Hybrid RIS-assisted long-term energy efficiency optimization method for cellular-free networks

Abstract

The present invention discloses a hybrid RIS-assisted long-term energy efficiency optimization method for a non-cellular network. The method comprises: establishing a multi-RAU multi-user link reception signal model; establishing a long-term energy efficiency optimization model based on the signal model, which performs hybrid RIS component switching scheduling, RAU precoding, hybrid RIS phase shifting, and network queue backlog stability control design based on physical layer channel and network layer queue information; transforming the long-term queue stability constraint into a joint optimization problem of minimizing Lyapunov drift and maximizing energy efficiency, and decoupling it into a transmission subproblem and a switching subproblem; transforming the discrete RIS component selection constraints based on the large-M method, and solving the transmission subproblem within each time slot using continuous convex approximation and semidefinite relaxation; deriving the maximum number of active components that can be enabled in the hybrid RIS, and transforming the component selection combinatorial optimization problem into multiple switching subproblems that can be solved in parallel using a greedy algorithm. The method can effectively stabilize the queue length within the Lyapunov framework and ensure system stability.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a hybrid RIS (Reconfigurable Intelligence Surface, RIS)-assisted long-term energy efficiency optimization method for a non-cellular network. Background Art

[0002] To improve user performance at the cell edge, cellular-free networks eliminate the concept of cell boundaries through limited collaboration among distributed Remote Antenna Units (RAUs). Each RAU collaboratively shares Channel State Information (CSI) and user data, significantly reducing inter-user interference, reducing transmission power consumption, and improving performance. Furthermore, to further improve network coverage, reconfigurable intelligent metasurfaces can adjust component phases and signal reflections to create a more favorable channel environment, improving signal coverage while also attracting extensive research due to their low energy consumption. By enabling RIS and cellular-free base stations to collaborate and serve users, and enabling network-level energy conservation for heterogeneous devices, the high energy consumption associated with cellular-free ultra-dense networks (UDNs) can be effectively mitigated.

[0003] On the other hand, considering that the collaboration in non-cellular networks is mainly concentrated in the physical layer, that is, the sharing of data and CSI, and centralized and semi-centralized processing at the CPU (Central Processing Unit, CPU). However, from the perspective of cross-layer optimization, since the user's QoS (Quality of service, QoS) requirements may be different at different times of the day, and the user data traffic is bursty, this also leads to different distribution of network energy consumption throughout the day. Therefore, in order to further increase the energy saving space, the energy saving optimization of non-cellular networks requires not only the coordinated hybrid precoding design of RIS and RAU at the physical layer, but also the network layer collaboration, heterogeneous device sleep, and user queue length optimization design considering the heterogeneity of different user data streams in different time slots, so as to further reduce system energy consumption and improve system stability.

[0004] However, in a non-cellular network, each base station cooperates to eliminate interference and reflects signals through RIS to increase channel freedom. While achieving greater performance gains compared to traditional centralized systems, traditional passive RIS suffers from

[0005] The double fading effect limits the practical deployment of RIS and reduces the actual application performance of the system. Active RIS can effectively overcome the double fading effect by increasing the gain of the transmitting element, but it also increases energy consumption. Under power constraints, even if the power consumption of a single active RIS element is low, the introduction of multiple distributed active RIS can increase the energy consumption of the wireless network. This energy consumption cannot be ignored. Moreover, because the static power consumption of active elements is greater than that of passive elements, when the number of active RIS elements is large, the static power consumption increases linearly with the number of elements. This further limits the energy available for signal amplification. As a result, it is possible that the number of RIS elements increases but the energy efficiency decreases.

[0006] To address these issues, hybrid RIS equips a few RIS components with amplifiers. This mitigates the performance loss caused by double fading while also reducing the high energy consumption associated with large-scale active RIS deployments. Considering that network traffic demands vary at different times, collaborative optimization can be performed based on physical and network layer conditions. For example, when user traffic demand is high, network layer queue lengths are long, and physical layer channel conditions are poor, the number of active hybrid RIS components can be increased to improve summation rates, reduce queue lengths, and end-to-end latency. Conversely, when conditions are poor, the number of active components can be reduced to conserve energy. Based on this, in order to further improve the energy efficiency of hybrid RIS-assisted cellular-free networks, it is necessary to fully consider the dynamic characteristics of network layer user traffic within the physical layer optimization framework, conducting layer-one-two coordinated transmission and energy efficiency optimization between RIS and RAU base stations to achieve a long-term balance between performance and power consumption. Summary of the Invention

[0007] The purpose of this invention is to provide a hybrid RIS-assisted long-term energy efficiency optimization method for non-cellular networks. Within a physical layer optimization framework, this method fully considers the dynamic characteristics of network layer user traffic and performs Layer 1 / 2 collaborative transmission and energy efficiency optimization between RIS and RAU base stations. This method achieves a long-term balance between performance and power consumption, further improving the system's energy efficiency.

[0008] To achieve the above objectives, the present invention adopts a technical solution: a hybrid RIS-assisted cellular-free network long-term energy efficiency optimization method, comprising the following steps:

[0009] Step S1: Establish a multi-RAU multi-user link reception signal model in a hybrid RIS-assisted cellular-free network;

[0010] Step S2: Based on the signal model, a long-term energy efficiency optimization model is established for hybrid RIS component switching scheduling, RAU precoding, hybrid RIS phase shift, and network queue backlog stability control design based on physical layer and network layer information. Based on the Lyapunov framework, the long-term queue stability constraint is transformed into a joint optimization problem of minimizing Lyapunov drift and maximizing energy efficiency. An alternating optimization strategy is used to decouple the problem into a transmission subproblem of RAU precoding and hybrid RIS phase shift design, and a switching subproblem of hybrid RIS component switching scheduling, which are optimized separately.

[0011] Step S3: For the transmission optimization problem, the discrete RIS component selection constraints are first transformed based on the big M method. The transmission subproblem is solved in each time slot using fractional programming techniques, continuous convex approximation, and semidefinite relaxation methods.

[0012] Step S4: For the switching subproblem, to achieve efficient RIS component selection, we first derived the maximum number of active components that can be turned on by the hybrid RIS. Based on the analyzed maximum number of active components, we transformed the component selection problem into multiple subproblems that can be solved in parallel using a greedy algorithm. This algorithm has lower complexity and better scalability to the growth of the number of RIS components.

[0013] In the step S1,

[0014] S11. Constructing the hybrid RIS-assisted cellular-free system receiving signal and system and rate system model: Consider a distributed cellular-free system consisting of a central processing unit (CPU) and N RAUs, each RAU is equipped with N a antennas, serving K single-antenna users. In order to improve the energy efficiency of the non-cellular system, hybrid RIS is used to assist system performance optimization. Hybrid RIS has L reflection units. It can be defined as well as Represents the user, RAU and RIS element collection respectively.

[0015] For each user k, the received signal comes from the direct signal of RAU and the reflected signal from RIS. It can be defined that the final equivalent signal is the sum of the direct signal and the reflected signal. Let the symbol vector sent by the user be For user k, the received signal r from RAU k It can be modeled as:

[0016]

[0017] in are the channels from RAU to user k and RIS respectively. represents the precoding vector of user k, and the precoding matrix of all users For RIS, its main function is to reflect and amplify the signal. is the reflection matrix of the hybrid RIS, where θ i ,|β i |Respectively RIS The phase and gain of each reflector unit, is the channel from RIS to user k, They represent the thermal noise generated at the hybrid RIS and the Gaussian white noise of user k respectively. v 2 and σ z 2 They represent the noise variance, I L represents the L-dimensional unit matrix, represents a complex domain, [*] T Indicates transpose operation, [*] H represents the conjugate transpose operation, diag(*) means taking the diagonal elements of the input matrix as the output vector; Diag(*) means returning the diagonal matrix with the input vector as the diagonal elements. Indicates that the random variable X satisfies the mean μ and variance σ 2 Complex Gaussian distribution, 0 N represents a zero vector of length N, and ∑· represents a summation operation.

[0018] The components of hybrid RIS include active components and passive components. is a collection of active components, the total number of active components is L a In addition, in order to make it more convenient to express, the diagonal matrix is ​​introduced Used to characterize component selection, where α i ∈{0,1}. If α i If θ is 1, it means that the component is an active component, and vice versa. The RIS phase shift matrix can be written as Θ = Φ + Ψ, where Φ = AΘ is the active component phase shift matrix, Ψ = (I L -A)Θ is the passive component phase shift matrix.

[0019] The signal-to-interference-plus-noise ratio (SINR) of user k can be expressed as:

[0020]

[0021] make is an equivalent channel that includes the direct path and the reflected path. The rate of user k can be defined as: R k =log2(1+γ k), |·| represents the absolute value operation, and ||·|| represents the Frobenius norm.

[0022] S12. Queue length modeling: Considering the randomness of network layer packet arrival, it is assumed that each RAU and hybrid RIS cooperate to serve users based on the physical layer channel information and network layer user queue information. It is used to store and process the network layer data of all users, that is, the queue backlog of all users in time slot t. In order to achieve a trade-off between the performance of the non-cellular network and the system stability, the system queue length can be modeled through the Lyapunov optimization framework to achieve a trade-off between system utility and system stability. Here, we consider discrete time slots, that is, t∈{1, 2, ..., T}, and assume that A k (t) represents the arrival data of user k in time slot t, and satisfies Indicates the desired operation. Obviously, the queue length can be updated as follows:

[0023]

[0024] Among them, R k (t) is the rate of user k in time slot t.

[0025] S13. Modeling the energy consumption and long-term energy efficiency of the entire system: System energy consumption primarily includes static power consumption and transmission power consumption, including the energy consumption of all RAUs and RIS. Consider that RAU energy consumption primarily consists of precoding energy consumption and RAU static power consumption. RIS power consumption is related to the number and type of components. The total system power consumption in time slot t can be modeled as:

[0026]

[0027] The first term in the above formula represents the precoding power consumption of all RAUs at time t, and the second and third terms represent the transmission energy consumption of the hybrid RIS. R The static power consumption of each RIS unit, P B Indicates the static circuit power consumption of all RAUs.

[0028] To achieve a trade-off between long-term energy efficiency and network stability in RIS-assisted cellular-free networks, the long-term energy efficiency (EE) of the system can be defined as:

[0029]

[0030] in, The numerator represents the time average and rate The denominator represents the long-term average network energy consumption

[0031] The step S2 includes the following steps:

[0032] S21. Establish the objective function of maximizing long-term energy efficiency:

[0033]

[0034] in It means that the objective function value is maximized after optimizing the RAU beamforming vector w, the hybrid RIS phase shift Θ, and the RIS element switch matrix A. Indicates the long-term energy efficiency of the system;

[0035] S22. Establish constraints, including user QoS constraints and RAU, hybrid RIS power consumption constraints, hybrid RIS constant modulus constraints, hybrid RIS component amplification constraints, and long-term queue stability constraints. The constraints are as follows:

[0036]

[0037] in, is the minimum QoS constraint for users, and is the maximum transmit power of the RAU and hybrid RIS.

[0038] S23. Energy efficiency conversion based on fractional programming: Based on Dinkelbach fractional programming technique, the energy efficiency objective function of time slot t is converted into: where it is defined

[0039]

[0040] And η(0)=0, Equation (7) shows that η(t) is determined by the resource allocation scheme of the past time slot. k (τ), P total (τ) represents the rate of user k in time slot τ and the total power consumption of the system, Meaning is defined as;

[0041] S24. Lyapunov-based Queue Stability Transformation: Constraints The long-term evolution of the infinite time scale is obviously not directly handled. In order to deal with this problem, Lyapunov drift is introduced for transformation. First, the Lyapunov function is defined as The quadratic Lyapunov function grows quadratically with the increase of queue length, and the smaller L(Q k (t)) can reduce queue backlog and delay. In order to make the queue length stable, the Lyapunov drift of time slot t is defined as: It can be deduced that the upper bound of the Lyapunov drift in time slot t is

[0042]

[0043] Where B is a constant that satisfies the following conditions: By minimizing the right side of (8) in each time slot, the network can be stabilized, that is, the constraint Based on the idea of ​​random optimization drift plus penalty, the trade-off factor V is introduced to transform the Yapunov drift into the objective function, and the objective function of the t time slot is transformed into:

[0044]

[0045] Then, an alternating optimization strategy is adopted to decouple the problem into the transmission subproblem of precoding design and the switching subproblem of hybrid RIS element switching scheduling, which are optimized separately.

[0046] The step S3 includes the following steps:

[0047] S31. Based on the large M method, we introduce a sufficiently large positive number M to simplify the constraints C5 and C6, and then introduce the auxiliary variable φ=[φ1,…,φ K ] The non-convexity caused by the coupling of the logarithmic term and SINR in the conversion rate formula, the optimization problem is transformed into:

[0048]

[0049]

[0050] C7, C8, C2, C3,

[0051] in represents the optimization of the RAU beamforming vector w and the auxiliary variable φ to minimize the objective function value; γ k is the SINR of user k; considering that the optimization problem is performed in each time slot, the time slot t index before the variable is omitted;

[0052] S32. Introducing auxiliary variable transformation constraint C 10 Non-convexity: Introducing slack variables ξ k ≥0 will constrain C 10 Converted to the following equivalent form:

[0053]

[0054] as well as

[0055]

[0056] Considering the rotation invariance of the precoding phase, constraint (10) can be transformed into The concave function Through the first-order Taylor expansion, it can be transformed into a second-order cone program (SOCP):

[0057]

[0058] in is the value of the auxiliary variable at the nth iteration.

[0059] S33. Form the final RAU transmission optimization problem:

[0060]

[0061]

[0062] C 15 :(11),(12),

[0063] in represents the Kronecker product, Represents a vectorized operation. τ′ k is the QoS slack variable of user k, ρ1 is the corresponding penalty function, and the problem It is a convex problem and can be solved using the CVX solver.

[0064] Next, based on the fixed RAU precoding and RIS element switching vector, hybrid RIS precoding is solved.

[0065] S34. Define variable conversion constraints C 10 Form: Definition Indicates the direct channel from RAU to user, Represents vector As a diagonal matrix P k The diagonal elements of . Therefore, the constraint C 10 Translates to:

[0066]

[0067] in,

[0068] S35. Transform the numerator and denominator of SINR in (13) by using the semidefinite relaxation (SDR) technique:

[0069] definition in And rank(U)=1, formula (13) can be transformed into:

[0070]

[0071] in, As can be seen from formula (14), the numerator and denominator of SINR are transformed into convex linear functions with respect to U. Indicates that the matrix U is a semi-positive matrix, rank(U) = 1 indicates that the matrix U has rank one;

[0072] S36. Introducing auxiliary variables The numerator and denominator of SINR in formula (14) are restricted respectively to transform the fractional structure of SINR, and the non-convexity of the auxiliary variable is transformed using continuous convex approximation:

[0073]

[0074] Regarding the non-convexity of Eq. (17), consider k Perform scaling of the first-order Taylor expansion to account for its non-convexity:

[0075]

[0076] in, Represents the auxiliary variable value of the tth iteration, and the gradient term is specifically Substituting (18) into (17) yields the following expression:

[0077]

[0078] So far, constraint C 10 The non-convexity brought about has been completely solved.

[0079] S37. Convert the hybrid RIS power consumption into SDR form: based on tr{ADiag(b)CDiag(b)}=b T (A T ⊙C)b, power consumption P of hybrid RIS act can be transformed into:

[0080]

[0081] Among them, ⊙, tr{*}, respectively represent the matrix Hadamard product and matrix trace, And ψ=diag(Φ), 0 L×1 represents an L-dimensional zero vector. diag(Φ) takes the diagonal elements of the matrix Φ as the output vector. Diag(b) returns a matrix with vector b as the diagonal element.

[0082] S38. Penalty function method to transform the rank-one constraint of semidefinite relaxation: At this point, the remaining non-convex part of the hybrid RIS phase shift optimization problem is mainly the rank-one constraint, which makes the entire problem still a non-convex problem. Next, a penalty function method is adopted to ensure the rank-one property of the U matrix. Specifically, the constraint tr(U)-λ is added: max (U)≤0 to ensure the rank of the U matrix. max (*) indicates the operation of taking the maximum eigenvalue. But the constraint tr(U)-λ max (U)≤0, it is still non-convex. The main reason is the operation of extracting the maximum eigenvalue of matrix U. The following derivation of λ max Convex lower bound of (U), as a surrogate function for optimization:

[0083]

[0084] Substitute equation (21) into the constraint tr(U)-λ max (U)≤0, and use the penalty function factor ρ′2 to add it to the objective function, and force the zero constraint through the penalty function to meet the rank(U)=1, U (t) is the solution of the tth iteration. v max is the eigenvector corresponding to the maximum eigenvalue. The objective function is transformed into:

[0085]

[0086] S39. The transformed RIS phase shift optimization problem is obtained:

[0087]

[0088]

[0089] C 18 :[U] L+1，L+1 =1,

[0090] C 19 :C 14 ,(15),(16),(19),

[0091] in, question It is a convex problem and can be solved using the CVX solver. n，n It means taking the element at the nth row and nth column of matrix U.

[0092] S310. Based on the solved U*, obtain the RIS beamforming phase shift: Where [1:L] means taking the first L elements.

[0093] The step S4 includes the following steps:

[0094] S41. Determine the maximum number of active components that can be turned on in the hybrid RIS under given channel conditions: For active component m, it is obvious that |β m |≥1: Maximum number of active components that can be turned on for:

[0095]

[0096] Where r satisfies:

[0097]

[0098] in […] maxi Indicates taking the largest i-th element, Ξ i，i Denotes the i-th diagonal element of the matrix Ξ. Next, the optimal components to be turned on in different time slots will be determined based on the maximum number of active components that can be turned on analyzed in S41.

[0099] S42. Initialize various parameters, including the set and The maximum number of active components that can be turned on is calculated by formula (22): And input the beamforming matrix W output in step S3 * =[w1 * , w2 * ,…,w K * ] and the phase shift matrix Θ * , determine the number of active components turned on L act , According to W * ,Θ * and collection Calculate the initial energy efficiency value E0;

[0100] S43. Traverse the collection through parallel processing For each element l in the set, open the RIS element l in turn and add it to the set Determine the feasibility of the RIS switch solution and calculate the new energy efficiency value if feasible If the solution fails, set

[0101] S44. By calculation Determine the optimal RIS switch element k at the current moment, where Represents from the set Find the value such that (E l -E0) maximum element index l;

[0102] S45. Determine whether the number of active components currently turned on is less than L act If it is less than, execute Then return to step S43; if not less than, jump to step S46;

[0103] S46. Output the final RIS switch optimization solution and set And set

[0104] Compared with the prior art, the present invention has the following advantages and beneficial effects: the present invention considers a hybrid RIS-assisted cellular-free network long-term energy efficiency optimization method. The present invention can decouple the combinatorial optimization problem of hybrid RIS component selection into multiple parallel sub-problems through a greedy algorithm, thereby reducing the complexity of the component selection algorithm, making the algorithm more scalable to the increase in the number of hybrid RIS components. In terms of performance, it can effectively stabilize the system queue length, ensure system stability, and achieve a compromise between network stability and system energy efficiency optimization performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 This is a flow chart of the hybrid RIS-assisted cellular-free network long-term energy efficiency optimization method provided by the present invention.

[0106] Figure 2 This is a performance comparison chart of the algorithm provided by the present invention with respect to the number of RAU antennas. The hybrid RIS has one enabled element, and the comparison algorithms are the traditional passive RIS, active RIS, and the random element scheme with one enabled element.

[0107] Figure 3 This is a performance comparison chart of the algorithm provided by the present invention with the average queue length according to the trade-off factor V. DETAILED DESCRIPTION

[0108] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0109] The present invention provides a hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method, the process of which is as follows: Figure 1 As shown, the following steps are included:

[0110] Step S1: Establish a multi-RAU multi-user link reception signal model in a hybrid RIS-assisted cellular-free network;

[0111] Step S2: Based on the signal model, a long-term energy efficiency optimization model is established for hybrid RIS component switching scheduling, RAU precoding, hybrid RIS phase shift, and network queue backlog stability control design based on physical layer and network layer information. Based on the Lyapunov framework, the long-term queue stability constraint is transformed into a joint optimization problem of minimizing Lyapunov drift and maximizing energy efficiency. An alternating optimization strategy is used to decouple the problem into a transmission subproblem of RAU precoding and hybrid RIS phase shift design, and a switching subproblem of hybrid RIS component switching scheduling, which are optimized separately.

[0112] Step S3: For the transmission optimization problem, the discrete RIS component selection constraints are first transformed based on the big M method. The transmission subproblem is solved in each time slot using fractional programming techniques, continuous convex approximation, and semidefinite relaxation methods.

[0113] Step S4: For the switching subproblem, to achieve efficient RIS component selection, we first derived the maximum number of active components that can be turned on by the hybrid RIS. Based on the analyzed maximum number of active components, we transformed the component selection problem into multiple subproblems that can be solved in parallel using a greedy algorithm. This algorithm has lower complexity and better scalability to the growth of the number of RIS components.

[0114] In the step S1,

[0115] S11. Constructing the hybrid RIS-assisted cellular-free system receiving signal and system and rate system model: Consider a distributed cellular-free system consisting of a central processing unit (CPU) and N RAUs, each RAU is equipped with N a antennas, serving K single-antenna users. In order to improve the energy efficiency of the non-cellular system, hybrid RIS is used to assist system performance optimization. Hybrid RIS has L reflection units. It can be defined as well as Represents the user, RAU and RIS element collection respectively.

[0116] For each user k, the received signal comes from the direct signal of RAU and the reflected signal from RIS. It can be defined that the final equivalent signal is the sum of the direct signal and the reflected signal. Let the symbol vector sent by the user be For user k, the received signal r from RAU k It can be modeled as:

[0117]

[0118] in are the channels from RAU to user k and RIS respectively. represents the precoding vector of user k, and the precoding matrix of all users For RIS, its main function is to reflect and amplify the signal. is the reflection matrix of the hybrid RIS, where θ i ,|β i |Respectively RIS The phase and gain of each reflector unit, is the channel from RIS to user k, They represent the thermal noise generated at the hybrid RIS and the Gaussian white noise of user k respectively. v 2 and σ z 2 They represent the noise variance, I L represents the L-dimensional unit matrix, represents a complex domain, [*] T Indicates transpose operation, [*] H represents the conjugate transpose operation, diag(*) means taking the diagonal elements of the input matrix as the output vector; Diag(*) means returning the diagonal matrix with the input vector as the diagonal elements. Indicates that the random variable X satisfies the mean μ and variance σ 2 Complex Gaussian distribution, 0 N represents a zero vector of length N, and ∑· represents a summation operation.

[0119] The components of hybrid RIS include active components and passive components. is a collection of active components, the total number of active components is L a In addition, in order to make it more convenient to express, the diagonal matrix is ​​introduced Used to characterize component selection, where α i ∈{0,1}. If α i If θ is 1, it means that the component is an active component, and vice versa. The RIS phase shift matrix can be written as Θ = Φ + Ψ, where Φ = AΘ is the active component phase shift matrix, Ψ = (I L -A)Θ is the passive component phase shift matrix.

[0120] The signal-to-interference-plus-noise ratio (SINR) of user k can be expressed as:

[0121]

[0122] make is an equivalent channel that includes the direct path and the reflected path. The rate of user k can be defined as: R k =log2(1+γ k), |·| represents the absolute value operation, and ||·|| represents the Frobenius norm.

[0123] S12. Queue length modeling: Considering the randomness of network layer packet arrival, it is assumed that each RAU and hybrid RIS cooperate to serve users based on the physical layer channel information and network layer user queue information. It is used to store and process the network layer data of all users, that is, the queue backlog of all users in time slot t. In order to achieve a trade-off between the performance of the non-cellular network and the system stability, the system queue length can be modeled through the Lyapunov optimization framework to achieve a trade-off between system utility and system stability. Here, we consider discrete time slots, that is, t∈{1, 2, ..., T}, and assume that A k (t) represents the arrival data of user k in time slot t, and satisfies Indicates the desired operation. Obviously, the queue length can be updated as follows:

[0124]

[0125] Among them, R k (t) is the rate of user k in time slot t.

[0126] S13. Modeling the energy consumption and long-term energy efficiency of the entire system: System energy consumption primarily includes static power consumption and transmission power consumption, including the energy consumption of all RAUs and RIS. Consider that RAU energy consumption primarily consists of precoding energy consumption and RAU static power consumption. RIS power consumption is related to the number and type of components. The total system power consumption in time slot t can be modeled as:

[0127]

[0128] The first term in the above formula represents the precoding power consumption of all RAUs at time t, and the second and third terms represent the transmission energy consumption of the hybrid RIS. R The static power consumption of each RIS unit, P B Indicates the static circuit power consumption of all RAUs.

[0129] To achieve a trade-off between long-term energy efficiency and network stability in RIS-assisted cellular-free networks, the long-term energy efficiency (EE) of the system can be defined as:

[0130]

[0131] in, The numerator represents the time average and rate The denominator represents the long-term average network energy consumption

[0132] The step S2 includes the following steps:

[0133] S21. Establish the objective function of maximizing long-term energy efficiency:

[0134]

[0135] in It means that the objective function value is maximized after optimizing the RAU beamforming vector w, the hybrid RIS phase shift Θ, and the RIS element switch matrix A. Indicates the long-term energy efficiency of the system;

[0136] S22. Establish constraints, including user QoS constraints and RAU, hybrid RIS power consumption constraints, hybrid RIS constant modulus constraints, hybrid RIS component amplification constraints, and long-term queue stability constraints. The constraints are as follows:

[0137]

[0138] in, is the minimum QoS constraint for users, and The maximum transmit power for each RAU and hybrid RIS.

[0139] S23. Energy efficiency conversion based on fractional programming: Based on Dinkelbach fractional programming technique, the energy efficiency objective function of time slot t is converted into: where it is defined

[0140]

[0141] And η(0)=0, equation (7) indicates that η(t) is determined by the resource allocation scheme of the past time slot.

[0142] S24. Lyapunov-based Queue Stability Transformation: Constraints The long-term evolution of the infinite time scale is obviously not directly handled. In order to deal with this problem, Lyapunov drift is introduced for transformation. First, the Lyapunov function is defined as The quadratic Lyapunov function grows quadratically with the increase of queue length, and the smaller L(Q k (t)) can reduce queue backlog and delay. In order to make the queue length stable, the Lyapunov drift of time slot t is defined as: It can be deduced that the upper bound of the Lyapunov drift in time slot t is

[0143]

[0144] Where B is a constant that satisfies the following conditions: By minimizing the right side of (8) in each time slot, the network can be stabilized, that is, the constraint Based on the idea of ​​random optimization drift plus penalty, the trade-off factor V is introduced to transform the Yapunov drift into the objective function, and the objective function of the t time slot is transformed into:

[0145]

[0146] Then, an alternating optimization strategy is adopted to decouple the problem into the transmission subproblem of precoding design and the switching subproblem of hybrid RIS element switching scheduling, which are optimized separately.

[0147] The step S3 includes the following steps:

[0148] S31. Based on the large M method, we introduce a sufficiently large positive number M to simplify the constraints C5 and C6, and then introduce the auxiliary variable φ=[φ1,…,φ K ] The non-convexity caused by the coupling of the logarithmic term and SINR in the conversion rate formula, the optimization problem is transformed into:

[0149]

[0150]

[0151] C7, C8, C2, C3,

[0152] in represents the optimization of the RAU beamforming vector w and the auxiliary variable φ to minimize the objective function value; γ k is the SINR of user k; considering that the optimization problem is performed in each time slot, the time slot t index before the variable is omitted; since the optimization problem is performed in each time slot, the time slot t index before the variable is omitted for convenience.

[0153] S32. Introducing auxiliary variable transformation constraint C 10 Non-convexity: Introducing slack variables ξ k ≥0 will constrain C 10 Converted to the following equivalent form:

[0154]

[0155] as well as

[0156]

[0157] Considering the rotation invariance of the precoding phase, constraint (10) can be transformed into The concave function Through the first-order Taylor expansion, it can be transformed into a second-order cone program (SOCP):

[0158]

[0159] in is the value of the auxiliary variable at the nth iteration.

[0160] S33. Form the final RAU transmission optimization problem:

[0161]

[0162]

[0163] C 15 :(11),(12),

[0164] in represents the Kronecker product, Represents a vectorized operation. τ′k is the QoS slack variable of user k, ρ1 is the corresponding penalty function, and the problem It is a convex problem and can be solved using the CVX solver.

[0165] Next, based on the fixed RAU precoding and RIS element switching vector, hybrid RIS precoding is solved.

[0166] S34. Define variable conversion constraints C 10 Form: Definition Indicates the direct channel from RAU to user, Represents vector As a diagonal matrix P k The diagonal elements of . Therefore, the constraint C 10 Translates to:

[0167]

[0168] in,

[0169] S35. Transform the numerator and denominator of SINR in (13) by using the semidefinite relaxation (SDR) technique:

[0170] definition in And rank(U)=1, formula (13) can be transformed into:

[0171]

[0172] in, As can be seen from formula (14), the numerator and denominator of SINR are transformed into convex linear functions with respect to U. Indicates that the matrix U is a semi-positive matrix, rank(U) = 1 indicates that the matrix U has rank one;

[0173] S36. Introducing auxiliary variables The numerator and denominator of SINR in formula (14) are restricted respectively to transform the fractional structure of SINR, and the non-convexity of the auxiliary variable is transformed using continuous convex approximation:

[0174]

[0175] Regarding the non-convexity of Eq. (17), consider k Perform scaling of the first-order Taylor expansion to account for its non-convexity:

[0176]

[0177] in, Represents the auxiliary variable value of the tth iteration, and the gradient term is specifically Substituting (18) into (17) yields the following expression:

[0178]

[0179] So far, constraint C 10 The non-convexity brought about has been completely solved.

[0180] S37. Convert the hybrid RIS power consumption into SDR form: based on tr{ADiag(b)CDiag(b)}=b T (A T ⊙C)b, power consumption P of hybrid RIS act can be transformed into:

[0181]

[0182] Among them, ⊙, tr{*}, respectively represent the matrix Hadamard product and matrix trace, And ψ=diag(Φ). L×1 represents an L-dimensional zero vector. diag(Φ) takes the diagonal elements of the matrix Φ as the output vector. Diag(b) returns a matrix with vector b as the diagonal element.

[0183] S38. Penalty function method to transform the rank-one constraint of semidefinite relaxation: At this point, the remaining non-convex part of the hybrid RIS phase shift optimization problem is mainly the rank-one constraint, which makes the entire problem still a non-convex problem. Next, a penalty function method is adopted to ensure the rank-one property of the U matrix. Specifically, the constraint tr(U)-λ is added:max (U)≤0 to ensure the rank of the U matrix. max (*) indicates the operation of taking the maximum eigenvalue. But the constraint tr(U)-λ max (U)≤0, it is still non-convex. The main reason is the operation of extracting the maximum eigenvalue of matrix U. The following derivation of λ max Convex lower bound of (U), as a surrogate function for optimization:

[0184]

[0185] Substitute equation (21) into the constraint tr(U)-λ max (U)≤0, and use the penalty function factor ρ′2 to add it to the objective function, and force the zero constraint through the penalty function to meet the rank(U)=1, U (t) is the solution of the tth iteration. v max is the eigenvector corresponding to the maximum eigenvalue. The objective function is transformed into:

[0186]

[0187] S39. The transformed RIS phase shift optimization problem is obtained:

[0188]

[0189]

[0190] C 18 :[U] L+1，L+1 =1,

[0191] C 19 :C 14 ,(15),(16),(19),

[0192] in, question It is a convex problem and can be solved using the CVX solver.

[0193] S310. Based on the solved U*, obtain the RIS beamforming phase shift: Where [1:L] means taking the first L elements.

[0194] The step S4 includes the following steps:

[0195] S41. Determine the maximum number of active components that can be turned on in the hybrid RIS under given channel conditions: For active component m, it is obvious that |β m |≥1: Maximum number of active components that can be turned on for:

[0196]

[0197] Where r satisfies:

[0198]

[0199] in […] maxi Indicates taking the largest i-th element, Ξ i，i Denotes the i-th diagonal element of the matrix Ξ. The proof is as follows: First, consider the constraint C2 and transform it into:

[0200]

[0201] Among them, |β min |=min[|β1|,…,|β L |]. yes The number of active components that can be turned on, e i Is a one-hot vector of length L, where the ith position is 1 and the rest are 0. Arranged in ascending order:

[0202]

[0203] Then by Obviously, the above maximum number of active components that can be turned on holds true. Next, the optimal components to be turned on in different time slots will be determined based on the maximum number of active components that can be turned on analyzed in S41.

[0204] S42. Initialize various parameters, including the set and The maximum number of active components that can be turned on is calculated by formula (22): And input the beamforming matrix W output in step S3 * =[w i * , w2 * ,…,w K * ] and the phase shift matrix Θ * , determine the number of active components turned on L act , According to W * ,Θ * and collection Calculate the initial energy efficiency value E0;

[0205] S43. Traverse the collection through parallel processing For each element l in the set, open the RIS element l in turn and add it to the set Determine the feasibility of the RIS switch solution and calculate the new energy efficiency value if feasible If the solution fails, set

[0206] S44. By calculation Determine the optimal RIS switch element k at the current moment, where Represents from the set Find the value such that (E l -E0) maximum element index l;

[0207] S45. Determine whether the number of active components currently turned on is less than L act If it is less than, execute Then return to step S43; if not less than, jump to step S46;

[0208] S46. Output the final RIS switch optimization solution and set And set

[0209] The technical means disclosed in the solutions of the present invention are not limited to those disclosed in the above-mentioned embodiments, but also include technical solutions composed of any combination of the above-mentioned technical features. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A hybrid RIS-assisted long-term energy efficiency optimization method for non-cellular networks, characterized by: The following steps are involved: Step S1: Establishing a multi-RAU multi-user link receiving signal model in a hybrid RIS-assisted cellular-free network; Step S2: Based on the signal model established in step S1, a long-term energy efficiency optimization model is established for hybrid RIS component switch scheduling, RAU precoding, hybrid RIS phase shift, and network queue backlog stability control design based on physical layer and network layer information. Based on the Lyapunov framework, the long-term queue stability constraint is transformed into a joint optimization problem of minimizing Lyapunov drift and maximizing energy efficiency. An alternating optimization strategy is used to decouple the joint optimization problem into a transmission subproblem of RAU precoding and hybrid RIS phase shift design, and a switching subproblem of hybrid RIS component switch scheduling, which are optimized separately. Step S3: For the transmission subproblem, the discrete RIS component selection constraints are transformed based on the large-M method, and the transmission subproblem is solved in each time slot using fractional programming techniques, continuous convex approximation, and semidefinite relaxation methods. Step S4: For the switching subproblem, first derive the maximum number of active components that can be turned on by the hybrid RIS. Based on the maximum number of active components, the component selection problem is transformed into multiple subproblems that can be solved in parallel using a greedy algorithm. The step S2 includes the following steps: S21. Establish the objective function of maximizing long-term energy efficiency: in It means that the objective function value is maximized after optimizing the RAU beamforming vector w, the hybrid RIS phase shift Θ, and the RIS element switch matrix A. Indicates the long-term energy efficiency of the system; S22. Establish constraints, including user QoS constraints and RAU, hybrid RIS power consumption constraints, hybrid RIS constant modulus constraints, hybrid RIS component amplification constraints, and long-term queue stability constraints. The constraints are as follows: in, is the minimum QoS constraint for users, and The maximum transmit power of each RAU and hybrid RIS; Represent the user and RIS element set respectively, K represents the number of single-antenna users, L represents the number of reflection units; σ v 2 represents the variance of the noise introduced by the hybrid RIS; is the set of active elements; Φ(t) is the phase shift matrix of active elements in time slot t; R k (t) is the rate of user k in time slot t; Q k (t) The queue backlog of user k in time slot t; G is the channel from RAU to RIS; w k (t) represents the precoding vector of user k in time slot t; θ l (t), β i (t) are the phase of the lth reflection unit and the gain of the i-th reflection unit of the hybrid RIS in time slot t; if α i If it is 1, it means that the component is an active component, and vice versa; Indicates the expected operation; |g| indicates the absolute value operation, ||g|| F represents the Frobenius norm; S23. Based on the Dinkelbach fractional programming technique, the energy efficiency objective function of time slot t is transformed into: where it is defined and η(0) = 0, Equation (7) indicates that η(t) is determined by the resource allocation scheme of the past time slot; represents the time average and rate, represents the long-term average network energy consumption; R k (τ), P total (τ) represents the rate of user k in time slot τ and the total power consumption of the system, Means "defined as"; S24. Constraints The long-term evolution of infinite time scale is included in , and Lyapunov drift is introduced for transformation; first, the Lyapunov function is defined as The Lyapunov drift of time slot t is defined as: The upper bound of the Lyapunov drift in time slot t is derived as Where B is a constant that satisfies the following conditions: By minimizing the right side of (8) in each time slot, the network tends to be stable, that is, the constraint is satisfied; based on the idea of ​​random optimization drift plus penalty, the trade-off factor V is introduced to transform the Yapunov drift into the objective function, and the objective function of the t time slot is transformed into: Then, an alternating optimization strategy is adopted to decouple the problem into the transmission subproblem of precoding design and the switching subproblem of hybrid RIS element switching scheduling, which are optimized separately.

2. The hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method according to claim 1, characterized in that: The step S3 includes the following steps: S31. Based on the large M method, we introduce a sufficiently large positive number M to simplify the constraints C5 and C6, and then introduce the auxiliary variable φ=[φ1,…,φ K ] The non-convexity caused by the coupling of the logarithmic term and SINR in the conversion rate formula, the optimization problem is transformed into: C7, C8, C2, C3, in represents the optimization of the RAU beamforming vector w and the auxiliary variable φ to minimize the objective function value; γ k is the SINR of user k; considering that the optimization problem is performed in each time slot, the time slot t index before the variable is omitted below; S32. Introducing auxiliary variable transformation constraint C 10 Non-convexity: Introducing slack variables ξ k ≥0 will constrain C 10 Converted to the following equivalent form: as well as Considering the rotation invariance of the precoding phase, constraint (10) is transformed into The concave function Through the first-order Taylor expansion, it is transformed into a second-order cone programming form: in is the value of the auxiliary variable at the nth iteration; is the equivalent channel for user k, which includes the direct path and the reflected path, {*} H To take the conjugate transpose operation, is the variance of the noise at the user, represents the channel from the hybrid RIS to the user; S33. Form the final RAU transmission optimization problem: C 15 :(11),(12), in represents the Kronecker product, vec{*} represents vectorized operation, τ′ k is the QoS slack variable of user k, ρ′1 is the corresponding penalty function factor, I K is a K-dimensional unit matrix, the problem It is a convex problem and is solved using the CVX solver; S34. Define variable conversion constraints C 10 Form: Definition Indicates the direct channel from RAU to user, Represents vector As a diagonal matrix P k diagonal elements, thereby constraining C 10 Translates to: in, S35. Transform the numerator and denominator of SINR in (13) by semidefinite relaxation technique: definition Where U ≥ 0 and rank(U) = 1, formula (13) is transformed into: in, U≥0 means that the matrix U is a semi-positive matrix, and rank(U)=1 means that the matrix U is rank one; S36. Introducing auxiliary variables The numerator and denominator of SINR in formula (14) are restricted respectively to transform the fractional structure of SINR, and the non-convexity of the auxiliary variable is transformed using continuous convex approximation: Regarding the non-convexity of Eq. (17), k Perform scaling of the first-order Taylor expansion to account for its non-convexity: in, Represents the auxiliary variable value of the tth iteration, and the gradient term is specifically Substituting (18) into (17) yields the following expression: S37. Convert the hybrid RIS power consumption into SDR form: based on tr{Adiag(b)Cdiag(b)}=b T (A T ⊙C)b, power consumption P of hybrid RIS act Translates to: Among them, ⊙, tr{*}, respectively represent the matrix Hadamard product and matrix trace, And ψ=diag(Φ), 0 L×1 represents the L-dimensional zero vector; diag(Φ) means taking the diagonal element of the matrix Φ as the output vector; diag(b) means returning the matrix with the vector b as the diagonal element; b T Indicates transposing vector b; S38. Use the penalty function method to ensure the rank of the U matrix, that is, add the constraint: tr(U)-λ max (U)≤0, to ensure the rank of the U matrix; where λ max (*) indicates the operation of taking the maximum eigenvalue; deriving λ max Convex lower bound of (U), as a surrogate function for optimization: Substitute equation (21) into the constraint tr(U)-λ max (U)≤0, and use the penalty function factor ρ′2 to add it to the objective function, and force the zero constraint through the penalty function to meet the rank(U)=1, U (t) is the solution of the tth iteration; v max is the eigenvector corresponding to the maximum eigenvalue; the objective function is transformed into: S39. The transformed RIS phase shift optimization problem is obtained: C 18 :[U] L+1,L+1 =1, C 19 :C 14 ,(15),(16),(19), in, question It is a convex problem and is solved using the CVX solver; [U] n,n It means taking the element of the nth row and nth column of matrix U; S310. According to the solved U * , obtain the RIS beamforming phase shift: Where [1:L] means taking the first L elements.

3. The hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method according to claim 1, characterized in that: The step S4 includes the following steps: S41. Determine the maximum number of active components that can be turned on in a hybrid RIS under given channel conditions: For active component m, it is obvious that |β m |≥1: Maximum number of active components that can be turned on for: Where r satisfies: in […] maxi Indicates taking the largest i-th element, Ξ i，i represents the i-th diagonal element of the matrix Ξ; S42. Initialize various parameters, including the set and The maximum number of active components that can be turned on is calculated using formula (17): And input the beamforming matrix W output in step S3 * =[w1 * , w2 * ,…,w K * ] and the phase shift matrix Θ * , determine the number of active components turned on L act , According to W * ,Θ * and collection Calculate the initial energy efficiency value E0; S43. Traverse the collection through parallel processing For each element l in the set, turn on the RIS element l in turn and add it to the set Determine the feasibility of the RIS switch solution and calculate the new energy efficiency value if feasible If the solution fails, set S44. By calculation Determine the optimal RIS switch element k at the current moment, where Represents a collection Find the value such that (E l -E0) maximum element index l; S45. Determine whether the number of active components currently turned on is less than L act If it is less than, execute Then return to step S43; if not less than, jump to step S46; S46. Output the final RIS switch optimization solution and set And set

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