CN109600813B - Wireless energy-carrying relay system and method for guaranteeing information security - Google Patents

Wireless energy-carrying relay system and method for guaranteeing information security Download PDF

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CN109600813B
CN109600813B CN201811478712.9A CN201811478712A CN109600813B CN 109600813 B CN109600813 B CN 109600813B CN 201811478712 A CN201811478712 A CN 201811478712A CN 109600813 B CN109600813 B CN 109600813B
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relay
terminal
energy
rank
safe
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CN109600813A (en
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赵赛
杨钊
田茂新
黄高飞
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China Southern Power Grid Internet Service Co ltd
Ourchem Information Consulting Co ltd
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Guangzhou University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W40/00—Communication routing or communication path finding
    • H04W40/02—Communication route or path selection, e.g. power-based or shortest path routing
    • H04W40/04—Communication route or path selection, e.g. power-based or shortest path routing based on wireless node resources
    • H04W40/10—Communication route or path selection, e.g. power-based or shortest path routing based on wireless node resources based on available power or energy
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H04L5/0058—Allocation criteria
    • H04L5/0064—Rate requirement of the data, e.g. scalable bandwidth, data priority
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W40/00—Communication routing or communication path finding
    • H04W40/02—Communication route or path selection, e.g. power-based or shortest path routing
    • H04W40/22—Communication route or path selection, e.g. power-based or shortest path routing using selective relaying for reaching a BTS [Base Transceiver Station] or an access point

Abstract

The invention relates to the technical field of wireless communication, in particular to a wireless energy-carrying relay system and a method for guaranteeing information safety, wherein the system comprises the following steps: the system comprises a source end, a plurality of relay ends, a legal receiving end, an energy collecting end and an eavesdropper, wherein the source end is connected with the relay ends; each relay terminal is respectively connected with the source terminal, the legal receiving terminal, the energy collecting terminal and the eavesdropper; the method comprises the steps of constructing a safe reachable rate maximization problem which guarantees safe communication of a physical layer and meets wireless energy constraint and independent power constraint of each relay end, and obtaining a local optimal safe beam forming matrix on each relay end which guarantees safety of the physical layer through an alternative optimization method. The invention can realize that the information wave beam and the energy wave beam of the relay aim at the target user, improves the frequency spectrum and the energy resource utilization rate of the relay wireless communication system, and simultaneously ensures the information communication safety of the system.

Description

Wireless energy-carrying relay system and method for guaranteeing information security
Technical Field
The invention relates to the technical field of wireless communication, in particular to a wireless energy-carrying relay system and a wireless energy-carrying relay method for guaranteeing information safety.
Background
As a key technology for solving the problems of channel fading and energy attenuation, the relay technology is particularly suitable for being combined with an energy-limited network. The wireless energy collection technology is a key technology particularly suitable for solving the problem of energy shortage of an energy-limited network. Therefore, the combination of relay technology and energy harvesting technology is of great significance for the research of energy-limited networks.
In recent years, a cooperative transmission mode for improving the physical layer security performance by using a trusted relay attracts more and more attention. There are three main relay protocols for cooperative secure transmission: amplify-and-forward and decode-and-forward. For these protocols, the most common design goal is to maximize the safe rate by properly selecting the beamforming weights of the relay peer. The amplifying and forwarding strategy is simple, and is more generally applicable to relay nodes in various scenes. However, the problem of secure beamforming with an amplify-and-forward strategy is more difficult to solve because the relay end amplifies the noise. To address this problem, a suboptimal and conservative approach is a null-space beamforming approach, i.e., one that places the information beam entirely within the null of the eavesdropper. But the null-space based beamforming schemes are not fully utilized in terms of spectral efficiency and energy efficiency.
Disclosure of Invention
In order to solve the problems of the existing relay transmission technology, the invention aims to provide a wireless energy-carrying relay system for guaranteeing information safety, which can realize that information beams and energy beams of relays are aligned to target users, improve the utilization rate of frequency spectrums and energy resources of a relay wireless communication system, and guarantee the information communication safety of the system.
The invention also provides a wireless energy-carrying relay method for guaranteeing information safety.
The relay system adopts the following technical scheme: a wireless energy-carrying relay system for guaranteeing information security comprises: the system comprises a source end, a plurality of relay ends, a legal receiving end, an energy collecting end and an eavesdropper, wherein the source end is connected with the relay ends; each relay terminal is respectively connected with the source terminal, the legal receiving terminal, the energy collecting terminal and the eavesdropper;
the method comprises the steps of constructing a safe reachable rate maximization problem which guarantees safe communication of a physical layer and meets wireless energy constraint and independent power constraint of each relay end, and obtaining a local optimal safe beam forming matrix on each relay end which guarantees safety of the physical layer through an alternative optimization method.
Preferably, the wireless energy-carrying relay system is a two-hop amplification forwarding multi-relay network, and each relay terminal is provided with N antennas; the energy receiving end is provided with M antennas; the source end, the legal receiving end and the eavesdropper are all provided with single antennas.
Preferably, there is no direct link connection between the source end and the legal receiving end, and in the first time slot, the source end sends a signal to the relay end; in the second time slot, the relay terminal multiplies the received signal by a beam forming matrix and forwards the signal to a legal receiving terminal and an energy receiving terminal, and meanwhile, an eavesdropper eavesdrops.
The relay method adopts the following technical scheme: a wireless energy-carrying relay method for guaranteeing information security comprises the following steps:
s1, in the two-hop amplification multi-relay network, each relay terminal is respectively connected with a source terminal, a legal receiving terminal, an energy collection terminal and an eavesdropper; each relay terminal is provided with N antennae, the energy receiving terminal is provided with M antennae, and the source terminal, the legal receiving terminal and the eavesdropper are provided with single antennae;
order to
Figure BDA0001892850060000021
Respectively representing channels from a source end to a kth relay end, from the kth relay end to a legal receiving end and from the kth relay end to an eavesdropper;
Figure BDA0001892850060000022
represents a channel from the kth relay terminal to the energy receiving terminal;
Figure BDA0001892850060000023
and
Figure BDA0001892850060000024
are independent identically distributed complex Gaussian random variables with zero mean and unit variance; fk∈CN×NA beamforming matrix representing the kth relay peer,
Figure BDA0001892850060000025
σ2additive white Gaussian noise Power, P, for a legitimate receiver and an eavesdroppersFor source side transmit power, F ═ diag (F)1,F2,…,FK),
Figure BDA0001892850060000026
Let the wireless energy constraint be:
Figure BDA0001892850060000027
wherein
Figure BDA0001892850060000028
Representing a channel from the kth relay terminal to an energy receiving terminal, wherein Q is a preset energy collection threshold of the energy receiving terminal;
making the individual power constraint of each relay as:
Figure BDA0001892850060000029
wherein, PkMaximum allowable transmission power for the kth relay node;
the safe reachable rate for ensuring the safe communication of the physical layer and meeting the wireless energy constraint and the independent power constraint of each relay terminal is as follows:
Figure BDA00018928500600000210
s2, constructing a safe reachable rate maximization problem which ensures the safe communication of the physical layer and meets the wireless energy constraint and the independent power constraint of each relay end, and comprising the following steps:
Figure BDA00018928500600000211
wherein the content of the first and second substances,
Figure BDA00018928500600000212
Figure BDA0001892850060000031
Figure BDA0001892850060000032
Figure BDA0001892850060000033
Figure BDA0001892850060000034
Figure BDA0001892850060000035
Figure BDA0001892850060000036
Figure BDA0001892850060000037
rank 1 relaxation is performed on the above-mentioned safe achievable rate maximization problem, order
Figure BDA0001892850060000038
Figure BDA0001892850060000039
And
Figure BDA00018928500600000310
Figure BDA00018928500600000311
solving a local optimal solution of the above rank 1 relaxation problem;
s3, initializing, wherein n is 0, and n is the iteration number;
Figure BDA00018928500600000312
Xnis KN2×KN2Is a positive number, calculating Rs(Xn)；
S4, fixing XnSolving for
Figure BDA00018928500600000313
Figure BDA00018928500600000314
S5, fixing
Figure BDA00018928500600000315
Solving the following convex optimization problem by using an interior point method to obtain Xn+1：
Figure BDA00018928500600000316
S6, n ═ n +1, and R is calculateds(Xn+1) Alternately updating through S2 and S3
Figure BDA00018928500600000317
And Xn+1Until convergence, i.e. Rs(Xn+1)-Rs(Xn) Is less than an element; obtaining a locally optimal solution X to the rank 1 relaxation problem*＝Xn+1；
S7, if X*Is a rank 1 solution, and obtains an optimal rank 1 solution f of the safe reachable rate maximization problem through characteristic decomposition*If X is*Instead of a rank 1 solution, a suboptimal rank 1 solution f of the safe reachable rate maximization problem is obtained through Gaussian randomization; finally, the F is matrixed to obtain a beam forming matrix F of each relayk。
The invention can ensure that the frequency spectrum and energy resources are effectively and fully utilized while the relay transmission system ensures the safe communication of the physical layer, and solves the problem of maximizing the safe rate of the multi-relay system by optimally designing the beam forming matrix of each relay terminal. Compared with the prior art, the invention has the following effective effects:
the safe reachable rate maximization problem for guaranteeing the safe communication of the physical layer is constructed, the safe beam forming matrix of each relay end is obtained through an alternative optimization method, and the safe reachable rate of the system is locally optimal while the wireless energy constraint and the independent power constraint of each relay end are met. The invention can realize that the information wave beam and the energy wave beam of the relay aim at the target user, improves the frequency spectrum and the energy resource utilization rate of the relay wireless communication system, and simultaneously ensures the information communication safety of the system.
Drawings
FIG. 1 is a diagram of a system model according to the present invention.
Fig. 2 is a diagram of performance effect of the present invention when different relay numbers and different wireless energy constraints are configured, the average achievable safe rate varies with the relay transmission power.
Fig. 3 is a diagram showing the convergence performance effect of the alternative iteration algorithm when different relay numbers are configured according to the present invention.
FIG. 4 is a basic flow chart of a simulation experiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.
Examples
As shown in fig. 1 to 4, the wireless energy-carrying relay system for guaranteeing information security of the present invention includes: the device comprises a source end, a plurality of relay ends, a legal receiving end, an energy collecting end and an eavesdropper, wherein each relay end is respectively connected with the source end, the legal receiving end, the energy collecting end and the eavesdropper. The wireless energy-carrying relay system is a two-hop amplification forwarding multi-relay network, and in the embodiment, the wireless energy-carrying relay system comprises K multi-antenna relay terminals, and each relay terminal is provided with N antennas; the energy receiving end is provided with M antennas; the source end, the legal receiving end and the eavesdropper are all provided with single antennas. Assuming that no direct link connection exists between the source end and the legal receiving end, in a first time slot, the source end sends a signal to the relay end; in the second time slot, the relay terminal multiplies the received signal by a beam forming matrix and forwards the multiplied signal to a legal receiving terminal and an energy receiving terminal, and meanwhile, an eavesdropper eavesdrops. Considering that the relay node knows the channel state information of the whole network, the whole two-hop amplification forwarding multi-relay network works in a time division multiplexing mode.
The invention constructs a safe reachable rate maximization problem of ensuring the safe communication of a physical layer and meeting the wireless energy constraint and the independent power constraint of each relay terminal based on the relay beam forming matrix optimization algorithm of the alternative optimization, and obtains the local optimal safe beam forming matrix on each relay terminal of the wireless energy-carrying relay system for ensuring the safety of the physical layer by the alternative optimization method.
In this embodiment, let
Figure BDA0001892850060000041
Respectively representing channels from a source end to a kth relay end, from the kth relay end to a legal receiving end and from the kth relay end to an eavesdropper;
Figure BDA0001892850060000042
representing the channel from the kth relay peer to the energy receiving peer,
Figure BDA0001892850060000043
Pkmaximum allowable transmission power for the kth relay node; fk∈CN×NA beamforming matrix representing the kth relay peer,
Figure BDA0001892850060000051
σ2the power of additive white Gaussian noise at a legal receiving end and an eavesdropper is obtained; psTransmitting power for the source end; q is a preset energy collection threshold of an energy receiving end; the safe achievable rate is:
Figure BDA0001892850060000052
the wireless energy constraints are:
Figure BDA0001892850060000053
the individual power constraint of each relay is as follows:
Figure BDA0001892850060000054
wherein, PkThe maximum allowable transmission power for the kth relay node.
The safe reachable rate maximization problem of ensuring the safe communication of the physical layer and meeting the wireless energy constraint and the independent power constraint of each relay terminal is constructed as follows:
Figure BDA0001892850060000055
wherein the content of the first and second substances,
Figure BDA0001892850060000056
Figure BDA0001892850060000057
Figure BDA0001892850060000058
Figure BDA0001892850060000059
Figure BDA00018928500600000510
Figure BDA00018928500600000511
Figure BDA00018928500600000512
Figure BDA00018928500600000513
the objective function of the above optimization problem is the safe achievable rate; the first constraint is the independent power constraint of each relay terminal; the second constraint is a wireless energy constraint; the optimization variables are vectorized representations of the beamforming matrices for each relay.
And solving the safety reachable rate maximization problem based on the alternative optimization. Rank 1 relaxation, i.e., ordering, is first performed on the above-described safe achievable rate maximization problem
Figure BDA00018928500600000514
Ignoring the non-convex rank 1 constraint, converting the safe achievable rate maximization problem into the following rank 1 relaxation problem:
Figure BDA0001892850060000061
Figure BDA0001892850060000062
Tr(D6X)≥Q.
wherein:
Figure BDA0001892850060000063
and:
Figure BDA0001892850060000064
and
Figure BDA0001892850060000065
solving the locally optimal solution of the above rank 1 relaxation problem comprises the following steps:
(1) initializing, wherein n is 0 and n is iteration times;
Figure BDA0001892850060000066
Xnis KN2×KN2Is a very small positive number, calculate Rs(Xn)；
(2) Fixed XnSolving for
Figure BDA0001892850060000067
Figure BDA0001892850060000068
(3) Fixing
Figure BDA0001892850060000069
Solving the following convex optimization problem by using an interior point method to obtain Xn+1：
Figure BDA00018928500600000610
(4) n is n +1, and R is calculateds(Xn+1) Alternately updating through the step (2) and the step (3)
Figure BDA00018928500600000611
And Xn+1Up to Rs(Xn+1) Convergence, i.e. Rs(Xn+1)-Rs(Xn)＜∈。
(5) Obtaining a locally optimal solution X of the rank 1 relaxation problem*＝Xn+1。
If X is*Is a rank 1 solution, and obtains an optimal rank 1 solution f of the original safe reachable rate maximization problem through characteristic decomposition*If X is*Instead of a rank 1 solution, a suboptimal rank 1 solution f of the original safe reachable rate maximization problem is obtained through Gaussian randomization. Finally, the F is matrixed to obtain a beam forming matrix F of each relayk。
Referring to fig. 4, the wireless energy-carrying relay method for guaranteeing information security of the embodiment specifically includes the following steps:
step 1, in a two-hop amplification multi-relay network, each relay terminal is provided with 2 antennas, an energy receiving terminal is provided with M antennas, and a source terminal, a legal receiving terminal and an eavesdropper are all provided with a single antenna.
If no special statement, P in simulation implementations/σ2＝10dB，Q/σ2＝2dB，M＝2，σ 21. Assuming all channel responses
Figure BDA0001892850060000071
And
Figure BDA0001892850060000072
are independent identically distributed complex gaussian random variables with zero mean and unit variance. 500 random channel realizations were generated in the simulation to calculate the average achievable security rate. Individual relay power constraint PkThe settings were as follows: p when k is oddk＝0.5PrK, P when K is an even numberk＝2Prand/K. Let Fk∈CN×NA beamforming matrix representing the kth relay peer,
Figure BDA0001892850060000073
step 2, constructing a safe reachable rate maximization problem which ensures the safe communication of the physical layer and meets the wireless energy constraint and the independent power constraint of each relay end, and comprising the following steps:
Figure BDA0001892850060000074
wherein the content of the first and second substances,
Figure BDA0001892850060000075
Figure BDA0001892850060000076
Figure BDA0001892850060000077
Figure BDA0001892850060000078
Figure BDA0001892850060000079
Figure BDA00018928500600000710
Figure BDA00018928500600000711
Figure BDA00018928500600000712
rank 1 relaxation is performed on the above-mentioned safe achievable rate maximization problem, order
Figure BDA00018928500600000713
Figure BDA00018928500600000714
And
Figure BDA00018928500600000715
Figure BDA00018928500600000716
the locally optimal solution of the above rank 1 relaxation problem is solved.
Step 3, initializing, wherein n is 0, and n is iteration times;
Figure BDA00018928500600000717
Xnis KN2×KN2Is a very small positive number, calculate Rs(Xn)；
Step 4, fixing XnSolving for
Figure BDA00018928500600000718
Figure BDA00018928500600000719
Step 5, fixing
Figure BDA00018928500600000720
Solving the following convex optimization problem by using an interior point method to obtain Xn+1：
Figure BDA0001892850060000081
And 6, alternately updating through the step (2) and the step (3)
Figure BDA0001892850060000082
And Xn+1Until convergence, i.e. Rs(Xn+1)-Rs(Xn) Is < ∈. Obtaining a locally optimal solution X of the rank 1 relaxation problem*＝Xn+1。
Step 7, if X*Is a rank 1 solution, and obtains an optimal rank 1 solution f of the original safe reachable rate maximization problem through characteristic decomposition*If X is*Instead of a rank 1 solution, a suboptimal rank 1 solution f of the original safe reachable rate maximization problem is obtained through Gaussian randomization. Finally, the F is matrixed to obtain a beam forming matrix F of each relayk。
By the embodiment, the performance effect graph of fig. 2, in which the average achievable safe rate changes with the relay transmission power, and the convergence performance effect graph of fig. 3, in which the alternating iterative algorithm is used, can be obtained. It can be seen from both sets of curves in fig. 3 that when the sum power at the relay is small, the average achievable safe rate without energy constraint is greater than the case where the energy constraint is 6dB, and the average achievable safe rate with 6dB energy constraint is greater than the case where the energy constraint is 10 dB. It can also be seen from fig. 3 that the average achievable safety rate of each energy constraint of the relay number K-4 is greater than the average achievable safety rate of each energy constraint of the relay number K-2. The performance curves of fig. 3 demonstrate the rationality and effectiveness of the system.
It can be seen from fig. 2 that the number of iterations increases with increasing power, and when the transmission sum power of the relay terminal is 20dB, the number of iterations is about 20. The performance curve of fig. 2 shows the fast convergence of the proposed alternate optimization based secure relay beamforming algorithm in the system.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be regarded as being equivalent to the scope of the present invention.

Claims (7)

1. A wireless energy-carrying relay system for guaranteeing information security is characterized by comprising: the system comprises a source end, a plurality of relay ends, a legal receiving end, an energy collecting end and an eavesdropper, wherein the source end is connected with the relay ends; each relay terminal is respectively connected with the source terminal, the legal receiving terminal, the energy collecting terminal and the eavesdropper;
constructing a safety reachable rate maximization problem which ensures the safety communication of a physical layer and meets the wireless energy constraint and the independent power constraint of each relay end, and obtaining a local optimal safety beam forming matrix on each relay end which ensures the safety of the physical layer by an alternative optimization method;
the safe achievable rate is:
Figure FDA0002506069640000011
wherein Fk∈CN×NRepresenting the kth relay peerThe beam-forming matrix is then used to shape the beam,
Figure FDA0002506069640000012
σ2additive white Gaussian noise Power, P, for a legitimate receiver and an eavesdroppersFor source side transmit power, F ═ diag (F)1，F2，...，FK)，
Figure FDA0002506069640000013
Figure FDA0002506069640000014
Respectively representing channels from a source end to a kth relay end, from the kth relay end to a legal receiving end and from the kth relay end to an eavesdropper;
the wireless energy constraint is:
Figure FDA0002506069640000015
wherein
Figure FDA0002506069640000016
Representing a channel from the kth relay terminal to an energy receiving terminal, wherein Q is a preset energy collection threshold of the energy receiving terminal;
the individual power constraint of each relay terminal is as follows:
Figure FDA0002506069640000017
wherein, PkMaximum allowable transmission power for the kth relay node;
the safe reachable rate maximization problem of ensuring the safe communication of the physical layer and meeting the wireless energy constraint and the independent power constraint of each relay end is as follows:
Figure FDA0002506069640000018
Figure FDA0002506069640000019
Figure FDA00025060696400000110
wherein the content of the first and second substances,
Figure FDA00025060696400000111
Figure FDA00025060696400000112
Figure FDA00025060696400000113
Figure FDA00025060696400000114
Figure FDA0002506069640000021
Figure FDA0002506069640000022
Figure FDA0002506069640000023
Figure FDA0002506069640000024
Jkis a KN2×KN2Of which is N2The diagonal elements are 1, the other diagonal elements are 0, and the positions of the diagonal elements which are 1 are from (k-1) N2+1 diagonal element to the kN2A diagonal element.
2. The wireless energy-carrying relay system for ensuring information security according to claim 1, wherein the wireless energy-carrying relay system is a two-hop amplify-and-forward multi-relay network, and each relay terminal is provided with N antennas; the energy receiving end is provided with M antennas; the source end, the legal receiving end and the eavesdropper are all provided with single antennas.
3. The wireless energy-carrying relay system for ensuring information security according to claim 1 or 2, wherein the source end and the legal receiving end have no direct link connection, and in the first time slot, the source end sends a signal to the relay end; in the second time slot, the relay terminal multiplies the received signal by a beam forming matrix and forwards the signal to a legal receiving terminal and an energy receiving terminal, and meanwhile, an eavesdropper eavesdrops.
4. The information-secured wireless energy-carrying relay system according to claim 2, wherein the two-hop amplify-and-forward multi-relay network operates in a time division multiplexing mode.
5. The wireless energy-carrying relay system for ensuring information security according to claim 1, wherein the problem of maximizing the safe reachable rate is solved based on an alternative optimization method: rank 1 relaxation is first performed on the safe achievable rate maximization problem, i.e. ordering
Figure FDA0002506069640000025
Ignoring the non-convex rank 1 constraint, the safe achievable rate maximization problem is transformed into the following rank 1 relaxation problem:
Figure FDA0002506069640000026
Figure FDA0002506069640000027
Tr(D6X)≥Q.
wherein the content of the first and second substances,
Figure FDA0002506069640000028
and is
Figure FDA0002506069640000029
And
Figure FDA00025060696400000210
6. the wireless energy-carrying relay system for guaranteeing information security according to claim 5, wherein a local optimal solution of the rank 1 relaxation problem is solved based on an alternative optimization method, so as to obtain an optimal or suboptimal rank 1 solution of the safe reachable rate maximization problem; solving a locally optimal solution of a rank 1 relaxation problem comprises the steps of:
(1) initialization: n is 0, and n is the iteration number; xnIs KN2×KN2The epsilon is a positive number;
(2) fixed XnSolving for
Figure FDA0002506069640000031
Figure FDA0002506069640000032
(3) Fixing
Figure FDA0002506069640000033
Solving the following convex optimization problem by using an interior point method to obtain Xn+1：
Figure FDA0002506069640000034
Figure FDA0002506069640000035
Tr(D6X)≥Q
(4) n is n +1, and R is calculateds(Xn+1) Alternately updating through the step (2) and the step (3)
Figure FDA0002506069640000036
And Xn+1Until convergence, i.e. Rs(Xn+1)-Rs(Xn)＜∈；
(5) Obtaining a locally optimal solution X of the rank 1 relaxation problem*＝Xn+1；
If X is*Is a rank 1 solution, and obtains an optimal rank 1 solution f of the safe reachable rate maximization problem through characteristic decomposition*(ii) a If X is*Instead of a rank 1 solution, a suboptimal rank 1 solution f of the safe reachable rate maximization problem is obtained through Gaussian randomization; finally, the F is matrixed to obtain a beam forming matrix F of each relay terminalk。
7. A wireless energy-carrying relay method for guaranteeing information security is characterized by comprising the following steps:
s1, in the two-hop amplification multi-relay network, each relay terminal is respectively connected with a source terminal, a legal receiving terminal, an energy collection terminal and an eavesdropper; each relay terminal is provided with N antennae, the energy receiving terminal is provided with M antennae, and the source terminal, the legal receiving terminal and the eavesdropper are provided with single antennae;
order to
Figure FDA0002506069640000037
Individual watchA channel from the source end to the kth relay end, from the kth relay end to the legal receiving end, and from the kth relay end to the eavesdropper;
Figure FDA0002506069640000038
represents a channel from the kth relay terminal to the energy receiving terminal;
Figure FDA0002506069640000039
and
Figure FDA00025060696400000310
are independent identically distributed complex Gaussian random variables with zero mean and unit variance; fk∈CN×NA beamforming matrix representing the kth relay peer,
Figure FDA00025060696400000311
σ2additive white Gaussian noise Power, P, for a legitimate receiver and an eavesdroppersFor source side transmit power, F ═ diag (F)1，F2，...，FK)，
Figure FDA00025060696400000312
Let the wireless energy constraint be:
wherein
Figure FDA00025060696400000314
Representing a channel from the kth relay terminal to an energy receiving terminal, wherein Q is a preset energy collection threshold of the energy receiving terminal;
making the individual power constraint of each relay as:
Figure FDA0002506069640000041
wherein, PkMaximum allowable transmission power for the kth relay node;
the safe reachable rate for ensuring the safe communication of the physical layer and meeting the wireless energy constraint and the independent power constraint of each relay terminal is as follows:
Figure FDA0002506069640000042
s2, constructing a safe reachable rate maximization problem which ensures the safe communication of the physical layer and meets the wireless energy constraint and the independent power constraint of each relay end, and comprising the following steps:
Figure FDA0002506069640000043
Figure FDA0002506069640000044
Figure FDA0002506069640000045
wherein the content of the first and second substances,
Figure FDA0002506069640000046
Figure FDA0002506069640000047
Figure FDA0002506069640000048
Figure FDA0002506069640000049
Figure FDA00025060696400000410
Figure FDA00025060696400000411
Figure FDA00025060696400000412
Figure FDA00025060696400000413
rank 1 relaxation is performed on the above-mentioned safe achievable rate maximization problem, order
Figure FDA00025060696400000414
Figure FDA00025060696400000415
And
Figure FDA00025060696400000416
Figure FDA00025060696400000417
solving a local optimal solution of the above rank 1 relaxation problem;
s3, initialization: n is 0, and n is the iteration number;
Figure FDA00025060696400000418
Xnis KN2×KN2Is a positive numberCalculating Rs(Xn)；
S4, fixing XnSolving for
Figure FDA00025060696400000419
Figure FDA00025060696400000420
S5, fixing
Figure FDA0002506069640000051
Solving the following convex optimization problem by using an interior point method to obtain Xn+1：
Figure FDA0002506069640000052
Figure FDA0002506069640000053
Tr(D6X)≥Q
S6, n ═ n +1, and R is calculateds(Xn+1) Alternately updating through S2 and S3
Figure FDA0002506069640000054
And Xn+1Until convergence, i.e. Rs(Xn+1)-Rs(Xn) Is less than an element; obtaining a locally optimal solution X to the rank 1 relaxation problem*＝Xn+1；
S7, if X*Is a rank 1 solution, and obtains an optimal rank 1 solution f of the safe reachable rate maximization problem through characteristic decomposition*If X is*Instead of a rank 1 solution, a suboptimal rank 1 solution f of the safe reachable rate maximization problem is obtained through Gaussian randomization; finally, the F is matrixed to obtain a beam forming matrix F of each relayk。
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