Uplink MIMO-NOMA system optimization method with maximum sum rate

Abstract

The invention provides an uplink MIMO-NOMA (Multiple Input Multiple Output-Non-Orthogonal Multiple Access) system optimization method with a maximized sum rate, which comprises the following steps: firstly, in order to suppress interference between a transmission cluster and a reflection cluster, providing an inter-cluster SIC method: clustering users according to transmission characteristics, adopting space division multiple access in each cluster, and performing inter-cluster SIC of NOMA transmission so as to reduce the interference between the clusters; secondly, a non-convex optimization problem aiming at maximizing the total rate of the system is formulated and solved by using an alternating optimization framework, in the framework, a receiving equalizer is optimized according to a minimum mean square error standard, and transmitting power control of a user is processed through successive convex approximation, so that sub-problems are easy to process; and finally, the beam forming of the active STAR-RIS adopts a sequential rotation design. According to the invention, the dual-fading effect is effectively overcome by adjusting the phase shift and amplitude of electromagnetic waves, an alternating optimization framework is also provided to solve the described non-convex problem, user power is controlled through continuous convex approximation, and active STAR-RIS beam forming is realized through sequential rotation.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to an active STAR-RIS-assisted uplink MIMO-NOMA system optimization method based on inter-cluster serial interference cancellation for maximizing speed. Background Technology

[0002] Recently, a novel concept of a reconfigurable smart surface (STAR-RIS) that simultaneously transmits and reflects signals has been proposed. Unlike traditional RIS that confines reflected signals to a half-space on the same side of the smart reflector, STAR-RIS can transmit incident signals to the opposite side of the smart reflector, significantly improving deployment flexibility. On the other hand, Orthogonal Multiple Access (OMA) uses orthogonal time / frequency resource blocks to serve each user. In contrast, Non-Orthogonal Multiple Access (NOMA) allows multiple users to obtain service on the same resource block by using superposition coding at the transmitter and serial interference cancellation (SIC) at the receiver. NOMA is considered an effective technique for increasing the number of users that can communicate with the base station simultaneously. The combination of NOMA and STAR-RIS can effectively enhance system performance. However, in passive RIS systems, the double-fading effect limits capacity gain. To overcome this fundamental limitation, the concept of active RIS has been proposed. Unlike passive RIS, which only reflects / transmits signals without amplification, active RIS can use amplifiers integrated into its components to amplify the reflected / transmitted signals. However, in complex scenarios with a large number of users and real-time requirements, the resulting computation, latency, and error propagation will severely limit system performance.

[0003] Traditional passive STAR-RIS suffers from double fading in the "base station-STAR-RIS-user" cascaded link, resulting in limited gain. However, active STAR-RIS can amplify the signal at the component level, thus overcoming the inherent performance bottleneck of passive RIS. But due to significant inter-cluster interference in multi-cluster, multi-user, and uplink scenarios, it is difficult to achieve ideal performance by directly using traditional NOMA intra-cluster SiC. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes an uplink MIMO-NOMA system optimization method that maximizes sum and rate. The aim is to establish an active STAR-RIS-assisted uplink multi-cluster MIMO-NOMA transmission framework, introducing a decoding approach of "inter-cluster SIC + intra-cluster SDMA," and maximizing system sum and rate by jointly optimizing the equalizer, user transmit power, and STAR-RIS beamforming, while satisfying power constraints and communication service quality constraints. The technical solution provided by this invention is as follows:

[0005] An optimization method for uplink MIMO-NOMA systems that maximizes sum and rate includes the following steps:

[0006] Step 1: In the uplink MIMO-NOMA system assisted by active STAR-RIS, users are divided into reflection clusters R and transmission clusters T according to the characteristics of user transmission direction. Space division multiple access multi-user access is adopted within the cluster. The overall decoding order of the cluster is determined by combining the average path loss difference of each cluster. Serial interference cancellation is adopted between the clusters to eliminate mutual interference between the transmission cluster and the reflection cluster.

[0007] Step 2: Construct a non-convex joint optimization model with the goal of maximizing system and rate. Introduce auxiliary variables to transform the original problem into a tractable form. Use an alternating optimization framework to decompose the problem into three sub-problems: base station equalizer optimization, user transmit power control and active STAR-RIS beamforming design.

[0008] Step 3: The equalizer optimization uses a closed-form expression with minimum mean square error to obtain the optimal receive vector; the transmit power control uses a continuous convex approximation method to handle non-convex constraints so that the subproblems can be solved in a convex manner; the phase shift and amplification coefficient of the active STAR-RIS beamforming adopt a sequential rotation strategy to discretize and search for the optimal phase, and normalize the amplitude coefficient under the constraint of total amplification power, so that the final joint optimization achieves the maximum sum rate.

[0009] Preferably, the active STAR-RIS-assisted uplink MIMO-NOMA system comprises: a base station equipped with M antennas, each user equipped with a single antenna, all users distributed in two areas adjacent to the STAR-RIS, and users in each area forming a cluster, denoted by cluster R and cluster T. The STAR-RIS is composed of... It consists of several active components, wherein the signal of cluster R is composed of Each active element reflects, while the signal of cluster T is generated by... Transmission of active components.

[0010] Preferred, use Let represent the u-th user in cluster R or cluster T, and the total system speed is:

[0011]

[0012] in For users The signal interference plus noise ratio is as follows:

[0013]

[0014]

[0015] in, These are intra-group interferences, namely , ; Inter-group interference, respectively ;

[0016] For users Beamforming vector, This is the channel vector between STAR-RIS and the base station. For users Channel vector with STAR-RIS It is an active STAR-RIS beamforming matrix, in which and These represent the amplitude coefficient and phase shift of the nth STAR-RI, respectively. Indicates the transmission power; It is the variance of additive white Gaussian noise at the active RIS. It is the variance of additive white Gaussian noise at the base station.

[0017] Preferably, step 2 introduces auxiliary variables. The optimization problem is:

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Constraint (16) limits the amplification power of the active STAR-RIS, constraint (17) limits the maximum transmit power of each user, and constraints (18) and (19) guarantee the quality of service for each user. Constraint (20) ensures the requirement of base station power normalization, and constraint (21) limits the amplitude coefficient of each active STAR-RIS unit.

[0026] Preferably, the equalizer optimization in step 3 is as follows: when given , and When selecting the minimum mean square error equalizer to maximize the user's signal-to-interference-plus-noise ratio, define... ,user The minimum mean square error equalizer is represented as:

[0027]

[0028]

[0029] in: , .

[0030] Preferably, the transmit power control in step 3 is as follows: given and against and Optimize the problem, which is represented as (P3):

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] in , ;

[0037] We use convex upper bound approximation to handle nonconvexity, introducing variables. The first term on the right side of inequality (29) is rewritten as:

[0038]

[0039] in Updated to in the t-th iteration Problem (P3) is transformed into (P4):

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] Problem (P4) is a standard convex optimization problem, and the target result is obtained using software packages.

[0046] Preferably, the active STAR-RIS beamforming in step 3 is as follows: given and Phase shifting for active STAR-RIS Optimize the problem, which is represented as (P5):

[0047]

[0048]

[0049]

[0050] The following variables are introduced to simplify the expression: , , , ;user The signal interference plus noise ratio is expressed as:

[0051]

[0052] in It's component interference plus noise at the base station. , ;

[0053] Following the cluster-based design sequence, the phase shift is designed first. Then, inter-cluster interference from cluster T is constructed and passed to cluster R for phase shift design. For each phase shift matrix, a sequential phase shift method is used to solve the problem. The first phase shift of active STAR-RIS devices The results of the next iteration are as follows:

[0054]

[0055] The rotation matrix for the nth phase shift is defined as follows: , define the first The solution for the second rotation is ,get:

[0056]

[0057] The formula for constructing the signal-to-interference-plus-noise ratio is:

[0058]

[0059] in:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] and These are the operators for extracting the real and imaginary parts of a complex number, respectively.

[0071] Applying penalty methods, the first The first iteration in the nth iteration The second-option rotation value is given by the following formula:

[0072]

[0073] in It is a penalty function, defined as when hour, ,otherwise It is a very small number when it is any other value;

[0074] After determining the phase configuration, the amplification factor of the active STAR-RIS element is optimized: Let Let be the amplification coefficient vector, for the th Each element has a corresponding weight defined as... The final coefficients are determined by applying a normalization factor. .

[0075] Compared with existing technologies, the beneficial effects achieved by this invention are as follows: For active STAR-RIS-assisted uplink MIMO-NOMA systems, this invention proposes an inter-cluster SIC method to improve the sum rate. Active STAR-RIS can effectively overcome the double fading effect by adjusting the phase shift and amplitude of the electromagnetic wave. An alternating optimization framework is proposed to solve the described non-convex problem, where user power is controlled by a continuous convex approximation, and active STAR-RIS beamforming is achieved through sequential rotation. Simulation results show that, compared with other benchmark schemes, the active STAR-RIS-assisted MIMO-NOMA system based on inter-cluster SIC achieves a higher sum rate. Attached Figure Description

[0076] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0077] Figure 1 This is a model diagram of the active STAR-RIS assisted uplink MIMO-NOMA system of the present invention;

[0078] Figure 2 This is a graph showing the relationship between system speed and signal-to-noise ratio;

[0079] Figure 3 This is a graph showing the trend of system and speed as a function of the number of reconfigurable units in STAR-RIS. Detailed Implementation

[0080] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] To make the above-mentioned objectives, features and effects of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0082] Example 1: An uplink MIMO-NOMA system optimization method for maximizing sum and rate includes the following steps:

[0083] Step 1: In the active STAR-RIS-assisted uplink MIMO-NOMA system, users are divided into reflection clusters R and transmission clusters T according to their transmission direction characteristics. Space division multiple access (SDMA) is used within each cluster. The overall decoding order of the cluster is determined by combining the average path loss difference of each cluster. By using serial interference cancellation (SIC) between clusters, mutual interference between the STAR-RIS transmission cluster and the reflection cluster is eliminated, thereby reducing the complexity of multi-cluster SIC and the impact of error propagation on system performance.

[0084] Step 2: Construct a non-convex joint optimization model with the goal of maximizing system and rate. Introduce auxiliary variables to transform the original problem into a tractable form. Adopt an alternating optimization framework to decompose the problem into three sub-problems: base station-side minimum mean square error (MMSE) equalizer optimization, user transmit power control, and active STAR-RIS beamforming design, thereby reducing the overall solution difficulty.

[0085] Step 3: In the solution process, to improve solvability and convergence: equalizer optimization adopts MMSE closed expression to obtain the optimal receive vector; transmit power control adopts continuous convex approximation method to handle non-convex constraints and make subproblems convex to solve; for the phase shift and amplification coefficient of active STAR-RIS element, a sequential rotation strategy is adopted to discretize and search for the optimal phase, and the amplitude coefficient is normalized under the total amplification power constraint, so that the final joint optimization achieves the maximum sum rate.

[0086] The active STAR-RIS-assisted uplink MIMO-NOMA system model described in step 1 is as follows: Figure 1 As shown, the base station is equipped with M antennas, and each user is equipped with a single antenna. All users are distributed in two areas adjacent to the primary STAR-RIS, and the users in each area form a cluster, denoted by cluster R and cluster T. It is assumed that all user clusters are blocked by buildings and cannot communicate directly with the base station, and an active STAR-RIS operating on a mode switching protocol is deployed to assist communication between the base station and users. The STAR-RIS consists of... It consists of several active components, wherein the signal of cluster R is composed of Each active element reflects, while the signal of cluster T is generated by... Transmission of active components.

[0087] This invention uses Rice distribution to simulate small-scale fading. Let represent the u-th user in cluster R or cluster T. The channel vector between STAR-RIS and , represented as:

[0088]

[0089] in , and users respectively Distance to STAR-RIS, path loss exponent, and Rice factor. and These are the deterministic line-of-sight (LoS) component and the random non-line-of-sight (NLoS) component, respectively. Similarly, the channel vector between STAR-RIS and the base station is... , represented as:

[0090]

[0091] in , and These are the distance between STAR-RIS and the base station, the path loss exponent, and the Rice factor, respectively. and This includes deterministic line-of-sight components and random non-line-of-sight components. The base station received the signal as follows: , represented as:

[0092]

[0093] in, It is an active STAR-RIS beamforming matrix, in which and These represent the amplitude coefficient and phase shift of the nth STAR-RI, respectively. and Representing transmit power and user respectively The symbol sent, yes Then there is additive white Gaussian noise at the active RIS. yes Additive white Gaussian noise at the rear base station. Considering the use of active STAR-RIS, The value may exceed 1. Furthermore, a uniformly quantized discrete phase shift model is employed, i.e. ,in This indicates the phase accuracy and phase shift of the STAR-RIS reconfigurable element. .

[0094] user The beamforming vector is To determine the decoding order as R, T based on the average path loss of each group, for simplicity, we define... The decoded signal is:

[0095]

[0096]

[0097] user The signal interference plus noise ratio (SINR) can be written as:

[0098]

[0099]

[0100] in, These are intra-group interferences, namely , Similarly, Inter-group interference, respectively Therefore, the total system speed is given by the following equation:

[0101]

[0102] Steps 2 and 3 maximize the overall system speed through the joint optimization of three subproblems. Due to the use of an active STAR-RIS amplifier, STAR-RIS amplification power constraints and component amplitude coefficient constraints need to be introduced. The optimization problem is formulated as follows: :

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Among them, constraint (10) limits the amplification power of the active STAR-RIS, constraint (11) limits the maximum transmit power of each user, constraint (12) guarantees the service quality of each user, constraint (13) guarantees the requirement of base station power normalization, and constraint (14) limits the amplitude coefficient of each active STAR-RIS unit.

[0110] Due to the non-convex constraints, problem (P1) is difficult to solve directly. To make it easier to handle, we introduce... This transforms problem (P1) into problem (P2):

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] in, Clearly, problem (P2) is still a non-convex problem. Furthermore, , and The problem is highly coupled, and to make it easier to handle, the AO method was developed to effectively solve it. Specifically, the equalizer at the base station, the power control at the user, and the beamforming at STAR-RIS are iteratively optimized until convergence is achieved.

[0119] Equalizer: When given , and When selecting the minimum mean square error equalizer to maximize the user's signal-to-interference-plus-noise ratio, define... ,user The minimum mean square error equalizer is represented as:

[0120]

[0121]

[0122] in: , .

[0123] Power control: given and against and To optimize, the optimization problem can be represented as (P3):

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] Since constraint (28) is non-convex, it can be rewritten in a more manageable form as follows:

[0130]

[0131] in , Observe that inequality (29) is still nonconvex because the first term on the right-hand side of inequality (29) is quasi-concave. To address the nonconvexity, we use a convex upper bound approximation and introduce variables. The first term on the right side of inequality (29) can be rewritten as:

[0132]

[0133] in Updated to in the t-th iteration Problem (P3) can be transformed into (P4):

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] Problem (P4) is a standard convex optimization problem, and the target result can be obtained using software packages.

[0140] Active STAR-RIS beamforming: given and Phase shifting for active STAR-RIS To optimize, the optimization problem can be represented as (P5):

[0141]

[0142]

[0143]

[0144] To simplify the expression, some new variables are introduced: , , , Then the user The signal-to-interference-plus-noise ratio can be rewritten as:

[0145]

[0146] in It's component interference plus noise at the base station. , .

[0147] Following the cluster-based design sequence, the phase shift is designed first. Then, inter-cluster interference from cluster T is constructed and passed to cluster R for phase shift design, and so on. For each phase shift matrix, this invention proposes a sequential phase shift method to solve the problem. The first phase shift of active STAR-RIS devices The results of the next iteration are as follows:

[0148]

[0149] The rotation matrix for the nth phase shift is defined as follows: At the same time, if ,mold The rotational phase shift still belongs to the set Definition of the first The solution for the second rotation is Then we can get:

[0150]

[0151] Obviously in the Secondary rotation matrix The design also provides the phase shift vector for the last rotation. Therefore, the SINR formula can be constructed as follows:

[0152]

[0153] in:

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164] and These are the operators for extracting the real and imaginary parts of a complex number, respectively. By applying the penalty method, the first... The first iteration in the nth iteration The second-option rotation value can be given by the following formula:

[0165]

[0166] in It is a penalty function, defined as when hour, ,otherwise For other values, it is a very small number. After determining the phase configuration, the amplification factor of the active STAR-RIS element was optimized. Let... Let be the amplification coefficient vector. For the _ _ Each element has a corresponding weight defined as... Accordingly, constraint (8) can be expressed as To satisfy this constraint, we first obtain an unnormalized solution. The final coefficients are determined by applying a normalization factor, i.e.

[0167]

[0168] To verify the effectiveness of the proposed scheme, the following schemes were compared: (1) Intra-cluster SIC + Active STAR-RIS: Active STAR-RIS is deployed in a MIMO-NOMA system with intra-cluster SIC; (2) Inter-cluster SIC + Passive STAR-RIS: Passive STAR-RIS is deployed in a MIMO-NOMA system with inter-cluster SIC; (3) Inter-cluster SIC + Random Phase Shift: Random phase shift is used in an inter-cluster SIC MIMO-NOMA system assisted by Active STAR-RIS.

[0169] The total power budgets for active STAR-RIS and passive STAR-RIS are respectively , ,in For the transmit power of all users, This refers to the power consumption of the phase-shifting switches and control circuitry in the STAR-RIS unit. The DC bias power used by the amplifier in each unit. To ensure fairness in the comparison, all schemes are evaluated under the same total power budget. Other specific simulation parameter settings are as follows: M=4, , , , D=10 , and .

[0170] Figure 2The relationship between system sum rate and signal-to-noise ratio (SNR) is presented. Simulation results show that the sum rate of the proposed scheme is superior to other schemes. Compared with scheme (1), it can be seen that the proposed scheme achieves a higher system sum rate at the same SNR, which is due to the joint design in each cluster to support the implementation of SDMA. Compared with scheme (1), the sum rate of the proposed scheme is improved by about 6 b / s / Hz at 20dB, which is because the active STAR-RIS is more flexible in terms of signal amplification and phase control. Compared with scheme (3), the proposed scheme has a significant improvement in sum rate due to the optimization of phase and amplitude.

[0171] Figure 3 The trend of the sum rate as a function of the number of reconfigurable elements in the STAR-RIS is presented. Simulation results show that the sum rate of all schemes increases with the number of array elements. This phenomenon is due to the fact that the addition of elements provides greater freedom for control, which can effectively alleviate the double fading in the cascaded BS-STAR-RIS-user link. Notably, at the same SNR, the sum rate obtained by the proposed scheme is consistently higher than that of the in-cluster SIC scheme and the passive STAR-RIS scheme, and this advantage is more pronounced at higher SNRs.

[0172] In summary, this invention proposes an inter-cluster SIC method to improve the sum rate for active STAR-RIS-assisted uplink MIMO-NOMA systems. Active STAR-RIS can effectively overcome the double fading effect by adjusting the phase shift and amplitude of the electromagnetic waves. An alternating optimization framework is proposed to solve the described non-convex problem, where user power is controlled by a continuous convex approximation, and active STAR-RIS beamforming is achieved through sequential rotation. Simulation results show that, compared with other benchmark schemes, the active STAR-RIS-assisted MIMO-NOMA system based on inter-cluster SIC achieves a higher sum rate.

[0173] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing an uplink MIMO-NOMA system to maximize sum and rate, characterized in that, Includes the following steps: Step 1: In the uplink MIMO-NOMA system assisted by active STAR-RIS, users are divided into reflection clusters R and transmission clusters T according to the characteristics of user transmission direction. Space division multiple access multi-user access is adopted within the cluster. The overall decoding order of the cluster is determined by combining the average path loss difference of each cluster. Serial interference cancellation is adopted between the clusters to eliminate mutual interference between the transmission cluster and the reflection cluster. Step 2: Construct a non-convex joint optimization model with the goal of maximizing system and rate. Introduce auxiliary variables to transform the original problem into a tractable form. Use an alternating optimization framework to decompose the problem into three sub-problems: base station equalizer optimization, user transmit power control and active STAR-RIS beamforming design. Step 3: The equalizer optimization uses a closed-form expression with minimum mean square error to obtain the optimal receive vector; the transmit power control uses a continuous convex approximation method to handle non-convex constraints so that the subproblems can be solved in a convex manner; the phase shift and amplification coefficient of the active STAR-RIS beamforming adopt a sequential rotation strategy to discretize and search for the optimal phase, and normalize the amplitude coefficient under the constraint of total amplification power, so that the final joint optimization achieves the maximum sum rate.

2. The uplink MIMO-NOMA system optimization method for maximizing sum and rate as described in claim 1, characterized in that, The active STAR-RIS-assisted uplink MIMO-NOMA system is as follows: the base station is equipped with M antennas, each user is equipped with a single antenna, all users are distributed in two areas adjacent to the STAR-RIS, and the users in each area form a cluster, denoted by cluster R and cluster T. The STAR-RIS is composed of... It consists of several active components, wherein the signal of cluster R is composed of Each active element reflects, while the signal of cluster T is generated by... Transmission of active components.

3. The uplink MIMO-NOMA system optimization method for maximizing sum and rate as described in claim 2, characterized in that, use Let represent the u-th user in cluster R or cluster T, and the total system speed is: ； in For users The signal interference plus noise ratio is as follows: ； ； in, These are intra-group interferences, namely , ; Inter-group interference, respectively ; For users Beamforming vector, This is the channel vector between STAR-RIS and the base station. For users Channel vector with STAR-RIS It is an active STAR-RIS beamforming matrix, in which and These represent the amplitude coefficient and phase shift of the nth STAR-RI, respectively. Indicates the transmission power; It is the variance of additive white Gaussian noise at the active RIS. It is the variance of additive white Gaussian noise at the base station.

4. The uplink MIMO-NOMA system optimization method for maximizing sum and rate as described in claim 3, characterized in that, Step 2: Introduce auxiliary variables The optimization problem is: ； ； ； ； ； ； ； Constraint (16) limits the amplification power of the active STAR-RIS, constraint (17) limits the maximum transmit power of each user, and constraints (18) and (19) guarantee the quality of service for each user. Constraint (20) ensures the requirement of base station power normalization, and constraint (21) limits the amplitude coefficient of each active STAR-RIS unit.

5. The uplink MIMO-NOMA system optimization method for maximizing sum and rate according to claim 4, characterized in that, The equalizer optimization in step 3 is as follows: when given , and When selecting the minimum mean square error equalizer to maximize the user's signal-to-interference-plus-noise ratio, define... ,user The minimum mean square error equalizer is represented as: ； ； in: , .

6. The uplink MIMO-NOMA system optimization method for maximizing sum and rate according to claim 4, characterized in that, The transmit power control in step 3 is as follows: given and against and Optimize the problem, which is represented as (P3): ； ； ； ； ； in , ; We use convex upper bound approximation to handle nonconvexity, introducing variables. The first term on the right side of inequality (29) is rewritten as: ； in Updated to in the t-th iteration Problem (P3) is transformed into (P4): ； ； ； ； ； Problem (P4) is a standard convex optimization problem, and the target result is obtained using software packages.

7. The uplink MIMO-NOMA system optimization method for maximizing sum and rate according to claim 4, characterized in that, Step 3 describes the active STAR-RIS beamforming as follows: given and Phase shifting for active STAR-RIS Optimize the problem, which is represented as (P5): ； ； ； The following variables are introduced to simplify the expression: , , , ;user The signal interference plus noise ratio is expressed as: ； in It's component interference plus noise at the base station. , ; Following the cluster-based design sequence, the phase shift is designed first. Then, inter-cluster interference from cluster T is constructed and passed to cluster R for phase shift design. For each phase shift matrix, a sequential phase shift method is used to solve the problem. The first phase shift of active STAR-RIS devices The results of the next iteration are as follows: ； The rotation matrix for the nth phase shift is defined as follows: , define the first The solution for the second rotation is ,get: ； The formula for constructing the signal-to-interference-plus-noise ratio is: ； in: ； ； ； ； ； ； ； ； ； ； and These are the operators for extracting the real and imaginary parts of a complex number, respectively. Applying penalty methods, the first The first iteration in the nth iteration The second-option rotation value is given by the following formula: ； in It is a penalty function, defined as when hour, ,otherwise It is a very small number when it is any other value; After determining the phase configuration, the amplification factor of the active STAR-RIS element is optimized: Let Let be the amplification coefficient vector, for the th Each element has a corresponding weight defined as... ; The final coefficients are determined by applying a normalization factor: .

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