A method for sum-rate optimization in a MA-assisted RSMA-RIS system

Abstract

This invention discloses a method for optimizing the neutral rate in an MA-assisted RSMA-RIS system. The method first presents an algorithm for updating the position of the movable antenna (MA), and then provides an algorithm for obtaining the optimal system neutral rate based on AO iteration. This invention can solve the problems of precoding design, antenna position, RIS reflection matrix design, and common rate partitioning scheme design in MA-assisted multi-user downlink RSMA-RIS systems. It obtains the optimal solution for the system neutral rate through iteration and can quickly converge to the optimal solution.

Description

Technical Field

[0001] This invention belongs to the field of network technology in mobile communication systems, and particularly relates to a method for neutral rate optimization in an MA-assisted RSMA-RIS system. Background Technology

[0002] Because movable antenna (MA) technology allows base station antennas to move freely in one-dimensional, two-dimensional, and three-dimensional space under certain constraints, it makes fuller use of spatial degrees of freedom, improves spatial resolution, and can more effectively adapt to the current wireless environment, thereby improving the system's communication performance. Currently, no literature studies the performance of MA-assisted RSMA-RIS systems. Therefore, this invention constructs a corresponding optimization problem for this scheme and proposes a low-complexity AO algorithm to solve this problem. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to address the shortcomings of existing technologies by providing a MA-assisted method for optimizing the neutral rate in an RSMA-RIS system. This method utilizes fractional programming (FP) to perform an equivalent transformation on the original problem, and while fixing some variables, optimizes the precoding matrix, common rate segmentation, reflection matrix, and antenna position separately. It has low complexity and can converge to the optimal value in a short time.

[0004] Technical solution: To achieve the above-mentioned objective, this invention provides a method for neutralization rate optimization in an MA-assisted RSMA-RIS system, comprising the following steps:

[0005] Step 1: An iterative algorithm based on Alternating Optimization (AO) is proposed to maximize the system's communication and rate. Specifically, when optimizing the precoding matrix, common rate segmentation, antenna position, and various auxiliary variables, other variables are fixed, and update schemes are given for each. This invention presents a low-complexity AO iterative algorithm that can quickly obtain the maximum sum and rate.

[0006] Step 2: This invention provides a scheme for updating the MA position as described in Step 1. Based on limitations on the movement range of each antenna and the spacing between antennas, the gradient ascent algorithm is used to update the antenna positions, maximizing the system and speed.

[0007] Step one includes:

[0008] This invention considers a downlink multi-user communication system, where the base station is equipped with M antennas, each of which can move within a region D. The base station simultaneously communicates with K far-field users, and the antennas and user sets are respectively... and Meanwhile, a reconfigurable smart surface (RIS) is placed away from the base station. The RIS contains N reflecting elements, each capable of independently adjusting the phase of the incident signal. There are two paths from the base station to the user: a direct path from the base station to the user, and a reflected path from the base station to the RIS to the user. Assume... H is the direct channel vector from the base station to the user; b，r =B H ΣA∈C N×M Let B be the equivalent channel matrix of the base station-RIS, where B is the received field response matrix of the RIS, ∑ is the channel fading matrix of the base station-RIS, and A is the transmitted field response matrix of the RIS. This is the channel vector from RIS to user k. Therefore, the equivalent channel vector from the base station to user k is...

[0009] Consider a single-layer RSMA system, where each user's information is divided into private and public information. Assume that each user's private information is encoded as {s1, s2, ..., s}. K All users' public information is merged and encoded into s. c Therefore, the transmitted symbols of all users can be defined as vectors s = {s1, s2, ..., s}. K s c Each information flow satisfies and Each information stream corresponds to a beam vector, therefore the beam matrix is ​​defined as W = [w1, ..., w2]. K w c Therefore, the received signal of the k-th user is: Where n k Let the noise at the k-th user have the power of: The signal-to-interference-plus-noise ratio (SIR) of the public information flow at user k is Similarly, the signal-to-interference-plus-noise ratio (SIR) of the private information stream at user k is Their corresponding public and private rates are R respectively. c,k =log(1+SINR) c,k ) and R k =log(1+SINR) k ).

[0010] First, the optimization problem corresponding to this system (P1) is given:

[0011]

[0012] sttr(WW H )≤P T ,

[0013]

[0014] X min ≤x≤X max

[0015]

[0016] Where P T X is the maximum transmit power of the base station. min and X max These are the lower and upper bounds for antenna movement, respectively, and D0 is the minimum spacing between antennas.

[0017] This invention proposes an optimization algorithm based on a transformation of the FP method. Therefore, the equivalent optimization problem (P2) after the FP transformation is given:

[0018]

[0019] sttr(WW H )≤P T ,

[0020] T k (μ, v, W, Φ, x) ≥ r c，k

[0021]

[0022] X min ≤x i ≤X max

[0023]

[0024] in Omitting the initialization and variable swapping steps, the specific steps to solve this equivalent problem are as follows:

[0025] The first step is to utilize Where w i It is the i-th column of matrix W. Update FP parameters.

[0026] The second step is to use expressions. Update λ k ,use Update λ w subscript Using κ [r+1] =(tr(WW) H )+1) / (P T +1) Update κ, where P TThis is the maximum transmission power of the base station.

[0027] The third step is to utilize Update the last column of matrix W, using Update the first K columns of W.

[0028] The fourth step is to first present the equivalent optimization problem when fixing other variables and optimizing the common rate partition separately, as follows:

[0029]

[0030] r c，k ≥0

[0031] Combining the shared rate constraint and the form of the objective function, the shared rate for all users is first calculated. Then use r c，k =min k R c，k , Update the public rate segment.

[0032] Step 5, given M1, M2, M3, M 1，i N 2，i N 3，i First, the equivalent optimization problem of optimizing the RIS reflection matrix separately is given below (P2.2):

[0033]

[0034] st|φ i | 2 =1,

[0035]

[0036] in,

[0037] Combining the dual problem and the SCA algorithm, using φ [r+1] =e jh Update the reflection vector φ, using Update ξ, where τ is the step size.

[0038]

[0039] in, 1 represents a single-column A vector, which is the transmit field response matrix from the base station to the RIS.

[0040] Step 6: First, we present the optimization problem corresponding to updating the antenna position (P2.3):

[0041]

[0042] X min ≤x i ≤X max

[0043]

[0044] The specific steps to solve this problem are as follows:

[0045] (1) Initialization Where x [r] It is the position vector formed by the positions of all antennas, where M is the total number of base station antennas. This is the feasible region of problem (P2.3); the step size α is set to 1; r is the current iteration number; the maximum number of iterations is r. max .

[0046] (2)Use Update the antenna position, where the subscript m represents the m-th antenna. If Then the reduction step size is 0.5α; otherwise, r = r + 1.

[0047] (3) If r < r max If yes, then return to (2); otherwise, output x. [r+1] .

[0048] Beneficial effects: Compared with the prior art, this invention solves the sum rate problem of RSMA-RIS system under downlink multi-user MA assistance, and proposes an efficient AO iterative algorithm based on FP deformation. It has been verified that this algorithm has low complexity and accurate results.

[0049] Specifically:

[0050] 1. This invention solves for the first time the joint optimization problem of MA-assisted RSMA-RIS system. In the prior art, MA, RIS and RSMA techniques are mostly studied independently, and no literature has yet addressed the synergistic optimization of the three. This invention is the first to construct the sum-rate maximization problem of this complex system and provides a complete solution, filling a technological gap.

[0051] 2. To address the difficulty of directly solving the original non-convex optimization problem (P1), this invention innovatively employs fractional programming to transform it into a more manageable form (P2), and designs an iterative algorithm based on alternating optimization. This algorithm decomposes the complex problem into a series of solvable subproblems by fixing other variables and iteratively optimizing the precoding matrix, common rate segmentation, RIS reflection matrix, and antenna position, significantly reducing computational complexity.

[0052] 3. By jointly optimizing antenna position, precoding, RIS phase shift, and rate splitting, this invention fully utilizes the spatial degrees of freedom provided by MA, the active channel control capability of RIS, and the interference management advantages of RSMA, resulting in a synergistic enhancement effect. Simulation results show that this scheme can effectively maximize system performance and rate, outperforming traditional fixed antenna or non-RSMA schemes.

[0053] 4. The alternating optimization algorithm proposed in this invention has a clear structure, and each update step has a closed-form solution or an efficient solution method (such as gradient ascent), which ensures that the entire iterative process can quickly converge to the optimal solution or a high-quality suboptimal solution, thus meeting the real-time requirements of practical communication systems. Attached Figure Description

[0054] Figure 1 This is a network structure diagram of an RSMA-RIS system with downlink multi-user MA assistance. Detailed Implementation

[0055] The technical solution of the present invention will be described in detail below, but the scope of protection of the present invention is not limited to the embodiments described.

[0056] This invention proposes a sum rate optimization method for RSMA-RIS systems with downlink multi-user MA assistance.

[0057] The following is an example:

[0058] This embodiment considers a downlink multi-user MA-assisted RSMA-RIS communication system. A single base station at (0m, 0m) simultaneously communicates with K far-field users, each distributed within an area of ​​[20m, 40m] × [0m, -20m]. The base station is equipped with M movable antennas, which can move freely within the area of ​​[-6λ, 6λ], and the spacing between adjacent antennas must be no less than D0 = 0.5λ. In addition, a reconfigurable smart surface with N reflective elements is placed at (12m, 16m). The carrier frequency for communication is f = 2.4GHz, corresponding to a wavelength of λ = c / f = 0.125m. The maximum transmit power P of the base station... T =30dBm, user noise power In addition, the number of transmit paths and the number of receive paths L t =L r =4, and the elevation angle of each signal propagation path is uniformly distributed within [0,π].

[0059] The method includes the following steps:

[0060] Step 1: First, an optimization iterative algorithm based on AO is presented to maximize the system's communication and speed. Specifically, the precoding matrix, common rate segmentation, antenna position, and other auxiliary variables are optimized separately while keeping other variables fixed, and update schemes are given for each. This algorithm alternately optimizes the following variables: precoding matrix W, common rate segmentation {r c,k The system calculates the RIS reflection matrix Φ and the antenna position x until the system and rate converge.

[0061] Step 2: This invention provides a scheme for updating the MA position as in (1). Based on limiting the movement range of each antenna and the spacing between antennas, the gradient ascent algorithm is used to update the antenna position to maximize the system and speed.

[0062] Step one includes:

[0063] Consider a downlink multi-user communication system. The base station is equipped with M antennas, each of which can move within a region D. The base station simultaneously communicates with K far-field users. The antennas and the user set are respectively... and Meanwhile, a reconfigurable smart surface (RIS) is placed away from the base station. The RIS contains N reflecting elements, each capable of independently adjusting the phase of the incident signal. There are two paths from the base station to the user: a direct path from the base station to the user, and a reflected path from the base station to the RIS to the user. Assume... H is the direct channel vector from the base station to the user; b，r =B H ∑A∈C N×M Let B be the equivalent channel matrix of the base station-RIS, where B is the received field response matrix of the RIS, ∑ is the channel fading matrix of the base station-RIS, and A is the transmitted field response matrix of the RIS. This is the channel vector from RIS to user k. Therefore, the equivalent channel vector from the base station to user k is...

[0064] Consider a single-layer RSMA system, where each user's information is divided into private and public information. Assume that each user's private information is encoded as {s1, s2, ..., s}. K All users' public information is merged and encoded into s. c Therefore, the transmitted symbols of all users can be defined as vectors s = {s1, s2, ..., s}. K s c Each information flow satisfies and Each information stream corresponds to a beam vector, therefore the beam matrix is ​​defined as W = [w1, ..., w2]. K wc Therefore, the received signal of the k-th user is: Where n k Let the noise at the k-th user have the power of: The signal-to-interference-plus-noise ratio (SIR) of the public information flow at user k is Similarly, the signal-to-interference-plus-noise ratio (SIR) of the private information stream at user k is Their corresponding public and private rates are R respectively. c，k =log(1+SINR) c，k ) and R k =log(1+SINR) k ).

[0065] First, the optimization problem corresponding to this system is given:

[0066]

[0067] sttr(WW H )≤P T ,

[0068]

[0069] X in ≤x i ≤X max

[0070]

[0071] Where P T X is the maximum transmit power of the base station. min and X max These are the lower and upper bounds for antenna movement, respectively, and D0 is the minimum spacing between antennas.

[0072] This invention proposes an optimization algorithm based on a transformation of the FP method. Therefore, the equivalent optimization problem after the FP transformation is given:

[0073]

[0074] sttr(WW H )≤P T ,

[0075] T k (μ, v, W, Φ, x) ≥ r c，k

[0076]

[0077] X min ≤x i ≤X max

[0078]

[0079] in

[0080] Omitting the initialization and variable swapping steps, the specific steps to solve this equivalent problem are as follows:

[0081] The first step is to utilize Where w i It is the i-th column of matrix W. Update FP parameters.

[0082] The second step is to use expressions. Update λ k ,use Update λ w subscript Using κ [r+1] =(tr(WW) H )+1) / (P T +1) Update κ, where P T This is the maximum transmission power of the base station.

[0083] The third step is to utilize Update the last column of matrix W, using Update the first K columns of W.

[0084] The fourth step is to first present the equivalent optimization problem when fixing other variables and optimizing the common rate partition separately, as follows:

[0085]

[0086] r c，k ≥0

[0087] Combining the shared rate constraint and the form of the objective function, the shared rate for all users is first calculated. Then use r c，k =min k R c，k , Update the public rate segment.

[0088] Step 5, given M1, M2, M3, N 1,i N 2,i N 3,i First, the equivalent optimization problem of optimizing the RIS reflection matrix separately is given as follows:

[0089]

[0090] st|φ i |2 =1,

[0091]

[0092] Combining the dual problem and the SCA algorithm, using φ [r+1] =e jh Update the reflection vector φ, using Update ξ, where τ = 0.1 is the step size.

[0093] in, 1 is a column vector of all 1s, representing the transmit field response matrix from the base station to the RIS. A is the transmit field response matrix from the base station to the RIS. i Let B be the transmit field response matrix from base station to user i, B be the receive field response matrix of RIS, and ∑ be the channel fading matrix from base station to RIS. i Let be the channel fading matrix from the base station to user i.

[0094] Step 6: Propose the optimization problem corresponding to updating the antenna position:

[0095]

[0096] X min ≤x i ≤X max

[0097]

[0098] The specific steps to solve this problem are as follows:

[0099] (1) Initialization Where x [r] It is the position vector formed by the positions of all antennas, where M is the total number of base station antennas. This is the feasible region of problem (P2.3); the step size α is set to 1; r is the current iteration number; the maximum number of iterations is r. max .

[0100] (2)Use Update the antenna position, where the subscript m represents the m-th antenna. If Then the reduction step size is 0.5α; otherwise, r = r + 1.

[0101] (3) If r <r max If yes, then return to (2); otherwise, output x. [r+1] .

[0102] Step 7, if |R [r+1] -R [r] |<∈andr <rmax If the condition is met, repeat steps one through six; otherwise, output W. [r+1] ,φ [r+1] , x [r+1] .

[0103] The above-described invention is merely a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several foreseeable improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for neutralization rate optimization in an MA-assisted RSMA-RIS system, characterized in that, Includes the following steps: (1) Establish the original optimization problem (P1) of the downlink multi-user MA-assisted RSMA-RIS communication system with the goal of maximizing the system and rate. Its constraints include base station transmit power constraints, RIS reflector modulus constraints, antenna movement range constraints and minimum spacing constraints between antennas. (2) The original optimization problem (P1) is non-convex and is equivalently transformed into optimization problem (P2) using fractional programming. (3) The optimization problem (P2) is solved iteratively using an alternating optimization framework. By fixing other variables, the precoding matrix, common rate segmentation, RIS reflection matrix and antenna position are optimized in sequence until the result converges. The alternating optimization iteration process in step (3) specifically includes the following steps: (a) Initialize system parameters and optimize variables; (b) Update the FP auxiliary variables based on the stored precoded matrix, and update the auxiliary variables related to system constraints; (c) Based on all the auxiliary variables updated in step (b), update the precoding matrix using a closed-form solution; (d) Calculate the common rate for each user using the updated precoding matrix from step (c), and update the common rate segmentation accordingly; (e) Based on the variables updated in steps (b) to (d) and with the antenna position variables fixed, construct and solve a subproblem about the RIS reflection vector, and update the RIS reflection matrix; (f) Based on the system channel state determined after step (e), update the antenna position vector using the gradient ascent method; (g) Calculate the current system and rate. If their relative changes are less than the threshold and the maximum number of iterations has not been reached, return to step (b); otherwise, output the optimization result. In step (b), the FP auxiliary variables include μ k ,ε k ,γ k ,v k Their update formulas are as follows: ； ； ； ； Among them, h k It is the equivalent channel vector of user k. It is the i-th column of the precoding matrix W. This represents the noise power of user k, where K is the number of users. It is a public stream precoding vector. It is the private stream precoding vector of user i. Represents the conjugate transpose of the original vector or matrix. This represents the optimal solution for the current step. In step (b), the auxiliary variables related to system constraints include λ. k The update formula for the auxiliary variable κ is: ； in, The maximum transmit power of the base station is W, the precoding matrix is ​​r, and the current iteration round number is r; auxiliary variable λ k The update formula is: ； as well as ； in, , , They are respectively with users Functions related to the rate constraints of user w.

2. The method according to claim 1, characterized in that, The update formula for the precoding matrix in step (c) is: public stream precoding vector w c The update formula is: ； Private stream precoding vector w m The update formula is: ； in, Let I represent the m-th user, and let I represent the identity matrix.

3. The method according to claim 2, characterized in that, Step (e) of updating the RIS reflection matrix includes: constructing subproblem P2.2 and iteratively solving it using duality theory and continuous convex approximation algorithm to update the reflection vector. Simultaneously, the dual variable ξ related to the rate constraint is updated, and its update formula is: ； in, express The i-th element, r c,k The common rate segment updated in step (d) is τ, where τ is the step size. This indicates the operation of taking the real part. , , The definition is given as follows: ； ； ； ； in, , , Let A be a vector of all 1 columns, representing the transmit field response matrix from the base station to the RIS. Let be the transmission response matrix from the base station to user i. Here is the receiver field response matrix of the RIS. The channel fading matrix from the base station to the RIS is... Let be the channel fading matrix from the base station to user i.

4. The method according to claim 1, characterized in that, The specific method for updating the antenna position vector x in step (f) is a gradient-ascending projection algorithm, including: (i) initializing the antenna position. Step antenna position update α, current iteration number r=0, and maximum iteration number M is the number of base station antennas. (ii) The feasible region of the optimization problem; (ii) Update the position of each antenna according to the gradient of the system and rate objective function Ψ(x) with respect to the antenna position as follows: ; Where the subscript m represents the m-th antenna; (iii) if Then the step size is reduced to And repeat step (ii); otherwise, let (iv) If If the result is positive, return to step (ii); otherwise, output the final antenna position. .

5. The method according to claim 3, characterized in that, The optimization problem (P2.2) in step (e) takes the form of: ； ； ； in, , , .

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