STAR-RIS-NOMA downlink communication system for maximizing rate sum based on joint optimization

Abstract

The invention relates to the technical field of communication, in particular to an STAR-RIS-NOMA downlink communication system for maximizing the rate sum based on joint optimization. Comprising a base station equipped with multiple antennas; the STAR-RIS is composed of M reconfigurable units, and the STAR-RIS divides a communication space into a reflection space and a transmission space; the users are divided into C clusters and are distributed in the reflection space and the transmission space; a base station performs joint optimization on a decoding sequence, a power distribution coefficient, a base station active beam forming vector and a transmission and reflection coefficient matrix of STAR-RIS. According to the STAR-RIS-NOMA downlink communication system for maximizing the rate sum based on joint optimization provided by the invention, a dynamic decoding sequence scheme based on an equivalent channel gain is provided by considering a beam forming gain introduced by STAR-RIS and a key inter-cluster interference influence. The scheme not only can adapt to channel reconstruction of STAR-RIS, but also theoretically proves that the SIC condition is automatically satisfied under the sequence, so that the complex SIC constraint is removed from the optimization problem.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a STAR-RIS-NOMA downlink communication system that maximizes rate and sum based on joint optimization. Background Technology

[0002] Reconfigurable smart surfaces (RIS), as a novel wireless communication enabling technology, can effectively enhance signal coverage and increase system capacity by modulating the propagation environment of electromagnetic waves. However, traditional RIS only possess a single reflection or transmission function, limiting their application in full-space coverage scenarios. To address this, STAR-RIS technology has emerged, where each unit can independently adjust both the reflection and transmission coefficients simultaneously, achieving intelligent full-space control of incident signals and providing a new technological path for building intelligent radio environments.

[0003] Although the combination of STAR-RIS and NOMA technologies theoretically offers significant performance advantages, it still faces numerous challenges in practical system deployment. First, strong nonlinear coupling exists between the reflection and transmission coefficient matrices of STAR-RIS, the base station active beamforming vector, the user power allocation coefficients, and the SIC decoding order, resulting in a highly nonconvex joint optimization problem. This nonconvexity stems not only from multivariate coupling but also from the fractional structure of the rate expression and the nonconvex feasible region constraint of STAR-RIS, making direct solutions difficult. Second, as the user base expands, the complexity of SIC processing in traditional NOMA systems increases exponentially, severely impacting real-time system performance. Furthermore, existing research often assumes ideal channel state information and a fixed decoding order, failing to adequately consider the impact of inter-cluster interference and dynamic channel conditions on system performance, leading to a significant gap between actual system performance and theoretical limits.

[0004] Therefore, it is urgent to propose a joint optimization method for base station beamforming vector, STAR-RIS transmission / reflection coefficient, user power allocation coefficient, and SIC decoding order suitable for STAR-RIS-NOMA downlink communication systems. This method aims to maximize the overall system rate while meeting user quality of service requirements, SIC, power, and STAR-RIS feasible domain requirements, thereby promoting the application and development of STAR-RIS and NOMA fusion technology in practical communication systems. Summary of the Invention

[0005] Based on this, a STAR-RIS-NOMA downlink communication system based on joint optimization to maximize the rate sum is provided to solve the technical problems mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, comprising:

[0008] A base station equipped with multiple antennas; a STAR-RIS consisting of M reconfigurable units, the STAR-RIS dividing the communication space into a reflection space and a transmission space; multiple users, the users being divided into C clusters and distributed in the reflection space and the transmission space; the base station maximizes the sum of achievable rates for all users in the system by jointly optimizing the decoding order, power allocation coefficients, base station active beamforming vectors, and the transmission and reflection coefficient matrices of the STAR-RIS.

[0009] As a preferred embodiment of the STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum provided by the present invention, the determination of the decoding order is based on the user's equivalent channel gain, and the formula for calculating the equivalent channel gain is:

[0010] ;

[0011] in, The representative index is The user's equivalent channel gain; for users within the same cluster, SIC decoding is performed in ascending order of their equivalent channel gain.

[0012] As a preferred embodiment of the STAR-RIS-NOMA downlink communication system based on joint optimization to maximize the rate sum provided by the present invention, after the decoding order is determined based on the equivalent channel gain, the rate compatibility constraint for serial interference elimination is automatically satisfied in subsequent optimization, and therefore is not used as a constraint condition and is removed in the subsequent joint optimization process.

[0013] As a preferred embodiment of the STAR-RIS-NOMA downlink communication system based on joint optimization to maximize the sum of rates provided by the present invention, the optimization of the power allocation coefficient is obtained by solving a closed-form equation system under the premise of the base station active beamforming vector and the STAR-RIS coefficient matrix. The equation system is constructed by sequentially ensuring the minimum rate requirement of users with lower equivalent channel gain and allocating all remaining power to users with higher equivalent channel gain.

[0014] As a preferred embodiment of the STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum provided by the present invention, the optimization method of the base station active beamforming vector includes:

[0015] a) Introduce auxiliary variables to reconstruct the user rate expression, transforming the original problem into an equivalent problem; b) Use semidefinite relaxation techniques to transform the beamforming vector optimization problem into a semidefinite programming problem; c) Use a continuous convex approximation method to handle the non-convex constraints in the transformed problem; d) Solve the relaxed convex optimization problem and use Gaussian randomization techniques to recover the active beamforming vector that satisfies the rank-one constraint.

[0016] As a preferred embodiment of the STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum provided by the present invention, the optimization method of the STAR-RIS transmission and reflection coefficient matrices includes:

[0017] The STAR-RIS coefficient vector is extracted as the optimization variable through mathematical transformation, and an augmented matrix is ​​constructed. The problem is transformed into an optimization problem with respect to the augmented matrix using semidefinite relaxation techniques. The rank-one solution is approximated by iteratively tightening the maximum eigenvalue constraint using a sequential constraint relaxation method, thereby obtaining a suboptimal solution for the STAR-RIS coefficient matrix.

[0018] As a preferred embodiment of the STAR-RIS-NOMA downlink communication system that maximizes rate sum based on joint optimization provided by the present invention, the joint optimization is implemented through a two-layer iterative algorithm:

[0019] Outer layer iteration: Calculate the equivalent channel gain for all users based on the current system parameters, and update the SIC decoding order within each cluster to be more appropriate; Inner layer iteration: Under a fixed decoding order, alternately perform power allocation coefficient optimization, base station active beamforming vector optimization, and STAR-RIS transmission and reflection coefficient matrix optimization until the inner layer objective function converges.

[0020] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the steps of the optimization method.

[0021] A computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the steps of the optimization method.

[0022] Meanwhile, through the above technical solutions, the present invention has at least the following beneficial effects:

[0023] 1. This invention provides a STAR-RIS-NOMA downlink communication system based on joint optimization to maximize the rate sum. In this system, an independent STAR-RIS assists communication between the BS and cluster users, and establishes a corresponding system rate sum maximization optimization problem. By jointly optimizing the decoding order, power allocation coefficient, base station active beamforming vector, and STAR-RIS transmission and reflection coefficient matrix, the system aims to maximize the total achievable rate sum of all users. The constraints include minimum QoS requirements, SIC decoding conditions, BS total transmit power constraints, and transmission and reflection coefficient constraints.

[0024] 2. This invention proposes a novel SIC decoding order scheme based on equivalent channel gain. The equivalent channel gain takes into account inter-cluster interference. It is deduced and proved that the decoding order determined based on the equivalent channel gain can guarantee the SIC condition.

[0025] 3. Unlike traditional NOMA systems that determine the decoding order solely based on direct channel gain, this invention fully considers the beamforming gain introduced by STAR-RIS and the critical inter-cluster interference, proposing a dynamic decoding order scheme based on equivalent channel gain. This scheme not only adapts to the channel reconstruction by STAR-RIS, but also theoretically proves that the SIC condition is automatically satisfied under this order, thereby removing complex SIC constraints from the optimization problem and greatly simplifying the problem-solving difficulty and computational complexity.

[0026] 4. This invention addresses the challenges of strong coupling and non-convexity in joint optimization by designing a two-layer iterative framework: an outer layer updates the decoding order, while an inner layer alternately optimizes power, beamforming, and STAR-RIS coefficients. This framework decomposes the original problem into multiple tractable subproblems and comprehensively utilizes advanced mathematical tools such as continuous convex approximation, semidefinite relaxation, and sequential constraint relaxation. This enables the efficient acquisition of high-quality suboptimal solutions for the global system performance, ensuring the feasibility and convergence of the algorithm. Attached Figure Description

[0027] Figure 1 This is a schematic diagram illustrating the signal propagation of traditional RIS and STAR-RIS. Figure 2 A schematic diagram of the three working protocols of STAR-RIS; Figure 3 This is a schematic diagram of the downlink NOMA transmission system of the present invention; Figure 4 This is a schematic diagram of the uplink NOMA transmission system of the present invention; Figure 5 This is a schematic diagram of convex and non-convex sets according to the present invention; Figure 6 This is a schematic diagram of the system model of the present invention; Figure 7 This is a schematic diagram illustrating the convergence of Algorithm 1 of the present invention; Figure 8 This is a schematic diagram illustrating the convergence of Algorithm 2 of the present invention; Figure 9This is a schematic diagram illustrating the convergence of Algorithm 3 of the present invention; Figure 10 This is a schematic diagram illustrating the effect of the number of RIS elements on the system speed in different systems according to the present invention; Figure 11 This is a schematic diagram illustrating the effect of the number of BS antennas on the system speed and efficiency of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0029] Reference Figures 1-11 A STAR-RIS-NOMA downlink communication system that maximizes rate and sum based on joint optimization.

[0030] I. Technical Introduction

[0031] 1.1 STAR-RIS (Simultaneous Transmission and Reflection Reconfigurable Smart Surface)

[0032] like Figure 1 This is a schematic diagram of signal propagation between traditional RIS and STAR-RIS.

[0033] 1.1.1 STAR-RIS Signal Model

[0034] from Figure 1 As can be seen, the entire space is divided into two half-spaces by STAR-RIS. When a wireless signal is transmitted to STAR-RIS from any direction, the incident signal will be split into two parts. One part is reflected by STAR-RIS to the same space as the incident signal, which is called the reflection space. The other part is transmitted through STAR-RIS to another space opposite to the incident signal, which can be called the transmission space. The reflected signal and the transmitted signal can be configured by the reflection and transmission coefficients of STAR-RIS to realize a highly flexible intelligent radio environment.

[0035] 1.1.2 STAR-RIS Operating Protocol

[0036] Each element in STAR-RIS must obey the law of conservation of energy, and the amplitude of each element can have three states: transmission amplitude is 0, reflection amplitude is 1; both transmission and reflection amplitudes are between 0 and 1; and transmission amplitude is 1, reflection amplitude is 0. Based on this characteristic, three operating protocols for STAR-RIS (such as...) are proposed. Figure 2 As shown in the figure, its technical features are analyzed as follows:

[0037] (1) Energy splitting (ES): such as Figure 2As shown in (a), the ES protocol requires all units to simultaneously support full-duplex transmission and reflection modes in the frequency domain. Each unit can independently adjust the transmission amplitude coefficient, reflection amplitude coefficient, and corresponding phase shift coefficient. Its spatial parameters satisfy... , , The agreement is achieved through joint optimization. Four-dimensional parameters provide the maximum degree of freedom for beamforming. However, as the system scales up, the dimensionality of the optimization variables also increases, especially when considering phase-shift coupling, which leads to an exponential increase in the complexity of STAR-RIS coefficient design.

[0038] (2) Mode switching (MS): such as Figure 2 As shown in (b), the MS protocol divides all STAR-RIS components into transmission subsets. and reflection subset Each component needs to meet the following constraints: and This protocol eliminates the effects of amplitude coupling through hardware constraints, simplifying the optimization variables to binary decision variables and phase shift optimization. The achievable beamforming gain of this mode is also lower than that of the ES mode.

[0039] (3) Time Switching (TS): such as Figure 2 As shown in (c), the TS protocol uses a time-division multiplexing mechanism, in time slots The internal configuration sets all units to transmission mode. ), in time slot The internal configuration sets all elements to reflective mode. Its time slot allocation must meet the following requirements. ,in The time of one transmission frame.

[0040] 1.2.NOMA

[0041] 1.2.1 Overview of NOMA Technology

[0042] NOMA technology innovatively constructs non-orthogonal resource dimensions such as the power domain and code domain, enabling multiple users to achieve superimposed transmission on shared time-frequency resources, effectively breaking through the spectral efficiency bottleneck of traditional OMA technology. The core features of this technology can be analyzed from three levels: serial interference cancellation mechanism, dynamic power adaptation strategy, and low signaling overhead design.

[0043] 1.2.2 NOMA Transmission System

[0044] (1) Downlink NOMA transmission system

[0045] Figure 3In this scenario, the Base Station (BS) transmits superimposed signals to two users using power domain multiplexing. The near-end user (User 1) has a higher channel gain due to its proximity to the BS, while the far-end user (User 2) experiences significant channel gain attenuation due to path loss. The BS employs a differentiated power allocation strategy, allocating lower power to the near-end user (with better channel conditions) and higher power to the far-end user (at the coverage edge), thus constructing a composite signal with a decorable power difference. This indicates that the BS sends to the first Unit power signal per user; This indicates that BS is assigned to the first Transmission power per user, Indicates BS to the number The channel gain for each user, then in a downlink NOMA transmission system, the user The received signal can be represented as:

[0046] ;

[0047] in This indicates the superimposed signal sent by the BS to the user. Indicates the first Gaussian white noise at each user location, and obeys .like Figure 3 As shown, the receiver uses SIC (Separate Injection Channel) technology to separate signals. User 1 needs to first decode and eliminate the remote user's signal components before demodulating its own target signal; User 2, due to its superior signal power, can directly decode the target signal without SIC processing. The effectiveness of this mechanism is directly affected by the power allocation ratio—the BS (Base Station) can dynamically balance the achievable rate thresholds of the two users by adjusting their power ratio, thereby adapting to the service quality requirements of different service types. According to Shannon's theorem, the achievable rates of User 1 and User 2 after decoding can be expressed as:

[0048] ;

[0049] ;

[0050] (2) Uplink NOMA transmission system

[0051] Figure 4 This demonstrates a typical application scenario for an uplink NOMA system, where near-end users and far-end users transmit signals to a single-antenna BS within a shared frequency band. Similar to the downlink assumptions, the superimposed signal received by the BS can be directly obtained as follows:

[0052] ;

[0053] At the Base Station (BS), Signal Separation by Channel Interference Capacity (SIC) is still employed. During this separation process, the BS dynamically adjusts the SIC decoding order based on a descending channel gain criterion: it prioritizes decoding and eliminating the signal component of User 1, which has better channel conditions, and then demodulates the information of User 2 from the remaining signal. Through this process, the transmission rate of User 1 is mainly constrained by its own transmit power and the interference from User 2, while the rate of User 2 is only related to its transmit power. After decoding, the achievable rates of User 1 and User 2 received by the base station can be expressed as:

[0054] ;

[0055] .

[0056] II. Multi-user Communication System

[0057] Constructing an efficient joint optimization mechanism is a core challenge in the design of STAR-RIS-NOMA systems. On the other hand, while SiC (Self-Integrated Clustering) can effectively suppress inter-cluster interference among NOMA users, its computational complexity increases exponentially with the expansion of the user base. Existing research shows that user-based NOMA techniques can significantly reduce the implementation complexity of SiC, but they introduce inter-cluster interference. To reduce inter-cluster and intra-cluster interference, power allocation and beamforming optimization techniques play a crucial role.

[0058] 2.1 System Model

[0059] Table 1 summarizes the symbols mainly used in this invention and their physical meanings.

[0060] Table 1: Symbols and Physical Meanings

[0061] 2.1.1 Scenario Description

[0062] like Figure 6 As shown, this invention considers a STAR-RIS-NOMA downlink communication system. Considering a real-world propagation environment, in addition to a direct link, the BS and user obtain an additional communication link for auxiliary communication through the deployment of STAR-RIS. The BS is equipped with... The STAR-RIS is a uniform linear array of root transmission antennas. A uniform planar array composed of [number] components. All users were divided into [groups] using clustering techniques. Each cluster, the cluster set, and the user set are defined as follows: and For any cluster Its user subset The following clustering constraints must be met: , Let the first... Number of users in a cluster Then the total number of users in the system satisfies .

[0063] 2.1.2 System Model Establishment

[0064] Based on the system scenario, it is known that there are direct links and reflected links between the BS and the user, defined as follows: Let be the direct link channel vector from BS to user k in cluster c. The reflection link between BS and user consists of three parts: the channel from BS to STAR-RIS, the STAR-RIS coefficient matrix, and the channel from STAR-RIS to user. Defined The channel matrix from BS to STAR-RIS For STAR-RIS to the 1st The th cluster The channel vectors of each user, the coefficient matrix of STAR-RIS uses It is indicated that it is defined as:

[0065] (1)

[0066] in, , So, for the first The th cluster For each user, the reflected link channel can be represented as: Therefore, the cascaded channel from the BS to the user can be represented as: .

[0067] In a clustered STAR-RIS-NOMA downlink transmission system, the BS provides services to multiple users through multi-cluster active beamforming vectors. Let... , Indicates the first The active beamforming vector of the i-th cluster, then the i-th The th cluster The signal received by a user can be modeled as follows:

[0068] (2)

[0069] in, For the first The th cluster The power allocation coefficients for each user satisfy the intra-cluster power constraints. , Indicates a symbol sent to the user. It is additive white Gaussian noise and satisfies ,in It is noise power. According to the formula... Therefore, the first The th cluster The signal received by a user can be divided into four parts, among which Indicates the signal the user expects to receive. This indicates that the user has received interference from other users within the cluster. This indicates inter-cluster interference caused by users in other clusters besides the user's own cluster, as well as Gaussian white noise interference generated by the user themselves.

[0070] In the STAR-RIS-NOMA system, the SIC (Self-Integrated Computational) among users within a cluster faces multidimensional complexity challenges. Specifically, each cluster contains [number of users]. When a user is present, the permutations and combinations of their decoding order exist. This combination of possibilities significantly increases the complexity of system optimization. Traditional NOMA systems, which determine the decoding order based on the monotonicity of user channel gain, face the following dual challenges in the STAR-RIS-NOMA scenario:

[0071] First, STAR-RIS can reconstruct the channel from the base station (BS) to the user by dynamically adjusting the transmission and reflection coefficient matrices, resulting in time-varying channel gain for the user. Second, inter-cluster interference disrupts the optimal decoding order based on local channel state information. To accurately characterize this complex scenario, we define... For clusters The Middle The index mapping function for each decoding user means that in the cluster The Middle The original user index value for decoding a user, for example in a cluster containing 3 users. This represents the original user index value of the first user to decode, and its value is determined as the decoding order is established. So, the user... During the SIC process, preceding users need to be eliminated sequentially. The interference, the SINR of its received signal can be modeled as:

[0072] (3)

[0073] in, The achievable rate for this user can be expressed as:

[0074] (4)

[0075] And for clusters Any two users and If satisfied According to the NOMA protocol, users User needs to be decoded first The signal, and through SIC technology, the user The signal is removed from the superimposed signal, at which point the user... For users The SINR of the decoded signal can be expressed as:

[0076] (5)

[0077] The corresponding achievable rate is .

[0078] To ensure the feasibility of SIC within a cluster, rate compatibility conditions must be met for any two users. This condition ensures that when For users At the minimum decodeable rate, the user Decoding User The rate is not lower than this threshold to ensure user safety. Users The signal is decoded and eliminated from the superimposed signal, thus enabling SIC to execute smoothly. Taking a three-user scenario as an example, the three users within the cluster need to meet the following requirements:

[0079] (6)

[0080] Promoted to include Clusters of individual users The number of SIC conditions that need to be satisfied is It is worth noting that these conditions are simultaneously affected by the base station's active beamforming vector, the intra-cluster power allocation coefficient, and the STAR-RIS transmission and reflection coefficient matrix.

[0081] Ultimately, the sum of reachable rates for all users in the STAR-RIS-NOMA system can be expressed as:

[0082] (7)

[0083] 2.2 Problem Formulation and Solution

[0084] 2.2.1 Establishing the Target Problem

[0085] To improve the speed and efficiency of the STAR-RIS-NOMA system, this invention constructs a joint optimization framework to collaboratively design the optimization problems of decoding order, power allocation coefficients, BS active beamforming vectors, and the transmission and reflection coefficient matrices of STAR-RIS, thereby maximizing the system's performance. The problem of maximizing the sum of reachable rates for all users can be specifically expressed as:

[0086]

[0087] (8)

[0088] (9)

[0089] (10)

[0090] (11)

[0091] (12)

[0092] (13)

[0093] in, , , , This represents the minimum QoS requirements for each user. This represents the maximum power budget of BS. In this optimization problem, the constraint formula... This ensures that all users in the system can meet the minimum rate requirement, and the constraint formula is correct. This ensures the feasibility of SIC within the cluster, and the constraint formula is as follows: The total transmit power of a base station is limited to not exceeding the base station's maximum transmit power budget, as shown in the formula. The power allocation factor for users within a cluster is limited by the formula. It is the amplitude and phase shift constraint of STAR-RIS. This is a constraint on the decoding order, where This represents the set of all possible decoding orders.

[0094] Observing the original optimization problem, we can see that its non-convexity mainly comes from the following three aspects: firstly, the objective function and constraints. and It includes a fractional form of the rate term; secondly, constraints. The feasible regions of STAR-RIS dependencies and amplitudes are non-convex; furthermore, there are coupling effects among variables such as decoding order, active beamforming vector, power allocation coefficients, and the STAR-RIS coefficient matrix. These non-convex characteristics make it difficult to directly solve for the global optimum. Therefore, an efficient algorithm is proposed to solve the suboptimal solution to this problem.

[0095] 2.2.2 Solving the Target Problem

[0096] To address the challenges of nonconvexity and variable coupling in the original optimization problem, this invention proposes a two-layer alternating optimization framework. The algorithm employs an outer-layer iteration to determine the user decoding order and an inner-layer iteration to jointly optimize system parameters. The outer-layer iteration dynamically adjusts the user decoding order within the cluster based on the equivalent channel gain, while the inner-layer iteration jointly optimizes the power allocation coefficients, the BS active beamforming vector, and the STAR-RIS transmission and reflection coefficient matrices under a fixed decoding order.

[0097] (1) Decoding order based on equivalent channel gain

[0098] Decoding order is a crucial issue in STAR-RIS-NOMA systems, and it is dynamically updated based on current system parameters during outer iterations. Due to user clustering, this invention introduces a novel scheme to determine the decoding order, compared to the traditional NOMA downlink communication method that relies on user channel gain.

[0099] For containing Clusters of individual users For example, given the active beamforming vector of the BS Transmission and reflection coefficient matrices of STAR-RIS Then, the optimal decoding order can be defined as:

[0100] (14)

[0101] in, The representative index is The user's equivalent channel gain is specifically defined as:

[0102] (15)

[0103] formula This indicates that in the STAR-RIS-NOMA system, the intra-cluster decoding order is essentially an active beamforming vector. Transmission and reflection coefficient matrices of STAR-RIS The function of power allocation coefficient. Irrelevant. Furthermore, for any two users within the same cluster... If the decoding order of these two users satisfies:

[0104] (16)

[0105] in, express The inverse function of .

[0106] Therefore, under the optimal decoding order, the following SIC conditions can be guaranteed:

[0107] (17)

[0108] Proof: If the equivalent channel gain of any two users within the same cluster satisfies the formula So according to the formula The equivalent channel gain for these two users satisfies the following condition:

[0109] (18)

[0110] For the formula After simple transformation, it can be written in the following form:

[0111]

[0112] By analyzing the formula Multiply both sides simultaneously In addition ,formula It can be transformed into:

[0113]

[0114] For the formula The terms inside the parentheses on both sides of an inequality can be divided to obtain the following:

[0115] ;

[0116] And the formula This means the SIC condition has been met, and the proof is now complete.

[0117] Under the decoding order based on equivalent channel gain, intra-cluster users can directly satisfy the SIC condition, and the SIC condition constraint formula in the original problem is... This becomes a redundant constraint; removing it will not change the optimal solution space of the optimization problem. We introduce decoding order standardization and set... Therefore, the original problem can be reconstructed into the following form:

[0118]

[0119] (twenty one)

[0120] (twenty two)

[0121] , (twenty three)

[0122] In the subsequent solution process, the equivalent substitution problem P4.1 of the original problem is solved to obtain the equivalent solution of the original optimization problem;

[0123] Among them, problem P4.1 is the decoding order optimization problem, including the objective function and the constraints of formulas (21)-(23), and the meanings of these are the same below.

[0124] (2) Optimization of power allocation coefficient

[0125] Given the active beamforming vector of BS Transmission and reflection coefficient matrices of STAR-RIS Since inter-cluster interference is independent of the power allocation coefficient, problem P4.1 can be decomposed into: Each is an independent subproblem. Without loss of generality, the first... The problem of optimizing the power allocation coefficients of a cluster can be expressed as:

[0126]

[0127] (twenty four)

[0128] The objective function of problem P4.2 contains a fractional form of the logarithmic rate term, but its non-convexity can be effectively avoided by deriving a closed solution. Problem P4.2 specifically refers to the power allocation coefficient optimization problem based on problem P4.1 proposed above, including the objective function and the constraints of formula (24). The meaning of the expression of problem P4.2 below is the same.

[0129] To verify the solvability of this problem, the following lemma 1 is proposed:

[0130] Lemma 1: Given the active beamforming vector of the BS Transmission and reflection coefficient matrices of STAR-RIS And the optimal decoding order If the following inequalities are satisfied:

[0131] (25)

[0132] Therefore, P4.2 is solvable.

[0133] Proof: From the expression for SINR And the expression for the equivalent channel gain ,user achievable rate It can be rewritten as:

[0134] (26)

[0135] definition It is the first The th cluster The minimum power allocation factor that allows a user to meet its QoS requirements. Assuming that any user within a cluster can meet its QoS requirements when allocated its minimum power allocation factor, then the following equation can be obtained:

[0136] (27)

[0137] Then, regarding the formula... By transforming it, we can obtain:

[0138] (28)

[0139] in, Cluster The sum of the minimum power allocation coefficients of all users in the cluster yields the sum of the minimum power allocations for that cluster:

[0140] (29)

[0141] in, .when When, that is, implying in the cluster The power allocation within the system cannot meet the minimum QoS requirements of all users. This may be due to resource allocation issues caused by the BS active beamforming vector and the STAR-RIS coefficient matrix. The aforementioned variables need to be optimized before solving this sub-problem. When, it means that an optimal one exists. Able to satisfy cluster If the minimum QoS requirements of all users are met, then problem P4.2 is solvable. Proof complete.

[0142] Based on the feasibility conditions provided by Lemma 1, when At that time, problem P4.2 has an optimal solution. Based on the introduced idea, to maximize the system's rate sum, power allocation should follow these principles: First, QoS guarantees should be provided for some users, prioritizing the minimum power requirements of users with low equivalent channel gain; second, margin optimization should be performed, that is, all remaining power should be allocated to users with the highest equivalent channel gain to maximize the system rate sum. Based on these allocation principles, the following equation can be established:

[0143] (30)

[0144] By expanding the formula The rate equations in the equations can be used to construct a system of recursive equations:

[0145] (31)

[0146] Solving the above system of equations will yield the cluster. The optimal power allocation factor for all users is shown in the following formula:

[0147] (32)

[0148] (3) BS active beamforming vector optimization

[0149] Given a power allocation coefficient STAR-RIS transmission and reflection coefficient matrix Under these conditions, this invention focuses on optimizing the BS active beamforming vector. To address the non-convexity of the objective function in the original problem (P4.1), two auxiliary variables are introduced. The rate expression is reconstructed, where and The definition is as follows:

[0150] (33)

[0151] (34)

[0152] Formula and formula Substitute into the SINR expression , No. Users in each cluster The achievable rate can be rewritten as:

[0153] (35)

[0154] Based on this reconstruction, the formula will then be... and formula Substituting into problem P4.1, problem P4.1 can be transformed into the following equivalent form:

[0155] ;

[0156] (36)

[0157] (37)

[0158] (38)

[0159] (39)

[0160] Among them, problem P4.3 specifically refers to the beamforming vector optimization problem based on problem P4.1 mentioned above, including the objective function and the constraints of formulas (36)-(39). The meaning of the expression in problem P4.3 below is the same.

[0161] Problem P4.3 achieves linearization of the objective function through auxiliary variables, but its constraints still present a non-convexity challenge. The constraint formula... Including the coupling of logarithmic functions and rational terms, constraint formulas The right side of the inequality involves non-convex terms of the quadratic form of the optimization variable. To eliminate non-convexity, the SDR technique is used to transform the relevant quadratic form. Specifically, matrix variables are introduced. , ,in The semidefinite constraint needs to be satisfied. and rank constraints The active beamforming vector optimization problem is transformed into a semi-definite matrix optimization problem, at which point the expression becomes... , The expression for finding the trace of a matrix can be further transformed into:

[0162]

[0163] (40)

[0164] (41)

[0165] (42)

[0166] (43)

[0167] (44)

[0168] (45)

[0169] Using the SDR technique, problem P4.4 has successfully eliminated the non-convex constraint caused by the quadratic term in P4.3. Specifically, since the trace operation is an affine mapping, its corresponding constraint formula... and formula It has been transformed into a convex form. However, problem P4.4 still exhibits the following two types of non-convexity: one is the... The rank constraint leads to the nonconvexity of the feasible region; secondly, the constraint formula is bound. The presence of a logarithmic function in the constraint results in non-convexity.

[0170] Problem P4.4 specifically refers to the beamforming vector optimization problem based on problem P4.3 mentioned above, including the objective function and the constraints of formulas (40)-(45). The meaning of the expression in problem P4.4 below is the same.

[0171] Regarding the constraint formula The nonconvexity of can be asymptotically derived based on the properties of joint convex functions. Note that the function for Since they are joint convex functions, the constraint formula is... The left side is a convex combination, therefore the constraint formula... It is a non-convex constraint. To construct a tractable convex constraint, the SCA method is used to approximate it. For example, a first-order Taylor expansion. This allows us to obtain a linear lower bound, as shown in the following equation:

[0172] (46)

[0173] in, and Representing variables respectively and exist The value in the next iteration, and That is A linear lower bound approximation, from which the constraint formula is derived. Can be equivalently converted Through the above transformation, solving problem P4.4 can be converted into solving the following problem asymptotically and iteratively:

[0174]

[0175] (47)

[0176] , , (48)

[0177] Through the combined action of SDR and SCA, problem P4.5 has successfully eliminated most of the non-convex constraints in the original problem P4.3. However, the rank-one constraint, due to its inherent non-convexity, has not been directly addressed. To advance the solution, this constraint can be temporarily relaxed, for example, by ignoring the rank-one constraint. This allows problem P4.5 to be solved as a standard SDP optimization problem, at which point the target problem can be efficiently solved using numerical optimization tools such as CVX.

[0178] Among them, problem P4.5 specifically refers to the beamforming vector optimization problem based on problem P4.4 mentioned above, including the objective function and the constraints of formulas (47)-(48). The meaning of the expression in problem P4.5 below is the same.

[0179] It is worth noting that, because the SCA technique replaces the original logarithmic constraint with its linear lower bound, the optimal solution of P4.5 constitutes a compact lower bound approximation of P4.3. Regarding the solution obtained after relaxation... The satisfaction of the rank-one constraint needs to be verified through posterior analysis. If Then it can be decomposed by eigenvalues. Accurately recover the original active beamforming vector ;like Then, the matrix is ​​decomposed by SVD and a candidate solution is generated by Gaussian randomization

[64] . Finally, feasible solutions that satisfy the power constraint and maximize the objective function are selected. Algorithm 1 summarizes the proposed iterative algorithm based on SDR-SCA. Since the value of the objective function in problem P4.5 is strictly non-decreasing, the algorithm will converge to the local optimum of the original problem P4.3.

[0180]

[0181] (4) Optimization of STAR-RIS transmission and reflection coefficient matrix

[0182] Given a base station beamforming vector Power allocation coefficient for each cluster Under the given conditions, the difficulty in solving problem P4.1 lies in optimizing the variables. The coupling between the objective function and constraints, and their being hidden within the expression, makes the optimization problem non-convex. To address this, the SDR technique is used to simplify the expression, extracting the optimization variables formally. Specifically, auxiliary variables are introduced. , as well as Therefore, the following transformations can be obtained:

[0183] (49)

[0184] Define auxiliary matrix With augmented vector ,formula It can be rewritten as ,in and The definition is as follows:

[0185] (50)

[0186] because ,definition , Satisfying positive semidefinite constraints and rank constraints ,and Therefore, the formula The leftmost part can be rewritten as:

[0187] (51)

[0188] After the above mathematical transformations, under the condition of fixed BS active beamforming vector and power allocation coefficients, the STAR-RIS transmission and reflection coefficient matrix optimization problem P4.1 can be expressed as:

[0189]

[0190] (52)

[0191] (53)

[0192] (54)

[0193] (55)

[0194] (56)

[0195] (57)

[0196] , (58)

[0197] Problem P4.6 specifically refers to the STAR-RIS transmission and reflection coefficient matrix optimization problem based on Problem P4.1 mentioned above, including the objective function and the constraints of formulas (52)-(58). The meaning of Problem P4.6 below is the same.

[0198] Analyzing the constraint structure on page 4.6, we can see that, apart from the constraint formula... and the formula ( Apart from the constraints, all other constraints are convex. For the constraint formulas... The transformation can be performed using the SCA method of the previous invention. As for the rank-one constraint formula... The proposed asymptotic rank relaxation method can transform it into the following convex constraint:

[0199] (59)

[0200] in, Representation matrix The largest eigenvalue, Is The relaxation coefficient in the next iteration reflects the degree of relaxation of the rank-one constraint. When it means that the rank-one constraint is ignored, when Time constraint formula This is equivalent to a constraint. Therefore, by continuously increasing during the iteration process... This allows us to obtain a formula that approximates the inclusion constraint formula. The solution. Because of the expression Since it is nondifferentiable, we need to construct its asymptotic approximation expression:

[0201] ;

[0202] in, Representation matrix exist The eigenvector corresponding to the largest eigenvalue in the next iteration. Using this approximation, solving problem P4.6 can be transformed into solving the following asymptotic problem:

[0203]

[0204] (60)

[0205] Formula (10), Formula (47), Formula (51) - Formula (55) (61)

[0206] Problem P4.7 specifically refers to the STAR-RIS transmission and reflection coefficient matrix optimization problem based on Problem P4.6 mentioned above, including the objective function and the constraints of formulas (10), (47), (51)-(55), and (60)-(61). The meanings of the expressions in Problem P4.7 below are all the same.

[0207] Problem P4.7 is also a standard SDP problem, which can be solved efficiently using numerical methods (CVX). Its relaxation coefficient... Iterative updates can be performed according to the following rules:

[0208] (62)

[0209] Algorithm 2 summarizes the proposed solution to problem P4.6 based on SCA-sequential relaxation. The specific details of the suboptimal solution.

[0210]

[0211] (5) Overall iterative algorithm, convergence and complexity

[0212] Based on the above discussion, Algorithm 3 proposed in this invention describes the details of the two-layer iterative algorithm for solving the original problem. Specifically, the inner layer iteration solves the joint optimization problem of power allocation coefficients, active beamforming vectors, and transmission and reflection beamforming vectors through alternating optimization. The outer layer iteration mainly updates the decoding order using the solution obtained from the inner layer iteration.

[0213] For the inner layer iteration, given the decoding order, the following inequality is maintained throughout the process of alternately solving the power allocation coefficients, active beamforming vectors, and reflection and transmission beamforming vectors:

[0214] (63)

[0215] The reason why the first inequality holds is that when fixed hour, The optimal closed-form solution is obtained through formula 32; the reason why the second inequality holds is that when fixed... At that time, obtained through Algorithm 1 It is the optimal solution to problem P4.3; and the reason why the last inequality holds is that when fixed At that time, obtained through Algorithm 2 This is the same optimal solution as above. As can be seen from Inequality 63, the objective function of problem P4.1 does not decrease in each iteration, and the reachable rate of the entire system has an upper limit. Therefore, for the inner iteration, the convergence of the objective function can be guaranteed.

[0216] For the outer iteration, according to steps 8) to 13) of Algorithm 3, the achievable rate of the system is monotonically non-decreasing after each iteration, therefore the outer loop can also guarantee convergence. Assuming both the inner and outer iterations remain convergent, the proposed algorithm is convergent.

[0217] The overall algorithm complexity depends on Algorithm 1 and Algorithm 2, therefore the analysis mainly focuses on the complexity of these two algorithms. The complexity of Algorithm 1 is... The time complexity of Algorithm 2 is .in , , , Let represent the maximum number of iterations and the solution accuracy of Algorithm 1, and the maximum number of iterations and the solution accuracy of Algorithm 2, respectively. Therefore, the overall complexity of Algorithm 3 can be expressed as: ,in These are the maximum number of iterations for the outer and inner iterations, respectively.

[0218] 2.3 Simulation Results and Analysis

[0219] The present invention has conducted extensive simulation experiments to verify the effectiveness of the proposed algorithm, and has also conducted comparative experiments with other benchmark algorithms to verify the effectiveness of the algorithm.

[0220] 2.3.1 Simulation Settings

[0221] The scenario studied in this invention is a BS. A user provides NOMA service, but due to obstruction by obstacles, the direct link between the BS and the user is blocked. Therefore, a STAR-RIS exists in the scenario to provide an additional link for communication between the user and the BS. Without loss of generality, this invention sets up a scenario with three user clusters, each containing three users. Cluster 1 is located in the reflection space, while clusters 2 and 3 are located in the transmission space. The coordinates of the BS and STAR-RIS are as follows: and The center coordinates of the three clusters are , , Users in each cluster are randomly distributed within a circle with a radius of 5m at the cluster center. The distance-related channel path loss model uses the formula... The same model, and channel modeling also refers to the formula. .

[0222] Specifically, adopt , , These represent the path loss from STAR-RIS to the user, the path loss exponent, and the Rician factor, respectively. , , These represent the path loss and path loss exponent from the base station to STAR-RIS, respectively. In addition, this invention sets minimum QoS requirements for all users. The path loss from BS to STAR-RIS and from STAR-RIS to the user are both set to -30dB, the path loss exponent is set to 2.2, the Rician factor is set to 3dB, and the noise power is set to -90dBm. Specific parameter settings can be found in Table 2.

[0223] Table 2: Experimental Parameters

[0224] 2.3.2 Analysis of Experimental Results

[0225] (1) Algorithm convergence

[0226] Figure 7The convergence of Algorithm 1 under different base station antennas is shown. It can be observed that, even with different numbers of base station antennas, Algorithm 1 can still achieve convergence within 7 attempts, verifying the effectiveness of the proposed algorithm. Figure 8 This shows the convergence of Algorithm 2 under different numbers of STAR-RIS components. Since the scale of the problem optimization increases with the number of STAR-RIS components, the figure shows that the algorithm requires more iterations to converge when the number of components increases. Figure 9 This demonstrates the convergence of the inner and outer layer iterations of Algorithm 3. For ease of verification, the number of BS antennas was set to 4 and the number of STAR-RIS components to 10 in this simulation. It can be observed that, with the support of Algorithms 1 and 2, both the inner and outer layer iterations in Algorithm 3 converged within 4 iterations, fully verifying the efficiency and superiority of the proposed algorithm framework.

[0227] (2) Comparative tests of different systems

[0228] To comprehensively evaluate the performance of the proposed algorithm in the STAR-RIS-NOMA system, this experiment set up three benchmark schemes for comparison and verification: (1) a traditional single-function RIS-assisted NOMA system with twice the number of components, wherein the transmission RIS and the reflection RIS are each equipped with (2) A conventional single-function RIS-assisted NOMA system with the same number of components, wherein the transmission RIS and the reflection RIS are each equipped with one component; (3) A traditional single-function RIS-assisted OMA system, wherein the transmission and reflection RIS are each equipped with a component; The system consists of several components. Traditional RIS systems, limited by their half-space coverage characteristics, require two independent RIS systems to simulate the omnidirectional coverage capability of STAR-RIS. The base station is equipped with four antennas, a maximum transmit power of 35dBm, and the number of RIS components is dynamically adjusted from 10 to 50 to analyze system scalability.

[0229] Figure 10The relationship between the system rate and the number of RIS components under different schemes is shown, and the following conclusions can be drawn: (1) The system capacity of all schemes increases monotonically with the increase of the number of RIS components. This is attributed to the fact that the passive beamforming gain of RIS is proportional to the square of the number of components. When the number of components increases from 10 to 50, the system rate of STAR-RIS-NOMA is significantly improved, which verifies the core role of large-scale RIS arrays in channel control; (2) STAR-RIS-NOMA has better system rate and performance than traditional RIS-NOMA under the same number of components. The mechanism is that STAR-RIS achieves full space coverage through ES mode, and each component can independently control the transmission and reflection coefficients, while traditional RIS needs to be decomposed into two functionally limited sub-arrays, resulting in a 50% reduction in the degree of freedom of control. (3) When using a RIS architecture with twice the number of components, the system rate is higher than that of STAR-RIS-NOMA. This is because traditional RIS can achieve higher signal integrity in single-function mode. It requires the deployment of twice the physical components, resulting in a linear increase in hardware complexity and manufacturing cost. In actual engineering, it is necessary to weigh performance gain against economic indicators. (4) The NOMA system has a significantly higher speed than the OMA system. This difference stems from NOMA's power domain multi-user multiplexing mechanism, which effectively overcomes the orthogonal resource block segmentation limitation of OMA through dynamic power allocation.

[0230] (3) Comparison of BS beamforming schemes

[0231] Figure 11 This paper demonstrates the impact of the number of base station (BS) antennas on the performance of a STAR-RIS-NOMA system. For comparative experiments, three benchmark schemes for determining the base station beamforming vector were considered: the zero-forcing algorithm, the maximum ratio transmission algorithm, and a random selection scheme. Other variables in these three schemes were solved using the algorithms and theorems provided in this invention. Figure 11 It can be seen that the system rate of all schemes increases with the number of base station antennas, and more antennas provide more active beamforming gain. The proposed algorithm and other benchmark algorithms achieve significant performance improvements compared to random acquisition, verifying the importance of joint optimization for STAR-RIS transmission and reflection coefficients, power allocation coefficients, and decoding order.

Claims

1. A STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, characterized in that, include: A base station equipped with multiple antennas; A STAR-RIS consisting of M reconfigurable units, wherein the STAR-RIS divides the communication space into a reflection space and a transmission space; Multiple users, which are divided into C clusters and distributed in the reflection space and the transmission space; The base station maximizes the sum of achievable rates for all users in the system by jointly optimizing the decoding order, power allocation coefficients, base station active beamforming vectors, and the transmission and reflection coefficient matrices of STAR-RIS.

2. The STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, as described in claim 1, is characterized in that... The decoding order is determined based on the user's equivalent channel gain, and the formula for calculating the equivalent channel gain is as follows: ； in, The representative index is The user's equivalent channel gain; For users within the same cluster, SIC decoding is performed in ascending order of their equivalent channel gain.

3. A STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, as described in claim 2, is characterized in that... After the decoding order is determined based on the equivalent channel gain, the rate compatibility constraint for serial interference cancellation is automatically satisfied in subsequent optimizations, and therefore is not used as a constraint and is removed in the subsequent joint optimization process.

4. The STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, as described in claim 1, is characterized in that... The optimization of the power allocation coefficient is obtained by solving a closed-form equation system given the active beamforming vector of the base station and the STAR-RIS coefficient matrix. The equation system is constructed by ensuring the minimum rate requirement of users with lower equivalent channel gain in sequence, and allocating all remaining power to users with higher equivalent channel gain.

5. A STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, as described in claim 1, is characterized in that... The optimization method for the active beamforming vector of the base station includes: a) Introduce auxiliary variables to reconstruct the user rate expression, transforming the original problem into an equivalent problem; b) Using semidefinite relaxation techniques, the beamforming vector optimization problem is transformed into a semidefinite programming problem; c) Use the continuous convex approximation method to handle non-convex constraints in the transformed problem; d) By solving the relaxed convex optimization problem, and using Gaussian randomization, the active beamforming vector that satisfies the rank-one constraint is recovered.

6. A STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, as described in claim 1, is characterized in that... The optimization method for the transmission and reflection coefficient matrices of STAR-RIS includes: The STAR-RIS coefficient vector is extracted as an optimization variable through mathematical transformation, and an augmented matrix is ​​constructed. The problem is transformed into an optimization problem with respect to the augmented matrix using a semidefinite relaxation technique; The sequential constraint relaxation method is adopted to approximate the rank-one solution by iteratively tightening the maximum eigenvalue constraint, thereby obtaining the suboptimal solution of the STAR-RIS coefficient matrix.

7. A STAR-RIS-NOMA downlink communication system based on joint optimization to maximize rate sum, as described in claim 1, is characterized in that... Joint optimization is achieved through a two-level iterative algorithm: Outer layer iteration: Calculate the equivalent channel gain for all users based on the current system parameters, and update the SIC decoding order within each cluster; Inner layer iteration: Under a fixed decoding order, power allocation coefficient optimization, base station active beamforming vector optimization, and STAR-RIS transmission and reflection coefficient matrix optimization are performed alternately until the inner layer objective function converges.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the optimization method as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the optimization method as described in any one of claims 1-7.

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