CN106507464B - Optimal power allocation method based on effective and safe capacity - Google Patents

Optimal power allocation method based on effective and safe capacity Download PDF

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Publication number
CN106507464B
CN106507464B CN201611154824.XA CN201611154824A CN106507464B CN 106507464 B CN106507464 B CN 106507464B CN 201611154824 A CN201611154824 A CN 201611154824A CN 106507464 B CN106507464 B CN 106507464B
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jammer
power
transmitter
eavesdropper
representing
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CN106507464A (en
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吕刚明
安广平
任品毅
杜清河
李国兵
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Xian Jiaotong University
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Xian Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/265—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the quality of service QoS
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/40—Jamming having variable characteristics
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/80—Jamming or countermeasure characterized by its function
    • H04K3/82—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection
    • H04K3/825—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection by jamming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/38—TPC being performed in particular situations

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Quality & Reliability (AREA)
  • Transmitters (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention discloses a kind of optimal power allocation methods based on effective and safe capacity, the system that this method uses includes 1 transmitter for being equipped with 1 omnidirectional antenna, 1 legitimate user and 1 listener-in, and it is equipped with 1 cooperation jammer of more omnidirectional antennas, this method includes that specific step is as follows: 1) transmitter and legitimate user communicate, and cooperation jammer transmitting interference signal introduces the interference of differentiation to legitimate user and listener-in；Safe capacity is found out according to the signal that legitimate user and listener-in receive, and the definition of the effective safe capacity of combination obtains the expression formula of effective and safe capacity；2) expression formula of effective and safe capacity is utilized, establish the relationship of cooperation jamming power and effective and safe capacity, and effective and safe capacity is optimized under conditions of the jammer mean power that cooperates is limited and cooperation jammer power is non-negative, final power distribution method is obtained as target using effective and safe maximum capacity.

Description

Optimal power distribution method based on effective safety capacity
The technical field is as follows:
the invention belongs to the technical field of wireless communication, and particularly relates to an optimal power distribution method based on effective safety capacity.
Background art:
security of wireless communications is becoming an increasingly prominent problem due to the openness of the wireless medium and the instability of wireless broadcasts. With the explosive growth of secure data transmissions, security of wireless communications has received increasing attention. The conventional way to implement security is encryption technology, which has an advantage in that even if an eavesdropper overhears the transmitted information, the transmitted information may not be obtained because the key cannot be obtained. However, encryption techniques have two significant drawbacks: firstly, a secret key can be stolen in the transmission process; secondly, the encryption technology is based on the calculation amount, and the stronger the calculation capacity of the computer, the higher the possibility that the key is cracked. With the deep understanding of the physical layer characteristics, scholars propose that secure communication can be achieved through physical layer security techniques. The physical layer security technology is to utilize the characteristics of the physical layer, such as fading or interference, to realize the security performance of the system. Common physical layer security techniques include key agreement, channel coding, cooperative interference, and the like. As an effective physical layer security technology, cooperative interference is interference introduced into a legal user and an eavesdropper in a differentiated manner, so that the interference on the eavesdropper is higher than that on the legal user, and the performance of a main channel is improved. Many studies have applied cooperative interference techniques in different scenarios to improve the security performance of wireless systems.
However, for many real-world communication systems, such as voice over internet protocol (voip) systems and video interactive systems, in addition to satisfying security performance, a certain Quality of Service (QoS) needs to be guaranteed. In this case, the requirement of service quality needs to be taken into account when measuring the performance of the system. However, most of the existing power allocation schemes based on wireless system performance do not consider the delay QoS or only consider the very strict or loose situation, so it is of great significance to research the differential delay QoS guarantee problem.
The invention content is as follows:
the invention aims to provide an optimal power distribution method based on effective safety capacity, aiming at the problems in the prior art, and the method not only can ensure the safety of wireless communication, but also can adapt to the guarantee of differential time delay QoS.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
the optimal power distribution method based on effective safe capacity adopts a system comprising 1 transmitter, 1 legal user and 1 eavesdropper which are all provided with 1 omnidirectional antenna, and 1 cooperative jammer which is provided with a plurality of omnidirectional antennas, wherein the cooperative jammer is assumed to know the channel state information of all channels; all channels are rayleigh block fading channels; by designing a beam forming vector at a cooperative jammer, differential interference is introduced to a legal user and an eavesdropper, and the method specifically comprises the following steps:
1) the transmitter communicates with a legal user, and the cooperative jammer transmits an interference signal to introduce differential interference to the legal user and an eavesdropper; calculating the safety capacity according to signals received by a legal user and an eavesdropper, and obtaining an expression of the effective safety capacity by combining the definition of the effective safety capacity;
2) and establishing a relation between the power of the cooperative jammer and the effective safety capacity by using an expression of the effective safety capacity, and optimizing the effective safety capacity under the conditions that the average power of the cooperative jammer is limited and the power of the cooperative jammer is not negative, so as to obtain a final power distribution method by taking the maximization of the effective safety capacity as a target.
The further improvement of the invention is that the specific implementation method of the step 1) is as follows:
101) the transmitter transmits data in the form of data frames to obtain signals received by a legal user and an eavesdropper in the ith frame;
102) the expression of the effective security capacity is obtained by using the signals received by the legal user and the eavesdropper.
A further improvement of the present invention is that, in step 101), the signals received by the legitimate user and the eavesdropper are:
wherein, PSRepresents the power of the transmitter, is constant; pJRepresents the power of the co-operative jammer, andxsrepresents a signal transmitted by a transmitter, and E [ | x [ ]s|2]1 is ═ 1; ω z represents the signal transmitted by the cooperative jammer, wherein,representing waves at co-operative jammersA beamforming vector, and ω ═ ω (ω ═ ω)1,ω2,...ωm)T，||ω||21 is ═ 1; z represents an interference signal, and E | z tint2]＝1；nDAnd nEThe cyclic symmetric complex Gaussian random variables represent zero mean values and are independently and uniformly distributed; h isS,D∈C1×1Representing the channel of the transmitter to the legitimate user; h isS,E∈C1×1A channel representing a transmitter to an eavesdropper; h isJ,D∈Cm×1Representing the channel of the co-operative jammer to the legitimate user, where hJ,D＝(hJ,D1,hJ,D2,...hJ,Dm)T；hJ,E∈Cm×1Representing a channel of a cooperating jammer to an eavesdropper, where hJ,E＝(hJ,E1,hJ,E2,...hJ,Em)T。
A further improvement of the invention is that in step 102), the expression of the effective safety capacity C (θ) is:
wherein, theta is a service quality index; t is the duration of one frame; b is the bandwidth; and R represents a safe rate.
The further improvement of the invention lies in establishing the relation between the power of the cooperative jammer and the effective safety capacity, which is as follows:
s.t:0≤R≤RS
PJ≥0
wherein, PJRepresenting the power allocated by the cooperative jammer in each channel state;representing a beamforming vector at a cooperating jammer; rSRepresenting a safe capacity;representing the maximum average power that the co-located jammer can allocate.
The invention is further improved in that the beamforming vectors at the co-operative jammers are designedObtaining a new expression of the safety capacity; then, the safety capacity is discussed to be greater than zero and equal to zero, and a new optimization problem is obtained;
s.t.PJ≥0
wherein,
PSrepresents the power of the transmitter Alice, is constant;representing the channel gain of the transmitter to legitimate users normalized to noise;representing the transmitter to eavesdropper normalized channel gain to noise;representing the channel gain of the cooperative jammer to the noise normalization of the eavesdropper;representing the square of a cosine value of an included angle between a cooperative jammer and a channel between a legal user and an eavesdropper;
and solving the new optimization problem through a Lagrange dual function, and obtaining the optimal solution of the new optimization problem through continuously iterating a Lagrange multiplier.
The further improvement of the present invention is that the lagrangian function for the new optimization problem is:
wherein λ isR、λPV is a Lagrange multiplier;
the corresponding lagrange dual function is:
in order to ensure that the water-soluble organic acid,
will limit the conditionsSubstitution into fz(PJ,λPV), can be obtained
Wherein,
solving of the new optimization problem:
because of the fact thatThen h isz(PJ,λPV) is about PJA convex function ofz(PJ,λPV) is taken when its first derivative is equal to 0
Order toTo obtain
Let a be PSzS,E、b＝zJ,Eα、c＝(1+PSzS,D)β、d＝αβPSzS,EzJ,E；
The above formula is written as
Order toIt is PJA decreasing function of;
obtaining the local optimum power P of the transmitter shown in the following formulaloopt
The optimum power P of the transmitter is then solved by the algorithm shown belowoptSolving a new optimization problem through an iterative algorithm;
step 1: initialization PoptAnd v value
Initialization Popt0; find vlV and vuSo that they respectively satisfyAnd
repeating the following steps 2 and 3 untilEstablishing, wherein epsilon is a very small positive real number, and solving a dual problem;
step 2:
step 2.1: v ═ v (v)l+νu) Per channel state, using the formulaRespectively determining the locally optimal power Ploopt；
Step 2.2: if h isz(Ploopt,λP,ν)＜fz(0,0,λPV), optimum power Popt＝Ploopt(ii) a Otherwise, Popt＝0；
And step 3: updating vlV and vu；
If it is notνuν; else vl＝ν。
Compared with the prior art, the invention has the following technical effects:
the invention introduces differential interference to a legal user and an eavesdropper by adopting a cooperative interference technology through the cooperation of the jammers so as to improve the safety performance of the system and overcome the defect that the encryption technology is invalid along with the increase of the calculated amount.
The invention considers the differentiated time delay QoS requirements of different users, does not purely start from the perspective of information theory, and only takes the traversal capacity or the interrupt capacity of the system as the optimization target to realize power distribution. The invention can meet the requirements of different time delay service quality of users, and has wide application in a voice telephone system and a video interaction system.
The invention comprehensively considers the performances of safety and time delay service quality and provides an optimal power distribution scheme based on effective safety capacity.
The following table gives a comparison of performance between the power allocation scheme proposed herein and other schemes;
from the above table, the present invention is superior to the equal power allocation scheme and the scheme without jammers.
Description of the drawings:
FIG. 1 illustrates transmission modes of a secure communication system in consideration of a delay QoS requirement
FIG. 2 is a comparison of effective safe capacity performance between different scenarios;
fig. 3 is a graph of the performance of the effective safety capacity when the transmitter and the co-jammer are at different powers;
FIG. 4 is a graph of effective safe capacity performance for total power and a change in the specific power of a cooperative jammer over the total power;
FIG. 5 is a comparison of delay quality of service performance between different schemes;
FIG. 6 shows power allocation under different channel conditions; fig. 6(a) is corresponding power distribution when a channel from a transmitter to a legal user and a channel from the transmitter to an eavesdropper changes, fig. 6(b) is corresponding power distribution when a channel from the transmitter to the legal user and a channel from a cooperative jammer to the eavesdropper changes, fig. 6(c) is corresponding power distribution when a channel from the transmitter to the eavesdropper and a channel from the cooperative jammer to the eavesdropper changes, and fig. 6(d) is corresponding power distribution when an included angle between a channel from the cooperative jammer to the legal user and the channel from the cooperative jammer to the eavesdropper changes.
The specific implementation mode is as follows:
the invention is described in further detail below with reference to the following figures and examples, which are intended to illustrate, but not to limit the invention.
The power distribution scheme based on the effective safety capacity in the field of wireless communication is characterized in that when the power distribution facing the effective safety capacity in the scene of an eavesdropper is considered, firstly, a cooperative interference technology is adopted to introduce differential interference to a legal user and the eavesdropper; and secondly, establishing a relation between the effective safety capacity and the distributed power of the cooperative jammers, and obtaining a power distribution scheme by taking the effective safety capacity as the maximum. Wherein the expression of the effective safe capacity is obtained according to the set scene, and the effective safe capacity of the system is maximized under the conditions that the power of the cooperative interference machine is not negative and the average power is limited.
The specific embodiment is as follows:
consider an eavesdropping scenario comprising 1 transmitter (Alice), 1 legitimate user (Bob) and 1 eavesdropper (Eve), all equipped with 1 omni-directional antenna; 1 cooperative Jammer (Jammer) equipped with m (m > 1) omnidirectional antennas. When an eavesdropper exists, the transmitter communicates with a legal user; the cooperative jammer sends interference signals to introduce differential interference to legal users and eavesdroppers. Assuming that the cooperative jammers know channel state information of all channels; all channels are rayleigh block fading channels, i.e. the state of the channel remains unchanged for the duration T of one frame, independent from each other between different users and different frames.
1) The transmitter communicates with a legal user, and the cooperative jammer transmits an interference signal to introduce differential interference to the legal user and an eavesdropper;
the transmitter transmits data in the form of data frames, and in the ith frame, signals received by a legal user and an eavesdropper are respectively:
wherein, YD[i]、YE[i]Respectively representing the signals received by a legitimate user and an eavesdropper at the ith frame. PSRepresents the power of the transmitter, is constant; pJ[i]Represents the power of the cooperative jammer at the i-th frame, an Representing the maximum average power that the jammer can allocate. x is the number ofsRepresents a signal transmitted by a transmitter, and E [ | x [ ]s|2]1 is ═ 1; ω z represents the signal transmitted by the cooperative jammer, wherein,represents a beamforming vector at the co-operative jammer, and ω ═ ω (ω ═ ω)1,ω2,...ωm)TM represents the number of antennas of the jammer, | | ω | | non-calculation21 is ═ 1; z represents an interference signal, and E | z tint2]＝1；nDAnd nEThe cyclic symmetric complex Gaussian random variables represent zero mean values and are independently and uniformly distributed; h isS,D∈C1×1Representing the channel of the transmitter to the legitimate user; h isS,E∈C1×1A channel representing a transmitter to an eavesdropper; h isJ,D∈Cm×1Representing the channel of the co-operative jammer to the legitimate user, where hJ,D＝(hJ,D1,hJ,D2,...hJ,Dm)T；hJ,E∈Cm×1Representing a channel of a cooperating jammer to an eavesdropper, where hJ,E＝(hJ,E1,hJ,E2,...hJ,Em)T. All channels are assumed to be rayleigh block fading channels.
And obtaining the Signal to Interference and Noise ratio (SINR) of the legal user and the eavesdropper:
further, the expression of the safety capacity is obtained as follows:
wherein, the SINRD、SINRESINR, R, at the location of legitimate users and eavesdroppersSRepresenting a safe capacity;
2) optimization problem for effective safety capacity
The effective capacity is defined as the constant arrival rate of data that the system can support while satisfying a certain statistical QoS requirement, and it characterizes the system's ability to provide real-time services. And obtaining a specific expression of the effective safe capacity according to the expression of the safe capacity obtained above, so as to model and solve the optimization problem and finally obtain an optimal power distribution scheme.
The general expression for effective capacity is as follows:
wherein, E [. C]Expressing the expectation;representing the service process of time accumulation, namely the bit number of the service user in 0-t time; s (i) represents discrete time stationary and ergodic service processes; theta represents an index of quality of service (QoS), and a larger theta represents a more demanding QoS requirement, i.e., the system can only allow a lower rate of delay violations.
When the service rate is a safe rate, the obtained effective capacity is referred to as an effective safe capacity.
Assuming that all channels are rayleigh block fading channels, s [ i ] is TR [ i ]. Where R [ i ] denotes a secure service rate for the duration T of the ith frame. Again, assume that R [ i ] is stationary and ergodic.
The expression for the effective safety capacity for bandwidth normalization is therefore:
wherein C (θ) represents the effective safety capacity, θ represents the QoS index, and T represents the duration of one frame; b represents a bandwidth; r represents the safe rate.
Therefore, in order to meet the requirement of real-time performance, the effective safety capacity needs to be as large as possible.
3) Establishment and solution of optimization problem
The invention aims at maximizing the effective safe capacity of the system, and establishes the following optimization problems:
s.t:0≤R≤RS
PJ≥0
wherein, PJRepresenting the power allocated by the cooperative jammer in each channel state;representing a beamforming vector at a cooperating jammer; r represents the safe rate, RSRepresenting a safe capacity;representing the maximum average power that the co-located jammer can allocate.
Solving an optimization problem:
the target function comprises a safe rate R, the expression of the safe capacity is not only related to the channel state, but also related to a beamforming vector omega at a cooperative jammer, and the beamforming vector omega is designed firstly according to the following design principle:
1) the cooperative jammer does not interfere with legal users;
2) the interference of the cooperative jammer to the eavesdropper is the largest;
that is to say that the first and second electrodes,
s.t:ωHhJ,D＝0
||ω||2＝1
solving the beam forming vector omega meeting the condition by a formula
In a clear view of the above, it is known that,wherein,for channel hJ,DAnd hJ,EThe included angle therebetween. And only ifWhen the number is equal, the equal sign is established.
And because of
That is, the designed beamforming vector ω does not cause interference to the legitimate user.
In summary, the designed beamforming vector satisfies the above two conditions.
At this time, the safety capacity may be RSIn the following writing:
without being provided withR is to beSThe discussion is divided into two cases of greater than and equal to 0:
when R isSWhen the pressure is higher than 0, the pressure is higher,
at this time, the process of the present invention,
on the contrary, when R isSWhen the content is equal to 0, the content,
the arrangement is not limited to the above-mentioned,
the original optimization problem is equivalent to:
s.t.PJ≥0
wherein,the optimization problem described above is in turn equivalent to
s.t.PJ≥0
Wherein,the lagrangian function for the above optimization problem is:
wherein λ isR、λPV is a Lagrange multiplier;
the corresponding lagrange dual function is:
the above problem is decomposed into many similar sub-problems to be solved:
in the absence of a catalyst, it is preferable that,
will limit the conditionsSubstitution into fz(PJ,λPV), can be obtained
Wherein,
solving an optimization problem:
because of the fact thatThen h isz(PJ,λPV) is about PJA convex function ofz(PJ,λPV) is taken when its first derivative is equal to 0.
Order toCan obtain
And do not let a ═ PSzS,E、b＝zJ,Eα、c＝(1+PSzS,D)β、d＝αβPSzS,EzJ,E；
The above formula can be written as
Order toIt is PJIs the decreasing function of.
The local optimum power P of the transmitter can be derived as shown belowloopt
In summary, the optimal power P of the transmitter can be solved by the algorithm shown belowopt；
A new optimization problem can be solved by an iterative algorithm;
step 1: initialization PoptAnd v value
Initialization Popt0; find vlV and vuSo that they respectively satisfyAnd
repeating the following steps 2 and 3 untilEstablishing, wherein epsilon is a very small positive real number, and solving a dual problem;
step 2:
step 2.1: v ═ v (v)l+νu) Per channel state, using the formulaRespectively determining the locally optimal power Ploopt；
Step 2.2: if h isz(Ploopt,λP,ν)＜fz(0,0,λPV), optimum power Popt＝Ploopt(ii) a Otherwise, Popt＝0；
And step 3: updating vlV and vu；
If it is notνuν; else vl＝ν。
Simulation parameter configuration
Fig. 1 shows a system model, that is, in the presence of an eavesdropper, a legitimate user and the eavesdropper perform communication, and a cooperative jammer is provided to introduce differential interference to the legitimate user and the eavesdropper, so as to improve the performance of the system.
Fig. 2 shows a comparison between the solution of the invention and other existing solutions, respectively a constant power allocation solution and a solution without co-operating jammers. As can be seen from the figure, the scheme provided by the invention is superior to the two existing schemes. In addition, fig. 2 also indicates the trend of the effective safety capacity varying with the delay service quality index θ in different schemes. As can be seen from the figure, as the delay quality of service index θ increases, the effective safety capacity decreases, which represents a compromise in performance between delay quality of service and safety capacity.
FIG. 3 shows that when θ is 10-1The performance of the transmitter and the co-operating jammer at different powers varies. As can be seen from the figure, increasing the power of the transmitter or the cooperative jammer can improve the desired and effective safety capacity. When the power of the cooperative jammer is small, the improvement of the effective safety capacity brought by increasing the power of the transmitter is not obvious; when the power of the cooperative jammer is larger, the improvement of the effective safety capacity brought by increasing the power of the transmitter is more obvious, and when the power of the transmitter is also larger, the improvement of the effective safety capacity brought by increasing the power of the transmitter is limited. When the power of the transmitter is smaller, the power of the cooperative jammer is increased, and the effective safety capacity is increased firstly and then tends to be stable; when the power of the transmitter is larger, the power of the cooperative jammer is increased, and the effective safety capacity is increased.
FIG. 4 shows that when θ is 10-1The total power and the performance of the co-operating jammers as a proportion of the total power changes. As can be seen, increasing the total power can lead to an increase in the effective safe capacity performance. When the total power is constant, the effective safety capacity decreases as the power of the cooperative jammers increases in proportion to the total power. And, with the increase of the total power, the proportion of the power of the corresponding cooperative jammer in the total power gradually increases when the effective safety capacity takes the maximum value.
Fig. 5 shows the comparison of the delay service quality performance between different schemes when the information arrival rates are respectively 6kbit/s and 8 kbit/s. Wherein, the lower the delay default rate is, the better the delay service quality performance is. When the information arrival rate is 6kbit/s, theta*＝10-2(ii) a When the information arrival rate is 8kbit/s, theta*＝10-2.5. As can be seen from the figure, the performance of the delay violation rate of the adaptive power allocation scheme provided by the invention is very close to the theoretical value, which verifies the correctness of the proposed scheme. Secondly, the adaptation proposed by the present inventionThe power allocation scheme has a lower delay violation rate than the other schemes shown, which proves the superiority of the proposed scheme. And finally, when the arrival rate of the information is 6kbit/s, the acquired delay service quality performance is caused by the condition that the arrival rate of the information is 8 kbit/s.
FIG. 6 shows that when θ is 10-1And (4) power distribution under the condition of different channel states. Assuming that the channel gain from the transmitter to the legal user, the channel gain from the transmitter to the eavesdropper and the channel gain from the cooperative jammer to the eavesdropper all obey exponential distribution with the mean value of 1, and dispersing the channels into 100 states according to equal probability distribution. The included angle between the cooperative jammer to the legal user and the cooperative jammer to the channel of the legal user is [0 degree, 90 degree ]]It is discretized into 18 states, and the angle difference between adjacent states is 5 deg.. As can be seen, for the case of very bad channel state, we do not allocate power; when the channel state is good to a certain degree, starting to distribute power; and as the channel gets better, the allocated power will get smaller. This is because, for the case of poor channel state, it is often necessary to allocate a large amount of power to ensure that the safe transmission rate reaches a certain value, which causes power waste, and at this time, power is not allocated. For the case of a good channel state, only a small amount of power needs to be allocated to ensure that the safe rate reaches a certain value, and at this time, little power is allocated.

Claims (1)

1. The optimal power distribution method based on effective safety capacity is characterized in that the system adopted by the method comprises 1 transmitter, 1 legal user and 1 eavesdropper which are all provided with 1 omnidirectional antenna, and 1 cooperative jammer which is provided with a plurality of omnidirectional antennas, wherein the cooperative jammer is assumed to know the channel state information of all channels; all channels are rayleigh block fading channels; by designing a beam forming vector at a cooperative jammer, differential interference is introduced to a legal user and an eavesdropper, and the method specifically comprises the following steps:
1) the transmitter communicates with a legal user, and the cooperative jammer transmits an interference signal to introduce differential interference to the legal user and an eavesdropper; calculating the safety capacity according to signals received by a legal user and an eavesdropper, and obtaining an expression of the effective safety capacity by combining the definition of the effective safety capacity; the specific implementation method comprises the following steps:
101) the transmitter transmits data in the form of data frames to obtain signals received by a legal user and an eavesdropper in the ith frame; the signals received by the legal user and the eavesdropper are respectively:
wherein, PSRepresents the power of the transmitter, is constant; pJRepresents the power of the co-operative jammer, andxsrepresents a signal transmitted by a transmitter, and E [ | x [ ]s|2]1 is ═ 1; ω z represents the signal transmitted by the cooperative jammer, wherein,represents a beamforming vector at the co-operative jammer, and ω ═ ω (ω ═ ω)1,ω2,...ωm)T，||ω||21 is ═ 1; z represents an interference signal, and E | z tint2]＝1；nDAnd nEThe cyclic symmetric complex Gaussian random variables represent zero mean values and are independently and uniformly distributed; h isS,D∈C1×1Representing the channel of the transmitter to the legitimate user; h isS,E∈C1×1A channel representing a transmitter to an eavesdropper; h isJ,D∈Cm×1Representing the channel of the co-operative jammer to the legitimate user, where hJ,D＝(hJ,D1,hJ,D2,...hJ,Dm)T；hJ,E∈Cm×1Representing a channel of a cooperating jammer to an eavesdropper, where hJ,E＝(hJ,E1,hJ,E2,...hJ,Em)T；
102) Obtaining an expression of effective safety capacity by utilizing signals received by a legal user and an eavesdropper; the expression for the effective safety capacity C (θ) is:
wherein, theta is a service quality index; t is the duration of one frame; b is the bandwidth; r represents a safe rate;
2) establishing a relation between the power of the cooperative jammer and the effective safety capacity by using an expression of the effective safety capacity, and optimizing the effective safety capacity under the conditions that the average power of the cooperative jammer is limited and the power of the cooperative jammer is not negative, so as to obtain a final power distribution method by taking the maximization of the effective safety capacity as a target;
the relationship between the power of the cooperative jammer and the effective safety capacity is established as follows:
s.t:0≤R≤RS
PJ≥0
wherein, PJRepresenting the power allocated by the cooperative jammer in each channel state;representing a beamforming vector at a cooperating jammer; rSRepresenting a safe capacity;representing the maximum average power that can be allocated by the cooperative jammer;
designing beamforming at a cooperative jammerShape vectorObtaining a new expression of the safety capacity; then, the safety capacity is discussed to be greater than zero and equal to zero, and a new optimization problem is obtained;
s.t.PJ≥0
wherein,
PSrepresents the power of the transmitter Alice, is constant;representing the channel gain of the transmitter to legitimate users normalized to noise;representing the transmitter to eavesdropper normalized channel gain to noise;representing the channel gain of the cooperative jammer to the noise normalization of the eavesdropper;representing the square of a cosine value of an included angle between a cooperative jammer and a channel between a legal user and an eavesdropper;
solving a new optimization problem through a Lagrange dual function, and obtaining an optimal solution of the new optimization problem through continuously iterating a Lagrange multiplier;
the lagrangian function for the new optimization problem is:
wherein λ isR、λPV is a Lagrange multiplier;
the corresponding lagrange dual function is:
in order to ensure that the water-soluble organic acid,
will limit the conditionsSubstitution into fz(PJ,λPV), can be obtained
Wherein,
solving of the new optimization problem:
because of the fact thatThen h isz(PJ,λPV) is about PJA convex function ofz(PJ,λPV) is taken when its first derivative is equal to 0
Order toTo obtain
Let a be PSzS,E、b＝zJ,Eα、c＝(1+PSzS,D)β、d＝αβPSzS,EzJ,E；
The above formula is written as
Order toIt is PJA decreasing function of;
obtaining the local optimum power P of the transmitter shown in the following formulaloopt
The optimum power P of the transmitter is then solved by the algorithm shown belowoptSolving a new optimization problem through an iterative algorithm;
step 1: initialization PoptAnd v value
Initialization Popt0; find vlV and vuSo that they respectively satisfyAnd
repeating the following steps 2 and 3 untilWherein ε is a very small positive real number, anSolving the solution of the dual problem;
step 2:
step 2.1: v ═ v (v)l+νu) Per channel state, using the formulaRespectively determining the locally optimal power Ploopt；
Step 2.2: if h isz(Ploopt,λP,v)＜fz(0,0,λPV), optimum power Popt＝Ploopt(ii) a Otherwise, Popt＝0；
And step 3: updating vlV and vu；
If it is notνuν; else vl＝ν。
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