguity, it is necessary to normalize v during the iterative process, that is, to divide v by its modulus value, so that the modulus value of v is 1, and the formula is expressed as: v=v/||v| |, ||·|| represent the operation of taking a two-norm.

The cycle minimization method is carried out as follows:

(5a) According to the following formula, set the iteration initial value vector of the outer antenna array weight vector:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$

Among them, v ₀ represents the iterative initial value vector of the outer antenna array weight vector, a _m represents the steering vector of the outer antenna array, * represents the conjugate operation, ||·|| represents the two-norm operation;

(5b) Let ε be the stop iteration parameter, the value range of ε is 0<ε<<1, and << means far less than;

(5c) Calculate the iterative initial value vector of the inner layer antenna array weight vector according to the following formula:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}$

Among them, u ₀ represents the iterative initial value vector of the inner antenna array weight vector, R ₀ represents the sample estimation matrix of the covariance matrix of the received data covariance matrix of the inner antenna array, s ₀ represents the coefficient vector of the inner antenna array, H represents the conjugate rotation Set operation, (·) ^-1 means inverse operation;

(5d) Calculate the iteration vector of the weight vector of the outer antenna array according to the following formula:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$

Among them, v ₁ represents the iterative vector of the weight vector of the outer antenna array, R ₁ represents the sample estimation matrix of the covariance matrix of the received data of the outer antenna array, s ₁ represents the coefficient vector of the outer antenna array, and H represents the conjugate transposition operation , (·) ^-1 represents the inverse operation, ||·|| represents the two-norm operation;

(5e) Determine whether the difference v ₁ -v ₀ between the iterative vector v ₁ of the outer antenna array weight vector and the iterative initial value vector v ₀ of the outer antenna array weight vector satisfies the stop iteration condition of the following formula, if satisfied, The iteration is terminated, and the iteration vector of the outer antenna array weight vector is obtained as the outer antenna array weight vector, and the iterative initial value vector of the inner antenna array weight vector is used as the inner antenna array weight vector; if not satisfied, the outer antenna array weight The iterative vector v ₁ of the vector is used as the iterative initial value vector v ₀ of the new outer antenna array weight vector, and step (5c) is performed until the stop iteration condition is satisfied, and the iteration is terminated, and the iterative vector of the outer antenna array weight vector is obtained as the outer layer antenna array weight vector, the iteration initial value vector of the inner layer antenna array weight vector is used as the inner layer antenna array weight vector;

||v ₁ -v ₀ ||≤ε

Among them, v ₁ and v ₀ represent the iteration vector and the initial value vector of the outer antenna array weight vector respectively, ε represents the stop iteration parameter, and the value range of ε is 0<ε<<1, and ||·|| Two-norm operation, << means far less than.

Step 6, beamforming.

The weight vector of the outer antenna array and the weight vector of the inner antenna array are directly producted to obtain the filter weight vector, and the data vector received by the radar is weighted and summed with the filter weight vector to minimize the output power of the radar antenna array. Form the main beam in the direction of the desired target to complete the beamforming.

Effect of the present invention can be verified by following simulation experiments:

1. Simulation conditions:

The simulation experiment of the present invention adopts a uniform linear array composed of 400 array elements, the array element spacing is half a wavelength, the target direction is 0 degrees, and 16 interference directions are [-80-70-60-50-40-30-20 -101020304050607080] degrees, the interference-to-noise ratio is 40dB. When the sub-array is divided, 20 array elements are selected in turn as a sub-array.

2. Simulation content

Simulation 1: The present invention selects 800 samples, uses the circular minimization method adopted when solving the weight vector in the present invention to perform simulation, performs statistics on the output SINR, and finally obtains an iterative convergence curve of the circular minimization method, such as Figure 2 shows.

Simulation 2: The present invention selects 800 samples, respectively uses the sampling matrix inversion method of the prior art and the two methods of the present invention for simulation, and performs statistics on the output SINR under the two methods, and finally obtains the output SINR Ratio changes with the input signal-to-noise ratio, such as the two curves marked with the present invention and the inversion of the sampling matrix in FIG. 3 .

Simulation 3: the present invention uses the sampling matrix inversion method of the prior art and the two methods of the present invention to simulate respectively when the input SINR is 40dB, and performs statistics on the output SINR under the two methods, and finally Two curves of the output signal-to-interference-noise ratio varying with the number of samples are obtained, such as the two curves marked with the present invention and the inversion of the sampling matrix in FIG. 4 .

Simulation 4: When the number of samples is 800 and the signal-to-noise ratio is -20dB, the present invention uses the sampling matrix inversion method of the prior art and the two methods of the present invention to simulate respectively, and the radar antenna array output normalization under the two methods Statistically, the power is calculated, and finally the beam patterns under the two methods are obtained, as shown in Figure 5.

3. Result analysis:

Fig. 2 is an iterative convergence curve diagram obtained by using the cycle minimization method in the present invention, the abscissa indicates the number of iterations, and the ordinate indicates the output signal-to-interference-noise ratio, and the physical unit is dB. It can be seen from Fig. 2 that when the number of samples is 800, the iterative process of the present invention to solve the filter weight vector using the circular minimization method only needs one step to converge, because the computational complexity of inverting the N-dimensional covariance matrix is O(N ³ ), so the present invention carries out the calculation complexity of the inverse operation to the 20-dimensional outer array covariance matrix and the 20-dimensional inner array covariance matrix is O(20 ³ ), then the total calculation The complexity is O(20 ³ +20 ³ )=O(2(20) ³ ), while the sampling matrix inversion method in the prior art needs to invert the 400-dimensional covariance matrix, and its computational complexity is O (400 ³ ). Obviously there is O(2(20) ³ )<<O(400 ³ ), that is, the computational complexity of the present invention is far lower than that of the sampling matrix inversion method in the prior art, which greatly saves the computational effort.

Fig. 3 is the present invention and prior art sampling matrix inversion method output SINR change curve diagram with input SNR, abscissa represents input SNR, ordinate represents output SINR, and physical unit is dB . It can be seen from FIG. 3 that with the increase of the input SNR, the output SINR of the present invention is much higher than that of the sampling matrix inversion method, and the performance improvement is more obvious. With the increase of signal energy, the sampling matrix inversion method directly uses the full-dimensional covariance matrix for calculation, which will lead to the cancellation of the target signal and seriously reduce the output SINR, while the present invention adopts the decomposition form of the filter weight vector Approaching the optimal solution, when the signal energy is large, a high output SINR can still be obtained, which is about 15dB higher than that of the sampling matrix inversion method.

Fig. 4 is a graph showing the output SINR of the sampling matrix inversion method of the present invention and the prior art as a function of the number of samples, the abscissa represents the number of samples, the ordinate represents the output SINR, and the physical unit is dB. It can be seen from FIG. 4 that the present invention starts to approach convergence when the number of samples is 100, while the sampling matrix inversion method starts to approach convergence when the number of samples reaches 1000. In practical applications, the interference environment usually changes rapidly, and thousands of independent and identically distributed samples are usually difficult to obtain, so the application of the sampling matrix inversion method is limited, and the present invention only needs hundreds of independent and identically distributed samples to obtain excellent performance , which is more suitable for practical application.

Fig. 5 is the beam pattern of the filter weight vector obtained by the sampling matrix inversion method of the present invention and the prior art in the range of -90 degrees to 90 degrees, the abscissa represents the angle, the physical unit is degree, and the ordinate represents the radar The antenna array outputs normalized power, the physical unit is dB, the solid line represents the present invention, the dotted line represents the sampling matrix inversion method in the prior art, and the arrow represents the interference direction. It can be seen from FIG. 5 that since the present invention adopts cyclic joint adaptive processing, the beam pattern forms lower sidelobes, reaching about -30dB, which is beneficial to the suppression of interference and noise. However, the sampling matrix inversion method uses a full-dimensional covariance matrix for calculation, which will lead to the cancellation of the target signal. Therefore, the beam pattern sidelobe of the sampling matrix inversion method is relatively high, about -15dB, which is not conducive to the suppression of interference and noise. .

The above simulation results show that: the present invention divides the original radar antenna array into the nested form of the outer array and the inner array due to the adoption of the sub-array division method and the cyclic minimization method, and the cyclic joint adaptive processing of the outer array With the inner array, the demand for independent and identically distributed samples is effectively reduced, the computational complexity is greatly reduced, and the interference can be effectively suppressed at the same time, and the filtering effect is better.

Claims (3)

1. A cyclic joint adaptive beamforming method based on subarray division, comprising the steps: (1) Subarray division: For multiple radar antenna array elements, p array elements are selected as a sub-array according to the average component order of the number of array elements N, forming M=N/p sub-arrays, and the outer array composed of M sub-arrays and An antenna array composed of nested inner arrays composed of p array elements, where N represents the number of radar antenna array elements, p represents the number of array elements contained in the sub-array of the radar antenna array, and M represents the number of sub-arrays of the radar antenna array number; (2) Obtain the steering vector: Using the steering vector formula, calculate the radar target signal steering vector, the outer antenna array steering vector and the inner antenna array steering vector respectively; (3) Direct integral solution of steering vector: The radar target signal steering vector is decomposed into the direct product of the outer antenna array steering vector and the inner antenna array steering vector; (4) Establish a cost function: According to the linear constraint minimum variance criterion, the cost function of the outer antenna array weight vector corresponding to the outer antenna array steering vector and the inner antenna array weight vector corresponding to the inner antenna array steering vector is established; (5) Solve the weight vector: (5a) According to the following formula, set the iteration initial value vector of the outer antenna array weight vector: ${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$ Among them, v ₀ represents the iterative initial value vector of the outer antenna array weight vector, a _m represents the steering vector of the outer antenna array, * represents the conjugate operation, ||·|| represents the two-norm operation; (5b) Let ε be the stop iteration parameter, the value range of ε is 0<ε<<1, and << means far less than; (5c) Calculate the iterative initial value vector of the inner layer antenna array weight vector according to the following formula: ${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}$ Among them, u ₀ represents the iterative initial value vector of the inner layer antenna array weight vector, Indicates the sample estimation matrix of the received data covariance matrix of the inner antenna array, v indicates the weight vector of the outer antenna array, L indicates the number of samples, X _i indicates the i-th sample, Represents the coefficient vector of the inner antenna array, a _p represents the steering vector of the inner antenna array, a _m represents the steering vector of the outer antenna array, H represents the conjugate transpose operation, ( ) ^-1 represents the inverse operation; (5d) Calculate the iteration vector of the weight vector of the outer antenna array according to the following formula: ${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$ Among them, v ₁ represents the iteration vector of the outer antenna array weight vector, Represents the sample estimation matrix of the received data covariance matrix of the outer antenna array, u represents the weight vector of the inner antenna array, Represents the coefficient vector of the outer antenna array, H represents the conjugate transpose operation, (·) ^-1 represents the inverse operation, ||·|| represents the two-norm operation; (5e) Determine whether the difference v ₁ -v ₀ between the iterative vector v ₁ of the outer antenna array weight vector and the iterative initial value vector v ₀ of the outer antenna array weight vector satisfies the stop iteration condition of the following formula, if satisfied, The iteration is terminated, and the iteration vector of the outer antenna array weight vector is obtained as the outer antenna array weight vector, and the iterative initial value vector of the inner antenna array weight vector is used as the inner antenna array weight vector; if not satisfied, the outer antenna array weight The iterative vector v ₁ of the vector is used as the iterative initial value vector v ₀ of the new outer antenna array weight vector, and step (5c) is performed until the stop iteration condition is satisfied, and the iteration is terminated, and the iterative vector of the outer antenna array weight vector is obtained as the outer layer antenna array weight vector, the iteration initial value vector of the inner layer antenna array weight vector is used as the inner layer antenna array weight vector; ||v ₁ -v ₀ ||≤ε Among them, v ₁ and v ₀ represent the iteration vector and the initial value vector of the outer antenna array weight vector respectively, ε represents the stop iteration parameter, and the value range of ε is 0<ε<<1, and ||·|| Two-norm operation, << means far less than; (6) Beamforming: Do the direct product operation of the outer antenna array weight vector and the inner antenna array weight vector to obtain the filter weight vector, and use the filter weight vector to weight and sum the data vectors received by the radar to minimize the output power of the radar antenna array , form the main beam in the direction of the desired target, and complete the beamforming. 2. the cyclic joint adaptive beamforming method based on subarray division according to claim 1, is characterized in that, the steering vector formula described in step (2) is as follows: The radar target signal steering vector formula is as follows: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ Among them, a _n represents the steering vector of the radar target signal, j represents the imaginary number unit, d represents the distance between the radar antenna array elements, θ represents the direction of the radar target, sin represents the sinusoidal operation, λ represents the operating wavelength of the radar, and N represents the radar antenna element The number, T represents the transpose operation; The steering vector formula of the outer antenna array is as follows: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ Among them, a _m represents the steering vector of the outer antenna array, j represents the imaginary number unit, d represents the distance between the radar antenna array elements, θ represents the direction of the radar target, sin represents the sine operation, λ represents the working wavelength of the radar, and p represents the radar antenna array The number of array elements contained in the sub-array, M indicates the number of sub-arrays of the radar antenna array, and T indicates the transposition operation; The steering vector formula of the inner antenna array is as follows: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ Among them, a _p represents the steering vector of the inner antenna array, j represents the imaginary number unit, d represents the distance between the radar antenna array elements, θ represents the direction of the radar target, sin represents the sinusoidal operation, λ represents the operating wavelength of the radar, and p represents the radar antenna array The number of array elements contained in the sub-array, T represents the transpose operation. 3. the cyclic joint adaptive beamforming method based on subarray division according to claim 1, is characterized in that, the cost function described in step (4) is as follows: $\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; min</span>}& \mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$ Among them, min represents the operation of minimizing the output power of the radar antenna array under the condition that the expected target signal direction gain is constant, f(u, v) represents the output power of the radar antenna array, u represents the weight vector of the inner antenna array, and v represents the outer layer antenna array weight vector, E represents the expectation operation, ||·|| represents the two-norm operation, H represents the conjugate transpose operation, X represents the radar antenna array data matrix, st represents the constraint operation, and a _p represents the internal Layer antenna array steering vector, a _m represents the outer antenna array steering vector, T represents the transpose operation.