CN114697103B - Physical layer secure transmission transmitting weight vector calculating method based on mirror image operation - Google Patents

Physical layer secure transmission transmitting weight vector calculating method based on mirror image operation Download PDF

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CN114697103B
CN114697103B CN202210305016.8A CN202210305016A CN114697103B CN 114697103 B CN114697103 B CN 114697103B CN 202210305016 A CN202210305016 A CN 202210305016A CN 114697103 B CN114697103 B CN 114697103B
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weight vector
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张学敬
陈阳
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/16—Implementing security features at a particular protocol layer
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/20—Network architectures or network communication protocols for network security for managing network security; network security policies in general
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Abstract

The invention discloses a physical layer safe transmission transmitting weight vector calculating method based on mirror image operation, and belongs to the field of signal safe transmission. The invention can generate an infinite set of new transmission weight vectors through iteration by only needing an initial set of transmission weight vectors. The calculation amount is less, and a new transmitting weight vector can be obtained through simple matrix operation. Compared with polygonal construction methods and other methods, the operation time of the method is greatly reduced. With a larger number N of transmit antennas, a shorter run time can still be maintained. Under the condition of single path, the invention has the security similar to ASM and multipath simulation effect, can accurately receive receipts in the azimuth of the receiver, and can maintain the error rate at a very high value in other azimuth, and an eavesdropper can not accurately receive and decode information.

Description

Physical layer secure transmission transmitting weight vector calculating method based on mirror image operation
Technical Field
The invention belongs to the field of signal safety transmission, in particular to a method based on polygon mirror image operation, which can quickly generate a weight vector design for signal safety transmission.
Background
With further development of the information age, wireless communication technology has been widely used in the fields of education, medical treatment, military, and the like. However, as the application level field is continuously expanded, potential safety hazards of information in the transmission process are gradually exposed. Both eavesdropping and attacks occur during the information transfer process. In order to realize safe transmission of signals and ensure the safety and confidentiality of information in the transmission process, a digital encryption technology or a communication confidentiality protocol is generally adopted. Currently, researchers are going into intensive research from the physical layer aspect, which is divided into two aspects of adjusting channel capacity and designing an actual communication system. In a phased array based secure communication system, the information needs to be weighted by weight vectors after being processed. Designing time-varying weight vectors becomes an important ring in encrypted communications. The design method based on the polygonal structure is a simple and rapid method for constructing the transmitting weight vector. The invention changes the phase angle of the vector by mirroring the vector polygon on the basis of the polygon structure, and finally rapidly obtains the time-varying transmitting weight vector.
Disclosure of Invention
The invention provides a new method for transmitting weight design, firstly, a group of known phase solutions are designed through a polygon structure, and on the basis, the vector sum is not changed due to mirror image operation, and under the condition of ensuring the solutions, a group of new transmitting weight vectors can be obtained through one or more groups of edges of the mirror image vector polygons.
In order to concretely realize the scheme is as follows: a physical layer security transmission transmitting weight vector calculating method based on mirror image operation comprises the following steps:
step 1: for MISO downlink systems, where N transmit antennas, 1 receiver and Q eavesdroppers are equipped; data y transmitted by QPSK modulation model k (k) The method comprises the following steps: y is k (k)＝h H w (k) x (k) +eta (k), wherein w (k) is a transmission weight vector, x (k) is a transmission symbol, h is a channel vector, and eta (k) is Gaussian random noise; specifically, the weight vector w (k) is expressed as
Figure BDA0003564459260000011
Wherein->
Figure BDA0003564459260000012
Figure BDA0003564459260000015
φ n For vector equation->
Figure BDA0003564459260000013
In which, to simplify the expression, |h 0 I is the beam gain of the receiver, N is the number of antennas, h n N-th element representing channel vector h, n=1, …, N;
step 2: obtaining a group of initial transmitting weight vectors by polygon construction method
Figure BDA0003564459260000014
After the initial transmit weight vector is obtained, the complex vector set is constructed in reverse>
Figure BDA0003564459260000021
Wherein (1)>
Figure BDA0003564459260000022
Figure BDA0003564459260000023
Representing the operation of taking the real part,/->
Figure BDA0003564459260000024
Representing an imaginary part taking operation;
step 3: combining complex vector sets v pre Randomly dividing the data into different subgroups, each subgroup taking the vector sum as a mirror image axis, carrying out mirror image operation, and changing the phase of the vector to obtain a new transmitting weight vector of each subgroup;
step 4: obtaining all transmitting full vectors of all subgroups, sequentially combining, and extracting phi in the combined transmitting full vectors n By means of
Figure BDA0003564459260000025
Calculating new transmission weights, namely: />
Figure BDA0003564459260000026
/>
Step 5: and repeating the flow by taking the transmitting weight of the previous time as an initial weight vector at each time, and iterating to obtain a new transmitting weight vector.
Compared with the prior art, the technology of the invention has the following advantages:
only an initial set of transmit weight vectors is needed to iteratively generate an infinite set of new transmit weight vectors. The calculation amount is less, and a new transmitting weight vector can be obtained through simple matrix operation. Compared with polygonal construction methods and other methods, the operation time of the method is greatly reduced. With a larger number N of transmit antennas, a shorter run time can still be maintained.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of the present invention in a mirror operation;
fig. 3 is a constellation diagram of the data received by the receiver (Bob) and eavesdropper (Eve) on the basis of the invention using QPSK modulation;
fig. 4 is a constellation diagram of the data received by the receiver (Bob) and eavesdropper (Eve) on the basis of the present invention using 16QAM modulation;
fig. 5 shows the bit error rate at the receiver (Bob) end of the present invention compared to the polygonal construction method under different signal-to-noise ratios.
Fig. 6 shows the bit error rate at the eavesdropper (Eve) end of the present invention compared to the polygonal construction method under different signal-to-noise ratios.
FIG. 7 is a graph showing the comparison of the calculation time of the present invention with the polygon construction method at different N values.
Fig. 8 shows the bit error rate at the receiver (Bob) end of the present invention at different azimuth angles from the polygonal construction method and ASM in the single path case.
Detailed Description
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, providing an initial set of transmitting weight vectors through a polygon construction method.
Considering a MIS0 downlink system equipped with N transmit antennas, the transmitted data can be expressed as:
y d (k)＝h H w(k)x(k)+η(k)
wherein w (k) is a transmission weight vector, x (k) is a transmission symbol, eta (k) is Gaussian random noise, h is a channel vector, and the expression is as follows:
Figure BDA0003564459260000031
L d is the number of paths, alpha l For the gain of the first path, ψ l The departure angle (AoD) of the first path, a (ψ), is the array guide vector, expressed as follows:
Figure BDA0003564459260000032
lambda is the wavelength and d represents the distance between adjacent sensors.
Thus, solving the transmit weight problem may be translated into solving an equation:
Figure BDA0003564459260000033
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA00035644592600000312
the initial transmit weight vector is obtained as: />
Figure BDA0003564459260000035
Step 2, constructing complex vectors
Figure BDA0003564459260000036
Wherein v is n Is->
Figure BDA0003564459260000037
Two-dimensional coordinate representation of (i.e.)
Figure BDA0003564459260000038
Setting a permutation matrix P, and randomly dividing complex vector groups into K groups, namely:
Figure BDA0003564459260000039
wherein P is an N×N permutation matrix.
And 3, finding a holder matrix of each complex vector group.
Defining each complex vector group
Figure BDA00035644592600000310
Is s k For each complex vector group, the sum, i.e.:
Figure BDA00035644592600000311
for each complex vector set there is mathematically a householder matrix:
Figure BDA0003564459260000041
Figure BDA0003564459260000042
so that
Figure BDA0003564459260000043
With respect to s k Is the mirror vector of:
Figure BDA0003564459260000044
since the mirror axis is the sum of the vector sets, the vector sum after mirror remains unchanged, as will be explained in more detail in fig. 2.
And 4, constructing an integral mirror image matrix Y. Integrating the householder matrix of each complex vector group to obtain an overall mirror matrix as follows:
Figure BDA0003564459260000045
and 5, restoring the mirrored complex vector group according to the original sequence, and calculating to obtain a new transmitting weight vector.
Right multiplying the mirrored matrix by the permutation matrix to obtain a new complex vector group:
Figure BDA0003564459260000046
from the following components
Figure BDA0003564459260000047
And->
Figure BDA0003564459260000048
The new transmit weight vector is obtained as:
Figure BDA0003564459260000049
and 6, repeating the operation at each time, and iterating to obtain a new transmission weight vector by taking the transmission weight at the previous time as an initial weight vector.
Simulation conditions and simulation data processing
1. Simulation conditions
The simulation parameters are shown in table 1:
table 1 simulation parameter table
Figure BDA00035644592600000410
Figure BDA0003564459260000051
2. Simulation data processing
Simulation 1, the invention adopts QPSK modulation and 16QAM modulation to transmit information, and verifies the algorithm security.
Setting 1 receiver (Bob) and 2 eavesdroppers (Eve), transmitting data by different transmission weight vectors constructed at different times, receiving information being shown by using constellation diagrams, simulation results being shown in fig. 3 and 4, table 2 being the first four time points
Figure BDA0003564459260000052
Where k=0 is the initial transmit weight based on the polygon construction method and k=1, 2,3 is the new transmit weight constructed using the present invention. Fig. 3 is a constellation diagram using QPSK modulation, and fig. 4 is a constellation diagram using 16QAM modulation.
TABLE 2 initial transmit weights and transmit weights for the first 3 moments
Figure BDA0003564459260000053
Figure BDA0003564459260000061
From the simulation result, the generated transmitting weights at different time points are completely random, so that the safety of data transmission is ensured. This is also shown in fig. 3 and 4, where red is the data received by the receiver (Bob) and green and blue is the data received by the eavesdropper (Eve), whose constellation is completely distorted and cannot decode the correct data.
Simulation 2, bit error rate simulation. Further specifically explaining the security of the algorithm under different signal to noise ratios.
The SNR is set from-5 dB to 20dB, probability statistics is applied to calculate and calculate the error rate of the receiver and the eavesdropper under different SNRs, and simulation results are shown in figures 5 and 6. Fig. 5 bit error rate at receiver (Bob) and fig. 6 bit error rate at eavesdropper (Eve).
From simulation results, the error rate of the receiver is higher under the condition of low signal-to-noise ratio, and the error rate is gradually reduced and maintained at a lower level along with the increase of the signal-to-noise ratio. This is theoretically normal. The eavesdropper maintains a very high error rate at both low and high signal-to-noise ratios, indicating that the eavesdropper cannot decode the data correctly at any signal-to-noise ratio.
And 3, simulating timeliness. The present invention and the polygon construction method are compared in calculation time.
The time point is set to 200, the number of transmitting antennas N is set to 100 to 2000, the step length is 50, and the running time of the two methods is calculated, as shown in fig. 7.
Compared with a polygonal construction method, the simulation result shows that the method has the advantages that the running time is greatly reduced, even when the N value is higher, the running time can still be kept lower, and the method is rapid and efficient.
And 4, simulation of single-path safety. The invention is compared with the polygonal construction method and ASM in a single path.
The invention is not only suitable for information security transmission under multipath, but also has good security and high efficiency under single path.
The Antenna Subset Modulation (ASM) technology adjusts the activation of the antennas during the transmission process to achieve the purpose of safe transmission. Setting a channel vector:
h＝a(θ T )
θ is the off angle (AoD), a (θ) is the array steering vector, expressed as follows:
Figure BDA0003564459260000062
where λ is the wavelength and d represents the distance between adjacent sensors.
The signal-to-noise ratio (SNR) is set to 10dB, the receiver is fixed at 60 °, and an eavesdropper breaks the parsed data from other angles. Setting the azimuth angle as [0 degrees, 180 degrees ], calculating the error rate under different angles, and the simulation result is shown in figure 8.
As can be seen from simulation results, the invention has the security similar to ASM and multipath simulation effects under the single-path condition, can accurately receive receipts in the azimuth of the receiver, and can not accurately receive and decode information by an eavesdropper under the other azimuth with the error rate maintained at a high value.
In summary, under the condition that a set of initial transmission weights are known, the invention can quickly construct a new transmission weight vector, and can safely transmit information under the conditions of single path and multiple paths.

Claims (1)

1. A physical layer security transmission transmitting weight vector calculating method based on mirror image operation comprises the following steps:
step 1, providing a group of initial transmitting weight vectors through a polygon construction method;
in a MISO downlink system equipped with N transmit antennas, considering a typical phased array structure, the transmitted data is expressed as:
y d (k)＝h H w(k)x(k)+η(k)
wherein w (k) is a transmission weight vector, x (k) is a transmission symbol, eta (k) is Gaussian random noise, h is a channel vector, and the expression is as follows:
Figure FDA0004123691810000011
L d is the number of paths, alpha l For the gain of the first path, ψ l The departure angle (AoD) of the first path, a (ψ), is the array guide vector, expressed as follows:
a(ψ)＝[1，e j2πdsin(ψ)/λ ，…，e j2π(N-1)dsin(ψ)/λ ] T
λ is the wavelength, d represents the distance between adjacent sensors;
solving the transmit weight problem translates into solving the equation:
Figure FDA0004123691810000012
wherein θ n ＝∠h n ，
Figure FDA0004123691810000013
The initial transmit weight vector is obtained as: />
Figure FDA0004123691810000014
φ n For vector equation->
Figure FDA0004123691810000015
Solution of (h) 0 I is the beam gain of the receiver, N is the number of antennas, h n Representing a channel vector hN-th element, n=1, …, N;
step 2, constructing complex vectors
Figure FDA0004123691810000016
Wherein v is n Is->
Figure FDA0004123691810000017
Two-dimensional coordinate representation of (i.e.)
Figure FDA0004123691810000018
Figure FDA0004123691810000019
Representing the operation of taking the real part,/->
Figure FDA00041236918100000110
Representing an imaginary part taking operation; setting a permutation matrix P, and randomly dividing complex vector groups into K groups, namely:
Figure FDA00041236918100000111
wherein P is an N×N permutation matrix;
step 3, finding a holder matrix of each complex vector group;
defining each complex vector group
Figure FDA0004123691810000021
Is s k For each complex vector group, the sum, i.e.:
Figure FDA0004123691810000022
for each complex vector set there is mathematically a householder matrix:
Figure FDA0004123691810000023
Figure FDA0004123691810000024
so that
Figure FDA0004123691810000025
With respect to s k Is the mirror vector of: />
Figure FDA0004123691810000026
Since the mirror axis is the sum of the vector sets, the vector sum after mirror image remains unchanged;
step 4, constructing an integral mirror matrix Y, integrating the householder matrix of each complex vector group, and obtaining the integral mirror matrix as follows:
Figure FDA0004123691810000027
step 5, restoring the mirrored complex vector group according to the original sequence, and calculating to obtain a new transmitting weight vector;
right multiplying the mirrored matrix by the permutation matrix to obtain a new complex vector group:
Figure FDA0004123691810000028
from the following components
Figure FDA0004123691810000029
And->
Figure FDA00041236918100000210
The new transmit weight vector is obtained as:
Figure FDA00041236918100000211
and 6, repeating the operation at each time, and iterating to obtain a new transmission weight vector by taking the transmission weight at the previous time as an initial weight vector.
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CN109379154A (en) * 2018-10-11 2019-02-22 重庆邮电大学 A kind of safe transmission scheme based on time reversal technology
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