RIS-assisted cellular-free large-scale MIMO network security energy efficiency optimization method

Abstract

The invention provides an RIS-assisted cellular-free large-scale MIMO network security energy efficiency optimization method. The method comprises the following steps: establishing an RIS-assisted cellular-free large-scale MIMO network model under a Rician fading channel; acquiring estimated channel state information of aggregation channels between the base station and the user equipment and between the base station and the eavesdropper by adopting a linear minimum mean square error estimation method; performing downlink channel data transmission based on the estimated channel state information; deriving a lower bound of a user reachable rate and an upper bound of an eavesdropper leakage rate according to a downlink channel data transmission result; deducing a safety reachable rate expression and a safety energy efficiency expression according to the lower bound of the user reachable rate and the upper bound of the eavesdropper leakage rate; based on the safety energy efficiency expression, a non-convex optimization problem containing RIS phase shift and power distribution is established, an iterative optimization algorithm is adopted for solving, and the iterative optimization algorithm decouples the original problem into an RIS phase shift optimization sub-problem and a power distribution optimization sub-problem for alternate solving until convergence is achieved to a local optimal solution meeting all constraints.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more particularly to a RIS-assisted method for optimizing the network energy efficiency of cellular-free massive MIMO networks. Background Technology

[0002] As wireless networks evolve towards 6G, the surge in data-intensive services has driven an urgent demand for high-speed traffic. Cellular-free massive MIMO networks, as an innovative architecture, serve users collaboratively through distributed access points, significantly reducing inter-cell interference and improving link robustness. However, the dense deployment of active access points also leads to high power consumption, posing a serious challenge to the long-term sustainable operation of the network.

[0003] RIS, as an emerging green communication technology, enhances signal coverage with extremely low energy consumption by passively controlling the electromagnetic wave propagation environment. Introducing RIS into non-cellular massive MIMO networks can effectively compensate for the high energy consumption caused by dense deployment, achieving a dual improvement in network spectral efficiency and energy efficiency, and providing a key path for the efficient and energy-saving operation of future networks.

[0004] The combination of RIS and non-cellular massive MIMO not only enhances the received signal of legitimate users through intelligent reflection but also effectively suppresses the signal reception capabilities of eavesdroppers, thereby significantly enhancing the physical layer security of the network. This collaborative architecture offers a highly promising solution to address the dual challenges of security and energy efficiency in future wireless networks.

[0005] While existing research has explored physical layer security in RIS-assisted non-cellular MIMO networks, systematic analysis and optimization of Security Efficiency (SEE) remains very limited, particularly in scenarios with multiple eavesdroppers and imperfect CSI. An accurate analytical framework and efficient joint resource allocation scheme are lacking to quantify and maximize the security efficiency of this architecture. Therefore, this study focuses on maximizing security efficiency in RIS-assisted non-cellular MIMO networks with multi-eavesdropper cooperation and imperfect CSI under Ricean fading channels. A complete performance analysis, theoretical derivation, and optimization algorithm are proposed, possessing significant theoretical value and practical application implications. Summary of the Invention

[0006] Based on the aforementioned problem of maximizing SEE in downlink RIS-assisted massive MIMO networks without cellular infrastructure and multiple eavesdroppers, this invention provides a RIS-assisted network security energy efficiency optimization method for massive MIMO networks without cellular infrastructure. First, uplink channel estimation is performed using the LMMSE method, in which all user equipment and eavesdroppers share the same pilot set. Based on imperfect channel state information, and by introducing artificial noise and coordinated beamforming precoding, closed-form lower bounds for SASR and SEE are derived, establishing an analytical performance benchmark. To solve the non-convex SEE maximization problem, a novel alternating optimization framework integrating Riemannian manifold optimization and path tracing algorithms is proposed. This method successfully transforms the original coupled problem into a series of tractable subproblems. Simulation results verify the superiority of the proposed alternating optimization algorithm in terms of performance and convergence robustness, achieving a significant SEE gain compared to the benchmark scheme.

[0007] The technical means employed in this invention are as follows:

[0008] A RIS-assisted energy efficiency optimization method for cellular-free massive MIMO network security includes: S1. Establish a RIS-assisted non-cellular large-scale MIMO network model under Ricean fading channel; S2. Based on the constructed non-cellular massive MIMO network model, uplink channel estimation is performed. The linear minimum mean square error estimation method is used to obtain the estimated channel state information of the aggregated channel between the base station and the single-antenna legitimate user equipment, and between the base station and the single-antenna eavesdropper. S3. Based on the estimated channel state information, downlink channel data transmission is performed. The base station uses conjugate beamforming to transmit signals to the single-antenna legitimate user equipment and injects artificial noise. The artificial noise is located in the null space of the single-antenna legitimate user channel state. S4. Based on the downlink channel data transmission results, derive the lower bound of the user's achievable rate and the upper bound of the eavesdropper's leakage rate; S5. Based on the lower bound of the user reachable rate and the upper bound of the eavesdropper leakage rate, derive the secure reachability and rate expression and the secure energy efficiency expression; S6. Based on the aforementioned safety and energy efficiency expression, establish a non-convex optimization problem involving RIS phase shift and power allocation, and solve it using an iterative optimization algorithm. The iterative optimization algorithm decouples the original problem into RIS phase shift optimization subproblems and power allocation optimization subproblems, which are solved alternately until they converge to a local optimum that satisfies all constraints.

[0009] Further, step S1 includes: S11, equipped with A base station (BS) with a uniform planar array, equipped with A smart reflective surface RIS of a uniform planar array A single-antenna legitimate user equipment (UE) and Each single-antenna eavesdropper Eve, equipped with one base station BS. Each antenna, and each smart reflector RIS, is composed of... It consists of several reflective units; S12. Connect all base stations (BS) to the central processing unit (CPU) via a high-speed backhaul link, and communicate with the CPU or neighboring base stations via wired or wireless links. The CPU coordinates the scheduling of all base stations (BS) and the intelligent reflector (RIS) to provide services to all single-antenna legitimate users in a cooperative manner, and maintains synchronization between nodes through a centralized algorithm executed by the CPU. S13. In a cellular-free massive MIMO network, all base stations (BS) and intelligent reflectors (RIS) cooperate to transmit confidential data to legitimate users with a single antenna. Therefore, an eavesdropper may attempt to eavesdrop on all... The confidential information of each user; it is assumed that all eavesdroppers are wirelessly connected to an eavesdropping fusion center, which is responsible for collecting and aggregating all eavesdropping signals; S14. Define the index set as follows: Represents the set of base stations (BS). Represents the set of Intelligent Reflector RIS. Represents a set of reflecting units. Represents the set of legal users with a single antenna. Indicates a group of eavesdroppers; S15. To accurately characterize the channel propagation characteristics between transceivers, both the direct link BS-UE / Eve and the reflected link BS-RIS-UE / Eve are considered, and it is assumed that each link corresponding to the transmission path of the direct link BS-UE / Eve and the reflected link BS-RIS-UE / Eve follows the Ricean fading model; therefore, from the... base stations To the individual users And from the base stations To the An eavesdropper The channels are represented as follows:

[0010]

[0011] in, and These represent large-scale path fading factors related to distance, which remain constant over multiple coherent time intervals; and The Rice factor represents the ratio of the intensity of the line-of-sight component to the intensity of the non-line-of-sight component; furthermore, express The line-of-sight component, express The line-of-sight component; express Non-line-of-sight components, express The non-line-of-sight components are assumed to be deterministic and prior known, while the non-line-of-sight components are modeled as Rayleigh fading, i.e. and ; By definition and Let be the effective channel fading coefficient, and define . and Given the mean vector, we obtain and .

[0012] The first base stations With the Each intelligent reflective surface The channel between, and the first Each intelligent reflective surface With the individual users , No. Each intelligent reflective surface With the An eavesdropper The channels between them are represented as follows:

[0013]

[0014]

[0015] in, , and Represents the large-scale fading coefficient. , and This represents the corresponding Rice factor; non-line-of-sight component. , and Corresponding to , and The Rayleigh distribution random part of the denominator, whose each element follows an independent and identically distributed complex Gaussian random distribution, i.e. Line-of-sight component , and Corresponding to , and The deterministic part; definition , and For each corresponding , and The effective channel coefficients are defined simultaneously. , and Its mean channel vector; S16. To characterize the line-of-sight component in the formula of step S15, a corresponding channel is constructed using a uniform rectangular planar array model, with a size of... The array response vector is represented as:

[0016] in, Represents the matrix Kronecker product. The azimuth angle representing the departure angle or the corresponding arrival angle. The pitch angle represents the departure angle or the corresponding arrival angle. S17. Assume the total number of antennas is... The array response vector along each coordinate axis is represented as:

[0017] in, Indicates along shaft or Number of antenna elements along the axial direction For carrier wavelength, This refers to the unit spacing; S18. Based on the array response vector defined in step S16, the line-of-sight channel along the reflection link BS-RIS-UE / Eve is represented as follows:

[0018]

[0019]

[0020] in, Indicates from arrive The azimuth angle of departure, Indicates from arrive The azimuth angle of departure, Indicates from arrive The pitch angle is the departure angle. Indicates from arrive The pitch angle and the departure angle; Indicates from arrive The azimuth and departure angle, Indicates from arrive The pitch angle and the launch angle; express from The azimuth angle and angle of arrival of the received signal. express from The elevation angle and angle of arrival of the received signal; Indicates from arrive The azimuth and departure angle, Indicates from arrive The azimuth and departure angle, Indicates from arrive pitch angle and launch angle from arrive The pitch angle and the launch angle; S19, will and Aggregation channels between and and The aggregation channel between them is represented as:

[0021]

[0022] in, express Phase shift vector, express The The reflection coefficient of each reflecting unit, where Let its phase value be defined; define the set of phase shifts for all RIS as . .

[0023] Further, step S2 includes: S21. In the downlink of a RIS-assisted non-cellular massive MIMO network using a time-division duplex protocol, the implementation of downlink precoding depends on the acquisition of channel state information (CSI). By utilizing the reciprocity between uplink and downlink channels, quasi-channel state information (CSI) can be efficiently obtained through uplink training. S22. During pilot-assisted channel estimation, all user equipment will simultaneously send their assigned pilot sequences to the base station. Each sequence contains... The symbol; since the pilot signals used in standardized communication networks are usually public and known, it is assumed that the eavesdropper has complete control over the pilot sequence information. The eavesdropper transmits the exact same pilot sequence as any legitimate user equipment, thereby launching a pilot spoofing attack.

[0024] S23, because it satisfies Therefore, pilot pollution, a common phenomenon in dense user scenarios, has been built into the network model; Indicates allocation to user equipment The orthogonality of the pilot sequences can be represented as follows: and ,in Representatives and user equipment A set of user equipment that share the same pilot signal; S24. Considering that user equipment and eavesdroppers may use different pilot transmission powers, the first... base stations The received pilot signal matrix is ​​represented as follows:

[0025] in, This indicates the transmit power used by the user equipment during the training phase. This indicates the transmission power used by the eavesdropper during the training phase. Item representation The additive white Gaussian noise matrix at point is modeled as independent and identically distributed random variables, following a distribution. In the pilot signal matrix formula, each eavesdropper, to enhance the information leakage effect, will intentionally send a random pilot sequence. Upon receiving the pilot signal matrix... back, Perform despreading operation to estimate aggregation channel The process is represented as:

[0026] in, , ; S25. Using the Linear Minimum Mean Square Error (LMMSE) estimation method, estimate the aggregation channel. Channel State Information (CSI):

[0027] S26, for derivation The closed-form LMMSE estimate is used to calculate the relevant statistical expectation and covariance matrix, i.e. , , and By utilizing the first and second-order statistical properties of complex Gaussian random variables and performing appropriate matrix operations, the analytical expression is derived as follows:

[0028]

[0029] in, , , , , , , , , , , , , , , , , , , , , ; S27. Substitute the two analytical expressions from step S26 into the formula from step S25 to obtain the... base stations With the individual users The closed-loop LMMSE estimate for the inter-channel aggregation is:

[0030] in, ; S28. Define the estimation error as... Channel estimation With estimation error Let be two uncorrelated random vectors that satisfy:

[0031]

[0032] in, , The expected value of the channel power is ,in .

[0033] Further, step S3 includes: S31. During the downlink transmission phase, all base stations simultaneously send data symbols to the user equipment and embed artificial noise superimposed on the downlink security signal to prevent eavesdropping without affecting the normal communication of the user equipment. S32. Each base station adopts conjugate beamforming technology and is based on the long-term power control coefficient. and The transmit power of each base station is allocated to the data symbols. and artificial noise symbols Above, among which and All have been normalized to meet the requirements. Accordingly, the first base stations The transmitted signal is represented as:

[0034] in, Transmission power allocated to useful data, and These correspond to the transmitted power of artificial noise and the beamforming vector, respectively. S33, according to the... base stations The transmitted signal, the first base stations The total transmit power is adjusted using a power control factor to ensure that it does not exceed the maximum permissible transmit power. That is, satisfying:

[0035] in, It is the Hadamard product of matrices. It is a matrix The Yes, and it satisfies:

[0036]

[0037]

[0038]

[0039] S34, based on the first base stations The transmitted signal will affect the user equipment. With eavesdroppers The signals received at each location are represented as follows:

[0040]

[0041] in, and They represent user equipment. and eavesdroppers The additive white Gaussian noise at the given location is defined as follows:

[0042]

[0043]

[0044] .

[0045] Furthermore, in step S4, for RIS-assisted non-cellular massive MIMO networks under Ricean fading channels, and under the conditions of multiple colluding eavesdroppers and incomplete channel state information, the total achievable safe rate (SASR) and security efficiency (SEE) are analyzed, including: S41. Establish lower bounds on user reachability and rate, specifically including: In RIS-assisted cellular massive MIMO networks, the "use-and-then-forget" (UatF) delimitation technique is employed to obtain closed-form lower bound expressions for user equipment and rates. This method is particularly effective when it is assumed that the base station only possesses large-scale channel statistics rather than instantaneous channel realization. Within this framework, deterministic equivalent terms... The effective channel gain is considered to be fully known to the receiver; therefore, the user equipment... The signal received at the location The equivalent expression is:

[0046] in, Represents the desired signal component. Corresponding to beamforming uncertainty, This indicates user-to-user interference originating from other user devices. Interference introduced by artificial noise. For noise interference; The reachability and speed of user equipment are expressed as:

[0047] in, This is a preprocessing factor used to represent the preprocessing parameters in the allocation process. After pilot training with each symbol, the coherence interval The proportion used for data transmission, user equipment The corresponding effective signal-to-interference-plus-noise ratio (SINR) is expressed as:

[0048] via user equipment From all the expected values ​​in the corresponding effective signal-to-interference-plus-noise ratio formula, the closed-form expression for the downlink achievable sum rate when all legitimate user equipment adopts the conjugate beamforming scheme is derived as follows:

[0049]

[0050] in, Represents the defined matrix The To simplify the symbolic representation in subsequent derivations, an auxiliary function is defined as follows: The remaining parameters are defined as follows:

[0051]

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[0070] in, The function is defined as if but Otherwise Its complement function is ; Based on the closed-form expression for downlink reachability and rate, the closed-form expression for downlink reachability and rate when all legitimate user equipment adopts the conjugate beamforming scheme is equivalently expressed as:

[0071] in, , , , , , , , , , , , ; S42. Establish an upper bound on the eavesdropper leakage rate, specifically including: Assuming all eavesdroppers have complete knowledge of the instantaneous channel information and simultaneously eavesdrop on all legitimate user equipment, in this scenario, all eavesdroppers connect to a centralized eavesdropping fusion center. This center uses maximum ratio combining (MRC) technology to coherently combine the received signals, applying the UatF method to the eavesdroppers. In the received signal, the leakage rate and SINR of all eavesdroppers coexisting are expressed as:

[0072]

[0073] By calculating all the expected values ​​in the above formula, we obtain the leakage rate expression for multiple eavesdroppers using the maximum ratio merging technique:

[0074]

[0075] in:

[0076]

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[0094] Based on the leakage rate expression, the closed-form expression for the leakage rate of all eavesdroppers when using the maximum ratio merging technique is equivalently written as:

[0095] in, , , , , , , , , , , , , , , , .

[0096] Further, step S5 includes: S51. Express the lower bound of SASR in a subtraction form:

[0097] The ramp function is defined as follows: ; S52, The total power consumption of the RIS-assisted non-cellular massive MIMO network is modeled as follows:

[0098] in, , , The first item in the table represents the total transmit power consumption of all base stations, where express The power amplifier efficiency; the second term correspond The power consumption of the backhaul link required to transmit data to the central processing unit, of which It is the first Fixed power consumption of the backhaul link, It is system bandwidth. Indicates dynamic power consumption related to flow rate; the third term Indicates static circuit power consumption, including The Antenna power consumption , The Power consumption of each reflector unit as well as power consumption ; S53. To simplify the expression in the subsequent derivation, the total power consumption of the RIS-assisted non-cellular massive MIMO network is equivalently rewritten as:

[0099] in, , , ; S54. Based on the formula in step S51 and the rewritten total power consumption formula, the spectral efficiency is defined as:

[0100] S55. Substitute the reachable rate of legitimate users, the leakage rate of eavesdropping users, and the rewritten total power consumption into the formula and spectrum efficiency formula in step S51 to obtain closed expressions for the lower bounds of SASR and SEE.

[0101] Further, step S6 includes: S61. For safety and energy efficiency optimization methods, develop an efficient resource allocation framework aimed at maximizing SEE and optimizing the joint adjustment of RIS phase shift. and the power control coefficients of the data signal and the artificial noise signal. The overall optimization problem can be described as follows:

[0102]

[0103]

[0104]

[0105]

[0106] Among them, formula Apply unity modulus constraints to all RIS, formula Ensure that the transmit power of each base station does not exceed the maximum limit. ,formula and The reachability rate for each legitimate user must not be lower than the minimum threshold. And the leakage rate of each eavesdropper does not exceed the upper limit. ; S62. Establish a non-convex optimization problem for RIS phase shifting, specifically including: By employing the Augmented Lagrange Multiplier (ALM) method, This is transformed into an unconstrained optimization problem on a Riemannian manifold, where inequality constraints are incorporated into the objective function as penalty terms. Therefore, The restatement is as follows:

[0107] Among them, the penalty parameter ,vector Let represent the Lagrange multiplier vector, and the remaining parameters are defined as follows:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] question This is an unconstrained optimization problem defined on a manifold. It is efficiently solved using the steepest descent method from the Manopt toolbox. The Riemann gradient of the objective function is calculated, serving as the Euclidean gradient's counterpart on the manifold. The Riemann gradient is obtained by projecting the Euclidean gradient onto the tangent space of the manifold. Therefore, the following derivation is made: The Euclidean gradient is:

[0117] in:

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[0126] Among them, indicator function exist Time equals Otherwise ; The Riemann gradient can be obtained by mapping the derived Euclidean gradient onto the tangent space of the manifold using projection operations, as shown in the following expression:

[0127] After obtaining the Riemann gradient, it is used as the descent direction to iteratively optimize the control variables. Updates are achieved through a pullback operation, which maps candidate points from the tangent space back to the manifold, thus maintaining geometric feasibility throughout the optimization process.

[0128] in, Indicates the step size; S63. Establish a non-convex optimization problem for power allocation, specifically including: For a given By introducing auxiliary variables , as well as ,in , will optimize the problem Equivalently reconstructed as:

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[0130]

[0131]

[0132]

[0133]

[0134] in, , , , , , ; During the inspection At that time, the path tracing (PF) algorithm was introduced, and the operator was... relaxation And by applying a multidimensional quadratic transformation, the objective function in convex approximation form is obtained:

[0135] in, ; Using convex inequalities, the formula can be... The non-convex constraint in the equation is approximated by its convex counterpart:

[0136]

[0137] in, ; Using convex inequalities, the constraint formulas Approximately expressed as:

[0138] in, ; By combining the chain rule with a first-order Taylor expansion, the formula is... The non-convex constraint in the equation is approximately transformed into the following convex form:

[0139] in, ; Further, under the PF framework The The next iteration is expressed as:

[0140] Finally, the PF optimization algorithm is used to solve the problem. Solve the problem; S64. Local optimal phase shift obtained based on IALMO algorithm The local optimal power control coefficients calculated by the PF algorithm An iterative optimization (AO) framework was constructed to solve the problem. By alternately solving the RIS phase shift optimization subproblem and the power allocation optimization subproblem, the algorithm is iteratively updated. and This continues until the network energy efficiency converges to a local maximum.

[0141] Compared with the prior art, the present invention has the following advantages: 1. This invention establishes a SEE analysis framework for RIS-assisted non-cellular MIMO networks by comprehensively considering Ricean fading channels, imperfect channel state information, and multi-eavesdropper cooperation scenarios, breaking through the limitation of existing research that mostly relies on ideal channels.

[0142] 2. By employing conjugate beamforming and artificial noise injection, this invention derives strictly closed-form expressions for the lower bound of the reachable rate of legitimate users and the upper bound of the information leakage rate of eavesdroppers, thereby obtaining high-precision closed-form expressions for SASR and SEE, laying a theoretical foundation for rapid evaluation and optimization of network performance.

[0143] 3. For the complex non-convex problem of SEE maximization, this invention innovatively proposes an efficient alternating optimization framework, which decouples the original problem into RIS phase shift optimization (using Riemannian manifold optimization and augmented Lagrangian method) and base station power allocation optimization (using path tracing and successive convex approximation), effectively solving the optimization problem.

[0144] 4. The simulation results not only verified the accuracy of the theoretical analysis and the superiority of the algorithm, but also revealed the non-monotonic relationship (i.e., the existence of an optimal configuration point) between security energy efficiency and key parameters such as the number of antennas, the number of RIS units, and the transmit power. This provides important design guidance for the hardware configuration and resource allocation of actual networks.

[0145] Based on the above reasons, this invention can be widely applied in fields such as wireless communication. Attached Figure Description

[0146] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0147] Figure 1 This is a flowchart of the method of the present invention.

[0148] Figure 2 The solution of this invention is applicable to RIS-assisted non-cellular massive MIMO networks with multiple eavesdroppers.

[0149] Figure 3 This is a simulation scene diagram to which the solution of this invention applies.

[0150] Figure 4 Provided for embodiments of the present invention and Simulation diagram showing the relationship between achievable speed and downlink transmission power when using RPS and FPT schemes under certain conditions.

[0151] Figure 5 Provided for embodiments of the present invention and Simulation diagram showing the relationship between network energy efficiency and downlink transmission power when using RPS and FPT schemes under certain conditions.

[0152] Figure 6 Provided for embodiments of the present invention , and Simulation diagram of the cumulative distribution function of network energy efficiency under the given conditions.

[0153] Figure 7 Provided for embodiments of the present invention , and Simulation diagram showing the relationship between network energy efficiency and iteration number under certain conditions.

[0154] Figure 8 Provided for embodiments of the present invention and Simulation diagram showing the relationship between network energy efficiency and the number of base station antennas and RIS units under certain conditions. Detailed Implementation

[0155] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0156] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0157] like Figure 1 As shown, this invention provides a RIS-assisted energy efficiency optimization method for cellular-free massive MIMO network security, comprising: S1. Establish a RIS-assisted non-cellular large-scale MIMO network model under Ricean fading channel; S2. Based on the constructed non-cellular massive MIMO network model, uplink channel estimation is performed. The linear minimum mean square error estimation method is used to obtain the estimated channel state information of the aggregated channel between the base station and the single-antenna legitimate user equipment, and between the base station and the single-antenna eavesdropper. S3. Based on the estimated channel state information, downlink channel data transmission is performed. The base station uses conjugate beamforming to transmit signals to the single-antenna legitimate user equipment and injects artificial noise. The artificial noise is located in the null space of the single-antenna legitimate user channel state. S4. Based on the downlink channel data transmission results, derive the lower bound of the user's achievable rate and the upper bound of the eavesdropper's leakage rate; S5. Based on the lower bound of the user reachable rate and the upper bound of the eavesdropper leakage rate, derive the secure reachability and rate expression and the secure energy efficiency expression; S6. Based on the aforementioned safety and energy efficiency expression, establish a non-convex optimization problem involving RIS phase shift and power allocation, and solve it using an iterative optimization algorithm. The iterative optimization algorithm decouples the original problem into RIS phase shift optimization subproblems and power allocation optimization subproblems, which are solved alternately until they converge to a local optimum that satisfies all constraints.

[0158] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11, equipped with A base station (BS) with a uniform planar array, equipped with A smart reflective surface RIS of a uniform planar array A single-antenna legitimate user equipment (UE) and Each single-antenna eavesdropper Eve, equipped with one base station BS. Each antenna, and each smart reflector RIS, is composed of... It consists of several reflective units; S12. Connect all base stations (BS) to the central processing unit (CPU) via a high-speed backhaul link, and communicate with the CPU or neighboring base stations via wired or wireless links. The CPU coordinates the scheduling of all base stations (BS) and the intelligent reflector (RIS) to provide services to all single-antenna legitimate users in a cooperative manner, and maintains synchronization between nodes through a centralized algorithm executed by the CPU. S13. In a cellular-free massive MIMO network, all base stations (BS) and intelligent reflectors (RIS) cooperate to transmit confidential data to legitimate users with a single antenna. Therefore, an eavesdropper may attempt to eavesdrop on all... The confidential information of each user; it is assumed that all eavesdroppers are wirelessly connected to an eavesdropping fusion center, which is responsible for collecting and aggregating all eavesdropping signals; S14. Define the index set as follows: Represents the set of base stations (BS). Represents the set of Intelligent Reflector RIS. Represents a set of reflecting units. Represents the set of legal users with a single antenna. Indicates a group of eavesdroppers; S15. To accurately characterize the channel propagation characteristics between transceivers, both the direct link BS-UE / Eve and the reflected link BS-RIS-UE / Eve are considered, and it is assumed that each link corresponding to the transmission path of the direct link BS-UE / Eve and the reflected link BS-RIS-UE / Eve follows the Ricean fading model; therefore, from the... base stations To the individual users And from the base stations To the An eavesdropper The channels are represented as follows:

[0159]

[0160] in, and These represent large-scale path fading factors related to distance, which remain constant over multiple coherent time intervals; and The Rice factor represents the ratio of the intensity of the line-of-sight component to the intensity of the non-line-of-sight component; furthermore, express The line-of-sight component, express The line-of-sight component; express Non-line-of-sight components, express The non-line-of-sight components are assumed to be deterministic and prior known, while the non-line-of-sight components are modeled as Rayleigh fading, i.e. and ; By definition and Let be the effective channel fading coefficient, and define . and Given the mean vector, we obtain and .

[0161] The first base stations With the Each intelligent reflective surface The channel between, and the first Each intelligent reflective surface With the individual users , No. Each intelligent reflective surface With the An eavesdropper The channels between them are represented as follows:

[0162]

[0163]

[0164] in, , and Represents the large-scale fading coefficient. , and This represents the corresponding Rice factor; non-line-of-sight component. , and Corresponding to , and The Rayleigh distribution random part of the denominator, whose each element follows an independent and identically distributed complex Gaussian random distribution, i.e. Line-of-sight component , and Corresponding to , and The deterministic part; definition , and For each corresponding , and The effective channel coefficients are defined simultaneously. , and Its mean channel vector; S16. To characterize the line-of-sight component in the formula of step S15, a corresponding channel is constructed using a uniform rectangular planar array model, with a size of... The array response vector is represented as:

[0165] in, Represents the matrix Kronecker product. The azimuth angle representing the departure angle or the corresponding arrival angle. The pitch angle represents the departure angle or the corresponding arrival angle. S17. Assume the total number of antennas is... The array response vector along each coordinate axis is represented as:

[0166] in, Indicates along shaft or Number of antenna elements along the axial direction For carrier wavelength, Let the element spacing be ; for simplicity, assume the element spacing is . .

[0167] S18. Based on the array response vector defined in step S16, the line-of-sight channel along the reflection link BS-RIS-UE / Eve is represented as follows:

[0168]

[0169]

[0170] in, Indicates from arrive The azimuth angle of departure, Indicates from arrive The azimuth angle of departure, Indicates from arrive The pitch angle is the departure angle. Indicates from arrive The pitch angle and the departure angle; Indicates from arrive The azimuth and departure angle, Indicates from arrive The pitch angle and the launch angle; express from The azimuth angle and angle of arrival of the received signal. express from The elevation angle and angle of arrival of the received signal; Indicates from arrive The azimuth and departure angle, Indicates from arrive The azimuth and departure angle, Indicates from arrive pitch angle and launch angle from arrive The pitch angle and the launch angle; S19, will and Aggregation channels between and and The aggregation channel (including direct links and RIS-assisted cascaded links) is represented as follows:

[0171]

[0172] in, express Phase shift vector, express The The reflection coefficient of each reflecting unit, where Let its phase value be defined; define the set of phase shifts for all RIS as . .

[0173] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: S21. In the downlink of a RIS-assisted non-cellular massive MIMO network using a time-division duplex protocol, the implementation of downlink precoding depends on the acquisition of channel state information (CSI). By utilizing the reciprocity between uplink and downlink channels, quasi-channel state information (CSI) can be efficiently obtained through uplink training. S22. During pilot-assisted channel estimation, all user equipment will simultaneously send their assigned pilot sequences to the base station. Each sequence contains... The symbol; since the pilot signals used in standardized communication networks are usually public and known, it is assumed that the eavesdropper has complete control over the pilot sequence information. The eavesdropper transmits the exact same pilot sequence as any legitimate user equipment, thereby launching a pilot spoofing attack.

[0174] S23, because it satisfies Therefore, pilot pollution, a common phenomenon in dense user scenarios, has been built into the network model; Indicates allocation to user equipment The orthogonality of the pilot sequences can be represented as follows: and ,in Representatives and user equipment A set of user equipment sharing the same pilot signal (including user equipment) itself); S24. Considering that user equipment and eavesdroppers may use different pilot transmission powers, the first... base stations The received pilot signal matrix is ​​represented as follows:

[0175] in, This indicates the transmit power used by the user equipment during the training phase. This indicates the transmission power used by the eavesdropper during the training phase. Item representation The additive white Gaussian noise matrix at point is modeled as independent and identically distributed random variables, following a distribution. It is worth noting that in the pilot signal matrix formula, each eavesdropper, in order to enhance the information leakage effect, will deliberately send a random pilot sequence. Upon receiving the pilot signal matrix... back, Perform despreading operation to estimate aggregation channel The process is represented as:

[0176] in, , ; S25. Using the Linear Minimum Mean Square Error (LMMSE) estimation method, estimate the aggregation channel. Channel State Information (CSI):

[0177] S26, for derivation The closed-form LMMSE estimate is used to calculate the relevant statistical expectation and covariance matrix, i.e. , , and By utilizing the first and second-order statistical properties of complex Gaussian random variables and performing appropriate matrix operations, the analytical expression is derived as follows:

[0178]

[0179] in, , , , , , , , , , , , , , , , , , , , , ; S27. Substitute the two analytical expressions from step S26 into the formula from step S25 to obtain the... base stations With the individual users The closed-loop LMMSE estimate for the inter-channel aggregation is:

[0180] in, ; S28. Define the estimation error as... Channel estimation With estimation error Let be two uncorrelated random vectors that satisfy:

[0181]

[0182] in, , The expected value of the channel power is ,in .

[0183] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31. During the downlink transmission phase, all base stations simultaneously send data symbols to the user equipment and embed artificial noise superimposed on the downlink security signal to prevent eavesdropping without affecting the normal communication of the user equipment. S32. Each base station adopts conjugate beamforming technology and is based on the long-term power control coefficient. and The transmit power of each base station is allocated to the data symbols. and artificial noise symbols Above, among which and All have been normalized to meet the requirements. Accordingly, the first base stations The transmitted signal is represented as:

[0184] in, Transmission power allocated to useful data, and These correspond to the transmitted power of artificial noise and the beamforming vector, respectively. S33, according to the... base stations The transmitted signal, the first base stations The total transmit power is adjusted using a power control factor to ensure that it does not exceed the maximum permissible transmit power. That is, satisfying:

[0185] in, It is the Hadamard product of matrices. It is a matrix The Yes, and it satisfies:

[0186]

[0187]

[0188]

[0189] S34, based on the first base stations The transmitted signal will affect the user equipment. With eavesdroppers The signals received at each location are represented as follows:

[0190]

[0191] in, and They represent user equipment. and eavesdroppers The additive white Gaussian noise at the given location is defined as follows:

[0192]

[0193]

[0194] .

[0195] In a preferred embodiment of this invention, step S4, for a RIS-assisted non-cellular massive MIMO network under Ricean fading channels, and under conditions of multiple colluding eavesdroppers and incomplete channel state information, analyzes the Total Secure Rate (SASR) and Secure Energy Efficiency (SEE). To this end, lower bounds for legitimate user equipment and rates, and upper bounds for the amount of information leaked to eavesdroppers, are first established. Based on these results, the secure reachability and rate are characterized in closed-form by quantifying the traversal rate difference between legitimate links and eavesdropping links. Furthermore, combined with the total power consumption model, an analytical expression for SEE is derived. The proposed formula is universal and applicable to any finite antenna array and Ricean fading conditions, providing a unified analytical framework for evaluating the security performance of practical RIS-assisted non-cellular massive MIMO networks, including: S41. Establish lower bounds on user reachability and rate, specifically including: In RIS-assisted cellular massive MIMO networks, the "use-and-then-forget" (UatF) delimitation technique is employed to obtain closed-form lower bound expressions for user equipment and rates. This method is particularly effective when it is assumed that the base station only possesses large-scale channel statistics rather than instantaneous channel realization. Within this framework, deterministic equivalent terms... The effective channel gain is considered to be fully known to the receiver; therefore, the user equipment... The signal received at the location The equivalent expression is:

[0196] in, Represents the desired signal component. Corresponding to beamforming uncertainty, This indicates user-to-user interference originating from other user devices. Interference introduced by artificial noise. For noise interference; The reachability and speed of user equipment are expressed as:

[0197] in, This is a preprocessing factor used to represent the preprocessing parameters in the allocation process. After pilot training with each symbol, the coherence interval The proportion used for data transmission, user equipment The corresponding effective signal-to-interference-plus-noise ratio (SINR) is expressed as:

[0198] via user equipment From all the expected values ​​in the corresponding effective signal-to-interference-plus-noise ratio formula, the closed-form expression for the downlink achievable sum rate when all legitimate user equipment adopts the conjugate beamforming scheme is derived as follows:

[0199]

[0200] in, Represents the defined matrix The To simplify the symbolic representation in subsequent derivations, an auxiliary function is defined as follows: The remaining parameters are defined as follows:

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219]

[0220] in, The function is defined as if but Otherwise Its complement function is ; Based on the closed-form expression for downlink reachability and rate, the closed-form expression for downlink reachability and rate when all legitimate user equipment adopts the conjugate beamforming scheme is equivalently expressed as:

[0221] in, , , , , , , , , , , , ; S42. Establish an upper bound on the eavesdropper leakage rate, specifically including: Assuming all eavesdroppers have complete knowledge of the instantaneous channel information and simultaneously eavesdrop on all legitimate user equipment, in this scenario, all eavesdroppers connect to a centralized eavesdropping fusion center. This center uses maximum ratio combining (MRC) technology to coherently combine the received signals, applying the UatF method to the eavesdroppers. In the received signal, the leakage rate and SINR of all eavesdroppers coexisting are expressed as:

[0222]

[0223] By calculating all the expected values ​​in the above formula, we obtain the leakage rate expression for multiple eavesdroppers using the maximum ratio merging technique:

[0224]

[0225] in:

[0226]

[0227]

[0228]

[0229]

[0230]

[0231]

[0232]

[0233]

[0234]

[0235]

[0236]

[0237]

[0238]

[0239]

[0240]

[0241]

[0242]

[0243]

[0244] Based on the leakage rate expression, the closed-form expression for the leakage rate of all eavesdroppers when using the maximum ratio merging technique is equivalently written as:

[0245] in, , , , , , , , , , , , , , , , .

[0246] In a specific implementation, as a preferred embodiment of the present invention, step S5 includes: S51. Express the lower bound of SASR in a subtraction form:

[0247] The ramp function is defined as follows: ; S52, The total power consumption of the RIS-assisted non-cellular massive MIMO network is modeled as follows:

[0248] in, , , The first item in the table represents the total transmit power consumption of all base stations, where express The power amplifier efficiency; the second term correspond The power consumption of the backhaul link required to transmit data to the central processing unit, of which It is the first Fixed power consumption of the backhaul link, It is system bandwidth. The third item represents the dynamic power consumption related to flow rate (unit: W / Gbits / s). Indicates static circuit power consumption, including The Antenna power consumption , The Power consumption of each reflector unit as well as power consumption ; S53. To simplify the expression in the subsequent derivation, the total power consumption of the RIS-assisted non-cellular massive MIMO network is equivalently rewritten as:

[0249] in, , , ; S54. Based on the formula in step S51 and the rewritten total power consumption formula, the spectral efficiency is defined as:

[0250] S55. Substitute the reachable rate of legitimate users, the leakage rate of eavesdropping users, and the rewritten total power consumption into the formula and spectrum efficiency formula in step S51 to obtain closed expressions for the lower bounds of SASR and SEE.

[0251] In a specific implementation, as a preferred embodiment of the present invention, step S6 includes: S61. For safety and energy efficiency optimization methods, develop an efficient resource allocation framework aimed at maximizing SEE and optimizing the joint adjustment of RIS phase shift. and the power control coefficients of the data signal and the artificial noise signal. The overall optimization problem can be described as follows:

[0252]

[0253]

[0254]

[0255]

[0256] Among them, formula Apply unity modulus constraints to all RIS, formula Ensure that the transmit power of each base station does not exceed the maximum limit. ,formula and The reachability rate for each legitimate user must not be lower than the minimum threshold. And the leakage rate of each eavesdropper does not exceed the upper limit. Since the objective function and multiple constraints are non-convex, direct solution... This is extremely difficult. To effectively address this challenge, an alternating optimization method is employed, iteratively optimizing sequentially. and This iterative process will continue until it converges to a local optimum that satisfies all constraints; S62. Establish a non-convex optimization problem for RIS phase shifting, specifically including: Manifold-based optimization is an advanced technique with low computational complexity, making it suitable for solving problems. (in fixed) When the value is obtained, the optimal solution is obtained. An effective method. Specifically, by employing the Augmented Lagrange Multiplier (ALM) technique, the... This is transformed into an unconstrained optimization problem on a Riemannian manifold, where inequality constraints are incorporated into the objective function as penalty terms. Therefore, The restatement is as follows:

[0257] Among them, the penalty parameter ,vector Let represent the Lagrange multiplier vector, and the remaining parameters are defined as follows:

[0258]

[0259]

[0260]

[0261]

[0262]

[0263]

[0264]

[0265]

[0266] question This is an unconstrained optimization problem defined on a manifold. It is efficiently solved using the steepest descent method from the Manopt toolbox. The Riemann gradient of the objective function is calculated, serving as the Euclidean gradient's counterpart on the manifold. The Riemann gradient is obtained by projecting the Euclidean gradient onto the tangent space of the manifold. Therefore, the following derivation is made: The Euclidean gradient is:

[0267] in:

[0268]

[0269]

[0270]

[0271]

[0272]

[0273]

[0274]

[0275]

[0276] Among them, indicator function exist Time equals Otherwise ; The Riemann gradient can be obtained by mapping the derived Euclidean gradient onto the tangent space of the manifold using projection operations, as shown in the following expression:

[0277] After obtaining the Riemann gradient, it is used as the descent direction to iteratively optimize the control variables. Updates are achieved through a pullback operation, which maps candidate points from the tangent space back to the manifold, thus maintaining geometric feasibility throughout the optimization process.

[0278] in, Indicates the step size; In this embodiment, an Iterative Enhanced Lagrange Manifold Optimization (IALMO) method is developed to adjust the RIS phase shift to maximize SEE. The algorithm iteratively calculates the Euclidean gradient using the Euclidean gradient formula, solves for the corresponding Riemann gradient using the Riemann gradient formula, performs a pullback step, and updates the Lagrange multipliers in the IALMO method. These operations are repeated until convergence. The truncation operator is defined as... ;

[0279] S63. Establish a non-convex optimization problem for power allocation, specifically including: For a given By introducing auxiliary variables , as well as ,in , will optimize the problem Equivalently reconstructed as:

[0280]

[0281]

[0282]

[0283]

[0284]

[0285] in, , , , , , ; During the inspection At that time, the path tracing (PF) algorithm was introduced, and the operator was... relaxation And by applying a multidimensional quadratic transformation, the objective function in convex approximation form is obtained:

[0286] in, ; Using convex inequalities, the formula can be... The non-convex constraint in the equation is approximated by its convex counterpart:

[0287]

[0288] in, ; Using convex inequalities, the constraint formulas Approximately expressed as:

[0289] in, ; By combining the chain rule with a first-order Taylor expansion, the formula is... The non-convex constraint in the equation is approximately transformed into the following convex form:

[0290] in, ; Further, under the PF framework The The next iteration is expressed as:

[0291] Finally, the PF optimization algorithm is used to solve the problem. Solve the problem;

[0292] S64. Local optimal phase shift obtained based on IALMO algorithm The local optimal power control coefficients calculated by the PF algorithm An iterative optimization (AO) framework was constructed to solve the problem. By alternately solving the RIS phase shift optimization subproblem and the power allocation optimization subproblem, the algorithm is iteratively updated. and This continues until the network energy efficiency converges to a local maximum.

[0293]

[0294] Example To verify the effectiveness of the present invention, the following simulation experiments were conducted: The specific simulation parameters for the RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security are as follows: The simulation study is based on a RIS-assisted cellular-free massive MIMO network scenario, in which... A BS in With the assistance of a RIS Provide services to individual users, while Each Eve eavesdrops on all UEs. The base station and RIS are deployed in fixed locations, and the UEs and Eves... Figure 3 The components are evenly and independently distributed within the circular area shown.

[0295] Large-scale path loss is modeled as a distance-dependent model: , , , as well as ,in This represents the corresponding spatial distance. For large-scale fading, the angle of arrival and departure angle of the line-of-sight link independently and uniformly change from... Interval extraction, all Rice factors are uniformly set to .

[0296] To conduct a comprehensive performance evaluation, the invention employs three benchmark schemes: 1. Random Phase Shift (RPS), among which... from Uniform sampling; 2. Full power transfer (FPT) without artificial noise, wherein and 3. A genetic algorithm (GA) was used to jointly optimize the RIS phase shift and power control coefficients. The remaining simulation parameters are summarized in Table 1.

[0297] Table 1 Simulation Parameters

[0298] Given that the analytical security performance boundary derived in step S4 is a core tool for network design, we first verify its performance at user reachable rates. Information leakage rate and network security reachability and speed ( Figure 4 ) and SEE ( Figure 5 The accuracy of these closed boundaries is examined. These closed boundaries are compared with Monte Carlo simulation results to investigate their performance under RPS and FPT schemes as downlink transmission power (…). The forms of change are shown. All indicators show a high degree of agreement, verifying the accuracy of the derived analytical expression and supporting its reliability for subsequent SEE optimization. For example... Figure 4 As shown, the rate , and All values ​​monotonically increase with downlink transmission power, eventually approaching a saturation limit. This trend indicates that while increasing downlink power can improve the desired performance, it also increases the overall performance of the transmission. However, this will also exacerbate the unfavorable situation. ,lead to It exhibits asymptotic characteristics. Furthermore, Figure 4 The display shows an increase in uplink pilot power ( This can significantly improve secure rate performance, highlighting the importance of channel estimation accuracy. The key impact. Finally. Figure 5 This reflects that SEE first peaks as downlink transmission power increases, and then declines. This indicates that while excessive transmission power can bring marginal gains in safety capacity, it will significantly increase energy consumption, ultimately leading to a decrease in SEE, thus emphasizing the necessity of optimal resource allocation.

[0299] Figure 6 and Figure 7 The proposed solution algorithm was comprehensively evaluated, with analyses conducted from both statistical performance and computational efficiency perspectives. Figure 6The cumulative distribution function shows that the proposed AO algorithm exhibits significant stochastic dominance, with its curve located on the far right. This result confirms that, compared to benchmark schemes such as the GA scheme and various hybrid methods, the AO algorithm achieves a significantly better SEE with the highest probability. Figure 7 The convergence behavior of the algorithm under different channel implementations is demonstrated, validating the computational efficiency of the proposed framework. The AO algorithm exhibits excellent convergence speed, stably reaching the maximum SEE within a finite number of iterations (typically less than 20). This rapid convergence is attributed to the robustness of its internal optimization steps: the initial transient oscillations of the PF algorithm and the smooth but slower convergence process of the IALMO algorithm jointly ensure the stability and speed of the outer AO loop. In summary, these results demonstrate that the AO-based framework achieves an effective trade-off between maximizing SEE and maintaining low computational complexity.

[0300] Figure 8 The proposed AO algorithm was compared and evaluated with the benchmark method under four different hardware configurations to achieve the highest SEE. It is clear that the proposed AO algorithm achieves optimal performance in all four scenarios, consistently obtaining the highest SEE value. For example, in the largest scale configuration (… Under these conditions, the AO scheme achieves its maximum SEE, significantly outperforming GA and various hybrid schemes. Although scaling up hardware leads to marginal improvements in SEE, the most crucial finding is that the performance difference brought about by the optimization algorithm far outweighs the performance gains achieved solely through hardware expansion. This confirms that the key bottleneck to maximizing SEE is not simply the physical scaling of MIMO and RIS units, but rather the refined centralized resource allocation scheme provided by the AO framework.

[0301] In summary, the simulation results demonstrate the superiority of the proposed alternative optimization algorithm in terms of performance and convergence robustness, achieving a significant SEE gain compared to the benchmark scheme.

[0302] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A RIS-assisted energy efficiency optimization method for cellular-free massive MIMO network security, characterized in that, include: S1. Establish a RIS-assisted non-cellular large-scale MIMO network model under Ricean fading channel; S2. Based on the constructed non-cellular massive MIMO network model, uplink channel estimation is performed. The linear minimum mean square error estimation method is used to obtain the estimated channel state information of the aggregated channel between the base station and the single-antenna legitimate user equipment, and between the base station and the single-antenna eavesdropper. S3. Based on the estimated channel state information, downlink channel data transmission is performed. The base station uses conjugate beamforming to transmit signals to the single-antenna legitimate user equipment and injects artificial noise. The artificial noise is located in the null space of the single-antenna legitimate user channel state. S4. Based on the downlink channel data transmission results, derive the lower bound of the user's achievable rate and the upper bound of the eavesdropper's leakage rate; S5. Based on the lower bound of the user reachable rate and the upper bound of the eavesdropper leakage rate, derive the secure reachability and rate expression and the secure energy efficiency expression; S6. Based on the aforementioned safety and energy efficiency expression, establish a non-convex optimization problem involving RIS phase shift and power allocation, and solve it using an iterative optimization algorithm. The iterative optimization algorithm decouples the original problem into RIS phase shift optimization subproblems and power allocation optimization subproblems, which are solved alternately until they converge to a local optimum that satisfies all constraints.

2. The RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security according to claim 1, characterized in that, Step S1 includes: S11, equipped with A base station (BS) with a uniform planar array, equipped with RIS, a smart reflective surface of a uniform planar array A single-antenna legitimate user equipment (UE) and Each single-antenna eavesdropper Eve, equipped with one base station BS. Each antenna, and each smart reflector RIS, is composed of... It consists of several reflective units; S12. Connect all base stations (BS) to the central processing unit (CPU) via a high-speed backhaul link, and communicate with the CPU or neighboring base stations via wired or wireless links. The CPU coordinates the scheduling of all base stations (BS) and the intelligent reflector (RIS) to provide services to all single-antenna legitimate users in a cooperative manner, and maintains synchronization between nodes through a centralized algorithm executed by the CPU. S13. In a cellular-free massive MIMO network, all base stations (BS) and intelligent reflectors (RIS) cooperate to transmit confidential data to legitimate users with a single antenna. Therefore, an eavesdropper may attempt to eavesdrop on all... The confidential information of each user; it is assumed that all eavesdroppers are wirelessly connected to an eavesdropping fusion center, which is responsible for collecting and aggregating all eavesdropping signals; S14. Define the index set as follows: Represents the set of base stations (BS). Represents the set of Intelligent Reflectors (RIS). Represents a set of reflecting units. Represents the set of legal users with a single antenna. Indicates a group of eavesdroppers; S15. To accurately characterize the channel propagation characteristics between transceivers, both the direct link BS-UE / Eve and the reflected link BS-RIS-UE / Eve are considered, and it is assumed that each link corresponding to the transmission path of the direct link BS-UE / Eve and the reflected link BS-RIS-UE / Eve follows the Ricean fading model; therefore, from the... base stations To the individual users And from the base stations To the An eavesdropper The channels are represented as follows: in, and These represent large-scale path fading factors related to distance, which remain constant over multiple coherent time intervals; and The Rice factor represents the ratio of the intensity of the line-of-sight component to the intensity of the non-line-of-sight component; furthermore, express The line-of-sight component, express The line-of-sight component; express Non-line-of-sight components, express The non-line-of-sight components are assumed to be deterministic and prior known, while the non-line-of-sight components are modeled as Rayleigh fading, i.e. and ; By definition and Let be the effective channel fading coefficient, and define . and Given the mean vector, we obtain and . The first base stations With the Each intelligent reflective surface The channel between, and the first Each intelligent reflective surface With the individual users , No. Each intelligent reflective surface With the An eavesdropper The channels between them are represented as follows: in, , and Represents the large-scale fading coefficient. , and This represents the corresponding Rice factor; non-line-of-sight component. , and Corresponding to , and The Rayleigh distribution random part of the denominator, whose each element follows an independent and identically distributed complex Gaussian random distribution, i.e. Line-of-sight component , and Corresponding to , and The deterministic part; definition , and For each corresponding , and The effective channel coefficients are defined simultaneously. , and Its mean channel vector; S16. To characterize the line-of-sight component in the formula of step S15, a corresponding channel is constructed using a uniform rectangular planar array model, with a size of... The array response vector is represented as: in, Represents the matrix Kronecker product. The azimuth angle representing the departure angle or the corresponding arrival angle. The pitch angle represents the departure angle or the corresponding arrival angle. S17. Assume the total number of antennas is... The array response vector along each coordinate axis is represented as: in, Indicates along shaft or Number of antenna elements along the axial direction For carrier wavelength, This refers to the unit spacing; S18. Based on the array response vector defined in step S16, the line-of-sight channel along the reflection link BS-RIS-UE / Eve is represented as follows: in, Indicates from arrive The azimuth angle of departure, Indicates from arrive The azimuth angle of departure, Indicates from arrive The pitch angle is the departure angle. Indicates from arrive The pitch angle and the departure angle; Indicates from arrive The azimuth and departure angle, Indicates from arrive The pitch angle and the launch angle; express from The azimuth angle and angle of arrival of the received signal. express from The elevation angle and angle of arrival of the received signal; Indicates from arrive The azimuth and departure angle, Indicates from arrive The azimuth and departure angle, Indicates from arrive pitch angle and launch angle from arrive The pitch angle and the launch angle; S19, will and Aggregation channels between and and The aggregation channel between them is represented as: in, express Phase shift vector, express The The reflection coefficient of each reflecting unit, where Let its phase value be defined; define the set of phase shifts for all RIS as . .

3. The RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security according to claim 1, characterized in that, Step S2 includes: S21. In the downlink of a RIS-assisted non-cellular massive MIMO network using a time-division duplex protocol, the implementation of downlink precoding depends on the acquisition of channel state information (CSI). By utilizing the reciprocity between uplink and downlink channels, quasi-channel state information (CSI) can be efficiently obtained through uplink training. S22. During pilot-assisted channel estimation, all user equipment will simultaneously send their assigned pilot sequences to the base station. Each sequence contains... The symbol; since the pilot signals used in standardized communication networks are usually public and known, it is assumed that the eavesdropper has complete control over the pilot sequence information. The eavesdropper transmits the exact same pilot sequence as any legitimate user equipment, thereby launching a pilot spoofing attack. S23, because it satisfies Therefore, pilot pollution, a common phenomenon in dense user scenarios, has been built into the network model; Indicates allocation to user equipment The orthogonality of the pilot sequences can be represented as follows: and ,in Representatives and user equipment A set of user equipment that share the same pilot signal; S24. Considering that user equipment and eavesdroppers may use different pilot transmission powers, the first... base stations The received pilot signal matrix is ​​represented as follows: in, This indicates the transmit power used by the user equipment during the training phase. This indicates the transmission power used by the eavesdropper during the training phase. Item representation The additive white Gaussian noise matrix at point is modeled as independent and identically distributed random variables, following a distribution. In the pilot signal matrix formula, each eavesdropper, to enhance the information leakage effect, will intentionally send a random pilot sequence. Upon receiving the pilot signal matrix... back, Perform despreading operation to estimate aggregation channel The process is represented as: in, , ; S25. Using the linear minimum mean square error estimation method, estimate the aggregation channel. Channel State Information (CSI): S26, for derivation The closed-form LMMSE estimate is used to calculate the relevant statistical expectation and covariance matrix, i.e. , , and By utilizing the first and second-order statistical properties of complex Gaussian random variables and performing appropriate matrix operations, the analytical expression is derived as follows: in, , , , , , , , , , , , , , , , , , , , , ; S27. Substitute the two analytical expressions from step S26 into the formula from step S25 to obtain the... base stations With the individual users The closed-loop LMMSE estimate for the inter-channel aggregation is: in, ; S28. Define the estimation error as... Channel estimation With estimation error Let be two uncorrelated random vectors that satisfy: in, , The expected value of the channel power is ,in .

4. The RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security according to claim 1, characterized in that, Step S3 includes: S31. During the downlink transmission phase, all base stations simultaneously send data symbols to the user equipment and embed artificial noise superimposed on the downlink security signal to prevent eavesdropping without affecting the normal communication of the user equipment. S32. Each base station adopts conjugate beamforming technology and is based on the long-term power control coefficient. and The transmit power of each base station is allocated to the data symbols. and artificial noise symbols Above, among which and All have been normalized to meet the requirements. Accordingly, the first base stations The transmitted signal is represented as: in, Transmission power allocated to useful data, and These correspond to the transmitted power of artificial noise and the beamforming vector, respectively. S33, according to the... base stations The transmitted signal, the first base stations The total transmit power is adjusted using a power control factor to ensure that it does not exceed the maximum permissible transmit power. That is, satisfying: in, It is a Hadamard product of matrices. It is a matrix The Yes, and it satisfies: S34, based on the first base stations The transmitted signal will affect the user equipment. With eavesdroppers The signals received at each location are represented as follows: in, and They represent user equipment. and eavesdroppers The additive white Gaussian noise at the given location is defined as follows: 。 5. The RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security according to claim 1, characterized in that, In step S4, for RIS-assisted non-cellular massive MIMO networks under Ricean fading channels, and under the conditions of multiple colluding eavesdroppers and incomplete channel state information, the overall achievable safe rate and security efficiency are analyzed, including: S41. Establish lower bounds on user reachability and rate, specifically including: In RIS-assisted cellular massive MIMO networks, the UatF delimitation technique is employed to obtain closed-form lower bound expressions for user equipment and rates. This method is particularly effective when it is assumed that the base station only possesses large-scale channel statistics rather than instantaneous channel realization. Within this framework, deterministic equivalent terms... The effective channel gain is considered to be fully known to the receiver; therefore, the user equipment... The signal received at the location The equivalent expression is: in, Represents the desired signal component. Corresponding to beamforming uncertainty, This indicates user-to-user interference originating from other user devices. Interference introduced by artificial noise. For noise interference; The reachability and speed of user equipment are expressed as: in, This is a preprocessing factor used to represent the preprocessing parameters in the allocation process. After pilot training with each symbol, the coherence interval The proportion used for data transmission, user equipment The corresponding effective signal-to-interference-plus-noise ratio is expressed as: via user equipment From all the expected values ​​in the corresponding effective signal-to-interference-plus-noise ratio formula, the closed-form expression for the downlink achievable sum rate when all legitimate user equipment adopts the conjugate beamforming scheme is derived as follows: in, Represents the defined matrix The To simplify the symbolic representation in subsequent derivations, an auxiliary function is defined as follows: The remaining parameters are defined as follows: in, The function is defined as if but Otherwise Its complement function is ; Based on the closed-form expression for downlink reachability and rate, the closed-form expression for downlink reachability and rate when all legitimate user equipment adopts the conjugate beamforming scheme is equivalently expressed as: in, , , , , , , , , , , , ; S42. Establish an upper bound on the eavesdropper leakage rate, specifically including: Assuming all eavesdroppers have complete knowledge of the instantaneous channel information and simultaneously eavesdrop on all legitimate user equipment, in this scenario, all eavesdroppers connect to a centralized eavesdropping fusion center. This center uses maximum ratio combining (MRC) technology to coherently combine the received signals, applying the UatF method to the eavesdroppers. In the received signal, the leakage rate and SINR of all eavesdroppers coexisting are expressed as: By calculating all the expected values ​​in the above formula, we obtain the leakage rate expression for multiple eavesdroppers using the maximum ratio merging technique: in: Based on the leakage rate expression, the closed-form expression for the leakage rate of all eavesdroppers when using the maximum ratio merging technique is equivalently written as: in, , , , , , , , , , , , , , , , .

6. The RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security according to claim 1, characterized in that, Step S5 includes: S51. Express the lower bound of SASR in a subtraction form: The ramp function is defined as follows: ; S52, The total power consumption of the RIS-assisted non-cellular massive MIMO network is modeled as follows: in, , , The first item in the table represents the total transmit power consumption of all base stations, where express The power amplifier efficiency; the second term correspond The power consumption of the backhaul link required to transmit data to the central processing unit, of which It is the first Fixed power consumption of the backhaul link, It is system bandwidth. Indicates dynamic power consumption related to flow rate; the third term Represents the static power consumption of the circuit, including The Antenna power consumption , The Power consumption of each reflector unit as well as power consumption ; S53. To simplify the expression in the subsequent derivation, the total power consumption of the RIS-assisted non-cellular massive MIMO network is equivalently rewritten as: in, , , ; S54. Based on the formula in step S51 and the rewritten total power consumption formula, the spectral efficiency is defined as: S55. Substitute the reachable rate of legitimate users, the leakage rate of eavesdropping users, and the rewritten total power consumption into the formula and spectrum efficiency formula in step S51 to obtain closed expressions for the lower bounds of SASR and SEE.

7. The RIS-assisted energy efficiency optimization method for non-cellular massive MIMO network security according to claim 1, characterized in that, Step S6 includes: S61. For safety and energy efficiency optimization methods, develop an efficient resource allocation framework aimed at maximizing SEE and optimizing the joint adjustment of RIS phase shift. and the power control coefficients of the data signal and the artificial noise signal. The overall optimization problem can be described as follows: Wherein, formula Apply unity modulus constraints to all RIS, formula Ensure that the transmit power of each base station does not exceed the maximum limit. ,formula and The reachability rate for each legitimate user must not be lower than the minimum threshold. And the leakage rate of each eavesdropper does not exceed the upper limit. ; S62. Establish a non-convex optimization problem for RIS phase shifting, specifically including: By employing the augmented Lagrange multiplier method, This is transformed into an unconstrained optimization problem on a Riemannian manifold, where inequality constraints are incorporated into the objective function as penalty terms. Therefore, The restatement is as follows: Among them, the penalty parameter ,vector Let represent the Lagrange multiplier vector, and the remaining parameters are defined as follows: question This is an unconstrained optimization problem defined on a manifold. It is efficiently solved using the steepest descent method from the Manopt toolbox. The Riemann gradient of the objective function is calculated, serving as the Euclidean gradient's counterpart on the manifold. The Riemann gradient is obtained by projecting the Euclidean gradient onto the tangent space of the manifold. Therefore, the following derivation is made: The Euclidean gradient is: in: Among them, indicator function exist Time equals Otherwise ; The Riemann gradient can be obtained by mapping the derived Euclidean gradient onto the tangent space of the manifold using projection operations, as shown in the following expression: After obtaining the Riemann gradient, it is used as the descent direction to iteratively optimize the control variables. Updates are achieved through a pullback operation, which maps candidate points from the tangent space back to the manifold, thus maintaining geometric feasibility throughout the optimization process. in, Indicates the step size; S63. Establish a non-convex optimization problem for power allocation, specifically including: For a given By introducing auxiliary variables , as well as ,in , will optimize the problem Equivalently reconstructed as: in, , , , , , ; During the inspection At that time, the path tracing (PF) algorithm was introduced, and the operator was... relaxation And by applying a multidimensional quadratic transformation, the objective function in convex approximation form is obtained: in, ; Using convex inequalities, the formula can be... The non-convex constraint in the equation is approximated by its convex counterpart: in, ; Using convex inequalities, the constraint formulas Approximately expressed as: in, ; By combining the chain rule with a first-order Taylor expansion, the formula can be transformed. The non-convex constraint in the equation is approximately transformed into the following convex form: in, ; Further, under the PF framework The The next iteration is expressed as: Finally, the PF optimization algorithm is used to solve the problem. Solve the problem; S64. Local optimal phase shift obtained based on IALMO algorithm The local optimal power control coefficients calculated by the PF algorithm An iterative optimization framework was constructed to solve the problem. By alternately solving the RIS phase shift optimization subproblem and the power allocation optimization subproblem, the algorithm is iteratively updated. and This continues until the network energy efficiency converges to a local maximum.

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