CN110247865B - Method for optimizing preprocessing filter in time reversal multi-user safety transmission system - Google Patents

Method for optimizing preprocessing filter in time reversal multi-user safety transmission system Download PDF

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CN110247865B
CN110247865B CN201910477509.8A CN201910477509A CN110247865B CN 110247865 B CN110247865 B CN 110247865B CN 201910477509 A CN201910477509 A CN 201910477509A CN 110247865 B CN110247865 B CN 110247865B
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CN110247865A (en
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雷维嘉
杨苗苗
王宏明
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Shenzhen Hongyue Information Technology Co ltd
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/022—Site diversity; Macro-diversity
    • H04B7/024—Co-operative use of antennas of several sites, e.g. in co-ordinated multipoint or co-operative multiple-input multiple-output [MIMO] systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03891—Spatial equalizers
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/03—Protecting confidentiality, e.g. by encryption
    • H04W12/033—Protecting confidentiality, e.g. by encryption of the user plane, e.g. user's traffic
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L2025/03592—Adaptation methods
    • H04L2025/03598—Algorithms
    • H04L2025/03611—Iterative algorithms

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Abstract

The invention discloses an optimization method of a preprocessing filter in a time reversal multi-user secure transmission system. And converting the joint optimization problem of the two sending filters into an independent optimization problem of each filter according to a reciprocity principle, further converting the joint optimization problem into a problem of searching a maximum eigenvalue and a corresponding eigenvector, and solving the problem by an iterative algorithm. The invention realizes safe transmission by adopting a time reversal transmission technology and utilizing a sending preprocessing filter and a multipath channel, optimally designs the preprocessing filter by aiming at improving secret transmission and speed, and can obtain better system safe transmission performance.

Description

Method for optimizing preprocessing filter in time reversal multi-user safety transmission system
Technical Field
The invention relates to the field of information communication, in particular to a method for designing a preprocessing filter to maximize the confidentiality and the speed of a system by utilizing a time reversal technology so as to realize the safe transmission of information.
Background
Wireless communication has become an integral part of our daily lives, however the openness and broadcastability of wireless networks makes them vulnerable to malicious activities. Thus, ensuring that only the intended user has access to confidential data remains a critical issue for ensuring the security of information transmitted over wireless networks. The traditional method for improving the information transmission security is to use an encryption technology in the upper layer of a protocol stack to protect the security of user data, i.e. to sacrifice the complexity for the security. The physical layer security is a method for improving the system security in the physical layer by using the characteristics of the wireless channel such as the reciprocity, the multipath property, the space uniqueness and the like. Physical layer security is the secure transmission of information over the physical layer by exploiting the randomness of the physical layer transmission medium. Compared with the encryption technology realized by the upper layer, the physical layer security has some characteristics. It uses the physical characteristics of the wireless channel to apply appropriate coding and signal processing techniques to ensure the message is confidential, and also to ensure that confidential messages can only be correctly decoded by the intended receiver. In addition, the implementation mode of the physical layer security technology is convenient. Therefore, the physical layer security technology can be used as a supplement to the traditional encryption technology and form powerful protection for the upper layer encryption information in the wireless transmission process, thereby effectively improving the security of wireless communication. The physical layer security aims to improve the signal quality advantage difference of a legal receiving end relative to an eavesdropping end by utilizing the characteristics of a wireless channel so as to realize secure communication. One of the most important methods is to utilize the spatial degree of freedom provided by multiple antennas equipped at the transmitting end, and to use beamforming to direct the signal to the legal receiving end to enhance the signal quality at the destination end and to suppress the signal strength at the eavesdropping end. Beamforming can be seen as a spatial filter, whose essence is to weight the signals transmitted via different transmit antennas so that the signals at the receiver add coherently, which can be designed according to channel state information, network topology. In the document [ ZHao P, Zhang M, Yu H, et al. bump beam forming design for sub correlation rate optimization in MU-MISO networks [ J ]. IEEE Transactions on Information forming and Security,2015,10(9): 1812-. Superimposing an emitted artificial noise or interference signal on top of an information-carrying signal to reduce the quality of the eavesdropper's received signal is another important way to enhance security performance. The artificial noise generally needs to be used in combination with a multi-antenna technology, and the confidentiality is optimized by jointly controlling the transmission directions of the artificial noise and signals through spatial beamforming by using the spatial degrees of freedom provided by a plurality of transmitting antennas. Both beamforming and artificial noise are needed to obtain better security performance in the case of a system equipped with multiple antennas.
Time Reversal (TR) can utilize a rich multipath radio propagation environment to generate a space-Time resonance effect, so-called focusing effect, thereby improving received signal strength while reducing interference. In the TR communication process, a receiving end firstly sends a pilot frequency pulse to a sending end, and the receiving end estimates the Impulse Response (CIR) of a Channel according to a received signal; and then the sending end performs time reversal and conjugation processing on the estimated channel impulse response to obtain a time reversal waveform, and finally the time reversal waveform is convoluted with the sending signal and then sent to the receiving end through a channel. Based on channel reciprocity, TR essentially uses a multipath channel as a matched filter, and due to the inherent characteristics of CIR, the energy of the signal after multipath transmission is focused on a specific time domain and space domain, i.e. TR can collect the energy of the signal from the surrounding environment with extremely low complexity by using multipath propagation. In a wireless communication system, Inter Symbol Interference (ISI) and Inter User Interference (IUI) deteriorate Quality of Service (QoS) of each User. Due to the time focusing characteristic of TR, the energy leakage between symbols is reduced, and thus the ISI effect can be significantly reduced, which makes the receiver simple in structure and does not require a high complexity equalizer. In addition to this, the spatial focusing effect of TR suppresses energy leakage to other receivers and focuses most of the signal energy at the intended user, which means we can get higher signal energy at the intended location and reduce the interfering signal energy around it. The use of TR thus enhances multi-user system capacity and communication range as well as anti-interception capability of the transmitted signal when transmitted in the wireless space. The document [ Wang L, Li R, Cao Ch, et al. SNR analysis of Time reversed signaling on target and indirect receivers in Distributed transmission [ J ]. IEEE Transactions on Communications,2016,64(5): 2176-.
Disclosure of Invention
The invention aims to provide a preprocessing filter for optimizing the secrecy and the speed of a time reversal multi-user system.
In a Single-Input Single-Output (SISO) two-user downlink multiple access system model, under the condition that the information of two users needs to be mutually kept secret, a TR (transmitter-receiver) technology is adopted, a sending preprocessing filter and a multipath channel are utilized to realize safe transmission, and the secret transmission and the speed of the sending filter maximization system are designed. The sir of one user depends on the transmit filter coefficients of all users, so that two pre-processing filters need to be jointly optimized, and the optimal solution of the pre-processing filter impulse response is obtained by solving the joint optimization problem.
In order to achieve the purpose, the invention adopts the following technical scheme: and a two-variable joint optimization problem is converted into two single-variable optimization problems, so that the solving complexity is reduced. And then obtaining the optimal solution of the impulse response of the preprocessing filter by an iterative algorithm for searching the maximum eigenvalue and the corresponding eigenvector so as to maximize the confidentiality and the speed of the system.
In the single-input single-output downlink multiple access system, a transmitting end and a receiving end are both provided with a single antenna, data of the transmitting end is filtered by a transmitting filter and then output, and information transmission is secret communication between two users; wherein the optimization of the transmit filter comprises the steps of:
(1) constructing a transmit filter to maximize system privacy and rate;
(2) replacing an interference item caused by another user to the user in the SINR expression of the user by the interference item of the user to the other user according to a reciprocity principle, and further converting the joint optimization of the two sending filters into independent optimization of each filter;
(3) and searching the maximum eigenvalue of the matrix formed by the optimal solution and the corresponding eigenvector thereof, and obtaining the optimal solution of the preprocessing filter through an iterative algorithm.
The optimization problem in the step (1) is as follows:
Figure BDA0002082761620000031
Figure BDA0002082761620000032
Figure BDA0002082761620000033
wherein R iss,1、Rs,2Reachable security rates, g, for user 1 and user 2, respectively1、g2The transmit filter impulse responses for user 1 and user 2, respectively.
Step (2) converts the joint optimization problem of the two sending filters into the independent optimization problem of each filter by applying a reciprocity principle, which specifically comprises the following steps:
Figure BDA0002082761620000034
Figure BDA0002082761620000035
wherein
Figure BDA0002082761620000036
To simplify the achievable privacy rate for user i.
Further rewriting the optimization problem into
Figure BDA0002082761620000037
Figure BDA0002082761620000038
Step (3) obtaining a local optimal solution according to first-order Karush-Kuhn-Tucher (KKT) necessary conditions
Figure BDA0002082761620000039
The satisfied relational expression converts the optimization problem into the problem of searching the maximum eigenvalue and the corresponding eigenvector, and obtains the preprocessing filter by an iterative algorithmAnd (5) optimal solution.
Different from the traditional wave beam forming technology based on multiple antennas, the invention adopts TR technology, designs the preprocessing filter by utilizing the time characteristic of the multipath channel, realizes safe transmission by the preprocessing filter and the matched filter formed by the multipath channel, ensures that the system can realize the safe transmission of information even if a single antenna is equipped, and fully utilizes the multipath fading characteristic while reducing the complexity of the system. Compared with a conventional TR preprocessing filtering system and a direct transmission system, the achievable secret rate of the system after the TR preprocessing filter after secret keeping and rate optimization is obviously superior to that of the system and the direct transmission system adopting the conventional TR preprocessing filter, and better system safety performance can be realized.
Drawings
FIG. 1 is a system model of the present invention;
FIG. 2 is a graph illustrating the convergence of the maximum eigenvalue solution iterative algorithm of the present invention;
FIG. 3 is a graph of the privacy rates of each user at different transmit powers for two users at the same distance from the base station;
FIG. 4 is the privacy and rate of two users at the same distance from the base station and with different sampling factors D;
fig. 5 shows the secret rates of two users with different transmission powers when the two users are at different distances from the base station.
Detailed Description
Considering a Single-Input Single-Output (SISO) two-user downlink multiple access system, a system model is shown in fig. 1. The transmitting end and the receiving end are both provided with a single antenna, and the transmitting end simultaneously transmits two independent data streams X to two users1And X2. The information of two users needs to be kept secret from each other, i.e. the two users mutually view each other as an eavesdropper. Because the transmitting end is only provided with a single antenna, beam forming cannot be used for enhancing the physical layer security. The TR technique is used to realize secure transmission by using a transmit preprocessing filter and a multipath channel, and the transmit filter is designed to maximize the secure transmission and the rate of the system. By using hi[m]The channel impulse response of user i (i is 1,2) is shown, and for the sake of convenience, two are assumedThe length of the channel impulse response of the user is L, namely h is equal to or more than L when m is less than 0i[m]0, m sequence index of the channel impulse response. Representing the channel impulse response in vector form, i.e. hi＝[hi[0],hi[1],…,hi[L-1]]TThe impulse response of the transmit filter is also represented in vector form, gi＝[gi[0],gi[1],…,gi[L-1]]T。
The sending end sends a symbol sequence with the length of M to two users simultaneously
Figure BDA0002082761620000041
The samples are up-sampled before entering the filter to increase the sample rate in order to mitigate inter-symbol interference. The up-sampling factor is D, defined as the ratio of the sampling rate to the baud rate. The up-sampling sequence is filtered by the sending filter and then output to the wireless channel. User i down-samples the received signal, i.e. extracts the integer times of the number of samples D as the sampling value of the symbol to obtain
Figure BDA0002082761620000042
Wherein
Figure BDA0002082761620000043
zi[m]Is a mean of 0 and a variance of σ2White gaussian noise. Y isi[m]Representing a down-sampled signal received by user i, l representing a pre-processing filter giAnd channel impulse response hiThe sequence index downsampled after convolution, n denotes the sequence index of the channel impulse response, j denotes the user index. Will Yi[m]Further divided into useful signal, intersymbol interference and noise, the above equation can be re-expressed as
Figure BDA0002082761620000044
Wherein the content of the first and second substances,
Figure BDA0002082761620000045
indicating another user, i.e. if i is 1, then
Figure BDA0002082761620000046
i is 2, then
Figure BDA0002082761620000047
Rewriting the above formula into a matrix operation form to obtain
Figure BDA0002082761620000048
Wherein
Figure BDA0002082761620000049
Represents the equivalent channel matrix HiK is 1,2, …,2LD-1. Equivalent channel matrix HiIs (2L)D-1) xL dimensional matrix, defined as
Figure BDA0002082761620000051
Wherein
Figure BDA0002082761620000052
Is (2L)D-1)×(2LD-1) the kth column of the identity matrix of dimension, ekIs the kth column of the identity matrix of dimension (2L-1) × (2L-1),
Figure BDA0002082761620000053
is a Toeplitz matrix of dimensions (2L-1). times.L and the first column is
Figure BDA0002082761620000054
Equivalent matrix HiIs effectively a matrix
Figure BDA0002082761620000055
The k × D row of (i.e. H)iIs formed by
Figure BDA0002082761620000056
Is formed by an integer multiple of rows of D.
The received Signal-to-interference-plus-noise ratio (SINR) of user i is
Figure BDA0002082761620000057
Wherein the content of the first and second substances,
Figure BDA0002082761620000058
p is the power of each User Symbol sequence transmitted by the transmitting end, and the first term and the second term of the denominator represent the Inter Symbol Interference (ISI) and Inter User Interference (IUI) power, respectively.
To another user
Figure BDA0002082761620000059
For the eavesdropper to eavesdrop the information of the user i, the received signal-to-interference-and-noise ratio is
Figure BDA00020827616200000510
Where the first term of the denominator is the ISI power in the signal containing the information of user i and the second term is the ISI power in the signal carrying the information of user i
Figure BDA00020827616200000511
The signal power of the information and the third term is the channel noise power. The situation that the information is most unfavorable for keeping secret is considered, namely, a user is assumed
Figure BDA00020827616200000512
The symbol sent to the user i can be correctly decoded, the signal transmitted by the channel is reconstructed according to the decoding result, the signal is eliminated from the received signal, and then the signal sent to the user i is detected. Thus, the user
Figure BDA00020827616200000513
The second term of the denominator of the SINR expression for the eavesdropped signal can be removed, i.e.
Figure BDA00020827616200000514
When the channel bandwidth is B, the user i is used as a legal receiving end and a user
Figure BDA00020827616200000515
The achievable rates when acting as eavesdropping terminals are respectively
Figure BDA00020827616200000516
Figure BDA0002082761620000061
RiIndicating the achievable rate, R, for user i as a legitimate receivere,iRepresenting a user
Figure BDA0002082761620000062
As the reachable rate when the eavesdropping end eavesdrops on the information of the user i.
The achievable secret rate of user i is
Rs,i＝[Ri-Re,i]+
Wherein [ x ]]+Representing taking the maximum of both 0 and x.
The problem of optimizing the pre-processing filter to maximize system privacy and rate can be expressed as
Figure BDA0002082761620000063
Figure BDA0002082761620000064
Figure BDA0002082761620000065
Wherein the constraint condition indicates that the power gain of the pre-processing filter coefficients is 1.
This optimization problem involves two user pre-processing filters g1And g2The sir of each user depends on the impulse response of all user transmit filters, and the optimization of one user transmit filter also affects the privacy rate of another user, so the solution of the optimization problem is very difficult. Consider the problem of such a reciprocity: if one user optimizes the filter by considering minimization of interference to the other user in addition to maximizing its received signal power, and the other user is similarly optimized, it means that the signal to interference plus noise ratio of both users is maximized. Therefore, to simplify the solution process, the SINR of user i is formulated as user
Figure BDA0002082761620000066
Replacing IUI item caused to user i with user i to user
Figure BDA0002082761620000067
Such that the signal-to-interference-and-noise ratio comprises the pre-filter impulse response g of user i onlyiI.e. by
Figure BDA0002082761620000068
The expressions of the reachable rate and the secret rate of the corresponding user i become
Figure BDA0002082761620000069
Figure BDA00020827616200000610
In this way it is possible to obtain,
Figure BDA00020827616200000611
contains only g in the expression ofiThus, g can be optimized separately1And g2Make it
Figure BDA00020827616200000612
And
Figure BDA00020827616200000613
and the maximization is realized, the two-variable joint optimization problem can be converted into two single-variable optimization problems, and the solving complexity is greatly reduced. Convert the original optimization problem into the following two sub-optimization problems
Figure BDA00020827616200000614
Figure BDA00020827616200000615
Simplifying objective functions
Figure BDA00020827616200000616
To obtain
Figure BDA0002082761620000071
Where I is an identity matrix of size dimension L x L,
Figure BDA0002082761620000072
Figure BDA0002082761620000073
because log2x is a monotonically increasing function such that log2x is maximum, onlyIt is sufficient to maximize x. Thus the above optimization problem can be rewritten as
Figure BDA0002082761620000074
Figure BDA0002082761620000075
Expressing the objective function in the above equation as
Figure BDA0002082761620000076
Wherein f (g)i) Is the product of a fractional quadratic function, Ai，Bi，Ae,i，Be,iIs a semi-positive definite matrix of dimension LxL, giIs a vector in the L dimension, according to the document [ Lee N, Yang H J, Chun J. Achievable sum-rate maxima AF relay modeling scheme in two-way relay channels [ C].ICC Workshops-2008IEEE International Conference on Communications Workshops,Beijing,2008:300-305.]Local optimal solution
Figure BDA00020827616200000711
The first-order Karush-Kuhn-Tucher (KKT) requirement is satisfied
Figure BDA0002082761620000077
Namely, it is
Figure BDA0002082761620000078
Order to
Figure BDA0002082761620000079
According to above f (g)i) Can be re-expressed as
Figure BDA00020827616200000710
Moving Q to the right of the above-mentioned middle number to the left can obtain
Figure BDA0002082761620000081
It can be seen that the optimal solution is solved
Figure BDA0002082761620000082
That is, the matrix Q-1Generalized eigenvalue decomposition of V, where the scalar quantity is
Figure BDA0002082761620000083
Can be regarded as a matrix Q-1Generalized eigenvalues of V, i.e. satisfy
Figure BDA0002082761620000084
Let f (g)i) Maximum solution
Figure BDA0002082761620000085
Is the matrix Q-1The eigenvector corresponding to the maximum eigenvalue of V, so solving the optimization problem is equivalent to solving the matrix Q-1And V is the normalized feature vector corresponding to the maximum feature value. But note that V and Q contain the eigenvectors to be solved for
Figure BDA0002082761620000086
Therefore, the conventional generalized eigenvalue decomposition method cannot be adopted for solving. Here, an iterative algorithm is used to solve
Figure BDA0002082761620000087
First give giAssigning an initial value
Figure BDA0002082761620000088
Obtaining V and Q, for Q-1Decomposing the generalized eigenvalue of V to obtain the maximum eigenvalue
Figure BDA0002082761620000089
And its corresponding normalized feature vector
Figure BDA00020827616200000810
Using the obtained normalized feature vector
Figure BDA00020827616200000811
To update V and Q, and further to obtain updated Q-1Maximum eigenvalue of V
Figure BDA00020827616200000812
And its corresponding normalized feature vector
Figure BDA00020827616200000813
Repeating the above process until the difference between the maximum characteristic value obtained by iterative computation of a certain time and the maximum characteristic value obtained by iteration of the last time is less than a preset value or the number of iterations is reached. The iterative algorithm for eigenvalue solution is summarized in table 1.
TABLE 1 maximum eigenvalue solving iterative algorithm
Figure BDA00020827616200000814
The present invention will be described in further detail below with reference to the accompanying drawings. The simulation results of the secret rate given in each of the following figures are 1 × 105Average under group channel realizations. In the simulation, the number of paths L is set to 10, the channel bandwidth B is set to 1MHz, the channel is a rayleigh fading channel, the channel attenuation includes large-scale fading and small-scale fading, that is, the coefficient of the channel impulse response is a complex gaussian random variable with the mean value of 0, and the variance is
Figure BDA00020827616200000815
In the formula, σ T10/B is the root mean square delay of the path, T s1/B is the sampling period. EtaiLarge scale fading coefficients for user i channel:
Figure BDA00020827616200000816
where c is 4 as a path loss exponent, η0For transmission losses at a reference distance, d010m is a reference distance, diIs the distance of the transmitter from user i. Setting η in simulation0＝10-5Power of channel noise σ2＝1×10-11W, the maximum iteration number in the maximum eigenvalue solution iterative algorithm is N equal to 50, and the convergence factor epsilon is 1 multiplied by 10-6。
FIG. 2 shows a matrix Q in an iterative solution process of eigenvectors (i.e., transmit filter impulse responses) for three sets of random channel coefficients-1V maximum characteristic change curve. In the simulation, the up-sampling factor D is 2, the transmission power P is 1W, and the distances between two users and the base station are both 100 m. As can be seen from the figure, the algorithm of the scheme of the invention has better convergence, and can be converged within 5 iterations generally.
Fig. 3 shows the simulation result of the variation of the achievable secret rate with the transmission power, the distance between two users and the base station is 100m, and the up-sampling factor D is 3. Wherein "conventional TR" indicates the use of a conventional time-reversal filter, i.e.
Figure BDA0002082761620000091
And (5) time simulation results. And simultaneously, a simulation result in direct transmission is also given, and the figure is marked as direct transmission. Direct transmission means that a transmitting end directly transmits a transmitting symbol to a receiving end through a channel without any preprocessing. The legal receiving end uses the path with the maximum power in the multi-path channel as the useful signal, and the rest paths are ISI. The eavesdropping end takes the first path of the multipath channel as the useful signal, and the remaining path is ISI. And IUI exists at both the legitimate end and the receiving end. Due to the fact thatTwo users are at the same distance from the transmitter, and according to the symmetrical performance, the long-term average achievable secret rates of the two users are the same, and the curves of the achievable secret rates of the two users are basically overlapped under the same scheme in the simulation diagram. It can be seen that the achievable privacy rate of the system after optimization of the TR pre-processing filter for privacy and rate is significantly better than that of a system employing a conventional TR pre-processing filter, while the privacy rate of the direct transmission without pre-processing is the lowest and does not increase substantially with increasing transmit power. This is because ISI and IUI of a received signal in a direct transmission system are very severe, interference power (ISI and IUI) thereof is large relative to channel noise, and signal power is expected to increase in synchronization with ISI and IUI power as transmission power increases, so that signal-to-interference-and-noise ratio does not substantially increase as transmission power increases. On the other hand, since the reception rates of the intended receiver and the eavesdropping receiver also change in synchronization, the secret rate is also substantially constant. In contrast, in a system using a conventional TR pre-processing filter, the achievable secret rate can be increased with an increase in the transmission power when the transmission power is small, but the secret rate is not increased with an increase in the transmission power when the transmission power is increased to a certain degree. In conventional TR systems, the transmit filter is not optimized for the secret rate, and the received signal power (for the signal carrying the desired user information) is increasing for both the desired user and the undesired user (i.e., the eavesdropper). When the power is small, the channel noise is large relative to ISI and IUI power, and since the received signal power of the desired user is higher, the transmission power is increased, and the received signal to interference plus noise ratio of the desired user is increased faster than that of the undesired user, the privacy rate is increased. When the transmission power is increased to a certain degree, the ISI and IUI powers are larger than the channel noise power, and when the transmission power is increased, the numerator and the denominator in the signal-to-interference-and-noise ratio expression are synchronously increased, so the signal-to-interference-and-noise ratio is not obvious along with the increase of the transmission power, and simultaneously, the received signal-to-interference-and-noise ratios of two users are synchronously increased, so the secret rate is not changed any more. In systems optimized for secret rate, the achievable secret rate continues to increase with increasing transmit power and is significantly better than conventional TR systems. This is because the preprocessing filters in the scheme are specifically targeted at privacyThe goal of rate maximization is optimized, with the desired user increasing in rate higher than the undesired user as power increases, so the privacy rate increases. As the transmission power increases, since ISI and IUI power increase, the channel noise power has less influence on the signal-to-interference-and-noise ratio, the SINR increase rate by the transmission power gradually decreases, and thus the increase rate of the secret rate gradually decreases. .
Fig. 4 shows the simulation results of the privacy and rate of the system at different sampling factors D, and the distance between two users and the base station is 100 m. The larger the sampling factor D, the lower the symbol rate, with the channel bandwidth unchanged. It can be seen that in the low power region, the smaller D, the higher the security and rate, but the lower the rate of increase of the security and rate when the transmission power is increased. This is because when the transmission power is small, the proportion of the channel noise power is larger in the denominator of the signal-to-interference-and-noise ratio, and when D is small, although ISI and IUI are larger, the transmission rate is higher because the symbol rate is higher. When the transmission power is increased, the signal power and ISI and IUI are synchronously increased, the smaller D, the larger ISI and IUI, and the smaller the influence of the channel noise power, so that the signal-to-interference-and-noise ratio is increased more slowly and the saturation value is lower, therefore, the increase of the privacy and rate is slower, and the achievable privacy and rate upper limit is lower. At higher D, although the symbol rate is lower, the signal-to-noise ratio can be increased continuously and rapidly with increasing transmit power due to the small ISI and IUI, so the privacy and rate increase is faster and the ultimate privacy and rate cap that can be achieved is also larger. It is therefore necessary to select a suitable value of the up-sampling factor D according to the available transmit power of the system, channel conditions, etc.
FIG. 5 shows the simulation results of the secret rates when the distances between two users and the base station are different, i.e. the distance d between user 1 and the base station180m, distance d of user 2 from base station2100 m. It can be seen that the privacy rate per user and the privacy and rate of the system after optimizing the TR pre-processing filter for privacy and rate are higher than the conventional TR pre-processing filter system and the direct transmission system, similar to the privacy performance when the two users are equidistant from the base station. In direct transmission systems and conventional TR pre-processing filter systemsThe difference between the privacy rates of the two users gradually decreases with increasing power. This is because when the power of the two systems is low, the interference power of the systems is small, the signal to interference plus noise ratio of the users depends mainly on the ratio of the desired signal power to the noise power, and the difference between the distances between the two users and the base station causes the desired signal powers of the two users to be greatly different, so the difference between the signal to interference plus noise ratios of the two users is large, and the privacy rate of the closer user is higher. Along with the increase of the power, the interference power of the system increases, and the interference power of the user close to the base station increases faster than that of the user far from the base station, so the SINR difference between the two users decreases, and the privacy rate difference also gradually decreases. In a system that optimizes the TR pre-processing filter for privacy rates, the difference between the privacy rates of the two users is large. This is because the secret rates of the users are optimized independently, and the problem of power allocation is not considered, and the receiving performance of the user at a close distance is always better than that of the other user, so the difference between the secret rates of the two users is large. If the signal power of the two users' information is further distributed, the gap of the secrecy rate can be reduced.

Claims (2)

1. The optimization method of the preprocessing filter in the time reversal multi-user safe transmission system is characterized in that: in the single-input single-output downlink multiple access system, a transmitting end and a receiving end are both provided with a single antenna, data of the transmitting end is filtered by a transmitting filter and then output, and information transmission is secret communication between two users; wherein the optimization of the transmit filter comprises the steps of:
(1) constructing a transmit filter to maximize system privacy and rate; the construction process is as follows:
the received signal-to-interference-and-noise ratio of user i (i-1, 2) is
Figure FDA0003104067500000011
Wherein i is 1
Figure FDA0003104067500000012
When i is 2
Figure FDA0003104067500000013
P is the power, sigma, of each user symbol sequence sent by the sending end2Is the variance of a Gaussian white noise sequence; gi＝[gi[0],gi[1],…,gi[L-1]]TRepresents the impulse response of the transmit filter, L being the length of the channel impulse response;
Figure FDA0003104067500000014
Figure FDA0003104067500000015
Figure FDA0003104067500000016
d is an upsampling factor; hiIs (2L)D-1) xL dimension of an equivalent channel matrix, is composed of
Figure FDA0003104067500000017
Is a matrix of integer multiples of D,
Figure FDA0003104067500000018
is a Toeplitz matrix of dimensions (2L-1). times.L and the first column is
Figure FDA0003104067500000019
hi＝[hi[0],hi[1],…,hi[L-1]]TIs a vector form of the channel impulse response, 01×(L-1)A zero matrix representing 1 × (L-1) dimensions;
Figure FDA00031040675000000110
represents the equivalent channel matrix HiL toDTransposing a line;
another user
Figure FDA00031040675000000111
The received signal-to-interference-and-noise ratio when eavesdropping on the information of user i for an eavesdropper is
Figure FDA00031040675000000112
User i has the secret rate formula of
Figure FDA00031040675000000113
Where B is the channel bandwidth, [ x [ ]]+Represents taking the maximum of both 0 and x;
transmit filter constructed to maximize system privacy and rate
Figure FDA00031040675000000114
Figure FDA00031040675000000115
Figure FDA00031040675000000116
Rs,1、Rs,2Reachable privacy rates for user 1 and user 2, respectively;
(2) in the SINR expression of the users according to the reciprocity principle, the interference item caused by another user to the user is replaced by the interference item of the user to another user, and then the joint optimization of the two sending filters is converted into the independent optimization of each filter, specifically:
the sir formula for user i becomes:
Figure FDA00031040675000000117
the expression for the privacy rate of the corresponding user i becomes:
Figure FDA0003104067500000021
optimization of g separately1And g2Make it
Figure FDA0003104067500000022
And
Figure FDA0003104067500000023
maximization, thereby converting the joint optimization of the two transmit filters into an independent optimization of each filter, i.e.
Figure FDA0003104067500000024
(3) Searching the maximum eigenvalue of a matrix formed by the optimal solution and the corresponding eigenvector thereof, and obtaining the optimal solution of the preprocessing filter through an iterative algorithm;
first give giAssigning an initial value
Figure FDA0003104067500000025
So as to obtain the V and the Q,
Figure FDA0003104067500000026
Figure FDA0003104067500000027
to Q-1Decomposing the generalized eigenvalue of V to obtain the maximum eigenvalue
Figure FDA0003104067500000028
And its corresponding normalized feature vector
Figure FDA0003104067500000029
Using the obtained normalized feature vector
Figure FDA00031040675000000210
To update V and Q, and further to obtain updated Q-1Maximum eigenvalue of V
Figure FDA00031040675000000211
And its corresponding normalized feature vector
Figure FDA00031040675000000212
And repeating the process until the difference between the maximum characteristic value obtained by iterative calculation of a certain time and the maximum characteristic value obtained by iteration of the last time is less than a preset value or the iteration times are reached.
2. The method of claim 1 for optimizing a preprocessing filter in a time-reversal multi-user secure transmission system, wherein: and (3) obtaining an optimal solution of the sending filter, specifically:
the optimization objective function is expressed as
Figure FDA00031040675000000213
According to the local optimum solution
Figure FDA00031040675000000214
Satisfied first-order KKT requirement
Figure FDA00031040675000000215
To obtain
Figure FDA00031040675000000216
Wherein the content of the first and second substances,
Figure FDA00031040675000000217
i is an identity matrix of dimension L × L;
optimal solution
Figure FDA00031040675000000218
Is a matrix Q-1V is the normalized eigenvector corresponding to the maximum eigenvalue; solving using iterative algorithms
Figure FDA00031040675000000219
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