CN116567645B - Safe energy efficiency robust design method in intelligent reflection surface-assisted cellular network - Google Patents

Abstract

The invention provides a safe energy efficiency robust design method in an intelligent reflection surface assisted cellular network, which comprises the steps of firstly, building an IRS assisted cellular network in a downlink, obtaining the safe energy efficiency of each legal user, secondly, building an optimization function aiming at maximizing the safe energy efficiency of the minimum legal user under the unit mode constraint of a BS transmitting power constraint and an IRS unit, finally, converting the uncertain interruption probability constraint in the optimization function into the determined interruption probability constraint through a Bernstein type inequality under the condition of non-ideal CSI, and then solving the optimization function by utilizing an alternate iteration algorithm. The invention researches the safety energy efficiency problem in the RS-assisted CF network, designs the BS active BF, the AN vector and the IRS passive BF through joint optimization, maximizes the safety energy efficiency of the minimum user and improves the safety performance of the network.

Description

Safe energy efficiency robust design method in intelligent reflection surface-assisted cellular network

Technical Field

The invention relates to the technical field of wireless communication, in particular to a safe energy efficiency robust design method in an intelligent reflection surface-assisted cellular network.

Background

With the rapid development of wireless applications, future mobile communications will face a number of key challenges such as spectrum resource shortage, security and privacy protection, energy efficiency, and environmental protection. Deploying more Base Stations (BS) may improve wireless data throughput. But in current cellular networks, BSs within one cell serve all users within that area, so inter-cell interference is more pronounced, especially near the cell edge. Although ultra dense networks (Ultra Dense Network, UDN) are considered to be a very promising technology, network capacity can be further improved. The UDN is still cell-centric by deploying more BSs to form a plurality of small cells. However, ultra-dense BS deployment will bring about more severe inter-cell interference. Studies have shown that cell-centric architecture, its throughput must be limited by inter-cell interference.

For this reason, a Cell-Free (CF) network architecture centered on a user is currently proposed. Unlike the conventional cell-centric design principle, the CF network adopts a user-centric design scheme, where multiple BSs in the network cooperate and serve users simultaneously. This eliminates cell boundaries, and all BSs efficiently cooperate through distribution, effectively integrate inter-cell interference, and improve system throughput and coverage probability. In recent years, CF networks have attracted increasing interest to researchers, such as precoding/Beamforming (BF), channel estimation, information security.

However, more densely deploying BSs, while enhancing network capacity and filling in coverage holes, would be a significant overhead in terms of their infrastructure and power consumption. Currently, intelligent Reflective Surfaces (IRS) are considered to be a very promising energy saving solution. It consists of a planar array of a large number of low cost, approximately passive reflecting elements, each of which is capable of being independently set to a specific phase shift offset. The IRS effectively improves the intensity of the received signal by adjusting the reflection unit to reflect the received signal to a required direction. Compared with the conventional relay, the IRS has no noise amplification and self-interference phenomenon, can greatly reduce energy consumption, and is easy to deploy. Moreover, by varying the phase offset of each passive element in the IRS, the reflected signal can be coherently superimposed with signals from other paths in the desired receiver, thereby increasing the received signal power and destructively suppressing interference in unintended receivers. Thus, in CF networks, replacing part of the BS with IRS can achieve both high rate and low power consumption.

Due to the broadcast nature of the wireless channel, any user in coverage may receive signals in free space and initiate various attacks (eavesdropping, monitoring, etc.), especially on CF networks. Nowadays, physical Layer Security (PLS) has become one of the technologies for solving wireless data Security transmission, and PLS has received increasing attention compared to conventional secure encryption mechanisms because it can protect wireless transmission without generating additional computational complexity and communication overhead. The IRS also shows good performance in improving the system security by increasing the signal intensity of legal users and weakening the signal intensity of illegal users. Under the influence of the potential advantage of IRS, the present invention will focus on studying PLS problems in IRS assisted CF networks.

Studies have shown that cooperative beamforming techniques can effectively enhance the security of CF networks. For example, document [Xia X,Fan Z,Luo W,et al.Joint Uplink Power Control,Downlink Beamforming,and Mode Selection for Secrecy Cell-Free Massive MIMO With Network-Assisted Full Duplexing[J].IEEE Systems Journal,2023,17(1):720-731.] proposes an efficient double loop algorithm aimed at maximizing the secure spectral efficiency (SPECTRAL EFFICIENCY, SE) of a full duplex CF network, suitable for the mutual collusion and non-collusion eavesdropper (Eavesdropper, eve) modes. Document [Zhang X,Guo D,An K,et al.Secure communications over cell-free massive MIMO networks with hardware impairments[J].IEEE Systems Journal,2019,14(2):1909-1920.] investigates the impact of hardware corruption on CF network security performance in the presence of pilot spoofing attacks and proposes successive convex approximations (Successive Convex Approximation, SCA) and path tracking algorithms to maximize the network's secure SE. Document [Zhang Y,Xia W,Zheng G,et al.Secure transmission in cell-free massive MIMO with low-resolution DACs over Rician fading channels[J].IEEE Transactions on Communications,2022,70(4):2606-2621.] analyzes the security of a digital-to-analog converter architecture based multiple-input multiple-output system and derives a secure SE accurate closure expression based on an additive quantization noise model, and then proposes a path-tracking based power control algorithm to maximize the secure SE.

In addition, after IRS is introduced, the joint precoding technology can enhance the security of the wireless communication system. For example, literature [Sun Y,An K,Zhu Y,et al.Energy-efficient hybrid beamforming for multilayer RIS-assisted secure integrated terrestrial-aerial networks[J].IEEE Transactions on Communications,2022,70(6):4189-4210.] explores the problem of secure transmission in a multi-layer IRS-assisted integrated ground-air network and proposes an optimization algorithm based on block coordinate descent. Literature [Dong L,Wang H M,Bai J.Active reconfigurable intelligent surface aided secure transmission[J].IEEE Transactions on Vehicular Technology,2021,71(2):2181-2186.] applies active IRS to PLS for the first time, and designs a substitution optimization (ALTERNATIVE OPTIMIZATION, AO) algorithm, which effectively relieves the double fading influence of the reflection link channel. Document [Zhang J,Du H,Sun Q,et al.Physical layer security enhancement with reconfigurable intelligent surface-aided networks[J].IEEE Transactions on Information Forensics and Security,2021,16:3480-3495.] applies a random geometry tool to derive an accurate closed-form expression of the received signal probability density function and cumulative distribution function with/without IRS assistance. Literature [Li J,Xu S,Liu J,et al.Reconfigurable intelligent surface enhanced secure aerial-ground communication[J].IEEE Transactions on Communications,2021,69(9):6185-6197.] introduces IRS into air-ground communication, and based on the joint optimization track and passive BF design, the security SE of the network is effectively improved.

In summary, the current research effort is focused on IRS communication of a single AP, and neglecting the BF problem of multi-AP cooperative security transmission. Meanwhile, research on the IRS-assisted CF network has important significance for further improving network capacity or reducing energy consumption. And multi-AP and multi-IRS systems are more challenging for joint BF designs for APs and IRS. In addition, existing works all assume that the link has ideal Channel State Information (CSI), but in practical applications, it is difficult for the AP to obtain CSI due to the passive nature of Eve. Therefore, a more realistic robust system model should be considered when studying network security resource allocation.

Disclosure of Invention

Aiming at the problem of safety energy efficiency (SECRECY ENERGY EFFICIENCY, SEE) in an IRS-assisted CF network, the invention provides an intelligent reflection surface-assisted safety energy efficiency robust design method in a cellular network, and improves the safety performance of the network.

The technical scheme of the invention is realized as follows:

a safe energy efficiency robust design method in an intelligent reflection surface-assisted cellular network comprises the following steps:

Step one, building an IRS-assisted cellular security network in a downlink, wherein the network comprises B BSs, R IRSs, K single-antenna legal users and J single-antennas Eve;

step two, obtaining the security energy efficiency of each legal user based on the IRS-assisted cellular security network;

Under the constraint of BS transmitting power and the constraint of unit mode of IRS unit, constructing an optimization function aiming at maximizing the safety energy efficiency of minimum legal user;

based on the non-ideal CSI condition, converting the uncertain outage probability constraint in the optimization function into the determined outage probability constraint through the Bernstein type inequality;

and fifthly, solving the optimization function by using an alternating iterative algorithm to obtain an optimal BF vector W, AN vector V and a phase shift theta.

The method for obtaining the security energy efficiency of each legal user by the cellular-going security network based on IRS assistance comprises the following steps:

each BS assigns a dedicated BF vector to each legitimate user, so the transmission signal x _b of the b-th BS is expressed as:

Wherein, the Representing BF vectors of the b-th BS to the k-th legal user, s _k representing transmission symbols of the k-th legal user, and satisfying { |s _k|² } = 1,AN vector representing the AN vector of the kth BS to the kth legal user, so that the kth legal user and the jth Eve which eavesdrops on the information thereof are respectively represented as:

Where y _k denotes the signal received by the kth legitimate user, A j-th Eve received signal representing eavesdropping on the k-th legal user information; Indicating the direct link channel from the b-th BS to the k-th legitimate user, Respectively representing direct link channels from the b-th BS to the j-th Eve; representing the reflected link channel from the b-th BS to the r-th IRS, Representing the reflected link channel from the r-th IRS to the kth user,Representing a reflected link channel from an irst to a jth Eve; Complex AWGN representing kth user, variance of Complex AWGN representing the jth Eve, variance ofTheta _r denotes the phase shift matrix of the r-th IRS and is denoted as theta _r＝diag(θ_r,1,…,θ_r,N), wherein |theta _r,n |1 is the n-th reflection unit of the r-th IRS;

the kth legal user and the expected signal of the jth Eve for stealing the information are respectively expressed as follows:

Wherein, define θ_r＝diag(Θ_r)、 G=[G₁,…,G_B]、μ=[θ^T,1]^T、 AndDefinition of the definitionAnd

On the basis of the above, the kth user-achievable SR can be expressed as:

Wherein, γ _k represents SINR of the kth legal user, γ _k,j represents SINR of the jth Eve received signal that eavesdrops on the kth legal user information, and the SINR is expressed as:

The total power consumption of the kth user is composed of the transmission power and the circuit power consumption, and is expressed as:

Wherein ζ represents power amplifier efficiency, P _c represents circuit power consumption, and P _c＝BP_B+P_U+RNP_R,P_B、P_U and P _R represent hardware power consumption of BS, user and IRS unit, respectively, and finally, SEE of kth user is defined as:

the optimization function targeting maximizing the security energy efficiency of the smallest legal user is:

wherein P _b denotes the maximum transmit power of the b-th BS; B _b is defined as:

the specific implementation method of the fourth step is as follows:

Defining the achievable rate of the jth Eve eavesdropping on the kth user as R _k,j when R _k,j exceeds the redundancy rate A security outage event for the kth user occurs at the BS, while, in Eve link with non-ideal CSI conditions,Can be restated as:

Wherein, the Representing the maximum safe outage probability of the kth legal user, wherein Δh _d,e,j represents the estimation error of the direct link channel, and Δf _e,j represents the estimation error of the reflected link channel;

First to The process is performed, which can be simplified as:

Wherein, the

Assume that there is a probability constraint and that:

Wherein, the AndBy introducing two relaxation variables λ and ε, the following relationship is always true:

By definition AndWherein the method comprises the steps ofAndThen, equation (13) can be converted into:

Wherein the method comprises the steps of

By introducing two auxiliary variablesAndWherein lambda= [ lambda ₁,…,λ_K ],Ε= [ ε ₁,…,ε_K ] andThen, equation (14) can be converted into:

the method for solving the optimization function by using the alternate iterative algorithm comprises the following steps:

s5.1, BS active Beam shaping and solution of AN vector

Introducing two auxiliary variablesAndWherein α= [ α ₁,…,α_K]、β＝[β₁,…,β_K ] andThus, for a given θ ^[t],Can be restated as:

Wherein, the Introducing an auxiliary variable zRestated as:

approximation thereof by first order taylor expansion The numerator on the left side of the inequality translates into a convex function as follows:

wherein t represents the t-th iteration, and therefore, Can be restated as

Obviously, the above formula satisfiesAndThen, an auxiliary variable is introducedWherein ρ= [ ρ ₁,…,ρ_K ] and Can be converted into:

Thus, the first and second substrates are bonded together, Can be restated as:

based on the above problem, the following two steps are adopted for solving:

s5.1.1, solving rho by fixing (W, V) firstly, fixing a variable (W, V), then solving rho, and enabling:

then, the optimal solution It can be calculated as:

S5.1.2, fixed ρ solving (W, V) introducing auxiliary variables Delta= [ delta ₁,…,δ_K ], thenCan be converted into:

Wherein, the For α _kδ_k, the upper bound is obtained:

According to the above-mentioned method, Can be translated into the following convex constraints:

based on the above-described analysis of the characteristics of the sample, The following problems can be restated:

By introducing three auxiliary variables AndWherein the method comprises the steps of χ=[χ₁,…,χ_K]、AndThenThe following constraints can be translated:

also, the two inequalities in the middle of the above equation can be converted into a convex constraint as follows:

Defining Eve's equivalent estimated channel and estimated error vector as:

to eliminate the estimation error, a sphere boundary method can be adopted The rewriting is as follows:

wherein, gaussian random vector Δe _j satisfies:

And the region radius ψ _k satisfies:

Wherein, the Chi-square random variable representing 2 degrees of freedom (MB+RN)Thus, the channel estimation error is expressed as:

assume that there is a function that satisfies:

Wherein, the AndIf and only if kappa is greater than or equal to 0, the function satisfies:

Then Establishment;

The first inequality in equation (30) is rewritten as:

Wherein, the

By combining the formula (36) and the formula (39), the following LMI can be obtained:

Wherein, the Meanwhile, the last inequality in equation (30) can be re-expressed as:

Wherein, the

Formula (42) is converted to LMI as follows:

Wherein, the

Finally, the optimization problem can be solvedRestated as

Solving using SDP techniquesThen using Gaussian randomization method to obtain its rank-one solution;

s5.2 solving IRS passive beam forming

Definition q=θ ^H andTwo auxiliary variables are then introducedAnd Based on W and V, the optimization problem is rewritten by fixing (W, V)The method comprises the following steps:

Wherein, the Satisfying that the element position is 1 at (m, m) and the others are 0, and in addition, And

Using singular value decomposition method, firstly toProcessing of rewriting GD _kG^H toWherein x _k,s,AndRespectively representing the corresponding singular value, left singular vector and right singular vector, then Θ ^HGD_kG^H Θ can be re-represented asNext, it is rewritten into the following form:

Wherein O _k,s＝[diag(o_k,s),0],v_k,s＝[diag(v_k,s),0]^H, at the same time, Θ can be expressed as Wherein the method comprises the steps ofThus, the first and second substrates are bonded together,The A _k and u _k,j of (A) can be converted into:

Next, the compound of formula (46) may be used The conversion is as follows:

GW _kG^H and GW using SVD method Respectively converted intoAndWherein the method comprises the steps of AndFor the corresponding singular value, left singular vector, right singular vector, then the following equation can be obtained:

Wherein, the AndNext, the following is obtained by updating the formulas (40) and (43):

At the same time, the method comprises the steps of, C _W,k and (C _W,k)C _L,k of the formula (52)AndUpdating;

Finally, problems Can be restated as:

By removing Rank-one constraint of (3) and solving by SDP technology, when the obtained solutionWhen rank-one constraint is not satisfied, a Gaussian randomization method is used for the secondary sideA feasible solution θ ^* is obtained.

Compared with the prior art, the method has the beneficial effects that BS active BF, AN vector and IRS passive BF are combined and optimally designed to maximize-minimum user SEE, corresponding solutions are provided for ideal and non-ideal CSI conditions, meanwhile, the relation between the SEE and the BS, the IRS, the users, eve, BER and transmitting power is revealed, feasibility and effectiveness of the method are proved, system performance and cost are demonstrated, trade-off exists between the SEE and the SE, and guidance is provided for CF safety network application assisted by IRS in the future.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a system model block diagram of an IRS-assisted cellular security network of the present invention.

FIG. 2 is a graph of the safety energy efficiency versus the number of iterations for different scenarios.

Fig. 3 is a graph showing the relationship between the security energy efficiency and the BS transmit power under different schemes.

Fig. 4 is a graph showing the relationship between the security energy efficiency and the number N of IRS units under different schemes.

Fig. 5 is a graph showing the relationship between the security energy efficiency and the number of Eve J under different schemes.

Fig. 6 is a graph showing the relationship between the security energy efficiency and the BS number B under different schemes.

Fig. 7 is a graph of the relationship between the security energy efficiency and the channel estimation error level under different schemes.

Fig. 8 is a comparison of total SEE with the SEE of the smallest user under different scenarios.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.

Aiming at the problem of safety energy efficiency (SECRECY ENERGY EFFICIENCY, SEE) in AN IRS-assisted CF network, the embodiment of the invention provides a safety energy efficiency robust design method in AN intelligent reflection surface-assisted cellular network, and the safety performance of the network is improved by the BS by utilizing artificial noise (ARTIFICIAL NOISE, AN) on the premise that a plurality of Eves and a plurality of legal users exist in the network. Assuming that Eve links have a scenario of non-ideal CSI, the BF optimization problem of robust SEEs is studied by introducing outage probability constraints. Considering user fairness, AN optimization problem of maximum-minimum user SEE is constructed by jointly designing BS active BF and AN and IRS passive BF. Next, an alternative iterative algorithm is proposed to solve the original problem, first by converting the uncertain outage probability constraint into a deterministic outage probability constraint by Bernstein-Type Inequality (BTI) and sphere boundary theory, and then based on S-Procedure, SCA, constraint concave-convex procedure (Constrained Concave-Convex Procedure, CCCP) and Semi-definite programming (Semi-Definite Programming, SDP) techniques. Finally, the feasibility and effectiveness of the proposed solution are confirmed by simulation results, and the trade-off between system performance and overhead and SEE and SE is demonstrated. The method comprises the following specific steps:

Step one, building an IRS-assisted cellular security network in a downlink, as shown in figure 1, comprising B BSs, R IRSs, K single-antenna legal users and J single antennas Eve, wherein each BS is provided with M antennas, each IRS is provided with N reflecting units, and the device is provided with AndRepresenting BS, IRS, IRS units, users, and sets of Eve, respectively.

Step two, obtaining the security energy efficiency of each legal user based on the IRS-assisted cellular security network;

each BS assigns a dedicated BF vector to each legitimate user, so the transmission signal x _b of the b-th BS is expressed as:

Wherein, the Representing BF vectors of the b-th BS to the k-th legal user, s _k representing transmission symbols of the k-th legal user, and satisfying { |s _k|² } = 1,AN vector representing the b-th BS for the k-th legitimate user. Thus, the kth legitimate user and the jth Eve that eavesdrop on its information received signals are represented as:

Where y _k denotes the signal received by the kth legitimate user, A j-th Eve received signal representing eavesdropping on the k-th legal user information; Indicating the direct link channel from the b-th BS to the k-th legitimate user, Respectively representing direct link channels from the b-th BS to the j-th Eve; representing the reflected link channel from the b-th BS to the r-th IRS, Representing the reflected link channel from the r-th IRS to the kth user,Representing a reflected link channel from an irst to a jth Eve; Complex AWGN representing kth user, variance of Complex AWGN representing the jth Eve, variance ofΘ _r represents the phase shift matrix of the r-th IRS and is denoted as Θ _r＝diag(θ_r,1,…,θ_r,N), where |θ _r,n |+.1 is the n-th reflection element of the r-th IRS, the superscript H represents the conjugate transpose, and the modulus of the phase shift element is assumed to be 1 for the purpose of studying the upper performance limit of the system.

The kth legal user and the expected signal of the jth Eve for stealing the information are respectively expressed as follows:

Wherein, define θ_r＝diag(Θ_r)、 G=[G₁,…,G_B]、μ=[θ^T,1]^T、 AndMeanwhile, for convenience, define And

On the basis of the above, the kth user-achievable SR can be expressed as:

Wherein, γ _k represents SINR of the kth legal user, γ _k,j represents SINR of the jth Eve received signal that eavesdrops on the kth legal user information, and the SINR is expressed as:

The total power consumption of the kth user is composed of the transmission power and the circuit power consumption, and is expressed as:

Where ζ represents power amplifier efficiency, P _c represents circuit power consumption, and P _c＝BP_B+P_U+RNP_R,P_B、P_U and P _R represent hardware power consumption of the BS, subscriber, and IRS units, respectively. Finally, define the SEE for the kth user as:

Under the constraint of BS transmitting power and the constraint of unit mode of IRS unit, constructing an optimization function aiming at maximizing the safety energy efficiency of minimum legal user;

Jointly optimizing BF vector w, AN vector v, and phase shift θ to maximize-minimize user SEE can be constructed as the following optimization problem:

wherein P _b denotes the maximum transmit power of the b-th BS; B _b is defined as:

Due to The BF matrix W, the matrix V and the phase shift vector theta are coupled to form non-convex constraint and the unit mode constraint of the IRS unit, so that the problem is difficult to solve.

Based on the non-ideal CSI condition, converting the uncertain outage probability constraint in the optimization function into the determined outage probability constraint through the Bernstein type inequality;

In an actual communication environment, the BS can accurately estimate CSI of a legitimate user link, and thus the estimation error is negligible. However, due to the passive nature of Eve, it is difficult for the BS to accurately estimate CSI of the Eve link. Thus, consider the case where the Eve link channel has non-ideal CSI, which can be expressed as:

Wherein, the AndRepresenting the actual estimated value of the corresponding channel, Δh _d,e,j and Δf _e,j representing the estimated error of the corresponding channel, and satisfyingAnd Δf _e,j～D^R＝CN(0,E_f,j), wherein,AndDefining the achievable rate of the jth Eve eavesdropping on the kth user as R _k,j when R _k,j exceeds the redundancy rateAt this time, a security break event for the kth user occurs at the BS. Based on this, in the event link with non-ideal CSI conditions,Can be restated as:

Wherein, the Representing the maximum safe outage probability of the kth legal user, wherein Δh _d,e,j represents the estimation error of the direct link channel, and Δf _e,j represents the estimation error of the reflected link channel;

First to The process is performed, which can be simplified as:

Wherein, the Δh _j＝Δh_d,e,j+G^HΘΔf_e,j However, the above-described transition has probability of breaking constraint, so its solution still has difficulty. To this end, the BTI theory of lemma 1 provides a viable solution, namely:

lemma 1 (BTI) assuming that there is a probability constraint and satisfying:

Wherein, the AndBy introducing two relaxation variables λ and ε, the following relationship is always true:

By definition AndWherein the method comprises the steps ofAndThen, applying lemma 1, equation (13) can be converted into:

Wherein the method comprises the steps of

By introducing two auxiliary variablesAndWherein lambda= [ lambda ₁,…,λ_K ],Ε= [ ε ₁,…,ε_K ] andThen, equation (14) can be converted into:

due to the coupling relationship of variables W, V and θ and the θ unit mode constraint, this results in And the objective function remains non-convex and difficult to handle. Thus, an iterative optimization scheme is presented below to process it.

And fifthly, solving the optimization function by using an alternating iterative algorithm to obtain an optimal BF vector W, AN vector V and a phase shift theta.

S5.1, BS active Beam shaping and solution of AN vector

Introducing two auxiliary variablesAndWherein α= [ α ₁,…,α_K]、β＝[β₁,…,β_K ] andThus, for a given θ ^[t],Can be restated as:

Wherein, the Due toIs not smooth, the introduction of an auxiliary variable z willRestated as:

In view of the following The left hand numerator of the inequality is a DC function that can be converted by a first order taylor expansion approximation into a convex function as follows:

Where [ t ] represents the t-th iteration. Thus, the first and second substrates are bonded together, Can be restated as

Due toAndMedium variable W and V coupling sumThere is a fractional constraint, thus solvingStill very difficult. Next, the score is constrained by the FP methodEquivalently converted into a subtracted form. Obviously, the above formula satisfiesAndThen, an auxiliary variable is introducedWherein ρ= [ ρ ₁,…,ρ_K ] andCan be converted into:

Thus, the first and second substrates are bonded together, Can be restated as:

based on the above problem, the following two steps are adopted for solving:

s5.1.1, solving rho by fixing (W, V) firstly, fixing a variable (W, V), then solving rho, and enabling:

then, the optimal solution It can be calculated as:

s5.1.2, fixed ρ solving for (W, V) due to AndIs not convex, after solving for p,Still difficult to handle. Introducing auxiliary variablesDelta= [ delta ₁,…,δ_K ], thenCan be converted into:

Wherein, the For α _kδ_k, the upper bound is obtained:

According to the above-mentioned method, Can be translated into the following convex constraints:

based on the above-described analysis of the characteristics of the sample, The following problems can be restated:

By introducing three auxiliary variables AndWherein the method comprises the steps of ThenThe following constraints can be translated:

also, the two inequalities in the middle of the above equation can be converted into a convex constraint as follows:

The first and last inequalities in equation (30) are non-probability constraints and therefore cannot be solved using the BTI method described above. For convenience, define Eve's equivalent estimated channel and estimated error vector as:

to eliminate the estimation error, a sphere boundary method can be adopted The rewriting is as follows:

wherein, gaussian random vector Δe _j satisfies:

And the region radius ψ _k satisfies:

Wherein, the Chi-square random variable representing 2 degrees of freedom (MB+RN)And up to now, substantially complete the closed form transformation process of the uncertain domain. Thus, the channel estimation error is expressed as:

In view of the semi-infinite constraint of the first and last inequalities in equation (30) and C4, the following quotients are introduced first to get the closed equivalent constraint:

lemma 2 (S-Procedure) assuming that there is a function to satisfy:

Wherein, the AndIf and only if kappa is greater than or equal to 0, the function satisfies:

Then This is true.

For convenience, the first inequality in equation (30) is rewritten as:

Wherein, the

According to the lemma 2, by combining the formula (36) and the formula (39), the following LMI can be obtained:

Wherein, the Meanwhile, the last inequality in equation (30) can be re-expressed as:

Wherein, the

Similar to the conversion of equation (41), equation (42) is converted to LMI as follows:

Wherein, the

Finally, the optimization problem can be solvedRestated as

Obviously, except forAndOther parts of the problem are all resolvable convex constraints. Thus, rank one constraint can be temporarily ignored and solved using SDP techniquesAfter which a gaussian randomization method is used to obtain its rank-one solution.

S5.2 solving IRS passive beam forming

Definition q=θ ^H andTwo auxiliary variables are then introducedAnd Based on W and V, the optimization problem is rewritten by fixing (W, V)The method comprises the following steps:

Wherein, the Satisfying that the element position is 1 at (m, m) and the others are 0, and in addition, AndIt can be found that due toVariable coupling and of (2)Semi-infinite constraint of (a) problemIt is difficult to solve. Next, using singular value decomposition (Singular Value Decomposition, SVD) method, first forProcessing of rewriting GD _kG^H toWherein the method comprises the steps ofAndRespectively representing the corresponding singular value, left singular vector and right singular vector, then Θ ^HGD_kG^H Θ can be re-represented asNext, it is rewritten into the following form:

wherein O _k,s＝[diag(o_k,s),0],V_k,s＝[diag(v_k,s),0]^H, at the same time, Θ can be expressed as Wherein the method comprises the steps ofThus, the first and second substrates are bonded together,The A _k and u _k,j of (A) can be converted into:

next, C5 in equation (46) can be converted to:

Applying lemma 2 pairs And (5) processing. GW _kG^H and GW using SVD methodRespectively converted intoAndWherein the method comprises the steps ofAndFor the corresponding singular value, left singular vector, right singular vector, then the following equation can be obtained:

Wherein, the AndNext, the following is obtained by updating the formulas (40) and (43):

At the same time, the method comprises the steps of, C _W,k and (C _W,k)C _L,k of the formula (52)AndUpdating;

Finally, problems Can be restated as:

By removing Is to be applied and the SDP technique is to be employed,Becomes an easily solved convex problem. Similarly, when the solution is obtainedWhen the rank-one constraint is not satisfied, a Gaussian randomization method can be used from the followingA feasible solution θ ^* is obtained. Based on the above analysis, the above solution process is summarized as algorithm 1.

Table 1 algorithm proposed based on non-ideal CSI

For algorithm 1, two sub-problems need to be solved in an alternating optimization mannerAndUntil the result converges. Since rank one constraint has been relaxed entirely, thereforeAndAre convex optimization problems, and the KKT solution can be ensured. In addition, since the BS transmit power is limited, the values of W and V are upper bound, θ is bounded by unit mode constraints, and thereforeThere is an upper bound on the objective function of (a). Based on this, the SEE of algorithm 1 should be monotonically non-decreasing and converge to at least one locally optimal solution, verified by the following simulation results.

The computational complexity of algorithm 1 is analyzed. For the followingWith equivalent b+3k+8kj LMI constraints and k+kj second order cone constraints. Setting the iteration precision asThen solve forThe computational complexity of (a) is about:

Wherein, the Representing a parameter of the barrier, For the followingThere are equivalent 2+RN+K+8KJ LMI constraints and K+KJ second order cone constraints. Setting the iteration precision asThen solve forThe computational complexity of (a) is about:

Wherein, the Thus, the algorithm 1 computes the complexity asWherein the method comprises the steps ofAnd

Simulation analysis, namely evaluating the performance of the proposed algorithm through simulation results.

Simulation settings b=2, r=2, k=2, and j=2. The heights of BS, IRS, user and Eve are respectively 12m, 8m, 1.5m and 1.5m, and the two-dimensional plane coordinates thereof are respectively (0 m,40 (b-1) +30m), (65 m,40 (r-1) +30m), (60 m,5 (k-1) +30m) and (55 m,5 (j-1) +32m). The number of each BS antenna and each IRS unit is m=2 and n=2, respectively. The maximum transmit power and power amplifier efficiency for each BS were set to P _b = 15dBm and ζ = 1/3, respectively. The channel model consists of large-scale and small-scale fading, wherein the large-scale fading model is as follows:

Where d, L ₀ and v represent the distance between the receiver and the transmitter, the path loss with reference to a distance of d ₀ =1m and the path loss index, respectively. The small scale fading model can be expressed as:

Wherein, the And K' represent the LoS path, NLoS path (rayleigh fading component) and rayleigh factor, respectively.Represented asWherein the method comprises the steps of

Wherein A _r、d_r andThe number of antennas, the antenna spacing and the angle of arrival, a _t、d_t andRespectively expressed as the number of antennas of the transmitter, the antenna spacing and the angle of separation. The maximum safe interrupt probability of the kth user is set asFurther, the maximum normalized error is defined as:

other parameter settings can be seen in table 2.

Table 2 symbol parameter list

For ease of comparison, the following legend is first defined:

ideal CSI: SEE for max-min user at ideal CSI;

Non-ideal CSI, SEE for max-min user, performing algorithm 1 under non-ideal CSI;

ideal CSI without IRS, SEE max-min user in ideal CSI case without IRS;

Non-ideal CSI without IRS, SEE for max-min user, performing algorithm 1 in case of non-ideal CSI without IRS;

SSEEM Total SEE maximization (Sum SEE Maximization, SSEEM) scheme, with minimum user's SEE at ideal CSI as an index;

max-min SSE, max-min user's safe spectral efficiency scheme, with the SEE of the minimum user at ideal CSI as an index.

(1) SEE versus iteration number fig. 2 shows the convergence of different schemes. Obviously, the SEE of all protocol curves increases gradually and then stabilizes after 6 iterations. Notably, the proposed "ideal CSI" and "non-ideal CSI" schemes exhibit higher SEE than the "ideal CSI without IRS" and "non-ideal CSI without IRS" schemes, which demonstrates the effectiveness of IRS to improve system SEE. Furthermore, the SEE of the "non-ideal CSI" scheme is slightly lower than the corresponding "ideal CSI" scheme, which illustrates that non-ideal CSI can lead to some loss of system performance.

(2) Relationship between SEE and BS transmit power by plotting fig. 3 to show the relationship between SEE and BS transmit power under different schemes. It can be found that under the schemes of "ideal CSI", "non-ideal CSI", "ideal CSI without IRS", "non-ideal CSI without IRS" and "SSEEM", the SEE becomes stable after gradually increasing with increasing transmit power. For the "Max-min SSE" scheme, the SEE curve shows a trend of increasing and then decreasing. This may be explained by increasing the transmit power when the BS transmit power is lower, which may increase the SE, thereby improving the SEE, whereas when the BS transmit power is higher (e.g., greater than 20 dBm), the increase in transmit power continues to be very limited to improve the SE, so the maximum SEE does not increase, consistent with the trend of curves for the "ideal CSI", "non-ideal CSI", "ideal CSI without IRS", "non-ideal CSI without IRS" and "SSEEM" schemes. Notably, the "Max-min SSE" scheme aims at maximizing SE for the smallest users, and thus SEE may decrease with increasing BS transmit power. At the same time, the highest SEE under the "ideal CSI" scheme can be observed. Furthermore, IRS assisted regimens exhibit better performance in terms of SEE, indicating the importance of IRS to increase SEE.

(3) Relationship between SEE and IRS unit number N fig. 4 shows the relationship between SEE and IRS unit number under different schemes. As can be seen from fig. 4, under the "ideal CSI" and "non-ideal CSI" schemes, SEE increases as the number of IRS units increases. However, since the "Max-min SSE" scheme aims at maximizing SE of the minimum user, as the number of IRS units increases only the increase of SE is guaranteed, its SEE is unknown. Fortunately, the SEE of the "Max-min SSE" scheme in fig. 4 can still improve with increasing number of IRS units. Meanwhile, as the number of IRS units increases, the "SSEEM" scheme aims at maximizing SEE, and under the premise of ensuring that the sum of SEE increases, the SEE of the smallest user is unknown. For example, the SEE under the "SSEEM" scheme in fig. 4 increases and then decreases slightly as the number of IRS units increases. Furthermore, under the "ideal CSI without IRS" and "non-ideal CSI without IRS" schemes, the SEE remains unchanged for any number of IRS units at all times, which is desirable.

(4) Relationship between SEE and number of Eve J the locations of the jth Eve and kth users are reset to (60 m,8 (k-1) +30m) and (55 m,4 (J-1) +31m), respectively, and fig. 5 is plotted to show the relationship of SEE and number of Eve for the proposed scheme based on different number of users. The results show that the SEE for all protocol curves decreases with increasing number of Eve. This may be explained by the fact that as more Eve results in a higher eavesdropping rate, the SEE correspondingly decreases. Meanwhile, it can be found that SEE decreases as the number of users increases. This is because as the number of users increases, interference between users becomes more severe, and channel gains of worst users may also be changed, resulting in a decrease in SEE.

(5) Relationship between SEE and BS number B here, the position of the B-th BS is reset to (0 m,15 (B-1) +20m), and fig. 6 is drawn to show the relationship between SEE and BS number B. The results show that as the number of BSs increases, SEE tends to increase and then decrease. This is because increasing the number of BSs provides more power to the user and thus SEE increases with it, but at the same time the circuit power consumption increases. Therefore, when the number of BSs is large, huge circuit power consumption conversely causes SEE to decrease. This reveals that in practical applications, there is a trade-off relationship between SEE and BS number (or SSE).

(6) The relation between SEE and channel estimation error level fig. 7 shows the relation between SEE and error level for different schemes. Wherein a "non-ideal CSI-scheme curve without interruption" is added as a comparison benchmark. The results show that the SEE of the "non-ideal CSI", "non-ideal CSI without IRS" and "non-ideal CSI without interruption" schemes decrease with increasing error level, as can be appreciated. At the same time, as the error level increases, the SEE of the "ideal CSI" scheme remains unchanged, which is desirable. Furthermore, it can be observed that the SEE of the "non-ideal CSI" scheme is lower than the "non-ideal CSI without interruption" scheme, because the relaxed outage probability constraint provides more freedom of BF selection.

(7) Comparison of SEE fairness in fig. 8, the total SEE and the minimum user SEE under different schemes are compared. The experiment increased the number of users to three and reset the user positions to (60 m,70 m), (60 m,90 m) and (60 m,120 m), respectively. The results show that the total SEE for the "SSEEM" and "SSEEM of non-ideal CSI" schemes is relatively high, but the minimum user SEE is low. In contrast, the proposed scheme of the present invention has a total SEE slightly lower than the "SSEEM" and "SSEEM" schemes of non-ideal CSI, but its minimum user SEE is relatively high. This may be interpreted as that the "SSEEM" approach aims to maximize the total SEE, but to sacrifice the SEE for the smallest user for the boost of the total SEE. However, the proposed solution of the present invention aims at maximizing the SEE of the minimum users to guarantee QoS and fairness for each user.

The invention researches the SEE problem in the CF safety network based on IRS assistance, and combines and optimally designs BS active BF, AN and IRS passive BF so as to maximize-minimize SEE of users. Meanwhile, corresponding solutions are provided for ideal and non-ideal CSI cases. Simulation shows that the scheme provided by the invention is superior to the existing scheme in the aspect of SEE. Meanwhile, the obtained result also reveals the relation between the SEE and the BS, the IRS, the user, the Eve, the BER and the transmitting power, reveals the trade-off between the system performance and the overhead and between the SEE and the SE, and provides guidance for CF safety network application assisted by the IRS in the future.

The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.

Claims (4)

1. The safe energy efficiency robust design method in the intelligent reflection surface assisted cellular network is characterized by comprising the following steps of:

Step one, building an IRS-assisted cellular security network in a downlink, wherein the network comprises B BSs, R IRSs, K single-antenna legal users and J single-antennas Eve;

step two, obtaining the security energy efficiency of each legal user based on the IRS-assisted cellular security network;

each BS assigns a dedicated BF vector to each legitimate user, so the transmission signal x _b of the b-th BS is expressed as:

Wherein, the Representing BF vectors of the b-th BS to the k-th legal user, s _k representing transmission symbols of the k-th legal user, and satisfying { |s _k|² } = 1,AN vector representing the b-th BS for the k-th legitimate user;

Thus, the kth legitimate user and the jth Eve that eavesdrop on its information received signals are represented as:

Where y _k denotes the signal received by the kth legitimate user, A j-th Eve received signal representing eavesdropping on the k-th legal user information; Indicating the direct link channel from the b-th BS to the k-th legitimate user, Respectively representing direct link channels from the b-th BS to the j-th Eve; representing the reflected link channel from the b-th BS to the r-th IRS, Representing the reflected link channel from the r-th IRS to the kth user,Representing a reflected link channel from an irst to a jth Eve; Complex AWGN representing kth user, variance of Complex AWGN representing the jth Eve, variance ofΘ _r represents the phase shift matrix of the r-th IRS and is denoted as Θ _r＝diag(θ_r,1,…,θ_r,N), where |θ _r,n |+.1 is the n-th reflection unit of the r-th IRS;

the kth legal user and the expected signal of the jth Eve for stealing the information are respectively expressed as follows:

Wherein, define θ_r＝diag(Θ_r)、

G=[G₁,…,G_B]、

μ=[θ^T,1]^T、

AndDefinition of the definitionAnd

On the basis of the above, the kth user-achievable SR can be expressed as:

Wherein, γ _k represents SINR of the kth legal user, γ _k,j represents SINR of the jth Eve received signal that eavesdrops on the kth legal user information, and the SINR is expressed as:

The total power consumption of the kth user is composed of the transmission power and the circuit power consumption, and is expressed as:

Wherein ζ represents power amplifier efficiency, P _c represents circuit power consumption, and P _c＝BP_B+P_U+RNP_R,P_B、P_U and P _R represent hardware power consumption of BS, user and IRS unit, respectively, and finally, SEE of kth user is defined as:

Under the constraint of BS transmitting power and the constraint of unit mode of IRS unit, constructing an optimization function aiming at maximizing the safety energy efficiency of minimum legal user;

based on the non-ideal CSI condition, converting the uncertain outage probability constraint in the optimization function into the determined outage probability constraint through the Bernstein type inequality;

and fifthly, solving the optimization function by using an alternating iterative algorithm to obtain an optimal BF vector W, AN vector V and a phase shift theta.

2. The method for robust design of security energy efficiency in an intelligent reflection-assisted cellular network according to claim 1, wherein the optimization function targeting maximizing security energy efficiency of minimum legitimate users is:

wherein P _b denotes the maximum transmit power of the b-th BS; B _b is defined as:

3. The method for designing security energy efficiency robustness in an intelligent reflection surface assisted cellular network according to claim 2, wherein the specific implementation method of the fourth step is as follows:

Defining the achievable rate of the jth Eve eavesdropping on the kth user as R _k,j when R _k,j exceeds the redundancy rate A security outage event for the kth user occurs at the BS, while, in Eve link with non-ideal CSI conditions,Can be restated as:

Wherein, the Representing the maximum safe outage probability of the kth legal user, Δh _d,e,j representing the estimation error of the direct link channel, Δf _e,j representing the estimation error of the reflected link channel;

First to The process is performed, which can be simplified as:

Wherein, the Deltah _j＝△h_d,e,j+G^HΘ△f_e,j and

Assume that there is a probability constraint and that:

Wherein, the AndBy introducing two relaxation variables λ and ε, the following relationship is always true:

By definition AndWherein the method comprises the steps ofAndThen, equation (13) can be converted into:

Wherein the method comprises the steps of

By introducing two auxiliary variablesAndWherein lambda= [ lambda ₁,…,λ_K ],Ε= [ ε ₁,…,ε_K ] andThen, equation (14) can be converted into:

4. the method for designing security energy efficiency robustness in an intelligent reflection-assisted cellular network according to claim 3, wherein the method for solving the optimization function by using the alternate iterative algorithm is as follows:

s5.1, BS active Beam shaping and solution of AN vector

Introducing two auxiliary variablesAndWherein α= [ α ₁,…,α_K]、β＝[β₁,…,β_K ] andThus, for a given θ ^[t],Can be restated as:

Wherein, the Introducing an auxiliary variable zRestated as:

approximation thereof by first order taylor expansion The numerator on the left side of the inequality translates into a convex function as follows:

wherein t represents the t-th iteration, and therefore, Can be restated as

Obviously, the above formula satisfiesAndThen, an auxiliary variable is introducedWherein ρ= [ ρ ₁,…,ρ_K ] and Can be converted into:

Thus, the first and second substrates are bonded together, Can be restated as:

based on the above problem, the following two steps are adopted for solving:

s5.1.1, solving rho by fixing (W, V) firstly, fixing a variable (W, V), then solving rho, and enabling:

then, the optimal solution It can be calculated as:

S5.1.2, fixed ρ solving (W, V) introducing auxiliary variables Delta= [ delta ₁,…,δ_K ], thenCan be converted into:

Wherein, the For α _kδ_k, the upper bound is obtained:

According to the above-mentioned method, Can be translated into the following convex constraints:

based on the above-described analysis of the characteristics of the sample, The following problems can be restated:

By introducing three auxiliary variables AndWherein the method comprises the steps of χ=[χ₁,…,χ_K]、AndThenThe following constraints can be translated:

also, the two inequalities in the middle of the above equation can be converted into a convex constraint as follows:

Defining Eve's equivalent estimated channel and estimated error vector as:

to eliminate the estimation error, a sphere boundary method can be adopted The rewriting is as follows:

wherein, gaussian random vector Δe _j satisfies:

And the region radius ψ _k satisfies:

Wherein, the Chi-square random variable representing 2 degrees of freedom (MB+RN)Thus, the channel estimation error is expressed as:

assume that there is a function that satisfies:

Wherein, the AndIf and only if kappa is greater than or equal to 0, the function satisfies:

Then Establishment;

The first inequality in equation (30) is rewritten as:

Wherein, the

By combining the formula (36) and the formula (39), the following LMI can be obtained:

Wherein, the Meanwhile, the last inequality in equation (30) can be re-expressed as:

Wherein, the

Formula (42) is converted to LMI as follows:

Wherein, the

Finally, the optimization problem can be solvedRestated as

Solving using SDP techniquesThen using Gaussian randomization method to obtain its rank-one solution;

s5.2 solving IRS passive beam forming

Definition q=θ ^H andTwo auxiliary variables are then introducedAnd Based on W and V, the optimization problem is rewritten by fixing (W, V)The method comprises the following steps:

Wherein, the Satisfying that the element position is 1 at (m, m) and the others are 0, and in addition, AndUsing singular value decomposition method, firstly toProcessing of rewriting GD _kG^H toWherein x _k,s,AndRespectively representing the corresponding singular value, left singular vector and right singular vector, then Θ ^HGD_kG^H Θ can be re-represented asNext, it is rewritten into the following form:

wherein O _k,s＝[diag(o_k,s),0],V_k,s＝[diag(v_k,s),0]^H, at the same time, Θ can be expressed as Wherein the method comprises the steps ofThus, the first and second substrates are bonded together,The A _k and u _k,j of (A) can be converted into:

Next, the compound of formula (46) may be used The conversion is as follows:

GW _kG^H and GW using SVD method Respectively converted intoAndWherein the method comprises the steps of AndFor the corresponding singular value, left singular vector, right singular vector, then the following equation can be obtained:

Wherein, the AndNext, the following is obtained by updating the formulas (40) and (43):

At the same time, the method comprises the steps of, C _W,k and (C _W,k)C _L,k of the formula (52)AndUpdating;

Finally, problems Can be restated as:

By removing Rank-one constraint of (3) and solving by SDP technology, when the obtained solutionWhen rank-one constraint is not satisfied, a Gaussian randomization method is used for the secondary sideA feasible solution θ ^* is obtained.