CN114785388A - Intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization method - Google Patents

Intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization method Download PDF

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CN114785388A
CN114785388A CN202210424206.1A CN202210424206A CN114785388A CN 114785388 A CN114785388 A CN 114785388A CN 202210424206 A CN202210424206 A CN 202210424206A CN 114785388 A CN114785388 A CN 114785388A
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CN114785388B (en
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孙宇楠
欧阳崇峻
杨鸿文
刘奕彤
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Beijing University of Posts and Telecommunications
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    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
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    • H04B7/00—Radio transmission systems, i.e. using radiation field
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Abstract

The invention provides an intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization method. Aiming at the characteristics of multi-user large-scale SIMO uplink M-order modulation communication under the scene that a direct beam path is blocked, the invention considers the limit of the transmitting power at the user side and the constraint condition required to be met by the intelligent omnidirectional surface device unit, and improves the uplink weighting and the rate of the system by jointly optimizing the beam forming at the user side and the reflection coefficient and the transmission coefficient of the intelligent super surface. The invention provides an algorithm based on manifold optimization and a gradient descent method to jointly optimize beam forming at a user side and a reflection coefficient and transmission coefficient matrix of an intelligent super surface, so that multi-user large-scale SIMO uplink M-order modulation weighting and rate under a scene that a direct beam is shielded can be effectively improved, and the complexity of solving an optimization problem and realizing a physical layer is reduced.

Description

Intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization method
1. Field of application
The invention relates to a rate optimization problem in a wireless communication physical layer, in particular to an intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization method.
2. Background of the invention
A Reconfigurable Intelligent super Surface (RIS) is a phase control Intelligent Surface composed of a large number of passive Reconfigurable components. In a scene where the direct path is blocked, the assistance of the RIS can bring considerable gain to the sum rate of the wireless communication system. However, the conventional RIS can only reflect an incident signal, and users located at opposite sides of the base station with respect to the RIS cannot receive or transmit a wireless signal.
Intelligent omnidirectional Surface (STAR-RIS) is provided. Each device unit of the STAR-RIS has a variable device structure, and the response characteristics of the device unit to wireless signals are controlled by controlling the operating state of the device unit. A wireless signal is incident from one side of STAR-RIS, and a part is reflected to the same side of the incident signal, which is called as a reflected signal; the remaining portion is transmitted to the other side, which is called a transmission signal. The reflection and transmission signals can be assigned by two parameters of the STAR-RIS device unit, which can be referred to as the reflection coefficient and the transmission coefficient.
In multi-user large-scale SIMO communication with STAR-RIS assistance, in order to maximize uplink M-order modulation and rate as much as possible on the premise of reducing power consumption, the power distribution mode on the transmitting side needs to be jointly designed with the reflection coefficient and the transmission coefficient of STAR-RIS. Most existing RIS assisted multi-user large-scale SIMO communication system designs only adopt a common reconfigurable intelligent super surface, can only reflect incident signals and cannot provide assistance for users positioned on the opposite side of a base station. In addition, since the form of the M-order modulation capacity is complicated, it is difficult to optimize and simplify it. In addition, currently, most of optimization researches on sum rate only consider the situation that input meets gaussian distribution, and do not consider an optimization scheme when M-order modulation is adopted. Therefore, the invention provides a STAR-RIS assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate Optimization method based on Manifold Optimization (MO). The invention provides an effective algorithm for jointly optimizing power distribution of an emitting side and reflection and transmission coefficients of STAR-RIS to obtain the maximum sum rate of up-and up-going M-order modulation by adopting an approximate formula to express M-order modulation weighting and rate and considering the power limit of the emitting side and the limit conditions met by the reflection coefficients and the transmission coefficients of STAR-RIS.
3. Summary and features of the invention
The invention provides a STAR-RIS (STAR-RIS) assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization algorithm, which can effectively improve multi-user large-scale SIMO uplink M-order modulation weighting and rate in a scene that a direct path is shielded, and reduce complexity of solving an optimization problem and realizing a physical layer.
In order to achieve the above object, the STAR-RIS assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization algorithm of the present invention comprises the following steps:
in multi-user large-scale SIMO uplink transmission under the scene that a STAR-RIS auxiliary direct path is shielded, a signal is incident to the STAR-RIS surface from a user antenna, can be divided into a reflection signal and a transmission signal, and is subjected to phase adjustment due to the phase control effect of the STAR-RIS. The reflected and transmitted signals serve users located on the same side of the base station with respect to STAR-RIS and users located on opposite sides, respectively, referred to as reflected and transmitted users. And jointly optimizing the transmission power distribution mode and the reflection and transmission coefficients of STAR-RIS by taking the ascending M-order modulation and speed maximization as criteria. The objective of the joint optimization problem is to maximize the upstream M-order modulation weights and rates for both reflective and transmissive users while satisfying the transmit-side power constraint and the energy conservation constraints obeyed by STAR-RIS reflection and transmission coefficients.
The original expression form of the M-order modulation and rate is complex, and the M-order modulation and rate is difficult to be solved optimally. Therefore, it can be considered to replace it with an approximate formula, namely:
Figure BDA0003607843390000021
where C represents the channel capacity, i.e., the maximum uplink and rate. M represents the modulation order, log (-) represents the logarithmic operation, and γ represents the signal-to-noise ratio. I, aiAnd biAre determined by the modulation scheme. The channel and rate original expression for determining the modulation mode can be obtained by approximation:
when the modulation method is QPSK, I is 1, a1＝1，b1＝0.6507；
When the modulation mode is 8PSK, I is 2, a1＝0.6130，b1＝0.1681；a2＝0.3855，b1＝0.8992；
When the modulation mode is 16QAM, I is 2, a1＝0.7177，b1＝0.1225；a2＝0.2804，b1＝0.8702；
For the interference which does not obey Gaussian distribution, a Gaussian random variable equivalent to the sum of the Gaussian random variable and the Gaussian noise can be used as approximate Gaussian noise on the premise that the entropy power is not changed. The noise power is then approximated as:
Figure BDA0003607843390000022
preferably, the STAR-RIS assisted multi-user massive SIMO upstream M-order modulation weighted sum rate may be expressed as:
Figure BDA0003607843390000023
Figure BDA0003607843390000024
wherein, the uplink M-order modulation users have K, can be divided into R reflection users and T refraction users, each user is provided with a single antenna, the base station side is provided with S receiving antennas, STAR-RIS has N reflection and transmission units, (.)HRepresenting the conjugate transpose operation of the matrix, | | · | | | represents the L2 norm operation. ω (k) represents the weight of the kth user,
Figure BDA0003607843390000025
representing the channel from STAR-RIS to the kth subscriber,
Figure BDA0003607843390000026
represents the reflection or transmission characteristics of STAR-RIS corresponding to the kth user, when this user is a reflecting user, i.e. k ≦ R, ΘkRepresents thetaR＝diag(θr，1，θr，2，...，θr，N) I.e. the reflection characteristic matrix of STAR-RIS, [ theta ]RThe (n, n) th element
Figure BDA0003607843390000027
Representing the reflection coefficient of the nth cell, j is an imaginary symbol,
Figure BDA0003607843390000028
representing the magnitude of the n-th cell reflection coefficient, phir，nA phase representing the reflection coefficient of the nth cell; when this user is a transmissive user, i.e., k > R, ΘkRepresents thetaT＝diag(θt，1，θt，2，...，θt，N) I.e. the transmission characteristic matrix of STAR-RIS, [ theta ]TThe (n, n) th element
Figure BDA00036078433900000210
Represents the transmission coefficient of the nth cell,
Figure BDA00036078433900000211
represents the amplitude of the transmission coefficient of the nth cell, phit，nRepresenting the phase of the transmission coefficient of the nth cell.
Figure BDA00036078433900000212
Representing the channel between STAR-RIS and the base station antenna,
Figure BDA0003607843390000031
representing the beamforming by the kth user based on transmit power,
Figure BDA0003607843390000032
representing an additive white gaussian noise power.
Typically, the transmit power of a user is limited, and therefore the allocated power for all users should not exceed a given maximum limit. In addition, the reflection coefficient and the transmission coefficient of STAR-RIS should also satisfy the law of conservation of energy, namely:
Figure BDA0003607843390000033
wherein, the joint optimization of the user-side emission power distribution and STAR-RIS reflection and transmission coefficients can adopt an iterative algorithm based on a gradient descent method on manifold: firstly, solving a gradient of an objective function with respect to a variable to be optimized, determining a manifold where the variable to be optimized is located according to constraint conditions satisfied by user emission power, STAR-RIS reflection and transmission coefficients, and calculating a projection of the gradient on a tangent space of the manifold; determining an optimization step length through a linear backtracking method, and moving a variable to be optimized along the projection direction of the gradient on the tangent space according to the determined step length; shrinking values of emission power and STAR-RIS reflection and transmission coefficients deviating from manifold back to manifold; and (4) iterating and alternately implementing the optimization process of each variable until the difference between two adjacent objective function values is smaller than a given threshold value.
Preferably, the uplink M-order modulation weighting and rate optimization problem may be expressed as:
Figure BDA0003607843390000034
Figure BDA0003607843390000035
Figure BDA0003607843390000036
wherein ,INRepresenting an NxN identity matrix, PmaxRepresenting the total transmit power constraint on the user side.
Preferably, the manifold in which the variable to be optimized is located is determined according to the constraint conditions satisfied by the user emission power, STAR-RIS reflection and transmission coefficient, and the projection of the calculated gradient on the tangent space of the manifold can be represented as:
Figure BDA0003607843390000037
Figure BDA0003607843390000038
for both energy partitioning and mode switching modes of STAR-RIS,
Figure BDA0003607843390000039
Figure BDA00036078433900000310
for the time-switch mode of STAR-RIS,
Figure BDA00036078433900000311
Figure BDA00036078433900000312
wherein ,
Figure BDA00036078433900000318
representation real part (·)*Indicating a take conjugate operation, an indicates a hadamard product.
Preferably, in the nth iteration, an optimization step length is determined through a linear backtracking method, and the variable to be optimized is moved along the projection direction of the gradient on the tangent space according to the determined step length, which can be expressed as:
Figure BDA00036078433900000313
Figure BDA00036078433900000314
Figure BDA00036078433900000315
wherein
Figure BDA00036078433900000316
And
Figure BDA00036078433900000317
the representative step size can be determined by a linear backtracking method.
Preferably, the values of the emission power and the STAR-RIS reflectance and transmittance coefficient deviating from the manifold are shrunk back to the manifold, and can be expressed as:
Figure BDA0003607843390000041
for both energy-split and mode-switch modes of STAR-RIS operation,
Figure BDA0003607843390000042
Figure BDA0003607843390000043
for the time-switched mode of STAR-RIS,
Figure BDA0003607843390000044
Figure BDA0003607843390000045
compared with the commonly used multi-user large-scale SIMO uplink M-order modulation transmission optimization scheme assisted by the reconfigurable intelligent reflecting surface, the scheme has the following advantages:
1. the optimization method considers the optimization scheme of M-order modulation time and rate, and simplifies the optimization scheme by adopting an approximate formula, so that an optimization algorithm is designed, the difficulty of problem solving is obviously reduced, and the optimization method has practical significance compared with an algorithm meeting Gaussian distribution input.
2. Compared with the traditional RIS-assisted wireless communication system, the intelligent radio environment in the original half space is expanded to the full space, the intelligent radio environment can serve more users, and the flexibility of the deployment of the intelligent reflecting surface is obviously improved.
3. The method utilizes methods such as manifold optimization and gradient descent method to jointly design the transmitting power distribution at the user side and the reflection coefficient matrix and the transmission coefficient matrix of STAR-RIS, maximizes the uplink M-order modulation weighting and rate of the system, iteratively obtains the suboptimal solution of the original problem, and effectively improves the uplink M-order modulation weighting and rate of the system. The method provided by the invention can obviously reduce the complexity of solving the optimization problem and realizing the physical layer.
4. Description of the drawings
(1) FIG. 1 is a STAR-RIS assisted multi-user SIMO upstream M-order modulation transmission scenario diagram.
(2) FIG. 2 is a STAR-RIS assisted multi-user SIMO upstream M-order modulation weighting and rate optimization algorithm flow chart.
5. Examples of specific embodiments
To further illustrate the method of practicing the present invention, an exemplary embodiment is given below. This example is merely representative of the principles of the present invention and does not represent any limitation of the present invention.
(1) STAR-RIS assisted multi-user large-scale SIMO uplink M-order modulation transmission scenario
The uplink M-order modulation users have K numbers, and can be divided into R reflection users and T refraction users, each user is provided with a single antenna, the base station side is provided with S receiving antennas, and STAR-RIS has N numbers of reflection and transmission units. The above fig. 1 gives a schematic diagram of the system transmission. The original expression form of the M-order modulation and rate is complex, and the M-order modulation and rate is difficult to be solved optimally. Therefore, it can be considered to replace it with an approximate formula, namely:
Figure BDA0003607843390000051
where C represents the channel capacity, i.e., the maximum uplink and rate. M represents the modulation order, log (-) represents the logarithmic operation, and γ represents the signal-to-noise ratio. I, aiAnd biAre determined by the modulation scheme. The channel and rate original expression for determining the modulation mode can be obtained by approximation:
when the modulation mode is QPSK, I is 1, a1＝1，b1＝0.6507；
When the modulation mode is 8PSK, I is 2, a1＝0.6130，b1＝0.1681；a2＝0.3855，b1＝0.8992；
When the modulation mode is 16QAM, I is 2, a1＝0.7177，b1＝0.1225；a2＝0.2804，b1＝0.8702；
For the interference which does not obey Gaussian distribution, a Gaussian random variable equivalent to the sum of the Gaussian random variable and the Gaussian noise can be used as approximate Gaussian noise on the premise that the entropy power is not changed. The STAR-RIS assisted multi-user massive SIMO upstream M-order modulation weighted sum rate can be expressed as:
Figure BDA0003607843390000052
wherein ,
Figure BDA0003607843390000053
Figure BDA0003607843390000054
each user is equipped with a single antenna, S receiving antennas are equipped at the base station side, STAR-RIS has N reflection and transmission units ·HRepresents the conjugate transpose operation of the matrix, | | | | - | represents the L2 norm operation. ω (k) represents the weight of the kth user,
Figure BDA0003607843390000055
representing the channel from STAR-RIS to the kth subscriber,
Figure BDA0003607843390000056
represents the reflection or transmission characteristic of STAR-RIS corresponding to the kth user, when this user is a reflecting user, i.e., k ≦ R, ΘkRepresents thetaR＝diag(θr，1，θr，2，...，θr，N) I.e. the reflection characteristic matrix of STAR-RIS, [ theta ]RThe (n, n) th element
Figure BDA0003607843390000057
Representing the reflection coefficient of the nth cell, j is an imaginary symbol,
Figure BDA0003607843390000058
represents the magnitude of the n-th cell reflection coefficient, phir，nA phase representing the reflection coefficient of the nth cell; when the user is a transmissive user, i.e. k>When R is, thetakRepresents thetaT＝diag(θt，1，θt，2，...，θt，N) I.e. the transmission characteristic matrix of STAR-RIS, [ theta ]TThe (n, n) th element
Figure BDA0003607843390000059
Represents the transmission coefficient of the nth cell,
Figure BDA00036078433900000510
represents the amplitude of the transmission coefficient of the nth cell, phit，nRepresenting the phase of the transmission coefficient of the nth cell.
Figure BDA00036078433900000511
Representing the channel between STAR-RIS and the base station antenna,
Figure BDA00036078433900000512
representing the beamforming by the kth user based on transmit power,
Figure BDA00036078433900000513
representing an additive white gaussian noise power.
Typically, the transmit power of a user is limited, and therefore the allocated power for all users should not exceed a given maximum limit. In addition, the reflection coefficient and the transmission coefficient of STAR-RIS should also satisfy the law of conservation of energy, namely:
Figure BDA00036078433900000514
the uplink M-order modulation weighting and rate optimization problem may be expressed as:
Figure BDA0003607843390000061
Figure BDA0003607843390000062
Figure BDA0003607843390000063
wherein ,INRepresenting an NxN identity matrix, PmaxRepresenting the total transmit power constraint on the user side.
The invention provides an uplink M-order modulation weighting and rate optimization method with low complexity, which can obtain a suboptimal solution or a local optimal solution of the original problem.
(2) The first algorithm is as follows: STAR-RIS assisted multi-user massive SIMO uplink M-order modulation weighting and rate optimization algorithm FIG. 2 shows a flow chart of an uplink M-order modulation weighting and rate optimization algorithm, and detailed optimization steps are listed below.
Step 1: setting P, theta according to the channel conditions and the constraints satisfied by the power allocation and the chosen STAR-RIS mode of operationRAnd thetaTIs initialized to 0, and the number of iterations n is initialized.
Step 2: determining the manifold where the variable to be optimized is located according to the constraint conditions met by the user emission power, STAR-RIS reflection and transmission coefficient, and calculating the projection of the gradient on the tangent space of the manifold. The projection of each variable to be optimized on the tangent space of the manifold can be expressed as:
Figure BDA0003607843390000064
Figure BDA0003607843390000065
for both energy-split and mode-switch modes of STAR-RIS operation,
Figure BDA0003607843390000066
Figure BDA0003607843390000067
for the time-switched mode of STAR-RIS,
Figure BDA0003607843390000068
Figure BDA0003607843390000069
wherein ,
Figure BDA00036078433900000610
representation taking the real part, (.)*Indicating a take conjugate operation, an indicates a hadamard product.
And 3, step 3: in the nth iteration, determining an optimization step length by a linear backtracking method, and moving the variable to be optimized along the projection direction of the gradient on the tangent space according to the determined step length, which can be represented as:
Figure BDA00036078433900000611
Figure BDA00036078433900000612
Figure BDA00036078433900000613
wherein
Figure BDA00036078433900000614
And
Figure BDA00036078433900000615
the representative step size can be determined by a linear backtracking method.
And 4, step 4: shrinking the values of the off-manifold emission power and the STAR-RIS reflection and transmission coefficients back onto the manifold can be expressed as:
Figure BDA0003607843390000071
for both energy partitioning and mode switching modes of STAR-RIS,
Figure BDA0003607843390000072
Figure BDA0003607843390000073
for the time-switched mode of STAR-RIS,
Figure BDA0003607843390000074
Figure BDA0003607843390000075
and 5: calculating a new value C of the objective functionn+1If the difference between the target function value and the last iteration is smaller than the set threshold value, terminating the iteration; otherwise, adding 1 to the iteration number and returning to the step 2.

Claims (6)

1. An intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization method. Aiming at the characteristics of multi-user large-scale SIMO uplink M-order modulation communication under the scene that a direct path is blocked, the invention considers the limit of the transmitting power at the user side and the constraint condition required to be met by the intelligent omnidirectional surface device unit, and improves the uplink weighting and the rate of the system by jointly optimizing the beam forming at the user side and the reflection coefficient and the transmission coefficient of the intelligent super surface. The invention provides an algorithm based on manifold optimization and a gradient descent method to jointly optimize beam forming at a user side and a reflection coefficient and transmission coefficient matrix of an intelligent super surface, so that multi-user large-scale SIMO uplink M-order modulation weighting and rate under a scene that a direct beam is shielded can be effectively improved, and the complexity of solving an optimization problem and realizing a physical layer is reduced.
Wherein, the joint optimization of the user-side emission power distribution and STAR-RIS reflection and transmission coefficients can adopt an iterative algorithm based on a gradient descent method on manifold: firstly, solving a gradient of an objective function with respect to a variable to be optimized, determining a manifold where the variable to be optimized is located according to constraint conditions met by user emission power, STAR-RIS reflection and transmission coefficients, and calculating a projection of the gradient on a tangent space of the manifold; determining an optimization step length through a linear backtracking method, and moving a variable to be optimized along the projection direction of the gradient on the tangent space according to the determined step length; shrinking values of the emission power deviating from the manifold and STAR-RIS reflection and transmission coefficients back to the manifold; and (4) carrying out the optimization processes of the variables iteratively and alternately until the difference between two adjacent objective function values is smaller than a given threshold value.
2. The intelligent omni-directional surface assisted multi-user massive SIMO upstream M-order modulation weighting and rate optimization algorithm of claim 1, wherein the STAR-RIS assisted multi-user massive SIMO upstream M-order modulation weighting and rate can be expressed as:
Figure FDA0003607843380000011
wherein ,
Figure FDA0003607843380000012
Figure FDA0003607843380000013
the uplink M-order modulation users have K numbers, can be divided into R reflection users and T refraction users, each user is provided with a single antenna, the base station side is provided with S receiving antennas, and STAR-RIS has N reflection and transmission units, (.)HRepresents the conjugate transpose operation of the matrix, | | | | - | represents the L2 norm operation. ω (k) represents the weight of the kth user,
Figure FDA0003607843380000014
representing the channel from STAR-RIS to the kth user,
Figure FDA0003607843380000015
representsThe reflection or transmission characteristic of STAR-RIS corresponding to the kth user, when this user is a reflecting user, i.e. k ≦ R, ΘkRepresents thetaR＝diag(θr，1，θr，2，...，θr，N) I.e. the reflection characteristic matrix of STAR-RIS, [ theta ]RThe (n, n) th element
Figure FDA0003607843380000016
Representing the reflection coefficient of the nth cell, j is an imaginary symbol,
Figure FDA0003607843380000017
representing the magnitude of the n-th cell reflection coefficient, phir，nA phase representing the reflection coefficient of the nth cell; when the user is a transmissive user, i.e. k>When R is, thetakRepresents thetaT＝diag(θt，1，θt，2，...，θt，N) I.e. the transmission characteristic matrix of STAR-RIS, [ theta ]TThe (n, n) th element
Figure FDA0003607843380000018
Represents the transmission coefficient of the nth cell,
Figure FDA0003607843380000019
represents the amplitude of the transmission coefficient of the nth cell, phit，nRepresenting the phase of the transmission coefficient of the nth cell.
Figure FDA00036078433800000110
Representing the channel between STAR-RIS and the base station antenna,
Figure FDA00036078433800000111
representing the beamforming by the kth user based on transmit power,
Figure FDA00036078433800000112
representing an additive white gaussian noise power.
I，aiAnd biAre all made by the modulation partyAnd (4) determining the formula. The channel and rate primitive expressions for determining the modulation mode are approximated to obtain:
when the modulation method is QPSK, I is 1, a1＝1，b1＝0.6507；
When the modulation mode is 8PSK, I is 2, a1＝0.6130，b1＝0.1681；a2＝0.3855，b1＝0.8992；
When the modulation mode is 16QAM, I is 2, a1＝0.7177，b1＝0.1225；a2＝0.2804，b1＝0.8702；
Typically, the transmit power of a user is limited, and therefore the allocated power for all users should not exceed a given maximum limit. In addition, the reflection coefficient and transmission coefficient of STAR-RIS should also satisfy the law of conservation of energy, namely:
Figure FDA00036078433800000113
3. the intelligent omni-directional surface assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization algorithm of claim 1, wherein the uplink M-order modulation weighting and rate optimization problem can be expressed as:
Figure FDA0003607843380000021
Figure FDA0003607843380000022
Figure FDA0003607843380000023
wherein ,INRepresenting an NxN identity matrix, PmaxRepresenting hair at user sideAnd (4) constraint of total power.
4. The intelligent omnidirectional surface-assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization algorithm according to claim 1, wherein the manifold where the variable to be optimized is located is determined according to the constraint conditions satisfied by the user emission power, STAR-RIS reflection and transmission coefficients, and the projection of the calculated gradient on the tangent space of the manifold can be represented as:
Figure FDA0003607843380000024
Figure FDA0003607843380000025
for both energy-split and mode-switch modes of STAR-RIS operation,
Figure FDA0003607843380000026
Figure FDA0003607843380000027
for the time-switched mode of STAR-RIS,
Figure FDA0003607843380000028
Figure FDA0003607843380000029
wherein ,
Figure FDA00036078433800000210
to show to get the factAnd (c)*Indicating a take conjugate operation, an indicates a hadamard product.
5. The intelligent omni-directional plane assisted multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization algorithm according to claim 1, wherein in the nth iteration, the optimization step length is determined by a linear backtracking method, and the variable to be optimized is moved along the projection direction of the gradient on the tangent space according to the determined step length, which can be expressed as:
Figure FDA00036078433800000211
Figure FDA00036078433800000212
Figure FDA00036078433800000213
wherein
Figure FDA00036078433800000214
And
Figure FDA00036078433800000215
the representative step size can be determined by a linear backtracking method.
6. The intelligent omnidirectional surface-aided multi-user large-scale SIMO uplink M-order modulation weighting and rate optimization algorithm of claim 1, wherein the narrowing of the values of the emission power and the STAR-RIS reflection and transmission coefficients that deviate from the manifold back onto the manifold can be expressed as:
Figure FDA00036078433800000216
for both energy partitioning and mode switching modes of STAR-RIS,
Figure FDA0003607843380000031
Figure FDA0003607843380000032
for the time-switched mode of STAR-RIS,
Figure FDA0003607843380000033
Figure FDA0003607843380000034
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