CN116192220A - IRS-assisted cognitive SWIPT system safety rate optimization method - Google Patents

IRS-assisted cognitive SWIPT system safety rate optimization method Download PDF

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CN116192220A
CN116192220A CN202310209562.6A CN202310209562A CN116192220A CN 116192220 A CN116192220 A CN 116192220A CN 202310209562 A CN202310209562 A CN 202310209562A CN 116192220 A CN116192220 A CN 116192220A
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irs
bob
alice
eve
phase shift
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李国权
何根玺
熊军洲
林金朝
庞宇
朱宏钰
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Chongqing University of Post and Telecommunications
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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
    • H04B7/04—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
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H04B17/3912—Simulation models, e.g. distribution of spectral power density or received signal strength indicator [RSSI] for a given geographic region
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to an IRS-assisted cognitive SWIPT system safety rate optimization method, and belongs to the technical field of wireless communication. The method comprises the following steps: and establishing an IRS-assisted cognitive SWIPT system safe transmission model. A resource allocation model for jointly optimizing the design of the secondary transmitter transmitting wave beam and artificial interference noise, the power division coefficient of the secondary legal user and the IRS phase shift design is established. And fixing IRS phase shift, a secondary transmitter beam forming vector and artificial interference noise, and obtaining an optimal power division coefficient of a secondary legal user based on first-order Taylor expansion and KKT conditions. And obtaining the optimal beam forming vector and artificial interference noise of the secondary transmitter by adopting SDR and SCA methods. And (3) giving an optimal beam forming vector of the secondary transmitter, artificial interference noise and an optimal power dividing coefficient of a secondary legal user, and solving an IRS phase shift matrix design by adopting an SCA method.

Description

IRS-assisted cognitive SWIPT system safety rate optimization method
Technical Field
The invention belongs to the technical field of wireless communication, and relates to an IRS-assisted safety rate optimization method for a cognitive SWIPT system.
Background
In order to improve the use efficiency of limited spectrum resources, a Cognitive Radio (CR) system that enhances spectrum efficiency through spectrum sharing between a Primary User (PU) and a Secondary User (SU) has been widely studied. On the other hand, wireless energy-carrying communication (SimultaneousWireless Information and PowerTransfer, SWIPT) is a promising solution for future wireless power supply communication, and can simultaneously transmit information and energy, thereby facilitating the deployment of energy-limited internet of things devices. However, since propagation loss is serious, transmission efficiency may drastically decrease with increasing distance, thereby greatly limiting the performance of the swift system. The transmission efficiency and coverage are improved if the channel conditions can be enhanced.
Smart reflective surfaces (Intelligent reflecting surface, IRS) are receiving widespread attention as potential technologies for 5G and 5G later systems. IRS is a super-surface made up of a large number of passive reflective elements, each of which can independently reflect an incident electromagnetic wave by controlling the reflection coefficient. In IRS-assisted wireless communication systems, the IRS-reflected signal may be combined with other signal components to enhance the desired signal or reduce unwanted interference, thereby significantly improving system performance.
The security problems of CR communication systems are further complicated by the high dynamics and openness of CR networks, while allowing SU to share the PU spectrum and thus be vulnerable to internal and external attacks, compared to other communication systems. The IRS is deployed in the CR network and is equipped with AN Artificial Noise (AN), which can increase the received signal strength of a legitimate user while weakening the received signal strength of AN eavesdropper.
Disclosure of Invention
In view of the above, the invention aims to provide an IRS-assisted safety rate optimization method for a cognitive SWIPT system. Firstly, a PS architecture is used at a secondary legal user, so that the secondary legal user can simultaneously harvest energy and decode information, and simultaneously AN is introduced into a secondary transmitter, thereby further improving the safety rate of the secondary legal user. The beamforming vector at the secondary transmitter and the AN, phase shift at the IRS, and PS partition coefficients of the secondary legitimate user are jointly optimized to maximize the safe rate of the secondary legitimate user under the minimum harvest energy threshold of the secondary legitimate user, the maximum transmit power constraint of the secondary transmitter, and the IRS phase shift constraint. The complexity of the problem increases significantly due to the introduction of PS ratio, which increases the coupling between the variables. Furthermore, the problem is non-convex, so the present invention proposes an efficient algorithm based on continuous convex Approximation (SCA) and alternating optimization (Alternating Optimization, AO) to solve.
In order to achieve the above purpose, the present invention provides the following technical solutions:
an IRS-assisted cognitive swift system safety rate optimization method, comprising the steps of:
s1: establishing an IRS-assisted cognitive SWIPT system transmission model;
s2: with the aim of maximizing the safety rate of the secondary legal user, a resource allocation model for jointly optimizing the beam forming vector and AN design of the secondary transmitter and the secondary legal user power division coefficient and IRS phase shift design is established by considering the constraint of the minimum collecting energy threshold value and the power division coefficient of the secondary legal user, the constraint of the maximum transmission power of the secondary transmitter, the constraint of IRS phase shift and the constraint of the interference power applied to the PU;
s3: fixing IRS phase shift, a secondary transmitter beam forming vector sum AN, and obtaining AN optimal power division coefficient of a secondary legal user based on first-order Taylor expansion and KKT conditions;
s4: fixing IRS phase shift and power division coefficient of secondary legal user, and obtaining optimal beam forming vector and AN of secondary transmitter by SDR and SCA method;
s5: the beam forming vector of the secondary transmitter, the AN and the power dividing coefficient of the secondary legal user are fixed, and the IRS phase shift matrix design is solved by adopting SDR and SCA methods.
Optionally, the S1 specifically includes:
the IRS-assisted cognitive SWIPT system consists of a secondary user transmitter Alice, a legal secondary user Bob, L PUs and K eavesdroppers Eve, wherein K is more than or equal to 2;
setting Bob, PU and Eve to be provided with single antennas, wherein the number of Alice antennas and the number of IRS reflecting elements are respectively represented by M and N, and M is more than or equal to 2;
assuming that all channels in the system experience quasi-static flat fading, the equivalent channel gains from Alice to IRS, bob, the first PU, and the kth Eve are respectively denoted as
Figure BDA0004112128820000021
Equivalent channel gains from IRS to Bob, the first PU and the kth Eve are denoted as +.>
Figure BDA0004112128820000022
And
Figure BDA0004112128820000023
to ensure secure transmission from Alice to Bob, AN is sent from Alice to interfere with Eve for strong security, the AN will transmit with the information signal; each reflective element of the IRS suppresses reception of Eve by adjusting the phase of the incident signal;
let CSI for all channels including Eve be completely known in Alice; bob adopts a PS structure, decodes information and acquires energy from a signal transmitted by Alice; the transmission signal transmitted by Alice is modeled as
x＝w 1 s+w 2 a (1)
wherein ,
Figure BDA0004112128820000024
and />
Figure BDA0004112128820000025
Represented as AN information signal and AN signal, respectively, < ->
Figure BDA0004112128820000026
And
Figure BDA0004112128820000027
respectively representing a beam forming vector and AN vector; since Bob uses PS, energy is directly derived from the information signal and the AN; let Alice's maximum transmit power be P A Then there is |w 1 | 2 +|w 2 | 2 ≤P A The method comprises the steps of carrying out a first treatment on the surface of the Consider only the first signal reflected from the IRS and ignore signals reflected two or more times;
the signal received by Bob is expressed as
Figure BDA0004112128820000031
The signals received by the first PU and the kth Eve are respectively expressed as
Figure BDA0004112128820000032
Figure BDA0004112128820000033
wherein
Figure BDA0004112128820000034
Equivalent channel gains between Alice and Bob, alice and kth Eve, and Alice and the l PU, respectively;
Figure BDA0004112128820000035
a diagonal phase shift matrix representing IRS, where θ= [ θ ] on its main diagonal 1 ,θ 2 ,···,θ N ]，θ n ∈[0,2π]The nth element denoted IRS phase shift, ">
Figure BDA0004112128820000036
Is additive white gaussian noise AWGN; wherein->
Figure BDA0004112128820000037
And
Figure BDA0004112128820000038
the distribution of circular symmetric complex Gaussian CSCG random vector with mean x and covariance Σ representing noise power is defined by
Figure BDA0004112128820000039
A representation;
to simultaneously perform energy harvesting EH and information decoding ID, consider a PS-based receiver architecture at Bob, bob adaptively dividing the received signal into two independent parts for EH and ID; representing ρ ε [0,1] as the PS ratio, where ρ is the received signal portion for ID and the remaining 1- ρ portions are for EH; the signal received by Bob's information detection circuit is expressed as
Figure BDA00041121288200000310
wherein
Figure BDA00041121288200000311
Additive noise with zero mean and unit variance due to baseband signal processing at the ID receiver; the SINR at Bob is given by
Figure BDA00041121288200000312
For EH, the received signal at Bob is written as
Figure BDA00041121288200000313
Bob's collected energy is
Figure BDA00041121288200000314
Wherein η is the energy collection efficiency; the SINR at the kth Eve is expressed as
Figure BDA00041121288200000315
The achievable rate at Bob and the achievable rate at kth Eve are expressed as
R B ＝log 2 (1+SINR B ) (10)
Figure BDA0004112128820000041
The safe rate is defined as
Figure BDA0004112128820000042
Transmissions in the secondary network cause interference to the PU, and the interference noise power applied to the first PU is expressed as
Figure BDA0004112128820000043
Optionally, the S2 specifically is:
to maximize Bob's safety rate, the design problem is expressed as follows
Figure BDA0004112128820000044
wherein ,emin An iΓ is the minimum energy threshold to be collected for Bob l,max For the maximum interference power applied to the first PU, C1 is the constraint of Alice maximum transmission power, C2 is the constraint of Bob minimum collection energy, C3 is the constraint of noise interference power at the PU, and C5 is the constraint of unit mode of the reflecting surface;
the problem equation (14) is a non-convex problem, with coupling between variables.
Optionally, the S3 specifically is:
fixing IRS phase shift and Alice beam forming vector sum AN, and obtaining Bob optimal power division coefficient based on first-order Taylor expansion and KKT conditions;
fix w 1 、w 2 And phi, at the same time define
Figure BDA0004112128820000045
Figure BDA0004112128820000046
SINR for Bob and kth Eve is expressed as
Figure BDA0004112128820000047
Figure BDA0004112128820000048
Definition of the definition
Figure BDA0004112128820000049
Definition of the definition
Figure BDA00041121288200000410
Figure BDA00041121288200000411
W 1 ≥0，W 2 0 or more, and Rank (W) 1 )＝1，Rank(W 2 ) SINR for =1, bob and kth Eve is expressed as follows:
Figure BDA0004112128820000051
Figure BDA0004112128820000052
conversion of the original problem into
Figure BDA0004112128820000053
wherein
Figure BDA0004112128820000054
/>
Next, the following optimization problem is obtained by writing the formula (20) in the form of log subtraction
Figure BDA0004112128820000055
The problem expression (21) is not a convex optimization problem, and the maximum value of the problem cannot be directly obtained; representing the second item as
Figure BDA0004112128820000056
To solve this problem, the problem is converted into a convex problem by using a first order taylor expansion for g (ρ); the third term and the fourth term do not contain the optimization variable ρ, and they are regarded as constants; performing first-order Taylor expansion on the g (ρ) to obtain
Figure BDA0004112128820000057
The problem (21) is reiterated as
Figure BDA0004112128820000058
wherein ρ(q) Is the value of ρ at the q-th iteration; when given ρ (q) When the problem formula (24) is a convex problem about ρ, solving by an iterative algorithm; in each iteration, the convex optimization tool CVX is used for solving the optimal rho; solving the optimal rho by adopting a Lagrangian multiplier method; introducing a Lagrangian multiplier beta, the Lagrangian function of problem formula (24) being
Figure BDA0004112128820000061
Obtained based on Karush-Kuhn-Tucker (KKT) condition
Figure BDA0004112128820000062
To obtain a closed-form solution for ρ, the following cases of solutions are discussed
(1) When the value of beta is to be taken as 0,
Figure BDA0004112128820000063
when ρ is not solved;
(2) When the value of beta is to be taken as 0,
Figure BDA0004112128820000064
when the optimal solution of rho is obtained
Figure BDA0004112128820000065
At the same time ρ 1 Needs to meet the requirements of
Figure BDA0004112128820000066
(3) When beta is not equal to 0,
Figure BDA0004112128820000067
when the optimal solution of rho is obtained
Figure BDA0004112128820000068
In summary, the optimal solution of ρ is ρ * ＝min{ρ 1 ,ρ 2 }。
Optionally, the S4 specifically is:
giving IRS phase shift, and obtaining Alice optimal beam forming vector and AN by adopting SDR and SCA methods;
definition of the definition
Figure BDA0004112128820000069
Will get ρ * Bringing into the original problem and giving an IRS phase shift matrix phi; the existence of rank-one constraint makes the optimization problem non-convex, and the application of SDR to relax rank-one constraint results in
Figure BDA0004112128820000071
wherein
Figure BDA0004112128820000072
/>
However, formula (31) has a complex form that is not smooth and difficult to handle; rewriting by introducing relaxation variable τ > 0
Figure BDA0004112128820000073
Problem equation (32) is still not a convex optimization problem, problem equation (32) is at coupled W 1 and W2 The upper is not co-concave; the problem (32) comprises a DC-type planning problem, iteratively solving a sub-optimal solution using the SCA method; first, function R sec (W 1 ,W 2 ) The rewrites into the following form
R B (W 1 ,W 2 )＝t 0 (W 1 ,W 2 )-t 0 (W 2 ) (33)
wherein
Figure BDA0004112128820000074
Figure BDA0004112128820000075
Then t 0 (W 2 ) First order differentiation of (a)
Figure BDA0004112128820000076
W 2 Local points in a given ith iteration
Figure BDA0004112128820000077
Is written as a first-order taylor expansion of
Figure BDA0004112128820000078
wherein
Figure BDA0004112128820000079
Further, the method comprises the steps of,
Figure BDA00041121288200000710
re-expressed as
Figure BDA00041121288200000711
wherein
Figure BDA00041121288200000712
Figure BDA0004112128820000081
μ k (W 1 ,W 2 ) First order differentiation of (a)
Figure BDA0004112128820000082
μ k (W 1 ,W 2 ) Local points in a given ith iteration
Figure BDA0004112128820000083
Is written as a first-order taylor expansion of
Figure BDA0004112128820000084
wherein
Figure BDA0004112128820000085
At a given point in the ith iteration
Figure BDA0004112128820000086
The problem formula (32) approximates:
Figure BDA0004112128820000087
the original problem has been converted into a convex problem that the CVX can solve; if W is obtained 1 and W2 The rank is one, w is recovered by eigenvalue decomposition 1 and w2 I.e.
Figure BDA0004112128820000088
and />
Figure BDA0004112128820000089
Otherwise, when the rank is not one, the method of Gaussian randomization is used for approximately recovering w 1 and w2 。
Optionally, the step S5 specifically includes:
giving Alice optimal beam forming vectors and Bob optimal power dividing coefficients, and solving an IRS phase shift matrix design by adopting SDR and SCA methods;
the following matrix is defined and is used,
Figure BDA00041121288200000810
Figure BDA00041121288200000811
Figure BDA00041121288200000812
and have->
Figure BDA00041121288200000813
Figure BDA00041121288200000814
Figure BDA00041121288200000815
Figure BDA00041121288200000816
The sub-problem is expressed as phase shift optimization with respect to IRS
Figure BDA0004112128820000091
To address the non-convex objective function in problem equation (49), the function is then
Figure BDA0004112128820000092
Restated as DC form
Figure BDA0004112128820000093
wherein
Figure BDA0004112128820000094
Figure BDA0004112128820000095
Then, the process is carried out,
Figure BDA0004112128820000096
is +.>
Figure BDA0004112128820000097
Figure BDA0004112128820000098
Local point +.>
Figure BDA0004112128820000099
Is written as a first-order taylor expansion of
Figure BDA00041121288200000910
wherein
Figure BDA00041121288200000911
The achievable rate of the kth Eve is restated as
Figure BDA00041121288200000912
wherein
Figure BDA00041121288200000913
Figure BDA00041121288200000914
Figure BDA00041121288200000915
First order differentiation of (a)
Figure BDA00041121288200000916
Figure BDA00041121288200000917
Local point +.>
Figure BDA00041121288200000918
Is written as a first-order taylor expansion of
Figure BDA00041121288200000919
wherein
Figure BDA00041121288200000920
The corresponding optimization problem is expressed as
Figure BDA0004112128820000101
Resolved by CVX, when obtained
Figure BDA0004112128820000102
At the time of recovery->
Figure BDA0004112128820000103
And w is equal to 1 and w2 As in the recovery of->
Figure BDA0004112128820000104
When the rank is 1, ">
Figure BDA0004112128820000105
Solving through eigenvalue decomposition; otherwise, when->
Figure BDA0004112128820000106
Is not one, and gaussian randomization is used to approximate v.
The invention has the beneficial effects that: simulation results show that compared with the existing algorithm, the algorithm has better performance.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a diagram of a system model problem build in accordance with the present invention;
FIG. 2 is a graph showing the variation of transmission power with Alice according to the present invention;
FIG. 3 is a graph showing the variation of the number of reflective elements of the IRS according to the present invention.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
Referring to FIGS. 1-3, the present invention contemplates an IRS-assisted cognitive SWIPT system as shown in FIG. 1, which consists of a secondary user transmitter (Alice), a legitimate secondary user (Bob), L PUs, and K (K.gtoreq.2) eavesdroppers (Eve). Suppose Bob, PU and Eve are all equipped with a single antenna, and Alice's number of antennas and IRS's number of reflective elements are denoted by M (M.gtoreq.2) and N, respectively. Assuming that all channels in the system experience quasi-static flat fading, the equivalent channel gains from Alice to IRS, bob, the first PU, and the kth Eve, respectively, can be expressed as
Figure BDA0004112128820000111
Figure BDA0004112128820000112
Equivalent channel gains from IRS to Bob, the first PU and the kth Eve can be expressed as +.>
Figure BDA0004112128820000113
And
Figure BDA0004112128820000114
to ensure a secure transmission from Alice to Bob, AN is sent from Alice to interfere with Eve for strong security, and the AN is transmitted with the information signal. Each reflective element of the IRS suppresses the reception of Eve by adjusting the phase of the incident signal. It is assumed that CSI for all channels (including Eve's channels) is completely known in Alice. In particular, bob adopts a PS structure, and acquires energy from a signal transmitted by Alice while decoding information. Thus, the transmission signal transmitted by Alice can be modeled as
x＝w 1 s+w 2 a (1)
wherein ,
Figure BDA0004112128820000115
and />
Figure BDA0004112128820000116
Represented as AN information signal and AN signal, respectively, < ->
Figure BDA0004112128820000117
And
Figure BDA0004112128820000118
respectively representing a beam forming vector and AN vector. Since Bob uses PS, energy can be directly derived from the information signal and the AN. Assume that Alice's maximum transmit power is P A Then there is |w 1 | 2 +|w 2 | 2 ≤P A . Due to the large amount of path loss, the present invention only considers the first signal reflected from the IRS and ignores signals reflected two or more times.
Thus, the signal received by Bob can be expressed as
Figure BDA0004112128820000119
Likewise, the signals received by the ith PU and the kth Eve, respectively, may be expressed as
Figure BDA00041121288200001110
Figure BDA00041121288200001111
wherein
Figure BDA00041121288200001112
Equivalent channel gains between Alice and Bob, alice and kth Eve, and Alice and the l PU, respectively.
Figure BDA00041121288200001113
A diagonal phase shift matrix representing IRS, where θ= [ θ ] on its main diagonal 1 ,θ 2 ,···,θ N ]，θ n ∈[0,2π]The nth element denoted IRS phase shift, ">
Figure BDA00041121288200001114
Is Additive White Gaussian Noise (AWGN). />
Figure BDA0004112128820000121
and />
Figure BDA0004112128820000122
Representing the noise power.
To perform both energy harvesting (Energy Harvesting, EH) and information decoding (Information Decoding, ID) at Bob, consider a PS-based receiver architecture, where Bob adaptively divides the received signal into two separate parts for EH and ID. ρ ε [0,1] is represented as the PS ratio, where ρ is the received signal portion for ID and the remaining 1- ρ portions are for EH. The signal received by Bob's information detection circuit can be expressed as
Figure BDA0004112128820000123
wherein
Figure BDA0004112128820000124
Is due to the additive noise with zero mean and unit variance generated by baseband signal processing at the ID receiver. The SINR at Bob is given by
Figure BDA0004112128820000125
For EH, the received signal at Bob may be written as
Figure BDA0004112128820000126
Thus, bob's collected energy is
Figure BDA0004112128820000127
Where η is the energy collection efficiency. Likewise, the SINR at kth Eve may be expressed as
Figure BDA0004112128820000128
Further, the achievable rate at Bob and the achievable rate at kth Eve can be expressed as
R B ＝log 2 (1+SINR B ) (10)
Figure BDA0004112128820000129
Thus, the safe rate can be defined as
Figure BDA00041121288200001210
On the other hand, the transmission in the secondary network may cause interference to the PU, and the interference noise power applied to the first PU may be expressed as
Figure BDA00041121288200001211
The objective of the present invention is to maximize Bob's achievable safe rate by jointly designing the transmit beam right amount at Alice, the phase shift matrix of AN and IRS, and PS factor at Bob while taking into account Alice transmit total power constraint, bob minimum collected energy threshold constraint, maximum interference noise constraint imposed on PU, and IRS phase shift constraint.
3. Further, in the step S2, in order to maximize the safety rate of Bob, therefore, the design problem is expressed as follows
Figure BDA0004112128820000131
wherein ,emin An iΓ is the minimum energy threshold to be collected for Bob l,max For the maximum interference power applied to the first PU, C1 is the constraint of Alice maximum transmission power, C2 is the constraint of Bob minimum collection energy, C3 is the constraint of noise interference power at the PU, and C5 is the constraint of unit mode of the reflecting surface.
It is apparent that problem equation (14) is a non-convex problem because there is coupling between the variables. The complexity of the problem is greatly increased by the addition of PS ratios and the combination of IRS and swits.
4. In step S3, IRS phase shift and Alice beamforming vector sum AN are fixed, and Bob' S optimal power division coefficient is obtained based on first-order taylor expansion and KKT conditions.
Fix w 1 、w 2 And phi, at the same time define
Figure BDA0004112128820000132
Figure BDA0004112128820000133
The SINR of Bob and kth Eve can be expressed as
Figure BDA0004112128820000134
Figure BDA0004112128820000135
Further, define
Figure BDA0004112128820000136
Furthermore, define->
Figure BDA0004112128820000137
W 1 ≥0，W 2 0 or more, and Rank (W) 1 )＝1，Rank(W 2 ) The SINR of Bob and kth Eve can be restated as follows +.>
Figure BDA0004112128820000138
Figure BDA0004112128820000139
Accordingly, the original problem can be converted into
Figure BDA0004112128820000141
wherein
Figure BDA0004112128820000142
Next, the following optimization problem can be obtained by writing the equation (20) as a log-subtraction form
Figure BDA0004112128820000143
Obviously, the problem expression (21) is not a convex optimization problem, and thus the maximum value of the problem cannot be directly found. Representing the second item as
Figure BDA0004112128820000144
To solve this problem, the problem is converted into a convex problem by using a first order taylor expansion for g (ρ). In particular, since the optimization variable ρ is not included in the third term and the fourth term, they are regarded as constants. The first-order Taylor expansion of g (ρ) can be obtained
Figure BDA0004112128820000145
Thus, the problem formula (21) is described again as
Figure BDA0004112128820000146
wherein ρ(q) Is the value of ρ at the q-th iteration. Obviously, when ρ is given (q) In this case, the problem expression (24) is a convex problem with ρ, and can be solved by an iterative algorithm. In each iteration, the optimal ρ can be solved using a convex optimization tool CVX. However, since the computational complexity of solving this problem using CVX is high, the lagrangian multiplier method is employed to solve the optimal ρ. Introducing a Lagrangian multiplier beta, the Lagrangian function of problem formula (24) being
Figure BDA0004112128820000151
Based on Karush-Kuhn-Tucker (KKT) conditions
Figure BDA0004112128820000152
In order to obtain a closed-form solution for ρ, the following cases of solutions need to be discussed
(1) When the value of beta is to be taken as 0,
Figure BDA0004112128820000153
when ρ is not solved;
(2) When the value of beta is to be taken as 0,
Figure BDA0004112128820000154
when the optimal solution of rho can be obtained
Figure BDA0004112128820000155
At the same time ρ 1 Needs to meet the requirements of
Figure BDA0004112128820000156
/>
(3) When beta is not equal to 0,
Figure BDA0004112128820000157
when the optimal solution of rho can be obtained
Figure BDA0004112128820000158
In summary, the optimal solution of ρ is ρ * ＝min{ρ 1 ,ρ 2 }。
5. Further, given IRS phase shift in step S4, alice' S optimal beamforming vector and AN are obtained by using SDR and SCA methods.
Definition of the definition
Figure BDA0004112128820000161
Will get ρ * Is brought into the original problem and given the IRS phase shift matrix Φ. Due to the existence of rank-one constraint, the optimization problem is not convex, and the application of SDR to relax the rank-one constraint can be obtained
Figure BDA0004112128820000162
wherein
Figure BDA0004112128820000163
However, equation (31) has a complex form that is not smooth and difficult to handle. Can be rewritten by introducing a relaxation variable τ > 0
Figure BDA0004112128820000164
Problem equation (32) is still not a convex optimization problem because problem equation (32) is at coupled W 1 and W2 The upper is not co-concave. In practice, the problem (32) comprises a DC-type planning problem, and the sub-optimal solution can be solved iteratively using the SCA method. First, function R sec (W 1 ,W 2 ) Can be rewritten in the following form
R B (W 1 ,W 2 )＝t 0 (W 1 ,W 2 )-t 0 (W 2 ) (33)
wherein
Figure BDA0004112128820000165
Figure BDA0004112128820000166
Then t 0 (W 2 ) First order differentiation of (a)
Figure BDA0004112128820000167
Thus W is 2 Local points in a given ith iteration
Figure BDA0004112128820000168
The first order taylor expansion of (a) can be written as
Figure BDA0004112128820000169
/>
wherein
Figure BDA0004112128820000171
Further, the method comprises the steps of,
Figure BDA0004112128820000172
can be re-expressed as
Figure BDA0004112128820000173
wherein
Figure BDA0004112128820000174
Figure BDA0004112128820000175
Similarly, mu k (W 1 ,W 2 ) First order differentiation of (a)
Figure BDA0004112128820000176
Thus, mu k (W 1 ,W 2 ) Local points (W) in a given ith iteration 1 i ,W 2 i ) The first order taylor expansion of (a) can be written as
Figure BDA0004112128820000177
wherein
Figure BDA0004112128820000178
Therefore, at a given point in the ith iteration
Figure BDA0004112128820000179
The problem equation (32) may be approximated as:
Figure BDA00041121288200001710
the original problem has been converted into a convex problem, which can be effectively solved by the CVX. It should be noted that since the SDR method relaxes the rank constraint, W cannot be guaranteed 1 and W2 Is a rank one matrix. In particular, if W is obtained 1 and W2 The rank is one, w can be recovered by eigenvalue decomposition 1 and w2 I.e.
Figure BDA00041121288200001711
and />
Figure BDA00041121288200001712
Otherwise, when the rank is not one, it is necessary to approximate recovery of w by means of gaussian randomization 1 and w2 。
5. Further, in the step S5, an Alice optimal beamforming vector and Bob optimal power division coefficient are given, and an IRS phase shift matrix design is solved by adopting an SDR and SCA method.
The following matrix is defined and is used,
Figure BDA00041121288200001713
Figure BDA0004112128820000181
Figure BDA0004112128820000182
and have->
Figure BDA0004112128820000183
/>
Figure BDA0004112128820000184
Figure BDA0004112128820000185
Figure BDA0004112128820000186
The phase shift optimization sub-problem with respect to IRS can be expressed as
Figure BDA0004112128820000187
To address the non-convex objective function in equation (49), the function is similarly applied
Figure BDA0004112128820000188
Restated as DC form
Figure BDA0004112128820000189
wherein
Figure BDA00041121288200001810
Figure BDA00041121288200001811
Then, the process is carried out,
Figure BDA00041121288200001812
first order differentiation of (a)
Figure BDA00041121288200001813
Thus, the first and second substrates are bonded together,
Figure BDA00041121288200001814
local point +.>
Figure BDA00041121288200001815
The first order taylor expansion of (a) can be written as
Figure BDA00041121288200001816
wherein
Figure BDA00041121288200001817
Further, the achievable rate for the kth Eve can be restated as
Figure BDA00041121288200001818
wherein
Figure BDA0004112128820000191
Figure BDA0004112128820000192
Similarly, the number of the devices to be used in the system,
Figure BDA0004112128820000193
first order differentiation of (a)
Figure BDA0004112128820000194
/>
Thus, the first and second substrates are bonded together,
Figure BDA0004112128820000195
local point +.>
Figure BDA0004112128820000196
The first order taylor expansion of (a) can be written as
Figure BDA0004112128820000197
wherein
Figure BDA0004112128820000198
The corresponding optimization problem can be expressed as
Figure BDA0004112128820000199
This problem can be directly solved by CVX when obtaining
Figure BDA00041121288200001910
When it is, it can recover->
Figure BDA00041121288200001911
And w is equal to 1 and w2 As well as the recovery of (a)
Figure BDA00041121288200001912
When the rank is 1, ">
Figure BDA00041121288200001913
The method can be directly solved through eigenvalue decomposition. Otherwise, when->
Figure BDA00041121288200001914
Is not one, a gaussian randomization can be used to approximate v.
For ease of understanding, the alternate optimization method of the embodiments of the present invention will now be described separately as follows:
1) The iteration index u=0,
Figure BDA00041121288200001915
W 1 (0) ，W 2 (0) andρ (0) ；
2) Cycling;
3) Given a given
Figure BDA00041121288200001916
W 1 (u-1) ，W 2 (u-1) Solving ρ (u) ；
4) Given ρ (u) ，
Figure BDA00041121288200001917
Solving, W 1 (u) ，W 2 (u) ；
5) Given ρ (u) ，W 1 (u) ，W 2 (u) Solving for
Figure BDA00041121288200001918
5)u←u+1；
6) Until a maximum number of iterations is reached or all values converge.
The application effect of the present invention will be described in detail with reference to simulation.
(1) Simulation conditions
In the present invention, the performance of the proposed algorithm is illustrated by simulation results. Assume that the locations of Alice, IRS, bob and 2 PUs are set to (0,0,10), (0,50,10), (15,50,0), (15, -100, 0) and (15, -120, 0). k Eves are uniformly distributed on the straight lines from (15,100,0) to (15,120,0). In addition, all channels experience large-scale fading, which uses a path loss model, i.e
D(d)＝C 0 (d/d 0 ) -α (63)
wherein ,C0 = -30dBm at reference distance d 0 The path loss when=1m, d represents the actual inter-link distance, and α is the path loss index. Alpha AI ＝2.5，
Figure BDA0004112128820000201
In addition, h ab Representing small-scale fading obeys the rice distribution, a particular model may be represented as
Figure BDA0004112128820000202
wherein κab Is rice factor, set kappa ab ＝5，
Figure BDA0004112128820000203
For the line-of-sight component, each element corresponding to the line-of-sight component and the line-of-sight component is independently and uniformly distributed, and has a zero mean value and a complex Gaussian random variable with unit variance. />
Figure BDA0004112128820000204
Is a non-line-of-sight component. Assuming that the channel from Alice to IRS, the first PU, bob and kth Eve experiences rayleigh fading, the channel from IRS to the first PU, bob and kth Eve is LoS, the les factor is set to->
Figure BDA0004112128820000205
and />
Figure BDA0004112128820000206
Other simulation parameters were set as follows: n=40, m= 5,K =2, j=2, η=0.8, Γ max ,l＝-90dBm，σ B ＝σ j ＝-90dBm，σ ID ＝-80dBm，e min ＝-45dBm。
(2) Simulation results
In this embodiment, fig. 2 is a graph showing the variation of transmission power budget with Alice; FIG. 3 is a graph showing the variation of the number of reflective elements of the IRS according to the present invention.
In fig. 2, the achievable security rate of the secondary network is illustrated in relation to Alice's transmission power budget. It can be observed that the achievable safe rate for all schemes increases with increasing Alice transmit power. The proposed IRS-AN scheme may achieve better security performance than other reference schemes. This is because when the minimum harvest energy threshold of the user is reached, the increased maximum transmit power may allow the user to allocate more power for the ID, while the introduction of IRS may enhance the reflected signal at Bob and attenuate the reflected signal at PU and Eves, thereby eliminating interference with PU while enhancing security. In addition, it can be observed that the gap between the privacy rates achievable by the proposed "IRS-AN" scheme and the "IRS, without AN" scheme is not as good as the gap between the privacy rates of the proposed "IRS-AN" scheme and the "Without IRS, AN" scheme. This is because, although both the AN and the IRS introduction can improve the security performance of the CR system, the IRS has a better effect than the AN in combating multiple eavesdroppers.
In fig. 3, the relationship between IRS reflector number and achievable safety rate was studied. It can be observed that the proposed solution performs better than the other baseline solutions. Furthermore, it can be seen that in schemes with IRS, the secondary network achievable safe rate increases with the number of reflective elements N. It can also be seen that the system with AN has a higher security rate than the system without AN. This is due to the IRS greatly improving the signal-to-noise ratio at the user and directionally reducing the signal-to-noise ratio at the eavesdropper. Moreover, the effect is more pronounced as the number of IRS reflective elements increases. The importance of introducing IRSs is further illustrated.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.

Claims (6)

1. An IRS-assisted cognitive SWIPT system safety rate optimization method is characterized by comprising the following steps of: the method comprises the following steps:
s1: establishing an IRS-assisted cognitive SWIPT system transmission model;
s2: with the aim of maximizing the safety rate of the secondary legal user, a resource allocation model for jointly optimizing the beam forming vector and AN design of the secondary transmitter and the secondary legal user power division coefficient and IRS phase shift design is established by considering the constraint of the minimum collecting energy threshold value and the power division coefficient of the secondary legal user, the constraint of the maximum transmission power of the secondary transmitter, the constraint of IRS phase shift and the constraint of the interference power applied to the PU;
s3: fixing IRS phase shift, a secondary transmitter beam forming vector sum AN, and obtaining AN optimal power division coefficient of a secondary legal user based on first-order Taylor expansion and KKT conditions;
s4: fixing IRS phase shift and power division coefficient of secondary legal user, and obtaining optimal beam forming vector and AN of secondary transmitter by SDR and SCA method;
s5: the beam forming vector of the secondary transmitter, the AN and the power dividing coefficient of the secondary legal user are fixed, and the IRS phase shift matrix design is solved by adopting SDR and SCA methods.
2. An IRS assisted cognitive swift system safety rate optimization method according to claim 1, characterized in that: the S1 specifically comprises the following steps:
the IRS-assisted cognitive SWIPT system consists of a secondary user transmitter Alice, a legal secondary user Bob, L PUs and K eavesdroppers Eve, wherein K is more than or equal to 2;
setting Bob, PU and Eve to be provided with single antennas, wherein the number of Alice antennas and the number of IRS reflecting elements are respectively represented by M and N, and M is more than or equal to 2;
assuming that all channels in the system experience quasi-static flat fading, the equivalent channel gains from Alice to IRS, bob, the first PU, and the kth Eve are respectively denoted as
Figure FDA0004112128800000011
Equivalent channel gains from IRS to Bob, the first PU and the kth Eve are denoted as +.>
Figure FDA0004112128800000012
and />
Figure FDA0004112128800000013
To ensure secure transmission from Alice to Bob, AN is sent from Alice to interfere with Eve for strong security, the AN will transmit with the information signal; each reflective element of the IRS suppresses reception of Eve by adjusting the phase of the incident signal;
let CSI for all channels including Eve be completely known in Alice; bob adopts a PS structure, decodes information and acquires energy from a signal transmitted by Alice; the transmission signal transmitted by Alice is modeled as
x＝w 1 s+w 2 a (1)
wherein ,
Figure FDA0004112128800000014
and />
Figure FDA0004112128800000015
Represented as AN information signal and AN signal, respectively, < ->
Figure FDA0004112128800000016
And
Figure FDA0004112128800000017
respectively representing a beam forming vector and AN vector; since Bob uses PS, energy is directly derived from the information signal and the AN; let Alice's maximum transmit power be P A Then there is |w 1 | 2 +|w 2 | 2 ≤P A The method comprises the steps of carrying out a first treatment on the surface of the Consider only the first signal reflected from the IRS and ignore signals reflected two or more times;
the signal received by Bob is expressed as
Figure FDA0004112128800000021
The signals received by the first PU and the kth Eve are respectively expressed as
Figure FDA0004112128800000022
Figure FDA0004112128800000023
/>
wherein
Figure FDA0004112128800000024
Equivalent channel gains between Alice and Bob, alice and kth Eve, and Alice and the l PU, respectively;
Figure FDA0004112128800000025
a diagonal phase shift matrix representing IRS, where θ= [ θ ] on its main diagonal 1 ,θ 2 ,···,θ N ]，θ n ∈[0,2π]The nth element denoted IRS phase shift, ">
Figure FDA0004112128800000026
Is additive white gaussian noise AWGN; wherein->
Figure FDA0004112128800000027
and />
Figure FDA0004112128800000028
The distribution of circular symmetric complex Gaussian CSCG random vector with mean x and covariance Σ representing noise power is represented by +.>
Figure FDA0004112128800000029
A representation;
to simultaneously perform energy harvesting EH and information decoding ID, consider a PS-based receiver architecture at Bob, bob adaptively dividing the received signal into two independent parts for EH and ID; representing ρ ε [0,1] as the PS ratio, where ρ is the received signal portion for ID and the remaining 1- ρ portions are for EH; the signal received by Bob's information detection circuit is expressed as
Figure FDA00041121288000000210
wherein
Figure FDA00041121288000000211
Additive noise with zero mean and unit variance due to baseband signal processing at the ID receiver; the SINR at Bob is given by
Figure FDA00041121288000000212
For EH, the received signal at Bob is written as
Figure FDA00041121288000000213
Bob's collected energy is
Figure FDA00041121288000000214
Wherein η is the energy collection efficiency; the SINR at the kth Eve is expressed as
Figure FDA00041121288000000215
The achievable rate at Bob and the achievable rate at kth Eve are expressed as
R B ＝log 2 (1+SINR B ) (10)
Figure FDA0004112128800000031
The safe rate is defined as
Figure FDA0004112128800000032
Transmissions in the secondary network cause interference to the PU, and the interference noise power applied to the first PU is expressed as
Figure FDA0004112128800000033
3. An IRS assisted cognitive swift system safety rate optimization method according to claim 2, characterized in that: the step S2 is specifically as follows:
to maximize Bob's safety rate, the design problem is expressed as follows
Figure FDA0004112128800000034
wherein ,emin An iΓ is the minimum energy threshold to be collected for Bob l,max For the maximum interference power applied to the first PU, C1 is the constraint of Alice maximum transmission power, C2 is the constraint of Bob minimum collection energy, C3 is the constraint of noise interference power at the PU, and C5 is the constraint of unit mode of the reflecting surface;
the problem equation (14) is a non-convex problem, with coupling between variables.
4. A method for optimizing the safe rate of an IRS-assisted cognitive SWIPT system according to claim 3, wherein: the step S3 is specifically as follows:
fixing IRS phase shift and Alice beam forming vector sum AN, and obtaining Bob optimal power division coefficient based on first-order Taylor expansion and KKT conditions;
fix w 1 、w 2 And phi, at the same time define
Figure FDA0004112128800000035
Figure FDA0004112128800000036
SINR for Bob and kth Eve is expressed as
Figure FDA0004112128800000037
Figure FDA0004112128800000038
Definition of the definition
Figure FDA0004112128800000041
Definitions->
Figure FDA0004112128800000042
W 2 ＝w 2 w 2 H ，W 1 ≥0，W 2 0 or more, and Rank (W) 1 )＝1，Rank(W 2 ) SINR for =1, bob and kth Eve is expressed as follows:
Figure FDA0004112128800000043
Figure FDA0004112128800000044
conversion of the original problem into
Figure FDA0004112128800000045
wherein
Figure FDA0004112128800000046
/>
Next, the following optimization problem is obtained by writing the formula (20) in the form of log subtraction
Figure FDA0004112128800000047
The problem expression (21) is not a convex optimization problem, and the maximum value of the problem cannot be directly obtained; representing the second item as
Figure FDA0004112128800000048
To solve this problem, the problem is converted into a convex problem by using a first order taylor expansion for g (ρ); the third term and the fourth term do not contain the optimization variable ρ, and they are regarded as constants; performing first-order Taylor expansion on the g (ρ) to obtain
Figure FDA0004112128800000049
The problem (21) is reiterated as
Figure FDA0004112128800000051
wherein ρ(q) Is the value of ρ at the q-th iteration; when given ρ (q) When the problem formula (24) is a convex problem about ρ, solving by an iterative algorithm; in each iterationSolving the optimal ρ using a convex optimization tool CVX; solving the optimal rho by adopting a Lagrangian multiplier method; introducing a Lagrangian multiplier beta, the Lagrangian function of problem formula (24) being
Figure FDA0004112128800000052
Obtained based on Karush-Kuhn-Tucker (KKT) condition
Figure FDA0004112128800000053
To obtain a closed-form solution for ρ, the following cases of solutions are discussed
(1) When the value of beta is to be taken as 0,
Figure FDA0004112128800000054
when ρ is not solved;
(2) When the value of beta is to be taken as 0,
Figure FDA0004112128800000055
when the optimal solution of rho is obtained
Figure FDA0004112128800000056
At the same time ρ 1 Needs to meet the requirements of
Figure FDA0004112128800000061
(3) When beta is not equal to 0,
Figure FDA0004112128800000062
when the optimal solution of rho is obtained
Figure FDA0004112128800000063
In summary, the optimal solution of ρ is ρ * ＝min{ρ 1 ,ρ 2 }。
5. An IRS assisted cognitive swift system safety rate optimization method according to claim 4, characterized in that: the step S4 specifically comprises the following steps:
giving IRS phase shift, and obtaining Alice optimal beam forming vector and AN by adopting SDR and SCA methods;
definition of the definition
Figure FDA0004112128800000064
Will get ρ * Bringing into the original problem and giving an IRS phase shift matrix phi; the existence of rank-one constraint makes the optimization problem non-convex, and the application of SDR to relax rank-one constraint results in
Figure FDA0004112128800000065
wherein
Figure FDA0004112128800000066
However, formula (31) has a complex form that is not smooth and difficult to handle; rewriting by introducing relaxation variable τ > 0
Figure FDA0004112128800000067
Problem equation (32) is still not a convex optimization problem, problem equation (32) is at coupled W 1 and W2 The upper is not co-concave; the problem (32) comprises a DC-type planning problem, iteratively solving a sub-optimal solution using the SCA method; first, function R sec (W 1 ,W 2 ) The rewrites into the following form
R B (W 1 ,W 2 )＝t 0 (W 1 ,W 2 )-t 0 (W 2 ) (33)
wherein
Figure FDA0004112128800000068
Figure FDA0004112128800000069
Then t 0 (W 2 ) First order differentiation of (a)
Figure FDA0004112128800000071
W 2 Local points in a given ith iteration
Figure FDA0004112128800000072
Is written as a first-order taylor expansion of
Figure FDA0004112128800000073
wherein
Figure FDA0004112128800000074
Further, R Ek (W 1 ,W 2 ) Re-expressed as
Figure FDA0004112128800000075
wherein
Figure FDA0004112128800000076
Figure FDA0004112128800000077
μ k (W 1 ,W 2 ) First order differentiation of (a)
Figure FDA0004112128800000078
μ k (W 1 ,W 2 ) Local points in a given ith iteration
Figure FDA0004112128800000079
Is written as +.>
Figure FDA00041121288000000710
wherein
Figure FDA00041121288000000711
At a given point in the ith iteration
Figure FDA00041121288000000712
The problem formula (32) approximates:
Figure FDA00041121288000000713
the original problem has been converted into a convex problem that the CVX can solve; if W is obtained 1 and W2 The rank is one, w is recovered by eigenvalue decomposition 1 and w2 I.e.
Figure FDA00041121288000000714
and />
Figure FDA00041121288000000715
Otherwise, when the rank is not one, the method of Gaussian randomization is used for approximately recovering w 1 and w2 。
6. An IRS assisted cognitive swift system safety rate optimization method according to claim 5, characterized in that: the step S5 specifically comprises the following steps:
giving Alice optimal beam forming vectors and Bob optimal power dividing coefficients, and solving an IRS phase shift matrix design by adopting SDR and SCA methods;
the following matrix is defined and is used,
Figure FDA0004112128800000081
Figure FDA0004112128800000082
Figure FDA0004112128800000083
and have->
Figure FDA0004112128800000084
Figure FDA0004112128800000085
Figure FDA0004112128800000086
Figure FDA0004112128800000087
The sub-problem is expressed as phase shift optimization with respect to IRS
Figure FDA0004112128800000088
To address the non-convex objective function in problem equation (49), the function is then
Figure FDA0004112128800000089
Restated as DC form
Figure FDA00041121288000000810
wherein
Figure FDA00041121288000000811
Figure FDA00041121288000000812
Then, the process is carried out,
Figure FDA00041121288000000813
first order differentiation of (a)
Figure FDA00041121288000000814
Figure FDA00041121288000000815
Local point +.>
Figure FDA00041121288000000816
Is written as a first-order taylor expansion of
Figure FDA00041121288000000817
wherein
Figure FDA00041121288000000818
The achievable rate of the kth Eve is restated as
Figure FDA00041121288000000819
wherein
Figure FDA0004112128800000091
Figure FDA0004112128800000092
Figure FDA0004112128800000093
First order differentiation of (a)
Figure FDA0004112128800000094
Figure FDA0004112128800000095
Local point +.>
Figure FDA0004112128800000096
Is written as a first-order taylor expansion of
Figure FDA0004112128800000097
wherein
Figure FDA0004112128800000098
The corresponding optimization problem is expressed as
Figure FDA0004112128800000099
Resolved by CVX, when obtained
Figure FDA00041121288000000910
At the time of recovery->
Figure FDA00041121288000000911
And w is equal to 1 and w2 As in the recovery of->
Figure FDA00041121288000000912
When the rank is 1, ">
Figure FDA00041121288000000913
Solving through eigenvalue decomposition; otherwise, when->
Figure FDA00041121288000000914
Is not one, and gaussian randomization is used to approximate v. />
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* Cited by examiner, † Cited by third party
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CN117528535A (en) * 2024-01-05 2024-02-06 南京邮电大学 Bidirectional safe transmission method for resisting malicious interference by using IRS and artificial noise
CN117528535B (en) * 2024-01-05 2024-03-26 南京邮电大学 Bidirectional safe transmission method for resisting malicious interference by using IRS and artificial noise

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