CN113423112A - RIS assisted multi-carrier NOMA transmission system parameter optimization method - Google Patents
RIS assisted multi-carrier NOMA transmission system parameter optimization method Download PDFInfo
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Abstract
The invention discloses a parameter optimization method of 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 low-complexity decoding sequence optimization method 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 of the invention can effectively improve the channel quality and improve the system energy efficiency.
Description
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 the above, the present invention provides a method for optimizing parameters of an 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:
step S1, establishing an energy efficiency maximization model, wherein the energy efficiency maximization model A1 is expressed as:
constraint conditions are as follows:
C6:θm∈[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 thetam,m=0,1,…,M,Is the reflection coefficient matrix of the RIS, diag [ ·]Representing vector diagonalization; k is the number of the users,representing a set of users; n is the number of sub-carriers,representing a set of subcarriers, specifying that each user can be and can only be allocated to one subcarrier; deltan,kAn indicator variable, delta, for subcarrier allocationn,kWith 1 is meant that subcarrier n is allocated to user k, δn,k0 denotes no partition, δ ═ δ { δ ═ δ1,1,…,δ1,K,…,δn,1,…,δn,K,…,δN,1,…,δN,KAllocating a state set for the sub-carriers; a isn,kDenotes the power allocated to user k on subcarrier n, a ═ a1,1,…,a1,K,…,an,1,…,an,K,…,aN,1,…,aN,KThe user power set is used as the power set; v. ofn,k,fnAnd gn,kChannel matrices representing subcarriers n to user k, subcarriers n to RIS and RIS to user k, respectively, (-)HRepresents a conjugate transpose; on(k) Indicating the decoding order, o, of user k on subcarrier nn(k) J denotes that user k is the j-th decoded user, and o ═ { o ═1(1),…,o1(K),…,on(1),…,on(K),…,oN(1),…,oN(K) Is a decoding order set; sigma2Represents the variance of additive white gaussian noise with a mean of 0; pcTotal circuit power consumed for the system; user k on subcarrier n has rate Rn,kIs shown as| · | represents modulo a complex number; suppose on(k)<on(j) Rate R at which the signal of user k is decoded at user jn,j→kIs shown asPmaxIs the maximum transmit power at the base station;
step S2, solving the energy efficiency maximization model, and the specific steps are as follows:
step S201, the mth element on the diagonal of the reflection coefficient matrix theta of the initial RIS is:
channel matrix of subcarrier n to user k is vn,kThe corresponding channel gain is | vn,kI, n ', k' areThe minimum subcarrier number and the user number, and the angle (·) represents the angle corresponding to the complex number; channel gain of user k isUser k selectionMaximum subcarrierOrder toδn,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 nn,k0, |; on subcarrier n, according to the method for all usersIs sorted from small to large, and the | v of the user k is recordedn,kThe | value is ordered as inThen on(k)=in(ii) a After all the subcarriers are sequenced, a decoding sequence set o is obtained;
step S203, after the subcarrier distribution state set delta and the decoding sequence set o are obtained, simplifying a constraint C3 of a model A1; the energy efficiency maximization model B1, which transforms model a1 into a reflection coefficient matrix Θ for user power set a and RIS, is:
constraint conditions are as follows:
C4:θm∈[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 an 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 user power set a is expressed as:
constraint conditions are as follows:
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,Is a(i)The n × k-th element of (1); the maximization model B3 for the reflectance matrix Θ for RIS is expressed as:
constraint conditions are as follows:
C2:θm∈[0,2π),m=1,…,M
step S2043, introducing a relaxation variable:
η=[η1,1,…,η1,K,…,ηn,1,…,ηn,K,…,ηN,1,…,ηN,K];
(·)*Represents a conjugate operation, thenIntroducing vector beta ═ beta1,1,…,β1,K,…,βn,1,…,βn,K,…,βN,1,…,βN,K]Model B3 is transformed into model B4, which model B4 is represented as:
constraint conditions are as follows:
C1:|sm|=1,m=1,…,M
and 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 the model B5 as follows:
constraint conditions are as follows:
C1:|sm|≤1,m=1,…,M
whereinAnd s(u-1)Is the value of the u-1 th iteration,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 a model B5 to calculate an 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 a threshold value epsilon1Then, 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 epsilon2Then, 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 S20451Is 10-4。
Further, a given threshold value ε in step S2052Is 10-4
The invention has the beneficial effects that:
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 the joint optimization of the user power and the RIS reflection coefficient, a Dinkelbach method is used for optimizing the user power, a continuous convex approximation method and a penalty function method are used for optimizing the RIS reflection coefficient, 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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within 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 the bookRepresenting a set of users, the number of subcarriers N,representing a set of sub-carriers, each definedA user can and can only be allocated to one subcarrier.
First step, an,kRepresenting the power, s, allocated to user k on subcarrier nn,kThe transmission data representing user k on subcarrier n is an independent random variable with a mean of 0 and a variance of 1. Deltan,kAn indicator variable, delta, for subcarrier allocationn,kWith 1 is meant that subcarrier n is allocated to user k, δn,k0 means no allocation. Transmission signal x of subcarrier nnCan be expressed as:
secondly, the number of the reflection units of the RIS is M, and the phase position of the mth reflection unit is recorded as thetamE [0,2 pi)), M1, 2, … M, diagonal matrixMatrix of reflection coefficients, diag [. cndot.) representing the RIS]Representing the vector diagonalization. By the symbol vn,k,Andchannel matrices representing subcarriers n to user k, subcarriers n to RIS and RIS to user k, respectively, (-)HRepresenting 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 sigma2. 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 channeln,kCan be expressed as:
third step, with on(k) Representing on subcarrier nDecoding order of user k, on(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, on(l)>on(k) The signal of (b) is treated as interference, the signal to interference plus noise ratio y of the kth user on subcarrier nn,kThe calculation is as follows:
where | represents the rate R of the user modulo a complex numbern,kCan be represented as Rn,k=log2(1+γn,k)。
Fourth, assume on(k)<on(j) Calculating the velocity of user k at user j is expressed as:
fifth step, PcFor the total circuit power consumed by the system, the total power consumed by the RIS assisted NOMA system is calculated as:
sixthly, calculating the energy efficiency of the system as follows:
to obtain subcarrier allocation, user decoding order within subcarriers, user power and RIS reflection coefficient and apply to the above system, let δ be { δ ═ δ1,1,…,δ1,K,…,δn,1,…,δn,K,…,δN,1,…,δN,KDenotes a subcarrier allocation status set, o ═ o1(1),…,o1(K),…,on(1),…,on(K),…,oN(1),…,oN(K) Is a decoding order set, a ═ a1,1,…,a1,K,…,an,1,…,an,K,…,aN,1,…,aN,KEstablishing an energy efficiency maximization model for a user power set, wherein the energy efficiency maximization model is expressed as follows:
constraint conditions are as follows:
C6:θm∈[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:
channel matrix of subcarrier n to user k is vn,kThe corresponding channel gain is | vn,kI, n ', k' areThe smallest subcarrier number and user number, angle (·) represents the angle corresponding to the complex number. Channel gain of user k isUser k selectionMaximum subcarrierOrder toAnd after all users select the subcarrier, obtaining a subcarrier distribution state set delta.
Step 2: obtaining the value of a subcarrier allocation state set delta by the step 1, and enabling users k | v not allocated to the subcarrier nn,kAnd | ═ 0. On subcarrier n, according to the method for all usersIs sorted from small to large, and the | v of the user k is recordedn,kThe | value is ordered as inThen on(k)=in(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 transforms model a1 into a reflection coefficient matrix Θ for user power set a and RIS, is:
constraint conditions are as follows:
C4:θm∈[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 user power set a is expressed as:
constraint conditions are as follows:
Θ(i-1)the matrix theta of the reflection coefficient of the RIS obtained for 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: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:
constraint conditions are as follows:
C2:θm∈[0,2π),m=1,…,M
step 4-3: introducing a relaxation variable:
η=[η1,1,…,η1,K,…,ηn,1,…,ηn,K,…,ηN,1,…,ηN,K];
β=[β1,1,…,β1,K,…,βn,1,…,βn,K,…,βN,1,…,βN,K]Model B3 is transformed into model B4, which model B4 is represented as:
constraint conditions are as follows:
C1:|sm|=1,m=1,…,M
step 4-4: the solution was iterated using the successive convex approximation method and the penalty function method for model B4, and in the u-th iteration model B4 was transformed into model B5 as follows:
constraint conditions are as follows:
C1:|sm|≤1,m=1,…,M
And 4-5: 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 less than the threshold value 10-4Then, 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 a 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 less than a threshold value 10-4Then, 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 invention is not described in detail, but is 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 could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (3)
1. A parameter optimization method for RIS assisted multi-carrier NOMA transmission system is characterized by comprising the following steps:
step S1, establishing an energy efficiency maximization model, wherein the energy efficiency maximization model A1 is expressed as:
constraint conditions are as follows:
C6:θm∈[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 thetam,m=0,1,…,M,Is the reflection coefficient matrix of the RIS, diag [ ·]Representing vector diagonalization; k is the number of the users,representing a set of users; n is the number of sub-carriers,representing a set of subcarriers, specifying that each user can be and can only be allocated to one subcarrier; deltan,kAn indicator variable, delta, for subcarrier allocationn,kWith 1 is meant that subcarrier n is allocated to user k, δn,k0 denotes no partition, δ ═ δ { δ ═ δ1,1,…,δ1,K,…,δn,1,…,δn,K,…,δN,1,…,δN,KAllocating a state set for the sub-carriers; a isn,kDenotes the power allocated to user k on subcarrier n, a ═ a1,1,…,a1,K,…,an,1,…,an,K,…,aN,1,…,aN,KThe user power set is used as the power set; v. ofn,k,fnAnd gn,kRespectively representing subcarriers n to user k, subcarriers n to RIS and RIS to userk channel matrix, (.)HRepresents a conjugate transpose; on(k) Indicating the decoding order, o, of user k on subcarrier nn(k) J denotes that user k is the j-th decoded user, and o ═ { o ═1(1),…,o1(K),…,on(1),…,on(K),…,oN(1),…,oN(K) Is a decoding order set; sigma2Represents the variance of additive white gaussian noise with a mean of 0; pcTotal circuit power consumed for the system; user k on subcarrier n has rate Rn,kIs shown as| · | represents modulo a complex number; suppose on(k)<on(j) Rate R at which the signal of user k is decoded at user jn,j→kIs shown asPmaxIs the maximum transmit power at the base station;
step S2, solving the energy efficiency maximization model, and the specific steps are as follows:
step S201, the mth element on the diagonal of the reflection coefficient matrix theta of the initial RIS is:
channel matrix of subcarrier n to user k is vn,kThe corresponding channel gain is | vn,kI, n ', k' areThe minimum subcarrier number and the user number, and the angle (·) represents the angle corresponding to the complex number; channel gain of user k isUser k selectionMaximum subcarrier n*,Order toδn,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 nn,k0, |; on subcarrier n, according to the method for all usersIs sorted from small to large, and the | v of the user k is recordedn,kThe | value is ordered as inThen on(k)=in(ii) a After all the subcarriers are sequenced, a decoding sequence set o is obtained;
step S203, after the subcarrier distribution state set delta and the decoding sequence set o are obtained, simplifying a constraint C3 of a model A1; the energy efficiency maximization model B1, which transforms model a1 into a reflection coefficient matrix Θ for user power set a and RIS, is:
constraint conditions are as follows:
C4:θm∈[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 an 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 user power set a is expressed as:
constraint conditions are as follows:
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,Is a(i)The n × k-th element of (1); the maximization model B3 for the reflectance matrix Θ for RIS is expressed as:
constraint conditions are as follows:
C2:θm∈[0,2π),m=1,…,M
Order tot=[t1,1,…,t1,K,…,tn,1,…,tn,K,…,tN,1,…,tN,x],(·)*Represents a conjugate operation, thenIntroducing vector beta ═ beta1,1,…,β1,K,…,βn,1,…,βn,K,…,βN,1,…,βN,K]Model B3 is transformed into model B4, which model B4 is represented as:
constraint conditions are as follows:
C1:|sm|=1,m=1,…,M
and 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 the model B5 as follows:
constraint conditions are as follows:
C1:|sm|≤1,m=1,…,M
whereinAnd s(u-1)Is the value of the u-1 th iteration,is s(u-1)The mth element of (1); r (·) represents taking a real part;
step S2045, obtaining the variable value of the u-th iterations, eta, beta are substituted into the model B5 to calculate the objective function when the value of the objective function is no longer changed or the absolute value of the change is less than the threshold value epsilon1Then, 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 epsilon2Then, 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.
2. A RIS assisted multi-carrier NOMA transmission system parameter optimization method according to claim 1, characterized in that, the given threshold value e in step S20451Is 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 S2052Is 10-4。
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