CN116015374A - Intelligent reflecting surface-assisted non-orthogonal multiple access energy-carrying network security beam forming method - Google Patents
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Abstract
A non-orthogonal multiple access energy-carrying network safety wave beam shaping method assisted by intelligent reflecting surface, a multi-antenna base station sends NOMA and interference signals to legal users together under the help of IRS, and a receiving end user obtains two parts of signals for information decoding and energy collection through a power distribution scheme. In addition, the transmitted artificial noise signals can be completely eliminated through zero forcing conditions at all legal user terminals, so that the eavesdropping can be effectively restrained under the condition that legal reception is not affected. The invention optimizes the beam forming vector, IRS phase shift and power distribution parameters in a combined way under the constraint conditions of satisfying the user service quality requirement, IRS reflection constraint, serial interference elimination decoding condition and the like, and maximizes the system and the speed. Compared with the random IRS phase shift and IRS-free scheme, the invention has obvious advantages, can ensure good communication performance while collecting energy, can effectively ensure transmission safety with the assistance of artificial noise, and has strong application value.
Description
Technical Field
The invention belongs to the field of multi-user non-orthogonal multiple access energy-carrying network safety, relates to a power distribution scheme of wireless energy-carrying communication, and particularly relates to a safe beam forming method for introducing artificial noise into an intelligent reflection surface-assisted non-orthogonal multiple access energy-carrying network, jointly optimizing a beam forming vector and intelligent reflection surface phase shift and power distribution parameters.
Background
In recent years, smart reflective surfaces (Intelligent Reflecting Surface, IRS) have received widespread attention in academia and industry as a cost effective solution to control and regulate wireless channels between transceivers. In addition, it can greatly improve spectrum efficiency, energy efficiency and network coverage, and simultaneously reduce network cost. In particular, IRSs can be easily deployed on indoor walls or buildings as two-dimensional planes consisting of a large number of passive reflective elements. The amplitude and the phase of an incident signal can be adjusted, so that the intensity and the direction of a wireless electromagnetic wave are highly controllable, and therefore, a reflected signal can be intentionally enhanced or weakened on different receivers, and the reconstruction of a wireless channel is realized. Furthermore, IRS is a passive device that only passively reflects an incoming signal without signal processing, and therefore does not introduce additional noise, while requiring much lower hardware cost and power consumption. These advantages have greatly driven the application of IRSs in communication networks.
In addition, wireless energy-carrying communication (Simultaneous Wireless Information and Power Transfer, swit) technology has attracted tremendous attention in recent years, considering that large-scale internet of things devices require continuous information transmission and energy transfer. Through the application of SWIPT, a user can acquire information and energy at the same time, which brings great convenience to the deployment of the energy-limited Internet of things equipment. As one of the designs of practical swift receivers, a Power Splitting (PS) scheme aims at Splitting the signal received by the receiver into two different Power streams, one part for decoding information and the other part for collecting energy. However, with the conventional wireless energy-carrying communication system, due to serious propagation loss, wireless power transmission efficiency may drastically decrease with increasing distance, thereby greatly limiting the performance of the wireless energy-carrying communication system. The efficiency and coverage of wireless power transfer will be improved if channel conditions can be enhanced. Because the IRS may increase channel gain, IRS-assisted swift networks may possess better performance.
In order to meet the massive connection of future networks and the higher service demands of users, non-orthogonal multiple access (NOMA) technology is regarded as a technical method which is expected to significantly improve the spectrum efficiency of wireless communication networks and realize large-scale connection. NOMA can support multiple users to share the same resources, e.g., time, frequency, code, etc., thus supporting massive connections of users and greatly improving spectral efficiency. For power domain NOMA transmission in the downlink, at the base station transmitting end, different power transmission signals are used for different user channel gains, superposition coding is performed in the power domain, at the receiving end, a serial interference cancellation technique (SuccessiveInterferenceCancellation, SIC) is used to cancel multiple access interference and decode the information desired to be received, so that the user with stronger channel gain can cancel co-channel interference caused by the user with weaker channel gain before decoding, thereby realizing correct demodulation. Existing NOMA studies consider that users' channel conditions vary widely, i.e., one class of users near a base station and another class of users at the edge of the base station, the base station will allocate more transmit power to users with worse channel conditions, and the vast difference in channel conditions will greatly free up the potential of NOMA. However, in a practical scenario, the difference in user channel conditions of NOMA networks is not always large. This is because the radio channel is determined by the propagation environment, which has a high degree of randomness and uncontrollability. Thus, the performance of NOMA will be greatly improved if the channel can be controlled and adjusted. The reflecting surface can dynamically adjust the phase offset of the reflected signal and artificially change the difference of the combined channels, so that the reflecting surface and the non-orthogonal multiple access combination can better exert the spectrum efficiency gain of the NOMA scheme.
In an actual communication scene, information of a user is easily acquired by an eavesdropper, and communication safety is also urgently required to be protected. Because of the nature of their parallel communications, NOMA systems are susceptible to different security and privacy related problems. When the channel difference between users is large, users closer to the base station can conveniently steal confidential information of remote users by virtue of the high channel gain, so that the communication safety of the users is influenced, that is, an untrusted eavesdropper generates interference to the legitimate users in the NOMA system with high probability. In order to guarantee secure transmission in NOMA networks, various methods based on physical layer security have been proposed, such as beamforming, cooperative relaying, artificial interference, etc. Furthermore, IRS has great potential in enhancing physical layer security of wireless networks because reflected signals can be passively beamformed to increase gain at legitimate receivers and suppressed at eavesdroppers by adjusting IRS reflective elements. The invention uses IRS and artificial noise to ensure network safety.
Disclosure of Invention
Aiming at the safety problem in the non-orthogonal multiple access energy-carrying network assisted by the intelligent reflecting surface, the invention provides the method for introducing artificial noise into the network and jointly optimizing the beam forming vector, the phase shift of the intelligent reflecting surface and the power distribution parameters to effectively improve the overall communication performance of the network.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
the invention provides a safe wave beam forming method of an intelligent reflecting surface (Intelligent Reflecting Surface, IRS) -assisted Non-orthogonal multiple access (Non-orthogonal Multiple Access, NOMA) energy-carrying network, wherein the network comprises a base station, an intelligent reflecting surface, legal users and eavesdroppers; the intelligent reflecting surface comprises a passive reflecting unit and a reflecting surface controller; a direct link and a reflection link exist between the base station and the user at the same time; the receiving end user utilizes a power distribution scheme to simultaneously decode information and collect energy; the channel state information of the legal user is known, and the eavesdropper cannot acquire the channel state information of the legal user for passive eavesdropping. By superposing a proper amount of artificial noise in the transmitted NOMA information, the beam forming vector, the intelligent reflecting surface phase shift and the power distribution parameter are jointly optimized, the sum of the maximum combination method user transmission rate is controlled, and simultaneously, the transmitted artificial noise signals can be completely eliminated through zero forcing conditions at all legal user terminals, so that the eavesdropping can be effectively restrained under the condition that legal reception is not influenced.
The safe beam forming method of the invention comprises the following steps:
Step one: and constructing an IRS-assisted NOMA energy-carrying network model according to actual conditions, wherein the NOMA energy-carrying network model comprises a network channel model, an IRS phase shift model and a receiver model. Specific:
in the present invention, consider a downlink NOMA network of IRS-assisted swits consisting of one base station, one IRS and K users, where there is a potential eavesdropper, as shown in fig. 1. The base station can be set to be equipped with N & gt1 uniform linear array antennas, the users are all single antenna users, and the kth user uses U k Is expressed as a set of users
The fixed coordinates of the user on the ground are (x k ,y k ,0). The IRS is provided with M adjustable reflection elements, the IRS adjusts the reflection coefficient of each element, namely the amplitude and the phase of each element through a controller thereof to control different channel gains so as to meet the requirements of NOMA and SWIPT on channel conditions, and meanwhile, the IRS can inhibit the interference of potential eavesdroppers on internal legal users to a certain extent. The reflective elements are uniformly distributed in a planar array, and the set of IRS reflective elements is expressed as +.>
/>
IRS phase shift model: the IRS phase shift can be expressed as
Wherein beta is m ＝[0,1]，θ m E 0,2 pi) represent the amplitude and phase of the mth reflective element of the IRS, respectively. Due to severe path loss, the signal reflected twice or more by the IRS is negligible A kind of electronic device. In the deployment of a real scenario, it is generally considered that the reflective elements of the IRS are designed to maximize the reflected signal, thus +.>
Network channel model: although the channel between the base station and the user may be blocked, the wireless channel still has a large scattering, so the channel between the user and the base station is set as a rayleigh channel, which is expressed as
The direct channel from the base station to the kth user can be expressed as
Wherein C is 0 Represents the path loss at a reference distance of 1m, d d,k Represents the distance from the base station to the kth user, alpha 1 Representing the path loss index.
Considering that there is typically a line-of-sight link between the base station and the reflecting surface, the channel is modeled here using a rice distribution, i.e
Wherein d d,r Represents the distance from the base station to the IRS, alpha 2 Representing the path loss index.
And
representing the line-of-sight and non-line-of-sight transmission components, respectively. Kappa (kappa) BI Representing the corresponding rice factor. Similarly, the channel between the IRS and the kth user may be expressed as
Wherein d r,k Representing the distance between IRS and kth user, alpha 3 Representing the path loss index.
And
representing the line-of-sight and non-line-of-sight transmission components, respectively. Kappa (kappa) IU Representing the corresponding rice factor.
Receiver model: the invention mainly uses a power distribution receiver, the distribution of the power distribution receiver is determined by power distribution parameters, and the received signal of each user is separated into an information decoder and an energy collector by a power distributor. For the kth user, it will signal power ρ k (0≤ρ k Less than or equal to 1) partial allocation to information decoder, remainder 1- ρ k Part of the signal power is distributed to the energy collectors.
Step two: and introducing artificial noise into the transmission precoding of the base station to obtain a base station transmitting signal and a user receiving signal. And eliminating artificial noise at the legal user through zero forcing condition without affecting the communication of the legal user, and respectively obtaining signals distributed to the information decoder and the energy collector through the received signals after eliminating the artificial noise, thereby obtaining the received signal-to-noise ratio, and receiving energy and rate, wherein the rate comprises interception rate and safe rate. Specifically:
assume that linear transmission precoding is performed at the base station, where each user is assigned one dedicated information beam. In order to break eavesdropping and ensure secure transmission by legitimate users, artificial noise is generated at the base station along with NOMA information. The transmitted signal at the base station can be expressed as
Wherein the method comprises the steps of
Represents the precoding vector of the kth user and satisfies ||w k || 2 ＝P k ，s k NOMA transfer information representing kth user and satisfying |s k | 2 ＝1。/>
Representing the vector of the artificial interference, and satisfies the following formula jam || 2 ＝P jam Z represents an interfering signal and satisfies |z| | 2 =1. The transmission power from the base station should be such that, depending on the maximum transmission power that the base station can achieve
Wherein P is s Representing the maximum value of the base station transmit power.
After transmission of two channels via the base station-user link, the signal received by the kth user can be expressed as
Wherein the method comprises the steps of
Represents the antenna noise of the kth user, which is 0 in mean and σ in variance k 2 Additive white gaussian noise.
In NOMA systems, SIC is used by each receiver to cancel multiple access interference. The SIC decoding order between users is mainly determined by channel quality. Thus, a user with a stronger channel gain should first decode messages from other users with weaker channels. However, because the variation of the IRS phase shift matrix will cause the variation of the channel gain, the decoding order of SIC is not only dependent on the transmit beamforming vector { w } k And also depends on IRS reflection phase shift {Φ }. Let pi (k) denote the decoding order of the kth user, pi (k) =m denote that the kth user's message is decoded at the receiver mth. Since the total number of decoding order combinations is a finite value, the optimal sum rate can be obtained by first solving the problem of any one decoding order and selecting the largest objective function value among all decoding orders. Without loss of generality, assume that the channel gain between the IRS and the legitimate user is satisfactory
0≤||h r，1 || 2 ≤...≤||h r，K || 2 ，0≤||h d，1 || 2 ≤...≤||h d，K || 2 (7)
Pi (k) =k is defined according to the channel hypothesis in (7). Thus, for this given decoding order, the proposed IRS-NOMA scheme should satisfy the following constraints
In order to avoid adverse effects on the legitimate receiver, a zero forcing condition may be set to directly eliminate the effects of the artificial interference from the receiving end of the legitimate user, which may ensure that the artificial interference is eliminated before SIC decoding. The interference cancellation zero forcing condition can be expressed as
The signal received by the kth user can be rewritten as
According to the power allocation in the receiver model of step one, for the kth user, the signal allocated to the information decoder can be expressed as
Wherein the method comprises the steps of
Representing additive noise generated during decoding of kth user information, which is 0 as the mean and delta as the variance k 2 Additive white gaussian noise.
For the kth user, the signal assigned to the energy collector can be expressed as
The energy provided by the energy harvester for the kth user can be expressed as
Wherein eta k ∈(0,1]Representing the energy conversion efficiency of the kth user energy harvester. In this context, always from a time-unit point of view, the power collected is the energy collected.
After eliminating the influence of the artificial interference, the received signal-to-noise ratio of the kth user can be expressed as
It can be observed from equation (14) that users with higher decoding order receive less or no interference from other users due to SIC. (8) The inequality in (a) avoids the case where most of the radio resources are allocated to some higher decoding order users. By using the inequality, the received signal power of the user with lower decoding order is larger than the received signal power of the user with higher decoding order. Thus, reasonable communication rates can be obtained at users of lower decoding order, so that rate fairness between users can be maintained.
For the Kth user, its signal-to-noise ratio can be expressed as
Similarly, the corresponding signal-to-noise ratio of the signal of the kth user decoded by the kth user can be expressed as
In NOMA network, according to SIC decoding condition, the corresponding signal-to-noise ratio of the signal of the kth user decoded by the first user should be no less than the target signal-to-noise ratio of the kth user, and is recorded as
I.e. +.>
So that the information of the kth user can be successfully removed from the first user, the target signal-to-noise ratio at the kth user can be expressed as +.>
The corresponding sum rate of the kth user can be expressed as
In addition, the eavesdropping signal-to-noise ratio of a potential eavesdropper to the kth user can be expressed as
Similar to the legal user case, in which
Representing antenna noise at the eavesdropper and additive noise when the information is decoded, respectively, the eavesdropper need only eavesdrop on the information of a legitimate user and does not need to collect energy.
The eavesdropping rate of the eavesdropper on the kth user can be expressed as
The security rate of the kth user can be expressed as
R sk ＝[R k -R ek ] + (21)
Step three: the design optimization problem, the sum of the transmission rates of the maximum combination method users, satisfies the service quality constraint, the energy threshold constraint, the power distribution parameter value condition of each legal user, the artificial noise and each legal user power constraint, the IRS reflection constraint, the SIC decoding condition of each legal user receiver end and the zero forcing condition for eliminating the artificial noise. Specific:
in order to maximize the total transmission rate of the users of the combination method and simultaneously ensure the network security performance, the optimization problem designed in the step three is as shown in the formula (22):
E k ≥e k , (22f)
0≤ρ k ≤1,(22i)
|β m |＝1,m＝1,2,...,M.(22j)
constraint (22 b) ensures that the signal-to-noise ratio of the kth information decoded by the first user exceeds gamma k Wherein gamma is k Representing user quality of service requirements for a kth user, constraint (22 c) ensuring sufficient interference capability for an eavesdropper, constraint (22 d) being a constraint of total transmit power of a base station, constraint (22 e) representing SIC decoding condition constraint, constraint (22 f) requiring that energy acquired by the kth user reach an energy threshold e k Constraint (22 g) represents zero forcing conditions for eliminating the influence of artificial interference on a normal user, constraint (22 h) and constraint (22 j) are IRS phase shift and amplitude conditions respectively, each reflecting element of IRS only adjusts the phase shift of an incident signal without amplifying the amplitude of the incident signal, and constraint (22 i) is a reasonable value interval of a power distribution parameter.
Step four: since the optimization problem in the third step is a non-convex optimization problem, and the base station beamforming vector, the IRS phase shift matrix and the power allocation parameters are highly coupled, and in addition, the IRS phase shift matrix is also expressed in a complex diagonal matrix form, the problem cannot be directly solved. Therefore, in the fourth step, auxiliary variables are introduced to replace IRS phase shift and channels, meanwhile, objective functions are approximated, then the original problem is decomposed into three non-convex problems, the non-convex problems are converted into convex problems by utilizing continuous convex approximation, and then an iterative algorithm based on alternate optimization is designed to be put into a CVX tool box for solving. Specific:
in the fourth step, firstly, auxiliary variables are introduced to approximate a complex IRS phase shift matrix, and a passive beam forming vector is defined
Rewriting channels into joint channels, definition
Then approximating the optimization objective (22 a), i.e. introducing z k Satisfies the following conditions
Then the optimization objective (22 a) can be changed to
Further, a geometric mean value is adopted
Approximation (23) as another constraint in the optimization problem, while the objective function is transformed to Z, where the objective function is transformed from a non-convex function to a linear function for further solution. It can be written as
(24) Can be expressed as a second order cone constraint system, first defined
When ζ=k, there is z 1，K =z. Is thatFurther processing is carried out, introducing an intermediate variable t 1,ξ-1 ζ=1, 2,..k, the condition in (25) can be further decomposed into
In addition, hyperbolic constraint w 2 Xy (x is not less than 0 and y is not less than 0) can be converted into 2w, x-y] H The I is less than or equal to x+y. Based on similar transformations, (26) can be re-expressed as a series of second order cone constraints as follows
The optimization problem (22) can be further converted into an optimization problem (28)
Although the objective function is initially convex, the problem is still a non-convex problem due to the existence of non-convex constraint, and in addition, three optimization variables of the base station beamforming vector, the IRS phase shift matrix and the power distribution parameter are still coupled together, if the three optimization variables are solved together, the problem is quite complex, and if two of the three optimization variables can be fixed, and the other one of the three optimization variables can be solved, the problem is quite simple. Based on the problems and thinking, the problems are decomposed into three sub-problems of transmit beamforming vector optimization, IRS phase shift optimization and power distribution parameter optimization, non-convex strip pieces of the sub-problems are converted, convex processing is carried out, the non-convex strip pieces are approximate to convex problems, and finally, the non-convex strip pieces are solved through an optimization algorithm of alternate iteration.
Transmit beamforming vector optimization: for any given IRS phase shift and power allocation parameters, the sub-problem with the transmit beamforming vector can be defined as an optimization problem (29) as shown below
γ k ≤z k -1,(29d)
v H H k w jam ＝0,(29h)
Due to the presence of the non-convex constraint (29 c) (29 g) (29 i), (29) is obviously a non-convex problem, which, if solved, must be transformed first, the constraint (29 c) can be equivalent to the following series of inequalities first
After introducing the IRS phase shift vector and definition of joint channel, the signal-to-noise ratio formula in (29 c) can be expressed as
To facilitate subsequent calculations and representations, an auxiliary constant A is introduced l And defines it as
The signal to noise ratio formula can be further simplified to be expressed as
After the above substitution, the non-convex strip (29 c) can be expressed as
Further, it can be converted into
However, the condition is still non-convex and difficult to solve. To solve this problem, the SCA is applied here to transform it and further introduce a Taylor series approximation to approximate it. For a slightly convex function f (x), it can be approximated by its tangential function
Wherein->
Is expressed as a formula by a first-order Taylor expansion of x
When (when)
The inequality takes an equal sign when.
Based on the above taylor series approximation, (35) can be approximated by proposition 1.
Proposition 1: an auxiliary function is first defined to assist in the calculation:
Q(w k ,z k ) At the position of
The nearby first-order taylor approximation can be expressed as
In this way Q (w k ,z k ) Can be approximately replaced by
And (3) proving: from the taylor series approximation in (36), the auxiliary function Q (w k ,z k ) The following calculation was performed
Wherein the method comprises the steps of
The calculation is performed as follows
Since the power-related calculation is performed here, the power-related calculation is performed in order to calculate the power-related value with the function Q (w k ,z k ) And (40) can be further approximated, i.e
When the condition is satisfied
And->
(41) The approximation in (1) takes the equal sign and proposition 1 is verified. />
Through the above calculation, Q (w k ,z k ) Can be approximated as
At this time, the non-convex strip (29 b) is converted into a form in which the linear function is equal to or greater than the convex function, and the non-convex strip in the original problem is converted into a convex condition.
However, due to the presence of the non-protruding elements (29 g) (29 i), the problem (29) remains a non-protruding one, and it is easy to find that w is present in both conditions j It is considered that linearization is performed as follows.
Proposition 2: defining an auxiliary function
F(w j ) At the tangent point
Can be expressed as a first order taylor approximation of
In this way, (42) can be approximated by (43) and the constraint (29 f) can be approximated by a convex constraint.
And (3) proving: based on the Taylor series approximation, (42) is a differentiable convex function that satisfies
Substituting (42) into equation (44) based on derivative law to obtain
When (when)
And->
When it is available
Since the power-related calculation is performed here, the power-related calculation is performed in order to calculate the power-related value with the function F (w j ) The above equation can be further approximated as
When the condition is satisfied
The approximation in (44) takes the equal sign and the proposition 2 is verified.
After the above calculation and substitution, F (w j ) Can be approximated as
(42) The function of (3) may also be converted (43) into the form of a linear function.
An inequality in the condition (29 g) is transformed into a form in which the convex function is smaller than or equal to the linear function, which can be approximated as convex. Accordingly, all similar inequalities in constraint (29 g) may be approximated as convex, as follows
Thus, (29 g) can be replaced by (48), which are approximately convex.
The function in (42) is similarly converted (43) into a linear function, a series of w in constraint (29 i) can be obtained j Is changed into a linear function while introducing constants for convenience of representation
The constraint (29 i) can be similarly approximated as convex
Similar to the above-described fall-over method, we can express the constraint (29 e) as
With the above approximation, (29) can be represented as (52), which is a convex problem.
IRS reflection phase shift optimization: for any given transmit beamforming vector and power allocation parameter, the sub-problem with v can be defined as follows (53)
max v Z(53a)
s.t.||2z 1,ξ ,(t 1,ξ-1 -z ξ ) H ||≤t 1,ξ-1 +z ξ ,(53b)
γ k ≤z k -1,(53d)
|v m |＝1,m＝1,2,...,M,(53e)
v H H k w jam ＝0,(53g)
Because of the presence of the non-convex constraint (53 c) (53 f) (53 h), (53) is obviously a non-convex problem, if it is to be resolved, these three conditions must be transformed first, and the constraint (53 c) is seen first, similar to (34), the constraint (53 c) can be transformed into
It may be noted that the transmit beamforming vector w k And the passive beamforming vector v has symmetry in the form of the condition, thus for a given transmit beamforming vectorQuantity w k ，w jam The following conversion can be performed
Then (54) can be converted into
However, the condition is still non-convex and difficult to solve. To solve this problem, as in the previous subsection, the SCA is applied to transform it and further a Taylor series approximation is introduced to approximate it.
Based on the taylor series approximation, (56) may be approximated by the following method.
Proposition 3: an auxiliary function is first defined to assist in the calculation:
from the Taylor series approximation, it can be approximated as
In this way G (v, z k ) Can be approximately replaced by
And (3) proving: from the Taylor series approximation in (36), the auxiliary function G (v, z k ) The following calculation was performed
Wherein the method comprises the steps of
The calculation can be performed as follows
Since the power-related calculation is performed here, in order to correlate with the function G (v, z k ) Can be further approximated by (60), i.e
When the condition is satisfied
And->
(61) The approximation in (1) takes the equal sign and proposition 3 is verified.
Through the calculation, G (v, z k ) Can be approximated as
At this time, the non-convex strip (53 c) is converted into a form having a linear function equal to or larger than a convex function, and the non-convex strip in the original problem is converted into a convex condition.
However, due to the presence of non-convex elements (53 f) (53 h), the problem (53) remains a non-convex problem, and it is easy to find the v quadratic function present in both conditions, similar to the previous, transmitting the beamforming vector w j And the passive beam forming vector v has symmetry in the form of a quadratic function, and the constraint condition (53 f) is converted according to the calculation of (55)
Similar to the previous method, it is contemplated to apply SCA to transform it and further introduce a Taylor series approximation to approximate it, thereby linearizing the right of the equation.
Proposition 4: defining an auxiliary function
S (v) at the tangent point
Can be expressed as a first order taylor approximation of
In this way, (63) can be approximated by (64), and the constraint (53 f) can be approximated by a convex constraint.
And (3) proving: according to the Taylor series approximation, (63) is a differentiable convex function that satisfies
Substituting (63) into equation (65) based on derivative law to obtain
When (when)
And->
When it is available
Since the power-dependent calculations are performed here, the above equation can be further approximated as to match the real character of the function S (v)
When the condition is satisfied
At that time, the approximation in (68) takes the equal sign and proposition 4 is verified.
After the above calculation and substitution, S (v) can be approximated as
(63) The function of (c) may also be converted (68) into the form of a linear function. />
An inequality in the condition (53 f) is transformed into a form in which the convex function is smaller than or equal to the linear function. Accordingly, all similar inequalities in constraint (53 f) may be approximated as convex, as follows
Similarly, the quadratic function of a series v in the constraint (53 g) can be changed to a linear function, and the constraint (53 g) can be similarly expressed approximately as
The equation now turns to a linear form to the left, and the constraint translates to a convex constraint.
At this point, all non-convex constraints are converted to convex constraints, and the sub-problem (53) is converted to a convex problem (71), at which point the problem is conveniently and efficiently solved using the CVX toolbox.
Optimizing power distribution parameters: and transmit beamforming vector w k Unlike the passive beamforming vector v, the power allocation parameter ρ is k For a scalar quantity, the constraints associated therewith are also mostly linear, and the direct solution from the problem (28) is simpler and reduces the complexity of the iterative algorithm.
Based on the problem (28), for any given transmit beamforming vector w k And a passive beamforming vector v, the power allocation parameter ρ may be related to k The sub-problems of (2) are defined as follows:
0≤ρ k ≤1 (72d)
similar to the first subsection, the constraint (72 b) may be equivalent to the following series of inequalities
I.e. can be expressed as
To facilitate subsequent calculations and representations, two constants are first defined, namely
The constraint (72 b) may be further expressed as
Through calculation, can obtain
Further calculations can be made
For constraint (72 c), to facilitate subsequent computation and representation, constants are first defined
The constraint (72 c) can be simply expressed as
ρ k ≤D k (80)
The constraint (72 d) is itself a linear inequality, and after the conversion, all three constraints become linear inequalities, so that the maximum value can be conveniently and directly solved for the objective function. The three linear inequalities are comprehensively considered to obtain the power distribution parameter rho l The range of the values is as follows
It should be noted that the above formula is established as follows
Therefore, when the simulation is actually performed, it is necessary to take care that this condition is satisfied and to reasonably set the values of the parameters.
At the introduction of constant B lk And C lk After simplifying the representation, the system communication rate of the kth user can be expressed as
Can be further expressed as calculated
Obviously the rate R of the kth user k Is related to the power allocation parameter ρ l Taking into account the previously obtained power allocation parameter ρ l Is apparent to be ρ, the value range (81) l After taking the maximum value D l R is time R k The maximum sum rate obviously takes a maximum value when the respective rates of the individual users are all at a maximum. Thus, in determining the transmit beamforming vector w k And the optimal value of the passive beamforming vector v, ρ l Is the optimal value of D l And the sum rate at this time takes the maximum value
The sub-problem (74) is effectively solved and the complexity is reduced by direct calculation when alternating iterations are performed afterwards.
Alternating iterative algorithm: due to the power allocation parameter ρ l Can be used to obtain the transmit beamforming vector w k And the optimal value of the passive beam forming vector v, so that the alternate iterative algorithm mainly aims at w k And v, designing. The original problem (28) is converted into two convex problems,namely (52) and (71). In this context, we have devised an iterative algorithm based on alternating optimization as follows to solve these problems:
for a given t-th iteration solution { w } k t ,w jam t ,v t For objective functions
And (3) representing. In the third step of calculation, there are
This means that the objective function solution obtained in the third step is the upper bound of the objective function and the sub-problem (52) yields a locally optimal solution. In the fourth step of calculation, when { w k t+1 ,w jam t+1 When given, there are
Again, this illustrates that the objective function solution obtained in the fourth step is the upper bound of the objective function and that the sub-problem (71) yields a locally optimal solution. Because of the convexity of the questions (52) and (71), each sub-question can be solved uniquely in each iteration. Thus, algorithm 1 can ensure convergence to at least one locally optimal solution.
Initial passive beamforming vector v in algorithm 1 (0) And transmit beamforming vector w k (0) K=1, 2,.. jam (0) Can be produced by:
IRS reflection element initialization: in the first step of algorithm 1, the phase shift of each reflective element is arbitrarily distributed between [0,2 pi ], while the reflection amplitude is always equal to 1.
Transmitted waveBeam shaping vector initialization: in order to facilitate meeting the constraint in the optimization problem and facilitating decoding in SIC decoding order, w can be determined by k (0) K=1, 2,..
After calculation by algorithm 1, the phase shift of the nth IRS-reflective element may be calculated by
Wherein Im (u) n ) And Re (u) n ) Representing the real and imaginary parts, respectively.
The beneficial effects of the invention are as follows: the invention provides a safe beam forming method for introducing artificial noise, jointly optimizing beam forming vectors, intelligent reflecting surface phase shift and power distribution parameters into an intelligent reflecting surface-assisted non-orthogonal multiple access energy carrying network. The network security performance can be greatly improved, and the purposes of simultaneously carrying out information decoding and energy collection can be realized.
Drawings
FIG. 1 is a schematic diagram of an IRS assisted NOMA energy-carrying network in which an eavesdropper exists;
FIG. 2 shows the present invention in comparison to a random phase shift and IRS-free scheme, and the rate as a function of the number of IRS reflective elements and the performance gain;
FIG. 3 shows the present invention in contrast to a random phase shift and IRS-free scheme, and the rate as a function of the number of base station antennas;
FIG. 4 shows the present invention in contrast to a random phase shift and IRS-free scheme, and the rate as a function of base station transmit power;
FIG. 5 is a graph showing the change of the interception rate with the number of IRS reflective elements for each user's security rate in the present invention;
FIG. 6 shows the security rate of each user, the eavesdropping rate varies with the number of base station antennas in the present invention;
FIG. 7 is a graph of the security rate of each user, the eavesdropping rate as a function of the base station transmit power, and the comparison of the present invention with an IRS-free scheme;
fig. 8 illustrates the effect of energy threshold on system communication, specifically, the change of power allocation parameters and system speed with energy threshold.
Detailed Description
For a better understanding, the present invention will be described in detail below with reference to the drawings and specific examples.
Step one: and constructing an IRS-assisted NOMA energy-carrying network model according to actual conditions, wherein the NOMA energy-carrying network model comprises a network channel model, an IRS phase shift model and a receiver model. Specific: in the IRS assisted NOMA energy-carrying network shown in fig. 1, where an eavesdropper is present, consider a three-dimensional coordinate system in which the base station antenna and IRS reflecting elements are a uniform linear array lying on the x-axis and a uniform planar array parallel to the y-z plane, respectively. The coordinates of the base station reference antennas are set to (5,0,0), the reference points of the IRS reflection elements are set to (0,50,0), and the spacing between the antennas is set to half a wavelength. The number of IRS reflective elements can be expressed as m=m y M z Wherein M is y And M z The number of elements representing IRS in the y-axis and the z-axis respectively, and M is set y When increasing the number of IRS reflection elements M, let M be z Linearly increases with increasing M. K users are set to be randomly and uniformly distributed in a circular area with the radius of 3m by taking (5,50,0) as the center of a circle. Setting relevant parameters of a channel: the path loss index of the direct channel is set to alpha 1 =3.5, the path loss index of the two-segment link of irs reflection channel is set to α 2 ＝2.2，α 3 Path loss C at reference distance 1m =2.2 0 Uniformly set as C 0 = -30dB, rice factor κ BI ＝κ IU =3 dB. In addition we assume that all users have the same parameters, i.e. antenna noise
User information decoding noise delta k 2 ＝δ 2 = -70dBm, user quality of service γ k Energy conversion efficiency η =γ=1 k =η=0.7, energy threshold e k ＝e＝-50dBm。
Step two: and introducing artificial noise into the transmission precoding of the base station to obtain a base station transmitting signal and a user receiving signal. The artificial noise is eliminated by zero forcing condition at the legal user, the communication of the legal user is not affected, the signals distributed to the information decoder and the energy collector are respectively obtained by the received signals after the artificial noise is eliminated, and the received signal-to-noise ratio, the received energy, the sum rate, the eavesdropping rate and the safety rate are obtained.
Step three: the design optimization problem, the sum of the transmission rates of the maximum combination method users meets the service quality constraint, the energy threshold constraint, the power distribution parameter value condition of each legal user, the artificial noise and each legal user power constraint, the IRS reflection constraint, the SIC decoding condition of each legal user receiver end and the zero forcing condition for eliminating the artificial noise, as shown in the problem (22).
Step four: since the optimization problem in the third step is a non-convex optimization problem, and the base station beamforming vector, the IRS phase shift matrix and the power allocation parameters are highly coupled, and in addition, the IRS phase shift matrix is also expressed in a complex diagonal matrix form, the problem cannot be directly solved. Therefore, in the fourth step, auxiliary variables are introduced to replace IRS phase shift and channels, meanwhile, objective functions are approximated and converted into problems (28), then the original problems are decomposed into three non-convex problems (29) (52) (71), then the non-convex problems are converted into convex problems by using continuous convex approximation, and then an iterative algorithm based on alternate optimization is designed and put into a CVX tool box for solving.
To demonstrate the gain on NOMA systems brought about by deploying IRS to change channel conditions, the present invention was compared to two reference schemes, a random phase shift and an IRS-free scheme. N=6 and p is set in fig. 2 s The sum rate of the "IRS free" scheme remains substantially unchanged, indicating that more configurable links and higher array gains can be obtained using a greater number of IRS reflective elements, which can enhance the communication performance of the overall system. At the same time, the performance benefit of optimizing IRS phase shift over random IRS phase shift is more significant. In FIG. 3 Set m=30, p s In fig. 4, n=6 and m=30 are set to=30 dBm, and the neutralization rate in each scheme increases with the number of antennas of the base station or the transmission power of the base station, because more antennas or transmission power can obtain more active beamforming gain. Meanwhile, the scheme performance in the invention is obviously superior to that of a reference scheme, and if the same system communication performance, namely equal sum rate is achieved, the required transmitting power is lower, and the energy is saved.
In order to further verify the safety performance of the IRS-assisted NOMA portable communication network, the change of the safety rate of system communication under different conditions is further analyzed. N=6 and p is set in fig. 5 s The total security rate of all users increases with the linear increase of the IRS reflective element number, which means that more IRS reflective elements in the present invention provide more configurable links, improve array gain, improve wireless channel conditions, and improve security communication performance of the system. In fig. 6, m=30 and p is set s In fig. 7, n=6 and m=30 are set, and the total security rate of all users increases with the increase of the number of base station antennas or the transmission power, because the greater number of base station antennas or the transmission power brings greater beamforming gain, and artificial noise can be increased to play a more obvious role in suppressing an eavesdropper, so that the safety communication performance of the system is improved. Combining fig. 5 to 7, the safe rate of user 2 is higher than that of user 1, which is reasonable at a predefined channel gain, and user 2 has a larger channel gain and a lower eavesdropping rate due to the closer distance. Meanwhile, the eavesdropping rate of legal users is reduced to a lower level, which shows that the artificial noise can obviously inhibit eavesdropping and realize the destruction to eavesdropping.
In the invention, SWIPT technology is used, a power distribution scheme is adopted for signals received by a user, a part of the signals are used for information decoding, a part of the signals are used for energy collection, if the energy threshold value is changed, a higher requirement is provided for the energy collection of the user, the information decoding part is indirectly influenced, and the communication performance of the system is influenced to a certain extent. The left side of fig. 8 shows the change in the power distribution parameter with the energy threshold increasing from-30 dBm to-20 dBm. As the energy threshold increases, the power allocation parameters for both users gradually decrease, as the power allocation parameters represent the partial duty cycle for the information decoding, whereas an increase in the energy threshold requires the users to collect more energy, the signal allocated to the energy harvesting portion increases, and the signal duty cycle for the information decoding portion decreases. Meanwhile, the power allocation parameter of the user 2 is larger than that of the user 1, and because the user 2 is closer in distance, the channel condition is better, the received power is larger, and more signals can be allocated for information decoding. The change in sum rate, total safe rate and total eavesdropping rate with the energy threshold increasing from-30 dBm to-20 dBm is shown on the right side of fig. 8. It is observed that the system and rate decrease with increasing energy threshold, and that the signal allocated to the information decoding part decreases as the power allocation parameter decreases with increasing energy threshold, and that the signal-to-noise ratio of the communication decreases, and that the sum rate of the system decreases. In addition, it is observed that the eavesdropping rate is substantially unchanged and the safety rate is reduced, since the eavesdropper does not need to collect energy, the eavesdropping rate is independent of the power distribution parameters and remains unchanged, and on the basis of this, the rate is reduced, and the safety rate is reduced.
Claims (10)
1. The intelligent reflecting surface assisted non-orthogonal multiple access energy carrying network safe beam forming method is characterized in that a network in the method comprises a base station, an intelligent reflecting surface, legal users and an eavesdropper; the intelligent reflecting surface comprises a passive reflecting unit and a reflecting surface controller; a direct link and a reflection link exist between the base station and the user at the same time; the receiving end user utilizes a power distribution scheme to simultaneously decode information and collect energy; a proper amount of artificial noise is superimposed in the transmitted NOMA information; the method comprises the following specific steps:
step one: constructing an IRS-assisted NOMA energy-carrying network model according to actual conditions, wherein the NOMA energy-carrying network model comprises a network channel model, an IRS phase shift model and a receiver model;
step two: introducing artificial noise in the transmission precoding of the base station to obtain a base station transmitting signal and a user receiving signal; eliminating artificial noise at legal users through zero forcing conditions without affecting communication of the legal users, respectively obtaining signals distributed to an information decoder and an energy collector through receiving signals after eliminating the artificial noise, and obtaining a receiving signal-to-noise ratio, receiving energy and rate;
step three: designing and optimizing problems, namely, the sum of transmission rates of users with the maximum combination method meets the service quality constraint, the energy threshold constraint, the power allocation parameter value condition of each legal user, the artificial noise and power constraint of each legal user, the IRS reflection constraint, the SIC decoding condition of each legal user receiver end and the zero forcing condition for eliminating the artificial noise;
Step four: firstly, introducing auxiliary variables to replace IRS phase shift and channels, approximating an objective function, decomposing an original problem into three non-convex problems, converting the non-convex problems into convex problems by using continuous convex approximation, and then designing an iterative algorithm based on alternate optimization and putting the iterative algorithm into a CVX tool box for solving.
2. The method of claim 1, wherein in the first step, in the IRS-assisted NOMA energy-carrying network model, a base station is configured with N > 1 uniform linear array antennas, the users are all single antenna users, and the kth user uses U k Is expressed as a set of users
The fixed coordinates of the user on the ground are (x k ,y k 0); the IRS is provided with M adjustable reflection elements, the IRS adjusts the reflection coefficient of each element through a controller thereof to control different channel gains, so that the requirements of NOMA and SWIPT on channel conditions are met, and meanwhile, the interference of potential eavesdroppers on internal legal users can be restrained; the reflective elements are uniformly distributed in a planar array, and the set of IRS reflective elements is expressed as +.>
3. The method for secure beamforming in a non-orthogonal multiple access energy-carrying network according to claim 1, wherein in step one, the IRS phase shift model is: IRS phase shift is expressed as 
Wherein beta is m ＝[0,1]，θ m E [0,2 pi ] represents the amplitude and phase of the mth reflective element of the IRS, respectively; in the deployment of a real scenario, it is considered that the reflective elements of the IRS are designed to maximize the reflected signal, thus +.>
4. The method of claim 1, wherein in step one, the network channel model is: setting the channel between the user and the base station as a Rayleigh channel, denoted as
The direct channel from the base station to the kth user can be expressed as:
wherein C is 0 Represents the path loss at a reference distance of 1m, d d,k Represents the distance from the base station to the kth user, alpha 1 Representing a path loss index;
considering that there is a line-of-sight link between the base station and the reflecting surface, the channel is modeled using a rice distribution.
5. The non-orthogonal multiple access carrier of claim 1The network security beamforming method is characterized in that in the first step, the receiver model is as follows: the allocation of the power allocation receiver is determined by the power allocation parameters, and the received signal of each user is separated by the power allocator into an information decoder and an energy collector; for the kth user, it will signal power ρ k (0≤ρ k Less than or equal to 1) partial allocation to information decoder, remainder 1- ρ k Part of the signal power is distributed to the energy collectors.
6. The method of claim 1, wherein in step two, it is assumed that linear transmission precoding is performed at the base station, wherein each user is allocated a dedicated information beam; to break eavesdropping and ensure safe transmission by legitimate users, artificial noise is generated at the base station along with NOMA information; the transmitted signal at the base station can be expressed as:
wherein the method comprises the steps of
Represents the precoding vector of the kth user and satisfies ||w k || 2 ＝P k ，s k NOMA transfer information representing kth user and satisfying |s k | 2 ＝1；/>
Representing the vector of the artificial interference, and satisfies the following formula jam || 2 ＝P jam Z represents an interfering signal and satisfies |z| | 2 ＝1；
Definition P s Representing the maximum value of the base station transmit power, the transmit power from the base station satisfies:
after transmission of two channels via the base station-user link, the signal received by the kth user can be expressed as:
wherein the method comprises the steps of
Represents the antenna noise of the kth user, which is 0 in mean and σ in variance k 2 Additive white gaussian noise;
in NOMA systems, each receiver uses SIC to cancel multiple access interference; the SIC decoding order between users is mainly determined by the channel quality; thus, a user with a stronger channel gain should first decode messages from other users with weaker channels; however, because the variation of the IRS phase shift matrix will cause the variation of the channel gain, the decoding order of SIC is not only dependent on the transmit beamforming vector { w } k -also dependent on IRS reflection phase shift { Φ }; let pi (k) denote the decoding order of the kth user, pi (k) =m denote that the kth user's message is decoded at the receiver mth; because the total number of decoding order combinations is a finite value, the optimal sum rate can be obtained by firstly solving the problem of any decoding order and selecting the largest objective function value in all decoding orders; without loss of generality, assume that the channel gain between the IRS and the legitimate user satisfies:
0≤||h r,1 || 2 ≤...≤||h r,K || 2 ，0≤||h d,1 || 2 ≤...≤||h d,K || 2 (7)
defining pi (k) =k according to the channel hypothesis in (7); thus, for this given decoding order, the proposed IRS-NOMA scheme should satisfy the following constraints:
setting a zero forcing condition to directly eliminate the influence of the artificial interference from the receiving end of the legal user, and ensuring that the artificial interference is eliminated before SIC decoding;
after the influence of the artificial interference is eliminated, the received signal-to-noise ratio of the kth user is expressed as:
by utilizing the inequality, the received signal power of the user with lower decoding order is larger than the received signal power of the user with higher decoding order, so that the speed fairness among the users can be maintained;
in NOMA network, according to SIC decoding condition, the corresponding signal-to-noise ratio of the signal of the kth user decoded by the first user should be no less than the target signal-to-noise ratio of the kth user, and is recorded as 
I.e. < ->
The information of the kth user can be successfully removed from the ith user, and the target signal-to-noise ratio of the kth user is expressed as:
the corresponding sum rate of the kth user can be expressed as:
furthermore, the eavesdropping signal-to-noise ratio of a potential eavesdropper on the kth user can be expressed as:
similar to the legal user case, in which
Respectively representing antenna noise at an eavesdropper and additive noise when information is decoded, wherein the eavesdropper only needs to eavesdrop on information of legal users and does not need to collect energy;
the eavesdropping rate of the eavesdropper on the kth user can be expressed as:
the security rate of the kth user can be expressed as:
R sk ＝[R k -R ek ] + (21)。
7. the method for secure beamforming in a non-orthogonal multiple access energy-carrying network according to claim 1, wherein, in order to maximize the total transmission rate of users in the combining method while guaranteeing the network security, the optimization problem designed in the step three is as shown in the formula (22):
E k ≥e k , (22f)
0≤ρ k ≤1, (22i)
|β m |＝1,m＝1,2,...,M. (22j)
constraint (22 b) ensures that the signal-to-noise ratio of the kth information decoded by the first user exceeds gamma k Wherein gamma is k Representing user quality of service requirements for a kth user, constraint (22 c) ensuring sufficient interference capability for an eavesdropper, constraint (22 d) being a constraint of total transmit power of a base station, constraint (22 e) representing SIC decoding condition constraint, constraint (22 f) requiring that energy acquired by the kth user reach an energy threshold e k Constraint (22 g) represents zero forcing conditions for eliminating the influence of artificial interference on a normal user, constraint (22 h) and constraint (22 j) are IRS phase shift and amplitude conditions respectively, each reflecting element of IRS only adjusts the phase shift of an incident signal without amplifying the amplitude of the incident signal, and constraint (22 i) is a reasonable value interval of a power distribution parameter.
8. The method for secure beamforming in a non-orthogonal multiple access energy-carrying network according to claim 1, wherein in step four, first, an auxiliary variable is introduced to approximate a complex IRS phase shift matrix, and a passive beamforming vector is defined:
rewriting channels as joint channels, defining:
then approximating the optimization objective (22 a), i.e. introducing z k Satisfies the following conditions
Then the optimization objective (22 a) can be:
by geometric mean
To approximate (23), and introducing an intermediate variable t 1,ξ-1 ζ=1, 2,.,. K, further translates the optimization problem (22) into an optimization problem (28): />
Two variables of a base station beam forming vector, an IRS phase shift matrix and a power distribution parameter are fixed, the other variable is solved, the problem is decomposed into three sub-problems of transmitting beam forming vector optimization, IRS phase shift optimization and power distribution parameter optimization, non-convex strip parts of the sub-problems are converted, convex processing is carried out, the non-convex strip parts are approximate to the convex problem, and finally the problem is solved through an optimization algorithm of alternate iteration.
9. The method for secure beamforming in a non-orthogonal multiple access energy-carrying network of claim 8, wherein:
the method aims at the optimization of the transmitting beam forming vector in the fourth step, and specifically comprises the following steps:
for any given IRS phase shift and power allocation parameters, the sub-problem with the transmit beamforming vector is defined as an optimization problem (29) as shown below:
s.t.||2z 1,ξ ,(t 1,ξ-1 -z ξ ) H ||≤t 1,ξ-1 +z ξ , (29b)
γ k ≤z k -1, (29d)
v H H k w jam ＝0,(29h)
to solve the non-convex problem (29), the non-convex constraints (29 c), (29 g), (29 i) are transformed:
constraint (29 c) is equivalent to the following series of inequalities:
after introducing the IRS phase shift vector and definition of the joint channel, an auxiliary constant A is introduced l The signal to noise ratio formula in (29 c) is:
after the above substitution, the non-convex strip (29 c) is expressed as:
however, the problem (35) is still non-convex, the SCA is used for transforming the problem, and a Taylor series approximation is introduced for approximation, so that the non-convex strip in the original problem is converted into a convex strip; the problem (29) is still a non-convex problem due to the presence of non-protruding elements (29 g) (29 i), w being present in both conditions j And then linearizes it:
the approximation in constraint (29 g) is convex as follows:
Thus, (29 g) can be replaced by (48), which are approximately convex;
the constraint (29 i) is approximately convex as follows:
similar to the above-described condition override method, constraint (29 e) is expressed as:
with the above approximation, (29) is denoted as the following convex problem (52), which can be solved;
γ k ≤z k -1,
v H H k w jam ＝0,
the IRS phase shift optimization in the fourth step is specifically as follows: for any given transmit beamforming vector and power allocation parameter, the sub-problem for v is defined as follows (53):
max v Z (53a)
s.t.||2z 1,ξ ,(t 1,ξ-1 -z ξ ) H ||≤t 1,ξ-1 +z ξ , (53b)
γ k ≤z k -1, (53d)
|v m |＝1,m＝1,2,...,M, (53e)
v H H k w jam ＝0, (53g)
to solve the problem (53), three non-convex constraints (53 c), (53 f), (53 h) need to be transformed;
transforming the constraint (53 c) into:
then (54) may be converted into:
transforming the non-convex strip piece by adopting SCA, introducing Taylor series approximation to perform approximate processing, and further converting the non-convex strip piece in the original problem (53 c) into a convex strip piece; because of the presence of the non-protruding elements (53 f) (53 h), the problem (53) is still a non-protruding one, and the v quadratic function is present in both conditions, which is linearized:
the inequality in the constraint (53 f) will be approximated as convex as follows:
the inequality in constraint (53 g) can be approximated as convex as follows:
At this time, all non-convex constraints are converted into convex constraints, the sub-problem (53) is converted into a convex problem (71), and the CVX tool box is adopted for solving;
the power distribution parameter optimization in the fourth step is specifically as follows: and transmit beamforming vector w k Unlike the passive beamforming vector v, the power allocation parameter ρ is k Is a primary scalar, based on the problem (28), for any given transmit beamforming vector w k And a passive beamforming vector v, will be related to the power allocation parameter ρ k The sub-problems of (2) are defined as follows:
0≤ρ k less than or equal to 1 (72 d) further represents constraint (72 b) as:
the calculation is carried out to obtain:
the constraint (72 c) is simplified to be expressed as:
ρ k ≤D k (80)
the constraint (72 d) itself is a linear inequality;
comprehensively considering three linear inequalities to obtain a power distribution parameter rho l The range of the values is as follows:
and the condition that the above formula (81) is satisfied is:
at the introduction of constant B lk And C lk After simplification, the system communication rate of the kth user is expressed as:
from the above formula (84), ρ l After taking the maximum value D l R is time R k Maximum, the rate is also maximum when the respective rate of each user is maximum; thus, in determining the transmit beamforming vector w k And the optimal value of the passive beamforming vector v, ρ l Is the optimal value of D l And the sum rate at this time takes the maximum value:
the sub-problem (74) is now effectively solved and the complexity can be reduced by direct calculation methods when iterating alternately afterwards.
10. The method for secure beamforming in a non-orthogonal multiple access energy-carrying network of claim 8, wherein: the alternating iterative algorithm in the fourth step is specifically as follows: due to the power allocation parameter ρ l Can be used to obtain the transmit beamforming vector w k And the optimal value of the passive beam forming vector v, so that the alternate iterative algorithm mainly aims at w k And v, designing; converting the original problem (28) into two convex problems, namely (52) and (71); iterative algorithms based on alternating optimization as shown below were designed to solve these problems:
algorithm 1 may ensure convergence to at least one locally optimal solution;
initial passive beamforming vector v in algorithm 1 (0) And transmit beamforming vector w k (0) K=1, 2,.. jam (0) Is produced by:
IRS reflection element initialization: in the first step of algorithm 1, the phase shift of each reflective element is arbitrarily distributed between [0,2 pi ], while the reflection amplitude is always equal to 1;
transmit beamforming vector initialization: in order to facilitate meeting the constraint in the optimization problem and facilitating decoding in SIC decoding order, w can be determined by k (0) K=1, 2,..
After calculation by algorithm 1, the phase shift of the nth IRS reflective element is calculated by:
wherein Im (u) n ) And Re (u) n ) Representing the real and imaginary parts, respectively.
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| 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 |
| CN117793758A (en) * | 2024-02-23 | 2024-03-29 | 电子科技大学 | Multi-variable joint optimization method in RIS-assisted NOMA system |
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