CN113423112B - RIS assisted multi-carrier NOMA transmission system parameter optimization method - Google Patents

RIS assisted multi-carrier NOMA transmission system parameter optimization method Download PDF

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CN113423112B
CN113423112B CN202110675019.6A CN202110675019A CN113423112B CN 113423112 B CN113423112 B CN 113423112B CN 202110675019 A CN202110675019 A CN 202110675019A CN 113423112 B CN113423112 B CN 113423112B
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ris
subcarrier
reflection coefficient
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CN113423112A (en
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陈明
徐芸
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Southeast University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a parameter optimization method for an RIS auxiliary multi-carrier NOMA transmission system, which takes the maximum system energy efficiency as a target and respectively establishes a subcarrier distribution model, a user decoding sequence model and a user power and RIS reflection coefficient model; aiming at a subcarrier distribution model, a matching method based on channel gain sequencing is provided; secondly, aiming at a user decoding sequence model in a subcarrier, a decoding sequence optimization method with low complexity is provided; and finally, aiming at the user power and RIS reflection coefficient model, a combined optimization method of alternating iteration of the user power and the RIS reflection coefficient is used. The method can effectively improve the channel quality and improve the system energy efficiency.

Description

RIS assisted multi-carrier NOMA transmission system parameter optimization method
Technical Field
The invention relates to the technical field of NOMA communication, in particular to a parameter optimization method of a RIS auxiliary multi-carrier NOMA transmission system.
Background
At present, in the application of maximizing the energy efficiency of multi-carrier NOMA downlink transmission assisted by RIS, a joint optimization method for maximizing the energy efficiency aiming at special scenes of two users and without considering a decoding sequence exists, but the research and the application of optimizing subcarrier allocation, multi-user power allocation and RIS reflection coefficient control are less while considering the decoding sequence.
Disclosure of Invention
In view of this, the present invention provides a method for optimizing parameters of a RIS assisted multi-carrier NOMA transmission system, so as to solve the problems mentioned in the background art. Aiming at an RIS-assisted multi-carrier NOMA downlink transmission system, the invention researches the joint optimization problem of subcarrier allocation, decoding sequence, power allocation and RIS reflection coefficient by taking the maximum system energy efficiency as an objective function and considering the constraint of the maximum transmission power and the RIS reflection coefficient of a base station.
In order to solve the problems, the invention adopts the technical scheme that:
a parameter optimization method for RIS auxiliary multi-carrier NOMA transmission system includes the following steps:
s1, establishing an energy efficiency maximization model, wherein the energy efficiency maximization model A1 is expressed as:
Figure BDA0003120635130000011
constraint conditions are as follows:
C1:
Figure BDA0003120635130000012
C2:
Figure BDA0003120635130000013
C3:
Figure BDA0003120635130000014
C4:
Figure BDA0003120635130000015
C5:
Figure BDA0003120635130000016
C6:θ m ∈[0,2π),m＝1,…,M
in the formula, the number of RIS reflecting units is M, and the phase of the mth reflecting unit is theta m ,m＝0,1,…,M，
Figure BDA0003120635130000021
Is the reflection coefficient matrix of the RIS, diag [ ·]Representing vector diagonalization; k is the number of the users,
Figure BDA0003120635130000022
representing a set of users; n is the number of sub-carriers,
Figure BDA0003120635130000023
representing a set of subcarriers, specifying that each user can be and can only be allocated to one subcarrier; delta. For the preparation of a coating n,k An indicator variable, delta, for subcarrier allocation n,k =1 denotes the allocation of subcarrier n to user k, δ n,k =0 for no allocation, δ = { δ = 1,1 ,…,δ 1,K ,…,δ n,1 ,…,δ n,K ,…,δ N,1 ,…,δ N,K Allocating a state set for the sub-carriers; a is n,k Representing the power allocated to user k on subcarrier n, a = { a = 1,1 ,…,a 1,K ,…,a n,1 ,…,a n,K ,…,a N,1 ,…,a N,K The user power set is used as the power set; v. of n,k ，f n And g n,k Channel matrices representing subcarriers n to user k, subcarriers n to RIS and RIS to user k, respectively, (-) H Represents a conjugate transpose; o. o n (k) Indicating the decoding order, o, of user k on subcarrier n n (k) = j representsUser k is the jth decoded user, o = { o = 1 (1),…,o 1 (K),…,o n (1),…,o n (K),…,o N (1),…,o N (K) Is a set of decoding orders; sigma 2 Represents the variance of additive white gaussian noise with a mean of 0; p c Total circuit power consumed for the system; user k on subcarrier n has rate R n,k Is shown as
Figure BDA0003120635130000024
| · | represents modulo a complex number; suppose o n (k)＜o n (j) Rate R at which the signal of user k is decoded at user j n,j→k Is shown as
Figure BDA0003120635130000025
P max Is the maximum transmit power at the base station;
s2, solving the energy efficiency maximization model, wherein the concrete steps are as follows:
step S201, the mth element on the diagonal of the reflection coefficient matrix theta of the initial RIS is:
Figure BDA0003120635130000026
channel matrix of subcarrier n to user k is v n,k The corresponding channel gain is | v n,k I, n ', k' are
Figure BDA0003120635130000027
The minimum subcarrier number and the user number, and the angle (·) represents the angle corresponding to the complex number; channel gain of user k is
Figure BDA0003120635130000028
User k selection
Figure BDA0003120635130000029
Maximum subcarrier
Figure BDA00031206351300000210
Order to
Figure BDA00031206351300000211
δ n,k ＝0,n≠n * (ii) a After all users select the subcarrier, obtaining a subcarrier distribution state set delta;
step S202, using the value of the sub-carrier distribution state set delta obtained in step S201 to make | v of the user k not distributed to the sub-carrier n n,k L =0; on subcarrier n, according to the method for all users
Figure BDA00031206351300000212
Is sorted from small to large, and the | v of the user k is recorded n,k The | value is ordered as i n Then o n (k)＝i n (ii) a After all subcarriers are sequenced, a decoding sequence set o is obtained;
step S203, after obtaining the subcarrier distribution state set delta and the decoding sequence set o, simplifying the constraint C3 of the model A1; the energy efficiency maximization model B1, which converts the model A1 into the reflection coefficient matrix Θ for the user power set a and the RIS, is:
Figure BDA0003120635130000031
constraint conditions are as follows:
C1:
Figure BDA0003120635130000032
C2:
Figure BDA0003120635130000033
C3:
Figure BDA0003120635130000034
C4:θ m ∈[0,2π),m＝1,…,M
step S204, iteratively solving the energy efficiency maximization model B1, wherein in the ith iteration, the solving process is as follows:
step S2041, splitting the energy efficiency maximization model B1 to respectively obtain a model for optimizing a user power set a and a model for optimizing a reflection coefficient matrix theta of the RIS; the model B2 for the user power set a is expressed as:
Figure BDA0003120635130000035
constraint conditions are as follows:
C1:
Figure BDA0003120635130000036
C2:
Figure BDA0003120635130000037
Θ (i-1) the matrix theta of the reflection coefficient of the RIS is obtained for the i-1 iteration; solving the model B2 by using a Dinkelbach method to obtain a user power set a of the ith iteration (i) ；
Step S2042,
Figure BDA0003120635130000038
Is a (i) The n × k-th element of (1); the maximization model B3 of the reflection coefficient matrix Θ with respect to RIS is expressed as:
Figure BDA0003120635130000041
constraint conditions are as follows:
C1:
Figure BDA0003120635130000042
C2:θ m ∈[0,2π),m＝1,…,M
step S2043, introducing a relaxation variable:
Figure BDA0003120635130000043
η＝[η 1,1 ,…,η 1,K ,…,η n,1 ,…,η n,K ,…,η N,1 ,…,η N,K ]；
order to
Figure BDA0003120635130000044
t＝[t 1,1 ,…,t 1,K ,…,t n,1 ,…,t n,K ,…,t N,1 ,…,t N,K ]，
Figure BDA0003120635130000045
(·) * Represents a conjugate operation, then
Figure BDA0003120635130000046
Introducing vector beta = [ beta ] 1,1 ,…,β 1,K ,…,β n,1 ,…,β n,K ,…,β N,1 ,…,β N,K ]Model B3 is transformed into model B4, said model B4 being represented as:
Figure BDA0003120635130000047
constraint conditions are as follows:
C1:|s m |＝1,m＝1,…,M
C2:
Figure BDA0003120635130000048
C3:
Figure BDA0003120635130000049
C4:
Figure BDA00031206351300000410
step S2044, carrying out iterative solution on the model B4 by using a continuous convex approximation method and a penalty function method, wherein in the u-th iteration, the model B4 is converted into a model B5 as follows:
Figure BDA0003120635130000051
constraint conditions are as follows:
C1:|s m |≤1,m＝1,…,M
C2:
Figure BDA0003120635130000052
C3:
Figure BDA0003120635130000053
C4:
Figure BDA0003120635130000054
wherein
Figure BDA0003120635130000055
And s (u-1) Is the value of the u-1 th iteration,
Figure BDA0003120635130000056
is s (u-1) The mth element of (1); r (·) represents taking a real part;
step S2045, substituting variable values S, eta and beta obtained by the u-th iteration into the model B5 to calculate the target function, and when the value of the target function is not changed any more or the absolute value of the change is smaller than a threshold value epsilon 1 Then, the iteration method is terminated, s is output, and the s is diagonalized to obtain a RIS reflection coefficient matrix theta; otherwise, carrying out the next iteration;
step S205, substituting the user power set a obtained in step S2041 and the RIS reflection coefficient matrix theta obtained in step S2045 in the ith iteration into the model B1 to calculate the value of the objective function, and when the value of the objective function is not changed any more or the absolute value of the change is smaller than the threshold value epsilon 2 Then, the iteration method is terminated, and a user power set a and an RIS reflection coefficient matrix theta are output; otherwise, the next iteration is carried out.
Further, the given threshold value epsilon in step S2045 1 Is 10 -4 。
Further, the step S205 is givenThreshold value epsilon 2 Is 10 -4
The beneficial effects of the invention are:
aiming at a multi-carrier NOMA downlink transmission system assisted by RIS, the invention takes the maximum system energy efficiency as an objective function, and performs joint optimization on subcarrier allocation, decoding sequence of users in subcarriers, user power and a reflection coefficient matrix of RIS. A corresponding mathematical optimization model is established for the problem, and the problem is decomposed into three sub-problems of subcarrier allocation, user decoding order optimization and user power and RIS reflection coefficient alternative optimization: aiming at the solution of the subcarrier allocation sub-problem, a matching method based on channel gain sequencing is provided; aiming at the solution of the decoding sequence of the user in the subcarrier, a decoding sequence optimization method with low complexity is provided; aiming at the sub-problem of joint optimization of the user power and the RIS reflection coefficient, a Dinkelbach method is used for optimizing the user power, a RIS reflection coefficient is optimized by a continuous convex approximation method and a penalty function method, and a joint optimization method of alternating iteration of the user power and the RIS reflection coefficient is provided. By adopting the method, the energy efficiency of the system can be effectively and simply improved.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Example 1
The embodiment provides a parameter optimization method for an RIS-assisted multi-carrier NOMA transmission system, which is used for researching the joint optimization problem of subcarrier allocation, decoding sequence, power allocation and RIS reflection coefficient by taking the maximum system energy efficiency as an objective function and considering the constraint of the maximum transmission power and the RIS reflection coefficient of a base station aiming at an RIS-assisted multi-carrier NOMA downlink transmission system. In order to solve the corresponding non-convex problem, the original problem is decomposed into four sub-problems, the four sub-problems are solved through three steps, firstly, a matching method based on the principle of channel gain maximization is provided, secondly, a user decoding sequence optimization method in sub-carriers with lower complexity is provided, and finally, when the sub-carrier distribution and decoding sequence are given, a Dinkelbach method is used for optimizing user power, and a continuous convex approximation and penalty function method is used for optimizing the RIS reflection coefficient.
Specifically, in this embodiment, in an RIS-assisted multi-carrier NOMA downlink transmission system, an RIS is placed between a base station and users, the base station transmits superimposed signals to K users through a direct channel and a reflected channel via the RIS by using a power domain multiplexing technique according to the NOMA principle, and the users are equipped with single antennas. Note book
Figure BDA0003120635130000061
Representing a set of users, the number of subcarriers being N,
Figure BDA0003120635130000062
representing a set of subcarriers, specifying that each user can, and can only, be allocated to one subcarrier.
First step, a n,k Representing the power, s, allocated to user k on subcarrier n n,k The transmitted data representing user k on subcarrier n is an independent random variable with a mean of 0 and a variance of 1. Delta. For the preparation of a coating n,k An indicator variable, delta, for subcarrier allocation n,k =1 denotes allocation of subcarrier n to user k, δ n,k =0 means no allocation. Transmission signal x of subcarrier n n Can be expressed as:
Figure BDA0003120635130000063
secondly, the number of the reflection units of the RIS is M, and the phase position of the mth reflection unit is recorded as theta m E [0,2 π), M =1,2, \ 8230A, M, diagonal matrix
Figure BDA0003120635130000064
Matrix of reflection coefficients, diag [. Cndot., representing the RIS]Representing vector diagonalization. By the symbol v n,k ，
Figure BDA0003120635130000065
And
Figure BDA0003120635130000066
channel matrices representing subcarriers n to user k, subcarriers n to RIS and RIS to user k, respectively, (. Cndot.) H Representing the conjugate transpose of the matrix. c represents that the user receives white Gaussian noise, the mean value of which is 0 and the variance of which is sigma 2 . The base station is assumed to perfectly acquire the channel state information of all channels, which are assumed to be flat-fading rayleigh channels. The signal y received by user k on subcarrier n, after passing through the direct channel and the reflected channel n,k Can be expressed as:
Figure BDA0003120635130000071
third step, with o n (k) Indicating the decoding order, o, of user k on subcarrier n n (k) = j indicates that user k is the jth decoded user. While demodulating the signal of user k on subcarrier n, the other non-demodulated users l, o n (l)＞o n (k) Is to be treated as interference, the signal to interference and noise ratio y of the kth user on the subcarrier n n,k The calculation is as follows:
Figure BDA0003120635130000072
where | represents the user's rate R modulo a complex number n,k Can be represented as R n,k ＝log 2 (1+γ n,k )。
Fourth, assume o n (k)＜o n (j) Calculating the velocity of user k at user j is represented as:
Figure BDA0003120635130000073
fifth step, P c Is the total consumption of the systemCalculating the total power consumed by the RIS assisted NOMA system as:
Figure BDA0003120635130000074
sixthly, calculating the energy efficiency of the system as follows:
Figure BDA0003120635130000075
to obtain subcarrier allocation, user decoding order within subcarriers, user power and RIS reflection coefficient and apply to the above system, let δ = { δ = here 1,1 ,…,δ 1,K ,…,δ n,1 ,…,δ n,K ,…,δ N,1 ,…,δ N,K Denotes a set of subcarrier allocation states, o = { o = 1 (1),…,o 1 (K),…,o n (1),…,o n (K),…,o N (1),…,o N (K) Is a decoding order set, a = { a = } 1,1 ,…,a 1,K ,…,a n,1 ,…,a n,K ,…,a N,1 ,…,a N,K And (5) establishing an energy efficiency maximization model for the user power set, wherein the energy efficiency maximization model is expressed as follows:
Figure BDA0003120635130000081
constraint conditions are as follows:
C1:
Figure BDA0003120635130000082
C2:
Figure BDA0003120635130000083
C3:
Figure BDA0003120635130000084
C4:
Figure BDA0003120635130000085
C5:
Figure BDA0003120635130000086
C6:θ m ∈[0,2π),m＝1,…,M
solving the energy efficiency maximization model, which comprises the following specific steps:
step 1: the mth element on the diagonal of the reflection coefficient matrix Θ of the initial RIS is:
Figure BDA0003120635130000087
channel matrix of subcarrier n to user k is v n,k The corresponding channel gain is | v n,k I, n ', k' are
Figure BDA0003120635130000088
The smallest subcarrier number and user number, angle (·) represents the angle corresponding to the complex number. Channel gain of user k is
Figure BDA0003120635130000089
User k selection
Figure BDA00031206351300000810
Largest sub-carrier
Figure BDA00031206351300000811
Order to
Figure BDA00031206351300000812
And after all users select the sub-carrier, obtaining a sub-carrier distribution state set delta.
Step 2: obtaining the value of the sub-carrier distribution state set delta by the step 1, and enabling the users k | v not distributed to the sub-carrier n n,k L =0. On subcarrier n, according to the method for all users
Figure BDA00031206351300000813
Value of (A)Sorting from small to large, remember | v of user k n,k The | value is ordered as i n Then o n (k)＝i n (ii) a And obtaining a decoding sequence set o after sequencing all the subcarriers.
And step 3: after the subcarrier allocation state set delta and the decoding sequence set o are obtained, the constraint C3 of the model A1 is simplified. The energy efficiency maximization model B1, which converts the model A1 into the reflection coefficient matrix Θ for the user power set a and the RIS, is:
Figure BDA0003120635130000091
constraint conditions are as follows:
C1:
Figure BDA0003120635130000092
C2:
Figure BDA0003120635130000093
C3:
Figure BDA0003120635130000094
C4:θ m ∈[0,2π),m＝1,…,M
and 4, step 4: and (3) iteratively solving the energy efficiency maximization model B1, wherein in the ith iteration, the solving process is as follows:
step 4-1: and splitting the energy efficiency maximization model B1 to respectively obtain a model for optimizing the user power set a and a model for optimizing the reflection coefficient matrix theta of the RIS. The model B2 for the user power set a is expressed as:
Figure BDA0003120635130000095
constraint conditions are as follows:
C1:
Figure BDA0003120635130000096
C2:
Figure BDA0003120635130000097
Θ (i-1) and the matrix theta of the reflection coefficient of the RIS is obtained from the (i-1) th iteration. Solving the model B2 by using a Dinkelbach method to obtain a user power set a of the ith iteration (i) 。
Step 4-2:
Figure BDA0003120635130000098
is a (i) The nth × k elements of (a), the maximization model B3 of the reflection coefficient matrix Θ with respect to RIS is expressed as:
Figure BDA0003120635130000099
constraint conditions are as follows:
C1:
Figure BDA00031206351300000910
C2:θ m ∈[0,2π),m＝1,…,M
step 4-3: introducing a relaxation variable:
Figure BDA0003120635130000101
η＝[η 1,1 ,…,η 1,K ,…,η n,1 ,…,η n,K ,…,η N,1 ,…,η N,K ]；
order to
Figure BDA0003120635130000102
t＝[t 1,1 ,…,t 1,K ,…,t n,1 ,…,t n,K ,…,t N,1 ,…,t N,K ]，
Figure BDA0003120635130000103
(·) * Represents a conjugate operation, then
Figure BDA0003120635130000104
Introducing vectors
β＝[β 1,1 ,…,β 1,K ,…,β n,1 ,…,β n,K ,…,β N,1 ,…,β N,K ]Model B3 is transformed into model B4, said model B4 being represented as:
Figure BDA0003120635130000105
constraint conditions are as follows:
C1:|s m |＝1,m＝1,…,M
C2:
Figure BDA0003120635130000106
C3:
Figure BDA0003120635130000107
C4:
Figure BDA0003120635130000108
step 4-4: the solution is iterated using the successive convex approximation method and the penalty function method for model B4, and in the u-th iteration model B4 is transformed into model B5 as follows:
Figure BDA0003120635130000109
constraint conditions are as follows:
C1:|s m |≤1,m＝1,…,M
C2:
Figure BDA00031206351300001010
C3:
Figure BDA00031206351300001011
C4:
Figure BDA00031206351300001012
wherein
Figure BDA00031206351300001013
And s (u-1) Is the value of the u-1 th iteration,
Figure BDA00031206351300001014
is s (u-1) R (-) represents the real part.
And 4-5: substituting variable values s, eta and beta obtained from the u-th iteration into the model B5 to calculate the target function, and when the value of the target function is not changed any more or the absolute value of the change is less than the threshold value 10 -4 Then, the iteration method is terminated, s is output, and the s is diagonalized to obtain a RIS reflection coefficient matrix theta; otherwise, the next iteration is carried out.
And 5: substituting the user power set a obtained in the step 4-1 and the RIS reflection coefficient matrix theta obtained in the step 4-5 in the ith iteration into the model B1 to calculate the value of the objective function, and when the value of the objective function is not changed any more or the absolute value of the variation is smaller than the threshold value 10 -4 Then, the iteration method is terminated, and a user power set a and an RIS reflection coefficient matrix theta are output; otherwise, the next iteration is carried out.
The details of the present invention are well known to those skilled in the art.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations can be devised by those skilled in the art in light of the above teachings. Therefore, the technical solutions that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the prior art according to the concepts of the present invention should be within the scope of protection determined by the claims.

Claims (3)

1. A parameter optimization method for RIS auxiliary multi-carrier NOMA transmission system is characterized by comprising the following steps:
s1, establishing an energy efficiency maximization model, wherein the energy efficiency maximization model A1 is expressed as:
Figure FDA0003839515020000011
constraint conditions are as follows:
C1:
Figure FDA0003839515020000012
C2:
Figure FDA0003839515020000013
C3:
Figure FDA0003839515020000014
C4:
Figure FDA0003839515020000015
C5:
Figure FDA0003839515020000016
C6:θ m ∈[0,2π),m＝1,…,M
in the formula, the number of RIS reflecting units is M, and the phase of the mth reflecting unit is theta m ,m＝0,1,…,M，
Figure FDA0003839515020000017
Is the reflection coefficient matrix of the RIS, diag [ ·]Representing vector diagonalization; k is the number of the users,
Figure FDA0003839515020000018
representing a set of users; n is the number of sub-carriers,
Figure FDA0003839515020000019
representing a set of subcarriers, specifying that each user can and can only be allocated to one subcarrier; delta n,k An indicator variable, delta, for subcarrier allocation n,k =1 denotes allocation of subcarrier n to user k, δ n,k =0 denotes no allocation, δ = { δ = 1,1 ,…,δ 1,K ,…,δ n,1 ,…,δ n,K ,…,δ N,1 ,…,δ N,K Allocating a state set for the sub-carriers; a is a n,k Represents the power allocated to user k on subcarrier n, a = { a = { n } 1,1 ,…,a 1,K ,…,a n,1 ,…,a n,K ,…,a N,1 ,…,a N,K The user power set is used as the power set; v. of n,k ，f n And g n,k Channel matrices representing subcarriers n to user k, subcarriers n to RIS and RIS to user k, respectively, (-) H Represents a conjugate transpose; o n (k) Indicating the decoding order, o, of user k on subcarrier n n (k) = j denotes that user k is the jth decoded user, o = { o } 1 (1),…,o 1 (K),…,o n (1),…,o n (K),…,o N (1),…,o N (K) Is a decoding order set; l denotes other non-demodulated users, o n (l)＞o n (k) The signal of (a) will be treated as interference; sigma 2 Represents the variance of additive white gaussian noise with a mean of 0; p c Total circuit power consumed for the system; user k on subcarrier n has rate R n,k Is shown as
Figure FDA0003839515020000021
| · | represents modulo a complex number; suppose o n (k)＜o n (j) Rate R at which user k's signal is decoded at user j n,j→k Is shown as
Figure FDA0003839515020000022
P max Is the maximum transmit power at the base station;
s2, solving the energy efficiency maximization model, wherein the concrete steps are as follows:
step S201, the mth element on the diagonal of the reflection coefficient matrix theta of the initial RIS is:
Figure FDA0003839515020000023
channel matrix of subcarrier n to user k is v n,k The corresponding channel gain is | v n,k L, n ', k' are
Figure FDA0003839515020000024
The minimum subcarrier number and the user number, and the angle (·) represents the angle corresponding to the complex number; channel gain of user k is
Figure FDA0003839515020000025
User k selection
Figure FDA0003839515020000026
Maximum subcarrier
Figure FDA0003839515020000027
Order to
Figure FDA0003839515020000028
δ n,k ＝0,n≠n * (ii) a After all users select the subcarrier, obtaining a subcarrier distribution state set delta;
step S202, obtaining the value of the sub-carrier distribution state set delta by step S201, and enabling | v of the user k not distributed to the sub-carrier n n,k L =0; on subcarrier n, according to the method for all users
Figure FDA0003839515020000029
Is sorted from small to large, and the | v of the user k is recorded n,k The | value is ordered as i n Then o n (k)＝i n (ii) a Obtaining a decoding order set omicron after all subcarriers are sequenced;
step S203, after the subcarrier distribution state set delta and the decoding order set omicron are obtained, the constraint C3 of the model A1 is simplified; the energy efficiency maximization model B1, which converts the model A1 into the reflection coefficient matrix Θ for the user power set a and the RIS, is:
Figure FDA0003839515020000031
constraint conditions are as follows:
C1:
Figure FDA0003839515020000032
C2:
Figure FDA0003839515020000033
C3:
Figure FDA0003839515020000034
C4:θ m ∈[0,2π),m＝1,…,M
step S204, iteratively solving the energy efficiency maximization model B1, wherein in the ith iteration, the solving process is as follows:
step S2041, splitting the energy efficiency maximization model B1 to respectively obtain a model for optimizing a user power set a and a model for optimizing a reflection coefficient matrix theta of RIS; the model B2 for the user power set a is expressed as:
Figure FDA0003839515020000035
constraint conditions are as follows:
C1:
Figure FDA0003839515020000036
C2:
Figure FDA0003839515020000037
Θ (i-1) the matrix theta of the reflection coefficient of the RIS is obtained for the i-1 iteration; solving the model B2 by using a Dinkelbach method to obtain the ith timeIterative user power set a (i) ；
Step S2042,
Figure FDA0003839515020000038
Is a (i) The n × k-th element of (1); the maximization model B3 of the reflection coefficient matrix Θ for RIS is expressed as:
Figure FDA0003839515020000041
constraint conditions are as follows:
C1:
Figure FDA0003839515020000042
C2:θ m ∈[0,2π),m＝1,…,M
step S2043, introduce a relaxation variable
Figure FDA0003839515020000043
η＝[η 1,1 ,…,η 1,K ,…,η n,1 ,…,η n,K ,…,η N,1 ,…,η N,K ]；
Order to
Figure FDA0003839515020000044
t＝[t 1,1 ,…,t 1,K ,…,t n,1 ,…,t n,K ,…,t N,1 ,…,t N,K ]，
Figure FDA0003839515020000045
(·) * Represents a conjugate operation, then
Figure FDA0003839515020000046
Introducing vector beta = [ beta ] 1,1 ,…,β 1,K ,…,β n,1 ,…,β n,K ,…,β N,1 ,…,β N,K ]Model B3 is transformed into model B4, said model B4 being represented as:
Figure FDA0003839515020000047
constraint conditions are as follows:
C1:|s m |＝1,m＝1,…,M
C2:
Figure FDA0003839515020000048
C3:
Figure FDA0003839515020000049
C4:
Figure FDA00038395150200000410
step S2044, carrying out iterative solution on the model B4 by using a continuous convex approximation method and a penalty function method, wherein in the u-th iteration, the model B4 is converted into a model B5 as follows:
Figure FDA0003839515020000051
constraint conditions are as follows:
C1:|s m |≤1,m＝1,…,M
C2:
Figure FDA0003839515020000052
Figure FDA0003839515020000053
C3:
Figure FDA0003839515020000054
Figure FDA0003839515020000055
C4:
Figure FDA0003839515020000056
wherein
Figure FDA0003839515020000057
And s (u-1) Is the value of the u-1 th iteration,
Figure FDA0003839515020000058
is s (u-1) The mth element of (1); r (·) represents taking a real part;
step S2045, substituting variable values S, eta and beta obtained in the u-th iteration into the model B5 to calculate the target function, and when the value of the target function is not changed any more or the absolute value of the change is smaller than a threshold value epsilon 1 Then, the iteration method is terminated, s is output, and the s is diagonalized to obtain a RIS reflection coefficient matrix theta; otherwise, carrying out the next iteration;
step S205, substituting the user power set a obtained in the step S2041 and the RIS reflection coefficient matrix theta obtained in the step S2045 in the ith iteration into the model B1 to calculate the value of the objective function, and when the value of the objective function is not changed any more or the absolute value of the change is smaller than the threshold value epsilon 2 When the iteration method is ended, outputting a user power set a and outputting an RIS reflection coefficient matrix theta; otherwise, the next iteration is carried out.
2. An RIS assisted multi-carrier NOMA transmission system parameter optimization method according to claim 1, characterized in that said given threshold value e in step S2045 1 Is 10 -4 。
3. A RIS assisted multi-carrier NOMA transport system parameter optimization method according to claim 1, characterized by the given threshold value ε in step S205 2 Is 10 -4 。
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