STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method

Abstract

The invention, which belongs to the technical field of RIS system analysis and optimization, provides an STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method comprising the following steps: step S1, constructing an STAR-RIS-assisted downlink MIMO-NOMA system; s2, acquiring an information rate expression of each NOMA user under different antenna configurations, and acquiring a corresponding equivalent Cauchy transform expression; s3, obtaining an expression of Cauchy transformation of the matrix B, and obtaining an asymptotic expression of a power normalization factor of a GSVD precoder; s4, acquiring a closed expression of the asymptotic information rate of each NOMA user; and step S5, through solving an optimization problem of maximizing each NOMA user and rate, obtaining an emission and reflection phase shift matrix of the optimized STAR-RIS panel. According to the invention, the information rate of the communication system can be analyzed and optimized in a complex channel environment.

Description

Technical Field

[0001] The invention belongs to the technical field of RIS system analysis and optimization, and in particular relates to a STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method. Background Art

[0002] Future communication systems will support emerging services such as virtual reality, autonomous driving, and augmented reality, which drives the need to improve the spectrum efficiency and capacity of wireless communication systems. As a key physical layer technology in 5G, Multiple-Input Multiple-Output (MIMO) technology significantly improves the spectrum efficiency and reliability of wireless links by utilizing the spatial degrees of freedom of the channel. However, when the number of NOMA users or streams is large and spatially indistinguishable, the MIMO system capacity of the orthogonal access scheme is limited. Therefore, Non-Orthogonal Multiple Access (NOMA) technology came into being, which effectively improves the system capacity by transmitting data on the same time-frequency resources and recovering the data using the serial interference cancellation mechanism at the receiving end.

[0003] In MIMO-NOMA systems, generalized singular value decomposition (GSVD) precoding has attracted much attention due to its superior communication performance and low implementation complexity. This scheme converts multi-NOMA user MIMO channels into multiple parallel single-input and single-output sub-channels, thereby significantly reducing the complexity of signal processing.

[0004] In recent years, the Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface (STAR-RIS) technology has been proposed as an emerging method. This technology expands the service coverage of traditional RIS from one-sided coverage to full space coverage by simultaneously transmitting and reflecting the incident signal. It not only overcomes the signal blocking problem caused by occlusion in traditional RIS, but also significantly improves the channel quality of the system. STAR-RIS can be seamlessly combined with NOMA technology. By flexibly configuring the coefficients of the transmitted and reflected signals, the coordinated base station allocates power to different NOMA users, thereby achieving efficient services for NOMA users on both sides of STAR-RIS.

[0005] However, existing research has not yet conducted an in-depth discussion on the performance of GSVD precoding in STAR-RIS-assisted MIMO-NOMA systems, and existing research on GSVD-NOMA mostly assumes Rayleigh channels or the derived results lack universality, which increases the difficulty of optimizing the system. Summary of the invention

[0006] The purpose of the present invention is to propose a STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method, which can analyze and optimize the information rate of the communication system in a complex channel environment.

[0007] The present invention is achieved through the following technical solutions:

[0008] The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method includes the following steps:

[0009] Step S1: construct a STAR-RIS-assisted downlink MIMO-NOMA system consisting of a base station, a NOMA user, and a STAR-RIS panel. The system has a Rice fading channel and uses GSVD precoding and decoding to eliminate interference between MIMO-NOMA subchannels to obtain the NOMA user received signal expression. The NOMA user received signal expression includes the equivalent channel matrix H i ;

[0010] Step S2: According to the NOMA user received signal expression, the information rate expression of each NOMA user under different antenna configurations is obtained, and the equivalent Cauchy transform expression of the information rate of each NOMA user is further obtained. The equivalent Cauchy transform expression involves the equivalent channel matrix H under different antenna configurations. i The resulting matrix B;

[0011] Step S3: Based on the equivalent Cauchy transform expression of the NOMA user information rate obtained in step S2, the matrix B is linearized using the linearization technique of the matrix polynomial, and the expression of the Cauchy transform of the matrix B is obtained using the operator value free probability theory, and the asymptotic expression of the power normalization factor of the GSVD precoder is obtained;

[0012] Step S4: Based on the Cauchy transform expression of the matrix B in step S3 and the equivalent Cauchy transform expression of the information rate in step S2, considering the case where the channel between the base station and the STAR-RIS panel is deterministic, a closed-form expression of the asymptotic information rate of each NOMA user is obtained;

[0013] Step S5: Based on the closed-form expression of the asymptotic information rate of each NOMA user obtained in step S4, the optimized transmission and reflection phase shift matrices of the STAR-RIS panel are obtained by solving the optimization problem of maximizing the sum of each NOMA user and the rate.

[0014] Furthermore, the step S1 specifically includes:

[0015] Step S11: A STAR-RIS-assisted downlink MIMO-NOMA system is composed of a base station, two NOMA users, and K STAR-RIS panels. The base station is equipped with T transmitting antennas, and the i-th NOMA user is equipped with R i The kth STAR-RIS panel is equipped with L k emitting and reflecting elements, 1≤i≤2, R2≤R1;

[0016] Step S12: The transmission signal of the base station is expressed as Among them, s i represents the signal sent by the base station for the i-th NOMA user, W is the precoding matrix of the precoder at the base station; κ1 and κ2 are the fractional powers allocated to the two NOMA users;

[0017] Step S13: The received signal of the i-th NOMA user is expressed as Among them, ρ i is the relative channel gain of the ith NOMA user, P is the base station transmit power, t is the power normalization factor of the GSVD precoder, and A i is the receiving filter of the i-th NOMA user, R 0，i is the channel from the base station to the i-th NOMA user, n i is the additive Gaussian white noise at the i-th NOMA user, R k，i is the channel from the kth STAR-RIS panel to the ith NOMA user, when i=1, Θ k，i represents the transmission phase shift matrix of the kth STAR-RIS panel, when i=2, Θ k，i represents the reflection phase shift matrix of the kth STAR-RIS panel, J k represents the channel from the base station to the kth STAR-RIS panel;

[0018] Step S14, channel J k and channel R k，i All are Rice fading channels, channel J k Expressed as Channel R k，i Expressed as in, and is the deterministic line-of-sight component, For channel J k The random component of the channel, For channel R k，i The random component of the channel, U k 、V k , T k，i and S k，i are unitary matrices representing the correlation between channel coefficients, M k and N k，i are non-negative matrices, representing and The variance of and is a complex Gaussian random matrix whose variables are independent and identically distributed, with zero mean and equal variance, and ⊙ represents the dot product;

[0019] Step S15: Based on the channel of step S14, obtain the channel The parameterized bilateral correlation matrix of Channel The parameterized bilateral correlation matrix of in, For Channel The parameterized left-hand side correlation matrix of For Channel The parameterized right-hand side correlation matrix, C and is an arbitrary Hermitian matrix, is the conjugate transpose of the matrix, when k = 0 When k>0 and is a diagonal matrix, D and is an arbitrary Hermitian matrix, ζ k (D) is the channel The parameterized left-hand side correlation matrix of For Channel The parameterized right-hand side correlation matrix of , To obtain the expectation, ∑ k (D) and is a diagonal matrix;

[0020] Step S16: define an equivalent channel matrix According to the formula For the channel matrix H i Perform GSVD according to the formula Get the precoding matrix W = P -1 and the decoding matrix of NOMA user i Then the received signal expression of NOMA user i is in, is a unitary matrix, P is a non-singular matrix, ∑ iis a rectangular diagonal matrix.

[0021] Furthermore, the step S2 specifically includes:

[0022] Step S21: When T≤R2, the rectangular diagonal matrix ∑ i Expressed as Then the information rate expressions of the two NOMA users are and The equivalent Cauchy transform expression corresponding to the information rate of two NOMA users is: and at this time, is the Cauchy transform of matrix B, which is given by the formula Given, where S=min(R1,T)+min(R2,T)-min(R1+R2,T), n i The covariance of i，k For the matrix The kth element on the diagonal, The size is The all-zero matrix of -1 is the inverse of the matrix;

[0023] Step S22: When R2≤T≤R1+R2, the rectangular diagonal matrix ∑ i Expressed as and Then the information rate expressions of the two NOMA users are and For I1 and I2, we can make the following formulas respectively: and The transformation shown in the figure further leads to the equivalent Cauchy transformation expression of the information rate expression of the two NOMA users. At this time, is the Cauchy transform of matrix B, which is given by the formula Given, where

[0024] Furthermore, the step S3 specifically includes:

[0025] Step S31: define variables Represents R i The unit matrix of order, 1≤i≤2;

[0026] Step S32: Apply matrix linearization techniques to construct a linearization matrix L of matrix B to linearize matrix B. The linearization matrix L is expressed as in,

[0027] Step S33: Based on the operator-valued free probability theory, the Cauchy transform of matrix B is related to the operator-valued Cauchy transform of the linearized matrix L. Considering the large-dimensional case, the Cauchy transform of matrix B is obtained. The expression is in, I represents the identity matrix,

[0028]

[0029]

[0030] Step S34: Based on the operator value free probability theory and the linearization technique of matrix polynomials, define the variables Considering the case of large dimensions, the asymptotic expression of the power normalization factor t of the GSVD precoder is obtained as in Satisfies the matrix equation

[0031]

[0032] Furthermore, the step S4 specifically includes:

[0033] Step S41: Set the channel between the base station and the STARRIS panel to be deterministic, i.e.

[0034] Step S42: Based on step S41, Simplified to:

[0035]

[0036] Will and Set to zero matrix;

[0037] step S43 , based on steps S3 The Cauchy transformation expression and steps of matrix B in S2 Considering the large-dimensional case, the closed-form expression of the asymptotic information rate of each NOMA user is obtained as and in,

[0038] det(.) means taking the determinant.

[0039] Furthermore, it is characterized in that: in step S5, the optimization problem is expressed as

[0040]

[0041] β k，1，l +β k，2，l =1,1≤k≤K,1≤l≤L k , where Θ∈{Θ 1，1 , ..., Θ K，2} are the emission and reflection phase shift matrices, and the projected gradient ascent method is used to solve the optimization problem.

[0042] Furthermore, solving the optimization problem includes the following steps:

[0043] Step S51, define variable θ i =Θ i 1, among which, is a vector of all 1s, Θ i =diag{Θ 1，i , Θ 2，i , ..., Θ K，i};

[0044] Step S52: Set the convergence threshold ε, iteration step length α, β k，1，l =β k，2，l = 0.5, the superscript j is introduced to indicate the jth iteration, the initial value is set to j = 0, and the emission and reflection phase shift matrices Θ are randomly generated (0) ,according to and calculate

[0045] Step S53: According to the formula When calculating the jth iteration Gradient in,

[0046] Step S54: According to the formula renew The symbol a(l) represents the lth element of vector a. |θ i (l)| represents θ i (l) modulus;

[0047] Step S55: Update the power normalization factor t of the GSVD precoder;

[0048] Step S56: Calculate If the calculated result is less than the convergence threshold ε, the optimal transmission and reflection phase shift matrix Θ is output; if not, j=j+1 is set and the process jumps to step S53 to start a new iteration operation.

[0049] Furthermore, the large-dimensional case refers to T→∞, L→∞, R i →∞,L / T=∈1,R i / T=∈2, where ∈1 and ∈2 are constants.

[0050] The present invention has the following beneficial effects:

[0051] 1. The present invention first constructs a STAR-RIS-assisted downlink MIMO-NOMA system consisting of a base station, a NOMA user and a STAR-RIS panel, and obtains an expression of a received signal of each NOMA user. Secondly, according to the expression of the received signal of the NOMA user, an expression of the information rate of each NOMA user under different antenna configurations is obtained, and an equivalent Cauchy transform expression of the information rate of each NOMA user is further obtained. Then, based on the obtained equivalent Cauchy transform expression of the information rate of the NOMA user, the matrix B is linearized using the linearization technique of the matrix polynomial, and the expression of the Cauchy transform of the matrix B is obtained using the operator value free probability theory, and the asymptotic expression of the power normalization factor of the GSVD precoder is obtained. Then, based on the equivalent Cauchy transform expression of the information rate of the NOMA user, the matrix B is linearized using the linearization technique of the matrix polynomial, and the operator value free probability theory is used to obtain the expression of the Cauchy transform of the matrix B, and the asymptotic expression of the power normalization factor of the GSVD precoder is obtained. The Cauchy transform expression and the equivalent Cauchy transform expression of the information rate in step S2, considering the case where the channel between the base station and the STAR-RIS panel is deterministic, obtain the closed-form expression of the asymptotic information rate of each NOMA user, and finally, based on the obtained closed-form expression of the asymptotic information rate of each NOMA user, by solving the optimization problem of maximizing the sum of each NOMA user and the rate, the optimized transmission and reflection phase shift matrices of the STAR-RIS panel are obtained. The Cauchy transform expression of the matrix B, the asymptotic expression of the power normalization factor of the GSVD precoder and the closed-form expression of the asymptotic information rate of each NOMA user obtained through the above process can be well consistent with the Monte Carlo simulation, thereby realizing the analysis and optimization of the information rate of the communication system in a complex channel environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The present invention is further described in detail below with reference to the accompanying drawings.

[0053] Figure 1 It is a flow chart of the present invention.

[0054] Figure 2 This is a simulation result diagram of the user information rate changing with the signal-to-noise ratio under different system antenna configurations of the present invention.

[0055] Figure 3This is a simulation result diagram of the power normalization factor changing with the number of receiving antennas under different numbers of STAR-RIS panels of the present invention.

[0056] Figure 4 The simulation results of the user information rate varying with the signal-to-noise ratio under different system antenna configurations are given for the special case that the channel between the base station and the STAR-RIS panel is deterministic.

[0057] Figure 5 This is a simulation result diagram comparing the user and information rates with signal-to-noise ratio under different numbers of STAR-RIS panels between the present invention and the non-optimization method. DETAILED DESCRIPTION

[0058] like Figure 1 As shown, the STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method includes the following steps:

[0059] Step S1: construct a STAR-RIS-assisted downlink MIMO-NOMA system consisting of a base station, a NOMA user, and a STAR-RIS panel. The system has a Rice fading channel and uses GSVD precoding and decoding to eliminate interference between MIMO-NOMA subchannels to obtain the NOMA user received signal expression. The NOMA user received signal expression includes the equivalent channel matrix H i ;

[0060] The specific steps include:

[0061] Step S11: A STAR-RIS-assisted downlink MIMO-NOMA system is composed of a base station, two NOMA users, and K STAR-RIS panels. The base station simultaneously transmits information to two users on both sides of the STAR-RIS panel. The base station is equipped with T transmitting antennas, and the i-th NOMA user is equipped with R i The kth STAR-RIS panel is equipped with L k emitting and reflecting elements, 1≤i≤2, R2≤R1;

[0062] In this embodiment, the number of STAR-RIS panels is K=2, and the number of transmitting and reflecting elements equipped on the STAR-RIS panels is L. k =30, There are two cases for antenna configuration: case 1: the number of base station transmitting antennas is T = 10, the number of user receiving antennas is R1 = 16, R2 = 16; case 2: the number of base station transmitting antennas is T = 10, the number of user receiving antennas is R1 = 16, R2 = 16;

[0063] Step S12: In the MIMO-NOMA system of the base station established in step S11, the transmitted signal is expressed as Among them, s i Indicates that the base station sends a signal for the i-th NOMA user, satisfying s i ~CN(0,I)and W is the precoding matrix of the precoder at the base station; κ1 and κ2 are the fractional powers allocated to the two NOMA users, satisfying 0≤κ i ≤1 and κ1+κ2=1;

[0064] In this embodiment, the fractional powers allocated to the two users are κ1=0.1, κ2=0.9;

[0065] Step S13: In the MIMO-NOMA system of the base station established in step S11, the received signal of the i-th NOMA user is expressed as Among them, ρ i is the relative channel gain of the i-th NOMA user, P is the base station transmit power, is the power normalization factor of the GSVD precoder, is the receiving filter of the i-th NOMA user, is the channel from the base station to the i-th NOMA user, n i is the additive Gaussian white noise at the i-th NOMA user, the mean of the additive Gaussian white noise is zero, and the covariance matrix is is the channel from the kth STAR-RIS panel to the ith NOMA user, when i=1, represents the transmission phase shift matrix of the kth STAR-RIS panel, when i=2, represents the reflection phase shift matrix of the kth STAR-RIS panel, with parameters and θ k，i，l ∈[0, 2π) represent the fractional power and phase shift of the transmitting side (i=1) or the reflecting side (i=2), respectively, and satisfy β k，1，l +β k，2，l =1, 1≤k≤K, 1≤l≤L k , represents the channel from the base station to the kth STAR-RIS panel;

[0066] In this embodiment, the relative channel gain of the user is ρ1=5, ρ2=1, and the fractional power on the transmitting side (i=1) or the reflecting side (i=2) is β k，1，l =β k，2，l =0.5, phase shift θ k,i,l Directly generate random values ​​between 0 and 2π;

[0067] Step S14: In order to capture the generalized spatial correlation structure of the channel, consider all channels J k and channel Rk ，i均 is a Rice fading channel with Weichselberger correlation structure, and its model is: Channel J k Expressed as Channel R k，i Expressed as Among them, the matrix and is the deterministic line-of-sight component, For channel J k The random component of the channel, For channel R k，i The channel random component, the deterministic matrix U k 、V k , T k，j and S k，i are unitary matrices representing the correlation between channel coefficients, M k and N k，i are non-negative matrices, representing and The variance of and is a complex Gaussian random matrix whose variables are independent and identically distributed, with zero mean and equal variance, that is, it satisfies and ⊙ represents dot product;

[0068] Step S15: Based on the channel of step S14, obtain the channel The parameterized bilateral correlation matrix of in, For Channel The parameterized left-hand side correlation matrix of For Channel The parameterized right-hand side correlation matrix of , and is an arbitrary Hermitian matrix, is the conjugate transpose of the matrix, when k = 0 When k>0 and is a diagonal matrix whose elements are and

[0069] Channel The parameterized bilateral correlation matrix of Among them, k (D) is the channel The parameterized left-hand side correlation matrix of For Channel The parameterized right-hand side correlation matrix of , and is an arbitrary Hermitian matrix, To obtain the expectation, Σ k (D) and is a diagonal matrix whose elements are and

[0070] Step S16: Use the GSVD precoding and decoding scheme to eliminate interference between MIMO-NOMA sub-channels and define the equivalent channel matrix According to the formula For the channel matrix H i Perform GSVD according to the formula Get the precoding matrix W = P -1 and the decoding matrix of NOMA user i Then the received signal expression of NOMA user i is So far, the derivation of the user receiving expression is completed, where: is a unitary matrix, P is a non-singular matrix, ∑ i is a rectangular diagonal matrix.

[0071] Step S2: According to the NOMA user received signal expression, the information rate expression of each NOMA user under different antenna configurations is obtained, and the equivalent Cauchy transform expression of the information rate of each NOMA user is further obtained. The equivalent Cauchy transform expression involves the equivalent channel matrix H under different antenna configurations. i The resulting matrix B;

[0072] Based on the user received signal expression obtained in step S1, the expression of the information rate and the matrix ∑ i Related to the matrix ∑ under different antenna configurations i The structure is different. Assuming that the channel gain of NOMA user 1 is greater than the channel gain of NOMA user 2, the information rate expression of the two NOMA users under different antenna configurations can be obtained, and the equivalent Cauchy transform expression of the information rate can be further obtained, which specifically includes the following steps:

[0073] Step S21: When T≤R2, the rectangular diagonal matrix Expressed as Then the information rate expressions of the two NOMA users are and in, S=min(R1,T)+min(R2,T)-min(R1+R2,T), n i The covariance of i,k For the matrix The kth element on the diagonal, The size is The all-zero matrix of

[0074] Because μ k The distribution of I is unknown. i It is difficult to obtain the expression of directly, so the information rates I1 and I2 of the two NOMA users are equivalently expressed as The Cauchy transform of and in, F μ is the empirical cumulative distribution function of μ, μ is the non-zero eigenvalue of matrix B, and B is given by the formula Given, the Cauchy transform It can be further expressed as is the Cauchy transform of the matrix B, which is given by the formula, where (·) -1 is the inverse of the matrix;

[0075] Step S22: When R2≤T≤R1+R2, the rectangular diagonal matrix ∑ i Expressed as and Then the information rate expressions of the two NOMA users are and For I1 and I2, we can make the following formulas respectively: and The transformation shown in the figure further leads to the equivalent Cauchy transformation expression of the information rate expression of the two NOMA users. At this time, is the Cauchy transform of matrix B, which is given by the formula Given, where Δ→0, and The formulas are When i=1 and i=2;

[0076] In this embodiment, Δ=10 -4 ;

[0077] Step S3: Based on the equivalent Cauchy transform expression of the NOMA user information rate obtained in step S2, the matrix B is linearized using the linearization technique of the matrix polynomial, and the expression of the Cauchy transform of the matrix B is obtained using the operator value free probability theory, and the asymptotic expression of the power normalization factor of the GSVD precoder is obtained;

[0078] The specific steps include:

[0079] Step S31: define variables Represents R i The unit matrix of order, 1≤i≤2;

[0080] Step S32: Apply matrix linearization techniques to construct a linearization matrix L of matrix B to linearize matrix B. The linearization matrix L is expressed as in,

[0081] Step S33: Based on the operator-valued free probability theory, the Cauchy transform of the matrix B is related to the operator-valued Cauchy transform of the linearized matrix L. Consider the case of large dimensions: T→∞, L→∞, R i →∞,L / T=∈1,R i / T=∈2, (∈1 and ∈2 are constants), and we get the Cauchy transformation of the matrix B The expression is Among them, Satisfies the matrix equation I represents the identity matrix, For the formula When k=0, For the formula Pick hour, For the formula Pick hour,

[0082] Step S34, the power normalization factor of the GSVD precoder can be restated as Based on operator-valued free probability theory and matrix polynomial linearization techniques, define variables And consider the case of large dimensions: T→∞, L→∞, R i →∞,L / T=∈1,R i / T=∈2 and z→0, the asymptotic expression of the power normalization factor t of the GSVD precoder is obtained as in Satisfies the matrix equation For the formula Pick hour,

[0083] Step S4: Based on the Cauchy transform expression of the matrix B in step S3 and the equivalent Cauchy transform expression of the information rate in step S2, considering the case where the channel between the base station and the STAR-RIS panel is deterministic, a closed-form expression of the asymptotic information rate of each NOMA user is obtained;

[0084] The specific steps include:

[0085] Step S41: Set the channel between the base station and the STARRIS panel to be deterministic, i.e.

[0086] Step S42: Based on step S41, Simplified to:

[0087] Will and Set to zero matrix;

[0088] Step S43: Based on the Cauchy transform expression of the matrix B in step S3 and the equivalent Cauchy transform expression of the information rate in step S2, consider the case of large dimensions: T→∞, L→∞, R i →∞,L / T=∈1,R i / T=∈2, the closed-form expression of the asymptotic information rate of two NOMA users is obtained as and So far, the closed-form expression of the user asymptotic information rate has been derived, where det(.) means taking the determinant, for ∑(z) is

[0089] Step S5: Based on the closed-form expression of the asymptotic information rate of each NOMA user obtained in step S4, the optimized transmission and reflection phase shift matrices of the STAR-RIS panel are obtained by solving the optimization problem of maximizing the sum of each NOMA user and the rate:

[0090] The specific steps include:

[0091] Step S51, optimize the transmission and reflection phase shift matrices of the STAR-RIS panel to maximize the sum of the two users and the rate to obtain the optimization problem as follows: Among them, Θ∈{Θ 1，1 , ..., Θ K，2} are the emission and reflection phase shift matrices, and the projected gradient ascent method is used to solve the optimization problem.

[0092] Step S52: define variable θ i =Θ i1, among which, is a vector of all 1s, Θ i =diag{Θ 1，i , Θ 2，i , ..., Θ K，i};

[0093] Step S53: Set the convergence threshold ε, iteration step length α, β k，1，l =β k，2，l = 0.5, the superscript j is introduced to indicate the jth iteration, the initial value is set to j = 0, and the emission and reflection phase shift matrices Θ are randomly generated (0) ,according to and calculate

[0094] Step S54: According to the formula When calculating the jth iteration Gradient in,

[0095] Step S55: According to the formula renew The symbol a(l) represents the lth element of vector a. |θ i (l)| represents θ i (l) modulus;

[0096] Step S56: Update the power normalization factor t of the GSVD precoder;

[0097] Step S57: Calculate If the calculated result is less than the convergence threshold ε, the optimal transmission and reflection phase shift matrix Θ is output; if not, j=j+1 is set and the process jumps to step S54 to start a new iteration operation.

[0098] At this point, the transmission and reflection phase shift matrix of the STAR-RIS panel that maximizes the system sum rate is obtained, and the system optimization is completed.

[0099] Figure 2 In the formula, the horizontal axis is the signal-to-noise ratio, the vertical axis is the user information rate, and the solid line represents the substitution of the Cauchy transform expression of the matrix B derived in step S3 into the formula The hollow circle represents the Monte Carlo simulation result of I1, and the cross represents the Monte Carlo simulation result of I2. Figure 2 Two different system antenna configurations are considered: case 1 and case 2. Figure 2It can be seen that under the two system antenna configurations, for I1 and I2, the solid line (referring to the analysis results) coincides with the corresponding mark (Monte Carlo simulation results), which means that the analysis results are in good agreement with the Monte Carlo simulation results, thus illustrating the accuracy of the Cauchy transform expression of the matrix B.

[0100] Figure 3 In the figure, the horizontal axis is the number of receiving antennas, the vertical axis is the power normalization factor t, the solid line represents the analysis result of the asymptotic expression of the power normalization factor B derived in step S3, and the hollow circle represents the Monte Carlo simulation result. Consider different numbers of STAR-RIS panels K = 0, 1, 4, the number of base station transmitting antennas is T = 16, and the number of receiving antennas of the two users is the same, which is R = 10 to 24. Figure 3 It can be seen that the analytical results are in good agreement with the Monte Carlo simulation results, which illustrates the accuracy of the asymptotic expression of the power normalization factor t.

[0101] Figure 4 In the figure, the horizontal axis is the signal-to-noise ratio, the vertical axis is the user information rate, the solid line represents the analysis result of the closed-form expression of the user asymptotic information rate derived from step S4, and the hollow circles and cross marks represent the Monte Carlo simulation results. Consider different system antenna configurations: case 1 and case 2, and the channel is deterministic. By Figure 4 It can be seen that the analytical results are in good agreement with the Monte Carlo simulation results, demonstrating the accuracy of the closed-form expression for the user's asymptotic information rate.

[0102] Figure 5 In , the horizontal axis is the signal-to-noise ratio, and the vertical axis is the user and information rate. The non-optimization method is to randomly set the phase shift matrix and set β k，1，l =β k，2，l = 0.5. Consider different numbers of STAR-RIS panels K = 2, 4. Figure 5 It can be seen that the present invention can effectively improve the user and information rate under different numbers of STAR-RIS panels.

[0103] The above description is only a preferred embodiment of the present invention, and therefore cannot be used to limit the scope of implementation of the present invention. That is, equivalent changes and modifications made according to the scope of the patent application of the present invention and the contents of the specification should still fall within the scope covered by the patent of the present invention.

Claims

1. STAR-RIS assisted GSVD precoding MIMO-NOMA system optimization method, characterized by: The steps include: Step S1: construct a STAR-RIS-assisted downlink MIMO-NOMA system consisting of a base station, a NOMA user, and a STAR-RIS panel. The system has a Rice fading channel and uses GSVD precoding and decoding to eliminate interference between MIMO-NOMA subchannels to obtain the NOMA user received signal expression. The NOMA user received signal expression includes the equivalent channel matrix H i ; Step S2: According to the NOMA user received signal expression, the information rate expression of each NOMA user under different antenna configurations is obtained, and the equivalent Cauchy transform expression of the information rate of each NOMA user is further obtained. The equivalent Cauchy transform expression involves the equivalent channel matrix H under different antenna configurations. i The resulting matrix B; Step S3: Based on the equivalent Cauchy transform expression of the NOMA user information rate obtained in step S2, the matrix B is linearized using the linearization technique of the matrix polynomial, and the expression of the Cauchy transform of the matrix B is obtained using the operator value free probability theory, and the asymptotic expression of the power normalization factor of the GSVD precoder is obtained; Step S4: Based on the Cauchy transform expression of the matrix B in step S3 and the equivalent Cauchy transform expression of the information rate in step S2, considering the case where the channel between the base station and the STAR-RIS panel is deterministic, a closed-form expression of the asymptotic information rate of each NOMA user is obtained; Step S5: Based on the closed-form expression of the asymptotic information rate of each NOMA user obtained in step S4, the optimized transmission and reflection phase shift matrices of the STAR-RIS panel are obtained by solving the optimization problem of maximizing the sum of each NOMA user and the rate.

2. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 1, characterized in that: The step S1 specifically includes: Step S11: A STAR-RIS-assisted downlink MIMO-NOMA system is composed of a base station, two NOMA users, and K STAR-RIS panels. The base station is equipped with T transmitting antennas, and the i-th NOMA user is equipped with R i The kth STAR-RIS panel is equipped with L k emitting and reflecting elements, 1≤i≤2, R2≤R1; Step S12: The transmission signal of the base station is expressed as Among them, s i represents the signal sent by the base station for the i-th NOMA user, W is the precoding matrix of the precoder at the base station; κ1 and κ2 are the fractional powers allocated to the two NOMA users; Step S13: The received signal of the i-th NOMA user is expressed as Among them, ρ i is the relative channel gain of the i-th NOMA user, P is the base station transmit power, t is the power normalization factor of the GSVD precoder, and A i is the receiving filter of the i-th NOMA user, R 0，i is the channel from the base station to the i-th NOMA user, n i is the additive Gaussian white noise at the i-th NOMA user, R k，i is the channel from the kth STAR-RIS panel to the ith NOMA user, when i=1, Θ k，i represents the transmission phase shift matrix of the kth STAR-RIS panel, when i=2, Θ k，i represents the reflection phase shift matrix of the kth STAR-RIS panel, J k represents the channel from the base station to the kth STAR-RIS panel; Step S14, channel J k and channel R k，i All are Rice fading channels, channel J k Expressed as Channel R k，i Expressed as in, and is the deterministic line-of-sight component, For channel J k The random component of the channel, For channel R k，i The random component of the channel, U k 、V k 、T k，i and S k，i are unitary matrices representing the correlation between channel coefficients, M k and N k，i are non-negative matrices, representing and The variance of and is a complex Gaussian random matrix whose variables are independent and identically distributed, with zero mean and equal variance, and ⊙ represents the dot product; Step S15: Based on the channel of step S14, obtain the channel The parameterized bilateral correlation matrix of Channel The parameterized bilateral correlation matrix of in, For Channel The parameterized left-hand side correlation matrix of For Channel The parameterized right-hand side correlation matrix, C and is an arbitrary Hermitian matrix, is the conjugate transpose of the matrix, when k = 0 When k>0 and is a diagonal matrix, D and is an arbitrary Hermitian matrix, ζ k (D) is the channel The parameterized left-hand side correlation matrix of For Channel The parameterized right-hand side correlation matrix of , To obtain the expectation, ∑ k (D) and is a diagonal matrix; Step S16: define an equivalent channel matrix According to the formula For the channel matrix H i Perform GSVD according to the formula Get the precoding matrix W = P -1 and the decoding matrix of NOMA user i Then the received signal expression of NOMA user i is in, is a unitary matrix, P is a non-singular matrix, ∑ i is a rectangular diagonal matrix.

3. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 2, characterized in that: The step S2 specifically includes: Step S21: When T≤R2, the rectangular diagonal matrix ∑ i Expressed as Then the information rate expressions of the two NOMA users are and The equivalent Cauchy transform expression corresponding to the information rate of two NOMA users is: and at this time, is the Cauchy transform of matrix B, which is given by the formula Given, where S=min(R1,T)+min(R2,T)-min(R1+R2,T), n i The covariance of i，k For the matrix The kth element on the diagonal, The size is The all-zero matrix of -1 is the inverse of the matrix; Step S22: When R2≤T≤R1+R2, the rectangular diagonal matrix ∑ i Expressed as and Then the information rate expressions of the two NOMA users are and For I1 and I2, we can make the following formulas respectively: and The transformation shown in the figure further leads to the equivalent Cauchy transformation expression of the information rate expression of the two NOMA users. At this time, is the Cauchy transform of matrix B, which is given by the formula Given, where 4. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 3, characterized in that: The step S3 specifically includes: Step S31: define variables Represents R i The unit matrix of order, l≤i≤2; Step S32: Apply matrix linearization techniques to construct a linearization matrix L of matrix B to linearize matrix B. The linearization matrix L is expressed as in, Step S33: Based on the operator-valued free probability theory, the Cauchy transform of matrix B is related to the operator-valued Cauchy transform of the linearized matrix L. Considering the large-dimensional case, the Cauchy transform of matrix B is obtained. The expression is in, I represents the identity matrix, Step S34: Based on the operator value free probability theory and the linearization technique of matrix polynomials, define the variables Considering the case of large dimensions, the asymptotic expression of the power normalization factor t of the GSVD precoder is obtained as in Satisfies the matrix equation 5. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 4, characterized in that: The step S4 specifically includes: Step S41: Set the channel between the base station and the STARRIS panel to be deterministic, i.e. Step S42: Based on step S41, Simplified to: Will and Set to zero matrix; Step S43: Based on the Cauchy transform expression of matrix B in step S3 and the equivalent Cauchy transform expression of information rate in step S2, considering the large dimensionality, the closed-form expression of the asymptotic information rate of each NOMA user is obtained as and in, 1≤l≤L k , det(·) means taking the determinant.

6. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 5, characterized in that: In step S5, the optimization problem is expressed as Among them, Θ∈{Θ 1，1 , ..., Θ K，2 } are the emission and reflection phase shift matrices, and the projected gradient ascent method is used to solve the optimization problem.

7. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 6, characterized in that: The solution to the optimization problem includes the following steps: Step S51, define variable θ i =Θ i 1, where is a vector of all 1s, Θ i =diag{Θ 1，i , Θ 2，i , ..., Θ K，i }; Step S52: Set the convergence threshold ε, iteration step length α, β k,1,l =β k,2,l = 0.5, the superscript j is introduced to indicate the jth iteration, the initial value is set to j = 0, and the emission and reflection phase shift matrices Θ are randomly generated (0) ,according to and calculate Step S53: According to the formula When calculating the jth iteration Gradient in, Step S54: According to the formula renew The symbol a(l) represents the lth element of vector a. |θ i (l)| represents θ i (l) modulus; Step S55: Update the power normalization factor t of the GSVD precoder; Step S56: Calculate If the calculated result is less than the convergence threshold ε, the optimal transmission and reflection phase shift matrix Θ is output; if not, j=j+1 is set and the process jumps to step S53 to start a new iteration operation.

8. The STAR-RIS-assisted GSVD precoding MIMO-NOMA system optimization method according to claim 7, characterized in that: The large-dimensional case refers to T→∞, L→∞, R i →∞,L / T=∈1,R i / T=∈2, where ∈1 and ∈2 are constants.

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