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

Abstract

The invention discloses a hybrid RIS-assisted cellular-free network long-term energy efficiency optimization method. The method comprises the following steps: establishing a multi-RAU multi-user link receiving signal model; according to the signal model, a long-term energy efficiency optimization model for performing hybrid RIS element switch scheduling and RAU precoding, hybrid RIS phase shift and network queue backlog stability control design according to a physical layer channel and network layer queue information is established; converting the long-term queue stability constraint into a joint optimization problem of minimizing Lyapunov drift and maximizing energy efficiency, and decoupling the joint optimization problem into a transmission sub-problem and a switching sub-problem; discrete RIS element selection constraints are converted based on a large M method, and a transmission sub-problem is solved in each time slot through continuous convex approximation and a semi-definite relaxation method; and deducing the maximum number of active elements which can be started by the hybrid RIS, and converting an element selection combination optimization problem into a plurality of switch sub-problems which can be solved in parallel through a greedy algorithm. According to the method, the queue length can be effectively stabilized under the Lyapunov framework, and the stability of the system is ensured.

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 non-cellular network long-term energy efficiency optimization method. Background Art

[0002] To improve the performance of users at the cell edge, the cellular-free network eliminates the concept of cell boundaries through limited collaboration of distributed RAUs (Remote Antenna Units, RAUs). Each RAU shares CSI (Channel State Information, CSI) and user data through collaboration, which can greatly eliminate interference between users, reduce transmission power consumption, and improve performance. In addition, to further improve the coverage characteristics of the network, reconfigurable intelligent metasurfaces can adjust the phase of components and adjust signal reflections to create a more favorable channel environment. While improving signal coverage, it has been widely studied for its low energy consumption characteristics. Through RIS and cellular-free base stations to collaborate to serve users and perform network-level energy saving of heterogeneous devices, the high energy consumption problem caused by cellular-free ultra-dense networks (UDNs) can be effectively alleviated.

[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's data traffic is bursty, this also leads to different distributions 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 not only requires the coordinated hybrid precoding design of RIS and RAU at the physical layer, but also requires 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 actual 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 may also increase the energy consumption of the wireless network. This part of energy consumption cannot be ignored. Moreover, since the static power consumption of active elements is greater than that of passive elements, when the number of active RIS elements is large under power constraints, the static power consumption will increase linearly with the number of elements, thereby further limiting the energy used to amplify the signal. As a result, the number of RIS elements may increase but the energy efficiency may decrease.

[0006] To solve the above problems, hybrid RIS can alleviate the performance loss caused by the double fading effect by equipping a few components in RIS with amplifiers, and can also reduce the high energy consumption caused by large-scale active RIS deployment. Considering that the network traffic demand is different at different times, collaborative optimization can be performed according to the conditions of the physical layer and the network layer. For example, when the user traffic demand is large, the network layer queue length is long, and the physical layer channel conditions are poor, the number of active components of the hybrid RIS that are turned on can be appropriately increased to increase the sum rate, reduce the queue length and end-to-end delay; otherwise, the number of active components can be reduced to save energy. Based on this point, in the hybrid RIS-assisted non-cellular network, in order to further improve the energy-saving performance of the system, it is necessary to fully consider the dynamic characteristics of the user traffic at the network layer under the physical layer optimization framework, and perform layer-one-two collaborative transmission and energy efficiency optimization of RIS and RAU base stations, so as to achieve a long-term balance between performance and power consumption. Summary of the invention

[0007] The purpose of the present invention is to provide a hybrid RIS-assisted cellular-free network long-term energy efficiency optimization method. In a hybrid RIS-assisted cellular-free network, under the physical layer optimization framework, the dynamic characteristics of network layer user traffic are fully considered, and layer-one-two collaborative transmission and energy efficiency optimization of RIS and RAU base stations are performed to achieve a long-term balance between performance and power consumption to further improve the energy-saving performance of the system.

[0008] To achieve the above object, the technical solution adopted by the present invention is: a hybrid RIS-assisted non-cellular 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 switch scheduling, RAU precoding, hybrid RIS phase shift, and network queue backlog stability control design based on the 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. The problem is decoupled into transmission sub-problems of RAU precoding and hybrid RIS phase shift design and switch sub-problems of hybrid RIS component switch scheduling by using an alternating optimization strategy, and they are optimized separately.

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

[0012] Step S4: For the switch sub-problem, in order to achieve efficient RIS component selection, the maximum number of active components that can be turned on by the hybrid RIS is first derived, and based on the analyzed maximum number of active components, the component selection problem is transformed into multiple sub-problems that can be solved in parallel through a greedy algorithm, which 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 together. 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 from the RAU and the reflected signal from the RIS. It can be defined that the final equivalent signal is the sum of the direct signal and the reflected signal. Let us assume that the symbol vector sent by the user is 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 signals. 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. It means that the random variable X satisfies the mean μ and the variance σ. 2 The complex Gaussian distribution of 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 1 is equal to 1, it indicates 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 including 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 the arrival of network layer packets, 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, discrete time slots, i.e., t∈{1, 2, …, T}, are considered. 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: The system energy consumption mainly includes static power consumption and transmission power consumption, including the energy consumption of all RAUs and RIS. Considering that the energy consumption of RAU is mainly the energy consumption of precoding and RAU static power consumption. The power consumption of RIS is related to the number and type of its components. The total system power consumption at 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] In order to achieve the 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 respectively. 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, long-term queue stability constraints, etc. The constraints are as follows:

[0036]

[0037] in, is the minimum QoS constraint for users, and is the maximum transmit power of 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 the definition

[0039]

[0040] And η(0) = 0, equation (7) indicates 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 impossible to deal with directly. 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 increasing queue length, and the smaller L(Q k (t)) can reduce queue backlog and delay. In order to stabilize the queue length, 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 switch scheduling, which are optimized separately.

[0046] The step S3 includes the following steps:

[0047] S31. Based on the big M method, we introduce a sufficiently large positive number M to simplify the constraints C5 and C6, and then introduce an 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 the optimization problem to be 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 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, the hybrid RIS precoding is solved.

[0065] S34. Define variable transformation constraints C 10 Form: Definition Indicates the direct channel from RAU to the user. Represents vector As a diagonal matrix P k The diagonal elements of . Thus, 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, It can be seen from formula (14) that 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 definite matrix, and rank(U) = 1 indicates that the matrix U is of rank one;

[0072] S36. Introducing auxiliary variables The numerator and denominator of SINR in equation (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 (17), consider k 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 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) represents taking the diagonal elements of the matrix Φ as the output vector. Diag(b) represents returning a matrix with vector b as the diagonal element.

[0082] S38. Transform the rank-one constraint of semidefinite relaxation based on penalty function method: So far, the remaining non-convex part of the hybrid RIS phase shift optimization problem is mainly the rank-one constraint, which makes the whole 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 is added: tr(U)-λ max (U)≤0 to ensure the rank unity of the U matrix. max (*) indicates the operation of taking the maximum eigenvalue. However, 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 the 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 use the penalty function to force the zero constraint to satisfy rank(U)=1, U (t) is the solution of the tth iteration. 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 is a convex problem and can be solved using the CVX solver. n，n It means taking the element of the nth row and nth column of matrix U.

[0092] S310. According to the solved U*, the RIS beamforming phase shift is obtained: 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 obviously necessary to satisfy |β m |≥1: Maximum number of active components that can be turned on for:

[0095]

[0096] Where r satisfies:

[0097]

[0098] in […] maxi means 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 are determined based on the maximum number of active components that can be turned on analyzed in S41.

[0099] S42. Initialize various parameters, including collection 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, turn on 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 it is 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 growth of the number of hybrid RIS components. In terms of performance, it can effectively stabilize the system queue length, ensure the stability of the system, 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 non-cellular 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 the number of RAU antennas. The hybrid RIS has 1 enabled element, and the comparison algorithms are the traditional passive RIS, active RIS, and the random element with 1 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 solution provided by the present invention will be described in detail below in conjunction with specific embodiments. It should be understood that the following specific implementation methods 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 switch scheduling, RAU precoding, hybrid RIS phase shift, and network queue backlog stability control design based on the 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. The problem is decoupled into transmission sub-problems of RAU precoding and hybrid RIS phase shift design and switch sub-problems of hybrid RIS component switch scheduling by using an alternating optimization strategy, and they are optimized separately.

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

[0113] Step S4: For the switch sub-problem, in order to achieve efficient RIS component selection, the maximum number of active components that can be turned on by the hybrid RIS is first derived, and based on the analyzed maximum number of active components, the component selection problem is transformed into multiple sub-problems that can be solved in parallel through a greedy algorithm, which 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 together. 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 from the RAU and the reflected signal from the RIS. It can be defined that the final equivalent signal is the sum of the direct signal and the reflected signal. Let us assume that the symbol vector sent by the user is 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 signals. 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. It means that the random variable X satisfies the mean μ and the variance σ. 2 The complex Gaussian distribution of 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 1 is equal to 1, it indicates 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 including 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 the arrival of network layer packets, 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, discrete time slots, i.e., t∈{1, 2, …, T}, are considered. 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: The system energy consumption mainly includes static power consumption and transmission power consumption, including the energy consumption of all RAUs and RIS. Considering that the energy consumption of RAU is mainly the energy consumption of precoding and RAU static power consumption. The power consumption of RIS is related to the number and type of its components. The total system power consumption at 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] In order to achieve the 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 respectively. 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, long-term queue stability constraints, etc. The constraints are as follows:

[0137]

[0138] in, is the minimum QoS constraint for users, and 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 the definition

[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 impossible to deal with directly. 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 increasing queue length, and the smaller L(Q k (t)) can reduce queue backlog and delay. In order to stabilize the queue length, 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 switch scheduling, which are optimized separately.

[0147] The step S3 includes the following steps:

[0148] S31. Based on the big M method, we introduce a sufficiently large positive number M to simplify the constraints C5 and C6, and then introduce an 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 the vectorized operation. τ′k is the QoS slack variable of user k, ρ1 is the corresponding penalty function, and the problem 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, the hybrid RIS precoding is solved.

[0166] S34. Define variable transformation constraints C 10 Form: Definition Indicates the direct channel from RAU to the user. Represents vector As a diagonal matrix P k The diagonal elements of . Thus, 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, It can be seen from formula (14) that 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 definite matrix, and rank(U) = 1 indicates that the matrix U is of rank one;

[0173] S36. Introducing auxiliary variables The numerator and denominator of SINR in equation (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 (17), consider k 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 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) represents taking the diagonal elements of the matrix Φ as the output vector. Diag(b) represents returning a matrix with vector b as the diagonal element.

[0183] S38. Transform the rank-one constraint of semidefinite relaxation based on penalty function method: So far, the remaining non-convex part of the hybrid RIS phase shift optimization problem is mainly the rank-one constraint, which makes the whole 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 is added: tr(U)-λmax (U)≤0 to ensure the rank unity of the U matrix. max (*) indicates the operation of taking the maximum eigenvalue. However, 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 the 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 use the penalty function to force the zero constraint to satisfy rank(U)=1, U (t) is the solution of the tth iteration. 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. According to the solved U*, the RIS beamforming phase shift is obtained: 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 obviously necessary to satisfy |β m |≥1: Maximum number of active components that can be turned on for:

[0196]

[0197] Where r satisfies:

[0198]

[0199] in […] maxi means taking the largest i-th element, Ξ i，i represents 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 when e i is a one-hot vector of length L with 1 at the i-th position and 0 at the rest. Arranged in ascending order:

[0202]

[0203] Then by Obviously, the above maximum number of 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 collection 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, turn on 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 it is 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 scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method, characterized by: The following steps are involved: Step S1: Establishing a multi-RAU multi-user link reception 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 element switch scheduling, RAU precoding, hybrid RIS phase shift, and network queue backlog stability control design based on physical layer and network layer information, and the long-term queue stability constraint is converted into a joint optimization problem of minimizing Lyapunov drift and maximizing energy efficiency based on the Lyapunov framework. The joint optimization problem is decoupled into transmission sub-problems of RAU precoding and hybrid RIS phase shift design and switch sub-problems of hybrid RIS element switch scheduling by using an alternating optimization strategy, and they are optimized separately; Step S3: For the transmission optimization problem, firstly, the discrete RIS component selection constraints are transformed based on the big M method, and the transmission sub-problem is solved in each time slot by using fractional programming techniques, continuous convex approximation and semidefinite relaxation method; For the switch sub-problem, the maximum number of active components that can be turned on by the hybrid RIS is first derived, and based on the maximum number of active components, the component selection problem is transformed into multiple sub-problems that can be solved in parallel through a greedy algorithm.

2. According to claim 1, a hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method is characterized by: 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 respectively. 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 for 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 υ 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 (k), 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 respectively; if α i If it is 1, it means that the component is an active component, and vice versa; represents the expected operation; |·| represents the absolute value operation, ||·|| F represents the Frobenius norm; S23. Based on Dinkelbach fractional programming technique, the energy efficiency objective function of time slot t is transformed into: where the definition and η(0) = 0, where (2) 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, Meaning is defined as; S24. Constraints contains the long-term evolution of infinite time scale, and introduces Lyapunov drift for transformation; first define the Lyapunov function 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 (3) 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 switch scheduling, which are optimized separately.

3. A hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method according to claim 2, characterized in that: The step S3 includes the following steps: S31. Based on the big M method, we introduce a sufficiently large positive number M to simplify the constraints C5 and C6, and then introduce an 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 of : 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 (5) 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 of user k including 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 the user. Represents vector As a diagonal matrix P k The diagonal elements of C 10 Translates to: in, S35. Transform the numerator and denominator of SINR in (8) by semidefinite relaxation technique: definition in And rank(U)=1, formula (13) is transformed into: in, Indicates that the matrix U is a semi-positive definite matrix, and rank(U) = 1 indicates that the matrix U has rank one; S36. Introducing auxiliary variables The numerator and denominator of SINR in equation (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 formula (12), k 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 Substituting (133) into (12), we obtain 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) represents taking the diagonal elements of the matrix Φ as the output vector; Diag(b) represents 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 unity of the U matrix, that is, add the constraint: tr(U)-λ max (U)≤0 to ensure the rank unity 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 (16) 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 use the penalty function to force the zero constraint to satisfy 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 is a convex problem and is solved using the CVX solver; [U] n，n It means taking the element of the nth row and the nth column of the matrix U; S310. According to the solved U*, the RIS beamforming phase shift is obtained: Where [1:L] means taking the first L elements.

4. A hybrid RIS-assisted non-cellular network long-term energy efficiency optimization method according to claim 2, characterized in that: The step S4 includes the following steps: 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 obviously necessary to satisfy |β m |≥1: Maximum number of active components that can be turned on for: Where r satisfies: in […] maxi means taking the largest i-th element, Ξ i，i represents the i-th diagonal element of the matrix Ξ; S42. Initialize various parameters, including collection and The maximum number of active components that can be turned on is calculated by 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 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 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 it is feasible If the solution fails, set 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; 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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