CN113630163A - Artificial noise assisted beam forming method with robustness for related stealing channels - Google Patents

Artificial noise assisted beam forming method with robustness for related stealing channels Download PDF

Info

Publication number
CN113630163A
CN113630163A CN202010374733.7A CN202010374733A CN113630163A CN 113630163 A CN113630163 A CN 113630163A CN 202010374733 A CN202010374733 A CN 202010374733A CN 113630163 A CN113630163 A CN 113630163A
Authority
CN
China
Prior art keywords
sinr
channel
user
noise ratio
eve
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202010374733.7A
Other languages
Chinese (zh)
Inventor
孟维晓
徐赛
王金明
韩帅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology
Original Assignee
Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN202010374733.7A priority Critical patent/CN113630163A/en
Publication of CN113630163A publication Critical patent/CN113630163A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • 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
    • H04B7/0619—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 using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]

Abstract

The invention discloses an artificial noise assisted beam forming scheme with robustness for a related stealing channel. Step 1: establishing a related multi-input single-output MISO interception channel model when the main channel CSI is incomplete; step 2: setting the transmitting power at the information source Alice, the interruption SINR at the legal user Bob and the non-tandem interception user Eve and the signal to interference plus noise ratio interruption probability SINR-OP at the legal user and the interception user; and step 3: establishing a non-convex optimization problem of interrupting SINR maximization at the position of a legal user Bob under the constraint condition of signal to interference noise ratio interruption probability SINR-OP at the position of the legal user Bob and a non-serial interception user Eve; and 4, step 4: and (4) converting the maximized non-convex optimization problem in the step (3) into a convex problem to solve. The invention ensures that the legal user Bob obtains higher target interrupt signal-to-interference-and-noise ratio SINR, thereby effectively improving the communication performance of the legal user Bob.

Description

Artificial noise assisted beam forming method with robustness for related stealing channels
Technical Field
The invention relates to the technical field of communication, in particular to an artificial noise assisted beam forming method with robustness for a relevant stealing channel.
Background
With the rapid development of 5G and air-space-ground integrated communication networks, security issues have received extensive attention from researchers as a research hotspot. Wireless communication networks are vulnerable to eavesdropping and impersonation attacks due to the broadcast nature of the wireless channel. In addition to key-based security methods, physical layer security techniques can also improve the security of communications. Currently, signal processing techniques for physical layer security have been extensively studied and effectively improve the security performance of communication systems. However, most of these techniques are based on the premise that the main channel and the eavesdropping channel are independent from each other. However, in practical communication systems, the presence of a correlation between stolen channels is inevitable, and such correlation has proven detrimental to the security performance of the communication system, such that the maximum achievable security rate is low under the constraints of the probability of a security disruption, and increasing signal power does not significantly reduce the security loss due to such correlation.
The multi-antenna-based beam forming is used as a core technology of physical layer security, so that the signal quality of a legal user can be enhanced, and the signal strength of an eavesdropping user can be limited. At the same time, embedding artificial noise into the beamformed signal can further reduce the received signal quality at eavesdropping users. Thus, beamforming techniques for physical layer security have never received reduced attention. However, existing artificial noise assisted beamforming studies are almost all based on the assumption that stealing channels are independent of each other, and this limitation results in the inability to obtain sufficiently desirable privacy performance in the case of related stealing channels. On the other hand, in practice there are often some application scenarios (e.g. pay-per-view video services, etc.) where high communication rate requirements are present and where privacy requirements are somewhat lower. In these applications, it is more meaningful to select an appropriate Quality of Service (QoS) index as a constraint to design artificial noise assisted beamforming. Therefore, in order to improve the security performance of the communication system as much as possible, it is necessary to design an artificial noise assisted beamforming method that is robust specific to the relevant stealing channel.
Disclosure of Invention
The invention provides an artificial noise assisted beam forming method with robustness facing to a related stealing channel, which enables a legal user Bob to obtain a higher target interruption signal-to-interference-and-noise ratio (SINR), thereby effectively improving the communication performance of the legal user Bob.
The invention is realized by the following technical method:
an artificial noise assisted beamforming method robust against an associated theft channel, the beamforming method comprising the steps of:
step 1: establishing a related multi-input single-output MISO interception channel model when the channel state information CSI of the main channel is incomplete;
step 2: setting the transmitting power at the source Alice, the interruption signal to interference plus noise ratio SINR and the signal to interference plus noise ratio interruption probability SINR-OP at the legal user Bob and the non-serial interception user Eve;
and step 3: establishing a non-convex optimization problem of interrupting the SINR maximization at the position of a legal user Bob under the constraint condition of the SINR interruption probability SINR-OP at the position of the legal user Bob and a non-serial eavesdropping user Eve;
and 4, step 4: and (4) converting the maximized non-convex optimization problem in the step (3) into a convex problem to solve.
Further, the multiple-input single-output MISO eavesdropping channel model in step 1 is,
Figure BDA0002479581300000021
Figure BDA0002479581300000022
wherein the content of the first and second substances,
Figure BDA0002479581300000023
refers to the primary channel vector from the source Alice to the legitimate user Bob,
Figure BDA0002479581300000024
refers to the eavesdropping channel vector from the source Alice to the kth non-colluding eavesdropping user Eve,
Figure BDA0002479581300000025
finger hdThe channel estimation vector of (a) is,
Figure BDA0002479581300000026
finger hdThe sum of the channel error vector of (a),
Figure BDA0002479581300000027
finger hkThe channel estimation vector of (a) is,
Figure BDA0002479581300000028
finger hkThe channel error vector of (a) is,
Figure BDA0002479581300000029
an N-dimensional column vector of a complex field, the set K being defined as
Figure BDA00024795813000000210
For the source Alice to be able to,
Figure BDA00024795813000000211
satisfy the requirement of
Figure BDA00024795813000000212
Figure BDA00024795813000000213
Satisfy the requirement of
Figure BDA00024795813000000214
And the following mathematical formula holds true:
Figure BDA00024795813000000215
Figure BDA00024795813000000216
wherein, Pk＝diag{ρ1,k,ρ2,k,…,ρN,kIt means that the channel stealing correlation matrix is stolen,
Figure BDA00024795813000000217
refers to a phase matrix of the stealing channel, the diagonal elements of which respectively correspond to the power correlation coefficient and the phase variable, alpha, between each sub-channel pair of the stealing channeldMean main channel gain variance, αkChannel gain variance, I, referring to the k-th eavesdropping channelNRefers to an N-dimensional identity matrix.
Further, the step 2 is specifically that when the signal source Alice transmits a signal carrying secret information
Figure BDA0002479581300000031
When the user is a legal user Bob, the received signals at the legal user Bob and the kth non-colluding eavesdropping user Eve are respectively
Figure BDA0002479581300000032
Figure BDA0002479581300000033
Wherein n isdComplex white Gaussian noise, n, of zero mean unit variance for user Bob by finger fitkRefers to the complex white gaussian noise with zero mean unit variance at Eve of the kth non-colluding eavesdropping user.
Further, the step 3 specifically includes using the SINR-OP as a constraint condition of QoS, which is defined as:
Pout(Γ)＝Pr{γ＜Γ}, (10)
wherein, gamma represents the interruption signal-to-interference-and-noise ratio SINR; when the goal of beamforming is to maximize the outage SINR at the legitimate user Bob, given the SINR outage probability SINR-OP constraint at the legitimate user Bob and the non-colluding eavesdropping user Eve, the optimization problem is expressed as,
Figure BDA0002479581300000034
wherein epsilondAnd 1- εeRespectively indicating the signal to interference plus noise ratio interruption probability SINR-OP required by the combination user Bob and the non-serial interception user Eve; p is the transmitting power of the information source Alice; gamma-shapeddThe target interruption signal to interference plus noise ratio (SINR) representing the legal user Bob is a variable; and gamma iseThe target interruption signal-to-interference-and-noise ratio SINR at the Eve representing the non-colluded user is a preset constant.
Further, the optimization problem formula (11) is converted into the equivalent form:
Figure BDA0002479581300000035
let epsilonk＝1-(1-ε)1/KAnd rank relaxation is carried out to obtain
Figure BDA0002479581300000041
Let sigmad＝W-ΓdV, for probability constraint Pr [ gamma ]d≤Γd}≤εdIs modified into the following form
Figure BDA0002479581300000042
Wherein x isd～CN(0,IN) Is a complex Gaussian vector of zero mean unit variance, and
Figure BDA0002479581300000043
Figure BDA0002479581300000044
Figure BDA0002479581300000045
the probability constraint (14) is conservatively converted to the following deterministic form using the bernstein inequality:
Figure BDA0002479581300000046
wherein σd＝-ln(εd)，s-(Λ)＝max{λmax(-Λ),0},λmax(-) is the largest eigenvalue of matrix- Λ.
Further, let Σe＝W-ΓeV, for probability constraint Pr [ gamma ]k≤Γe}≥1-εkIs modified into the following form
Figure BDA0002479581300000047
Wherein x isk～CN(0,IN) Is a complex Gaussian vector of zero mean unit variance, and
Figure BDA0002479581300000048
Figure BDA0002479581300000049
Figure BDA00024795813000000410
the probability constraint (19) is conservatively converted into the following deterministic form using the bernstein inequality:
Figure BDA00024795813000000411
wherein σk＝-ln(εk)，s+(Λ)＝max{λmax(Λ),0}，λmax(Λ) is the maximum eigenvalue of matrix Λ.
Further, said formula (23) is converted into,
Figure BDA0002479581300000051
wherein, mud，νd，μkV and vkIs a relaxation variable due to gammadIs a variable, so the optimization problem equation (24) is a non-convex optimization problem, but for any fixed ΓdThe optimization problem formula (24) is a semi-definite programming problem;
therefore, it is most preferable
Figure BDA0002479581300000054
Can optimize toolkit CVX and p gamma by jointly using standard convexdAt [0, Γ ]d,u]The range is found by performing a binary search, wherein,
Figure BDA0002479581300000052
obtained by
Figure BDA0002479581300000053
The maximum target outage signal to interference plus noise ratio SINR at the legitimate user Bob that can be achieved as artificial noise assisted beamforming.
The invention has the beneficial effects that:
the invention maximizes the communication rate obtained by the legal user under the constraint condition of the given signal-to-interference-and-noise ratio interruption probability SINR-OP of the legal user and the eavesdropping user, and aims to improve the confidentiality of the communication system as much as possible.
Drawings
Fig. 1 is a diagram of a MISO eavesdropping channel model.
Figure 2 is a graph of the privacy performance of the artifact-assisted beamforming method of the present invention.
FIG. 3 is a schematic flow chart of the method of the present invention.
Detailed Description
The technical method in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying 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.
Example 1
As shown in fig. 1 and 3, an artificial noise assisted beamforming method having robustness for an associated stealing channel includes the following steps:
step 1: establishing a related multi-input single-output MISO interception channel model when the channel state information CSI of the main channel is incomplete;
step 2: setting the transmitting power at the source Alice, the interruption signal to interference plus noise ratio SINR and the signal to interference plus noise ratio interruption probability SINR-OP at the legal user Bob and the non-serial interception user Eve;
and step 3: establishing a non-convex optimization problem of interrupting the SINR maximization at the position of a legal user Bob under the constraint condition of the SINR interruption probability SINR-OP at the position of the legal user Bob and a non-serial eavesdropping user Eve;
and 4, step 4: and (4) converting the maximized non-convex optimization problem in the step (3) into a convex problem to solve.
Consider a correlated Multiple Input Single Output (MISO) eavesdropping channel model as shown in fig. 1; the signal source (Alice) is provided with N transmitting antennas, and both the legal user (Bob) and the K non-serial eavesdropping users (Eve) are only provided with a single antenna. All communication links are assumed to be quasi-static flat fading rayleigh channels, and Alice only has incomplete primary Channel State Information (CSI) and statistical eavesdropping Channel CSI. Meanwhile, it is also assumed that the transmitting antenna channels at Alice are independent of each other and there is a certain correlation between stealing channels.
Further, the multiple-input single-output MISO eavesdropping channel model in step 1 is,
Figure BDA0002479581300000061
Figure BDA0002479581300000062
wherein the content of the first and second substances,
Figure BDA0002479581300000063
refers to the primary channel vector from the source Alice to the legitimate user Bob,
Figure BDA0002479581300000064
refers to the eavesdropping channel vector from the source Alice to the kth non-colluding eavesdropping user Eve,
Figure BDA0002479581300000065
finger hdThe channel estimation vector of (a) is,
Figure BDA0002479581300000066
finger hdThe sum of the channel error vector of (a),
Figure BDA0002479581300000067
finger hkThe channel estimation vector of (a) is,
Figure BDA0002479581300000068
finger hkThe channel error vector of (a) is,
Figure BDA0002479581300000069
an N-dimensional column vector of a complex field, the set K being defined as
Figure BDA00024795813000000610
For the source Alice to be able to,
Figure BDA00024795813000000611
satisfy the requirement of
Figure BDA00024795813000000612
Figure BDA00024795813000000613
Satisfy the requirement of
Figure BDA00024795813000000614
And the following mathematical formula holds true:
Figure BDA0002479581300000071
Figure BDA0002479581300000072
wherein, Pk＝diag{ρ1,k,ρ2,k,…,ρN,kIt means that the channel stealing correlation matrix is stolen,
Figure BDA0002479581300000073
refers to a phase matrix of the stealing channel, the diagonal elements of which respectively correspond to the power correlation coefficient and the phase variable, alpha, between each sub-channel pair of the stealing channeldMean main channel gain variance, αkChannel gain variance, I, referring to the k-th eavesdropping channelNRefers to an N-dimensional identity matrix.
Further, the step 2 is specifically that when the signal source Alice transmits a signal carrying secret information
Figure BDA0002479581300000074
When the user is a legal user Bob, the received signals at the legal user Bob and the kth non-colluding eavesdropping user Eve are respectively
Figure BDA0002479581300000075
Figure BDA0002479581300000076
Wherein n isdComplex white Gaussian noise, n, of zero mean unit variance for user Bob by finger fitkRefers to the complex white gaussian noise with zero mean unit variance at Eve of the kth non-colluding eavesdropping user.
To enhance security, signal transmission is performed using an artificial noise assisted beamforming method, and in particular, the transmission signal x is constructed,
x＝ws+v, (7)
where w is a beamformer used to transmit data symbols s-CN (0,1), V refers to an artificial noise vector and its covariance matrix is V ═ E { vv ═ EH}. Therefore, SINR scores at Bob and the k-th Eve
Figure BDA0002479581300000077
Figure BDA0002479581300000078
Since the correlation between stolen channels compromises the security performance of the communication, the maximum security rate achievable under the security interruption probability constraint is not always adequate for the particular application. Therefore, it is of great practical significance to provide a beamforming method under the QoS constraint. For example, for some application scenarios that require slightly lower security but are sensitive to communication QoS (e.g., pay commercial video services), a dramatic increase in communication performance at Bob is often traded for a slight decrease in security level.
Further, the step 3 is specifically to, in consideration that the uncertain part of the channel obeys gaussian distribution, adopt the SINR-OP as a constraint condition of the QoS, which is defined as:
Pout(Γ)＝Pr{γ＜Γ}, (10)
wherein, gamma represents the interruption signal-to-interference-and-noise ratio SINR; when the goal of beamforming is to maximize the outage SINR at the legitimate user Bob, given the SINR outage probability SINR-OP constraint at the legitimate user Bob and the non-colluding eavesdropping user Eve, the optimization problem is expressed as,
Figure BDA0002479581300000081
wherein epsilondAnd 1- εeRespectively indicating the signal to interference plus noise ratio interruption probability SINR-OP required by the combination user Bob and the non-serial interception user Eve; p is the transmitting power of the information source Alice; gamma-shapeddThe target interruption signal to interference plus noise ratio (SINR) representing the legal user Bob is a variable; and gamma iseThe target interruption signal-to-interference-and-noise ratio SINR at the Eve representing the non-colluded user is a preset constant.
Further, the optimization problem formula (11) is converted into the equivalent form:
Figure BDA0002479581300000082
let epsilonk＝1-(1-ε)1/KAnd rank relaxation is carried out to obtain
Figure BDA0002479581300000083
Let sigmad＝W-ΓdV, for probability constraint Pr [ gamma ]d≤Γd}≤εdIs modified into the following form
Figure BDA0002479581300000084
Wherein x isd～CN(0,IN) Is a complex Gaussian vector of zero mean unit variance, and
Figure BDA0002479581300000091
Figure BDA0002479581300000092
Figure BDA0002479581300000093
the probability constraint (14) is conservatively converted to the following deterministic form using the bernstein inequality:
Figure BDA0002479581300000094
wherein σd＝-ln(εd)，s-(Λ)＝max{λmax(-Λ),0},λmax(-) is the largest eigenvalue of matrix- Λ. In other words, if the expression (18) is satisfied, the probability limiting condition (14) is also necessarily satisfied.
Further, let Σe＝W-ΓeV, for probability constraint Pr [ gamma ]k≤Γe}≥1-εkIt is rewritten into the following form,
Figure BDA0002479581300000095
wherein x isk～CN(0,IN) Is a complex Gaussian vector of zero mean unit variance, and
Figure BDA0002479581300000096
Figure BDA0002479581300000097
Figure BDA0002479581300000098
the probability constraint (19) is conservatively converted into the following deterministic form using the bernstein inequality:
Figure BDA0002479581300000099
wherein σk＝-ln(εk)，s+(Λ)＝max{λmax(Λ),0}，λmax(Λ) is the maximum eigenvalue of matrix Λ. In other words, if equation (23) holds, probability limiting condition (19) must also hold.
Further, the optimization problem formula (23) is converted into,
Figure BDA0002479581300000101
wherein, mud，νd，μkV and vkIs a relaxation variable due to gammadIs a variable, so the optimization problem equation (24) is a non-convex optimization problem, but for any fixed ΓdThe optimization problem formula (24) is a semi-definite programming problem;
therefore, it is most preferable
Figure BDA0002479581300000102
Can optimize toolkit CVX and p gamma by jointly using standard convexdAt [0, Γ ]d,u]The range is found by performing a binary search, wherein,
Figure BDA0002479581300000103
obtained by
Figure BDA0002479581300000104
The maximum target outage signal to interference plus noise ratio SINR at the legitimate user Bob that can be achieved as artificial noise assisted beamforming.
Fig. 2 shows the power-related relationshipNumber expected value ρ and target outage SINR Γ at BobdWherein power correlation coefficients between respective sub-channel pairs of the stealing channel obey [ rho-0.1, rho +0.1 ]]Uniform distribution of the range, the correlation matrix ΘkSetting as an identity matrix, adopting delta to characterize the size of main channel CSI error and satisfying
Figure BDA0002479581300000105
Other parameters are set as follows: alpha is alphad＝α k1, K3, N8 or 4, ∈d＝0.1，εe0.9 or 0.7, Γe0dB, 10dBW, Δ 0.1 or 0.

Claims (7)

1. An artificial noise assisted beamforming method robust against an associated stealing channel, the method comprising:
step 1: establishing a related multi-input single-output MISO interception channel model when the channel state information CSI of the main channel is incomplete;
step 2: setting the transmitting power at the source Alice, the interruption signal to interference plus noise ratio SINR and the signal to interference plus noise ratio interruption probability SINR-OP at the legal user Bob and the non-serial interception user Eve;
and step 3: establishing a non-convex optimization problem of interrupting the SINR maximization at the position of a legal user Bob under the constraint condition of the SINR interruption probability SINR-OP at the position of the legal user Bob and a non-serial eavesdropping user Eve;
and 4, step 4: and (4) converting the maximized non-convex optimization problem in the step (3) into a convex problem to solve.
2. The beamforming method according to claim 1, wherein the multiple-input single-output MISO eavesdropping channel model in step 1 is,
Figure FDA0002479581290000011
Figure FDA0002479581290000012
wherein the content of the first and second substances,
Figure FDA0002479581290000013
refers to the primary channel vector from the source Alice to the legitimate user Bob,
Figure FDA0002479581290000014
refers to the eavesdropping channel vector from the source Alice to the kth non-colluding eavesdropping user Eve,
Figure FDA0002479581290000015
finger hdThe channel estimation vector of (a) is,
Figure FDA0002479581290000016
finger hdThe sum of the channel error vector of (a),
Figure FDA0002479581290000017
finger hkThe channel estimation vector of (a) is,
Figure FDA0002479581290000018
finger hkThe channel error vector of (a) is,
Figure FDA0002479581290000019
an N-dimensional column vector of a complex field, the set K being defined as K
Figure FDA00024795812900000110
For the source Alice to be able to,
Figure FDA00024795812900000111
satisfy the requirement of
Figure FDA00024795812900000112
Figure FDA00024795812900000113
Satisfy the requirement of
Figure FDA00024795812900000114
And the following mathematical formula holds true:
Figure FDA00024795812900000115
Figure FDA00024795812900000116
wherein, Pk＝diag{ρ1,k,ρ2,k,…,ρN,kIt means that the channel stealing correlation matrix is stolen,
Figure FDA00024795812900000117
refers to a phase matrix of the stealing channel, the diagonal elements of which respectively correspond to the power correlation coefficient and the phase variable, alpha, between each sub-channel pair of the stealing channeldMean main channel gain variance, αkChannel gain variance, I, referring to the k-th eavesdropping channelNRefers to an N-dimensional identity matrix.
3. The beamforming method according to claim 1, wherein the step 2 is specifically performed when the source Alice transmits a signal carrying secret information
Figure FDA0002479581290000021
When the user is a legal user Bob, the received signals at the legal user Bob and the kth non-colluding eavesdropping user Eve are respectively
Figure FDA0002479581290000022
Figure FDA0002479581290000023
Wherein n isdComplex white Gaussian noise, n, of zero mean unit variance for user Bob by finger fitkRefers to the complex white gaussian noise with zero mean unit variance at Eve of the kth non-colluding eavesdropping user.
4. The beamforming method according to claim 1, wherein the step 3 specifically adopts a signal to interference plus noise ratio (SINR) -OP as a constraint condition of quality of service (QoS), which is defined as:
Pout(Γ)＝Pr{γ＜Γ}, (10)
wherein, gamma represents the interruption signal-to-interference-and-noise ratio SINR; when the goal of beamforming is to maximize the outage SINR at the legitimate user Bob, given the SINR outage probability SINR-OP constraint at the legitimate user Bob and the non-colluding eavesdropping user Eve, the optimization problem is expressed as,
Figure FDA0002479581290000024
wherein epsilondAnd 1- εeRespectively indicating the signal to interference plus noise ratio interruption probability SINR-OP required by the combination user Bob and the non-serial interception user Eve; p is the transmitting power of the information source Alice; gamma-shapeddThe target interruption signal to interference plus noise ratio (SINR) representing the legal user Bob is a variable; and gamma iseThe target interruption signal-to-interference-and-noise ratio SINR at the Eve representing the non-colluded user is a preset constant.
5. The beamforming method according to claim 4, wherein the optimization problem equation (11) is transformed into the equivalent form:
Figure FDA0002479581290000025
let epsilonk＝1-(1-ε)1/KAnd rank relaxation is carried out to obtain
Figure FDA0002479581290000031
Let sigmad＝W-ΓdV, for probability constraint Pr [ gamma ]d≤Γd}≤εdIs modified into the following form
Figure FDA0002479581290000032
Wherein x isd～CN(0,IN) Is a complex Gaussian vector of zero mean unit variance, and
Figure FDA0002479581290000033
Figure FDA0002479581290000034
Figure FDA0002479581290000035
the probability constraint (14) is conservatively converted to the following deterministic form using the bernstein inequality:
Figure FDA0002479581290000036
wherein σd＝-ln(εd)，
Figure FDA0002479581290000037
λmax(-) is the largest eigenvalue of matrix- Λ.
6. The beamforming method of claim 5, wherein let Σe＝W-ΓeV, for probability constraint Pr [ gamma ]k≤Γe}≥1-εkIs modified into the following form
Figure FDA0002479581290000038
Wherein x isk～CN(0,IN) Is a complex Gaussian vector of zero mean unit variance, and
Figure FDA0002479581290000039
Figure FDA00024795812900000310
Figure FDA00024795812900000311
the probability constraint (19) is conservatively converted into the following deterministic form using the bernstein inequality:
Figure FDA00024795812900000312
wherein σk＝-ln(εk)，s+(Λ)＝max{λmax(Λ),0}，λmax(Λ) is the maximum eigenvalue of matrix Λ.
7. The beamforming method according to claim 6, wherein the formula (23) is converted into,
Figure FDA0002479581290000041
wherein, mud，νd，μkV and vkIs a relaxation variable due to gammadIs a variable, so the optimization problem equation (24) is a non-convex optimization problem, but for any fixed ΓdThe optimization problem formula (24) is a semi-definite programming problem;
therefore, it is most preferable
Figure FDA0002479581290000042
Can optimize toolkit CVX and p gamma by jointly using standard convexdAt [0, Γ ]d,u]The range is found by performing a binary search, wherein,
Figure FDA0002479581290000043
obtained by
Figure FDA0002479581290000044
The maximum target outage signal to interference plus noise ratio SINR at the legitimate user Bob that can be achieved as artificial noise assisted beamforming.
CN202010374733.7A 2020-05-06 2020-05-06 Artificial noise assisted beam forming method with robustness for related stealing channels Pending CN113630163A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010374733.7A CN113630163A (en) 2020-05-06 2020-05-06 Artificial noise assisted beam forming method with robustness for related stealing channels

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010374733.7A CN113630163A (en) 2020-05-06 2020-05-06 Artificial noise assisted beam forming method with robustness for related stealing channels

Publications (1)

Publication Number Publication Date
CN113630163A true CN113630163A (en) 2021-11-09

Family

ID=78376767

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010374733.7A Pending CN113630163A (en) 2020-05-06 2020-05-06 Artificial noise assisted beam forming method with robustness for related stealing channels

Country Status (1)

Country Link
CN (1) CN113630163A (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108712199A (en) * 2018-05-03 2018-10-26 西安交通大学 Two-dimentional robust beam-forming method under MISO tapping channels based on outage probability constraint
CN110213816A (en) * 2019-05-24 2019-09-06 南京理工大学 Low complex degree high performance power distribution method based on safe space modulation
CN110233701A (en) * 2019-05-25 2019-09-13 西南电子技术研究所（中国电子科技集团公司第十研究所） Wirelessly communicate the decoding method of physical layer communication safety

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108712199A (en) * 2018-05-03 2018-10-26 西安交通大学 Two-dimentional robust beam-forming method under MISO tapping channels based on outage probability constraint
CN110213816A (en) * 2019-05-24 2019-09-06 南京理工大学 Low complex degree high performance power distribution method based on safe space modulation
CN110233701A (en) * 2019-05-25 2019-09-13 西南电子技术研究所（中国电子科技集团公司第十研究所） Wirelessly communicate the decoding method of physical layer communication safety

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
张立健等: "基于概率QoS 约束的鲁棒人工噪声辅助多用户MISO 安全传输方案", 《信息工程大学学报》, pages 1 - 6 *

Similar Documents

Publication Publication Date Title
Chen et al. User pairing and pair scheduling in massive MIMO-NOMA systems
Nandan et al. Secure beamforming for MIMO-NOMA-based cognitive radio network
Alavi et al. Robust beamforming techniques for non-orthogonal multiple access systems with bounded channel uncertainties
Cho et al. Interference alignment for uplink cellular systems with limited feedback
CN105072607B (en) It is a kind of to eavesdrop the safety of physical layer optimization method based on SDP in user cognition network more
Wang et al. Multicast secrecy rate maximization for reconfigurable intelligent surface backscatter communication
Wiesel et al. Optimization of the MIMO compound capacity
Park et al. Rate-splitting multiple access for quantized multiuser MIMO communications
KR20090062905A (en) Transmission interference cancelation method for mu-mimo
Yang et al. Outage performance of MIMO MRC systems with unequal-power co-channel interference
Choi et al. SecureLinQ: Joint precoding and scheduling for secure device-to-device networks
Wang et al. Exploiting constructive interference in symbol level hybrid beamforming for dual-function radar-communication system
CN113179113A (en) Beam forming method and system under satellite communication multicast signal transmission mode
CN116545482A (en) Multi-user MIMO downlink transmission method adopting low-precision DAC with assistance of RIS
CN113630163A (en) Artificial noise assisted beam forming method with robustness for related stealing channels
CN114286336B (en) Multi-cell network safe transmission method based on artificial noise
Xu et al. Correlation-based secure transmission for correlated MISO wiretap channels
Lei et al. Optimization of pre-processing filter for time-reversal multi-user secure transmission systems based on artificial noise
CN112134603B (en) Method for synthesizing safe transmission emission signal of MU-MIMO system
CN112994762B (en) MIMO-NOMA downlink self-adaptive wireless transmission method based on statistical CSI
CN110071748B (en) Artificial noise power distribution method of multiple-sending-single-receiving system
Sun et al. Nonlinear-precoded multiuser secure transmission with cooperative jamming and adaptive limited feedback
CN114501580A (en) Cooperative rate segmentation network security transmission method with untrusted relay threat
Zheng et al. QoS-constrained federated learning empowered by intelligent reflecting surface
Gui et al. Robust directional modulation design for secrecy rate maximization in multiuser networks

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination