CN110247865A - The optimization method of pre-processing filter in time reversal multi-user's secure transmission system - Google Patents
The optimization method of pre-processing filter in time reversal multi-user's secure transmission system Download PDFInfo
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Classifications
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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
Abstract
The invention discloses a kind of optimization method of pre-processing filter in time reversal multi-user secure transmission system, transmitting terminal sends two independent data flows to two users simultaneously, and the information of two users needs mutually secrecy.The independent optimization problem that the combined optimization problem of two transmitting filters is converted to each filter according to the principle of reciprocity is further converted into the problem of finding maximum eigenvalue and its corresponding feature vector, and is solved by iterative algorithm.The present invention optimizes pre-processing filter as target using improving secrecy transmission and rate, can get better system safe transmission performance by using time reversal transmission technology using pre-processing filter and multipath channel realization safe transmission is sent.
Description
Technical field
The present invention relates to the information communications fields, and pre-processing filter maximization is specifically designed using time reversal technology
The secrecy and rate of system realize the safe transmission of information.
Background technique
Wireless communication has become a part indispensable in our daily lifes, however wireless network is open and wide
The property broadcast makes it be easy the attack by rogue activity.Thereby it is ensured that only prospective users ability confidential data, guarantee are wireless
The safety of network traffic is still a most important problem.Improve information transmission safety conventional method be
Secure user data is protected in protocol stack upper layer using encryption technology, that is, sacrifices complexity to exchange safety for.And physical layer
Safety is to improve the side of security of system in physical layer using features such as heterogeneite, multipath, the space uniqueness of wireless channel
Method.Safety of physical layer is to realize the safe transmission of information on a physical layer by exploring the randomness of physical layer transmission medium.With
The encryption technology that upper layer is realized is compared, and safety of physical layer has Some features.It is the physical characteristic application using wireless channel
Suitable coding and signal processing technology guarantee the confidentiality of message, and also ensure that confidential information can only be expected connects
Receipts machine is correctly decoded.In addition, the implementation of safety of physical layer technology is more convenient.Therefore safety of physical layer technology can be used as
To the supplement of conventional encryption technique, strong protection is formed during wireless transmission to upper layer encryption information, to effectively mention
The safety of high wireless communication.Safety of physical layer is intended to be improved legitimate receipt end using the characteristic of wireless channel and eavesdrops end relatively
Signal quality advantage difference, and then realize secure communication.Among these most important method first is that utilize transmitting terminal be equipped with
Signal is directed toward legitimate receipt end using wave beam forming to enhance the signal matter of destination by the spatial degrees of freedom that multiple antennas provides
Amount, while inhibiting to eavesdrop the signal strength at end.Wave beam forming can be considered as spatial filter, and essence is to via different hairs
The signal for penetrating antenna transmission is weighted so that the signal coherence at receiver is superimposed, it can according to channel state information,
Network topology structure is designed.Document [Zhao P, Zhang M, Yu H, et al.Robust beamforming design
for sum secrecy rate optimization in MU-MISO networks[J].IEEE Transactions on
Information Forensics and Security, 2015,10 (9): 1812-1823.] have studied multiple input single output
Using maximization network secrecy and rate as the wave of target under (Mingle-Input Single-Output, MISO) multi-user scene
Beam Shape design converts convex optimization problem for former problem using the first approximation technology of Semidefinite Programming and Taylor expansion, thus
Obtain the optimal solution of optimization problem.Superposition transmitting man made noise or interference signal reduce listener-in on the signal of carrying information
Received signal quality be another enhancing security performance important method.Man made noise generally requires in conjunction with multi-antenna technology
It uses, the spatial degrees of freedom provided using multiple transmitting antennas, man made noise and signal is jointly controlled by spatial beams forming
The direction of the launch, optimize security performance.Either wave beam forming or man made noise require to be equipped with the feelings of multiple antennas in system
Preferable security performance can be obtained under condition.
Time reversal, (Time Reversal, TR) can use multipath radio propagation environment abundant to generate space-
Resonance time effect, i.e., so-called focusing effect, to improve received signal strength while reducing interference.It was communicated in TR
Cheng Zhong, receiving end send pilot pulse to transmitting terminal first, and receiving end estimates the impulse response of channel according to the signal received
(Channel Impulse Response,CIR)；Then transmitting terminal does time reversal and conjugation to the channel impulse response of estimation
Processing obtains time reversal waveform, and finally by it, passing through channel is sent to receiving end later with signal progress convolution is sent.According to
Channel heterogeneite, TR are substantially using multipath channel as matched filter, due to the inherent characteristic of CIR, by Multipath Transmission
In specific time domain and airspace, i.e. TR can use multipath transmisstion and answered from ambient enviroment with extremely low the Voice segment of signal afterwards
The energy of miscellaneous degree collecting signal.In a wireless communication system, intersymbol interference (Inter Symbol Interference, ISI)
Service quality (the Quality of of each user is degrading with inter-user interference (Inter User Interference, IUI)
Service, QoS).Since TR has time focus characteristics, reduce intersymbol energy leakage, therefore can be significantly reduced
The influence of ISI can make receiver structure simple in this way and not need the balanced device of high complexity.In addition to this, the sky of TR
Between focusing effect inhibit the energy leakage to other receivers, and most of signal energy is focused at prospective users, this
Mean that we can obtain higher signal energy at desired location and reduce surrounding interference signal energy.Therefore
Multi-user system capacity and communication range can be enhanced using TR and emit anti-intercepting and capturing when signal transmits in wireless space
Ability.Document [Wang L, Li R, Cao Ch, et al.SNR analysis of time reversal signaling on
target and unintended receivers in distributed transmission[J].IEEE
Transactions on Communications, 2016,64 (5): 2176-2191.] analyze Distributed Time reversion
Signal-to-noise ratio of (Distributed Time-Reversal, the DTR) Transmission system at intended receivers and unexpected receiver,
Prove that the security performance of system can be improved in TR transmission.
Summary of the invention
The purpose of the present invention is to provide the secrecy and speed of a kind of pre-processing filter optimization time reversal multi-user system
Rate, this method utilize the arteries and veins of time reversal Technology design transmitting filter in the case where two users' information needs mutually secrecy
Punching response, maximizes the secrecy and rate of system.
In single-input single-output (Single-Input Single-Output, SISO) two users' downlink multi-access system model
In, in the case that the information of two users needs mutually secrecy, using TR technology, utilize transmission pre-processing filter and multipath channel
Realize safe transmission, design transmitting filter maximizes the secrecy transmission and rate of system.The Signal to Interference plus Noise Ratio of one user depends on
In the transmitting filter coefficient of all users, it is therefore desirable to carry out combined optimization to two pre-processing filters, solve this joint
Optimization problem obtains the optimal solution of pre-processing filter impulse response.
To achieve the goals above the present invention adopts the following technical scheme: the combined optimization problem of two variables is converted
For two univariate optimization problems, solving complexity is reduced.Then by find maximum eigenvalue and its corresponding feature to
The optimal solution that the iterative algorithm of amount obtains pre-processing filter impulse response maximizes the secrecy of system and rate.
In single-input single-output downlink multi-access system, transmitting terminal and receiving end are equipped with single antenna, the data of transmitting terminal
It is exported after transmitting filter filters, information is transmitted as the secret communication between two users；The wherein optimization of transmitting filter
The following steps are included:
(1) construction transmitting filter maximizes system secrecy and rate；
(2) according to the principle of reciprocity by the Signal to Interference plus Noise Ratio expression formula of user, another user is caused by user security risk dry to this
The distracter that item replaces with this user to another user is disturbed, and then the combined optimization of two transmitting filters is converted to respectively
The independent optimization of filter；
(3) maximum eigenvalue and its corresponding feature vector by the optimal matrix being deconstructed into are found, and is calculated by iteration
Method obtains the optimal solution of pre-processing filter.
Optimization problem described in step (1) are as follows:
Wherein Rs,1、Rs,2The respectively reachable secrecy rate of user 1 and user 2, g1、g2Respectively user 1 and user 2
Transmitting filter impulse response.
The combined optimization problem of two transmitting filters is converted to the independence of each filter with the principle of reciprocity by step (2)
Optimization problem, specifically:
WhereinFor the reachable secrecy rate of simplified user i.
According to the monotonicity of objective function, further optimization problem is rewritten as
Step (3) obtains locally optimal solution according to single order Karush-Kuhn-Tucher (KKT) necessary conditionMeet
Optimization problem is converted to the problem of finding maximum eigenvalue and its corresponding feature vector, and passes through iterative algorithm by relational expression
Obtain the optimal solution of pre-processing filter.
Different from traditional beamforming technique based on multiple antennas, the present invention uses TR technology, utilizes multipath channel
Time response designs pre-processing filter, realizes that safety passes by the matched filter that pre-processing filter and multipath channel are formed
It is defeated, it ensure that the safe transmission of information may be implemented in system when being equipped with single antenna, reducing system complexity
Multipath fading characteristic is taken full advantage of simultaneously.Compared with conventional TR pre-processes filtering system and direct Transmission system, for secrecy
With it is rate optimized after TR pre-processing filter after system reachable secrecy rate be substantially better than using routine TR pretreatment filter
Better security of system energy may be implemented in the system of device and direct Transmission system.
Detailed description of the invention
Fig. 1 is system model of the invention；
Fig. 2 is the convergence that maximum eigenvalue of the present invention solves iterative algorithm；
Fig. 3 is the secrecy rate of two users and base station distance each user under different transmission power when identical；
Fig. 4 is the secrecy and rate of two users and base station distance user under difference decimation factor D when identical；
Fig. 5 is the secrecy rate of two users with two users under different transmission power when base station distance difference.
Specific embodiment
Consider single-input single-output (Single-Input Single-Output, SISO) two users' downlink multi-access system,
System model is as shown in Figure 1.Transmitting terminal and receiving end are equipped with single antenna, and transmitting terminal sends two solely to two users simultaneously
Vertical data flow X1And X2.The information of two users needs mutually secrecy, i.e., two users regard other side mutually as listener-in.Because of hair
Sending end is only equipped with single antenna, cannot enhance safety of physical layer using wave beam forming.Here TR technology is used, it is pre- using sending
It handles filter and multipath channel realizes safe transmission, design transmitting filter maximizes the secrecy transmission and rate of system.With
hi[m] indicates the channel impulse response of user i (i=1,2), in order to express easily, it is assumed that the channel impulse response of two users
Length is all L, i.e., as m < 0 or m >=L, hiThe sequence index of [m]=0, m channel impulse response.By channel impulse response
It is expressed as vector form, i.e. hi=[hi[0],hi[1],…,hi[L-1]]T, the impulse response of transmitting filter also is indicated as vector
Form, gi=[gi[0],gi[1],…,gi[L-1]]T。
Transmitting terminal sends the symbol sebolic addressing that length is M to two users simultaneouslyInto filtering
First it is up-sampled before device, improves sample rate, it is therefore an objective to mitigate intersymbol interference.The up-sampling factor is D, is defined as adopting
The ratio of sample rate and baud rate.Up-sampling sequence exports after transmitting filter filters, and enters wireless channel.I pairs of user
It receives signal and carries out down-sampling, i.e. sampled value of the sample value of the integral multiple serial number of extraction D as symbol, obtain
Whereinzi[m] is that mean value is 0, variance σ2White Gaussian noise.Yi[m] indicates user i
The down-sampled signal that receives, l indicate pre-processing filter giWith channel impulse response hiThe sequence rope of down-sampling after convolution
Draw, n indicates the sequence index of channel impulse response, j indicates user index.By Yi[m] is further divided into useful signal, intersymbol
Interference, inter-user interference and several parts of noise, then above formula can be expressed as again
Wherein,Indicate another user, even i=1, thenI=2, thenAbove formula is rewritten as square
The form of battle array operation, obtains
WhereinIndicate equivalent channel matrix HiRow k transposition, k=1,2 ..., 2LD-1.Equivalent channel matrix Hi
For (2LD- 1) × L ties up matrix, is defined as
WhereinIt is (2LD-1)×(2LD- 1) the kth column for the unit matrix tieed up, ekIt is the unit of (2L-1) × (2L-1) dimension
The kth of matrix arranges,It is the Toeplitz matrix of (2L-1) × L dimension and first is classified asEquivalent matrix
HiRow k be actually matrixKth × D row, i.e. HiBe byD integral multiple row composition matrix.
The reception of user i believes that dry (Signal-to-interference-plus-noise ratio, SINR) ratio of making an uproar is
Wherein,P is that transmitting terminal transmission is each
The power of a user symbol sequence, the first item and Section 2 of denominator respectively indicate intersymbol interference (Inter Symbol
Interference, ISI) and inter-user interference (Inter User Interference, IUI) power.
Depending on another userFor listener-in, the information of eavesdropping user i, then it receives Signal to Interference plus Noise Ratio and is
Wherein the first item of denominator is the ISI power in the signal comprising user's i information, and Section 2 is to carry userLetter
The signal power of breath, Section 3 are channel noise power.Here consider to the worst situation of information privacy, i.e. hypothesis user
The symbol for being sent to oneself can be correctly decoded, its signal after transmission is reconstructed according to decoded result, and by its from
It eliminates in received signal, then is detected for the signal for being sent to user i.In this way, userThe letter of tapped signal is dry to make an uproar
Section 2 than expression formula denominator can be removed, i.e.,
When channel width is B, user i is as legitimate receipt end and userIt is respectively as achievable rate when eavesdropping end
RiIndicate achievable rate of the user i as legitimate receipt end when, Re,iIndicate userAs eavesdropping end eavesdropping user i
Information when achievable rate.
The reachable secrecy rate of user i is
Rs,i=[Ri-Re,i]+
Wherein [x]+It indicates to take the maximum value in both 0 and x.
Optimization pre-processing filter is expressed as system secrecy and the maximized problem of rate
Wherein, constraint condition indicates that the power gain of pre-processing filter coefficient is 1.
This optimization problem is related to two user's pre-processing filter g1And g2Combined optimization, the Signal to Interference plus Noise Ratio of each user
Depending on the impulse response of all user's transmitting filters, another use also will affect to the optimization of user's transmitting filter
The secrecy rate at family, therefore the solution of this optimization problem is extremely difficult.Consider such a reciprocal problem: if a user
In Optimal Filter, while in addition to considering to make the received signal power maximum of oneself, it is also considered that done to another user
Minimum is disturbed, and another user also carries out the same optimization, then means that the Signal to Interference plus Noise Ratio of two users all maximizes.Cause
This, is in order to simplify solution procedure, by the Signal to Interference plus Noise Ratio formula of user i, userThe IUI caused by user i replaces with user
I is to userIUI item, just only include a prefilter impulse response g of user i in such Signal to Interference plus Noise Ratioi, i.e.,
The achievable rate of relative users i and the expression formula of secrecy rate become
In this way,Expression formula in only include gi, therefore g can be separately optimized1And g2MakeWithIt maximizes, two
Variable combined optimization problem can be converted to two single argument optimization problems, and the complexity of solution substantially reduces.Original is optimized
Problem is converted to the sub- optimization problem of following two
Abbreviation objective functionIt obtains
Wherein I is the unit matrix that size is L × L dimension,
Because of log2X is monotonically increasing function, to make log2X is maximum, it is only necessary to so that x is maximum.Therefore above-mentioned optimization
Problem can be rewritten as again
Objective function in above formula is expressed as
Wherein f (gi) be score quadratic function product, Ai, Bi, Ae,i, Be,iIt is the positive semidefinite matrix of L × L dimension, giIt is L dimension
Vector, according to document [Lee N, Yang H J, Chun J.Achievable sum-rate maximizing AF relay
beamforming scheme in two-way relay channels[C].ICC Workshops-2008IEEE
International Conference on Communications Workshops, Beijing, 2008:300-305.],
Locally optimal solutionSingle order Karush-Kuhn-Tucher (KKT) necessary condition of satisfaction is
I.e.
It enablesAccording to f above
(gi) definition, then above formula can be expressed as again
The Q of right side of the equal sign in above formula is moved on into the left side, it is available
As can be seen that solving optimal solutionThe problem of i.e. matrix Q-1The generalized eigenvalue decomposition problem of V, wherein scalarIt can be regarded as matrix Q-1The generalized eigenvalue of V, that is, meet
Make f (gi) maximum solutionIt is exactly matrix Q-1The corresponding feature vector of the maximum eigenvalue of V, therefore solving optimization is asked
Topic is equivalent to solution matrix Q-1The corresponding normalization characteristic vector of the maximum eigenvalue of V.It is noted that comprising wait ask in V and Q
The feature vector of solutionTherefore it cannot be solved using the method for conventional generalized eigenvalue decomposition.Here it is calculated using iteration
Method solvesG is given firstiAssign an initial valueV and Q are obtained, to Q-1V carries out generalized eigenvalue decomposition, obtains its maximum
Characteristic valueAnd its corresponding normalization characteristic vectorWith obtained normalization characteristic vectorIt goes to update V and Q,
Updated Q is further found out again-1The maximum eigenvalue of VAnd its corresponding normalization characteristic vectorRepeat above-mentioned mistake
Journey, until the difference between the maximum eigenvalue that certain obtained maximum eigenvalue of iterative calculation and last iteration obtain is less than some
Preset value, or until reaching the number of iterations.The iterative algorithm that characteristic value solves is summarised in table 1.
1 maximum eigenvalue of table solves iterative algorithm
Below in conjunction with attached drawing, the present invention is described in further detail.The secrecy rate provided in each figure below
Simulation result be 1 × 105Average value under group channel realization.Number of paths L=10, channel width B=are set in emulation
1MHz, channel are rayleigh fading channel, and fading channel includes large-scale fading and multipath fading, i.e., channel impulse response is
Number is the multiple Gauss stochastic variable that mean value is 0, and variance is
In formula, σT=10/B is that the root mean square in path postpones, Ts=1/B is the sampling period.ηiFor the big ruler of user's i channel
Spend fading coefficients:
In formula, c=4 is path loss index, η0For the transmission loss at reference distance, d0=10m is reference distance, di
It is transmitter at a distance from user i.η is set in emulation0=10-5, channel noise power σ2=1 × 10-11W, maximum eigenvalue are asked
Solving iteration maximum times in iterative algorithm is N=50, convergence factor ε=1 × 10-6。
Fig. 2 is under three groups of random channel coefficients, and feature vector (i.e. transmitting filter impulse response) iteratively solves process
Middle matrix Q-1The change curve of the maximum eigenvalue of V.Factor D=2 are up-sampled in emulation, send power P=1W, two users and base
The distance stood all is 100m.It can be seen from the figure that the algorithm of the present invention program has preferable convergence, generally repeatedly at 5 times
It can be restrained in generation.
Fig. 3 is the simulation result changed up to secrecy rate with transmission power, and two users are at a distance from base station
100m up-samples factor D=3.What wherein " conventional TR " was indicated is to invert filter using Conventional Time, i.e.,When simulation result.Simulation result when direct transmission is also provided simultaneously, is labeled as " directly passing in figure
It is defeated ".Directly transmission, which refers to, sends symbol without any pretreatment, is directly over channel by transmitting terminal and sends receiving end to.Its
For a prominent diameter as useful signal, remaining path is ISI using in multipath channel at middle legitimate receipt end.End is eavesdropped with more
For first diameter of diameter channel as useful signal, remaining path is ISI.And there is IUI in legal end and receiving end.Due to two
A user distance transmitter is identical, and according to symmetrical performance, their long-term average reachable secrecy rate is identical, the table in analogous diagram
It is now substantially coincident up to the curve of secrecy rate for two users under same scheme.It can be seen that excellent for secrecy and rate
The reachable secrecy rate of system is substantially better than the system using routine TR pre-processing filter after change TR pre-processing filter, and does not have
Have it is minimum by the pretreated secrecy rate directly transmitted, and substantially not with send power increase and increase.This aspect is
Because the ISI and IUI that receive signal in direct Transmission system are very serious, jamming power (ISI and IUI) is made an uproar relative to channel
Sound is larger, and with the growth for sending power, desired signal power and ISI, IUI power synchronous increase, so Signal to Interference plus Noise Ratio is basic
Do not increase with the increase of transmission power.It on the other hand is since it is desirable that the receiving velocity of receiver and interception receiver is also same
Step variation, therefore secrecy rate is also basically unchanged.And the system for using routine TR pre-processing filter, sending, power is smaller
When, it can increase with the increase for sending power up to secrecy rate, but after sending power increase to a certain extent, secrecy rate
No longer increase with the increase for sending power.In conventional TR system, the excellent of transmitting filter is not carried out for secrecy rate
Change, it is expected that the received signal power of user and undesired user (i.e. listener-in) is (for the signal for carrying expectation user information
Speech) all increasing.When power is smaller, interchannel noise is larger relative to ISI, IUI power, due to it is expected the reception signal of user
Power is higher, sends power at this time and increases, the undesired user to be faster than it is expected that the reception Signal to Interference plus Noise Ratio of user is increased speed, so
Secrecy rate increased.And after sending power increase to a certain extent, ISI, IUI power are big compared with channel noise power,
When sending power and increasing, molecule in Signal to Interference plus Noise Ratio expression formula is synchronous with denominator to be increased, so Signal to Interference plus Noise Ratio is with sending power increasing
Add it is unobvious, while two users reception Signal to Interference plus Noise Ratio it is synchronous increase, therefore secrecy rate no longer changes.And for secrecy speed
In the system of rate optimization, continue to increase up to secrecy rate with the increase for sending power, and be substantially better than conventional TR system.This
It is to be specific to the maximized target of secrecy rate because of pre-processing filter in scheme to be optimized, with the increasing of power
Add, it is expected that the rate increase of user is higher compared with undesired user, so secrecy rate increases.With send power increase, by
Increase therewith in ISI and IUI power, influence of the channel noise power to Signal to Interference plus Noise Ratio is smaller and smaller, sends power bring
SINR, which increases speed, to be gradually decreased, therefore the speedup of secrecy rate is also gradually reduced.
Fig. 4 gives the secrecy of system and the simulation result of rate under different decimation factor D, two users and base station away from
From being all 100m.Under conditions of channel width is constant, decimation factor D is bigger, and character rate is lower.It can be seen that in low function
In rate region, D is smaller, maintains secrecy and rate is higher, but it is also lower to send secrecy and increasing speed for rate when power increases.This is
Because in the denominator of Signal to Interference plus Noise Ratio, the specific gravity of channel noise power is bigger when transmission power is smaller, D hours, although ISI and
IUI is larger, but since character rate is higher, so transmission rate is higher.When sending power and increasing, due to signal power and
ISI is synchronous with IUI to be increased, and D is smaller, and ISI and IUI are bigger, and the influence of channel noise power is smaller, therefore the growth of Signal to Interference plus Noise Ratio is got over
Slowly, and saturation value is lower, thus maintain secrecy and rate increase it is slower and reachable secrecy and rate-limit it is lower.And it is larger in D
When, although character rate is lower, since ISI and IUI are small, Signal to Interference plus Noise Ratio can with send power increase and continue and rapidly
Increase, therefore maintain secrecy with rate increase faster, final attainable secrecy and rate-limit are also bigger.Therefore it needs according to system
The value of factor D can be suitably up-sampled with selections such as transmission power, channel conditions.
Fig. 5 is the simulation result of two users Yu the asynchronous secrecy rate of base distance between sites, and user 1 is at a distance from base station
d1=80m, user 2 and base station distance d2=100m.As can be seen that the confidentiality with two users with base station distance when equal
Can be similar, for the secrecy rate of each user and the secrecy and speed of system after secrecy and rate optimized TR pre-processing filter
Rate is all higher than conventional TR pre-processing filter system and direct Transmission system.Direct Transmission system and routine TR pre-processing filter
In system, the secrecy rate of two users is gradually reduced with the increase gap of power.This is because the two systems are in power
When lower, the jamming power of system is smaller, and the Signal to Interference plus Noise Ratio of user depends primarily on the ratio between desired signal power and noise power,
And two users' difference at a distance from base station causes the desired signal power of two users to differ larger, so the Signal to Interference plus Noise Ratio of two users
Gap is larger, higher apart from closer user cipher device rate.With the increase of power, the jamming power of system increases therewith, from
The jamming power growth rate of the close user in base station is fast compared with the user remote from base station, so the SINR gap of two users subtracts therewith
Small, secrecy speed difference is away from being also gradually reduced.For in the system for the rate optimized TR pre-processing filter of maintaining secrecy, the guarantor of two users
Close speed difference is away from larger.This is because be the secrecy rate independent optimization of each user, and the problem of do not account for power distribution, away from
Receptivity from closer user is better than another user always, therefore the gap of the secrecy rate of two users is larger.If
Further the signal power for sending two users' information is allocated, the gap of their secrecy rate can be reduced.
Claims (5)
1. the optimization method of pre-processing filter in time reversal multi-user's secure transmission system, it is characterised in that: single input list
It exports in downlink multi-access system, transmitting terminal and receiving end are equipped with single antenna, and the data of transmitting terminal are filtered by transmitting filter
It is exported after wave, information is transmitted as the secret communication between two users；Wherein transmitting filter optimization the following steps are included:
(1) construction transmitting filter maximizes system secrecy and rate；
(2) according to the principle of reciprocity by the Signal to Interference plus Noise Ratio expression formula of user, another user is to this distracter caused by user security risk
This user is replaced with to the distracter of another user, and then the combined optimization of two transmitting filters is converted into each filtering
The independent optimization of device；
(3) maximum eigenvalue and its corresponding feature vector by the optimal matrix being deconstructed into are found, and is obtained by iterative algorithm
To the optimal solution of pre-processing filter.
2. according to claim 1 in time reversal multi-user secure transmission system pre-processing filter optimization method,
Be characterized in that: the construction process of the step (1) is as follows:
The reception Signal to Interference plus Noise Ratio of user i (i=1,2) is
In formula, when i=1When i=2P is the power that transmitting terminal sends each user symbol sequence, σ2For height
The variance of this white noise sequence；gi=[gi[0],gi[1],…,gi[L-1]]TIndicate the impulse response of transmitting filter, L is letter
The length of road impulse response；
D is the up-sampling factor；HiFor (2LD- 1) × L dimension equivalent channel matrix, be byD integral multiple row composition matrix,It is the Toeplitz matrix of (2L-1) × L dimension and first is classified ashi=[hi[0],hi[1],…,
hi[L-1]]TIt is the vector form of channel impulse response, 01×(L-1)Indicate the null matrix of 1 × (L-1) dimension；Indicate equivalent letter
Road matrix HiLDCapable transposition；
Another userFor listener-in's eavesdropping user i information when reception Signal to Interference plus Noise Ratio be
The secrecy rate equation of user i is
Wherein, B is channel width, [x]+It indicates to take the maximum value in both 0 and x；
The transmitting filter of construction turns to system secrecy and rate maximum
Rs,1、Rs,2The respectively reachable secrecy rate of user 1 and user 2.
3. according to claim 2 in time reversal multi-user secure transmission system pre-processing filter optimization method,
Be characterized in that: step (2) combined optimization by two transmitting filters is converted to the independent optimization of each filter, specifically
Are as follows:
The Signal to Interference plus Noise Ratio formula of user i becomes:
The expression formula of the secrecy rate of relative users i becomes:
G is separately optimized1And g2MakeWithIt maximizes, so that the combined optimization of two transmitting filters is converted to each filtering
The independent optimization of device, as
4. according to claim 1 in any one of -3 time reversal multi-user secure transmission systems pre-processing filter optimization
Method, it is characterised in that: step (3) obtains the optimal solution of transmitting filter, specifically:
Optimization object function is expressed as
According to locally optimal solutionThe single order KKT necessary condition of satisfactionIt obtains
Wherein,I is that size is L
The unit matrix of × L dimension.
Optimal solutionFor matrix Q-1The corresponding normalization characteristic vector of the maximum eigenvalue of V；It is solved using iterative algorithm
5. according to claim 4 in time reversal multi-user secure transmission system pre-processing filter optimization method,
It is characterized in that: first to giAssign an initial valueV and Q are obtained, to Q-1V carries out generalized eigenvalue decomposition, and it is maximum special to obtain it
Value indicativeAnd its corresponding normalization characteristic vectorWith obtained normalization characteristic vectorIt goes to update V and Q, into
One step finds out updated Q again-1The maximum eigenvalue of VAnd its corresponding normalization characteristic vectorRepeat above-mentioned mistake
Journey, until the difference between the maximum eigenvalue that certain obtained maximum eigenvalue of iterative calculation and last iteration obtain is less than in advance
The value of setting, or until reaching the number of iterations.
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