A robust design method for secure, energy-efficient and mobile-friendly networks assisted by smart reflectors

Abstract

This paper proposes a robust design method for security and energy efficiency in a decellularized network assisted by an intelligent reflector. The method comprises the following steps: first, building a decellularized security network assisted by an IRS in the downlink and obtaining the security energy efficiency of each legitimate user; second, constructing an optimization function to maximize the security energy efficiency of the minimum legitimate user under the constraints of the base station transmit power and the unit modulus of the IRS unit; finally, under non-ideal CSI conditions, the uncertain outage probability constraint in the optimization function is converted into a certain outage probability constraint using a Bernstein-type inequality; and then solving the optimization function using an alternating iterative algorithm. This paper studies the security and energy efficiency problem in a RS-assisted CF network. By jointly optimizing the base station active BF, the AN vector, and the IRS passive BF, the method maximizes the security energy efficiency of the minimum user and improves the network security performance.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a smart reflective surface-assisted, secure, energy-efficient, and robust design method for a decellularized network. Background Art

[0002] With the rapid development of wireless applications, future mobile communications will face many key challenges, such as spectrum resource shortages, security and privacy protection, energy efficiency, and environmental protection. Deploying more base stations (BSs) can increase wireless data throughput. However, in current cellular networks, the BSs within a cell serve all users in that area, resulting in inter-cell interference, especially between users near the cell edge. Although ultra-dense networks (UDNs) are considered a promising technology that can further increase network capacity, UDNs are still cell-centric, deploying more BSs to form multiple small cells. However, ultra-dense BS deployment will lead to more severe inter-cell interference. Research has shown that the throughput of a cell-centric architecture is inevitably limited by inter-cell interference.

[0003] To this end, a user-centric Cell-Free (CF) network architecture is currently being proposed. Unlike traditional cell-centric design principles, CF networks adopt a user-centric approach, where multiple base stations (BSs) collaborate and serve users simultaneously. This eliminates cell boundaries, and through distributed and efficient collaboration among all BSs, inter-cell interference is effectively mitigated, improving system throughput and coverage probability. In recent years, CF networks have attracted increasing research interest in areas such as precoding / beamforming (BF), channel estimation, and information security.

[0004] However, while denser deployment of base stations can enhance network capacity and fill coverage gaps, it comes at a significant cost in terms of infrastructure and power consumption. Currently, intelligent reflecting surfaces (IRSs) are considered a promising energy-saving solution. They consist of a planar array of a large number of low-cost, nearly passive reflective elements, each of which can be independently configured with a specific phase shift. By adjusting the reflective elements to reflect the received signal in the desired direction, IRSs effectively improve the received signal strength. Compared to conventional relays, IRSs avoid noise amplification and self-interference, significantly reduce energy consumption, and are easy to deploy. Furthermore, by varying the phase shift of each passive element in the IRS, the reflected signal can be coherently superimposed with signals from other paths at the desired receiver, thereby increasing the received signal power and destructively suppressing interference at unintended receivers. Therefore, in CF networks, replacing some base stations with IRSs can achieve both high data rates and low energy consumption.

[0005] Due to the broadcast characteristics of wireless channels, any user within the coverage area may receive signals in free space and launch various attacks (eavesdropping, surveillance, etc.), especially for CF networks. Nowadays, physical layer security (PLS) has become one of the technologies to solve the problem of secure wireless data transmission. Compared with traditional security encryption mechanisms, PLS has attracted more and more attention because it can protect wireless transmission without incurring additional computational complexity and communication overhead. IRS has also shown good performance in improving system security by increasing the signal strength of legitimate users and weakening the signal strength of illegal users. Influenced by this potential advantage of IRS, the present invention will focus on the PLS problem in CF networks based on IRS assistance.

[0006] Research has shown that collaborative beamforming technology can effectively enhance the security of CF networks. For example, the paper [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.] proposed an effective dual-ring algorithm to maximize the secure spectrum efficiency (SE) of full-duplex CF networks, applicable to both collusive and non-collusive eavesdropper (Eve) modes. The paper [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.] studied the impact of hardware damage on the security performance of CF networks under pilot spoofing attacks, and proposed a successive convex approximation (SCA) and path tracking algorithm to maximize the network's security SE. The paper [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.] analyzed the security of a multiple-input multiple-output system based on a digital-to-analog converter architecture, and derived an exact closed-form expression for the security SE based on an additive quantization noise model. A power control algorithm based on path tracking was then proposed to maximize the security SE.

[0007] In addition, after the introduction of IRS, joint precoding technology can enhance the security of wireless communication systems. For example, the 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.] studied the problem of secure transmission in integrated ground-air networks assisted by multi-layer IRS and proposed an optimization algorithm based on block coordinate descent. The literature [Dong L, Wang HM, Bai J. Active reconfigurable intelligent surface aided secure transmission [J]. IEEE Transactions on Vehicular Technology, 2021, 71 (2): 2181-2186.] applied active IRS to PLS for the first time and designed an alternative optimization (AO) algorithm to effectively alleviate the impact of double fading in the reflection link channel. The literature [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 random geometry tools to derive exact closed-form expressions for the probability density function and cumulative distribution function of the received signal with and without IRS assistance. The 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 trajectory and passive BF design, the network's security SE is effectively improved.

[0008] In summary, current research has largely focused on IRS communication within a single AP, while neglecting the BF problem of multi-AP collaborative secure transmission. Furthermore, research on IRS-assisted CF networks is crucial for further improving network capacity or reducing energy consumption. Furthermore, multi-AP and multi-IRS systems pose significant challenges for the joint BF design of APs and IRSs. Furthermore, existing work assumes perfect channel state information (CSI) for links. However, in practice, due to the passive nature of Eve, it is difficult for APs to obtain CSI. Therefore, more realistic robust system models should be considered when studying network security resource allocation. Summary of the Invention

[0009] Aiming at the problem of security energy efficiency (SEE) in IRS-assisted CF network, the present invention proposes a robust design method for security energy efficiency in decellularized network assisted by intelligent reflective surface, which improves the security performance of the network.

[0010] The technical solution of the present invention is achieved as follows:

[0011] A smart reflector-assisted robust design method for security, energy efficiency, and performance in a decellularized network is provided, comprising the following steps:

[0012] Step 1: Build a downlink IRS-assisted decellularized secure network, including B base stations, R IRSs, K single-antenna legitimate users, and J single-antenna Eves. Each base station has M antennas, and each IRS has N reflectors.

[0013] Step 2: Obtain the security energy efficiency of each legitimate user based on the IRS-assisted decellularized security network;

[0014] Step 3: Under the constraints of BS transmit power and the unit modulus of the IRS unit, an optimization function is constructed to maximize the security energy efficiency of the minimum legal user;

[0015] Step 4: Based on non-ideal CSI conditions, the uncertain outage probability constraint in the optimization function is transformed into a certain outage probability constraint through the Bernstein inequality;

[0016] Step 5: Use the alternating iterative algorithm to solve the optimization function and obtain the optimal BF vector W, AN vector V and phase shift θ.

[0017] The method for obtaining the security energy efficiency of each legitimate user in the IRS-assisted decellularized security network is as follows:

[0018] Each BS allocates a dedicated BF vector to each legitimate user, so the transmission signal x of the b-th BS isb Expressed as:

[0019]

[0020] in, represents the BF vector of the b-th BS for the k-th legal user, s k represents the transmission symbol of the kth legal user and satisfies {|s k | 2}=1, represents the AN vector of the b-th BS to the k-th legal user; therefore, the signals received by the k-th legal user and the j-th Eve who eavesdrops on its information are respectively expressed as:

[0021]

[0022] Among them, y k represents the signal received by the kth legal user, It represents the signal received by the j-th Eve who eavesdrops on the k-th legitimate user information; represents the direct link channel from the bth BS to the kth legal user, denote the direct link channel from the bth BS to the jth Eve respectively; represents the reflection link channel from the bth BS to the rth IRS, represents the reflection link channel from the rth IRS to the kth user, represents the reflection link channel from the rth IRS to the jth Eve; represents the complex AWGN of the kth user, and the variance is represents the complex AWGN of the j-th Eve, and the variance is ;Θ r represents the phase shift matrix of the rth IRS and is denoted as Θ r =diag(θ r,1 ,…,θ r,N ), where |θ r,n |≤1 is the nth reflection unit of the rth IRS; the superscript H indicates the conjugate transpose;

[0023] The expected signals of the kth legitimate user and the jth Eve who steals his information are expressed as:

[0024]

[0025] Among them, the definition θ r =diag(Θ r ), G=[G1,…,GB ]、 μ=[θ T ,1] T 、 and definition and

[0026] Based on the above, the SR achievable by the k-th user can be expressed as:

[0027]

[0028] Among them, γ k represents the SINR of the kth legal user, γ k,j The SINR of the received signal of the j-th Eve who eavesdrops on the k-th legitimate user information is expressed as:

[0029]

[0030] The total power consumption of the kth user consists of transmission power and circuit power consumption, which can be expressed as:

[0031]

[0032] Where ζ represents the power amplifier efficiency, P c represents the circuit power consumption, and P c =BP B +P U +RNP R , P B 、P U and P R They represent the hardware power consumption of BS, user and IRS units respectively; finally, the SEE of the kth user is defined as:

[0033]

[0034] The optimization function to maximize the security energy efficiency of the minimum legal user is:

[0035]

[0036] Among them, P b represents the maximum transmit power of the b-th BS; B b is defined as:

[0037]

[0038] The specific implementation method of step four is:

[0039] Define the achievable rate of the jth Eve eavesdropping on the kth user as R k,j , when R k,j Exceeding the redundancy rate When , a security interruption event of the kth user occurs at the BS; under the condition that the Eve link has non-ideal CSI, can be restated as:

[0040]

[0041] in, Denotes the maximum security interruption probability of the kth legitimate user, Δh d,e,j Denotes the estimation error of the direct link channel, Δf e,j represents the estimation error of the reflection link channel;

[0042] First of all, Processing can be simplified to:

[0043]

[0044] in,

[0045] Assume there is a probability constraint that satisfies:

[0046]

[0047] in, and By introducing two slack variables λ and ε, the following relationship always holds:

[0048]

[0049] By definition and in and Then, formula (13) can be transformed into:

[0050]

[0051] in

[0052]

[0053] By introducing two auxiliary variables and where λ=[λ1,…,λ K ]、 ε=[ε1,…,ε K ]and Then, formula (14) can be converted to:

[0054]

[0055] The method for solving the optimization function using the alternating iterative algorithm is:

[0056] S5.1. BS active beamforming and AN vector solution

[0057] Introduce two auxiliary variables and where α=[α1,…,α K ]、β=[β1,…,β K ]and Therefore, for a given θ [t] , can be restated as:

[0058]

[0059] in, Introducing an auxiliary variable z will Rephrased as:

[0060]

[0061] Approximate it by first-order Taylor expansion The numerator on the left side of the inequality is transformed into the following convex function:

[0062]

[0063] where [t] represents the tth iteration; therefore, It can be restated as

[0064]

[0065] Obviously, the above formula satisfies and Then, introduce an auxiliary variable where ρ=[ρ1,…,ρ K ]and can be transformed into:

[0066]

[0067] therefore, can be restated as:

[0068]

[0069] Based on the above problem, the following two steps are used to solve it:

[0070] S5.1.1. Fix (W, V) and solve for ρ: First, fix the variables (W, V), and then solve for ρ; let:

[0071]

[0072] Then, the optimal solution It can be calculated as:

[0073]

[0074] S5.1.2. Solving (W,V) with Fixed ρ: Introducing Auxiliary Variables δ=[δ1,…,δ K ],So can be transformed into:

[0075]

[0076] in, For α k δ k , we can get its upper bound as:

[0077]

[0078] According to the above formula, It can be transformed into the following convex constraint:

[0079]

[0080] Based on the above analysis, It can be restated as the following question:

[0081]

[0082] By introducing three auxiliary variables and in χ=[χ1,…,χ K ]、 and but It can be transformed into the following constraints:

[0083]

[0084] Similarly, the two inequalities in the middle of the above formula can be transformed into convex constraints as follows:

[0085]

[0086] The equivalent estimated channel and estimated error vector of Eve are defined as:

[0087]

[0088] In order to eliminate the estimation error, the sphere boundary method can be used to Rewritten as:

[0089]

[0090] Among them, the Gaussian random vector Δe j satisfy:

[0091]

[0092] And the area radius ψ k satisfy:

[0093]

[0094] in, represents a chi-squared random variable with 2(MB+RN) degrees of freedom The inverse cumulative distribution function of ; therefore, the channel estimation error is expressed as:

[0095]

[0096] Suppose there exists a function that satisfies:

[0097]

[0098] in, and If and only if there exists κ ≥ 0, the function satisfies:

[0099]

[0100] So Established;

[0101] Rewrite the first inequality in equation (30) as:

[0102]

[0103] in,

[0104]

[0105] Combining Equation (36) and Equation (39), we can obtain the following LMI:

[0106]

[0107] in, At the same time, the last inequality in equation (30) can be reformulated as:

[0108]

[0109] in,

[0110]

[0111] Equation (42) is converted into the following LMI:

[0112]

[0113] in,

[0114] Finally, the optimization problem can be Re-expressed as

[0115]

[0116] Solved using SDP technology Then the Gaussian randomization method is used to obtain its rank-one solution;

[0117] S5.2 Solution of IRS Passive Beamforming

[0118] Define Q = θθ H and Then introduce two auxiliary variables and Based on the obtained W and V, rewrite the optimization problem by fixing (W, V) for:

[0119]

[0120] in, The element position (m,m) is 1, and the others are 0. In addition, and

[0121] Using the singular value decomposition method, we first Processing, GD k G H Rewrite as where x k,s 、 and denote the corresponding singular values, left singular vectors, and right singular vectors respectively; then, Θ H GD k G H Θ can be reformulated as Next, rewrite it as follows:

[0122]

[0123] Among them, 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 in therefore, A in k and u k,j Can be converted into:

[0124]

[0125]

[0126] Next, we can use the formula (46) Converts to:

[0127]

[0128] Use SVD method to transform GW k G H and Converted into and in and are the corresponding singular values, left singular vectors, and right singular vectors; then, the following equations can be obtained:

[0129]

[0130] in, and Next, update equations (40) and (43) to obtain the following:

[0131]

[0132] at the same time, C W,k and C L,k Respectively from formula (52) and Make updates;

[0133] Finally, the question can be restated as:

[0134]

[0135] By removing The rank-one constraint is solved by SDP technology; when the solution is obtained When the rank-one constraint is not satisfied, the Gaussian randomization method is used to select Obtain a feasible solution θ * .

[0136] Compared with the existing technology, the present invention has the following beneficial effects: the present invention jointly optimizes the design of the BS active BF, AN vector and IRS passive BF to maximize the minimum user's SEE; for ideal and non-ideal CSI conditions, the present invention proposes corresponding solutions, and reveals the relationship between SEE and BS, IRS, user, Eve, BER and transmission power, proving the feasibility and effectiveness of the method of the present invention, and illustrating the trade-off between system performance and overhead, as well as SEE and SE, providing guidance for future IRS-assisted CF security network applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0137] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0138] Figure 1 This is a system model structure diagram of the IRS-assisted de-cellularized security network of the present invention.

[0139] Figure 2 This is the relationship curve between safety energy efficiency and number of iterations under different schemes.

[0140] Figure 3 This is the relationship curve between security energy efficiency and BS transmission power under different schemes.

[0141] Figure 4 The relationship curve between safety energy efficiency and the number of IRS units N under different schemes.

[0142] Figure 5 It is the relationship curve between safety energy efficiency and Eve number J under different schemes.

[0143] Figure 6 The relationship curve between security energy efficiency and the number of BSs B under different schemes.

[0144] Figure 7 This is the relationship curve between security energy efficiency and channel estimation error level under different schemes.

[0145] Figure 8 Comparison results of total SEE and minimum user SEE under different schemes. DETAILED DESCRIPTION

[0146] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0147] To address the security energy efficiency (SEE) problem in IRS-assisted CF networks, embodiments of the present invention provide a robust design method for security energy efficiency in decellularized networks assisted by intelligent reflectors. Assuming multiple Eves and multiple legitimate users exist in the network, and that the BS utilizes artificial noise (AN) to improve network security. Assuming a scenario where the Eve link has non-ideal CSI, the BF optimization problem for robust SEE is studied by introducing an outage probability constraint. Considering user fairness, a maximize-minimize user SEE optimization problem is constructed by jointly designing the BS active BF and AN and the IRS passive BF. Next, we first transform the uncertain outage probability constraint into a deterministic one using Bernstein-type inequality (BTI) and sphere bounds theory. We then propose an alternating iterative algorithm to solve the original problem based on S-Procedure, SCA, Constrained Concave-Convex Procedure (CCCP), and Semi-Definite Programming (SDP). Finally, simulation results confirm the feasibility and effectiveness of the proposed solution and demonstrate the trade-offs between system performance and overhead, as well as between SEE and SE. The specific steps are as follows:

[0148] Step 1: Build a downlink IRS-assisted decellularized security network, such as Figure 1 As shown, there are B BSs, R IRSs, K single-antenna legal users and J single-antenna Eves; each BS has M antennas, and each IRS has N reflection units; let and They represent the set of BS, IRS, IRS unit, user and Eve respectively.

[0149] Step 2: Obtain the security energy efficiency of each legitimate user based on the IRS-assisted decellularized security network;

[0150] Each BS allocates a dedicated BF vector to each legitimate user, so the transmission signal x of the b-th BS is b Expressed as:

[0151]

[0152] in, represents the BF vector of the b-th BS for the k-th legal user, s k represents the transmission symbol of the kth legal user and satisfies {|s k | 2}=1, represents the AN vector of the b-th BS to the k-th legal user. Therefore, the signals received by the k-th legal user and the j-th Eve who eavesdrops on its information are respectively expressed as:

[0153]

[0154] Among them, y k represents the signal received by the kth legal user, It represents the signal received by the j-th Eve who eavesdrops on the k-th legitimate user information; represents the direct link channel from the bth BS to the kth legal user, denote the direct link channel from the bth BS to the jth Eve respectively; represents the reflection link channel from the bth BS to the rth IRS, represents the reflection link channel from the rth IRS to the kth user, represents the reflection link channel from the rth IRS to the jth Eve; represents the complex AWGN of the kth user, and the variance is represents the complex AWGN of the j-th Eve, and the variance is Θ r represents the phase shift matrix of the rth IRS and is denoted as Θ r =diag(θ r,1 ,…,θ r,N ), where |θ r,n |≤1 is the nth reflection unit of the rth IRS; the superscript H represents the conjugate transpose; in order to study the upper limit of the system performance, the modulus of the phase shift unit is assumed to be 1.

[0155] The expected signals of the kth legitimate user and the jth Eve who steals his information are expressed as:

[0156]

[0157] Among them, the definition θ r =diag(Θ r ), G=[G1,…,G B ]、 μ=[θ T ,1] T 、 and At the same time, for convenience, define and

[0158] Based on the above, the SR achievable by the k-th user can be expressed as:

[0159]

[0160] Among them, γ k represents the SINR of the kth legal user, γ k,j The SINR of the received signal of the j-th Eve who eavesdrops on the k-th legitimate user information is expressed as:

[0161]

[0162] The total power consumption of the kth user consists of transmission power and circuit power consumption, which can be expressed as:

[0163]

[0164] Where ζ represents the power amplifier efficiency, P c represents the circuit power consumption, and P c =BP B +P U +RNP R , P B 、P U and P R Denote the hardware power consumption of BS, user and IRS unit respectively. Finally, the SEE of the kth user is defined as:

[0165]

[0166] Step 3: Under the constraints of BS transmit power and the unit modulus of the IRS unit, an optimization function is constructed to maximize the security energy efficiency of the minimum legal user;

[0167] Jointly optimizing the BF vector w, AN vector v, and phase shift θ to maximize or minimize the user's SEE can be formulated as the following optimization problem:

[0168]

[0169] Among them, P b represents the maximum transmit power of the b-th BS; B b is defined as:

[0170]

[0171] because The BF matrix W, the matrix V and the phase shift vector θ in the equation are coupled to form non-convex constraints, as well as the unit mode constraint of the IRS unit, which makes this problem difficult to solve.

[0172] Step 4: Based on non-ideal CSI conditions, the uncertain outage probability constraint in the optimization function is transformed into a certain outage probability constraint through the Bernstein inequality;

[0173] In a real communication environment, the BS can accurately estimate the CSI of the legitimate user link, so the estimation error can be ignored. However, due to the passive nature of Eve, it is difficult for the BS to accurately estimate the CSI of the Eve link. Therefore, considering the case where the Eve link channel has non-ideal CSI, it can be expressed as:

[0174]

[0175] in, and represents the actual estimated value of the corresponding channel, Δh d,e,j and Δf e,j Represents the estimation error of the corresponding channel and satisfies and Δf e,j ~D R =CN(0,E f,j ),in, and Define the achievable rate of the jth Eve eavesdropping on the kth user as R k,j , when R k,j Exceeding the redundancy rate When , a security interruption event of the kth user occurs at the BS. Based on this, under the condition that the Eve link has non-ideal CSI, can be restated as:

[0176]

[0177] in, Denotes the maximum security interruption probability of the kth legitimate user, Δh d,e,j Denotes the estimation error of the direct link channel, Δf e,j represents the estimation error of the reflection link channel;

[0178] First of all, Processing can be simplified to:

[0179]

[0180] in, Δh j =Δh d,e,j +G H ΘΔf e,j and However, the above transformation is subject to probabilistic interruption constraints, so its solution is still difficult. Therefore, the BTI theory of Lemma 1 provides a feasible solution, namely:

[0181] Lemma 1 (BTI): Assume there exists a probability constraint that satisfies:

[0182]

[0183] in, and By introducing two slack variables λ and ε, the following relationship always holds:

[0184]

[0185] By definition and in and Then, applying Lemma 1, Equation (13) can be transformed into:

[0186]

[0187] in

[0188]

[0189] By introducing two auxiliary variables and where λ=[λ1,…,λ K ]、 ε=[ε1,…,ε K ]and Then, formula (14) can be converted to:

[0190]

[0191] Due to the coupling relationship between variables W, V and θ and the unit mode constraint of θ, The objective function is still non-convex and difficult to handle. Therefore, an iterative optimization scheme is proposed below to handle it.

[0192] Step 5: Use the alternating iterative algorithm to solve the optimization function and obtain the optimal BF vector W, AN vector V and phase shift θ.

[0193] S5.1. BS active beamforming and AN vector solution

[0194] Introduce two auxiliary variables and where α=[α1,…,α K ]、β=[β1,…,β K ]and Therefore, for a given θ [t] , can be restated as:

[0195]

[0196] in, because The objective function is non-smooth, so an auxiliary variable z is introduced. Rephrased as:

[0197]

[0198] Given that The numerator on the left side of the inequality is a DC function, which can be transformed into the following convex function through the first-order Taylor expansion approximation:

[0199]

[0200] Where [t] represents the tth iteration. Therefore, It can be restated as

[0201]

[0202] because and The variables W and V are coupled and There is a fraction constraint, so solve It is still very difficult. Next, we use the FP method to constrain the score Equivalently converted into a subtraction form. Obviously, the above formula satisfies and Then, introduce an auxiliary variable where ρ=[ρ1,…,ρ K ]and can be transformed into:

[0203]

[0204] therefore, can be restated as:

[0205]

[0206] Based on the above problem, the following two steps are used to solve it:

[0207] S5.1.1. Fix (W, V) and solve for ρ: First, fix the variables (W, V), and then solve for ρ; let:

[0208]

[0209] Then, the optimal solution It can be calculated as:

[0210]

[0211] S5.1.2. Fix ρ and solve (W,V): Since and The non-convex constraint of , after solving ρ, It is still difficult to handle. Introducing auxiliary variables δ=[δ1,…,δ K ],So can be transformed into:

[0212]

[0213] in, For α k δ k , we can get its upper bound as:

[0214]

[0215] According to the above formula, It can be transformed into the following convex constraint:

[0216]

[0217] Based on the above analysis, It can be restated as the following question:

[0218]

[0219] By introducing three auxiliary variables and in but It can be transformed into the following constraints:

[0220]

[0221] Similarly, the two inequalities in the middle of the above formula can be transformed into convex constraints as follows:

[0222]

[0223] Since the first and last inequalities in equation (30) are non-probabilistic constraints, the above BTI method cannot be used to solve them. For convenience, the equivalent estimated channel and estimated error vector of Eve are defined as:

[0224]

[0225] In order to eliminate the estimation error, the sphere boundary method can be used to Rewritten as:

[0226]

[0227] Among them, the Gaussian random vector Δe j satisfy:

[0228]

[0229] And the area radius ψ k satisfy:

[0230]

[0231] in, represents a chi-squared random variable with 2(MB+RN) degrees of freedom The inverse cumulative distribution function of ; So far, the closed form transformation process of the uncertainty domain has been basically completed. Therefore, the channel estimation error is expressed as:

[0232]

[0233] Given that the first and last inequalities in Eq. (30) and C4 have semi-infinite constraints, in order to obtain closed equivalence constraints, we first introduce the following lemma:

[0234] Lemma 2 (S-Procedure): Suppose there exists a function that satisfies:

[0235]

[0236] in, and If and only if there exists κ ≥ 0, the function satisfies:

[0237]

[0238] So Established.

[0239] For convenience, the first inequality in equation (30) is rewritten as:

[0240]

[0241] in,

[0242]

[0243] According to Lemma 2, and combined with Equations (36) and (39), we can obtain the following LMI:

[0244]

[0245] in, At the same time, the last inequality in equation (30) can be reformulated as:

[0246]

[0247] in,

[0248]

[0249] Similar to the transformation of Equation (41), Equation (42) is transformed into the following LMI:

[0250]

[0251] in,

[0252] Finally, the optimization problem can be Re-expressed as

[0253]

[0254] Obviously, except and The rank-one constraint of , the rest of the above problem are solvable convex constraints. Therefore, we can temporarily ignore the rank-one constraint and use the SDP technique to solve , and then use the Gaussian randomization method to obtain its rank-one solution.

[0255] S5.2 Solution of IRS Passive Beamforming

[0256] Define Q = θθ H and Then introduce two auxiliary variables and Based on the obtained W and V, rewrite the optimization problem by fixing (W, V) for:

[0257]

[0258] in, The element position (m,m) is 1, and the others are 0. In addition, and It can be found that due to The variable coupling and The semi-infinite constraint problem It is difficult to solve. Next, we use the Singular Value Decomposition (SVD) method to first Processing, GD k G H Rewrite as in and denote the corresponding singular values, left singular vectors, and right singular vectors respectively; then, Θ H GD k G H Θ can be reformulated as Next, rewrite it as follows:

[0259]

[0260] Among them, 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 in therefore, A in k and u k,j Can be converted into:

[0261]

[0262]

[0263] Next, C5 in equation (46) can be transformed into:

[0264]

[0265] Apply Lemma 2 to Use SVD method to process GW k G H and Converted into and in and are the corresponding singular values, left singular vectors, and right singular vectors; then, the following equations can be obtained:

[0266]

[0267] in, and Next, update equations (40) and (43) to obtain the following:

[0268]

[0269] at the same time, C W,k and C L,k Respectively from formula (52) and Make updates;

[0270] Finally, the question can be restated as:

[0271]

[0272] By removing The rank-one constraint and SDP technology are used. becomes an easily solvable convex problem. Similarly, when the solution When the rank-one constraint is not satisfied, Gaussian randomization can be used to Obtain a feasible solution θ * Based on the above analysis, the above solution process is summarized as Algorithm 1.

[0273] Table 1 Algorithms proposed based on non-ideal CSI

[0274]

[0275] For Algorithm 1, it is necessary to alternately optimize and solve two sub-problems and , until the result converges. Since the rank-one constraints have all been relaxed, and Both are convex optimization problems, and their KKT solutions can be guaranteed. In addition, due to the limited BS transmission power, the values ​​of W and V have upper bounds, and θ is bounded due to the unit modulus constraint, so The objective function of has an upper limit. Based on this, the SEE of Algorithm 1 should be monotonically non-decreasing and converge to at least a local optimal solution, which is verified by the following simulation results.

[0276] Analyze the computational complexity of Algorithm 1. , with equivalent B+3K+8KJ LMI constraints and K+KJ second-order cone constraints. Set the iteration accuracy to , then solve The computational complexity is approximately:

[0277]

[0278] in, represents the barrier parameter, for There are equivalent 2+RN+K+8KJ LMI constraints and K+KJ second-order cone constraints. Set the iteration accuracy to Then solve The computational complexity is approximately:

[0279]

[0280] in, Therefore, the total computational complexity of Algorithm 1 is in and

[0281] Simulation analysis: The performance of the proposed algorithm is evaluated through simulation results.

[0282] The simulation settings are B=2, R=2, K=2 and J=2. The heights of BS, IRS, user and Eve are 12m, 8m, 1.5m and 1.5m respectively, and their two-dimensional plane coordinates are (0m, 40(b-1)+30m), (65m, 40(r-1)+30m), (60m, 5(k-1)+30m) and (55m, 5(j-1)+32m). The number of each BS antenna and each IRS unit is M=2 and N=2 respectively. The maximum transmission power and power amplifier efficiency of each BS are set to P respectively. b =15dBm and ζ = 1 / 3. The channel model consists of large-scale and small-scale fading, where the large-scale fading model is as follows:

[0283]

[0284] Where d, L0, and υ represent the distance between the receiver and transmitter, the path loss with a reference distance of d0 = 1 m, and the path loss exponent, respectively. The small-scale fading model can be expressed as:

[0285]

[0286] in, and K′ represent the LoS path, NLoS path (Rayleigh fading component), and Rayleigh factor, respectively. is represented as in

[0287]

[0288] Among them, A r d r and A represents the number of antennas, antenna spacing and arrival angle of the receiver respectively. t d t and are the number of transmitter antennas, antenna spacing, and departure angle, respectively. The maximum safe interruption probability of the kth user is set to Furthermore, the maximum normalized error is defined as:

[0289]

[0290] Other parameter settings can be found in Table 2.

[0291] Table 2 Symbol parameter list

[0292]

[0293] To facilitate comparison, first define the following legend:

[0294] Ideal CSI: Maximize the SEE of the smallest user under ideal CSI;

[0295] Non-ideal CSI: Execute Algorithm 1 under non-ideal CSI to maximize the SEE of the minimum user.

[0296] Ideal CSI without IRS: Maximizes the SEE of the smallest user under the ideal CSI without IRS;

[0297] Non-ideal CSI without IRS: Execute Algorithm 1 under non-ideal CSI without IRS to maximize the SEE of the minimum user.

[0298] SSEEM: Sum SEE Maximization (SSEEM) scheme, which uses the minimum SEE of the user under ideal CSI as the metric;

[0299] Max-min SSE: This scheme maximizes the security spectrum efficiency of the minimum user, using the SEE of the minimum user under ideal CSI as the indicator.

[0300] (1) Relationship between SEE and number of iterations: Figure 2The convergence of the different schemes is shown. Clearly, the SEE of all schemes gradually increases before stabilizing after six iterations. Notably, the proposed "ideal CSI" and "non-ideal CSI" schemes exhibit higher SEEs than the "ideal CSI without IRS" and "non-ideal CSI without IRS" schemes, demonstrating the effectiveness of IRS in improving system SEE. Furthermore, the SEE of the "non-ideal CSI" scheme is slightly lower than that of the corresponding "ideal CSI" scheme, indicating that non-ideal CSI can lead to a certain loss in system performance.

[0301] (2) Relationship between SEE and BS transmission power: By drawing Figure 3 The relationship between SEE and BS transmit power under different schemes is shown. It can be seen that under the "Ideal CSI," "Non-Ideal CSI," "Ideal CSI without IRS," "Non-Ideal CSI without IRS," and "SSEEM" schemes, SEE gradually increases with increasing transmit power and then stabilizes. In contrast, the SEE curve for the "Max-minSSE" scheme shows a trend of first increasing and then decreasing. This can be explained by the fact that when BS transmit power is low, increasing transmit power can improve SE, thereby improving SEE. Conversely, when BS transmit power is high (e.g., greater than 20dBm), further increasing transmit power has very limited improvement in SE, resulting in no increase in maximum SEE. This trend is consistent with the curves for the "Ideal CSI," "Non-Ideal CSI," "Ideal CSI without IRS," "Non-Ideal CSI without IRS," and "SSEEM" schemes. It is worth noting that the "Max-min SSE" scheme aims to maximize the SE of the minimum user, so the SEE may decrease with increasing BS transmit power. Furthermore, it can be observed that the "Ideal CSI" scheme has the highest SEE. Moreover, the IRS-assisted scheme shows better performance in terms of SEE, which indicates the importance of IRS in improving SEE.

[0302] (3) Relationship between SEE and the number of IRS units N: Figure 4 The relationship between SEE and the number of IRS units under different schemes is shown. Figure 4 It can be observed that under the “ideal CSI” and “non-ideal CSI” schemes, the SEE increases with the increase in the number of IRS units. However, since the “Max-min SSE” scheme aims to maximize the SE of the minimum user, it only guarantees the increase of SE with the increase in the number of IRS units, so its SEE is unknown. Fortunately, Figure 4The SEE of the "Max-min SSE" scheme can still be improved as the number of IRS units increases. At the same time, as the number of IRS units increases, the "SSEEM" scheme aims to maximize the SEE. Under the premise of ensuring the increase of the total SEE, the SEE of the minimum user is unknown. For example, Figure 4 The SEE under the "SSEEM" scheme first increases and then slightly decreases with the increase in the number of IRS units. In addition, under the "Ideal CSI without IRS" and "Non-Ideal CSI without IRS" schemes, the SEE remains unchanged for any number of IRS units, which is in line with expectations.

[0303] (4) Relationship between SEE and the number of Eves J: Reset the positions of the j-th Eve and the k-th user to (60m, 8(k-1)+30m) and (55m, 4(j-1)+31m), respectively, and plot Figure 5 The relationship between the SEE and the number of Eves for the proposed schemes under different numbers of users is shown. The results show that the SEE for all schemes decreases with increasing numbers of Eves. This can be explained by the fact that more Eves lead to a higher eavesdropping rate, thus reducing the SEE accordingly. Furthermore, it can be seen that the SEE decreases with increasing numbers of users. This is because increasing the number of users increases the interference between users, which may also change the channel gain of the worst-case user, leading to a decrease in the SEE.

[0304] (5) Relationship between SEE and the number of BSs B: Here, the position of the b-th BS is reset to (0m, 15(b-1) + 20m) and plotted. Figure 6 The results show the relationship between SEE and the number of BSs, B. The results show that as the number of BSs increases, SEE first increases and then decreases. This is because increasing the number of BSs provides more power to users, which increases SEE, but also increases circuit power consumption. Therefore, when the number of BSs is large, the increased circuit power consumption actually leads to a decrease in SEE. This reveals that in real applications, there is a trade-off between SEE and the number of BSs (or SSE).

[0305] (6) Relationship between SEE and channel estimation error level: Figure 7The relationship between SEE and error level for different schemes is shown. The curve for the "Non-ideal CSI without outage" scheme is included as a baseline for comparison. The results show that the SEE for the "Non-ideal CSI," "Non-ideal CSI without IRS," and "Non-ideal CSI without outage" schemes decreases as the error level increases, which is understandable. Meanwhile, the SEE for the "Ideal CSI" scheme remains constant as the error level increases, which is expected. Furthermore, it can be observed that the SEE for the "Non-ideal CSI" scheme is lower than that for the "Non-ideal CSI without outage" scheme because the relaxed outage probability constraint provides more freedom in BF selection.

[0306] (7) Comparison of SEE fairness: Figure 8 In

[15] , the total SEE and minimum user SEE under different schemes were compared. The experiment increased the number of users to three and reset the user positions to (60m, 70m), (60m, 90m), and (60m, 120m), respectively. The results show that the total SEE of the "SSEEM" and "SSEEM with non-ideal CSI" schemes is relatively high, but the minimum user SEE is very low. In contrast, the total SEE of the scheme proposed in this invention is slightly lower than that of the "SSEEM" and "SSEEM with non-ideal CSI" schemes, but its minimum user SEE is relatively high. This can be explained as: the "SSEEM" scheme aims to maximize the total SEE, but sacrifices the SEE of the minimum user in exchange for an increase in the total SEE. However, the scheme proposed in this invention aims to maximize the SEE of the minimum user to ensure QoS and fairness for each user.

[0307] This paper investigates the SEE problem in IRS-assisted CF secure networks and jointly optimizes the design of the BS active BF, AN, and IRS passive BF to maximize or minimize user SEE. Furthermore, corresponding solutions are proposed for both ideal and non-ideal CSI conditions. Simulations demonstrate that the proposed solution outperforms existing solutions in terms of SEE. The results also reveal the relationship between SEE and the BS, IRS, user, Eve, BER, and transmit power. They demonstrate the trade-offs between system performance and overhead, and between SEE and SE, providing guidance for future applications of IRS-assisted CF secure networks.

[0308] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A smart reflector-assisted, secure, energy-efficient, and robust design method for decellularized networks, characterized in that: The steps are as follows: Step 1: Build a downlink IRS-assisted decellularized secure network, including B base stations, R IRSs, K single-antenna legitimate users, and J single-antenna Eves. Each base station has M antennas, and each IRS has N reflectors. Step 2: Obtain the security energy efficiency of each legitimate user based on the IRS-assisted decellularized security network; Each BS allocates a dedicated BF vector to each legitimate user, so the transmission signal x of the b-th BS is b Expressed as: in, represents the BF vector of the b-th BS for the k-th legal user, s k represents the transmission symbol of the kth legal user and satisfies {|s k | 2 }=1, represents the AN vector of the b-th BS to the k-th legal user; Therefore, the signals received by the kth legitimate user and the jth Eve who eavesdrops on their information are expressed as: Among them, y k represents the signal received by the kth legal user, It represents the signal received by the j-th Eve who eavesdrops on the k-th legitimate user information; represents the direct link channel from the bth BS to the kth legal user, denote the direct link channel from the bth BS to the jth Eve respectively; represents the reflection link channel from the bth BS to the rth IRS, represents the reflection link channel from the rth IRS to the kth user, represents the reflection link channel from the rth IRS to the jth Eve; represents the complex AWGN of the kth user, and the variance is represents the complex AWGN of the j-th Eve, and the variance is Θ r represents the phase shift matrix of the rth IRS and is denoted as Θ r =diag(θ r,1 ,…,θ r,N ), where |θ r,n |≤1 is the nth reflection unit of the rth IRS; the superscript H indicates the conjugate transpose; The expected signals of the kth legitimate user and the jth Eve who steals his information are expressed as: Among them, the definition θ r =diag(Θ r ), G=[G1,…,G B ]、 μ=[θ T ,1] T 、 and definition and Based on the above, the SR achievable by the k-th user can be expressed as: Among them, γ k represents the SINR of the kth legal user, γ k,j The SINR of the received signal of the j-th Eve who eavesdrops on the k-th legitimate user information is expressed as: The total power consumption of the kth user consists of transmission power and circuit power consumption, which can be expressed as: Where ζ represents the power amplifier efficiency, P c represents the circuit power consumption, and P c =BP B +P U +RNP R , P B 、P U and P R They represent the hardware power consumption of BS, user and IRS units respectively; finally, the SEE of the kth user is defined as: Step 3: Under the constraints of BS transmit power and the unit modulus of the IRS unit, an optimization function is constructed to maximize the security energy efficiency of the minimum legal user; Step 4: Based on non-ideal CSI conditions, the uncertain outage probability constraint in the optimization function is transformed into a certain outage probability constraint through the Bernstein inequality; Step 5: Use the alternating iterative algorithm to solve the optimization function and obtain the optimal BF vector W, AN vector V and phase shift θ.

2. The method for designing a secure, energy-efficient, and robust network in a smart reflective surface-assisted decellularized network according to claim 1, wherein: The optimization function to maximize the security energy efficiency of the minimum legal user is: Among them, P b represents the maximum transmit power of the b-th BS; B b is defined as:

3. The method for designing a secure, energy-efficient, and robust network in a smart reflective surface-assisted decellularized network according to claim 2, wherein: The specific implementation method of step four is: Define the achievable rate of the jth Eve eavesdropping on the kth user as R k,j , when R k,j Exceeding the redundancy rate When , a security interruption event of the kth user occurs at the BS; under the condition that the Eve link has non-ideal CSI, can be restated as: in, Denotes the maximum security interruption probability of the kth legal user, △h d,e,j Denotes the estimation error of the direct link channel, △f e,j represents the estimation error of the reflection link channel; First of all, Processing can be simplified to: in, △h j =△h d,e,j +G H Θ△f e,j and Assume there is a probability constraint that satisfies: in, and By introducing two slack variables λ and ε, the following relationship always holds: By definition and in and Then, formula (13) can be transformed into: in By introducing two auxiliary variables and where λ=[λ1,…,λ K ]、 ε=[ε1,…,ε K ]and Then, formula (14) can be converted to:

4. The method for designing a secure, energy-efficient, and robust network in a smart reflective surface-assisted decellularized network according to claim 3, wherein: The method for solving the optimization function using the alternating iterative algorithm is: S5.

1. BS active beamforming and AN vector solution Introduce two auxiliary variables and where α=[α1,…,α K ]、β=[β1,…,β K ]and Therefore, for a given θ [t] , can be restated as: in, Introducing an auxiliary variable z will Rephrased as: Approximate it by first-order Taylor expansion The numerator on the left side of the inequality is transformed into the following convex function: where [t] represents the tth iteration; therefore, It can be restated as Obviously, the above formula satisfies and Then, introduce an auxiliary variable where ρ=[ρ1,…,ρ K ]and can be transformed into: therefore, can be restated as: Based on the above problem, the following two steps are used to solve it: S5.1.

1. Fix (W, V) and solve for ρ: First, fix the variables (W, V), and then solve for ρ; let: Then, the optimal solution It can be calculated as: S5.1.

2. Solving (W,V) with Fixed ρ: Introducing Auxiliary Variables δ=[δ1,…,δ K ],So can be transformed into: in, For α k δ k , we can get its upper bound as: According to the above formula, It can be transformed into the following convex constraint: Based on the above analysis, It can be restated as the following question: By introducing three auxiliary variables and in χ=[χ1,…,χ K ]、 and but It can be transformed into the following constraints: Similarly, the two inequalities in the middle of the above formula can be transformed into convex constraints as follows: The equivalent estimated channel and estimated error vector of Eve are defined as: In order to eliminate the estimation error, the sphere boundary method can be used to Rewritten as: Among them, the Gaussian random vector △e j satisfy: And the area radius ψ k satisfy: in, represents a chi-squared random variable with 2(MB+RN) degrees of freedom The inverse cumulative distribution function of ; therefore, the channel estimation error is expressed as: Suppose there exists a function that satisfies: in, and If and only if there exists κ ≥ 0, the function satisfies: So Established; Rewrite the first inequality in equation (30) as: in, Combining Equation (36) and Equation (39), we can obtain the following LMI: in, At the same time, the last inequality in equation (30) can be reformulated as: in, Equation (42) is converted into the following LMI: in, Finally, the optimization problem can be Re-expressed as Solved using SDP technology Then the Gaussian randomization method is used to obtain its rank-one solution; S5.2 Solution of IRS Passive Beamforming Define Q = θθ H and Then introduce two auxiliary variables and Based on the obtained W and V, rewrite the optimization problem by fixing (W, V) for: in, The element position (m,m) is 1, and the others are 0. In addition, and Using the singular value decomposition method, we first Processing, GD k G H Rewrite as where x k,s 、 and denote the corresponding singular values, left singular vectors, and right singular vectors respectively; then, Θ H GD k G H Θ can be reformulated as Next, rewrite it as follows: Among them, 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 in therefore, A in k and u k,j Can be converted into: Next, we can use the formula (46) Converts to: Use SVD method to transform GW k G H and Converted into and in and are the corresponding singular values, left singular vectors, and right singular vectors; then, the following equations can be obtained: in, and Next, update equations (40) and (43) to obtain the following: at the same time, C W,k and C L,k Respectively from formula (52) and Make updates; Finally, the question can be restated as: By removing The rank-one constraint is solved by SDP technology; when the solution is obtained When the rank-one constraint is not satisfied, the Gaussian randomization method is used to select Obtain a feasible solution θ * .

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