A group connection bd-ris assisted uplink communication system and rate maximization transmission method

Abstract

This invention discloses a group-connected BD-RIS-assisted uplink communication system and a method for maximizing transmission rate, relating to the field of wireless communication technology. The method first establishes a channel model between the user, base station, and BD-RIS, derives the decoded signal expression for the user at the base station, and calculates the user's signal-to-interference-plus-noise ratio (SNR) and achievable rate. Then, it constructs an optimization problem with the goal of maximizing the system's sum and rate, with the optimization variables being the equalizer, user transmit power, and BD-RIS phase shift matrix. Finally, it employs an alternating optimization strategy, sequentially optimizing the equalizer based on the minimum mean square error criterion, transforming the non-convex problem into a convex problem to solve for the transmit power, and optimizing the phase shift matrix using the BFGS quasi-Newton method, iterating until the system performance converges. This invention overcomes the design limitations of traditional reconfigurable smart reflectors, fully leverages the control advantages of BD-RIS, effectively improves the sum and rate of the uplink communication system, and provides a new solution for future wireless network performance optimization.

Description

Technical Field

[0001] This invention relates to the field of beyond-diagonal reconfigurable intelligent surface technology in wireless communication, specifically to an uplink communication system and a method for maximizing transmission rate assisted by a group-connected beyond-diagonal reconfigurable intelligent surface (BD-RIS). Background Technology

[0002] Reconfigurable Intelligent Surface (RIS) is a cutting-edge technology that can dynamically reconfigure the wireless propagation environment. It consists of a large number of programmable electromagnetic units. By adjusting the electromagnetic characteristics of the units, the amplitude, phase, polarization and other parameters of electromagnetic waves can be intelligently controlled to enhance useful signals and suppress interference. It is regarded as a key technology for future wireless networks.

[0003] Traditional RIS systems use diagonal phase shift matrices, which can only optimize diagonal elements, limiting design freedom. BD-RIS breaks through this limitation. Its reflective element ports are interconnected, and a scattering parameter matrix is ​​used to characterize the relationship between elements. The phase shift matrix is ​​not limited to diagonal form, and the phase and amplitude of the signal can be controlled simultaneously, providing greater design freedom for improving the performance of communication systems.

[0004] Currently, research on BD-RIS mainly focuses on downlink communication systems, with research objectives including maximizing data rate, maximizing signal-to-noise ratio, and minimizing power. However, BD-RIS-assisted uplink communication systems have not been studied in depth. In uplink scenarios, each user has an independent maximum transmit power constraint, which is significantly different from the downlink scenario, where only the total power constraint of the base station needs to be considered. This makes it impossible to directly apply downlink design schemes to uplink scenarios. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a group-connected BD-RIS-assisted uplink communication system and a method for maximizing transmission rate, thereby achieving an effective improvement in system performance and rate.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows: A group-connected BD-RIS-assisted uplink communication system and a method for maximizing transmission rate include the following steps: S1. Establish channel models between users and base stations, between BD-RIS and base stations, and between users and BD-RIS; S2. Based on the demodulation rules of the Orthogonal Multiple Access (OMA) system, obtain the mathematical expression of the decoded signal of the user at the base station through the equalizer; S3. Calculate the expression for the signal-to-interference-plus-noise ratio (SINR) and achievable data rate for different users; S4. Under the premise of satisfying the minimum quality of service requirements and maximum transmit power constraints of each user, establish an optimization problem P1. The optimization objective is to maximize the sum rate of the system, and the optimization variables are the equalizer, the transmit power of each user and the BD-RIS phase shift matrix. S5. An alternating optimization strategy is adopted, with fixed user transmit power and BD-RIS phase shift matrix, and the equalizer is optimized based on the minimum mean-square error (MMSE) criterion; S6. Using a fixed equalizer and BD-RIS phase shift matrix, auxiliary variables are introduced to transform the non-convex optimization problem into a convex optimization problem P4, and the optimal user transmit power is solved. S7. With fixed equalizer and user transmit power, the phase shift matrix optimization problem is transformed into a single-variable unconstrained optimization problem P9. The optimal BD-RIS phase shift matrix is ​​solved by the BFGS quasi-Newton method. S8. Repeat steps S5-S7 until the system performance converges.

[0007] Furthermore, in step S1, the channel between the base station and the user is a Rayleigh fading channel, denoted as... The channels from the base station to BD-RIS and from BD-RIS to the user are Ricean fading channels, denoted as follows: , .

[0008] Furthermore, the Rayleigh fading channel and the Rice fading channel are modeled as follows: (1.1) (1.2) (1.3) in, Indicates base station and user Path loss index between. This indicates small-scale fading, which follows a complex Gaussian distribution with a mean of 0 and a variance of 1. ~ CN (0,1), and These respectively represent the connection from the base station to BD-RIS and the connection from BD-RIS to the user. The path loss index. and Represents Rice factor, and Indicates the line-of-sight link component. and Indicates non-line-of-sight link components. , It follows a complex Gaussian distribution with a mean of 0 and a variance of 1, i.e. , ~ CN (0,1).

[0009] Furthermore, in step S2, the user at the base station is processed by the equalizer. and users The decoded signal is represented as: (1.4) (1.5) in, The user at the base station in the first time slot The decoded signal, The user at the base station in the second time slot The decoded signal, User equalizer, User equalizer, , , It is the phase shift matrix of BD-RIS. Indicates user transmission power, Indicates user The transmission power, Indicated by user The symbol sent, Indicated by user The symbol sent, ~ CN (0, ) is additive white Gaussian noise at the base station.

[0010] Furthermore, in step S3, according to the decoding rules of the OMA system, 2K users transmit signals to the base station in two time slots. Therefore, in the first time slot, the users... The signal-to-interference-plus-noise ratio and the user in the second time slot The signal-to-interference-plus-noise ratios are expressed as follows: (1.6) (1.7) Users in the first time slot The achievable data rate and users in the second time slot The achievable data rates are expressed as follows: (1.8) (1.9).

[0011] Furthermore, in step S4, the process of establishing the optimization problem P1 is as follows: (1.10) (1.11) (1.12) (1.13) (1.14) (1.15) (1.16) in, , This indicates the user's minimum data rate requirement. The maximum transmit power of a user is represented by Equation (1.11), which ensures that the data transmission rate of each user meets the quality of service requirements. Equation (1.12) is the transmit power constraint of each user. Equations (1.13)-(1.15) are the phase shift matrix constraints of the grouped BD-RIS. Equation (1.16) is the normalized power constraint of the equalizer.

[0012] Furthermore, the equalizer optimization process in step S5 is as follows: Based on the given user transmit power and BD-RIS phase shift matrix equalizer It is the optimal receive beamformer for maximizing the signal-to-interference-plus-noise ratio for each user, within the first time slot. And users in the second time slot The MMSE-based equalizers are represented as follows: (1.17) (1.18) in, .

[0013] Furthermore, the process of solving for the optimal user transmit power in step S6 is as follows: For a given equalizer and BD-RIS phase shift matrix Optimization problem P1 is transformed into problem P2: (1.19) (1.20) (1.21) Introduce an auxiliary variable Transform problem P2 into problem P3: (1.22) (1.23) (1.24) (1.25) Since constraint (1.25) is non-convex, it needs to be processed; constraint (1.25) is rewritten as: (1.26) in

[0014] Since the first term on the right-hand side of inequality (1.26) is quasi-concave, the constraint (1.26) remains non-convex; therefore, an auxiliary variable is introduced. Rewrite the first term on the right-hand side of inequality (1.26) as follows: (1.27) in The expression in the t-th iteration is: (1.28) Therefore, problem P3 is transformed into problem P4: (1.29) (1.30) (1.31) (1.32).

[0015] Furthermore, the process of solving for the optimal BD-RIS phase shift matrix in step S7 is as follows: For a given equalizer and user transmit power The original problem P1 is rewritten as the optimization problem P5: (1.33) (1.34) (1.35) (1.36) (1.37) The optimization problem is represented as: (1.38) (1.39) (1.40) (1.41) (1.42) Problem P6 is transformed into problem P7 according to the maximum-minimum criterion, where The lowest SINR for the user: (1.43) (1.44) (1.45) (1.46) (1.47) (1.48) Transform problem P7 into problem P8: (1.49) (1.50) (1.51) (1.52) (1.53) (1.54) in, This represents the reference impedance, taken as 50. , yes The real symmetric matrix, Indicates the group connection size, when This is the traditional single-connection RIS; Considered as concerning the upper triangular part element The function matrix, substituting equations (1.53) and (1.54) into equation (1.52), will optimize the objective. Indicated as about By introducing a penalty function, problem P8 is transformed into a single-variable unconstrained optimization problem P9, which is then optimized sequentially using the BFGS quasi-Newton method. unconstrained variables

[0016] (1.55) in, , It is a sufficiently large positive number as a penalty factor.

[0017] Beneficial effects: (1) The present invention significantly improves system performance and rate: Compared with the traditional RIS scheme, the group-connected BD-RIS can simultaneously regulate the phase and amplitude of the signal, which can enhance the power of the useful signal and suppress multi-user interference. Combined with the alternating optimization strategy, the system performance and rate can be maximized while meeting the minimum service quality requirements of users. Simulation results show that the more BD-RIS reflection units there are and the larger the group size, the more obvious the improvement in system performance and rate.

[0018] (2) This invention breaks through the design limitations of traditional RIS and improves the flexibility of the solution: Traditional RIS only supports diagonal phase shift matrices, which limits the degree of design freedom. The BD-RIS adopted in this invention supports off-diagonal phase shift matrices and characterizes the relationship between reflecting elements through scattering parameter matrices, providing higher design freedom for communication systems. This feature can be adapted to more complex wireless transmission scenarios and achieve better signal modulation effects.

[0019] (3) This invention fills the technical gap in uplink communication scenarios and has practical application value: Existing BD-RIS related research mostly focuses on downlink systems, while uplink scenarios have user-independent power constraints, and downlink schemes cannot be directly reused. This invention models uplink communication systems assisted by BD-RIS, and the proposed alternating optimization method can effectively solve the variable coupling problem in uplink scenarios, providing a feasible solution for uplink communication system performance optimization. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the group-connected BD-RIS-assisted uplink communication system and the rate-maximizing transmission method according to an embodiment of the present invention; Figure 2 This is a model diagram of the group-connected BD-RIS-assisted uplink communication system according to an embodiment of the present invention; Figure 3 These are system and rate curves under different numbers of BD-RIS units; Figure 4 These are system and rate curves under different total power budgets. Detailed Implementation

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0022] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] This invention considers a BD-RIS-assisted uplink SIMO communication system, wherein the base station is equipped with One antenna for simultaneous service Each user has a single antenna. The BD-RIS is deployed near the user, with a number of reflector elements of [number missing]. The channel between the user and the base station consists of a direct channel (user → base station) and a cascaded channel (user → BD-RIS → base station). Each user transmits data in two time slots. The base station antenna is considered a uniform linear array, and the reflector element of each BD-RIS is considered a uniform rectangular array. A schematic diagram of the system model of this invention is shown below. Figure 2 As shown.

[0024] Example 1 See Figure 1 A group-connected BD-RIS-assisted uplink communication system and a method for maximizing transmission rate, comprising the following steps: S1. Establish channel models between users and base stations, between BD-RIS and base stations, and between users and BD-RIS; S2. Based on the demodulation rules of the OMA system, obtain the mathematical expression of the decoded signal of the user at the base station through the equalizer; S3. Calculate the expression for the signal-to-interference-plus-noise ratio and achievable data rate for different users; S4. Under the premise of satisfying the minimum quality of service requirements and maximum transmit power constraints of each user, establish an optimization problem P1. The optimization objective is to maximize the sum rate of the system, and the optimization variables are the equalizer, the transmit power of each user and the BD-RIS phase shift matrix. S5. An alternating optimization strategy is adopted, with fixed user transmit power and BD-RIS phase shift matrix, and the equalizer is optimized based on the MMSE criterion. S6. Using a fixed equalizer and BD-RIS phase shift matrix, auxiliary variables are introduced to transform the non-convex optimization problem into a convex optimization problem P4, and the optimal user transmit power is solved. S7. With fixed equalizer and user transmit power, the phase shift matrix optimization problem is transformed into a single-variable unconstrained optimization problem P9. The optimal BD-RIS phase shift matrix is ​​solved by the BFGS quasi-Newton method. S8. Repeat steps S5-S7 until the system performance converges.

[0025] This embodiment constructs a complete process of "channel modeling → signal decoding → rate calculation → multivariate optimization → iterative convergence". It establishes differentiated channel models between users and base stations, BD-RIS and base stations, and users and BD-RIS. Combining the demodulation rules of the OMA system, it derives the decoded signal expression and calculates the signal-to-interference-plus-noise ratio (SINR) and data rate. Under the premise of satisfying the user's minimum service quality and maximum transmit power constraints, it establishes an optimization problem P1 with the goal of maximizing system performance and rate, including equalizers, user transmit power, and the BD-RIS phase shift matrix. An alternating optimization strategy is adopted, sequentially optimizing the equalizer based on the MMSE criterion and then introducing auxiliary variables to optimize the non-convex interface. The problem is transformed into a convex optimization problem P4 to solve for the transmit power, and the phase shift matrix optimization problem is transformed into a single-variable unconstrained optimization problem P9, which is solved using the BFGS quasi-Newton method. The iteration continues until the system performance converges. Compared with traditional methods, this approach is specifically designed for BD-RIS-assisted uplink communication scenarios, adapting to the characteristics of user-independent power constraints. It fills the technical gap in existing research on multi-focus downlink systems. At the same time, through multi-variable collaborative optimization and flexible control of the BD-RIS off-diagonal phase shift matrix (which can simultaneously adjust the signal phase and amplitude), combined with an efficient optimization solution strategy, the system performance and speed are significantly improved, and it has stronger scenario adaptability and engineering practicality.

[0026] In a specific example, in step S1, the channel between the base station and the user is a Rayleigh fading channel, denoted as... The channels from the base station to BD-RIS and from BD-RIS to the user are Ricean fading channels, denoted as follows: , .

[0027] Unlike traditional RIS systems that use a simplified single fading model for all links, this embodiment employs differentiated modeling based on link propagation characteristics. Transmission between base stations and users is susceptible to obstruction by buildings and obstacles, lacking a stable line-of-sight path. Therefore, a Rayleigh fading channel is used to accurately characterize signal fluctuations caused by multipath scattering. Meanwhile, BD-RIS can be pre-deployed in locations such as rooftops or open high places, actively establishing line-of-sight links between the base station and BD-RIS, and between BD-RIS and users. Therefore, a Ricean fading channel is used to highlight the dominant role of line-of-sight signals. This modeling approach closely aligns with actual deployment scenarios, providing accurate channel parameter support for subsequent signal optimization and avoiding performance loss due to modeling errors.

[0028] It should be noted that since BD-RIS can be pre-deployed in a suitable location, the line-of-sight (LoS) links between BD-RIS and its serving users, and between the base station and BD-RIS, can be guaranteed. Therefore, the base station to BD-RIS and BD-RIS to user are modeled as Ricean fading channels suitable for scenarios with dominant line-of-sight links, where the received signal is mainly a direct line-of-sight signal.

[0029] In a specific example, the Rayleigh fading channel and the Rice fading channel are modeled as follows: (1.1) (1.2) (1.3) in, Indicates base station and user Path loss index between. This indicates small-scale fading, which follows a complex Gaussian distribution with a mean of 0 and a variance of 1. ~ CN (0,1), and These respectively represent the connection from the base station to BD-RIS and the connection from BD-RIS to the user. The path loss index. and Represents Rice factor, and Indicates the line-of-sight link component. and Indicates non-line-of-sight link components. , It follows a complex Gaussian distribution with a mean of 0 and a variance of 1, i.e. , ~ CN (0,1).

[0030] This embodiment introduces the Rice factor into the formula. and The power ratio between line-of-sight and non-line-of-sight links can be flexibly adjusted. A larger Rice factor indicates stronger line-of-sight signal dominance and higher channel stability. Compared to traditional RIS channel modeling that ignores the line-of-sight component, the formula in this invention can accurately quantify the gain advantage of BD-RIS line-of-sight links, providing a clear direction for subsequent phase-shift matrix optimization and ensuring that the optimization strategy can specifically enhance the line-of-sight signal power.

[0031] In a specific example, in step S2, due to the significant path loss caused by multiple reflections, this invention only considers the signal reflected once by the BD-RIS. Therefore, through the equalizer, the user at the base station... and users The decoded signal is represented as: (1.4) (1.5) in, The user at the base station in the first time slot The decoded signal, The user at the base station in the second time slot The decoded signal, User equalizer, User equalizer, , , It is the phase shift matrix of BD-RIS. Indicates user transmission power, Indicates user The transmission power, Indicated by user The symbol sent, Indicated by user The symbol sent, ~ CN (0, ) is additive white Gaussian noise at the base station.

[0032] This example explicitly separates the direct link signal from the BD-RIS reflected link signal, while also incorporating multi-user interference terms. Compared to traditional RIS schemes that do not distinguish between the two types of link signals, the expression of this invention clearly reflects the signal enhancement mechanism of BD-RIS and provides a clear mathematical basis for separating useful and interfering signals when calculating the signal-to-interference-plus-noise ratio (SINR). Furthermore, by limiting consideration to only a single reflected signal, the algorithm's complexity is significantly reduced while maintaining computational accuracy. This avoids the exponential increase in computational load caused by multiple reflections, thus improving the engineering feasibility of the solution.

[0033] In a specific example, in step S3, according to the decoding rules of the OMA system, 2K users transmit signals to the base station in two time slots. Therefore, in the first time slot, the users... The signal-to-interference-plus-noise ratio and the user in the second time slot The signal-to-interference-plus-noise ratios are expressed as follows: (1.6) (1.7) Users in the first time slot The achievable data rate and users in the second time slot The achievable data rates are expressed as follows: (1.8) (1.9).

[0034] The signal-to-interference-plus-noise ratio (SIR) formula in this example combines the signals from the direct link and the BD-RIS reflected link to calculate the total useful power. It also incorporates multi-user interference and noise into the denominator, accurately measuring the signal quality for each user. Compared to traditional RIS schemes that do not fully consider the collaborative gain of the two types of links, the formula in this invention more accurately reflects the rate improvement effect of BD-RIS on users. The rate formula is derived based on Shannon's theorem and uses division by the number of time slots (2) to reflect the resource allocation strategy of transmitting 2K users in two time slots, balancing system throughput and user fairness.

[0035] In a specific example, in step S4, the process of establishing the optimization problem P1 is as follows: (1.10) (1.11) (1.12) (1.13) (1.14) (1.15) (1.16) in, , This indicates the user's minimum data rate requirement. The maximum transmit power of a user is represented by Equation (1.11), which ensures that the data transmission rate of each user meets the quality of service requirements. Equation (1.12) is the transmit power constraint of each user. Equations (1.13)-(1.15) are the phase shift matrix constraints of the grouped BD-RIS. Equation (1.16) is the normalized power constraint of the equalizer.

[0036] The optimization problem P1 constructed in this example simultaneously considers the equalizer, user transmit power, and BD-RIS phase shift matrix as optimization variables, which differs from the traditional RIS scheme that only optimizes the phase shift matrix or power as a single variable. Among the constraints, Equation (1.11) avoids the "rate starvation" problem, ensuring the basic communication needs of edge users; Equations (1.13)-(1.15) are designed to address the structural characteristics of group-connected BD-RIS, ensuring both the conjugate symmetry and unity of the matrix, and flexibly adjusting the positions of non-zero elements through the group size G, making it more flexible than the constraints of traditional single-connected RIS; the equalizer normalization constraint in Equation (1.16) avoids signal distortion caused by receiver power overload. This optimization problem comprehensively considers the user-independent power constraints in the uplink scenario, filling the technical gap that traditional downlink BD-RIS schemes cannot reuse.

[0037] In a specific example, the equalizer optimization process in step S5 is as follows: Based on the given user transmit power and BD-RIS phase shift matrix equalizer It is the optimal receive beamformer for maximizing the signal-to-interference-plus-noise ratio for each user, within the first time slot. And users in the second time slot The MMSE-based equalizers are represented as follows: (1.17) (1.18) in, .

[0038] This example employs the MMSE criterion to optimize the equalizer. Compared to traditional zero-forcing (ZF) equalizers, which only suppress interference and ignore noise amplification, the MMSE equalizer achieves an optimal balance between interference and noise suppression, maximizing the user's signal-to-interference-plus-noise ratio (SNR). The equalizer expression is directly derived from channel parameters, transmit power, and phase shift matrix, possessing a clear theoretical basis and computability. In the alternating optimization framework, first fixing the power and phase shift matrix to optimize the equalizer provides better receiver conditions for subsequent power and phase shift matrix optimizations, improving the overall algorithm's convergence efficiency and final performance.

[0039] In a specific example, the process of solving for the optimal user transmit power in step S6 is as follows: For a given equalizer and BD-RIS phase shift matrix Optimization problem P1 is transformed into problem P2: (1.19) (1.20) (1.21) Introduce an auxiliary variable Transform problem P2 into problem P3: (1.22) (1.23) (1.24) (1.25) Since constraint (1.25) is non-convex, it needs to be processed; constraint (1.25) is rewritten as: (1.26) in

[0040] Since the first term on the right-hand side of inequality (1.26) is quasi-concave, the constraint (1.26) remains non-convex; therefore, an auxiliary variable is introduced. Rewrite the first term on the right-hand side of inequality (1.26) as follows: (1.27) in The expression in the t-th iteration is: (1.28) Therefore, problem P3 is transformed into problem P4: (1.29) (1.30) (1.31) (1.32) This example addresses the non-convex constraint problem P2 by introducing auxiliary variables, gradually transforming the originally difficult non-convex optimization problem into the standard convex optimization problem P4. Compared to traditional brute-force search or suboptimal algorithms, convex optimization problems can be solved directly using mature toolkits such as CVX, significantly reducing the engineering implementation difficulty. The strategy of iteratively updating auxiliary variables ensures that the transformed problem approximates the optimal solution of the original problem, overcoming the obstacle of solving non-convex problems and guaranteeing the accuracy of the optimization results. Furthermore, the power constraint is adapted to the characteristic of limited independent user power in uplink scenarios, differing from the design approach of total base station power constraints in downlink scenarios.

[0041] It should be noted that since problem P4 is a standard convex optimization problem, it can be solved using existing convex optimization toolkits.

[0042] In a specific example, the process of solving for the optimal BD-RIS phase shift matrix in step S7 is as follows: For a given equalizer and user transmit power The original problem P1 is rewritten as the optimization problem P5: (1.33) (1.34) (1.35) (1.36) (1.37) Given the equalizer and user transmit power, phase shift optimization can improve the system's signal-to-interference-plus-noise ratio (SINR) and further increase the system's sum rate. The optimization problem is expressed as: (1.38) (1.39) (1.40) (1.41) (1.42) Problem P6 is transformed into problem P7 according to the maximum-minimum criterion, where The lowest SINR for the user: (1.43) (1.44) (1.45) (1.46) (1.47) (1.48) Due to the non-convex phase shift matrix constraint of BD-RIS, it is very difficult to transform problem P7 into a convex problem. Therefore, we transform problem P7 into problem P8: (1.49) (1.50) (1.51) (1.52) (1.53) (1.54) in, This represents the reference impedance, taken as 50. , yes The real symmetric matrix, Indicates the group connection size, when This is the traditional single-connection RIS; Considered as concerning the upper triangular part element The function matrix, substituting equations (1.53) and (1.54) into equation (1.52), will optimize the objective. Indicated as about By introducing a penalty function, problem P8 is transformed into a single-variable unconstrained optimization problem P9, which is then optimized sequentially using the BFGS quasi-Newton method. unconstrained variables

[0043] (1.55) in, , It is a sufficiently large positive number as a penalty factor.

[0044] This example addresses the challenging problem of non-convex phase shift matrix optimization in BD-RIS, employing a combined solution strategy of "maximum-minimum criterion + penalty function + BFGS quasi-Newton method." The maximum-minimum criterion ensures that the sum of the user signal-to-interference-plus-noise ratios (SNR) is monotonically increasing, improving the algorithm's effectiveness. The introduction of the penalty function integrates the phase shift matrix constraints into the objective function, transforming it into an unconstrained optimization problem, reducing the difficulty and satisfying the minimum service quality requirements for all users. The BFGS quasi-Newton method offers faster convergence than gradient descent and lower computational cost than Newton's method, efficiently solving high-dimensional phase shift matrix optimization problems. Furthermore, by flexibly adjusting the group size G, this scheme is compatible with traditional single-connected RIS (G=N), demonstrating its compatibility and scalability.

[0045] Simulation verification: Configure system parameters as shown in the table below:

[0046] Figure 3 A graph depicting the relationship between the number of RIS units and the system speed is shown. The number of base station antennas is set in the simulation. =2, number of users =4, total system power budget =30dBm. From Figure 3It can be seen that all four RIS schemes achieved higher system performance and speed than the scheme without RIS. This is because RIS has the function of enhancing the useful signal and suppressing interference signals, which can improve system performance. Furthermore, except for the scheme without RIS, the system performance and speed increase with the increase of the number of reflection units. This is because more reflection units are used to reshape the phase or amplitude of the incident signal, thus achieving better system performance. From... Figure 2 It can also be seen that group-connected BD-RIS achieves higher system performance and speed than traditional single-connected RIS. This is because BD-RIS can change not only the phase of the signal but also its amplitude, thus achieving better system performance than traditional single-connected RIS. Furthermore, the larger the group size of the group-connected BD-RIS, the better the system performance. This is because the larger the group size provides greater design freedom, resulting in better performance. In addition, from... Figure 3 It can also be seen that, compared with the random phase scheme, the algorithm proposed in this invention can significantly improve the system and speed, demonstrating the superiority of the algorithm in this invention.

[0047] Figure 4 The graphs show the relationship between the total power budget and the system speed for different systems. The number of reflection elements is set to [value missing] in the simulation. =24, Number of base station antennas =2, number of users =4. From Figure 4 It can be seen that as the total system power budget increases, the system speed also increases. This is because with a higher total system power budget, users have higher transmit power to improve their SINR, thereby increasing the system speed. Figure 4 It can also be seen that all four RIS schemes achieve higher system performance and speed than the non-RIS scheme. Furthermore, compared with the random phase scheme, the algorithm proposed in this invention can significantly improve system performance and speed. In addition, the group-connected BD-RIS achieves higher system performance and speed than the traditional single-connected RIS, and the larger the group size of the group-connected BD-RIS, the better the system performance, the reason for which has been explained in this invention.

[0048] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. 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 group-connected BD-RIS-assisted uplink communication system and a method for maximizing transmission rate, characterized in that, Includes the following steps: S1. Establish channel models between users and base stations, between BD-RIS and base stations, and between users and BD-RIS; S2. Based on the demodulation rules of the orthogonal multiple access system, obtain the mathematical expression of the decoded signal of the user at the base station through the equalizer; S3. Calculate the expression for the signal-to-interference-plus-noise ratio and achievable data rate for different users; S4. Under the premise of satisfying the minimum quality of service requirements and maximum transmit power constraints of each user, establish an optimization problem P1. The optimization objective is to maximize the sum rate of the system. The optimization variables are the equalizer, the transmit power of each user and the BD-RIS phase shift matrix. S5. An alternating optimization strategy is adopted to optimize the equalizer based on the minimum mean square error criterion by fixing the user transmit power and the BD-RIS phase shift matrix. S6. Using a fixed equalizer and BD-RIS phase shift matrix, auxiliary variables are introduced to transform the non-convex optimization problem into a convex optimization problem P4, and the optimal user transmit power is solved. S7. With fixed equalizer and user transmit power, the phase shift matrix optimization problem is transformed into a single-variable unconstrained optimization problem P9. The optimal BD-RIS phase shift matrix is ​​solved by the BFGS quasi-Newton method. S8. Repeat steps S5-S7 until the system performance converges.

2. The group-connected BD-RIS-assisted uplink communication system and rate-maximizing transmission method according to claim 1, characterized in that, In step S1, the channel between the base station and the user is a Rayleigh fading channel, denoted as... The channels from the base station to BD-RIS and from BD-RIS to the user are Ricean fading channels, denoted as follows: , .

3. The uplink communication system and rate-maximizing transmission method with group connection BD-RIS assistance according to claim 2, characterized in that, The Rayleigh fading channel and the Rice fading channel are modeled as follows: (1.1) (1.2) (1.3) in, Indicates base station and user Path loss index between. This indicates small-scale fading, which follows a complex Gaussian distribution with a mean of 0 and a variance of 1. ~ CN (0,1), and These respectively represent the connection from the base station to BD-RIS and the connection from BD-RIS to the user. The path loss index. and Represents Rice factor, and Indicates the line-of-sight link component. and Indicates non-line-of-sight link components. , It follows a complex Gaussian distribution with a mean of 0 and a variance of 1, i.e. , ~ CN (0,1).

4. The uplink communication system and rate-maximizing transmission method with group connection BD-RIS assistance according to claim 1, characterized in that, In step S2, the user at the base station is processed by the equalizer. and users The decoded signal is represented as: (1.4) (1.5) in, The user at the base station in the first time slot The decoded signal, The user at the base station in the second time slot The decoded signal, User equalizer, User equalizer, , , It is the phase shift matrix of BD-RIS. Indicates user The transmission power, Indicates user The transmission power, Indicated by user The symbol sent, Indicated by user The symbol sent, ~ CN (0, ) is additive white Gaussian noise at the base station.

5. The group-connected BD-RIS-assisted uplink communication system and rate-maximizing transmission method according to claim 1, characterized in that, In step S3, according to the decoding rules of the OMA system, 2K users transmit signals to the base station in two time slots. Therefore, in the first time slot, the users... The signal-to-interference-plus-noise ratio and the user in the second time slot The signal-to-interference-plus-noise ratios are expressed as follows: (1.6) (1.7) Users in the first time slot The achievable data rate and users in the second time slot The achievable data rates are expressed as follows: (1.8) (1.9)。 6. The group-connected BD-RIS-assisted uplink communication system and rate-maximizing transmission method according to claim 1, characterized in that, In step S4, the process of establishing the optimization problem P1 is as follows: (1.10) (1.11) (1.12) (1.13) (1.14) (1.15) (1.16) in, , This indicates the user's minimum data rate requirement. The maximum transmit power of a user is represented by Equation (1.11), which ensures that the data transmission rate of each user meets the quality of service requirements. Equation (1.12) is the transmit power constraint of each user. Equations (1.13)-(1.15) are the phase shift matrix constraints of the grouped BD-RIS. Equation (1.16) is the normalized power constraint of the equalizer.

7. The group-connected BD-RIS-assisted uplink communication system and rate-maximizing transmission method according to claim 6, characterized in that, The equalizer optimization process in step S5 is as follows: Based on the given user transmit power and BD-RIS phase shift matrix equalizer It is the optimal receive beamformer for maximizing the signal-to-interference-plus-noise ratio for each user, within the first time slot. And users in the second time slot The MMSE-based equalizers are represented as follows: (1.17) (1.18) in, .

8. The group-connected BD-RIS-assisted uplink communication system and rate-maximizing transmission method according to claim 7, characterized in that, The process of solving for the optimal user transmit power in step S6 is as follows: For a given equalizer and BD-RIS phase shift matrix Optimization problem P1 is transformed into problem P2: (1.19) (1.20) (1.21) Introduce an auxiliary variable Transform problem P2 into problem P3: (1.22) (1.23) (1.24) (1.25) Since constraint (1.25) is non-convex, it needs to be processed; constraint (1.25) is rewritten as: (1.26) in Since the first term on the right-hand side of inequality (1.26) is quasi-concave, the constraint (1.26) remains non-convex; therefore, an auxiliary variable is introduced. Rewrite the first term on the right-hand side of inequality (1.26) as follows: (1.27) in The expression in the t-th iteration is: (1.28) Therefore, problem P3 is transformed into problem P4: (1.29) (1.30) (1.31) (1.32)。 9. The group-connected BD-RIS-assisted uplink communication system and rate-maximizing transmission method according to claim 8, characterized in that, The process of solving for the optimal BD-RIS phase shift matrix in step S7 is as follows: For a given equalizer and user transmit power The original problem P1 is rewritten as the optimization problem P5: (1.33) (1.34) (1.35) (1.36) (1.37) The optimization problem is represented as: (1.38) (1.39) (1.40) (1.41) (1.42) Problem P6 is transformed into problem P7 according to the maximum-minimum criterion, where The lowest SINR for the user: (1.43) (1.44) (1.45) (1.46) (1.47) (1.48) Transform problem P7 into problem P8: (1.49) (1.50) (1.51) (1.52) (1.53) (1.54) in, This represents the reference impedance, taken as 50. , yes The real symmetric matrix, Indicates the group connection size, when This is the traditional single-connection RIS; Considered as concerning the upper triangular part element The function matrix, substituting equations (1.53) and (1.54) into equation (1.52), will optimize the objective. Indicated as about By introducing a penalty function, problem P8 is transformed into a single-variable unconstrained optimization problem P9, which is then optimized sequentially using the BFGS quasi-Newton method. unconstrained variables (1.55) in, , It is a sufficiently large positive number as a penalty factor.

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