A sum rate optimization method for a STAR-RIS assisted rate-splitting multiple access system

Abstract

The present application relates to a kind of STAR-RIS assisted rate division multiple access system and rate optimization method, belong to wireless communication technical field.The present application is by the method of joint beam forming and rate allocation optimization, to improve the communication performance of simultaneously transmissive and reflective intelligent reconfigurable surface (STAR-RIS) assisted downlink rate division multiple access (RSMA) system, provides effective technical reference for improving the communication performance of wireless communication system.The present application constructs the optimization problem of maximum sum rate, and optimization parameter is beam forming vector, rate allocation vector and STAR-RIS transmission and reflection beam forming matrix, then use block coordinate descent method (BCD) The optimization problem is decomposed into two subproblems, wherein the beam forming vector, rate allocation vector are optimized using successive convex approximation (SCA), and STAR-RIS transmission and reflection beam forming matrix is optimized based on fractional programming (FP) and quadratic constraint quadratic programming (QCQP) method, finally, sum rate maximization under the condition of active power is realized by alternating iteration.

Description

TECHNICAL FIELD

[0001] The application relates to a sum-rate optimization method for a STAR-RIS assisted rate-splitting multiple access system and belongs to the technical field of wireless communication. BACKGROUND

[0002] In recent years, Reconfigurable Intelligent Surfaces (RISs), also known as Intelligent Reflecting Surfaces (IRSs), have been widely recognized as a promising solution to improve network coverage and data rates to meet the demand for ubiquitous wireless connectivity. RIS is based on a planar array of metamaterials, containing multiple passive reflecting elements, each of which can be independently adjusted in phase shift and amplitude by an intelligent controller, thereby precisely manipulating the propagation path of the incident signal. As a planar metasurface with a large number of reconfigurable passive elements, RIS has shown broad prospects for development. By adjusting the phase and amplitude of each element, RIS can effectively improve the propagation of incident signals and create a favorable transmission environment. However, traditional RIS can only reflect signals, so it can only serve users within the 180° half-plane on the same side of the RIS. To overcome this limitation, a new type of RIS, called simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS), is proposed. This new type of RIS can simultaneously transmit and reflect incident signals to users on both sides of the RIS. Therefore, compared with traditional RIS which can only reflect signals, STAR-RIS not only achieves full spatial coverage, but also introduces new degrees-of-freedom (DoF), thereby improving the overall system performance.

[0003] With the rapid development of advanced multimedia applications such as virtual reality, the next generation of wireless networks needs to have high spectral efficiency and large-scale connectivity. Non-orthogonal multiple access (NOMA) can provide services to multiple users simultaneously on the same frequency or time resources by grouping users in the power domain, thereby achieving higher spectral efficiency than traditional orthogonal multiple access (OMA). In NOMA systems, users need to decode all interfering signals when receiving information, which significantly increases the computational complexity of signal processing. To solve this problem, the concept of rate-splitting multiple access (RSMA) is proposed. The core idea of RSMA is to divide the message transmitted to users into common messages and private messages. Common messages are decoded by multiple users, while private messages are only received by specific users. When decoding common messages, users first need to process the interference of other users; while decoding private messages, the private message interference of other users is treated as noise. By adjusting the division ratio between common messages and private messages, the balance between computational complexity and data transmission rate can be achieved in RSMA. However, in the wireless network environment, the practical application of RSMA faces multiple challenges, including the reasonable division of common and private messages, the efficient management of private message transmission resources, and the guarantee of message synchronization during transmission.

[0004] The deployment of STAR-RIS has great potential in enhancing channel strength and achieving full spatial coverage, especially in cases where the link quality between the base station and the user is poor. By adopting RSMA, multiple users can be served simultaneously and interference can be managed flexibly by splitting messages into multiple sub-messages, resulting in higher spectral efficiency and system capacity compared to traditional multiple access schemes. The combination of STAR-RIS and RSMA presents a new paradigm for wireless communication architecture, effectively combining the advantages of both to improve system performance in Internet of Everything (IoE) networks. On the one hand, the deployment of large-scale STAR-RIS elements brings passive array gain, reducing the need for a large number of antenna arrays in RSMA systems. On the other hand, the optimal amplitude and phase shift design of STAR-RIS effectively reduces the impact of channel randomness and simplifies the complex design of the Successive Interference Cancellation (SIC) receiver in RSMA systems.

[0005] In summary, although the above research has made some progress in the combination of STAR-RIS and RSMA, most of the analysis is only for specific scenarios or conditions, and the existing research still lacks consideration of resource allocation, power control, and channel randomness. SUMMARY

[0006] The purpose of the present application is to provide a sum-rate optimization method for a STAR-RIS-assisted rate-splitting multiple access system, aiming to solve the technical problem that existing research mostly only analyzes specific scenarios or conditions, and lacks consideration of resource allocation, power control, and channel randomness.

[0007] To achieve the above purpose, the technical solution of the present application is as follows: a sum-rate optimization method for a STAR-RIS-assisted rate-splitting multiple access system, the specific steps are as follows:

[0008] Step 1: Establish a STAR-RIS-assisted RSMA downlink communication system model;

[0009] Step 2: According to the established communication system model, taking the base station beamforming matrix, STAR-RIS phase shift matrix, and rate allocation vector as the optimization problem, determine the target of maximizing the sum rate, and construct the problem statement of the optimization objective;

[0010] Step 3: Given the STAR-RIS phase shift matrix, optimize the base station transmit beamforming matrix and rate allocation vector;

[0011] Step 4: Given the base station transmit beamforming matrix and rate allocation vector, optimize the STAR-RIS phase shift matrix;

[0012] Step 5: Jointly optimize the base station transmit beamforming matrix, rate allocation vector, and STAR-RIS phase shift matrix to maximize the system sum rate.

[0013] The Step 1 is specifically as follows:

[0014] Step 1.1: The communication system consists of a base station, a STAR-RIS, and users, assuming that the base station BS consists of N t uniform linearly arranged antennas, the STAR-RIS consists of M passive element units arranged uniformly in a plane, and there are N users with single-root antennas;

[0015] Step 1.2: All channels in the communication system use the Ricean fading channel model, assuming that the channel gain from BS to STAR-RIS is represented as the channel gain from STAR-RIS to users is represented as

[0016]

[0017] where ω B-S and are the RIS factors of BS-STAR-RIS link and STAR-RIS-user link, G LoS and r i LoS denote the line-of-sight component of Rayleigh distribution, G NLoS and r i NLoS denote the non-line-of-sight component;

[0018] Step 1.3: Assuming that the BS, STAR-RIS and users can all obtain ideal channel state information, and the BS antenna adopts a uniform linear array, STAR-RIS uses an energy splitting protocol to divide the coverage area into transmission and reflection zones, and the transmission and reflection coefficients are and According to the principle of energy conservation, it satisfies The refraction and reflection coefficient matrices are:

[0019]

[0020] denotes whether the user is a transmission zone user or a reflection zone user;

[0021] Based on the basic idea of RSMA, the signal sent by the BS is:

[0022]

[0023] where s0denotes the public message, denotes the private message for each user;

[0024] The basic idea of RSMA is to divide the message sent to the m i th user into two parts: the public part and the private part. The public part of all users is combined and encoded into a single public message s0using a standard codebook, on the other hand, each private part is encoded as a private message

[0025] Step 1.4: Since there is no link between the BS and the user, when the BS sends a signal to the user, it is transmitted to the user through STAR-RIS transmission or reflection, and the received signal y i for the m i th user is:

[0026]

[0027] where the large-scale path loss between the BS and the m i th user is denoted as a represents the path loss component, d B-S and respectively represent the distance between the BS and the STAR-RIS and the distance between the STAR-RIS and the m i th user, H represents the transpose of the matrix, n i ~ CN(0, σ 2 ) represents the additive white Gaussian noise for the m i th user, Θ i,p is the refraction and reflection coefficient matrix for the m i th user;

[0028] The signal-to-interference-plus-noise ratio (SINR) of the common signal and the private signal at the m i th user are respectively:

[0029]

[0030] Step 1.5: The achievable rate (bps / Hz) of the decoded common stream and the intended private stream for the m i th user are respectively:

[0031] c i = log2(1+ γ c,i )

[0032]

[0033] To ensure that all users successfully decode the common message, the rate of the common message is selected as min i∈N c i and the rate a i assigned to the m i th user, the constraint of the data rate of the received common message for each user is:

[0034]

[0035] The transmit power of each user satisfies the constraint of implementing SIC operation at the receiving end:

[0036]

[0037] where θ is the minimum difference between the power of the decoded signal and the power of the interference signal between the users that have not been decoded plus the noise power, the sum rate of the system is the sum of the common rate and the achievable private stream rate, which is expressed as:

[0038]

[0039] where R i is the sum rate of the system.

[0040] The Step2 is specifically:

[0041] To jointly optimize the beamforming matrix w at the BS, the STAR-RIS phase shift matrix Θ i,p and the rate allocation vector in the system network, the system sum rate is maximized, and thus the optimization problem of the following formula is constructed:

[0042]

[0043] Wherein, R min represents the minimum rate required by all users, w = [w0; w1;...; w N ] represents the beamforming matrix at the BS, a = [a1, a2,..., a N ] T represents the rate allocation vector constraint; C1 represents the minimum rate limit of all users, C2 ensures that each user can decode the common information, C3 represents the SIC power constraint, P is the maximum transmit power of the base station, C4 represents the maximum transmit power constraint of the BS, C5 and C6 represent the refractive and reflective power constraints of the STAR-RIS, and C7 represents the constraint of the data rate of each user receiving the common message.

[0044] The Step3 is specifically:

[0045] Given the phase shift matrix Θ i,p of the active STAR-RIS, the base station transmit beamforming matrix w and the rate allocation vector a are optimized, the non-convex constraint is processed by the SCA method, and the optimization problem is simplified as follows:

[0046]

[0047] Introducing the slack variables ψ i and η i , the optimization problem is reconstructed as:

[0048]

[0049] s.t.C8:α i +log2(1+ψ i )≥R i

[0050]

[0051] C3, C4, C7

[0052] Wherein, ψ = [ψ1, ψ2,..., ψ N ] and η = [η1, η2,..., η N], the objective function of the equivalent problem is convex, and the equations C10, C11 and C3 make the whole problem non-convex, so new non-negative relaxation variables a are introduced i The equation C10 is re-expressed as:

[0053]

[0054] In the equation By replacing the real number after any rotation of the phase-shift beam-forming w i , so the constraint can be equivalent to Where represents the real part of the complex number The convex function is replaced by the first-order Taylor series The equation is re-expressed as:

[0055]

[0056] Where the superscript (n-1) represents the value of the variable at the (n-1) th iteration, and the variable a is introduced The equation C11 is re-expressed as:

[0057]

[0058] The non-convexity in the equation is approximated by the difference of two convex functions DC, and the equation is approximated as:

[0059]

[0060] The left side is the first-order Taylor series of By using the DC approximation, C3 is re-expressed as:

[0061]

[0062] The non-convex problem is transformed into:

[0063]

[0064] s.t.C4, C7, C8, C9, C12-C16

[0065]

[0066] Thus, the optimization problem belongs to a convex problem, and the CVX tool package in Matlab is used to solve the problem.

[0067] The Step4 is specifically:

[0068] Step4.1: Given the base station beam-forming vector w and the rate allocation vector a, optimize Θ i,p, the objective function is processed by using the FP change, and the problem is converted into a standard QCQP quadratic constraint quadratic programming problem, that is, φ m represents the reflection or transmission coefficient of the mth unit of STAR-RIS, defined as a complex number, and φ represents the reflection or transmission coefficient vector of all units of STAR-RIS, and auxiliary variables By using Lagrange dual transformation, the objective function in the formula is equivalent to:

[0069]

[0070] The first term measures the logarithmic utility of channel capacity, and the second term is the ratio of channel gain and noise, that is, The optimal solution of the elements in τ is:

[0071]

[0072] The formula is re-expressed as:

[0073]

[0074] s.t.C1, C2, C5, C6

[0075] f2(φ,τ,υ) represents the objective function after optimization and adjustment of the Lagrange relaxation variable;

[0076] Step4.2: Simplify the above problem, since the above formula is non-convex, introduce A 1,c , A 1,p , B 1,p and B 1,c auxiliary variables:

[0077]

[0078] According to the above formula, the and in SINR are equivalent to:

[0079]

[0080] Let:

[0081]

[0082] A 2,p =A 1,p +C,

[0083]

[0084] B 2,p =B 1,p +D

[0085] The denominator of SINR is equivalent to:

[0086]

[0087] Step 4.3: Define Then the constraint conditions C1 and C2 are transformed into:

[0088]

[0089] After the above transformation, the optimization problem is transformed into:

[0090]

[0091] s.t.(34), (35), C5, C6

[0092] Where:

[0093]

[0094] Step 4.4: The optimal solution of υ and τ can be obtained by the above, and the best transmission and reflection coefficient matrix is obtained using the CVX toolbox.

[0095] The Step 5 is specifically:

[0096] Step 5.1: Initialize noise, path loss parameters, simulated channel information, coordinates of base station, STAR-RIS, user, iteration number T, maximum iteration number K, and set convergence precision ε;

[0097] Step 5.2: Obtain the optimal solution of rate and, base station transmit beamforming matrix and STAR-RIS phase shift matrix by solving w (t) , Θ (t) ;

[0098] Step 5.3: Until Stop iteration.

[0099] The beneficial effects of the present application are that compared with the traditional RIS assisted RSMA scheme and the STAR-RIS assisted NOMA scheme, the present application can significantly improve the communication performance of the system, and provides an effective technical reference for improving the communication performance of the wireless communication system. BRIEF DESCRIPTION OF DRAWINGS

[0100] Figure 1 is a STAR-RIS assisted RSMA communication system model diagram constructed by the present application;

[0101] Figure 2 is a diagram showing the change of the present application and the rate with the iteration number;

[0102] Figure 3 This is a graph showing how the sum rate of each scheme in this invention changes with the number of STAR-RIS components;

[0103] Figure 4 This is a graph showing how the sum rate of each scheme in this invention changes with the total power of the system;

[0104] Figure 5 This is a graph showing how the sum rate of each scheme of the present invention changes with the number of antennas. Detailed Implementation

[0105] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0106] Example 1: As Figure 1 As shown, a STAR-RIS-assisted RSMA communication system model is constructed, considering a downlink multiple-input single-output (MISO) communication system model. This system consists of a base station, a STAR-RIS, and multiple users. It is assumed that the base station (BS) consists of N... t The STAR-RIS system consists of M uniformly linearly arranged antennas, with each user having a single antenna. A method for rate optimization in a STAR-RIS-assisted rate division multiple access system is described, with the following steps:

[0107] Step 1: Establish a STAR-RIS-assisted RSMA downlink communication system model;

[0108] Step 2: Based on the established communication system model, taking the base station beamforming matrix, STAR-RIS phase shift matrix, and rate allocation vector as optimization problems, determine the goal of maximizing sum and rate, and construct the problem statement of optimization objective;

[0109] Step 3: Given the STAR-RIS phase shift matrix, optimize the base station transmit beamforming matrix and rate allocation vector;

[0110] Step 4: Given the base station transmit beamforming matrix and rate allocation vector, optimize the STAR-RIS phase shift matrix;

[0111] Step 5: Combine the optimized base station transmit beamforming matrix, rate allocation vector, and STAR-RIS phase shift matrix to maximize system performance and rate.

[0112] Specifically, all channels in the communication system adopt the Ricean fading channel model, assuming the channel gain from BS to STAR-RIS is expressed as... The channel gain from STAR-RIS to the user is expressed as...

[0113]

[0114] where ω B-S and are the Rician K-factor of BS-STAR-RIS link and STAR-RIS-user link, G LoS and r i LoS denote the Rician K-factor of the line-of-sight component, G NLoS and r i NLoS denote the non-line-of-sight component.

[0115] Assume that the BS, STAR-RIS and users can obtain the ideal channel state information, and the BS antenna adopts a uniform linear array, STAR-RIS uses an energy partition protocol to divide the coverage area into a transmission area and a reflection area, and the transmission and reflection coefficients are and According to the principle of energy conservation, it satisfies The refraction and reflection coefficient matrices are:

[0116]

[0117] denote whether the user is a transmission area user (t) or a reflection area user (r). The signal sent by the BS is

[0118]

[0119] where s0 denotes a public message, denotes a private message for each user.

[0120] In the simulation system scenario, the distance from the base station to the STAR-RIS is set to 100 m, and the distance from the user to the STAR-RIS is set to 50 m. The number of base station antennas N = 5, the user is a single antenna, and the number of STAR-RIS elements is 8. The noise power is set to 90 dBm, and the convergence accuracy ε = 10 -3 .

[0121] In order to verify the performance difference of STAR-RIS assisted RSMA under different conditions, the number of BS antennas is fixed at 2, the number of STAR-RIS elements and the total power of BS are changed, and the results are shown in Figure 2 It can be seen from Figure 2 that with the increase of the number of elements and the power, the algorithm can converge within the 8th iteration, which has good convergence performance. At the same time, it can also be observed that in this algorithm, the convergence speed of the curve when the number of STAR-RIS elements is 8 and the power is 30 dBm is not as fast as when the number of STAR-RIS elements is 4. When the number of elements is small, the convergence rate is faster than when the number of elements is large.

[0122] From the channel of BS-STAR-RIS-user, it can be seen that as the number of STAR-RIS elements increases, the number of phase adjustment schemes that can be selected also increases. In order to illustrate the influence of the transmission and reflection coefficient matrix on the channel gain, assuming that the base station transmit power is 20 dBm, the sum rate of different schemes under different element numbers is compared, and the results are shown in Figure 3 It can be seen that with the increase of the number of elements, the sum rate of various schemes shows an upward trend. Specifically, when the number of STAR-RIS elements increases from 4 to 64, the total rate of the STAR-RIS assisted RSMA system increases from 5.4 bps / Hz to 11.4 bps / Hz, an increase of 111%. In addition, compared with OMA and NOMA, the combination of STAR-RIS and RSMA system has higher total sum rate gain, and when the number of STAR-RIS elements is small, it is still 32% higher than the total rate of NOMA, and much higher than OMA. When the number of STAR-RIS elements is large, it is 28% higher than NOMA.

[0123] In order to show the power gain effect of the proposed method, the sum rate performance of each scheme under different base station transmit powers is compared, and the results are shown in Figure 4 It can be seen from Figure 4 that with the increase of transmit power, the sum rate of each scheme increases, and compared with the NOMA system, the RSMA system can significantly improve the sum rate. It can be observed that with the increase of total power, compared with the traditional RIS, the total rate of STAR-RIS is increased to 37.3%. This is because RSMA can enhance the channel capacity by decoding part of the multi-user interference and regarding the rest of the interference as noise.

[0124] From Figure 5As can be seen, the spectral efficiency of different schemes also increases with the increase of the number of antennas. Specifically, the gain of the STAR-RIS-RSMA scheme is the most significant, and when the number of antennas increases from 4 to 16, its spectral efficiency increases from about 8 bps / Hz to 12 bps / Hz. The gains of the STAR-RIS-NOMA and traditional RIS-RSMA schemes also increase with the increase of the number of antennas, but are not as significant as STAR-RIS-RSMA. In contrast, the gain of the traditional RIS-NOMA is the smallest. As can be seen, the application of RSMA in STAR-RIS significantly improves the spectral efficiency of the system, which is mainly due to its effective interference management and flexible message splitting mechanism. RSMA divides the transmission message into common and private messages, enabling users to better handle interference and improve transmission efficiency, rather than simply relying on the beamforming gain brought by the increase in the number of antennas. Compared with other schemes, STAR-RIS-RSMA takes advantage of RSMA and can flexibly manage interference when multiple users share resources, thereby achieving greater spectral efficiency gain.

[0125] The specific embodiments of the present application are described in detail above with reference to the accompanying drawings, but the present application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present application.

Claims

1. A sum rate optimization method for a STAR-RIS assisted rate splitting multiple access system, characterized in that: Step 1: establishing a STAR-RIS assisted RSMA downlink communication system model; Step 2: according to the established communication system model, taking the base station beam forming matrix, the STAR-RIS phase shift matrix and the rate allocation vector as the optimization problem, determining the target of maximizing the sum rate, and constructing the problem statement of the optimization target; Step 3: given the STAR-RIS phase shift matrix, optimizing the base station transmit beam forming matrix and the rate allocation vector; Step 4: given the base station transmit beam forming matrix and the rate allocation vector, optimizing the STAR-RIS phase shift matrix; Step 5: jointly optimizing the base station transmit beam forming matrix, the rate allocation vector and the STAR-RIS phase shift matrix to maximize the system sum rate; The Step 1 is specifically: Step1.1: The communication system consists of a base station, a STAR-RIS and a user, assuming that the base station BS consists of a uniform linear array of antennas, the STAR-RIS consists of a uniform planar array of P passive element units, and there are users with a single antenna; Step 1.2: All channels in the communication system adopt the Rician fading channel model, and the channel gain from the BS to the STAR-RIS is denoted as , and the channel gain from the BS to the STAR-RIS is denoted as : ； wherein and are the Rician factors of the BS-STAR-RIS link and the STAR-RIS-User link, respectively, and denote the Rician line-of-sight components of the BS-to-STAR-RIS and STAR-RIS-to-User links, respectively, and denote the Rician non-line-of-sight components of the BS-to-STAR-RIS and STAR-RIS-to-User links, respectively. Step 1.3: Assuming that the BS, STAR-RIS, and user can all obtain ideal channel state information, and the BS antenna adopts a uniform linear array, the STAR-RIS uses an energy splitting protocol to divide the coverage area into a transmission area and a reflection area, and the transmission and reflection coefficients are and , according to the principle of energy conservation, it satisfies , and the refraction and reflection coefficient matrices are: ； ； indicates whether the user is a transmission area user or a reflection area user; Based on the basic idea of RSMA, the signal transmitted by the BS is: ； wherein represents a public message, represents a private message for each user; Step 1.4: When the BS sends signals to users, the signals are transmitted to users by STAR-RIS transmission or reflection, and the received signals for the first user are ​ ； Among them, BS and the Large-scale path loss between users is represented as , Represents the path loss component. and Represent the distance between BS and STAR-RIS and the distance between STAR-RIS and the first... The distance between users, where H represents the transpose of the matrix. Represented as the first Additive white Gaussian noise for each user For the first The user's refraction and reflection coefficient matrix; User The signal-to-interference-and-noise ratio of the public signal and the private signal at the user are respectively: ； 。 2. The sum-rate optimization method for STAR-RIS aided rate-splitting multiple access systems according to claim 1, wherein After the Step 1.4, it further includes: Step 1.5: User The achievable rates for the decoded common stream and the intended private stream are denoted as: ； The rate selection for the common message is , the given common message and the rate assigned to the user , the constraint on the data rate at which each user receives the common message is: ； At the receiving end, SIC operation is realized, and the constraint of the transmission power of each user is: ； wherein is the minimum difference between the decoded signal power and the un-decoded inter-user interference signal power plus the noise power, the sum rate of the system is the sum of the common rate and the achievable private stream rates, denoted as: ； wherein is the system and rate.

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