A dual-RIS-assisted RSMA-ISAC system and rate optimization method

Abstract

The present application relates to the technical field of wireless communication, and particularly relates to a double-RIS-aided RSMA-ISAC system and a rate optimization method. In the existing integrated sensing and communication system, the single-RIS coverage range is limited, the multi-user interference management is difficult under the double-RIS architecture, and there is a lack of joint optimization scheme with the system and rate as the target. The present application firstly initializes the double-RIS-aided RSMA-ISAC system parameters; establishes an optimization model containing the base station power, the radar signal-to-noise ratio, the double-RIS phase shift, the user minimum rate and the public rate allocation constraint with the maximum system and rate as the target; converts the objective function by using the weighted least mean square error algorithm; decomposes the problem into three sub-problems by using the alternating optimization method, and converts the non-convex constraint into a convex optimization problem by using the first-order Taylor expansion and the penalty function method, respectively, and iteratively solves to obtain the optimal base station beamforming matrix, the public rate allocation vector and the double-RIS passive beamforming matrix.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a dual RIS-assisted RSMA-ISAC system and a rate optimization method. Background Technology

[0002] Integrated Sensing and Communication (ISAC) is a key technology in 6G communication, aiming to deeply integrate communication and sensing functions by sharing spectrum and hardware resources to alleviate challenges such as spectrum scarcity and link obstruction. Reconfigurable Intelligent Surface (RIS) can reshape the wireless propagation environment on demand by adjusting the phase of a large number of passive reflective elements, offering significant advantages in enhancing link gain, suppressing interference, and improving coverage. It has become an important enabling technology for ISAC systems.

[0003] In practical deployments, a single RIS exhibits significant performance bottlenecks: while a stable auxiliary link can be established when the RIS is deployed close to the base station, the auxiliary link between the RIS and the user is also prone to failure if the direct link between the base station and the user is interrupted. Furthermore, the signal coverage of a single RIS is limited, making it difficult to maintain stable system performance in multi-user, multi-obstruction scenarios over the long term. In contrast, a dual-RIS architecture, through collaborative deployment (one near the base station and one near the user), can achieve greater coverage distance and superior performance gains. Simultaneously, Rate-Splitting Multiple Access (RSMA) flexibly adapts to the differentiated channel conditions of multiple users by splitting user messages into common and private streams, effectively mitigating multi-user interference and improving spectrum efficiency.

[0004] For RIS-assisted ISAC systems, some research has been conducted in the prior art. For example, Chinese patent CN118138083A discloses a dual-RIS-assisted MU-MIMO beamforming method based on maximizing energy efficiency. This method improves system energy efficiency by alternately optimizing base station transmit beamforming, user receive beamforming, and dual-RIS reflection coefficients. However, this scheme uses a traditional MU-MIMO transmission mechanism, failing to fully utilize the advantages of RSMA in interference management, and its optimization objective focuses on energy efficiency rather than system performance and data rate. Chinese patent CN118249868A discloses a secure beamforming method for RSMA-ISAC systems. This method introduces interference symbols and solves the secure rate maximization problem based on a semi-definite relaxation algorithm, treating the sensed target as a potential eavesdropper. Although this scheme integrates RSMA and ISAC, its system architecture only uses a single RIS, making it difficult to fully address the problems of signal coverage blind spots and insufficient link gain in multi-user scenarios.

[0005] In summary, no existing technology has disclosed or proposed an ISAC system scheme that can simultaneously utilize the coverage and gain advantages of dual RIS and the flexible interference management capabilities of RSMA. How to design an efficient non-convex optimization algorithm within this novel dual RIS-RSMA-ISAC architecture, with the goal of maximizing system performance and data rate, while comprehensively considering multiple constraints such as base station transmit power, radar echo signal-to-noise ratio, dual RIS constant-mode phase, minimum user rate, and common rate allocation, has become a pressing technical problem in this field. Summary of the Invention

[0006] This invention aims to address the performance bottlenecks in existing RIS-assisted ISAC systems, such as limited coverage and easy link interruption with a single RIS architecture; although a dual RIS architecture can improve coverage, multi-user interference issues still limit system capacity; and traditional multiple access methods (such as SDMA and NOMA) have insufficient interference management capabilities in multi-user scenarios. A dual RIS-assisted RSMA-ISAC system and a rate optimization method are provided, including: S1: Initialize system parameters, including the number of base station antennas, the number of users, the number of dual RIS reflector units, the upper limit of transmit power, the minimum user rate requirement, the radar signal-to-noise ratio threshold, etc. S2: Based on the constraints of the maximum transmit power of the base station, the radar echo signal-to-interference-plus-noise ratio, the phase shift constraint of the dual RIS, the minimum user rate requirement constraint, and the non-negativity constraint of the common rate, a resource optimization model is constructed with the goal of maximizing the number of system users and the rate. S3: The weighted minimum mean square error algorithm is used to construct the relationship between rate and weighted minimum mean square error. The objective function and constraints are transformed, and an equivalent relationship between rate and mean square error is established by introducing an equalizer and weight coefficients. S4: The optimization problem is transformed into three sub-problems using the alternating optimization method. The weighted minimum mean square error method and the penalty function method are used to solve them, and the optimal base station beamforming matrix, common rate allocation vector and dual RIS passive beamforming matrix are obtained, thus obtaining the resource allocation scheme with the maximum system and rate. S5: Determine if the system and rate have converged; if so, calculate and output the base station beamforming matrix. Common rate allocation vector The first RIS passive beamforming matrix The passive beamforming matrix of the second RIS Then terminate; otherwise, proceed to S6; S6: Determine if the current iteration count is greater than the maximum iteration count; if so, output the base station beamforming matrix. Common rate allocation vector The first RIS passive beamforming matrix The passive beamforming matrix of the second RIS Then terminate; otherwise, update the current iteration number. Then proceed to the next iteration and return to S41.

[0007] Furthermore, the system parameters described in S1 include at least: Number of transmit antennas of the base station Number of users The number of reflective elements in the first RIS The number of reflective elements in the second RIS Maximum transmission power of base stations , No. Minimum speed requirement for each user Radar echo signal-to-noise ratio threshold , No. noise power per user Noise power at the target location Convergence threshold and maximum number of iterations .

[0008] Furthermore, in S2, the system and the resource allocation scheme model with the highest speed are as follows:

[0009] in, ; , ; ; ; ; ; in, This represents the user's minimum rate requirement constraint. This indicates a common stream decodeable rate constraint. This indicates a non-negativity constraint for common rate allocation. This indicates the radar echo signal-to-noise ratio constraint. This indicates the maximum transmit power constraint for the base station. , These represent the unit mode phase shift constraints of the first RIS and the second RIS, respectively; Active beamforming matrix for base stations, It is the beamforming vector of the common flow. For the first Beamforming vectors for a user's private stream For the first Beamforming vectors for each user's private stream, where , Assign vectors to the common rates of users. , These are the passive beamforming matrices for the first RIS and the second RIS, respectively; For the first The achievable rate for each user For the first Minimum rate requirement for each user For the first The actual public rate for each user For the first The rate at which each user decodes the public stream. For the first The rate at which each user decodes a private stream; Echo signal-to-noise ratio; This is the radar echo signal-to-noise ratio threshold; This is the maximum transmission power of the base station. , The first RIS and the second The first reflection unit and the second RIS The reflection coefficient of each reflecting unit. For the first A vector of reflection coefficients of RIS, where ; From the base station to the Channel vectors for each user For base station to the Channels for individual users for To the Channels for individual users for To the Channels for individual users; , , From base station to channels, base stations to Channel, arrive The channel; This is a composite channel from the base station to the target. This refers to the channel from the base station to the sensing target. for The channel to the target being sensed. For the first Noise power per user.

[0010] Furthermore, in S3, the step of constructing the relationship between the rate and the weighted minimum mean square error using the weighted minimum mean square error algorithm specifically includes: For the For each user, a serial interference cancellation decoding method is used, that is, the common stream is decoded first, the common stream components are eliminated, and then the private stream is decoded. Specifically: Will Individual users on public flow and private stream The estimates are expressed as follows: , ; No. Common mean square error at each user and private mean square error They are represented as follows: , ; , ; The signal-to-interference-plus-noise ratios (SIRs) of the expected public and private streams are as follows: , ; No. The rate at which each user decodes the public and private streams is: , ; Introducing positive weighting coefficients and Applying these methods to the public and private flows respectively, construct the corresponding weighted mean square error functions: , ; The equalizer parameters and weighting coefficients are optimized to establish a correlation between the rate and the weighted minimum mean square error. , ; The value of the optimal equalizer is obtained from the first-order optimality condition: , Optimal weights: , ; The problem Rephrased as :

[0011] in, , These represent equalizers for the public and private streams, respectively. Indicates the first Downlink signals received by each user Indicates public data flow, Indicates the first Private data streams for each user Indicates from the base station to the... Channel vectors for each user Indicates taking the real part, , Represented as the first The equivalent received power term for each user when decoding a public stream and decoding a private stream after eliminating the public stream; The weight vector for decoding the minimum mean square error of the public and private streams; This is the equalizer vector.

[0012] Furthermore, S4 specifically includes: S41: Fixed To obtain information about the variables The optimization subproblem is transformed into a convex optimization problem by constructing a non-convex constraint surrogate function through a first-order Taylor expansion. The optimal solution is then obtained using the CVX toolbox. ; S42: Fixed To obtain information about the variables The optimization subproblem is solved by approximating the nonconvex quadratic form with a lower bound using a first-order Taylor expansion, and by using the penalty function method to relax the unit modulus constraint of the first RIS to a convex constraint, thus transforming the nonconvex problem into a convex optimization problem. The optimal solution is obtained by using the interior point method. ; S43: Fixed To obtain information about the variables The optimization subproblem is solved by using the penalty function method to relax the unit modulus constraint of the second RIS to a convex constraint, thus transforming the non-convex problem into a convex optimization problem. The optimal solution is obtained by using the interior point method. .

[0013] Furthermore, in S41, the specific form of the first-order Taylor expansion is:

[0014] in, , , Represents the active beamforming matrix of the base station According to the column vectorization The Kronecker product is represented by vec(·), which denotes the vectorization operation. Indicates the first The solution after the next iteration.

[0015] Furthermore, in S4, the penalty function method is as follows: Add a penalty term to the objective function ,in, This is the penalty factor corresponding to the RIS unit modulus constraint. Let i be the current solution in the i-th iteration; apply the unit modulus constraint. Relaxation is a convex constraint and through Gradually increasing the value forces the solution to approximate the unit modulus.

[0016] Furthermore, in S5, the condition for determining whether the system and rate converge is: ;in, This is the preset convergence threshold.

[0017] Furthermore, the dual RIS includes a first RIS and a second RIS, wherein the first RIS is deployed near the base station and serves both communication and sensing; the second RIS is deployed at the cell edge or in a signal-obstructed area to enhance the channel gain between the base station and the user; and, in the sensing modeling, only the sensing channels related to the first RIS are retained, while the reflection path between the second RIS and the target is ignored.

[0018] Furthermore, the solution process formed by the weighted minimum mean square error algorithm, the alternating optimization method, the first-order Taylor expansion and the penalty function method executes steps S41, S42 and S43 sequentially in each outer iteration, and the order of steps S42 and S43 can be interchanged or executed in parallel.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: First, this invention combines the coverage enhancement capability of dual RIS with the flexible interference management capability of RSMA, effectively overcoming the coverage limitations of single RIS, extending the signal coverage distance, and improving the flexibility of multi-user access.

[0020] Second, this invention aims to maximize system performance and rate. By jointly optimizing the base station active beam, common rate allocation, and dual RIS passive beam, simulation results show that, under the premise of satisfying radar perception quality and user communication quality, this method is superior to single RIS-RSMA-ISAC, dual RIS-SDMA-ISAC, and dual RIS-NOMA-ISAC schemes in different transmit power ranges, with significant improvements in system performance and rate.

[0021] Third, for highly non-convex optimization problems, this invention designs a joint solution framework of WMMSE-alternating optimization-Taylor expansion-penalty function method, which effectively handles the complex non-convex constraints caused by dual RIS coupling and RSMA rate splitting, with fast convergence speed and strong practicality. Attached Figure Description

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will now be described in detail with reference to the accompanying drawings, wherein... Figure 1 This is a flowchart of a dual RIS-assisted RSMA-ISAC system and a rate optimization method according to the present invention.

[0023] Figure 2 This is a comparison chart of the system and rate performance of the method of the present invention and different comparative methods under the maximum transmit power of different base stations. Detailed Implementation

[0024] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0025] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0026] Example 1 I. System Hardware Configuration and Parameter Definition This embodiment constructs a dual RIS-assisted RSMA-ISAC system. The system includes: a system equipped with... The base station (BS) with a root antenna, and two reconfigurable smart surfaces ( , ), Each user has a single antenna and a sensing target. The base station performs a dual task: on the one hand... On the one hand, it provides communication services to users, and on the other hand, it performs location detection on perceived targets.

[0027] Base station: Full-duplex base station, equipped with The base station uses a uniform linear array antenna (ULA) and integrates a baseband processing unit, RF transceiver link, and beamforming controller. The base station connects to the RIS controller via fiber optic cable or a high-speed data interface to issue phase shift configuration commands to the RIS.

[0028] Deployed near the base station, within the line-of-sight link between the base station and the target, and with an available reflection link between the base station and the user, it is mainly used to cooperate with the base station to complete target perception and enhance communication for some users. Depend on It consists of a passive reflective unit, each unit integrating a PIN diode or varactor diode, and its reflection phase is independently adjusted by the RIS controller.

[0029] Deployed at the edge of the cell or in areas with severe signal obstruction, by Composed of passive reflective units, it also uses a RIS controller for phase modulation. Its core function is to enhance the effective channel gain between the base station and the user and alleviate the problem of obstructed direct link.

[0030] RIS controller: It can be implemented using a field-programmable gate array (FPGA) or a microcontroller unit (MCU). It communicates with the base station through a control link to receive the phase shift matrix configuration instructions from the base station and generate corresponding bias voltage or current signals to drive the phase shifters of each unit of the RIS.

[0031] User equipment: A single-antenna terminal, such as a smartphone or IoT sensor, capable of receiving downlink signals and performing serial interference cancellation (SIC) decoding.

[0032] Target to be sensed: It is a passive reflector. The base station achieves sensing by transmitting ISAC signals and receiving their echoes.

[0033] Considering The distance to the target is usually far, and both are in a strong non-line-of-sight link environment. The two-way path loss from reflection to the target and back to the base station is much greater than... The two-way path loss between the target and the target is ignored in the perception modeling process of this invention. The reflection path between the target and the target is retained only. Related sensory channels.

[0034] definition For user index set, The dual RIS reflection unit sets are respectively , , , The phase shift matrix of RIS is defined as follows: , Each RIS element is composed of... express, , They represent the first The first RIS The reflection amplitude and phase of each reflecting unit. To obtain the maximum reflection gain, set... .

[0035] Based on the basic transmission principle of RSMA, the first The information received by each user is typically divided into public information and private information, which are recorded separately. and Public information corresponding to all receiving ends. A common flow is formed after joint encoding. Private information is encoded independently to form corresponding private data streams. The beamforming vector of the common flow at the base station is defined as... ;No. The beamforming vector of a user's private stream is defined as follows: ;No. The beamforming vector of a user's private stream is defined as follows: , Active beamforming of a base station is defined as follows: The matrix defines the transmitted signal at the base station as follows: ,in, , .

[0036] Therefore, the first The signal received by each downlink communication user is ;in, For the first The mean of each user is 0, and the variance is... noise, Indicates from the base station to the... The channel vector for each user is specifically expressed as follows: . For base station to the Channels for individual users , They are respectively , To the Channels for individual users , , From base station to channels, base stations to Channel, arrive The channel.

[0037] No. Individual users decode public stream The rate is

[0038] Subsequently, serial interference cancellation technology is used to remove the public information stream. After eliminating the interference of the public signal, the private information streams of other users are regarded as noise.

[0039] Decoding Private Information Streams The rate is

[0040] Because the public stream needs to be decoded by all users, the public stream... The decoding rate does not exceed .

[0041] Define the user's common rate allocation vector as , Satisfy the following relationship

[0042] Finally, the first The achievable rate for each user is

[0043] For sensing tasks, the base station connects with... The perception process is completed collaboratively via a reflection link. Because the system uses RSMA technology, target perception can be achieved directly using the transmitted communication signals.

[0044] Define the composite channel from base station to target as Then we have:

[0045] in, This represents the channel from the base station to the sensing target. express The channel to the target is then used. At this time, the base station receives the echo signal from the target as follows:

[0046] in, This indicates the ISAC signal transmitted by the base station. This represents additive white Gaussian noise at the target location. .

[0047] To measure the system's sensing capability, this embodiment selects the echo signal-to-noise ratio (SNR) as a performance evaluation index, and its expression is:

[0048] in, This represents the equivalent channel of the target echo.

[0049] II. Specific Implementation of the Method and Procedure like Figure 1 As shown, this embodiment provides a dual RIS-assisted RSMA-ISAC system and a rate optimization method, which specifically includes the following steps: S1: System parameter initialization In the initialization module of the base station or RIS controller, configure the following parameters: number of transmit antennas for the base station. Number of users , Number of reflective elements , Number of reflective elements , No. Minimum speed requirement for each user Radar echo signal-to-noise ratio threshold , No. noise power per user Noise power at the target location Convergence threshold and maximum number of iterations .

[0050] S2: Constructing a resource optimization model In the base station's optimization processing unit (e.g., a digital signal processor (DSP) or ARM core), based on the base station's maximum transmit power constraint, radar echo signal-to-interference-plus-noise ratio constraint, dual RIS phase shift constraint, minimum user rate requirement constraint, and non-negativity constraint of common rate, with the goal of maximizing system users and rate, the following resource optimization model is constructed:

[0051] in, This represents the user's minimum rate requirement constraint. This indicates a common stream decodeable rate constraint. This indicates a non-negativity constraint for common rate allocation. This indicates the radar echo signal-to-noise ratio constraint. This indicates the maximum transmit power constraint for the base station. and They represent and Unit mode phase shift constraint; Active beamforming matrix for base stations, It is the beamforming vector of the common flow. For the first Beamforming vectors for a user's private stream; Assign vectors to the common rates of users; for Passive beamforming matrix; for Passive beamforming matrix; For the first The achievable rate for each user; For the first Minimum rate requirement for each user; For the first The actual public rate for each user; No. The rate at which each user decodes the public stream; Echo signal-to-noise ratio; This is the radar echo signal-to-noise ratio threshold; This represents the maximum transmit power of the base station. for No. The reflection coefficient of each reflecting unit; for No. The reflection coefficient of each reflecting unit.

[0052] S3: Transformation based on weighted minimum mean square error (WMMSE) To solve the above non-convex optimization problem, the WMMSE algorithm is first used to construct the relationship between the rate maximization objective and the weighted minimum mean square error, and the objective function and constraints are transformed.

[0053] Specifically, for the first For each user, a serial interference cancellation decoding method is used, which means first decoding the common stream, and then decoding the private stream after eliminating the common stream components.

[0054] Definition of the first Each user has access to public and private streams. and ,in and These are equalizers for public and private streams, respectively. The public and private mean square errors for each user are expressed as follows:

[0055]

[0056] in, {·} indicates taking the real part. , .

[0057] make , ,have to , .

[0058] Therefore, the minimum mean square error is expressed as follows: , .

[0059] The signal-to-interference-plus-noise ratio (SIR) of the expected public and private streams is converted to: , .

[0060] No. The decoding rates for public and private streams for each user are as follows: , .

[0061] Introducing positive weighting coefficients and Applying these values ​​to the public and private flows respectively, we construct the corresponding weighted mean square error functions:

[0062]

[0063] Further optimization of the equalizer parameters and weighting coefficients was performed to establish a correlation between the rate and the weighted minimum mean square error: , .

[0064] The value of the optimal equalizer can be obtained from the first-order optimality condition: , ; The optimal weight is: , .

[0065] question Rephrased as:

[0066] in, The weight vector for decoding the minimum mean square error of the public and private streams. Let be the equalizer vector. Since these two variables have been determined during the optimization process and their optimal solution has been obtained through relevant algorithms, given... After initializing the values, calculations can be performed directly.

[0067] Step S4: Alternating optimization solution Since the problem obtained from S3 is still highly non-convex and variable-coupled, this embodiment uses the alternating optimization method to transform the optimization problem into three sub-problems, which are solved by the weighted minimum mean square error method, the semidefinite relaxation method, and the successive convex approximation method, respectively, to obtain the optimal base station beamforming matrix, common rate allocation vector, and dual RIS passive beamforming matrix, thereby obtaining the resource allocation scheme with the maximum system and rate.

[0068] Subproblem S41: Optimizing the active beamforming matrix and common rate allocation vector

[0069] fixed To obtain information about the variables The optimization subproblem is transformed into a convex optimization problem by constructing a non-convex constraint surrogate function through a first-order Taylor expansion. The optimal solution is then obtained using the CVX toolbox. The details are as follows: when When fixed, the problem It can be converted to:

[0070] because , For convex constraints, there are only constraints. It remains a non-convex constraint. Regarding non-convex constraints... We construct a global lower bound approximation at the current iteration point using a first-order Taylor expansion, and replace the non-convex terms in the original constraint with this approximation, thus transforming the subproblem into a convex optimization problem. After the above transformation, the lower bound expression of the constraint is obtained as follows:

[0071] in, , , Represents the active beamforming matrix of the base station According to the column vectorization The Kronecker product is represented by vec(·), which denotes the vectorization operation. Indicates the first The solution after the next iteration.

[0072] At this point, the subproblem Converting it to a convex optimization problem allows for direct solution using the CVX toolbox.

[0073] In one variant of this embodiment, if the running speed of the CVX toolbox cannot meet the real-time requirements, convex optimization algorithms such as the primal-dual interior point method can be used to iteratively solve the subproblem in order to improve the iteration efficiency.

[0074] Subproblem S42: Optimization Passive beamforming matrix

[0075] fixed To obtain information about the variables The optimization problem is solved by approximating the non-convex quadratic form with a lower bound using a first-order Taylor expansion, and then employing a penalty function method to... The modulo-1 constraint is relaxed to a convex constraint, ultimately transforming the problem into a standard convex optimization problem, which is solved using the interior-point method. The details are as follows: Fixed base station active beamforming matrix Common flow rate allocation vector and Passive beamforming matrix This leads to the following subproblems.

[0076] Due to the subproblem The relevant constraints still contain non-convex quadratic terms. First, regarding the constraints... Perform convexity transformation. Using the matrix-vectorized identity, rewrite the matrix quadratic form in the constraints as a vector quadratic form: .in, This is a positive semi-definite matrix constructed from the transmitted beamforming vector. Indicates by and Unit dimension The matrix obtained by Kronecker product extension For the matrix Vectorization.

[0077] In the Next iteration point At this point, construct a global lower bound. Based on the first-order lower bound property of convex functions, we have...

[0078] in, Indicates the first During the next iteration The local point values.

[0079] because and reflection vector There exists an explicit functional relationship, which allows us to further rearrange the above lower bound as about The quadratic function form: .

[0080] definition Then the matrix with vector They represent about The coefficients of the quadratic term and the coefficients of the linear term are respectively: .

[0081] To further process this non-convex term, an equivalent transformation from complex variables to real variables is introduced.

[0082] Define the real extension vector and the corresponding real extension matrix as follows: , ;in, {·} indicates taking the real part.

[0083] Subsequently, at the current iteration point At this point, we again use the maximization and minimization methods to construct a first-order lower bound for this real quadratic form, and obtain: .

[0084] definition The above equation further transforms the linear expression of the response number field, constraining... The left side is arranged as follows: ;in, , , .

[0085] Therefore, the original constraint regarding The non-convex expression was successfully transformed into a linear approximation form.

[0086] Next, we will address the objective function and constraints. and ,Will and Organized into a list of things to do Quadratic terms:

[0087]

[0088] definition , , , , , Then we have:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] Finally, the objective function is transformed into a function about variables. concave function, constraint , Transform into convex constraints The transformed subproblem can be written as:

[0095] The problem at this time The main difficulty lies in the unit modulus constraint. The nonconvexity of .

[0096] Therefore, the penalty function method is used to relax the constraint, and the constraint is processed in combination with the penalty term strategy.

[0097] Assumption for The penalty factor corresponding to the unit modulus constraint is then Convert to:

[0098] This problem is a standard convex optimization problem, which can be solved using the interior-point method in the base station's DSP or FPGA. The solution is then performed. As the iterations proceed, the penalty factor is gradually increased. This forces the solution to approximate the unit modulus.

[0099] S43: Optimization Passive beamforming matrix

[0100] fixed To obtain information about the variables The optimization problem. Similar to S42, regarding... The non-convex part is expanded using a first-order Taylor series, and a penalty function is applied to the unit modulus constraint, transforming the non-convex problem into a standard convex optimization problem. Finally, the interior point method is used to solve it. Details are as follows: Constraints and constraints It can also be processed as about The quadratic term has

[0101]

[0102] definition and Then there is

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] Finally, the constraint on the unit modulus is relaxed, and the constraint is handled by combining a penalty term strategy. Assuming... for The penalty factor corresponding to the unit modulus constraint transforms the optimization problem into...

[0109] The final question The interior-point method can be used to solve this problem. The optimization of the two RIS systems is performed alternately until the internal iterations converge.

[0110] S5: Determine if the system and rate converge. After each outer iteration, calculate the current system users and rate. If the following conditions are met: If convergence is achieved, the base station beamforming matrix is ​​calculated and output. Common rate allocation vector , Passive beamforming matrix , Passive beamforming matrix Then it terminates.

[0111] At this time, the base station beamforming output module will output the currently optimized beamforming output. , , , The parameters are stored respectively in the base station's configuration register and the RIS controller's parameter memory, and then transmitted via the control link. , Issued to and The phase shift matrix is ​​then configured. Subsequently, the base station begins transmitting ISAC signals according to the optimized beamforming matrix to perform communication and sensing tasks.

[0112] If convergence is not achieved, proceed to S6.

[0113] S6: Iteration Count Determination If the system and rate do not converge, then determine the current iteration number. Is it greater than the maximum number of iterations? .

[0114] If the target has been reached, the iteration is terminated, and the beamforming matrix and RIS phase shift matrix obtained in the last iteration are output, configured in the same way as S5, and then the process is terminated.

[0115] If it is not achieved, then let = Then proceed to the next iteration and return to S41.

[0116] III. Simulation Verification and Effect Description To verify the effectiveness of the method of this invention, a Monte Carlo simulation was performed on the Matlab simulation platform in this embodiment. The application effect of this invention will be described in detail below with reference to the simulation.

[0117] 1. Simulation conditions Set the number of transmit antennas of the base station to The number of users in the system is set to ,set up The number of reflective elements and The number of reflective elements is Set the base station to ,Will and Position set and All users' locations are in a... Randomly generated within a circular region with a radius of 3 centered at a point, the target is located within a circle centered at a point... It is randomly generated within a circular region with a radius of 3.

[0118] The large-scale path loss model used in this invention is .in, The path loss is calculated when the relative distance is 1 meter. The distance is relative. This is the actual distance. Set the path loss coefficient. , .

[0119] Connecting base stations to users and The channel to the user is set as the Rayleigh channel, connecting the base station to two RIS. arrive The channel is set as a line-of-sight channel, connecting the base station to the target. To the target and The channel to the user is set to Rice channel. Based on the configured channel, the base station to user and base station to... Base station to Base station to target To users, To the target To users, arrive The path loss coefficients are respectively set as ,2.2,2.2,3,2.8,2.8,2.8,2.8,2.

[0120] Rice's fading model can be expressed as .in, Rice factor, This corresponds to the direct component of the channel. This refers to the non-direct component of the corresponding channel. The distance from the base station to the target... To the target and The Rice factors of the channels to the users are set to 1, 5, and 5 respectively, and the noise power of all users is... Noise power at the target location , No. Minimum speed requirement for each user Radar echo signal-to-noise ratio threshold Convergence threshold Maximum number of iterations .

[0121] 2. Simulation Results In this embodiment, Figure 2 The user and rate are given as a function of the base station's maximum transmit power. The changing performance curve.

[0122] from Figure 2 It can be seen that: The method of this invention consistently outperforms other comparative methods across the entire power range. In contrast, the performance improvement of the single RIS-assisted RSMA-ISAC method is relatively limited.

[0123] The method of this invention is superior to the Space Division Multiple Access (SDMA) method overall, demonstrating that the collaborative transmission mechanism of common and private flows can more effectively mitigate multi-user interference and improve the overall system rate. In contrast, Non-Orthogonal Multiple Access (NOMA) relies on a fixed serial interference cancellation decoding order, and its performance is significantly affected by user channel sequencing and power allocation strategies.

[0124] In dual RIS-assisted scenarios, although NOMA can improve spectral efficiency to some extent compared to traditional SDMA, its overall performance is still lower than that of the method of this invention, which verifies the advantages of the method of this invention in complex multi-user ISAC systems.

[0125] The simulation results above fully verify the effectiveness and superiority of the dual RIS-assisted RSMA-ISAC system and rate optimization method proposed in this invention.

[0126] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0127] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0128] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A dual RIS-assisted RSMA-ISAC system and a rate optimization method, characterized in that, Includes the following steps: S1: Initialize the parameters of a dual RIS-assisted RSMA-ISAC system; S2: Based on the constraints of the maximum transmit power of the base station, the radar echo signal-to-interference-plus-noise ratio, the phase shift constraint of the dual RIS, the minimum user rate requirement constraint, and the non-negativity constraint of the common rate, a resource optimization model is constructed with the goal of maximizing the number of system users and the rate. S3: The weighted minimum mean square error algorithm is used to construct the relationship between rate and weighted minimum mean square error. The objective function and constraints are transformed, and an equivalent relationship between rate and mean square error is established by introducing an equalizer and weight coefficients. S4: The optimization problem is transformed into three sub-problems using the alternating optimization method. The weighted minimum mean square error method and the penalty function method are used to solve them, and the optimal base station beamforming matrix, common rate allocation vector and dual RIS passive beamforming matrix are obtained, thus obtaining the resource allocation scheme with the maximum system and rate. S5: Determine if the system and rate have converged; if so, calculate and output the base station beamforming matrix. Common rate allocation vector The first RIS passive beamforming matrix The passive beamforming matrix of the second RIS Then terminate; otherwise, proceed to S6; S6: Determine if the current iteration count is greater than the maximum iteration count; If so, output base station beamforming matrix Common rate allocation vector The first RIS passive beamforming matrix The passive beamforming matrix of the second RIS Then terminate; otherwise, update the current iteration number. Then proceed to the next iteration and return to S41.

2. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 1, characterized in that, The system parameters described in S1 include at least the following: Number of transmit antennas of the base station Number of users The number of reflective elements in the first RIS The number of reflective elements in the second RIS Maximum transmission power of base stations , No. Minimum speed requirement for each user Radar echo signal-to-noise ratio threshold , No. noise power per user Noise power at the target location Convergence threshold and maximum number of iterations .

3. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 2, characterized in that, In S2, the system and the resource allocation scheme model with the highest speed are as follows: in, ； ， ； ； ； ； ； in, This represents the user's minimum rate requirement constraint. This indicates a common stream decodeable rate constraint. This indicates a non-negativity constraint for common rate allocation. This indicates the radar echo signal-to-noise ratio constraint. This indicates the maximum transmit power constraint for the base station. , These represent the unit mode phase shift constraints of the first RIS and the second RIS, respectively; Active beamforming matrix for base stations, It is the beamforming vector of the common flow. For the first Beamforming vectors for a user's private stream For the first Beamforming vectors for each user's private stream, where , Assign vectors to the common rates of users. , These are the passive beamforming matrices for the first RIS and the second RIS, respectively; For the first The achievable rate for each user For the first Minimum rate requirement for each user For the first The actual public rate for each user For the first The rate at which each user decodes the public stream. For the first The rate at which each user decodes a private stream; Echo signal-to-noise ratio; This is the radar echo signal-to-noise ratio threshold; This is the maximum transmission power of the base station. , The first RIS and the second The first reflection unit and the second RIS The reflection coefficient of each reflecting unit. For the first A vector of reflection coefficients of RIS, where ; From the base station to the Channel vectors for each user For base station to the Channels for individual users for To the Channels for individual users for To the Channels for individual users; , , From base station to channels, base stations to Channel, arrive The channel; This is a composite channel from the base station to the target. This refers to the channel from the base station to the sensing target. for The channel to the target being sensed. For the first Noise power per user.

4. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 3, characterized in that, In S3, the step of using the weighted least mean square error algorithm to construct the relationship between the rate and the weighted least mean square error specifically includes: For the For each user, a serial interference cancellation decoding method is used, that is, the common stream is decoded first, the common stream components are eliminated, and then the private stream is decoded. Specifically: Will Individual users on public flow and private stream The estimates are expressed as follows: 、 ； No. Common mean square error at each user and private mean square error They are represented as follows: 、 ； 、 ； The signal-to-interference-plus-noise ratios (SIRs) of the expected public and private streams are as follows: 、 ； No. The rate at which each user decodes the public and private streams is: 、 ； Introducing positive weighting coefficients and Applying these methods to the public and private flows respectively, construct the corresponding weighted mean square error functions: 、 ； The equalizer parameters and weighting coefficients are optimized to establish a correlation between the rate and the weighted minimum mean square error. 、 ； The value of the optimal equalizer is obtained from the first-order optimality condition: , Optimal weights: , ; The problem Rephrased as : in, , These represent equalizers for the public and private streams, respectively. Indicates the first Downlink signals received by each user Indicates public data flow, Indicates the first Private data streams for each user Indicates from the base station to the... Channel vectors for each user Indicates taking the real part, , Represented as the first The equivalent received power term for each user when decoding a public stream and decoding a private stream after eliminating the public stream; The weight vector for decoding the minimum mean square error of the public and private streams; This is the equalizer vector.

5. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 4, characterized in that, S4 specifically includes: S41: Fixed To obtain information about the variables The optimization subproblem is transformed into a convex optimization problem by constructing a non-convex constraint surrogate function through a first-order Taylor expansion. The optimal solution is then obtained using the CVX toolbox. ; S42: Fixed To obtain information about the variables The optimization subproblem is solved by approximating the nonconvex quadratic form with a lower bound using a first-order Taylor expansion, and by using the penalty function method to relax the unit modulus constraint of the first RIS to a convex constraint, thus transforming the nonconvex problem into a convex optimization problem. The optimal solution is obtained by using the interior point method. ; S43: Fixed To obtain information about the variables The optimization subproblem is solved by using the penalty function method to relax the unit modulus constraint of the second RIS to a convex constraint, thus transforming the non-convex problem into a convex optimization problem. The optimal solution is obtained by using the interior point method. .

6. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 5, characterized in that, In S41, the specific form of the first-order Taylor expansion is as follows: in, , , Represents the active beamforming matrix of the base station According to the column vectorization The Kronecker product is represented by vec(·), which denotes the vectorization operation. Indicates the first The solution after the next iteration.

7. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 5, characterized in that, The penalty function method is as follows: Add a penalty term to the objective function ,in, This is the penalty factor corresponding to the RIS unit modulus constraint. Let i be the current solution in the i-th iteration; apply the unit modulus constraint. Relaxation is a convex constraint and through Gradually increasing the value forces the solution to approximate the unit modulus.

8. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 3, characterized in that, In S5, the condition for determining whether the system and rate converge is: in, This is the preset convergence threshold.

9. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 1, characterized in that, The dual RIS includes a first RIS and a second RIS, wherein the first RIS is deployed near the base station and serves both communication and sensing. The second RIS is deployed at the cell edge or in areas with signal obstruction to enhance the channel gain between the base station and the user; and, in the perception modeling, only the perception channels related to the first RIS are retained, while the reflection path between the second RIS and the target is ignored.

10. The dual RIS-assisted RSMA-ISAC system and rate optimization method according to claim 1, characterized in that, The solution process formed by the weighted minimum mean square error algorithm, the alternating optimization method, the first-order Taylor expansion and the penalty function method executes steps S41, S42 and S43 in sequence in each outer iteration, and the order of steps S42 and S43 can be interchanged or executed in parallel.

Images