CN112822703B - Intelligent reflecting surface assisted performance gain optimization method for non-orthogonal multiple access system - Google Patents

Intelligent reflecting surface assisted performance gain optimization method for non-orthogonal multiple access system Download PDF

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CN112822703B
CN112822703B CN202110150180.1A CN202110150180A CN112822703B CN 112822703 B CN112822703 B CN 112822703B CN 202110150180 A CN202110150180 A CN 202110150180A CN 112822703 B CN112822703 B CN 112822703B
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谭艺枝
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Guangdong University of Technology
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Abstract

The invention provides a performance gain optimization method of an intelligent reflector-assisted non-orthogonal multiple access system, which is used for carrying out channel estimation on a cascade channel in the established intelligent reflector-assisted non-orthogonal multiple access system; under the premise of different decoding orders, taking the average effective signal-to-interference-and-noise ratio of the maximized user as an optimization target, carrying out combined optimization on the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix, and respectively obtaining the maximum value of the average effective signal-to-interference-and-noise ratio of the user under the corresponding decoding order and the local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix corresponding to the maximum value; and comparing the maximum values of the user average effective signal to interference plus noise ratios in different decoding orders, and outputting the local optimal solution of the corresponding channel estimation vector, power distribution coefficient and reflection coefficient matrix as the final local optimal solution when the numerical value is larger. The invention can greatly optimize the performance gain of the non-orthogonal multiple access system, thereby improving the transmission performance such as the throughput and the like of the system.

Description

Intelligent reflecting surface assisted performance gain optimization method for non-orthogonal multiple access system
Technical Field
The invention relates to the technical field of wireless communication, in particular to an intelligent reflector assisted performance gain optimization method for a non-orthogonal multiple access system.
Background
Non-Orthogonal Multiple Access (NOMA) Access technology, as a Multiple Access technology with great potential for future mobile networks, is a key technology of the later 5G communication, and unlike the traditional OMA (OMA) technology, NOMA allows Multiple users to share the same resources of time, frequency, space and the like through superposition coding at a transmitting end and Serial Interference Cancellation (SIC) at a receiving end, thereby significantly improving the spectrum efficiency of the system.
Chinese application CN108601088A, published in 9, 28, 2018, provides a cooperative communication method based on non-orthogonal multiple access, including the following steps: a relay node receives a source node signal and channel state information; the relay node decodes the source node signal by utilizing continuous interference elimination to obtain a decoded signal; carrying out superposition coding on the decoded signals according to the power distribution coefficient, and simultaneously sending the superposed signals to a plurality of destination nodes by the relay node and the plurality of destination nodes through downlink non-orthogonal multiple access; the destination node utilizes continuous interference elimination to decode the superposed signal and recover the information; calculating the transmitting power and power distribution coefficient of all nodes according to the channel state information and user requirements, and sending the obtained information to the relay node by a plurality of source nodes and the relay node through uplink non-orthogonal multiple access; the invention uses the non-orthogonal multiple access technology, satisfies the user rate, minimizes the total consumption of the system, and effectively enlarges the access of the user number, but the technical scheme provided by the patent only realizes the aim of multi-user shared access from an ideal technical level, and has poor effect of optimizing the performance gain of the system.
An Intelligent Reflection Surface (IRS) has excellent spectral efficiency and energy efficiency performance, and is also an emerging technology of the last 5G communication system. The intelligent reflecting surface is composed of a large number of passive reflecting elements, each reflecting element can independently change the reflection phase shift of an incident signal, and the intelligent reflecting surface can flexibly set the transmission of the reflected signal by adjusting the reflection phase shift so as to achieve the communication targets of improving the received signal power, reducing interference, safe transmission and the like. In practical application, the intelligent reflecting surface is fundamentally different from the traditional relay, the intelligent reflecting surface is used as a reconfigurable diffuser, special energy sources are not needed for decoding, channel estimation and transmission, signals are reflected in a full-duplex and noiseless mode without self-interference, only passive reflecting components with low energy consumption are used, and energy consumption and hardware deployment cost are greatly saved compared with the traditional relay. Therefore, the adoption of the intelligent reflector to assist wireless communication is considered as a promising, efficient and green solution for communication of the internet of things. In a typical two-user non-orthogonal multiple access system with transmission assisted by an intelligent reflecting surface, a serial interference cancellation receiver of a strong user performs serial interference cancellation by using estimated channel state information, and channel estimation introduces estimation errors, which causes signal-to-interference-and-noise ratio (SINR) of the strong user to be reduced in a data transmission stage; in addition, the signal to interference and noise ratio of the strong users also depends on the power allocation strategy. Therefore, it is very necessary to jointly optimize channel estimation and power allocation in the NOMA system with the aid of the intelligent reflecting surface.
Disclosure of Invention
The invention provides a method for optimizing the performance gain of a non-orthogonal multiple access system assisted by an intelligent reflector, which aims to solve the problem of how to optimize the performance gain of the system in the non-orthogonal multiple access system assisted by the intelligent reflector for transmission, and improves the performance gain of the non-orthogonal multiple access system.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
the invention provides an intelligent reflector assisted performance gain optimization method for a non-orthogonal multiple access system, which comprises the following steps:
s1: establishing an intelligent reflecting surface assisted non-orthogonal multiple access system, wherein the system comprises a base station, an intelligent reflecting surface, a first user and a second user; the base station, the intelligent reflecting surface, the first user and the second user form a cascade channel of the base station, the intelligent reflecting surface and the user; the intelligent reflecting surface comprises a reflection coefficient matrix;
s2: the base station sends pilot signals to a first user and a second user after the pilot signals are reflected by an intelligent reflecting surface, and the first user and the second user carry out channel estimation on the cascade channel according to the received pilot signals; the channel estimation process comprises a channel estimation vector;
s3: the base station sends the superposition coded signals, the superposition coded signals are transmitted to a first user and a second user after being reflected by the intelligent reflecting surface, and the first user and the second user decode the received superposition coded signals according to different decoding orders after receiving the superposition coded signals; the superposition coding signal comprises a power distribution coefficient;
s4: respectively performing joint optimization on a channel estimation vector, a power distribution coefficient and a reflection coefficient matrix by taking the average effective signal-to-interference-and-noise ratio of the first user as a maximum value as an optimization target on the premise of different decoding orders;
s5: respectively calculating the maximum value of the average effective signal-to-interference-and-noise ratio of the first user in the current decoding order and the corresponding local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix;
s6: and comparing the maximum values of the first user average effective signal-to-interference-and-noise ratios in different decoding orders, and outputting the local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix corresponding to the first user average effective signal-to-interference-and-noise ratio with the maximum value as the final local optimal solution.
Preferably, in S1, various signals sent by the base station are reflected by the intelligent reflecting surface and then transmitted to the first user and the second user simultaneously; the concatenated channel has channel state information including:
the reflection coefficient matrix theta of the intelligent reflecting surface is an M multiplied by M complex matrix, wherein M is the number of passive reflecting elements contained in the intelligent reflecting surface;
the channel response coefficient h from the base station to the intelligent reflecting surface is a vector, the obedience mean value is zero covariance matrix and is lambda 2 Gaussian distribution of I, where λ 2 A covariance matrix determinant representing a channel response coefficient h, wherein I is a vector and represents an identity matrix;
the channel response coefficient from the intelligent reflecting surface to the ith user is g i ,i∈K＝{1,2}，g i As a vector, obey a mean value of zero covariance matrix of
Figure BDA0002932450810000031
Wherein K represents a set of integers,
Figure BDA0002932450810000032
representing the channel response coefficient g i I is a vector, and represents an identity matrix.
Preferably, in S2, the specific method for channel estimation is as follows:
d for cascade channel of base station-intelligent reflector-user i To show that:
d i ＝g i Θh，i∈K＝{1，2} (1)
the pilot signal sent by the base station is t, and the pilot signal received by the ith user is z i And then:
Figure BDA0002932450810000033
wherein z is i In the form of a vector, the vector,
Figure BDA0002932450810000034
is vector, represents the additive white Gaussian noise of the ith user, and obeys the variance of zero covariance matrix as sigma 2 Gaussian distribution of I, where σ 2 Representing additive white gaussian noise
Figure BDA0002932450810000035
The covariance matrix determinant of (1), wherein I is a vector and represents an identity matrix;
the ith user is based on the received pilot signal z i For cascade channel d i Make an estimation, as
Figure BDA0002932450810000036
Then:
Figure BDA0002932450810000037
wherein the content of the first and second substances,
Figure BDA0002932450810000038
for the channel estimation of the ith user,
Figure BDA0002932450810000039
estimating vector v for ith user i The conjugate of (2) is transposed vector.
Preferably, in S3, if the superposition coded signal sent by the base station is denoted as y:
Figure BDA00029324508100000310
wherein s is 1 For signals sent to the first user, s 2 For signals transmitted to the second user, P is the transmit power of the base station, α 1 Representing the power distribution coefficient, alpha, of the first user 2 Represents the power distribution coefficient of the second user and satisfies alpha 1 +α 2 ＝1。
Preferably, in S3, the superposition coded signal received by the user is denoted as y i Then:
Figure BDA0002932450810000041
wherein n is i Additive Gaussian noise representing the ith user, subject to mean of zero variance of
Figure BDA0002932450810000042
A gaussian distribution of (a).
Preferably, in S3, the decoding order comprises a first decoding order and a second decoding order; the first decoding order is: decoding the second user first, and then decoding the first user; the second decoding order is: the first user is decoded first and then the second user is decoded.
Preferably, in S4, taking maximizing the first user average effective signal-to-interference-and-noise ratio as an optimization objective, under the premise of the first decoding order, the objective function and the constraint condition are:
Figure BDA0002932450810000043
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002932450810000044
decoding a signal s for a first user 1 The average effective signal-to-interference-and-noise ratio of (c),
Figure BDA0002932450810000045
decoding signal s for ith user 2 Is of the mean effective signal to interference plus noise ratio, gamma 0 Is the average effective signal to interference plus noise ratio threshold, v i Is a vector, representing the channel estimation vector of the ith user; h is the reflection coefficient of the light beam,
Figure BDA0002932450810000046
theta is a reflection coefficient matrix of the intelligent reflecting surface,
Figure BDA0002932450810000047
is a conjugate transpose matrix of Θ; the constraint condition is that the average effective signal to interference plus noise ratio of the second user is more than or equal to the average effective signal to interference plus noise ratio threshold value.
Preferably, said first user decoded signal s 1 Average effective signal to interference plus noise ratio of
Figure BDA0002932450810000048
The specific calculation process is as follows:
on the premise of the first decoding order, the first user decodes the signal s, which is obtained by equation (4) 2 Is recorded as the average effective SINR
Figure BDA0002932450810000049
Then:
Figure BDA00029324508100000410
wherein E {. Is } represents an averaging operation, d 1 Is a cascade channel of a base station-an intelligent reflecting surface-a first user,
Figure BDA00029324508100000411
for the first user pair d 1 The channel estimation of (2) is performed,
Figure BDA00029324508100000412
variance of additive gaussian noise for the user;
substituting formulae (1), (2), and (3) into formula (6) yields:
Figure BDA00029324508100000413
Figure BDA00029324508100000414
wherein λ is 2 A covariance matrix determinant of a channel response coefficient h from the base station to the intelligent reflecting surface; sigma 2 Representing additive white gaussian noise
Figure BDA00029324508100000415
The covariance matrix determinant of (a); vec (-) is a vectorization function; v. of 1 Estimating a vector for a channel of a first user;
Figure BDA00029324508100000416
is v is 1 The conjugate transpose vector of (1); t is a vector and represents a pilot signal transmitted by the base station;
Figure BDA00029324508100000417
a conjugate transpose vector representing t;
Figure BDA00029324508100000418
is the variance of the additive gaussian noise of the user; g 1 Is a vector and represents the response coefficient of the intelligent reflecting surface to the first user;
Figure BDA00029324508100000419
is a vector, representing g 1 Conjugation of (1);
Figure BDA00029324508100000420
the kronecker product is calculated; omega 1 Is a vector, representing g 1 And
Figure BDA0002932450810000051
the average value of the kronecker product;
successful decoding of signal s by the first user 2 Then, a serial interference elimination method is adopted to obtain a first user decoding signal s 1 Average effective signal to interference and noise ratio of
Figure BDA0002932450810000052
Namely:
Figure BDA0002932450810000053
the same thing can be used to obtain the second user decoding signal s 2 Average effective signal to interference and noise ratio of
Figure BDA0002932450810000054
Namely:
Figure BDA0002932450810000055
Figure BDA0002932450810000056
wherein v is 2 A vector is estimated for the channel of the first user,
Figure BDA0002932450810000057
is v is 2 Conjugate transposed vector of g 2 Is a vector, represents the response coefficient of the intelligent reflecting surface to the first user,
Figure BDA0002932450810000058
is a vector, representing g 2 Conjugated of (e), ω 2 Is g 2 And
Figure BDA0002932450810000059
average of kronecker products.
Preferably, in S5, the method adopted when calculating the maximum value of the average effective snr of the first user in the current decoding order is an alternating iteration method and an interior point method;
since maximizing the mean effective snr of the first user is a function of the channel estimation vector v i Power distribution coefficient alpha i The non-convex optimization problem highly coupled with the reflection coefficient H is difficult to directly obtain an optimal solution, so that the optimization problem is converted into a convex optimization problem based on an alternating iteration method, and the inner point method is used for solving: firstly, splitting the original optimization problem of three variables into a fixed variable, and solving the other two variables in an iterative manner; fix the other twoEach variable is solved by iteration; and alternately carrying out the two iterative solving processes until convergence, and solving a channel estimation vector, a power distribution coefficient and a reflection coefficient.
Preferably, the specific process of calculating the maximum value of the mean effective snr of the first user in the current decoding order by using the alternating iteration method and the interior point method is as follows:
on the premise of the first decoding order, in the case where the reflection coefficient H is known, the auxiliary variable μ is set 1 ＝1/α 1 The constant of character k i ＝λ 2 ω i vec (H), matrix constant
Figure BDA00029324508100000510
Character constant
Figure BDA00029324508100000511
And introducing a relaxation variable τ, equivalent of equation (5):
Figure BDA00029324508100000512
Figure BDA00029324508100000513
Figure BDA00029324508100000514
the method is simplified as follows:
Figure BDA0002932450810000061
solving equation (11) by using an algorithm based on a constrained concave-convex process
Figure BDA0002932450810000062
Figure BDA0002932450810000063
ρ(μ 1 )＝-lnμ 1 The first order Taylor expansion is expressed as:
Figure BDA0002932450810000064
Figure BDA0002932450810000065
Figure BDA0002932450810000066
wherein the content of the first and second substances,
Figure BDA0002932450810000067
and
Figure BDA0002932450810000068
are each v 1 、τ、v i And mu 1 Is determined by the probability value of (a),
Figure BDA0002932450810000069
is that
Figure BDA00029324508100000610
The conjugate of (a) the transposed vector (v),
Figure BDA00029324508100000611
is a vector
Figure BDA00029324508100000612
The conjugate transpose vector (c) of (a), re { · } represents the operation of the real part, the equation (11) is converted into a convex optimization problem, and in the (l + 1) th iteration based on the constrained concave-convex process algorithm, the optimization problem is represented as:
Figure BDA00029324508100000613
Figure BDA00029324508100000614
Figure BDA00029324508100000615
wherein, l represents the number of iterations,
Figure BDA00029324508100000616
for the solution of the equations (12 a), (12 b) and (12 c) in the first iteration, when the algorithm converges, the equations (12 a), (12 b) and (12 c) are solved by the interior point method to obtain the channel estimation vector v i And the power distribution coefficient alpha 1 A local optimal solution of;
at v i And alpha i In the known case, let character constants
Figure BDA00029324508100000617
Character constant
Figure BDA00029324508100000618
Character constant
Figure BDA00029324508100000619
Character constant
Figure BDA00029324508100000620
Character constant
Figure BDA00029324508100000621
Character constant
Figure BDA00029324508100000622
Figure BDA00029324508100000623
And introducing a relaxation variable epsilon, equivalent of formula (5):
max H,ε≥0 ε (13a)
Figure BDA00029324508100000624
Figure BDA00029324508100000625
equations (13 a), (13 b) and (13 c) are solved by using a constrained concave-convex process algorithm
Figure BDA00029324508100000626
The first order Taylor expansion is expressed as:
Figure BDA0002932450810000071
wherein the content of the first and second substances,
Figure BDA0002932450810000072
is a feasible value of epsilon, the equations (13 a), (13 b) and (13 c) are converted into a convex optimization problem, and in the (l + 1) th iteration based on the constrained concave-convex process algorithm, the optimization problem is expressed as:
max H,ε≥0 ε (14a)
Figure BDA0002932450810000073
Figure BDA0002932450810000074
wherein l represents the number of iterations, point
Figure BDA0002932450810000075
For the solutions of the equations (14 a), (14 b) and (14 c) at the l-th iteration, when the algorithm converges, the equations (14 a), (14 b) and (14 c) are solved by the interior point method to obtain the local optimal solution of the reflection coefficient H, based on which
Figure BDA0002932450810000076
By singular valuesAnd solving the H through decomposition to obtain a local optimal solution of the reflection coefficient matrix theta.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention carries out channel estimation on a cascade channel in an intelligent reflector assisted non-orthogonal multiple access system, under the premise of different decoding orders, takes the average effective signal-to-interference-and-noise ratio of the maximized user as an optimization target, carries out joint optimization on a channel estimation vector, a power distribution coefficient and a reflection coefficient matrix, and respectively obtains the maximum value of the average effective signal-to-interference-and-noise ratio of the user under the corresponding decoding order and the corresponding local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix; and comparing the maximum values of the user average effective signal-to-interference-and-noise ratios in different decoding orders, and outputting the local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix corresponding to the user average effective signal-to-interference-and-noise ratio with the maximum value as the final local optimal solution. The invention optimizes the performance gain of the non-orthogonal multiple access system greatly by carrying out combined optimization on the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix, thereby improving the transmission performance such as the throughput and the like of the system.
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Fig. 1 is a flowchart of a method for optimizing performance gain of an intelligent reflector assisted non-orthogonal multiple access system according to embodiment 1;
fig. 2 is a schematic diagram of the intelligent reflector-assisted non-orthogonal multiple access system according to embodiment 1.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The embodiment provides a performance gain optimization method for an intelligent reflector assisted non-orthogonal multiple access system, as shown in fig. 1, the method includes the following steps:
s1: establishing an intelligent reflector assisted non-orthogonal multiple access system, as shown in fig. 2, the system comprising a base station, an intelligent reflector, a first user and a second user; the base station, the intelligent reflecting surface, the first user and the second user form a cascade channel of the base station, the intelligent reflecting surface and the user; the intelligent reflecting surface comprises a reflection coefficient matrix;
s2: the base station sends pilot signals to a first user and a second user after the pilot signals are reflected by an intelligent reflecting surface, and the first user and the second user carry out channel estimation on the cascade channel according to the received pilot signals; the channel estimation process comprises a channel estimation vector;
s3: the base station sends the superposition coded signals, the superposition coded signals are transmitted to a first user and a second user after being reflected by the intelligent reflecting surface, and the first user and the second user decode the received superposition coded signals according to different decoding orders after receiving the superposition coded signals; the superposition coding signal comprises a power distribution coefficient;
s4: respectively performing joint optimization on a channel estimation vector, a power distribution coefficient and a reflection coefficient matrix by taking the average effective signal-to-interference-and-noise ratio of the first user as a maximum value as an optimization target on the premise of different decoding orders;
s5: respectively calculating the maximum value of the average effective signal-to-interference-and-noise ratio of the first user in the current decoding order and the corresponding local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix;
s6: and comparing the maximum values of the average effective signal-to-interference-and-noise ratios of the first users in different decoding orders, and outputting the local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix corresponding to the average effective signal-to-interference-and-noise ratio of the first user with the maximum value as the final local optimal solution.
In the S1, various signals sent by the base station are reflected by the intelligent reflecting surface and then transmitted to the first user and the second user simultaneously; the concatenated channel has channel state information including:
the reflection coefficient matrix theta of the intelligent reflecting surface is an M multiplied by M complex matrix, wherein M is the number of passive reflecting elements contained in the intelligent reflecting surface;
the channel response coefficient h from the base station to the intelligent reflecting surface is a vector, the obedience mean value is zero covariance matrix and is lambda 2 Gaussian distribution of I, where λ 2 A covariance matrix determinant representing a channel response coefficient h, wherein I is a vector and represents an identity matrix;
the channel response coefficient from the intelligent reflecting surface to the ith user is g i ,i∈K＝{1,2}，g i As a vector, obey a mean value of zero covariance matrix of
Figure BDA0002932450810000091
Wherein K represents a set of integers,
Figure BDA0002932450810000092
representing the channel response coefficient g i I is a vector, representing an identity matrix.
In S2, the specific method of channel estimation is:
d for cascade channel of base station-intelligent reflector-user i To show that:
d i ＝g i Θh，i∈K＝{1，2} (1)
the pilot signal sent by the base station is t, and the pilot signal received by the ith user is z i Then:
Figure BDA0002932450810000093
wherein z is i In the form of a vector, the vector,
Figure BDA0002932450810000094
is a vector, representing the sum of the i-th userWhite Gaussian noise, obeying variance as zero covariance matrix as sigma 2 Gaussian distribution of I, where σ 2 Representing additive white gaussian noise
Figure BDA0002932450810000095
The covariance matrix determinant of (1), wherein I is a vector and represents an identity matrix; the length of the pilot signal t in this embodiment is 8;
the ith user is based on the received pilot signal z i For cascade channel d i Make an estimation, as
Figure BDA0002932450810000096
Then:
Figure BDA0002932450810000097
wherein the content of the first and second substances,
Figure BDA0002932450810000098
for the channel estimation of the ith user,
Figure BDA0002932450810000099
channel estimation vector v for ith user i The conjugate of (2) is transposed vector.
In S3, if the superposition coded signal sent by the base station is denoted as y:
Figure BDA00029324508100000910
wherein s is 1 For signals sent to the first user, s 2 For signals transmitted to the second user, P is the transmit power of the base station, α 1 Representing the power distribution coefficient, alpha, of the first user 2 Represents the power distribution coefficient of the second user and satisfies alpha 1 +α 2 ＝1。
In S3, the superposition coding signal received by the user is marked as y i And then:
Figure BDA00029324508100000911
wherein n is i Additive Gaussian noise representing the ith user, subject to mean of zero variance of
Figure BDA00029324508100000912
A gaussian distribution of (a).
In the S3, the decoding order comprises a first decoding order and a second decoding order; the first decoding order is: decoding the second user first, and then decoding the first user; the second decoding order is: firstly, decoding a first user, and then decoding a second user;
the decoding rule of the non-orthogonal multiple access system is to perform ascending order according to the channel gain of each user, and the ascending order is used as the decoding order of the system. After each user receives the information sent by the base station, serial interference elimination is sequentially executed according to the decoding order to delete the user information before the decoding order, so that the achievable rate of the user is improved by eliminating the interference, and the decoding order is an important influence factor influencing the performance of the non-orthogonal multiple access system.
In S4, the maximum first user average effective snr is taken as an optimization objective, and on the premise of the first decoding order, the objective function and the constraint condition are:
Figure BDA0002932450810000101
wherein the content of the first and second substances,
Figure BDA0002932450810000102
decoding a signal s for a first user 1 The average effective signal-to-interference-and-noise ratio of (2),
Figure BDA0002932450810000103
decoding signal s for ith user 2 Of (a) is a mean effective signal to interference plus noise ratio, gamma 0 Is the average effective signal to interference plus noise ratio threshold, v i Is a vector, represents the ith useA channel estimation vector of the user; h is the reflection coefficient of the light beam,
Figure BDA0002932450810000104
theta is a reflection coefficient matrix of the intelligent reflecting surface,
Figure BDA0002932450810000105
is a conjugate transpose matrix of Θ; the constraint condition is that the average effective signal to interference plus noise ratio of the second user is more than or equal to the average effective signal to interference plus noise ratio threshold value.
Said first user decoded signal s 1 Average effective signal to interference plus noise ratio of
Figure BDA0002932450810000106
The specific calculation process is as follows:
on the premise of the first decoding order, the first user decodes the signal s, which is obtained by equation (4) 2 Is recorded as the average effective signal-to-interference-and-noise ratio
Figure BDA0002932450810000107
Then:
Figure BDA0002932450810000108
wherein E {. Is } represents an averaging operation, d 1 Is a cascade channel of a base station-an intelligent reflecting surface-a first user,
Figure BDA0002932450810000109
for the first user pair d 1 The channel estimation of (2) is performed,
Figure BDA00029324508100001010
variance of additive gaussian noise for the user;
substituting the formulas (1), (2) and (3) into the formula (6) to obtain:
Figure BDA00029324508100001011
Figure BDA00029324508100001012
wherein λ is 2 A covariance matrix determinant of a channel response coefficient h from the base station to the intelligent reflecting surface; sigma 2 Representing additive white gaussian noise
Figure BDA00029324508100001013
The covariance matrix determinant of (a); vec (-) is a vectorization function; v. of 1 Estimating a vector for a channel of a first user;
Figure BDA00029324508100001014
is v is 1 The conjugate transpose vector of (1); t is a vector and represents a pilot signal transmitted by a base station;
Figure BDA00029324508100001015
a conjugate transposed vector representing t;
Figure BDA00029324508100001016
is the variance of the additive gaussian noise of the user; g 1 Is a vector and represents the response coefficient of the intelligent reflecting surface to the first user;
Figure BDA00029324508100001017
is a vector, representing g 1 Conjugation of (1);
Figure BDA00029324508100001018
the kronecker product is calculated; omega 1 Is a vector, representing g 1 And
Figure BDA00029324508100001019
an average value of kronecker products;
successful decoding of signal s by the first user 2 Then, a serial interference elimination method is adopted to obtain a first user decoding signal s 1 Average effective signal to interference and noise ratio of
Figure BDA00029324508100001020
Namely:
Figure BDA00029324508100001021
the same thing can be used to obtain the second user decoding signal s 2 Average effective signal to interference and noise ratio of
Figure BDA0002932450810000111
Namely:
Figure BDA0002932450810000112
Figure BDA0002932450810000113
wherein v is 2 A vector is estimated for the channel of the first user,
Figure BDA0002932450810000114
is v is 2 Conjugate transposed vector of g 2 Is a vector, represents the response coefficient of the intelligent reflecting surface to the first user,
Figure BDA0002932450810000115
is a vector, representing g 2 Conjugated of (e), ω 2 Is g 2 And
Figure BDA0002932450810000116
average of kronecker products.
In the step S5, the method adopted when calculating the maximum value of the average effective snr of the first user in the current decoding order is an alternating iteration method and an interior point method;
since maximizing the mean effective snr of the first user is a function of the channel estimation vector v i Power distribution coefficient alpha i The non-convex optimization problem highly coupled with the reflection coefficient H is difficult to directly obtain the optimal solution, so the optimization problem is converted into a convex optimization problem based on an alternating iteration methodThe problem is solved by an interior point method: firstly, splitting the original optimization problem of three variables into a fixed variable, and solving the other two variables in an iterative manner; fixing the other two variables, and solving one variable iteratively; and alternately carrying out the two iterative solving processes until convergence, and solving a channel estimation vector, a power distribution coefficient and a reflection coefficient.
The specific process of calculating the maximum value of the first user average effective signal-to-interference-and-noise ratio in the current decoding order by adopting the alternating iteration method and the interior point method is as follows:
on the premise of the first decoding order, in the case of a known reflection coefficient H, an auxiliary variable μ is set 1 ＝1/α 1 The constant of character k i ＝λ 2 ω i vec (H), matrix constant
Figure BDA0002932450810000117
Character constant
Figure BDA0002932450810000118
And introducing a relaxation variable τ, equivalent equation (5) to:
Figure BDA0002932450810000119
Figure BDA00029324508100001110
Figure BDA00029324508100001111
the method is simplified as follows:
Figure BDA00029324508100001112
solving equation (11) by using an algorithm based on a constrained concave-convex process
Figure BDA00029324508100001113
Figure BDA00029324508100001114
ρ(μ 1 )＝-lnμ 1 The first order Taylor expansion is expressed as:
Figure BDA0002932450810000121
Figure BDA0002932450810000122
Figure BDA0002932450810000123
wherein the content of the first and second substances,
Figure BDA0002932450810000124
and
Figure BDA0002932450810000125
are each v 1 、τ、v i And mu 1 The value of the probability of (c) is,
Figure BDA0002932450810000126
is that
Figure BDA0002932450810000127
The conjugate of the transposed vector of (a),
Figure BDA0002932450810000128
is a vector
Figure BDA0002932450810000129
The conjugate transpose vector (c) of (a), re { · } represents the operation of the real part, the equation (11) is converted into a convex optimization problem, and in the (l + 1) th iteration based on the constrained concave-convex process algorithm, the optimization problem is represented as:
Figure BDA00029324508100001210
Figure BDA00029324508100001211
Figure BDA00029324508100001212
wherein, l represents the number of iterations,
Figure BDA00029324508100001213
for the solution of the equations (12 a), (12 b) and (12 c) in the first iteration, when the algorithm converges, the equations (12 a), (12 b) and (12 c) are solved by the interior point method to obtain the channel estimation vector v i And the power distribution coefficient alpha 1 A local optimal solution of (a);
at v i And alpha i In the known case, let character constants
Figure BDA00029324508100001214
Character constant
Figure BDA00029324508100001215
Character constant
Figure BDA00029324508100001216
Character constant
Figure BDA00029324508100001217
Character constant
Figure BDA00029324508100001218
Character constant
Figure BDA00029324508100001219
Figure BDA00029324508100001220
And introducing a relaxation variable epsilon, equivalent of formula (5):
max H,ε≥0 ε (13a)
Figure BDA00029324508100001221
Figure BDA00029324508100001222
equations (13 a), (13 b) and (13 c) are solved by using a constrained concave-convex process algorithm
Figure BDA00029324508100001223
The first order Taylor expansion is expressed as:
Figure BDA00029324508100001224
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00029324508100001225
is a feasible value of epsilon, the equations (13 a), (13 b) and (13 c) are converted into a convex optimization problem, and in the (l + 1) th iteration based on the constrained concave-convex process algorithm, the optimization problem is expressed as:
max H,ε≥0 ε (14a)
Figure BDA00029324508100001226
Figure BDA0002932450810000131
wherein l represents the number of iterations, point
Figure BDA0002932450810000132
Solving the equations (14 a), (14 b) and (14 c) by an interior point method when the algorithm converges for the solution of the equations (14 a), (14 b) and (14 c) at the l-th iteration to obtain a local optimal solution of the reflection coefficient H,according to
Figure BDA0002932450810000133
And solving H through singular value decomposition to obtain a local optimal solution of the reflection coefficient matrix theta.
After the above steps are completed, on the premise of the second decoding order, the maximum value of the average effective signal-to-interference-and-noise ratio of the first user is calculated, and the calculation process is the same as that in the first decoding order, and is not described herein again.
The whole process is as follows: in the performance gain optimization method of the intelligent reflector assisted non-orthogonal multiple access system, due to the high coupling of variables, the maximum value of the average effective signal-to-noise ratio of a user is obtained by adopting an alternative iteration method based on a constrained concave-convex process, and meanwhile, a corresponding channel estimation vector v is obtained i Coefficient of power distribution α 1 And a locally optimal solution of the reflection coefficient matrix theta. The specific solving process is as follows: firstly, under the condition of known theta, an optimization problem is converted into a difference convex programming problem, a convex optimization problem is converted by adopting a constraint-based concave-convex process algorithm, and v is obtained by using an interior point method i And alpha 1 (ii) a Then at known v i And alpha 1 Under the condition of (3), the optimization problem is converted into another differential convex programming problem, and a theta is solved by adopting a constraint concave-convex process algorithm and an interior point method; the two steps are alternately repeated until the algorithm converges to obtain the final local optimal solution.
The terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. This need not be, nor should it be exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (5)

1. An intelligent reflector assisted performance gain optimization method for a non-orthogonal multiple access system, the method comprising the steps of:
s1: establishing an intelligent reflecting surface assisted non-orthogonal multiple access system, wherein the system comprises a base station, an intelligent reflecting surface, a first user and a second user; the base station, the intelligent reflecting surface, the first user and the second user form a cascade channel of the base station, the intelligent reflecting surface and the user; the intelligent reflecting surface comprises a reflection coefficient matrix;
s2: the base station sends a pilot signal to be reflected by the intelligent reflecting surface and then transmitted to a first user and a second user, and the first user and the second user carry out channel estimation on the cascade channel according to the received pilot signal; the channel estimation process comprises a channel estimation vector;
s3: the base station sends the superposition coded signals, the superposition coded signals are transmitted to a first user and a second user after being reflected by the intelligent reflecting surface, and the first user and the second user decode the received superposition coded signals according to different decoding orders after receiving the superposition coded signals; the superposition coding signal comprises a power distribution coefficient;
and if the superposition coded signal transmitted by the base station is marked as y, then:
Figure FDA0003881545240000011
wherein s is 1 For signals sent to the first user, s 2 For signals transmitted to the second user, P is the transmission power of the base station, alpha 1 Representing the power distribution coefficient, alpha, of the first user 2 Represents the power distribution coefficient of the second user and satisfies alpha 1 +α 2 ＝1；
The superposition coded signal received by the user is marked as y i And then:
Figure FDA0003881545240000012
wherein n is i Additive Gaussian noise representing the ith user, subject to mean of zero variance of
Figure FDA0003881545240000013
A gaussian distribution of (d); d i Representing a cascade channel of a base station, an intelligent reflecting surface and a user;
the decoding order comprises a first decoding order and a second decoding order; the first decoding order is: decoding the second user first, and then decoding the first user; the second decoding order is: firstly, decoding a first user, and then decoding a second user;
s4: respectively, under the premise of different decoding orders, taking the average effective signal-to-interference-and-noise ratio of the first user as a maximum value as an optimization target, and performing combined optimization on a channel estimation vector, a power distribution coefficient and a reflection coefficient matrix;
taking the maximum first user average effective signal-to-interference-and-noise ratio as an optimization target, and under the premise of a first decoding order, an objective function and constraint conditions are as follows:
Figure FDA0003881545240000014
wherein the content of the first and second substances,
Figure FDA0003881545240000021
decoding a signal s for a first user 1 The average effective signal-to-interference-and-noise ratio of (c),
Figure FDA0003881545240000022
decoding signal s for ith user 2 Of (a) is a mean effective signal to interference plus noise ratio, gamma 0 Is the average effective signal to interference plus noise ratio threshold, v i Is a vector, representing the channel estimation vector of the ith user; h is the reflection coefficient of the light beam,
Figure FDA0003881545240000023
theta is a reflection coefficient matrix of the intelligent reflecting surface,
Figure FDA0003881545240000024
is a conjugate transpose matrix of Θ; the constraint condition is that the average effective signal to interference plus noise ratio of the second user is more than or equal to the threshold of the average effective signal to interference plus noise ratio;
said first user decoded signal s 1 Average effective signal to interference plus noise ratio of
Figure FDA0003881545240000025
The specific calculation process is as follows:
on the premise of a first decoding order, a first user decodes a signal s 2 Is recorded as the average effective signal-to-interference-and-noise ratio
Figure FDA0003881545240000026
Then:
Figure FDA0003881545240000027
wherein E {. Is } represents an averaging operation, d 1 Is a cascade channel of a base station-an intelligent reflecting surface-a first user,
Figure FDA0003881545240000028
is a first user pair d 1 The channel estimation of (2) is performed,
Figure FDA0003881545240000029
variance of additive gaussian noise for the user;
further, the following can be obtained:
Figure FDA00038815452400000210
Figure FDA00038815452400000211
wherein λ is 2 A covariance matrix determinant of a channel response coefficient h from a base station to the intelligent reflecting surface; sigma 2 Representing additive white gaussian noise
Figure FDA00038815452400000212
The covariance matrix determinant of (a); vec (·) is a vectorization function; v. of 1 Estimating a vector for a channel of a first user;
Figure FDA00038815452400000213
is v is 1 The conjugate transpose vector of (1); t is a vector and represents a pilot signal transmitted by a base station;
Figure FDA00038815452400000214
a conjugate transpose vector representing t;
Figure FDA00038815452400000215
variance of additive gaussian noise for the user; g is a radical of formula 1 Is a vector and represents the response coefficient of the intelligent reflecting surface to the first user;
Figure FDA00038815452400000216
is a vector, representing g 1 Conjugation of (1);
Figure FDA00038815452400000217
calculating a kronecker product; omega 1 Is a vector, representing g 1 And
Figure FDA00038815452400000218
an average value of kronecker products;
successful decoding of signal s by the first user 2 Then, a method of serial interference cancellation is adopted to obtain a first user decoding signal s 1 Average effective signal to interference plus noise ratio of
Figure FDA00038815452400000219
Namely:
Figure FDA00038815452400000220
the same thing can be used to obtain the second user decoding signal s 2 Average effective signal to interference and noise ratio of
Figure FDA00038815452400000221
Namely:
Figure FDA00038815452400000222
Figure FDA00038815452400000223
wherein v is 2 A vector is estimated for the channel of the first user,
Figure FDA0003881545240000031
is v 2 Conjugate transposed vector of g 2 Is a vector, represents the response coefficient of the intelligent reflecting surface to the first user,
Figure FDA0003881545240000032
is a vector, representing g 2 The conjugate of (a) to (b), omega 2 Is g 2 And
Figure FDA0003881545240000033
an average value of kronecker products;
s5: respectively calculating the maximum value of the average effective signal-to-interference-and-noise ratio of the first user in the current decoding order and the corresponding local optimal solution of a channel estimation vector, a power distribution coefficient and a reflection coefficient matrix;
s6: and comparing the maximum values of the first user average effective signal-to-interference-and-noise ratios in different decoding orders, and outputting the local optimal solution of the channel estimation vector, the power distribution coefficient and the reflection coefficient matrix corresponding to the first user average effective signal-to-interference-and-noise ratio with the maximum value as the final local optimal solution.
2. The method according to claim 1, wherein in S1, various signals transmitted by a base station are reflected by the intelligent reflecting surface and then transmitted to a first user and a second user simultaneously; the concatenated channel has channel state information including:
the reflection coefficient matrix theta of the intelligent reflecting surface is an M multiplied by M complex matrix, wherein M is the number of passive reflecting elements contained in the intelligent reflecting surface;
the channel response coefficient h from the base station to the intelligent reflecting surface is a vector, the obedience mean value is zero covariance matrix and is lambda 2 Gaussian distribution of I, wherein λ 2 A covariance matrix determinant representing a channel response coefficient h, wherein I is a vector and represents an identity matrix;
the channel response coefficient from the intelligent reflecting surface to the ith user is g i ,i∈K＝{1,2}，g i As a vector, obey a mean value of zero covariance matrix of
Figure FDA0003881545240000034
Wherein K represents a set of integers,
Figure FDA0003881545240000035
representing the channel response coefficient g i I is a vector, and represents an identity matrix.
3. The method of claim 2, wherein in S2, the specific method of channel estimation is as follows:
d for cascade channel of base station-intelligent reflector-user i To show that:
d i ＝g i Θh，i∈K＝{1，2} (1)
the pilot signal sent by the base station is t, and the pilot signal received by the ith user is z i And then:
Figure FDA0003881545240000036
wherein z is i Is a vector of the number of the cells,
Figure FDA0003881545240000037
is vector, represents the additive white Gaussian noise of the ith user, and obeys the variance of zero covariance matrix as sigma 2 Gaussian distribution of I, where σ 2 Representing additive white gaussian noise
Figure FDA0003881545240000038
The covariance matrix determinant of (1), wherein I is a vector and represents an identity matrix;
the ith user is based on the received pilot signal z i For cascade channel d i Make an estimate of
Figure FDA0003881545240000039
Then:
Figure FDA0003881545240000041
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003881545240000042
for the channel estimation of the ith user,
Figure FDA0003881545240000043
estimating vector v for ith user i The conjugate of (2) is transposed vector.
4. The method of claim 1, wherein in step S5, the method for calculating the maximum value of the mean effective snr of the first user in the current decoding order is an alternating iteration method and an interior point method.
5. The method of claim 4, wherein the specific process of calculating the maximum value of the first user average effective SINR in the current decoding order by the alternative iteration method and the interior point method comprises:
on the premise of the first decoding order, in the case of a known reflection coefficient H, an auxiliary variable μ is set 1 ＝1/α 1 The constant of a character k i ＝λ 2 ω i vec (H), matrix constant
Figure FDA0003881545240000044
Character constant
Figure FDA0003881545240000045
Figure FDA0003881545240000046
And introducing a relaxation variable τ, equivalent of equation (5):
Figure FDA0003881545240000047
Figure FDA0003881545240000048
Figure FDA0003881545240000049
the method is simplified as follows:
Figure FDA00038815452400000410
solving equation (11) by using an algorithm based on a constrained concave-convex process
Figure FDA00038815452400000411
Figure FDA00038815452400000412
ρ(μ 1 )＝-lnμ 1 The first order Taylor expansion is expressed as:
Figure FDA00038815452400000413
Figure FDA00038815452400000414
Figure FDA00038815452400000415
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00038815452400000416
and
Figure FDA00038815452400000417
are each v 1 、τ、v i And mu 1 The value of the probability of (c) is,
Figure FDA00038815452400000418
is that
Figure FDA00038815452400000419
The conjugate of (a) the transposed vector (v),
Figure FDA00038815452400000420
is a vector
Figure FDA00038815452400000421
The conjugate transpose vector (c) of (a), re { · } represents the operation of the real part, the equation (11) is converted into a convex optimization problem, and in the (l + 1) th iteration based on the constrained concave-convex process algorithm, the optimization problem is represented as:
Figure FDA00038815452400000422
Figure FDA0003881545240000051
Figure FDA0003881545240000052
wherein, l represents the number of iterations,
Figure FDA0003881545240000053
for the solution of the equations (12 a), (12 b) and (12 c) in the first iteration, when the algorithm converges, the equations (12 a), (12 b) and (12 c) are solved by the interior point method to obtain the channel estimation vector v i And a power distribution coefficient alpha 1 A local optimal solution of (a);
at v i And alpha i In the known case, let character constants
Figure FDA0003881545240000054
Character constant
Figure FDA0003881545240000055
Character constant
Figure FDA0003881545240000056
Character constant
Figure FDA0003881545240000057
Character constant
Figure FDA0003881545240000058
Character constant
Figure FDA0003881545240000059
Figure FDA00038815452400000510
And introducing a relaxation variable epsilon, equating formula (5) as:
Figure FDA00038815452400000511
Figure FDA00038815452400000512
Figure FDA00038815452400000513
equations (13 a), (13 b), and (13 c) are solved using a constrained concave-convex process-based algorithm, and
Figure FDA00038815452400000514
the first order Taylor expansion is expressed as:
Figure FDA00038815452400000515
wherein the content of the first and second substances,
Figure FDA00038815452400000516
is a feasible value of epsilon, the equations (13 a), (13 b) and (13 c) are converted into a convex optimization problem, and in the (l + 1) th iteration based on the constrained concave-convex process algorithm, the optimization problem is expressed as:
Figure FDA00038815452400000517
Figure FDA00038815452400000518
Figure FDA00038815452400000519
wherein l represents the number of iterations, point
Figure FDA00038815452400000520
For the solutions of the equations (14 a), (14 b) and (14 c) in the first iteration, when the algorithm converges, solving the equations (14 a), (14 b) and (14 c) by the interior point method to obtain the local optimal solution of the reflection coefficient H, according to which
Figure FDA00038815452400000521
And solving H through singular value decomposition to obtain a local optimal solution of the reflection coefficient matrix theta.
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