CN112881973A - Self-correction beam design method based on RBF neural network - Google Patents

Self-correction beam design method based on RBF neural network Download PDF

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CN112881973A
CN112881973A CN202110072472.8A CN202110072472A CN112881973A CN 112881973 A CN112881973 A CN 112881973A CN 202110072472 A CN202110072472 A CN 202110072472A CN 112881973 A CN112881973 A CN 112881973A
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周逸凡
王英民
任笑莹
王奇
牛奕龙
诸国磊
郑琨
陶林伟
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Abstract

The invention discloses a self-correction beam design method based on a RBF neural network, which is used for realizing the formation of a fitted beam by using the RBF neural network to approach the optimal weight value solved by an MVDR algorithm. By constructing the RBF neural network, the covariance matrix of the sample is obtained, the optimal weight vector is calculated by using the MVDR algorithm, then the weight iterative correction is completed by adopting the recursive least square method, and finally the optimal beam weight vector is obtained, so that the RBF neural network output, namely the improved array beam output, is obtained. The method has the advantages of rapid RBF neural network approximation, simple structure, strong fault tolerance and induction capability, strong anti-interference performance while reducing the calculation amount of the MVDR algorithm, and capability of rapidly and accurately identifying and orienting incoming wave signals containing interference and noise.

Description

Self-correction beam design method based on RBF neural network
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a self-correcting beam design method.
Background
The neural network is the basis of a deep learning algorithm, is a general term of a class of deep learning algorithm structures which are gradually known in recent years along with the fire and heat of machine learning, and the basic principle is to automatically search inherent rules and basic attributes in a sample by using an information transfer method similar to biological neural network signal transmission, and self-organize and self-adaptively change network parameters and structures so as to achieve the aim of optimizing output. The self-adaption, self-organization and self-learning characteristics of the method enable the method to have good application prospects in signal processing. From the basic model of neural networks, there are mainly: feedforward, feedback, self-organizing, and random networks. These 4 types each have different network models. The feed-forward network mainly comprises a sensor network, a BP network and an RBF network; the feedback network mainly comprises a Hopfield network; the self-organization network mainly comprises an ART network; the random network is mainly a Boltzmann machine network. In systems such as signal processing and pattern recognition, a multi-layer feedforward network is a widely applied model. In practical application, the BP neural network is used mostly, but the BP neural network has the problem of local optimization, and the training speed is slow and the efficiency is low. The RBF neural network is a forward feedback network and is superior to the BP neural network in the aspects of approximation capability, classification capability, learning speed and the like.
The beam forming technology plays an irreplaceable important role in the field of wireless communication, such as array processing of sonar, radar and the like. In general, beamforming can be roughly divided into two categories: conventional beamforming and adaptive beamforming. Conventional beamforming refers to a conventional beamforming technique performed by spatial matched filtering; adaptive beamforming refers to a beamforming technique that adaptively controls a beam by using an algorithm to achieve a certain purpose of suppressing interference. Common beamforming methods are the least mean square error (LMS) algorithm, the Sampling Matrix Inversion (SMI) algorithm, and the minimum variance distortion free response (MVDR) algorithm. The basic principle of the LMS algorithm is based on a steepest gradient descent method, searching is carried out along the negative direction of the gradient estimation value of the weight, the weight is optimal, and adaptive beam forming under the minimum mean square error meaning is realized, but the LMS algorithm cannot balance the contradiction between convergence speed and steady-state error; the SMI algorithm guarantees the gain of a given direction signal according to the maximum signal-to-interference-and-noise ratio criterion, so that the total output power of the array antenna is minimum, and the purpose of suppressing interference is achieved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a self-correction beam design method based on an RBF neural network, which is used for approaching the optimal weight value solved by an MVDR algorithm by the RBF neural network so as to realize the formation of a fitted beam. By constructing the RBF neural network, the covariance matrix of the sample is obtained, the optimal weight vector is calculated by using the MVDR algorithm, then the weight iterative correction is completed by adopting the recursive least square method, and finally the optimal beam weight vector is obtained, so that the RBF neural network output, namely the improved array beam output, is obtained. The method has the advantages of rapid RBF neural network approximation, simple structure, strong fault tolerance and induction capability, strong anti-interference performance while reducing the calculation amount of the MVDR algorithm, and capability of rapidly and accurately identifying and orienting incoming wave signals containing interference and noise.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: constructing an RBF neural network;
the number of array elements is set to be N, N nodes are arranged on an input layer and an output layer of the RBF neural network, and M nodes are arranged on a hidden layer;
covariance matrix R of input layer input signal as array received signal1,R2,…,RNIs represented by R ═ R1,R2,…,RN]；
The radial basis function of the hidden layer adopts a Gaussian function, and the output signal of the hidden layer is expressed as:
Figure BDA0002906369740000021
Figure BDA0002906369740000022
wherein sigmaiFor the variance of the Gaussian function at the i-th neuron node, c, obtained by the least-squares methodiIs the function center point on the ith neuron node;
the output layer is represented as
Figure BDA0002906369740000023
ω11,ω12,…,ωMNThe connection weight from the hidden layer to the output layer;
step 2: designing a beam by using an RBF neural network;
step 2-1: setting RBF neural network parameters:
dividing the training sample X into M classes by using a K-means clustering algorithm; c (M) is the clustering center vector of the mth class, wherein M is 1,2, … and M; the minimum distance between the cluster centers is set as sigma (m); setting a network expected error e;
step 2-2: RBF neural network learning;
step 2-2-1: obtaining a normalized sample rn＝X/||X||；
Step 2-2-2: solving a covariance matrix:
Figure BDA0002906369740000024
k is the fast beat number;
step 2-2-3: computing optimal weight vector by using MVDR algorithm
Figure BDA0002906369740000025
Wopt＝[Wopt1,Wopt2,…,Woptj,…,WoptN]，
Figure BDA0002906369740000031
R is the coordinate vector of the array element as the direction vector of the incident signal, d1,d2,…,dNAs a coordinate vector of the interference source, fsIs the signal frequency of the array element, c is the sound velocity, i is the imaginary number; form a sample pair (R, W)opt) R as input to RBF neural network, WoptAs the output of the RBF neural network; let j equal 1;
step 2-2-4: the jth sample RjInputting RBF neural network to obtain output
Figure BDA0002906369740000032
Step 2-2-5: will be provided with
Figure BDA0002906369740000033
And the optimal weight vector W obtained by calculation in the step 2-2-3optjComparing and calculating the expected error
Figure BDA0002906369740000034
If it is
Figure BDA0002906369740000035
If the error is larger than the expected error e, entering the step 2-2-6, otherwise, entering the step 2-2-7;
step 2-2-6: completing the iterative correction of the weight by using a recursive least square method, and returning to the step 2-2-4;
step 2-2-7: stopping the loop operation, and then
Figure BDA0002906369740000036
As the jth optimal beam output
Figure BDA0002906369740000037
For the jth sample RjAfter the RBF neural network learning is finished, j is added with 1, and the step 2-2-4 is returned to train the next sample; ending the circulation until all samples are traversed;
step 2-3: the optimal beam weight vector obtained in step 2-2
Figure BDA0002906369740000038
To obtain a final output of
Figure BDA0002906369740000039
I.e. the array beam output.
The invention has the following beneficial effects:
the method can clearly find the incoming wave direction of the signal under the conditions of different incident angles of the signal and the interference, and can visually display the interference direction at the groove in the beam diagram when the incident angle of the signal is near 0 degree. Compared with the MVDR algorithm, the self-correction beam forming method based on the RBF neural network has the advantages that the identification force of the incoming wave signal direction is completely the same, the angle resolution force of identifying the interference direction in the beam groove is basically the same, the inverse operation of the covariance matrix is not needed, and the operation speed is greatly improved. Compared with the CBF algorithm, the CBF loses the capability of judging the signal and the interference under the condition that the interference is obviously stronger than the signal, and the method can still more clearly and accurately distinguish the incoming wave direction of the signal and the interference. Therefore, the method has the remarkable advantages of high operation speed, high fitting precision and strong anti-interference capability
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FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a block diagram of the beamformer architecture of the method of the present invention.
FIG. 3 is a diagram of a method for solving optimal weight vectors in beamforming by the RBF neural network according to the present invention.
FIG. 4 is a comparison graph of the MVDR method and the RBF neural network beam forming effect in the present invention, wherein (a) is a beam direction diagram, (b) is an RBF neural network error learning diagram, and (c) is a 6-dimensional weight and network fitting weight diagram.
Fig. 5 is a diagram of incident signals and interference beams at different angles according to an embodiment of the present invention.
FIG. 6 is a comparison graph of the CBF method and RBF neural network beam forming effect according to the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
As shown in fig. 2, in conventional beamforming, processing such as weighting, time delay, summation, etc., is performed on each of a plurality of array elements arranged in a geometric shape to form an output signal having spatial directivity. Beamforming is also a method of appropriately processing a multi-element array in order to provide the desired response to acoustic waves in certain spatial directions. The invention combines a neural network and a beam forming technology, and designs a self-adaptive beam forming method based on an RBF neural network.
When signals originating from the signal sources are transmitted over the channel to each array, there is a relative time delay between the output signals of each array due to the difference in the wave path. Such a time delay is appropriately compensated so that the compensated output signals are simultaneously superimposed in a desired direction to maximize a beam output value in the desired direction. At the same time, the beam outputs in other directions will be smaller, thus suppressing interference signals in undesired directions, which will act as spatial filtering.
The output from the weighted array can be expressed as: y (n) ═ wHx (n), and the matrixing is represented as Y ═ WHAnd (4) X'. Wherein Y ═ Y1,y2,……yN]Denotes the output amplitude of the array, W ═ W1,w2,……wN]A weight vector representing the array, X ═ X1,x2,……xN]An input vector representing N array elements.
If the space has one from theta0Directional narrow-band signals, the signals are transmitted to array elements of the array through the channels, and the response of the array to the signals is a (theta)0) Because of the wave path difference, there is a relative time delay between the output signals of each array element, and therefore, it is necessary to properly compensate for this time delay so that the compensated output signals are superimposed in the same direction as desired. The current weight vector is:
w0＝a(θ0)
at this time, the output vector y (n) is a (θ)0)Ha(θ0) The weighted signal for each channel is maximized and coherently superimposed. Such a beamforming algorithm, referred to as spatial domain matched filtering, may also be referred to as Conventional Beamforming (CBF).
The conventional beam forming generally adopts uniform weighting, is simple to operate and has strong applicability, but the beam has high side lobe and low resolution, and can not effectively inhibit noise interference. In the general case, the input vector of an array element is considered to be the superposition of the incident signal and the additive directional noise interference. Therefore, there are: x (t) ═ as (t) + n (t). When the signal-to-noise ratio is increased, the robustness of the CBF algorithm is reduced. While the Minimum Variance Distortionless Response (MVDR) algorithm satisfies the minimum noise variance criterion, the output power is minimal when both the desired signal and direction are known.
Figure BDA0002906369740000051
The above formula is an expression of the MVDR optimal weight vector, where R ═ E [ X [ ]H(t)X(t)]R is the covariance matrix of the input signal array, and the superscript H indicates the conjugate transpose. It can be derived from the expression of the MVDR weight vector that the size of the weight vector will change with the variance matrix of the noise plus interference, so the MVDR algorithm can maximize the signal-to-noise ratio obtained by the array output in the desired direction, thereby achieving the best beamforming effect.
The weight vector is a nonlinear function of the covariance matrix, the inverse operation of the covariance matrix is needed in the solving process, and the operation amount and the array element number are in a square relation, so that the MVDR algorithm has large calculation amount, can bring difficulty to real-time operation, and is not suitable for the requirement of updating the real-time property of the optimal weight vector. Considering that the RBF neural network is a parallel structure and can quickly approximate the characteristics of a nonlinear function, the MVDR algorithm is improved based on the RBF neural network, namely the RBF neural network is adopted to approximate the weight vector of the MVDR algorithm, the nonlinear mapping process from an array covariance matrix to an optimal weight vector is completed, and the RBF neural network is used for replacing the matrix inversion process of the original MVDR algorithm.
As shown in fig. 1 and 3, a self-correcting beam design method based on an RBF neural network includes the following steps:
step 1: constructing an RBF neural network;
the number of array elements is set to be N, N nodes are arranged on an input layer and an output layer of the RBF neural network, and M nodes are arranged on a hidden layer;
covariance matrix R of input layer input signal as array received signal1,R2,…,RNIs represented by R ═ R1,R2,…,RN]；
The radial basis function of the hidden layer adopts a Gaussian function, and the output signal of the hidden layer is expressed as:
Figure BDA0002906369740000052
Figure BDA0002906369740000053
wherein sigmaiFor the variance of the Gaussian function at the i-th neuron node, c, obtained by the least-squares methodiIs the function center point on the ith neuron node;
the output layer is represented as
Figure BDA0002906369740000054
ω11,ω12,…,ωMNThe connection weight from the hidden layer to the output layer;
step 2: designing a beam by using an RBF neural network;
step 2-1: setting RBF neural network parameters:
dividing the training sample X into M classes by using a K-means clustering algorithm; c (M) is the clustering center vector of the mth class, wherein M is 1,2, … and M; the minimum distance between the cluster centers is set as sigma (m); setting a network expected error e;
step 2-2: RBF neural network learning;
step 2-2-1: obtaining a normalized sample rn＝X/||X||；
Step 2-2-2: solving a covariance matrix:
Figure BDA0002906369740000061
k is the fast beat number;
step 2-2-3: computing optimal weight vector by using MVDR algorithm
Figure BDA0002906369740000062
Wopt＝[Wopt1,Wopt2,…,Woptj,…,WoptN]，
Figure BDA0002906369740000063
R is the coordinate vector of the array element as the direction vector of the incident signal, d1,d2,…,dNAs a coordinate vector of the interference source, fsIs the signal frequency of the array element, c is the sound velocity, i is the imaginary number; form a sample pair (R, W)opt) R as input to RBF neural network, WoptAs the output of the RBF neural network; let j equal 1;
step 2-2-4: the jth sample RjInputting RBF neural network to obtain output
Figure BDA0002906369740000064
Step 2-2-5: will be provided with
Figure BDA0002906369740000065
And the optimal weight vector W obtained by calculation in the step 2-2-3optjComparing and calculating the expected error
Figure BDA0002906369740000066
If it is
Figure BDA0002906369740000067
If the error is larger than the expected error e, entering the step 2-2-6, otherwise, entering the step 2-2-7;
step 2-2-6: completing the iterative correction of the weight by using a recursive least square method, and returning to the step 2-2-4;
step 2-2-7: stopping the loop operation, and then
Figure BDA0002906369740000068
As the jth optimal beam output
Figure BDA0002906369740000069
For the jth sample RjAfter the RBF neural network learning is finished, j is added with 1, and the step 2-2-4 is returned to train the next sample; ending the circulation until all samples are traversed;
step 2-3: the optimal beam weight vector obtained in step 2-2
Figure BDA00029063697400000610
To obtain a final output of
Figure BDA00029063697400000611
I.e. the array beam output.
Through the above steps, under the condition of not defining the number of neurons and the learning rate, when the input is the covariance sample R after the signal normalization, the network can output the optimal weight vector W in the beam forming without supervisionoptAnd improved array beam output results.
The specific embodiment is as follows:
the simulation is carried out aiming at the six-element standard linear array (the array element spacing is half wavelength), Gaussian white noise is taken as noise received by the base array, CW incident signals under the conditions of different signal-to-noise ratios are simulated by utilizing the beam forming algorithm provided by the invention, and the processed results are shown in figures 4, 5 and 6.
Setting parameters: a standard linear array with the array element number of 6 is arranged, the array element spacing is half wavelength, the matrix received noise is Gaussian white noise, the power is 0dB, two CW single-frequency pulse signals with the signal-to-noise ratios of 10dB and 100dB respectively enter the matrix from the directions of-10 degrees and 10 degrees, the signal frequency is 3000Hz, and the sound velocity is 1500 m/s.
The fitting time of the MVDR algorithm beam pattern and the RBF neural network is 2.07 seconds as shown in fig. 4 (a); the variation curve of the error decreasing with the increase of the iteration number is shown in fig. 4(b), fig. 4(c) shows the learning condition of the error between the weight of the MVDR and the weight fitted at the current moment in the training process of the RBF neural network, when the error does not passTraining learning converges to a preset value of 10-2The training is stopped at that moment.
TABLE 1 fitting error of MVDR method and RBF neural network
Figure BDA0002906369740000071
As can be seen from Table 1, the RBF neural network has higher fitting precision for the weight fitting of the MVDR algorithm.
Fig. 5 is a beam pattern obtained by computing and processing interference-containing signals incident from different directions by a beam forming algorithm based on the RBF neural network. Fig. 5(a) and (b) show that when the signal angle is around 0 °, the output power is 0dB, and the position of the notch on the beam pattern is the interference angle, so that the interference and the signal can be visually and clearly distinguished through the beam pattern processed by the algorithm. When the signal is incident from a larger angle, as shown in fig. 5(c), the beam pattern cannot show the interference position at the groove, but the signal can still be clearly resolved.
With the same parameter settings as in fig. 5, the beam pattern of CBF and the beam pattern fitted through RBF neural network are shown in fig. 6 for a monochromatic signal with SNR of 10dB incident from the-10 ° direction and an interfering signal with SNR of 100dB incident from the 10 ° direction.
It can be seen from the above figure that, for signals and interferences incident in two different directions with different signal-to-noise ratios in the same frequency band, the CBF method can only determine whether the signals or the interferences are according to the signal-to-noise ratio, and the beam forming algorithm based on the RBF neural network can still accurately distinguish the signals and the interferences even if the signal-to-noise ratio of the signals is lower than the interferences, and visually display the interferences in the beam grooves. Meanwhile, compared with a CBF algorithm, a beam pattern fitted by the RBF method has a wider main lobe, so that the RBF method has a stronger interference suppression effect on an incident signal under the condition of a smaller signal incident angle.

Claims (1)

1. A self-correction beam design method based on an RBF neural network is characterized by comprising the following steps:
step 1: constructing an RBF neural network;
the number of array elements is set to be N, N nodes are arranged on an input layer and an output layer of the RBF neural network, and M nodes are arranged on a hidden layer;
covariance matrix R of input layer input signal as array received signal1，R2，...，PNIs represented by R ═ R1，R2，...，RN]；
The radial basis function of the hidden layer adopts a Gaussian function, and the output signal of the hidden layer is expressed as:
Figure FDA0002906369730000011
Figure FDA0002906369730000012
wherein sigmaiFor the variance of the Gaussian function at the i-th neuron node, c, obtained by the least-squares methodiIs the function center point on the ith neuron node;
the output layer is represented as
Figure FDA0002906369730000013
ω11，ω12，...，ωMNThe connection weight from the hidden layer to the output layer;
step 2: designing a beam by using an RBF neural network;
step 2-1: setting RBF neural network parameters:
dividing the training sample X into M classes by using a K-means clustering algorithm; the clustering center vector of the mth class is set as c (M), and M is 1, 2. The minimum distance between the cluster centers is set as sigma (m); setting a network expected error e;
step 2-2: RBF neural network learning;
step 2-2-1: obtaining a normalized sample rn＝X/||X||；
Step 2-2-2: solving a covariance matrix:
Figure FDA0002906369730000014
k isFast shooting number;
step 2-2-3: computing optimal weight vector by using MVDR algorithm
Figure FDA0002906369730000015
Wopt＝[Wopt1，Wopt2，...，Woptj，...，WoptN]，
Figure FDA0002906369730000016
R is the coordinate vector of the array element as the direction vector of the incident signal, d1，d2，...，dNAs a coordinate vector of the interference source, fsIs the signal frequency of the array element, c is the sound velocity, i is the imaginary number; form a sample pair (R, W)opt) R as input to RBF neural network, WoptAs the output of the RBF neural network; let j equal 1;
step 2-2-4: the jth sample RjInputting RBF neural network to obtain output
Figure FDA0002906369730000017
Step 2-2-5: will be provided with
Figure FDA0002906369730000018
And the optimal weight vector W obtained by calculation in the step 2-2-3optjComparing and calculating the expected error
Figure FDA0002906369730000019
If it is
Figure FDA00029063697300000110
If the error is larger than the expected error e, entering the step 2-2-6, otherwise, entering the step 2-2-7;
step 2-2-6: completing the iterative correction of the weight by using a recursive least square method, and returning to the step 2-2-4;
step 2-2-7: stopping the loop operation, and then
Figure FDA0002906369730000021
As the jth optimal beam output
Figure FDA0002906369730000022
For the jth sample RjAfter the RBF neural network learning is finished, j is added with 1, and the step 2-2-4 is returned to train the next sample; ending the circulation until all samples are traversed;
step 2-3: the optimal beam weight vector obtained in step 2-2
Figure FDA0002906369730000023
To obtain a final output of
Figure FDA0002906369730000024
I.e. the array beam output.
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CN114594445A (en) * 2022-05-09 2022-06-07 中国人民解放军空军预警学院 Intelligent radar composite interference resisting method and device
CN115952840A (en) * 2023-03-09 2023-04-11 深圳时识科技有限公司 Beam forming method, arrival direction identification method, device and chip thereof

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