CN109194378B - Physical layer safety wave beam shaping method based on linear neural network - Google Patents

Physical layer safety wave beam shaping method based on linear neural network Download PDF

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CN109194378B
CN109194378B CN201810885113.2A CN201810885113A CN109194378B CN 109194378 B CN109194378 B CN 109194378B CN 201810885113 A CN201810885113 A CN 201810885113A CN 109194378 B CN109194378 B CN 109194378B
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雷维嘉
李环
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Chongqing University of Post and Telecommunications
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Abstract

The invention discloses a physical layer safety beam forming method based on a linear neural network, which utilizes the reciprocity of channels in a multi-input single-output system, a single-antenna legal receiving end sends a training sequence, and a multi-antenna sending party secret signal and a weight of artificial noise beam forming are obtained through neural network training. In the invention, three processes of channel estimation, channel state information feedback and beamforming design are combined into a reverse training process by using a linear neural network, only one training sequence is required to be sent, and feedback is not required.

Description

Physical layer safety wave beam shaping method based on linear neural network
Technical Field
The invention belongs to the field of information communication, and particularly relates to a method for realizing confidential transmission of information by designing a beam forming vector of a useful signal and artificial noise by using a linear neural network.
Background
The physical layer security technology utilizes the characteristics of time-varying property, randomness, reciprocity and the like of a wireless channel to realize the secret transmission of information from a physical layer. The difference between the transmission quality of a legal channel and the transmission quality of an eavesdropping channel is manufactured and enlarged by utilizing a signal processing technology, and the acquisition of the secret capacity is an important link for realizing the safety of a physical layer, wherein the most commonly used technology is a multi-antenna beam forming technology and an artificial noise auxiliary interference technology. In the physical layer security, the beam forming technology is utilized, the signal strength of a legal user can be improved, and the quality of a received signal of an eavesdropper is reduced, so that the capacity difference between a legal channel and an eavesdropping channel is formed, and the capability of transmitting confidential information is obtained. With multi-antenna beamforming, the achievable security performance is related to the Channel State Information (CSI) available to the sender. And when the interception channel CSI can not be obtained at all, the beamforming can not be designed to minimize the intensity of the received signal of an eavesdropper, and at the moment, the adoption of artificial noise is an effective means for improving the safety performance. The sender transmits both the secret information and the artificial noise, which is located in the orthogonal space of the channel between the sender and the legitimate receiver. Due to the fact that the characteristics of the legal channel and the characteristic of the eavesdropping channel are different, the eavesdropping device can be guaranteed to be interfered while the legal receiver is not affected by artificial noise, and safety performance is enhanced. In the existing research on physical layer security by using a beamforming technology, it is generally assumed that accurate legal channel CSI is available, and different beamforming and artificial noise schemes are designed according to the acquisition condition of eavesdropping channel CSI. For a scheme designed under the condition that accurate CSI can be obtained, if the scheme is applied to a scene with errors in CSI, the performance of an algorithm is reduced to a certain extent. In the scheme with robustness designed under the condition of inaccurate interception of the channel CSI, the performance is relatively reduced under the condition that the interception of the channel CSI has errors, but the complexity of the algorithm is increased, and meanwhile, if the legal channel CSI has errors, the safety performance is also obviously reduced. Existing beamforming designs generally rely on the CSI of the channel. The CSI is generally obtained by a receiving end through channel estimation, the CSI is fed back to a transmitting end through a feedback channel, the transmitting end carries out beamforming design, and the channel estimation and beamforming design are carried out separately. Feedback overhead exists in a CSI feedback link, the capacity of a feedback channel can limit the accuracy of the feedback CSI, and meanwhile deviation exists in channel estimation, so that the beamforming performance is influenced. However, in a Multiple-Input Single-Output (MISO) channel, because there are Multiple transmit antennas, training sequences transmitted by each antenna are orthogonal to each other when CSI estimation is performed, channel overhead for transmitting the training sequences is large, and meanwhile, a receiving end needs to feed back CSI of Multiple channels obtained through estimation, and the feedback overhead is also large, which may greatly affect transmission efficiency of a system.
The neural network is a powerful machine learning method, is widely applied and has the characteristic of storing and utilizing empirical knowledge. When the neural network is applied to information processing engineering, a large-scale parallel processing mode can be adopted, and the neural network has good performance in the aspects of fault tolerance, self-adaptive learning and self-organization capability. The linear neural network is a simple neuron network, and the structure of the linear neural network is shown in fig. 3. The network is composed of one or more linear neurons, the transfer function is linear, and functions of classification, fitting, approximation and the like can be realized. The approximation characteristic of the linear neural network is that the actual output signal is continuously approximated to the expected signal by continuously adjusting the weight in the learning process. These characteristics enable the linear neural network to be applied in the design of beamforming.
Disclosure of Invention
The invention aims to provide a design method of sending end secret signals and artificial noise beamforming by combining a linear neural network, which does not depend on CSI of a channel and has lower realization complexity.
The invention for realizing the purpose adopts the following technical scheme: during training, a single-antenna legal receiver sends a training sequence to train a transmitter secret signal and an artificial noise beam forming weight of a multi-antenna by utilizing reciprocity of a channel, during secret information transmission, beam forming is carried out on the secret signal and the artificial noise by utilizing the weight obtained by training, and a training model is as shown in figure 2. The specific steps of the training process are as follows:
(1) transmitting a training signal sequence at a legal receiver, and determining a signal received by the transmitter after channel transmission, namely an input signal of a linear neural network;
(2) determining the expected output of the linear neural network according to the requirement of the transmitter on the beam forming weight of the confidential signal;
(3) determining expected output of a linear neural network according to the requirement of a sender on artificial noise beamforming weight;
(4) and (3) constructing a linear neural network model according to the input signals and the expected output in the steps (1), (2) and (3), and training the network.
Specifically, the training signal sequence in step (1) is generated by using a pseudo-random signal generator, and the signal can also be synchronously generated at the sender.
Specifically, the expected output of the linear neural network in step (2) is a training signal sequence sent by a legal receiver. The training purpose is to make the combined received signal from the sender as close as possible to the training signal from the legitimate receiver to ensure the minimum error between the received signal from the legitimate receiver and the security signal from the sender during the forward transmission of the security signal.
Specifically, the expected output of the linear neural network of step (3) is zero. The training purpose is to make the power of the combined received signal at the sender as low as possible to ensure that the design of the artificial noise beamforming weight minimizes the leakage at the legitimate receiver.
Further, the invention also includes a step of normalizing the weight value trained by the network. Ensuring that the beamforming process does not change the total power of the signals.
Further, a linear transfer function purelin is used in an output node of the linear neural network.
Compared with the conventional design method of the secret signal and the artificial noise beamforming, the design method of the secret signal and the artificial noise beamforming in the invention does not depend on the CSI of a channel, and the weight of the safe beamforming is obtained by adopting the training of a linear neural network. During training, a single-antenna legal receiving end sends a training sequence to train a secret signal and an artificial noise beam forming weight of a sending party of the multi-antenna by using reciprocity of a channel, and beam forming is carried out on the secret signal and the artificial noise by using the weight obtained by training during secret information transmission. The invention combines three processes of channel estimation, channel state information feedback and beam forming design into a reverse training process by using a neural network, only needs to send a training sequence, has small training overhead, does not need feedback, and realizes complexity reduction, thereby being significant for practical application.
Drawings
FIG. 1 is a system model of the present invention;
FIG. 2 is a block diagram of a model during reverse training;
FIG. 3 is a linear neural network structure;
FIG. 4 is a comparison of bit error rates of Bob when weighted using weights obtained from linear neural network training and when MRT transmit diversity;
fig. 5 shows the MSE between the transmit beamforming weight and the MRT transmit weight obtained by training varies with the signal-to-noise ratio;
FIG. 6 is a simulation result of Bob's average bit error rate when training sequences of different lengths are used;
FIG. 7 is a comparison between the error code performance of Bob and Eve and the scheme when the legal channel CSI is accurately known in the present invention;
FIG. 8 is a graph showing the relationship between the privacy rate and the power allocation factor α comparing the simulation results of the present invention and the conventional scheme under two CSI conditions;
fig. 9 is a graph showing the relationship between the secret rate and the total power P of the transmitting end by comparing the simulation results of the present invention and the conventional scheme under two CSI conditions.
Detailed Description
The present invention is analyzed in detail below with reference to the accompanying drawings.
The present invention includes a wireless communication model of a sender Alice, a legitimate receiver Bob and an eavesdropper Eve, as shown in fig. 1. In the model, Eve is a passive eavesdropper and does not transmit signals, so Alice cannot obtain CSI of the eavesdropper channel. Alice has N antennas (N > 1), and Bob and Eve are equipped with single antennas. The invention uses a safe transmission scheme of sending beam forming and artificial noise, Alice sends the artificial noise while sending the secret signal, and the beam forming vectors of the secret signal and the artificial noise are obtained through a linear neural network. The secret signal and the artificial noise are s and z, respectively, and are both unit power. Suppose Alice has a total transmission power P, where the security signal is transmitted at a power PsThe power of transmitting the artificial noise is Pz. Defining a power allocation factor alpha as PsRatio to P, Ps＝αP，Pz＝(1-α)P。
Alice sends a signal of
Figure BDA0001755441650000031
Wherein ws＝[ws1,ws2,…,wsN]TBeamforming vectors, w, for secret signalsz＝[wz1,wz2,…,wzN]TThe wave beam forming vector of the artificial noise satisfies | | ws||＝1，||wzWhere | l | · | represents the 2-norm of the vector.
After being transmitted through the channel, the signals received by Bob and Eve are respectively
Figure BDA0001755441650000032
Figure BDA0001755441650000033
Wherein h is [ h ]1,h2,…,hN]TIs the channel coefficient vector between Alice and Bob, g ═ g1,g2,…,gN]TIs the eavesdropping channel coefficient vector between Alice and Eve, nB、nEComplex additive white Gaussian noise at Bob and Eve respectively, and the variance is
Figure BDA0001755441650000034
Instantaneous received signal-to-noise ratio at Bob is
Figure BDA0001755441650000041
Legal channel capacity of
Figure BDA0001755441650000042
Eve has an instantaneous received signal-to-noise ratio of
Figure BDA0001755441650000043
Eavesdropping on a channel capacity of
Figure BDA0001755441650000044
Can achieve a secret rate of
RS＝max{0,CB-CE} (8)
In the case that the CSI of the eavesdropping channel cannot be obtained, the conventional design method is to generate omnidirectional artificial noise to interfere with the eavesdropper, but Bob should have no influence, that is, the power of the artificial noise at Bob should be 0. The beamforming vector of the secret signal should be such that the signal power at the legitimate receiver is maximized, i.e. wsc＝h*/| h |, this li*Representing the conjugate transpose of the vector. And the artificial noise beamforming should make the artificial noise be in the main channel null space, i.e. beamforming matrix
Figure BDA0001755441650000045
Should satisfy hTWzcz is 0, where
Figure BDA0001755441650000046
A vector of gaussian random noise is generated,
Figure BDA0001755441650000047
representing a set of complex numbers. It can be seen that the basis of the beamforming design of the secret signal and the artificial noise is the CSI of the channel, and the CSI needs to be obtained through channel estimation and feedback links.
In the invention, the design of beam forming is not alreadyOn the premise of obtaining CSI, Bob sends a training signal sequence by using reciprocity of channels, a linear neural network is adopted to train according to a certain criterion to obtain a beam forming vector of a secret signal and artificial noise, and a training model is shown in FIG. 2. Assuming that the training signal is a unit power signal xBjWhere j is 1,2, …, L is the training symbol number, and L is the training sequence length, that is, the number of training samples input by the neural network in the next section of the present invention. x is the number ofBjGenerated using a pseudo-random signal generator, the signals can also be generated synchronously at Alice. x is the number ofBjThe signal received by Alice after channel transmission is
Figure BDA0001755441650000048
Wherein P isBIs the power at which Bob transmits the training signal sequence, nAIs an N x 1-dimensional complex additive white Gaussian noise vector at Alice, assuming that the channel noise power at Alice and Bob is the same, i.e., NAThe variance of the middle element is
Figure BDA0001755441650000049
Alice weights and combines the signals received by each antenna by using the weighting vector w, and the combined signal is obtained as
Figure BDA0001755441650000051
Where the noise n ═ w in the combined signalTnAIs a linear combination of complex Gaussian noise, still complex Gaussian noise, with a variance of
Figure BDA0001755441650000052
We adopt some criterion to train weight w to make the weighted combined signal yAjAnd transmit signal xBjAnd certain requirements, such as minimum mean square error, are met. If the signal x is to be detectedBjInstead, the forward transmission sent by Alice to Bob uses the same weight to the signalThe weighting processing is carried out, so that the signal received at Bob is
Figure BDA0001755441650000053
Compared with the equation (10), the signal portions in the two equations are the same, and the noise has the variance of
Figure BDA0001755441650000054
Complex gaussian noise. If the weight value w can enable yAjIf certain training criteria are met, y can be made to be equalBjThe training criteria are met. Therefore, when the channel has reciprocity, the beamforming weights obtained by training in the direction opposite to the data transmission direction are equivalent to training in the data transmission direction. In the MISO system, the weight is adjusted at the transmitting end during forward training, the receiving end is required to feed back the received signal to the transmitting end without error, not only is feedback channel resource consumed, but also the training time is prolonged due to the delay of feedback, and the realization is complex. And the reverse training does not need feedback, and the realization is simple.
In the invention, the approximation characteristic of the linear neural network is utilized, the weight value is continuously adjusted in the learning process, so that the actual output signal continuously approximates to the expected signal, and the finally obtained weight value is the required beamforming weight value. In FIG. 3, uiIs the input, i.e. the received signal, w, of each antenna of AliceiIs the weight from input to neuron, b is the bias, the output of neuron is
Figure BDA0001755441650000055
The output node uses a linear transfer function purelin, and the input and the output of the output node are simple proportional functions. The final output of the linear network is
y＝purelin(v) (13)
And a training process is needed again after the channel changes obviously. Need in neural network trainingAnd carrying out multiple iterations, wherein the weight value is gradually converged in the iterations. Let the input vector of the mth iteration in a certain training be u (m) ═ u1(m),u2(m),…,uN(m)]The network connection weight vector is w (m) ═ w1(m),w2(m),
,wN(m)]The corresponding network output is y (m), the expected output of the network is d (m), the error between the actual output of the network and the expected output is e (m) ═ d (m) -y (m), m ═ 1,2, … are training iterations. The LMS learning rule adjusts the weights and biases of the network according to the errors, and reduces the mean of the sum of squares of the errors, i.e., minimizes the mean square error. Mean square error of
Figure BDA0001755441650000056
Wherein L is the number of input training samples. According to the gradient descent method, the adjustment rule of the network weight and the bias is
w(m+1)＝w(m)+ηu(m)Te(m) (15)
b(m+1)＝b(m)+ηe(m) (16)
Where η is the learning rate, which determines the convergence rate of the network and the accuracy of the converged weights.
Comparing fig. 2 with fig. 3, it can be seen that the left part of fig. 2 is a linear neural network with N nodes in the input layer and 1 node in the output layer. The input layer signal of the neural network is the training signal sequence received by each antenna of Alice, and is written into a matrix form
Figure BDA0001755441650000061
R＝[r1,r2,…,rL]In one row rl(L ═ 1,2, …, L) is a training sample, which is a training input vector, which is a received signal vector corresponding to one transmitted symbol received at each antenna of Alice, and has a total of L training vectors.
For a secret signal, the invention uses a beamforming vectorThe amount is such that the received signal-to-noise ratio at Bob is maximized, i.e., the signal received at Alice (the actual output of the network) is expected to be as close as possible to the training signal transmitted by Bob during training, so that the error between the received signal at Bob and the security signal transmitted at Alice is minimized when the security signal is being transmitted in the forward direction. Therefore, when the beamforming weight of the secret signal is trained, the expected output d ═ d of the neural network1,d2,…,dL]For training signal xB＝[xB1,xB2,…,xBL]。
For artificial noise, the present invention wants to minimize the leakage at the legal end by using beamforming, that is, it is desirable to have the power (the actual output of the network) as low as possible after combining the received signals at Alice during training, so that the desired network output signal is zero, i.e., d is 0.
The steps of the linear neural network using the LMS algorithm to train the weights are summarized as follows:
(1) initializing, and assigning a smaller random variable to the weight value and the bias;
(2) input samples rlCalculating the actual output and the mean square error based on the given desired output
Figure BDA0001755441650000064
(3) If it is
Figure BDA0001755441650000065
If the training frequency is less than a certain preset smaller value (such as epsilon) or the training frequency reaches the preset maximum training frequency, stopping training to obtain the connection weight and the bias of the input layer and the output layer, otherwise, continuing the step (4);
(4) and (4) calculating new connection weight and bias by using an LMS algorithm, and returning to the step (2).
Finally, the weight w trained by the network needs to be normalized, that is to say
Figure BDA0001755441650000062
Ensuring that the beamforming process does not change the total power of the signals.
The present invention will be described in further detail below with reference to the accompanying drawings. In the simulation, the number of antennas N of Alice is 4; all channels are Rayleigh flat fading channels, elements in a legal channel coefficient vector h and an eavesdropping channel coefficient vector g are complex Gaussian random variables which are independently and identically distributed, the mean value is 0, and the variance is 1; the channel noise variance at each antenna is the same, all normalized to 1, i.e.
Figure BDA0001755441650000063
During reverse training, Bob transmits training sequence with the same power as Alice transmits secret signal, i.e., Ps＝PB。
Fig. 4 shows a comparison of the error performance of Bob when weighted with weights obtained by linear neural network training and the error performance of Bob when transmitting diversity with Maximum Ratio Transmission (MRT) having the best performance. In simulation, the modulation mode is QPSK modulation, the training sequence length of the neural network is 100, and when MRT is adopted, the transmission weight is wMRT＝h*The figure shows that the performance of signal transmission beamforming by using the weight obtained by the reverse training of the linear neural network is very close to the performance of MRT.
FIG. 5 shows a transmit beamforming weight vector w obtained by training when the channel variation is given 20000 timessAnd MRT sends weight value wMRTMean Square Error (MSE) values between. It can be seen that the difference between the weight obtained by training and the optimal weight is small, and PsThe higher the error, the smaller. The simulation results of fig. 4 and 5 prove that the method for reverse training of weights by using a neural network is feasible and effective.
Fig. 6 shows the simulation result of the average bit error rate of Bob when training sequences of different lengths are used, and the modulation scheme is still QPSK modulation. It can be seen that as the length of the training sequence increases, the average bit error rate is smaller, because the longer the training sequence is, the smaller the error of the obtained beamforming weight is. However, even if the length of the training sequence is only 10, the bit error rate which is very close to the length of the training sequence of 100 can still be obtained, which shows that a relatively accurate weight can be obtained under a very short training sequence length, and shows that the neural network algorithm adopted by the invention has very high learning efficiency and very small training overhead, which is very significant for practical application.
Fig. 7 is a secure transmission scheme of secret signal beamforming plus artificial noise according to the present invention, where when QPSK modulation is used, the bit error rate simulation results of a legal receiver Bob and an eavesdropper Eve have a power allocation factor α of 0.8, and beamforming of secret signal and artificial noise is obtained by using a neural network training method, where the training sequence length is 100. Meanwhile, the performance of the conventional beam forming and artificial noise safe transmission scheme is simulated, and the beam forming vector w of the confidential signal of the transmission scheme issc＝h*/| h |, artificial noise beamforming matrix
Figure BDA0001755441650000071
Satisfy hTWzc0. In simulation, the invention considers the condition with the least adverse security, namely that Eve not only knows the CSI of the eavesdropping channel, but also knows the beamforming vector of the secret signal sent by Alice, and judges after equalizing the received signal according to the beamforming vector. It can be seen that the bit error performance of Bob and Eve in the invention is very close to the comparison scheme when the legal channel CSI is known accurately, the bit error rate of Eve is much higher than Bob, about 0.5, and basically cannot decrease with the increase of the transmission power, which indicates that the safe transmission scheme of the invention is effective.
Fig. 8 and fig. 9 show simulation results of the secret rate, and simultaneously compare the simulation results of the conventional beamforming and the artificial noise secure transmission scheme under the two CSI conditions, that is, the CSI of the legal channel can be accurately obtained, and Bob performs minimum mean square error estimation on the channel, and then feeds back the estimated CSI to Alice (there is no feedback channel capacity limitation in the simulation, and the fed-back CSI is not quantized). The length of the training sequence used for estimating a channel in the weight training and the 2 nd comparison scheme of the invention is both 100. However, in contrast to scheme 2, Alice sequentially transmits training sequences through 4 transmit antennas, so the total training length is 400, whereas Bob only needs to transmit training sequences, and the total training sequence length is 100. The secret rate is obtained by averaging Monte Carlo simulation results of 20000 random channel changes. Fig. 8 shows the simulation result of the secret rate when the total power P of the transmitting end is 5dBW and the power distribution factor α changes. It can be seen that the secret rate obtained by the present invention is slightly lower than the secret rate when the channel CSI is accurately obtained, but the gap decreases as the power allocation factor α increases. This is because in the simulation, the power of the training signal sequence sent by Bob is set to be equal to the power of the secret signal sent by Alice, when α increases, the power of the secret signal increases, the power of the training signal also increases, the signal-to-noise ratio of the training signal received by Alice increases correspondingly, the weight training error decreases, the weight accuracy increases, and therefore, the performance gap with the scheme under the ideal CSI decreases. Compared with the comparison scheme 2 which needs channel estimation, the security rate of the invention is better than that of the comparison scheme 2. Fig. 9 shows the simulation result of the secret rate when the power allocation factor α is 0.7 and the total power P of the transmitting end changes. It can be seen that the security rate obtained by the present invention is slightly lower than the security rate when the channel CSI is accurately obtained, and the security rate is better than that of the comparison scheme 2 that needs to perform channel estimation.

Claims (6)

1. A physical layer safe beam forming method based on a linear neural network is characterized in that: a safe transmission scheme of sending beam forming and artificial noise is used, namely, a sender sends a secret signal and simultaneously sends the artificial noise; the beam forming vectors of the secret signals and the artificial noise are obtained through linear neural network training, during training, a single-antenna legal receiver sends a training sequence to train a sender secret signal and an artificial noise beam forming weight of a multi-antenna, and during secret information transmission, the weight obtained through training is used for carrying out beam forming on the secret signal and the artificial noise; the specific steps of the training process are as follows:
(1) transmitting a training signal sequence at a legal receiver, and determining a signal received by the transmitter after channel transmission, namely an input signal of a linear neural network;
(2) determining the expected output of the linear neural network according to the requirement of the transmitter on the beam forming weight of the confidential signal;
(3) determining expected output of a linear neural network according to the requirement of a sender on artificial noise beamforming weight;
(4) and (3) constructing a linear neural network model according to the input signals and the expected output in the steps (1), (2) and (3), and training the network.
2. The physical layer secure beamforming method based on linear neural network of claim 1, wherein: the training signal sequence in step (1) is generated by a pseudo-random signal generator, and the signal can also be synchronously generated at the sender.
3. The physical layer secure beamforming method based on linear neural network as claimed in claim 2, wherein: and (3) the expected output of the linear neural network in the step (2) is a training signal sequence sent by a legal receiver.
4. The physical layer secure beamforming method based on linear neural network of claim 3, wherein: and (3) the expected output of the linear neural network is zero.
5. The physical layer secure beamforming method based on linear neural network according to any of claims 1 to 4, wherein: and the step of normalizing the weight value trained by the network is also included.
6. The physical layer secure beamforming method based on linear neural network of claim 5, wherein: a linear transfer function purelin is used in an output node of the linear neural network.
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