CN110225579B - Cooperative interference physical layer secure transmission method based on wireless energy supply - Google Patents

Cooperative interference physical layer secure transmission method based on wireless energy supply Download PDF

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CN110225579B
CN110225579B CN201910505170.8A CN201910505170A CN110225579B CN 110225579 B CN110225579 B CN 110225579B CN 201910505170 A CN201910505170 A CN 201910505170A CN 110225579 B CN110225579 B CN 110225579B
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高明
丁威
刘宇
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Xidian University
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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
    • 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
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • 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
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/243—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account interferences
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/16—Implementing security features at a particular protocol layer

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Abstract

The invention discloses a safe transmission method of a cooperative interference physical layer based on wireless energy supply.A cooperative interference node sends an interference signal by using expected collection power, and the safe transmission performance of a system under five conditions is researched; starting from known channel CSI, the confidentiality performances of different interference cooperation schemes under the conditions of known ideal condition of all channel CSI, unknown condition of eavesdropper CSI, known cooperative channel gain sequencing and limited feedback rate channel CSI are respectively researched, closed solutions of connection interruption probability and confidentiality interruption probability under various conditions are deduced, and an expression under high SNR approximation is given; the connection interruption probability and the confidentiality interruption probability of the system have a certain compromise relationship, and system parameters can be selected and designed according to different system requirements to achieve compromise between safety and confidentiality.

Description

Cooperative interference physical layer secure transmission method based on wireless energy supply
Technical Field
The invention relates to the technical field of network safety transmission, in particular to a cooperative interference physical layer safety transmission method based on wireless energy supply.
Background
The sending of the interference signal consumes energy, and although a Friendly cooperative interference node (FJ) can assist the secure transmission of the legitimate user information, it consumes its own energy at the same time. Due to the selfishness and independence of the nodes, the interfering nodes should not damage the benefits of the interfering nodes and can even receive additional compensation and rewards while helping the legal transmission. Therefore, the transmitter of the legal user needs to provide the extra energy required by the FJ node to send interference, and the energy required by the cooperative node is compensated in a wireless energy supply manner, so that the cooperative node can be stimulated to participate in cooperative secure transmission, which is more consistent with the situation that the actual cooperative node participates in cooperation.
The documents Jiang and Chen study that a power station activates legitimate users to transmit information by wireless energy supply, and pb (power beacon) serves as a power source for a transmitter. Jiang also investigated the physical layer security performance of systems where single antenna PB powers multi-antenna transmitters through wireless functionality in the presence of single antenna and multi-antenna eavesdroppers Eve, noting that this scheme enhances the security of the system by transmitting AN through the transmitter. Huang uses a model similar to the literature, except that two different scenarios, namely collusion and non-collusion, of multiple eavesdroppers are considered, and the probability of security interruption (SOP) and the average secret rate of a transmitter using both Maximum Ratio Transmission (MRT) and Transmit Antenna Selection (TAS) methods are studied assuming that the Outdated channel CSI (OCSI) is known.
Disclosure of Invention
The invention aims to provide a safe transmission method of a cooperative interference physical layer based on wireless energy supply.
The technical scheme adopted by the invention is as follows:
a safe transmission method of a cooperative interference physical layer based on wireless energy supply comprises the following steps:
a: establishing a limited rate feedback cooperative interference interception transmission model considering MISO, wherein the model comprises a multi-antenna information source node S, a single-antenna legal user D, a wireless power supply cooperative interference node J and a single-antenna interception node E;
the cooperative nodes are a plurality of or multiple antennas, and for the convenience of calculation and analysis, the cooperative nodes with single antenna are regarded as a special case of selecting an optimal cooperative node from the plurality of cooperative nodes;
suppose S has the number of antennas NSAnd the number of antennas in J configuration is NJThe other nodes adopt single antennas; assuming a Rayleigh channel with quasi-static channels, namely the channel CSI in each transmission block is unchanged, and the channel CSI among different transmission blocks is independently changed;
b: because the cooperative interference node is a selfish node with limited energy, the energy for sending the interference signal comes from energy collection of the sending power of the source node, and an expected value for collecting the energy is adopted to replace a real-time value; the time division transmission protocol is adopted, and the whole transmission process is divided into two stages;
b1: in the first stage, a source node S serves as an energy source to supply energy to a cooperative interference node J in a wireless mode;
defining alpha as a time division ratio, and assuming that the length of one time slot is T, wherein alpha T is just started, 0 < alpha < 1 is used for wireless energy supply of a first stage, and the rest time slots (1-alpha) T are used for information transmission;
in the first stage, the energy signal received by the cooperative interference node J from the source node S is represented as
Figure GDA0002802233170000021
Wherein P isSIs the transmission power of the source node, HSJRepresenting a wireless energizing channel, is NJ×NSAnd each element is subject to independent homography, and the zero mean variance is lambda1Complex gaussian random variable of xSRepresents NSX 1 energy signal vector and satisfies the total power constraint
Figure GDA0002802233170000031
nSRepresents NSA Gaussian additive white noise vector of 1 and
Figure GDA0002802233170000032
thus, at the end of the first phase, the cooperative interfering node J obtains a total energy of
Figure GDA0002802233170000033
Wherein eta, 0 < eta < 1 represents energy conversion efficiency;
due to the selfishness and friendliness of the cooperative interfering node J, i.e. the interfering signal is transmitted with the expectation of collecting energy, the transmit power of the node J is written as
Figure GDA0002802233170000034
B2: in the second stage, the source node S transmits information to the destination node D, meanwhile, the cooperative interference node sends an interference signal, and the eavesdropping node eavesdrops useful information;
according to the channel CSI known by the cooperative nodes, the following two cooperative interference schemes are adopted: a linear beam forming BF method and an antenna selection AS method;
b2-1: linear beam forming BF method
Because the cooperative node is configured with multiple antennas, the multiple antennas are utilized to form a beam forming transmission signal so as to enhance the reliability and safety of receiving by the destination node;
thus, the received signal of the legitimate user is represented as
Figure GDA0002802233170000035
Wherein h issdIs NSA vector of x 1, representing the legal channel coefficients; h isjdIs NJA vector of x 1, representing an interference channel from the cooperative node J to the eavesdropping node E; h issdAnd hjdSubject to a zero mean variance of λ2And λ4Independently and equally distributing complex Gaussian random variables; the beamforming of the source node uses maximum ratio transmission, w1＝h'sd/||hsdIs NSX 1 beamforming vector, w2Is N of an interfering signalJA beamforming vector of x 1 and | | w2||21, z is the interference signal per unit power, ndIs that the mean value of the legal user receiver is 0 and the variance is N0The AWGN signal of (1);
similarly, the received signal at the eavesdropper E is denoted as
Figure GDA0002802233170000041
Wherein h isseIs NSA vector of x 1, representing the eavesdropping channel coefficient; h isjeIs NJA vector of x 1, representing an interference channel from the cooperative node J to the eavesdropping node E; h issdAnd hjdSubject to a zero mean variance of λ3And λ5Independent identically distributed complex gaussian random variables of neIs the mean value of the eavesdropper receiver is 0 and the variance is N0The AWGN signal of (1);
thus, in conjunction with equation (3), the end-to-end SINR of legitimate user D is expressed as
Figure GDA0002802233170000042
Order to
Figure GDA0002802233170000043
The above formula can be abbreviated as
Figure GDA0002802233170000044
It is assumed that the noise at the eavesdropper is ignored because the interference signal dominates at the eavesdropper, which is considered to be a worst case;
thus, in conjunction with equation (3), the end-to-end signal-to-interference ratio, SIR, of the eavesdropper E is expressed as
Figure GDA0002802233170000045
The beamforming vector w is shown by the equations (7) and (8)2And channel hjdAnd hjeIn connection with designing different beamforming vectors w based on the known channel CSI information2To enhance the transmission and security performance of the system;
b2-2: an antenna selection method;
according to the principle of AS, the cooperative node selects an optimal antenna from a plurality of antennas to transmit interference signals according to a set standard, so AS to achieve the purpose of enhancing the system security;
assuming that k is the index of the selected antenna, the SINR at the legitimate user D and the SIR at the eavesdropper E are expressed as follows according to equations (7) and (8), respectively
Figure GDA0002802233170000051
Wherein
Figure GDA0002802233170000052
Representing the channel coefficients between the kth antenna of the cooperative node J and the legitimate user D,
Figure GDA0002802233170000053
representing the channel coefficients between the kth antenna of the cooperative node J and the eavesdropper E. .
The invention adopts the cooperative interference nodes to send the interference signals by using the expected collection power, and researches the safe transmission performance of the system under five conditions. Starting from known channel CSI, the confidentiality performances of different interference cooperation schemes under the conditions of known ideal condition of all channel CSI, unknown condition of eavesdropper CSI, known cooperative channel gain sequencing and limited feedback rate channel CSI are respectively researched, closed solutions of connection interruption probability and confidentiality interruption probability under various conditions are deduced, and an expression under high SNR approximation is given; the connection interruption probability and the confidentiality interruption probability of the system have a certain compromise relationship, and system parameters can be selected and designed according to different system requirements to achieve compromise between safety and confidentiality.
Further, simulation and comparative analysis are carried out on a plurality of schemes, and traversal reachable secret rate gain which can be obtained under high SNR compared with the situation of no feedback is analyzed and researched; the important role of the key parameters of the system on the safety performance and the advantages of the limited rate feedback method in the practical use are proved.
Drawings
FIG. 1 is a finite rate feedback cooperative jamming interception transmission model of the present invention;
FIG. 2 is a plot of connection interruption probability as a function of SNR for the present invention;
FIG. 3 is a plot of connection interruption probability as a function of SNR for the present invention;
FIG. 4 is a graph of the probability of privacy disruption as a function of SNR for the present invention;
FIG. 5 is a graph of connection interruption probability as a function of the number of feedback bits B in accordance with the present invention;
FIG. 6 is a plot of connection interruption probability and privacy interruption probability as a function of time slot division factor α in accordance with the present invention;
fig. 7 is a graph of the required minimum number of feedback bits B versus the probability limit of the privacy disruption in accordance with the present invention.
Detailed Description
As shown in fig. 1, the present invention comprises the steps of:
a: establishing a limited rate feedback cooperative interference interception transmission model considering MISO, wherein the model comprises a multi-antenna information source node S, a single-antenna legal user D, a wireless power supply cooperative interference node J and a single-antenna interception node E;
the cooperative node may be a plurality of antennas or a plurality of antennas, and for convenience of calculation and analysis, the cooperative node with a single antenna may be regarded as a special case of selecting an optimal cooperative node from a plurality of cooperative nodes;
suppose S has the number of antennas NSAnd the number of antennas in J configuration is NJThe other nodes adopt single antennas; the channel is assumed to be quasi-static Rayleigh channel, that is, the channel CSI in each transmission block is unchanged, and the channel CSI between different transmission blocks is independently changed;
b: because the cooperative interference node is a selfish node with limited energy, the energy for sending the interference signal comes from energy collection of the sending power of the source node, and an expected value for collecting the energy is adopted to replace a real-time value; the time division transmission protocol is adopted, and the whole transmission process is divided into two stages;
b1: in the first stage, a source node S serves as an energy source to supply energy to a cooperative interference node J in a wireless mode;
defining alpha as a time division ratio, and assuming that the length of one time slot is T, wherein alpha T is just started, 0 < alpha < 1 is used for wireless energy supply of a first stage, and the rest time slots (1-alpha) T are used for information transmission;
in the first stage, the energy signal received by the cooperative interference node J from the source node S can be represented as
Figure GDA0002802233170000061
Wherein P isSIs the transmission power of the source node, HSJRepresenting a wireless energizing channel, is NJ×NSAnd each element is subject to independent homography, and the zero mean variance is lambda1Complex gaussian random variable of xSRepresents NSX 1 energy signal vector and satisfies the total power constraint
Figure GDA0002802233170000071
nSRepresents NSA Gaussian additive white noise vector of 1 and
Figure GDA0002802233170000072
thus, at the end of the first phase, the cooperative interfering node J obtains a total energy of
Figure GDA0002802233170000073
Wherein η (0 < η < 1) represents energy conversion efficiency;
due to the selfishness and friendliness of the cooperative interfering node J, i.e. transmitting the interfering signal with the expectation of collecting energy, the transmit power of the node J can be written as
Figure GDA0002802233170000074
B2: in the second stage, the source node S transmits information to the destination node D, meanwhile, the cooperative interference node sends an interference signal, and the eavesdropping node eavesdrops useful information;
according to the channel CSI known by the cooperative nodes, the following two cooperative interference schemes are adopted: a linear beam forming BF method and an antenna selection AS method;
b2-1: linear beam forming BF method
Because the cooperative node is configured with multiple antennas, the multiple antennas can be used for forming a beam forming transmission signal so as to enhance the reliability and safety of receiving by the destination node;
thus, the received signal of a legitimate user can be represented as
Figure GDA0002802233170000075
Wherein h issdIs NSA vector of x 1, representing the legal channel coefficients; h isjdIs NJA vector of x 1, representing an interference channel from the cooperative node J to the eavesdropping node E; h issdAnd hjdSubject to a zero mean variance of λ2And λ4Independently and equally distributing complex Gaussian random variables; the beamforming of the source node uses maximum ratio transmission, w1＝h'sd/||hsdIs NSX 1 beamforming vector, x source signal per unit power, w2Is N of an interfering signalJA beamforming vector of x 1 and | | w2||21, z is the interference signal per unit power, ndIs that the mean value of the legal user receiver is 0 and the variance is N0The AWGN signal of (1);
similarly, the received signal at the eavesdropper E can be expressed as
Figure GDA0002802233170000081
Wherein h isseIs NSA vector of x 1, representing the eavesdropping channel coefficient; h isjeIs NJA vector of x 1, representing an interference channel from the cooperative node J to the eavesdropping node E; h issdAnd hjdEach element in (1) is respectively subject to a zero mean squareThe difference is lambda3And λ5Independent identically distributed complex gaussian random variables of neIs the mean value of the eavesdropper receiver is 0 and the variance is N0An AWGN signal;
thus, in conjunction with equation (3), the end-to-end SINR of the legitimate user D can be expressed as
Figure GDA0002802233170000082
Order to
Figure GDA0002802233170000083
The above formula can be abbreviated as
Figure GDA0002802233170000084
It is assumed here that the noise at the eavesdropper is negligible, since at the eavesdropper the interfering signal dominates, and this is also an assumption that is common in the literature, which can be regarded as a worst case scenario;
thus, in conjunction with equation (3), the end-to-end signal-to-interference ratio, SIR, of the eavesdropper E can be expressed as
Figure GDA0002802233170000085
The beamforming vector w can be seen from equations (7) and (8)2And channel hjdAnd hjeIn connection with this, different beamforming vectors w may be designed based on the known channel CSI information2To enhance the transmission and security performance of the system.
B2-2: an antenna selection method;
according to the principle of AS, the cooperative node selects an optimal antenna from a plurality of antennas to transmit interference signals according to a set standard, so AS to achieve the purpose of enhancing the system security;
assuming that k is the index of the selected antenna, the SINR at the legitimate user D and the SIR at the eavesdropper E can be expressed as equation (7) and (8), respectively
Figure GDA0002802233170000091
Wherein
Figure GDA0002802233170000092
Representing the channel coefficients between the kth antenna of the cooperative node J and the legitimate user D,
Figure GDA0002802233170000093
representing the channel coefficients between the kth antenna of the cooperative node J and the eavesdropper E.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Step A: establishing a system model, and considering a finite rate feedback cooperative interference interception transmission model of MISO (MISO) as shown in FIG. 1, wherein the finite rate feedback cooperative interference interception transmission model comprises a multi-antenna information source node S, a single-antenna legal user D, a wireless power supply cooperative interference node J and a single-antenna interception node E. The method considers a typical interception model for interference cooperation assistance, and the cooperation nodes cooperate information transmission of legal users on the premise of not consuming own resources, so that the interception resistance of the system is enhanced. The cooperative node may be a plurality of antennas or a plurality of antennas, and here, for the convenience of calculation and analysis, the cooperative node with a single antenna may be regarded as a special case of selecting an optimal cooperative node from a plurality of cooperative nodes. Since the energy of the cooperative node comes from the wireless energy supply of the source node, the power of the transmission interference of the cooperative node is changed along with the change of the transmission power of the source node, which is a typical characteristic different from other systems. It is assumed here that S has the number of antennas NSAnd the number of antennas in J configuration is NJThe other nodes all adopt single antennas. The channel is assumed to be quasi-static Rayleigh channel, i.e. the channel CSI is constant in each transport block and varies independently from transport block to transport block.
Since the cooperative interfering node is a selfish and energy-limited node, the energy for transmitting the interfering signal comes from energy collection of the transmission power of the source node, and here, in order to simplify the complexity of the interfering node, a desired value for collecting the energy is adopted instead of a real-time value. Thus, this not only simplifies the processing complexity of the interfering node, but also reduces the overhead of obtaining channel CSI, and the interfering node does not consume its own energy in an average sense. The Time Division (TD) transmission protocol is adopted, and the whole transmission process is divided into two stages. In the first stage, a source node S serves as an energy source to supply energy to a cooperative interference node J in a wireless mode; and in the second stage, the source node S transmits information to the destination node D, and meanwhile, the cooperative interference node sends an interference signal, and the eavesdropping node eavesdrops useful information. Defining alpha as a time division ratio, and assuming that the length of one time slot is T, wherein alpha T is just started, 0 < alpha < 1 is used for wireless energy supply of the first stage, and the rest time slot (1-alpha) T is used for information transmission.
In the first stage, the energy signal received by the cooperative interference node J from the source node S can be represented as
Figure GDA0002802233170000101
Wherein P isSIs the transmission power of the source node, HSJRepresenting a wireless energizing channel, is NJ×NSAnd each element is subject to an independent homography (i.i.d.) with a zero mean variance of λ1Complex gaussian random variable of xSRepresents NSX 1 energy signal vector and satisfies the total power constraint
Figure GDA0002802233170000102
nSRepresents NSA Gaussian additive white noise vector of 1 and
Figure GDA0002802233170000111
thus, at the end of the first phase, the cooperative interfering node J obtains a total energy of
Figure GDA0002802233170000112
Wherein eta (0 < eta < 1) represents energy conversion efficiency. Since the noise energy is small compared to the transmitted signal energy, the noise energy is ignored here. Due to the selfishness and friendliness of the cooperative interfering node J, i.e. transmitting the interfering signal with the expectation of collecting energy, the transmit power of the node J can be written as
Figure GDA0002802233170000113
Assuming that the source node knows the instantaneous CSI of the legitimate channel, the instantaneous CSI of the eavesdropped channel is unknown. The rationality of this assumption is that the CSI of a legitimate channel can be obtained by various training-based channel estimation methods, such as MMSE, etc., and at the same time, a more ideal channel CSI can be obtained by increasing the pilot power, etc.; however, since the eavesdropper is passive and does not actively report the channel CSI of the eavesdropper or may report the inaccurate channel CSI, it is assumed that the source node does not know the state information of the source node and the eavesdropper channel. On the other hand, due to the complexity of the cooperative node and the limitation of system scheduling, the instantaneous CSI of the channel to which the cooperative interference node is connected is not easily obtained, and three situations of known ideal CSI, known channel gain ordering and partial CSI based on finite rate feedback are considered, wherein the safety performance under the CSI based on the channel gain ordering and the finite rate feedback is intensively researched and compared with the ideal CSI. According to the channel CSI known to the cooperative nodes, the following two cooperative interference schemes may be mainly adopted: linear Beamforming (BF) and Antenna Selection (AS). The source node S adopts a beam forming method to enhance information transmission by utilizing all antenna degrees of freedom, and the cooperative node plays a role of artificial interference in the information transmission stage by utilizing the collected expected power. Because the cooperative node is also configured with multiple antennas, different cooperative interference schemes can be adopted according to the performance, implementation complexity and overhead required by the system.
Cooperative interference transmission scheme
Due to the fact that multiple antennas are configured at the cooperative nodes, the multiple antennas can be used for forming beam forming transmission signals so as to enhance the reliability and safety of receiving of the destination node. Thus, the received signal of a legitimate user can be represented as
Figure GDA0002802233170000121
Wherein h issdIs NSA vector of x 1, representing the legal channel coefficients; h isjdIs NJThe vector of x 1 represents the interference channel from the cooperative node J to the eavesdropping node E. h issdAnd hjdSubject to a zero mean variance of λ2And λ4Independently and equally distributing complex Gaussian random variables. The beamforming of the source node uses maximum ratio transmission, w1＝h'sd/||hsdIs NSX 1 beamforming vector, x source signal per unit power, w2Is N of an interfering signalJA beamforming vector of x 1 and | | w2||21, z is the interference signal per unit power, ndIs that the mean value of the legal user receiver is 0 and the variance is N0The AWGN signal of (a). Similarly, the received signal at the eavesdropper E can be expressed as
Figure GDA0002802233170000122
Wherein h isseIs NSA vector of x 1, representing the eavesdropping channel coefficient; h isjeIs NJThe vector of x 1 represents the interference channel from the cooperative node J to the eavesdropping node E. h issdAnd hjdSubject to a zero mean variance of λ3And λ5Independent identically distributed complex gaussian random variables of neIs the mean value of the eavesdropper receiver is 0 and the variance is N0An AWGN signal.
Thus, in conjunction with (3), the end-to-end signal to interference and noise ratio (SINR) of legitimate user D may be expressed as
Figure GDA0002802233170000123
Order to
Figure GDA0002802233170000124
The above formula can be abbreviated as
Figure GDA0002802233170000125
It is assumed here that the noise at the eavesdropper is negligible, since at the eavesdropper the interfering signal dominates, and this is also an assumption that is common in the literature and can be considered as a worst case scenario. Thus, the end-to-end signal-to-interference ratio (SIR) in conjunction with (3-3) an eavesdropper E can be expressed as
Figure GDA0002802233170000131
The beamforming vector w can be seen from equations (7) and (8)2And channel hjdAnd hjeIn connection with this, different beamforming vectors w may be designed based on the known channel CSI information2To enhance the transmission and security performance of the system.
Antenna selection method
Antenna selection is a common method for enhancing physical layer security with low complexity and energy saving[52]And is particularly suitable for systems with limited computing power and energy. Considering the selfishness of the nodes and the limitation of the collected wireless energy, the AS is an effective energy-saving and safety-enhancing method. According to the principle of AS, the cooperative node selects a best antenna from a plurality of antennas to transmit interference signals according to a certain standard, thereby achieving the purpose of enhancing the system security. Assuming k is the index of the selected antenna, according to equations (7) and (8)) The SINR at the legitimate user D and the SIR at the eavesdropper E can be expressed as
Figure GDA0002802233170000132
Wherein
Figure GDA0002802233170000133
Representing the channel coefficients between the kth antenna of the cooperative node J and the legitimate user D,
Figure GDA0002802233170000134
representing the channel coefficients between the kth antenna of the cooperative node J and the eavesdropper E.
Cooperative interference method based on known channel CSI
A method of transmit beamforming design and AS is mainly presented to minimize the impact on legitimate users while compromising the channel quality of eavesdroppers. Different cooperative interference methods and strategies may be designed for the CSI scenario of a known channel.
In the first case: ideally, both the cooperative node-destination node and the cooperative node-eavesdropper CSI are known
When h is generatedjdIs ideal and known, the zero-forcing method can be adopted at the legitimate user receiver to completely eliminate the interference from the cooperative node J. At the same time, the known h can be utilizedjeMaximizes interference at the eavesdropper. Thus, the beamforming vector w2Is a solution to the following optimization problem:
Figure GDA0002802233170000141
according to the research results of Ding[53]The solution to the optimization problem of the above equation can be expressed as
Figure GDA0002802233170000142
Wherein N isJ×NJMatrix array
Figure GDA0002802233170000149
Is hjdThe orthogonal complement of column space can be expressed as
Figure GDA0002802233170000143
In the second case: CSI-only cooperative node-destination node is known
When h is generatedjdIs ideal and known, the zero-forcing method can still be adopted at the legal user receiver to completely eliminate the interference from the cooperative node J. Due to hjeIs unknown, it is impossible to design a beamforming matrix to increase interference at an eavesdropper using channel CSI between cooperating nodes and the eavesdropper as in the first case. Therefore, here we use aligning the null space of the cooperative interference to the legitimate users so that the interference to the legitimate users is 0, while random interference is generated for eavesdroppers. The method for designing the beam forming vector firstly needs to match the matrix
Figure GDA0002802233170000144
Singular Value Decomposition (SVD) to obtain
Figure GDA0002802233170000145
Thus, corresponds to NJ-1 non-zero singular value of NJ-1 left singular value vector uiIs opened into
Figure GDA0002802233170000146
Column space of (u)iCan be expressed as
Figure GDA0002802233170000147
Linear combination of column vectors, thereby
Figure GDA0002802233170000148
Thus, the beamforming vector may be from NJ-1 left singular value vector uiThe interference at the position of a legal user can be ensured to be 0 by randomly selecting one of the two interference signals, the interference at the position of an eavesdropper is random interference at the moment, the interference at the position of the eavesdropper is a beamforming vector of joint design in 4.3.1, and the interference at the position of the eavesdropper is the maximum interference which can be achieved.
In the third case: channel gain ordering of cooperative node-destination node is known
When h is generatedjdWhen the channel gain ordering is known, the AS method can be adopted, and according to equation (9), the antenna index corresponding to the minimum channel gain is selected, so that the influence of the cooperative interference node on the legal user is minimized. Therefore, the criteria for AS selection are
Figure GDA0002802233170000151
Wherein h isidIs hjdThe ith element of (1). Note that the antenna index selected by this scheme is a random antenna selection for eavesdropping channels.
In a fourth case: h isjdFinite rate feedback: codebook selection method based on minimum interference of legal user
Partial channel CSI between the cooperative interfering node and the legitimate users can be obtained through finite rate feedback. In the finite rate feedback model, a legal user estimates and quantizes channel CSI between a cooperative node and a destination node, an optimal codebook is selected to quantize the channel CSI, and a codebook set can be obtained through Random Vector Quantization (RVQ), namely, the size of the codebook set is 2BAnd selecting one codebook from the pre-quantization codebook set as channel CSI to be fed back to the cooperative node, wherein B is the number of feedback bits. Quantization codebook set
Figure GDA0002802233170000152
Is composed of 2BN isJThe dimensional unit norm vector is composed and the codebook set is known to both the cooperative node and the legitimate users. According to certain selection criteria, sumThe user transmits the selected codebook index through a feedback channel.
Because the channel CSI corresponding to the codebook is quantized channel CSI and has a certain deviation from the actual channel CSI, certain interference to the legal user is inevitable. The criteria for selecting the beamforming vector with the interference minimization at the legal user as the optimization target are as follows
Figure GDA0002802233170000153
Wherein
Figure GDA0002802233170000154
Is a Channel Direction Information (CDI) vector.
In the fifth case: h isjdFinite rate feedback: codebook selection method based on channel orthogonality
Compared to the fourth case: the same feedback is required, similar to using a finite feedback scheme, except that the beamforming vector w is constructed2The method of (2) is different. Different from the case of the fourth casejdThe codebook vector closest to the orthogonality is used as a beamforming vector, so that the interference to legal users is reduced as much as possible. This subsection is first selected and hjdAnd the closest codebook vector is used as feedback information, and then a beam forming vector orthogonal to a legal channel is constructed according to the feedback information. Therefore, the selection criteria of the codebook are as follows
Figure GDA0002802233170000161
Feedback-based index derivation and hjdNearest codebook vector
Figure GDA0002802233170000162
The cooperative node is in
Figure GDA0002802233170000163
The interference signal is transmitted in the orthogonal direction, so that the interference signal can be ensuredThe interference to legitimate channels is as small as possible. Thus, utilize
Figure GDA0002802233170000164
Beamforming vector w2A method similar to 4.3.2 may be employed for construction. The essence of the method of the subsection lies in the selected codebook
Figure GDA0002802233170000165
Closer to the real channel hjdConstructed beamforming vector w2The more close to the orthogonal direction of the real channel, the interference of the legal user can be minimized.
Safety performance
For the proposed cooperative jamming system, the connection interruption probability and the confidentiality interruption probability and the traversal reachable confidentiality rate are considered as security indexes. For descriptive and computational convenience, define gsd＝||hsd||2,gJS＝||HSJ||2,
Figure GDA0002802233170000166
Thus, equations (7) - (9) can be written as follows:
Figure GDA0002802233170000167
according to Simon's confirmation, gsdRespectively obey parameter of 2NsThe corresponding PDF can be written as
Figure GDA0002802233170000168
It is noted that when an AS is employed,
Figure GDA0002802233170000171
gsethe sum of the exponential distribution Gaussian variable and the unit direction random variable is known to obey the exponential distribution according to Shah's confirmation, and the corresponding PDF is
Figure GDA0002802233170000172
The system safety index under the cooperative interference method is deduced and researched, and the influence of each parameter on the system performance is researched and analyzed.
Connection interruption probability and privacy interruption probability
(1) The ideal situation is as follows: the cooperative node-destination node and the cooperative node-eavesdropper CSI are known
From the COP definition, when the capacity of the legitimate user channel is not sufficient to support the transmission rate, i.e. CD＜RtAn interrupt event occurs. Therefore, for the ideal CSI case of 4.3.1, substituting equations (10) and (12) for equation (18) can result in
Figure GDA0002802233170000173
And
Figure GDA0002802233170000174
from [55 ]]Can know gjeObey Gamma (N)J-1,λ5) The PDF of which is
Figure GDA0002802233170000175
Substituting equation (18) to obtain the connection interruption probability in case 1 can be written as
Figure GDA0002802233170000176
Wherein
Figure GDA0002802233170000177
The definition of the secret interruption probability, the formula (20) and the analytic formula of the secret interruption probability of the system obtained by substituting and using calculation are as follows
Figure GDA0002802233170000178
Wherein
Figure GDA0002802233170000181
The connection interruption probability and the transmission power P of the system are shown by the equation (22)STime slot dividing factor alpha, source node antenna number and sending rate RtIs related to, and follows PSIs decreased with increasing alpha and RtIs increased. When P is presentS→ infinity, the connection interruption probability of the system can be written as
Figure GDA0002802233170000182
So that the diversity order can be obtained as d ═ NSI.e. the number of transmit antennas. From equation (23), the probability of secret interruption and the transmission power P can be seenSIndependently, only the slot division factor α, the number of cooperating antennas and the secret rate ReIn relation to this, when α is given, the privacy interruption probability approaches a constant, and the privacy rate decreases as the number of cooperative node antennas increases, i.e., the anti-eavesdropping capability increases, because more degrees of freedom are provided by more cooperative node antennas.
(2) CSI-aware of cooperative-destination node
In contrast to case 1, where the interfering channels CSI are both known, here the cooperating nodes to eavesdroppers interfering channels CSI are unknown. At this time, the SNR of the legitimate user is not changed, and the expression of the connection interruption probability is shown in equation (22), which is not further described here. For SIR of an eavesdropper, the precoding vector of the cooperative node at the moment is known as w2＝uiThen, then
Figure GDA0002802233170000183
Obeying an exponential distribution, i.e. degenerating from a Gamma distribution in case 1 to an exponential distribution
Figure GDA0002802233170000184
Thus, in a similar manner, it is possible to obtainThe secret interruption probability of the system is analyzed as
Figure GDA0002802233170000185
As in case 1, the probability of interruption of privacy and the transmission power PSIndependently of the slot division factor alpha and the secret rate ReIn relation, the privacy break probability approaches a constant when given α. The difference is that the privacy interruption probability is independent of the number of antennas of the cooperative node, that is, the privacy rate is not reduced with the increase of the number of antennas of the cooperative node, because the CSI of the channel from the cooperative node to the eavesdropper is unknown, the design of the beamforming vector cannot utilize the channel information, and the increase of the number of antennas of the cooperative node cannot provide more freedom for the eavesdropper. Therefore, it is impossible to increase the number of antennas by the cooperative node to improve the eavesdropping resistance of the system.
(3) The channel gain ordering of the cooperative node-destination node is known and the cooperative node adopts AS
Different from the interference channel h from the cooperative node to the legal user in case 2jdIt is completely known, here, it is assumed that the sequence of the channel gains of the antennas corresponding to the interference channels from the cooperative node to the legitimate user is known, the cooperative node may adopt an AS scheme, and at this time, the destination node only needs to feed back the index of the corresponding optimal antenna, and complete CSI of the channel is not needed, which not only can reduce the complexity and overhead of the system, but also can save the energy of the cooperative node. The selected transmit antenna is randomly selected for an eavesdropper and is optimal for a legitimate user. Therefore, the system security can be increased while the interference of the legal receiving node is reduced. At this time
Figure GDA0002802233170000191
Since the selected antenna is randomly selected for an eavesdropper,
Figure GDA0002802233170000192
obeying exponential distribution Exp (lambda)5) And the selected antenna is the antenna with the minimum channel gain for the legal userLine, then its CDF can be calculated as
Figure GDA0002802233170000193
Thus, its PDF can be expressed as
Figure GDA0002802233170000195
Can be regarded as a parameter lambda4/NJIs used as the index distribution of (1). Substituting the expression of the SINR of the legal user into the expression of the connection interruption probability of the system in the 3 rd case can be written as
Figure GDA0002802233170000194
Wherein (a) is the reaction ofsdThe CDF is substituted and arranged to obtain the product, (b) g is developed by a binomial equationjdIs obtained by substituting PDF of (a), (b) is obtained according to [56 ]]And calculating and finishing to obtain the product.
Figure GDA0002802233170000201
Using a method similar to case 2, the secret interruption probability of the system can be obtained as
Figure GDA0002802233170000202
Since equation (27) is more complex, in order to better study the influence of system parameters, an analytic equation of the outage probability of the system at high transmission power is derived here. When P is presentSThe connection interruption probability of the system can be calculated as → ∞ time
Figure GDA0002802233170000203
Unlike cases 1 and 2, the connection interruption probability and the transmission power P of the systemSIs not related, and follows PSTends to be constant so that the diversity order d is 0. This is because the transmission power of the cooperative node is derived from the wireless energy supply of the source node, the transmission power of the cooperative node is proportional to the transmission power of the source node, and the interference signal and the useful signal power transmitted by the cooperative node increase on the same scale as the transmission power of the source node increases, so that the diversity order is 0. In addition, the connection interruption probability is related to the number of cooperative node antennas and decreases with the increase of the number of cooperative node antennas, because the larger the number of cooperative node antennas, the more the degree of freedom of selectable antennas is provided, the higher the probability of occurrence of antennas with small interference to legitimate users is, but the increase of the number of antennas leads to the increase of bits required for feedback indexing. The probability of simultaneous connection interruption is also related to the time slot division factor alpha, the number of source node antennas and the transmission rate RtAre all related, and the probability of connection interruption is dependent on a and RtIncreases and decreases as the number of source node antennas increases. The expression for the probability of interruption of privacy of the system is the same as in case 2, with the transmission power PSIndependently of the slot division factor alpha and the secret rate ReIt is related. This is because the antenna selection criterion only considers the channel CSI between the cooperating node and the destination node, which is equivalent to random selection for an eavesdropper.
(4)hjdFinite rate feedback: codebook selection method based on minimum interference of legal user
Case 2 is a cooperative node to destination node channel hjdIs completely known, case 3 is hjdIs known, here considering channel hjdIs known, i.e. a channel CSI model employing finite rate feedback. Since the feedback quantized channel CSI has a certain error from the ideal CSI, it can be regarded as the partial channel CSI is known, the orthogonal space of the channel is not exactly the same as the ideal case, unlike cases 1 and 2, gjdNot equal to 0, namely, part of interference signals sent by the cooperative interference node can be leaked to a legal user end, interference can be generated on the legal user end, and a beamforming vector is designed by selecting channel CSI corresponding to a codebook with the minimum leakage interference. Coordinating the trust of a node to a legitimate user according to equation (16)Channel gain of
Figure GDA0002802233170000211
The two random variables of which are independent of each other,
Figure GDA0002802233170000212
is the inner product of two unit vectors with a CDF of
Figure GDA0002802233170000213
x∈[0,1]. U is M-2BThe minimum value of the independent and uniformly distributed random variables, the CDF of which can be expressed as
Figure GDA0002802233170000214
The system connection interruption probability in case 4 is given by the following theorem, defined by COP.
Theorem 1: the channel CSI from the cooperative node to the destination node adopts finite rate feedback, hjeIn case that the CSI is unknown, the connection interruption probability expression of the cooperative interference system can be written as
Figure GDA0002802233170000215
Wherein phi1Is given by
Figure GDA0002802233170000216
And (3) proving that: substituting the SINR expression of the legal user according to the definition of the connection interruption probability, and obtaining the SINR expression by adopting a similar expression (27)
Figure GDA0002802233170000221
Wherein
Figure GDA0002802233170000222
Therefore, g needs to be calculatedjdCDF of (A) is as follows
Figure GDA0002802233170000223
Thus, g can be obtainedjdPDF of
Figure GDA0002802233170000224
By substituting the formula (36) into
Figure GDA0002802233170000225
The probability of a connection interruption in the system can be obtained by substituting equation (37) for equation (32).
Following the derivation of the probability of a privacy disruption, g is known from the existing theoremjeObeying exponential distribution Exp (lambda)5) Using a method similar to case 2, the SOP can be obtained as the analytic formula
Figure GDA0002802233170000231
From equation (32), the connection interruption probability and transmission power P of the system are knownSThe number of cooperative node antennas, the number of source node antennas, a time slot division factor alpha and a secret rate ReIn relation to the above, as the feedback bit B increases, the more accurate the channel CSI is, the less interference the cooperative node has on a legitimate user, the connection interruption probability decreases as the number of feedback bits increases, and increases as the number of cooperative node antennas increases, because the larger the number of cooperative node antennas, the coarser the quantization of the channel under the same feedback bit is, and the more interference the cooperative interference signal leaks. Probability of connection interruption with alpha and RtIncreases and decreases as the number of source node antennas increases. The expression for the probability of interruption of privacy of the system is the same as in case 2, with the transmission power PSIndependently of the slot division factor alpha and the guardSecret rate ReIt is related. This is because the antenna selection criterion only considers feedback optimization of the channel CSI between the cooperating node and the destination node, which is random for eavesdroppers.
(5)hjdFinite rate feedback: codebook selection method based on interference channel orthogonality
Different from the case 4 construction of the beam forming vector with the minimum interference to the legal user, the limited rate feedback is adopted, but the codebook index closest to the actual channel is selected and fed back to the cooperative node, and the cooperative node designs the beam vector by using the fed-back codebook as the CSI of the real channel, so that the beam vector is orthogonal to the interference channel, and the interference generated by the legal user is minimum. According to RVQ theory, actual channel direction
Figure GDA0002802233170000232
And quantizing the channel direction
Figure GDA0002802233170000233
Can be expressed as
Figure GDA0002802233170000234
Wherein
Figure GDA0002802233170000235
s is and
Figure GDA0002802233170000236
a unit norm vector orthogonal and independent of v. w is a2Is based on
Figure GDA0002802233170000237
The null space of (2) to avoid interference to legitimate users as much as possible.
Thus is provided with
Figure GDA0002802233170000238
Approximating a model according to quantization units[46]，w2Is a unit norm vector independent of s, then Z ═ sHw2|2～β(1,NJ-2)，||hjd||2Obedience parameter is (N)J,λ4) Gamma distribution of [47 ]]It can be known that X | | | hjd||2sin2Theta obeys a parameter of (N)J-1,λ4δ) of a Gamma distribution, wherein
Figure GDA0002802233170000241
Thereby gjdCan be represented as
Figure GDA0002802233170000242
From the above formula, gjdObeying a parameter of λ4An exponential distribution of δ. Due to the limited rate CSI feedback,
Figure GDA0002802233170000243
this results in residual interference of the cooperating nodes to legitimate users, and the residual interference depends on the number of bits B of the feedback CSI. When the feedback bit number B → ∞ is fed back, i.e., full feedback, the residual interference approaches 0. gjeObeying exponential distribution Exp (lambda)5) The analytical expression of the secret break probability is the same as the expression (38). From the definition of the connection interruption probability, the connection interruption probability is analytically calculated as follows by a method similar to case 3
Figure GDA0002802233170000244
At high SNR, the Gaussian white noise at the receiver is negligible and the connection interruption probability of the system can be calculated as
Figure GDA0002802233170000245
Wherein
Figure GDA0002802233170000251
Given coding rate RtThe number of feedback bits B required for each node antenna, the time slot division factor alpha, and the successful transmission probability xi can be calculated from the equations (4-43) as follows
Figure GDA0002802233170000252
From equation (43), the connection interruption probability and transmission power P of the system are knownSIndependently of the number of cooperative node antennas, the number of source node antennas, the time slot division factor alpha and the secret rate ReIn relation to the above, as the feedback bit B increases, the more precise the δ → 0 channel CSI is, the less interference the cooperative node has on a legitimate user, the connection interruption probability decreases as the number of feedback bits increases, and increases as the number of cooperative node antennas increases, because the larger the number of cooperative node antennas, the coarser the quantization of the channel under the same feedback bit, the more interference the cooperative interference signal leaks, and the number of feedback bits should increase linearly with the number of cooperative antennas. Probability of connection interruption with alpha and RtIncreases and decreases as the number of source node antennas increases. The expression for the probability of interruption of privacy of the system is the same as in case 2, with the transmission power PSIndependently of the slot division factor alpha and the secret rate ReIt is related.
Discussion: (1) as can be seen from the above analysis and research, the probability of the security disruption of the system is constant and minimum under the condition of the ideal CSI known under the same system parameters. When the sequencing CSI of the cooperative interference channel gain is known, using AS, i.e. case 3, the cooperative interference node simultaneously generates interference to the legitimate user and the eavesdropper, but the selected antenna minimizes the interference to the legitimate user, so that the influence to the legitimate user is smaller than the influence of the eavesdropper. Under the cooperative interference situation of limited rate feedback, a certain error exists between a feedback channel and an ideal channel CSI, so that a certain interference is caused to a legal user, and the performance of the legal user is damaged. In addition, for non-ideal CSI (AS and finite rate feedback), at high SNR, legal user
Figure GDA0002802233170000253
I.e., independent of SNR and tends to be constant, so that there is an error floor effect. As the feedback bit B increases, the feedback CSI approaches the true CSI, the residual interference approaches 0, and the system performance approaches the ideal CSI situation. Therefore, the accuracy of CSI estimation and feedback has a significant impact on system performance. In addition, from the view point of complexity and overhead of the system, a large amount of system overhead and transmission power are required to obtain a more ideal channel CSI, thereby affecting the transmission performance of the system, while the method based on the feedback channel ranking index only needs to feed back the log2 NJBit, less feedback information is needed, but at the same time the performance gain achieved is limited. The method based on the limited rate feedback can obtain relatively accurate channel CSI, the overhead of the system can be controlled according to the performance requirement, and the compromise between better performance and complexity can be achieved.
(2) Consider the comparison case where there is no cooperative node or the cooperative node does not participate in cooperative interference, when gamma isD＝ρs||hsd||2,
Figure GDA0002802233170000261
The corresponding connection interruption probability and the secrecy interruption probability are respectively
Figure GDA0002802233170000262
Figure GDA0002802233170000263
From the above formula, when ρ iss→ ∞ time, pso→1，pco→ 0, it can be known that when there is no cooperative interference node, the information of the legitimate user can be intercepted by the eavesdropper with probability 1, so it is necessary to design an anti-eavesdropping interference algorithm to reach the compromise of speed and security. Several proposed schemes design different interference depending on different channel CSIThe scheme not only can well achieve the compromise of reliability and safety, but also has practical application significance.
Simulation and result analysis
And carrying out Mentor Carlo simulation verification on the theoretical result and analyzing the simulation result. The simulation parameters are set as follows except for special description: the independent simulation times is 1 multiplied by 106Coding rate R sent by source nodet2bps, the required privacy rate Re1bps, the conversion efficiency factor η for energy collection is 0.8, the slot division factor α is 0.1, and the channel parameter λ1＝10,λ2＝λ3＝λ4＝λ5SNR is defined as the transmit signal-to-noise ratio P of the source node, 1S/N0. Numerical simulations and analyses were performed for five cases, ideal CSI (case 1), cooperative node-destination node channel CSI known (case 2), cooperative node-destination node channel gain ordering known (case 3), finite rate feedback based on legitimate user interference minimization (case 4), and finite rate feedback based on channel orthogonality (case 5), respectively.
FIG. 2 shows a plot of the connection interruption probability of a system as a function of SNR, where the solid line represents NS＝2,NJAntenna configuration of 2, with dotted line representing NS＝4,NJThe number of feedback bits B is 8 for an antenna configuration of 2. It can be seen from the figure that the theoretical result of the derivation is well matched with the actual simulation result, and at the same time the progressive expression is also consistent with the simulation result in the high SNR region, as analyzed above, the connection interruption probability decreases with the increase of the number of source node antennas, and for case 1 and the diversity gain is the number of source node antennas NS(ii) a In other cases, the connection interruption probability of the system is reduced along with the increase of the number of the source node antennas, but the error rate flat bottom effect exists, namely the error rate flat bottom effect tends to be constant along with the increase of SNR, and the error rate flat bottom effect is reduced along with the increase of the number of the source node antennas. As can be seen from the figure, the connection outage probability for case 3 is the worst, followed by cases 4 and 5, and the connection outage probabilities for cases 1 and 2 are the best performing, because case 1 and the CSI that fully utilizes the interfering channel design good beam vectors. Therefore, a better channel CSI pair system is obtainedThe performance of (2) plays an important role.
FIG. 3 shows a plot of the connection interruption probability of a system as a function of SNR, where the solid line represents NS＝2,NJAntenna configuration of 2, with dotted line representing NS＝2,NJThe number of feedback bits B is 8 for the antenna configuration of 3, and it can be seen from the figure that the derived theoretical result is well matched with the actual simulation result. In case 1, the connection interruption probability is irrelevant to the number of cooperative node antennas, while the connection interruption probability in other cases is reduced with the increase of the number of cooperative node antennas, but all the cases have the effect of flat bottom of error codes, that is, the connection interruption probability tends to be constant with the increase of the SNR and is reduced with the increase of the number of cooperative node antennas. Likewise, the connection outage probability for case 3 is worst, followed by cases 4 and 5, and the connection outage probabilities for cases 1 and 2 are optimal because case 1 and the CSI that fully utilizes the interfering channel design a good beam vector.
FIG. 4 is a graph showing the probability of privacy disruption of a system as a function of SNR, where the solid line represents NS＝2,NJAntenna configuration of 2, with dotted line representing NS＝2,NJThe number of feedback bits B is 8 for an antenna configuration of 4. As can be seen from the figure, the derived theoretical results are in good agreement with the actual simulation results. When the number of the cooperative node antennas is 2, the system has the same probability of the privacy interruption as can be seen from the analysis in the ideal case, which is consistent with the simulation result. When the number of the cooperative node antennas is greater than 2, the known channel CSI is utilized to jointly design the beam vector in case 1, so that the spatial degree of freedom of the channel is fully utilized, and the confidentiality interruption probability of the system is effectively reduced. The probability of the privacy interruption in other situations is reduced along with the increase of the number of the cooperative node antennas, but the flat bottom effect exists, namely the constant value is approached along with the increase of the SNR.
Fig. 5 shows the variation of the connection interruption probability of the system with the number of feedback bits B, where SNR is 15dB, NS＝4,NJThe feedback bit number B is 4, 8. Cases 1, 2 and 3 are independent of the number of feedback bits B, so the outage probability does not change as B changes. The connection interruption probability of cases 4 and 5 is related to the number of feedback bits and increases with the number of bitsBut decreases and gradually approaches scenario 1. This is because as the number of bits B increases, the higher the channel quantization accuracy, the closer to the true channel, and the connection interruption probability of the system increases rapidly. Note that when the number of feedback bits is small, B<2, the connection failure probability performance of the method based on antenna selection is better than that of the method based on finite rate feedback, because too few feedback bits lead to too coarse channel CSI quantization, and the increased interference leaked to the destination node leads to the decreased SINR of the destination node and reduced reliability. With the increase of the feedback bit B, the accuracy of channel quantization is improved, and the accuracy is closer to the true channel CSI, the interference of the interference signal sent by the interfering node leaking to the destination node tends to 0, and the connection interruption probability of the system tends to an ideal situation.
FIG. 6 is a graph showing the connection interruption probability and the privacy interruption probability of a system as a function of a slot division factor α, where N isS＝2,NJThe feedback bit number B is 2, 6. In the figure, COP and SOP without cooperative nodes are also given as a comparison term. As can be seen from the figure, as α increases, the connection interruption probability of the system in five cases increases, i.e. the reliability decreases, because the time slots for transmitting data are shorter and shorter, and the corresponding transmission rate is higher and higher; on the other hand, as α increases, the probability of interruption of privacy of the system in five cases decreases, i.e., security increases, because the cooperative nodes can collect more energy for transmitting the interference signal, the data transmission time slot becomes shorter, the SINR required by the eavesdropper increases, and it is less prone to eavesdropping. Therefore, a compromise relationship between reliability and safety exists, the connection interruption probability of a system without cooperative nodes is low, but the confidentiality interruption probability is high, and the cooperative nodes play an important role in data transmission with priority on safety.
FIG. 7 shows a variation curve of the minimum number of feedback bits B required by the system with different numbers of antennas of the cooperative node under the constraint of the probability ξ of privacy interruption, where N isS4. It can be seen from the figure that in order to achieve the same secret interruption probability, the required minimum feedback bit number B increases with the increase of the number of cooperative node antennas; the increased number of antennas requires more quantization to achieve the same accuracy of quantizationA bit. Note that as the probability of privacy interruption increases, the minimum number of feedback bits B required decreases; the required privacy interruption probability can be achieved with only a small bit feedback.
The invention relates to a safe transmission system performance of a wireless energy supply cooperative interference system, wherein a cooperative interference node sends an interference signal by using expected collection power, and the safe transmission performance of the system under five conditions is researched. Starting from known channel CSI, the confidentiality performances of different interference cooperation schemes under the conditions of known ideal condition of all channel CSI, unknown condition of eavesdropper CSI, known cooperative channel gain sequencing and limited feedback rate channel CSI are respectively researched, closed solutions of connection interruption probability and confidentiality interruption probability under various conditions are deduced, and an expression under high SNR approximation is given; the connection interruption probability and the confidentiality interruption probability of the system have a certain compromise relationship, and system parameters can be selected and designed according to different system requirements to achieve compromise between safety and confidentiality. Furthermore, the system traversal reachable secret rate is deduced and researched, simulation and comparative analysis are carried out on a plurality of schemes, and the traversal reachable secret rate gain which can be obtained under the condition of high SNR and when the feedback is not carried out is analyzed and researched; the important role of the key parameters of the system on the safety performance and the advantages of the limited rate feedback method in the practical use are proved.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (1)

1. A safe transmission method of a cooperative interference physical layer based on wireless energy supply is characterized in that: the method comprises the following steps:
a: establishing a limited rate feedback cooperative interference interception transmission model considering MISO, wherein the model comprises a multi-antenna information source node S, a single-antenna legal user D, a wireless power supply cooperative interference node J and a single-antenna interception node E;
the cooperative nodes are a plurality of or multiple antennas, and for the convenience of calculation and analysis, the cooperative nodes with single antenna are regarded as a special case of selecting an optimal cooperative node from the plurality of cooperative nodes;
suppose S has the number of antennas NSAnd the number of antennas in J configuration is NJThe other nodes adopt single antennas; assuming a Rayleigh channel with quasi-static channels, namely the channel CSI in each transmission block is unchanged, and the channel CSI among different transmission blocks is independently changed;
b: because the cooperative interference node is a selfish node with limited energy, the energy for sending the interference signal comes from energy collection of the sending power of the source node, and an expected value for collecting the energy is adopted to replace a real-time value; the time division transmission protocol is adopted, and the whole transmission process is divided into two stages;
b1: in the first stage, a source node S serves as an energy source to supply energy to a cooperative interference node J in a wireless mode;
defining alpha as a time division ratio, and assuming that the length of one time slot is T, wherein alpha T is just started, 0 < alpha < 1 is used for wireless energy supply of a first stage, and the rest time slots (1-alpha) T are used for information transmission;
in the first stage, the energy signal received by the cooperative interference node J from the source node S is represented as
Figure FDA0002802233160000011
Wherein P isSIs the transmission power of the source node, HSJRepresenting a wireless energizing channel, is NJ×NSAnd each element is subject to independent homography, and the zero mean variance is lambda1Complex gaussian random variable of xSRepresents NSX 1 energy signal vector and satisfies the total power constraint
Figure FDA0002802233160000012
nSRepresents NSA Gaussian additive white noise vector of 1 and
Figure FDA0002802233160000013
thus, at the end of the first phase, the cooperative interfering node J obtains a total energy of
Figure FDA0002802233160000014
Wherein eta, 0 < eta < 1 represents energy conversion efficiency;
due to the selfishness and friendliness of the cooperative interfering node J, i.e. the interfering signal is transmitted with the expectation of collecting energy, the transmit power of the node J is written as
Figure FDA0002802233160000021
B2: in the second stage, the source node S transmits information to the destination node D, meanwhile, the cooperative interference node sends an interference signal, and the eavesdropping node eavesdrops useful information;
according to the channel CSI known by the cooperative nodes, the following two cooperative interference schemes are adopted: a linear beam forming BF method and an antenna selection AS method;
b2-1: linear beam forming BF method
Because the cooperative node is configured with multiple antennas, the multiple antennas are utilized to form a beam forming transmission signal so as to enhance the reliability and safety of receiving by the destination node;
thus, the received signal of the legitimate user is represented as
Figure FDA0002802233160000022
Wherein h issdIs NSA vector of x 1, representing the legal channel coefficients; h isjdIs NJA vector of x 1, the vector of x 1,representing an interference channel from the cooperative node J to the eavesdropping node E; h issdAnd hjdSubject to a zero mean variance of λ2And λ4Independently and equally distributing complex Gaussian random variables; the beamforming of the source node uses maximum ratio transmission, w1＝h'sd/||hsdIs NSX 1 beamforming vector, w2Is N of an interfering signalJA beamforming vector of x 1 and | | w2||21, z is the interference signal per unit power, ndIs that the mean value of the legal user receiver is 0 and the variance is N0The AWGN signal of (1);
similarly, the received signal at the eavesdropper E is denoted as
Figure FDA0002802233160000023
Wherein h isseIs NSA vector of x 1, representing the eavesdropping channel coefficient; h isjeIs NJA vector of x 1, representing an interference channel from the cooperative node J to the eavesdropping node E; h issdAnd hjdSubject to a zero mean variance of λ3And λ5Independent identically distributed complex gaussian random variables of neIs the mean value of the eavesdropper receiver is 0 and the variance is N0The AWGN signal of (1);
thus, in conjunction with equation (3), the end-to-end SINR of legitimate user D is expressed as
Figure FDA0002802233160000031
Order to
Figure FDA0002802233160000032
The above formula can be abbreviated as
Figure FDA0002802233160000033
It is assumed that the noise at the eavesdropper is ignored because the interference signal dominates at the eavesdropper, which is considered to be a worst case;
thus, in conjunction with equation (3), the end-to-end signal-to-interference ratio, SIR, of the eavesdropper E is expressed as
Figure FDA0002802233160000034
The beamforming vector w is shown by the equations (7) and (8)2And channel hjdAnd hjeIn connection with designing different beamforming vectors w based on the known channel CSI information2To enhance the transmission and security performance of the system;
b2-2: an antenna selection method;
according to the principle of AS, the cooperative node selects an optimal antenna from a plurality of antennas to transmit interference signals according to a set standard, so AS to achieve the purpose of enhancing the system security;
assuming that k is the index of the selected antenna, the SINR at the legitimate user D and the SIR at the eavesdropper E are expressed as follows according to equations (7) and (8), respectively
Figure FDA0002802233160000035
Wherein
Figure FDA0002802233160000036
Representing the channel coefficients between the kth antenna of the cooperative node J and the legitimate user D,
Figure FDA0002802233160000037
representing the channel coefficients between the kth antenna of the cooperative node J and the eavesdropper E.
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