CN115037394B

CN115037394B - GSIC-based multiple RISs-assisted NOMA system design method

Info

Publication number: CN115037394B
Application number: CN202210508742.XA
Authority: CN
Inventors: 富燊; 王鸿; 马昊淳
Original assignee: Nanjing University of Posts and Telecommunications
Current assignee: Nanjing University of Posts and Telecommunications
Priority date: 2022-05-11
Filing date: 2022-05-11
Publication date: 2023-07-28
Anticipated expiration: 2042-05-11
Also published as: CN115037394A

Abstract

The invention discloses a multi-RISs auxiliary NOMA system design method based on group serial interference deleting GSIC, which establishes an optimization problem P1 of the phase shift design of a user transmitting power, an equalizer and RIS on the premise of meeting the minimum transmission rate requirement of each user, takes the total transmission power of the system as an optimization target, and optimizes the phase shift of the transmitting power, the equalizer and the RIS of each user by using the variable; according to the expression of the equalizer, converting into a problem P2, optimizing the transmitting power of a user by using a parallel iteration method, and substituting the transmitting power into the expression of the equalizer to optimize the equalizer; the problem P2 is converted into a pure phase shift optimization problem P3, the phase shift of the RIS is designed by adopting a parallel iteration method, and the expression of the signal to noise ratio of a user is simplified; an objective function is inserted to maximize the sum of SINR of all users, the solution is converted into a problem P4, the phase shift is optimized by using a sequential rotation method, the solution is converted into a problem P5, and a penalty function method is used to obtain an RIS phase shift optimal solution.

Description

GSIC-based multiple RISs-assisted NOMA system design method

Technical Field

The invention belongs to the technical field of wireless communication, and relates to a multi-intelligent reflecting surface RIS-assisted non-orthogonal multiple access NOMA system design method based on Group Serial Interference Cancellation (GSIC).

Background

Smart reflective surfaces (RIS) are very promising candidates for improving the performance of future sixth generation wireless communication networks and thus have attracted considerable attention from many researchers. Since the RIS reflects only signals and operates in full duplex mode, the RIS can improve communication performance without the need for an active radio frequency chain, thereby reducing the energy consumption and hardware cost of the system. Therefore, RIS has economical and environmental protection properties. Non-orthogonal multiple access (NOMA) technology is one of the key technologies for the next generation wireless communication system, and is also attracting attention and research. NOMA techniques are distinguished from conventional orthogonal multiple access techniques, such as frequency division multiple access techniques, time division multiple access techniques, and the like, in that users employing non-orthogonal multiple access techniques do not require the use of mutually orthogonal resources. Because NOMA techniques employ superposition coding and successive interference cancellation techniques, higher energy efficiency can be achieved than conventional orthogonal multiple access techniques.

The prior transmission method of NOMA system assisted by multiple RISs under the condition of configuring multiple antennas with respect to a base station does not fully jointly optimize the transmitting power of users, an equalizer and the phase offset of RISs. For the RIS assisted OMA scheme, the advantage of the NOMA system for reducing power consumption is not utilized, and mutually orthogonal resources must be used for transmission of multiple users. For NOMA schemes without RIS assistance, the advantage of RIS in helping the user to increase signal strength cannot be exploited. For the RIS-assisted NOMA scheme under the random phase shift condition, the phase shift of the RIS cannot be reasonably regulated by utilizing the channel state, so that the system performance is improved. Thus, the above schemes have limitations, so we provide a new scheme to minimize the total transmission power of the system.

Disclosure of Invention

The purpose is as follows: in order to overcome the defects in the prior art, the invention provides a multi-RISs auxiliary NOMA system design method based on GSIC, so that the power consumption of the NOMA system is greatly reduced.

The technical scheme is as follows: in order to solve the technical problems, the invention adopts the following technical scheme:

a multi-intelligent reflecting surface-assisted non-orthogonal multiple access system design method based on group serial interference deletion comprises the following steps:

s1, establishing a mathematical expression of a total received signal at a base station;

s2, establishing channel models between a user and a base station, between an RIS and the base station and between the user and the RIS required in the system;

s3, dividing the users into a cell center user and a cell edge user according to the propagation distance, and demodulating the cell center user and the cell edge user in sequence by using the GSIC; after the signal demodulation of the cell center user is finished, deleting the signal of the cell center user and then continuously demodulating the signal of the cell edge user; respectively obtaining the restored data of each user and the expression of the SINR;

s4, on the premise of meeting the minimum transmission rate requirement of each user, establishing an optimization problem P1 of the phase offset design of the user transmitting power, the equalizer and the RIS, taking the total transmission power of the system as an optimization target, and optimizing variables as the phase offset of the transmitting power, the equalizer and the RIS of each user;

s5, further obtaining an expression of a user signal to noise ratio according to the expression of the optimal equalizer of each user, so that an optimization problem P1 is converted into a joint optimization problem P2 of user transmitting power and RIS phase offset;

s6, according to the characteristics of the optimization problem P2, when the optimization problem P2 takes an optimal solution, the constraint condition of the minimum rate requirement in the optimization problem P2 takes an equal sign, and simultaneously, the transmission power of a user is optimized by using a parallel iteration method and is substituted into an expression of an equalizer, so that the equalizer is further optimized;

s7, converting the optimization problem P2 into a pure phase shift optimization problem P3, and designing the phase shift of the RIS by adopting a parallel iteration method to further simplify the expression of the signal to noise ratio of the user;

s8, representing the SINR by a compact form, inserting an objective function to maximize the sum of SINR of all users, and converting the optimization problem P3 into an optimization problem P4;

s9, optimizing phase shift by using a sequential rotation method, and further obtaining an expression of a user signal-to-interference-plus-noise ratio (SINR);

s10, the optimization problem P4 is further converted into an optimization problem P5, and an optimal solution of the phase shift is obtained by using a penalty function method.

In some embodiments, in S1, the total received signal z at the base station _B Expressed as:

where i represents the ith center user, j represents the jth edge user, h _C，i And h _E，j Representing user i in the cell center group and cell edge group, respectivelyDirect-connection channel parameter, alpha, between user j and base station BS _C，i And alpha _E，j Transmission coefficients, x, representing cell center user i and cell edge user j, respectively _C，i And x _E，j The transmission data of the cell center user i and the transmission data of the cell edge user j are respectively,representing the channel vector, G, between user j of a cell edge group and the RIS it serves _j Representing the channel matrix, Φ, between the jth RIS and the base station BS _j The phase shift matrix representing the jth intelligent reflection surface RIS, denoted +.>Wherein τ _j，n Representing the phase shift of the nth reflective element in the jth cell edge user, N representing the number of reflective elements in each IRS, n= {1,2,3,..;

due to practical circuit limitations, the RIS phase offset is set to be uniformly discrete, τ _j，n Is defined asWherein B is the number of resolution bits, i.e. ->

p represents Gaussian noise at the base stationWherein->Is the noise power; the number of users of the cell center group and the number of users of the cell edge group are U; and each edge user is equipped with a separate RIS, the jth edge user is assisted in communication by the jth RIS.

In some embodiments, in S2, the direct channel between the user and the base station BS is modeled as rice fading, denoted as

Wherein h is _C，i And h _E，j Representing direct channel parameters, d, between user i in the cell center group and user j and Base Station (BS) in the cell edge group, respectively _C，i And d _E，j Respectively representing the propagation distances between the ith cell center user and the jth cell edge user and the BS, ρ _B，C Is the path loss index between the central user and the BS,and->Represents the line-of-sight path gain (LoS), ρ, between the ith cell center user and the jth cell edge user and the BS, respectively _B，E Refers to the path loss index, K, between the edge user and the BS _B，U Refers to the rice K factor of the channel between the user and BS, the small scale fading vector q _C，i And q _E，j Is subject to +.>

The user-RIS-related channel is also modeled as rice fading, denoted as

g _j Is the channel parameter between the jth cell edge user and the corresponding jth RIS, G _j Is the channel parameter between BS and jth RIS, L _j Is the propagation distance, ρ, between the jth cell edge user and the corresponding jth RIS _I，U Is the path loss index between the user and the RIS,is the LoS gain, K between the jth cell edge user and the jth RIS _I，U Refers to the rice K factor of the channel between the RIS and the user, the small scale fading vector q _j Is subject to +.>d _j Is the propagation distance between BS and jth RIS, ρ _B，I Is the path loss index between BS and RIS, < >>Is the LoS gain, K, between BS and the jth RIS _B，I Refers to the rice K factor of the channel between BS and RIS, fading vector Q in small scale _j Each element of (a) follows +.>

In some embodiments, in S3, data detection of the user is performed, and the detection scheme is implemented group by group; the reason is that the later decoded group is not interfered with by the user signal of the previous group with the help of Group Serial Interference Cancellation (GSIC); specifically, the signals of each user in the cell center group are designed first, then the signals of the cell center group are deleted, and then the cell edge group is detected:

when decoding the signals of the cell center users, the signals of the cell edge users are regarded as noise; let w be _C，i Is the equalizer of the i-th cell center user, the recovered data is expressed as

Wherein the method comprises the steps ofData recovered for the ith central user; />Is w _C，i Is a conjugate transpose of (2);

when the signals of the cell edge users are decoded, deleting the decoded signals of the cell center users; let w be _E，j Equalizer for jth cell edge user, the recovered data is expressed as

Wherein the method comprises the steps ofData recovered for the jth edge user; />Is w _E，j Is a conjugate transpose of (2);

signal-to-interference-and-noise ratio gamma of ith cell center user _C，i ：

Signal-to-interference-and-noise ratio gamma of jth cell edge user _E，j Expressed as

Wherein the method comprises the steps ofIs the noise power.

In some embodiments, in S4, the optimization problem P1 is expressed as:

s.t.Q1：log ₂ (1+γ _C，i )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j )≥r _E，j ^(th) ，1≤j≤U

wherein P is the total transmission power of the system; w (w) _C，i And w _E，j Equalizer representing the ith center user and equalizer of the jth edge user, respectively, r _C，i ^(th) And the rE is a function of the R, _j ^(th) minimum data rates representing user i in the cell center group and user j in the cell edge group, respectively; constraints Q1 and Q2 guarantee the quality of service for the user, constraint Q3 is used to ensure that each phase shifter belongs to a predefined set.

In some embodiments, in S5,

wherein I represents an identity matrix of a×a, a refers to the number of antennas at the base station; by substituting the equalizer into the SINR expression, the signal-to-interference-and-noise ratio (SINR) γC of the ith cell center user is retrieved _，i ⁽¹⁾ And the SINR gamma of the jth cell edge user _E，j ⁽¹⁾ The method comprises the following steps:

wherein the intra-group interference of the ith central userInter-group interference of the ith central user +.>And intra-group interference of jth edge user +.>The expression of (2) is as follows:

converting the optimization problem P1 into a joint optimization problem P2 of the user transmit power and the phase offset of the RIS

s.t.Q1：log ₂ (1+γ _C，i ⁽¹⁾ )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽¹⁾ )≥r _E，j ^(th) ，1≤j≤U

In some embodiments, in S6, as known from the countercheck method, the optimization problem P2 satisfies the constraint conditions Q1 and Q2 when obtaining the optimal solution; thus there is

Wherein,,transmit power for the ith central user, < >>The transmission power of the jth edge user is the optimal transmission power of different users is interactive; that is, when the transmission power of each user is optimized, the transmission power of other users is affected; therefore, a parallel iteration method is adopted, and when the ith user is optimized for the t time, the transmission power of other users takes the iteration result of the (t-1); obtain the transmission power of the ith center user after the t-th iteration +.>And the transmission power of the jth edge user after the t iteration +.>Namely expressed as:

wherein the intra-group interference of the ith central userInter-group interference of the ith central user +.>And intra-group interference of jth edge user +.>The results of the (t-1) th iteration of (c) are as follows:

then substitute w _C，i And w _E，j In the expression of (2), the optimal equalizer of the ith central user after the t-th iteration is obtainedAnd the optimal equalizer for the jth edge user after the t-th iteration +.>

In some embodiments, in S7, each RIS is for a givenAnd->And +.>And->To design an optimal phase shift; the optimization problem P2 is converted into a pure phase shift optimization problem P3:

(P3)Find：{Φ _i }

s.t.Q1：log ₂ (1+γ _C，i ⁽¹⁾ )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽¹⁾ )≥r _E，j ^(th) ，1≤j≤U

adopting a parallel iteration method, when the phase offset of the kth RIS is optimized for the t time, the phase offsets of other RISs take the iteration result of (t-1); i.e. in the t-th iteration, the phase offset of the other RIS is considered constant;

when designing the phase offset of the kth RIS, the SINR of user i of the cell center group is further reduced to gamma _C，i ⁽²⁾ ：

Wherein parameter M is defined ₁ And M ₂ ，

SINR of user j of cell edge group is further reduced to gamma _E，j ⁽²⁾ ：

Wherein parameter M is defined ₃ 、M ₄ And M ₅ ，

In some embodiments, S8 comprises:

defining parameter T _C，i，k 、v _k And q _C，i，k ^H The method comprises the following steps:

thus, SINR gamma of the ith center user _C，i ⁽³⁾ Further converted into:

to obtain SINR of edge users, a parameter T is defined _E，j，k And q _E，j，k ^H The method comprises the following steps:

thus SINR gamma of the jth edge user _E，j ⁽³⁾ Further converted into:

to minimize the total transmission power in (t+1) iterations, an objective function is inserted to maximize the sum of SINR for all users; then, the problem P3 is converted into the problem P4:

s.t.Q1：log ₂ (1+γ _C，i ⁽³⁾ )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽³⁾ )≥r _E，j ^(th) ，1≤j≤U

in some embodiments, S9 comprises:

firstly, designing the phase offset of the RIS of the 1 st group, then performing phase shift design on the RIS of the 2 nd group, and so on; for each RIS, a sequential phase shift approach is proposed to solve problem P4; thus, the resulting optimized phase shift of the kth RIS in the t-th iterationIs that

Wherein the rotation matrix of the phase shift of the nth reflective element of the kth RIS is givenWherein θ is _k，n A twiddle factor representing the phase shift of the nth reflective element of the kth RIS, if +.>The rotational phase shift modulo 2 pi still belongs to the set +.>The phase shift solution for the nth rotation of the kth RIS in the nth iteration is defined as +.>

Thus, a result is obtained

Rotation matrix Ω of the nth reflective element at the kth RIS _k，n In the design of (2), the phase shift vector of the last rotation is givenThus, the SINR gamma of the i-th cell center user _C，i ⁽⁴⁾ And jth cell edge userSINR gamma of (2) _E，j ⁽⁴⁾ Is rewritten as:

definition of parameter f _{C，i，k，n} (θ _k，n )、ρ _{C，i，k，n} 、ω _{C，i，k，n} 、f _{E，j，k，n} (θ _k，n )、ρ _{E，j，k，n} 、ω _{E，j，k，n} 、/>And->Wherein the method comprises the steps of

Wherein,,and->Representing the extraction of the real and imaginary parts of a complex number, respectively.

In some embodiments, S10 comprises:

definition of parameter y ₁ (θ _k，n )、y ₂ (θ _k，n ) And y ₃ (θ _k，n ) Wherein, the method comprises the steps of, wherein, there is only one optimization variable in question P5;

obtaining the optimal rotation value of the nth reflection element of the kth RIS by applying a punishment method

Wherein the index function l (ε) is defined as follows: if ε+.0, then L (ε) = 0, otherwise it is L (ε) = -L, where penalty parameter L is a very large positive number.

The beneficial effects are that: the multiple RISs-assisted NOMA system design method based on the GSIC provided by the invention has the following advantages: GSIC is used to cancel inter-group interference and to suppress intra-group interference by designing the transceiver. In order to minimize the total transmission power of the system, we design a parallel iterative algorithm to obtain optimal power control, and optimize the phase offset of RIS by sequential rotation method, so as to greatly reduce the total emission power consumption of the NOMA system assisted by multi-intelligent reflection surface RIS. Compared with other NOMA and Orthogonal Multiple Access (OMA) schemes, the invention can greatly reduce the total transmitting power consumption of the system on the premise of meeting the minimum transmission rate of the user.

Drawings

Fig. 1 is a diagram of a multi-intelligent reflector assisted non-orthogonal multiple access system uplink transmission model according to an embodiment of the present invention;

FIG. 2 is a graph of total emitted power consumption of the system for different numbers of RIS reflective elements in an embodiment;

fig. 3 is a graph of total transmission power consumption of the system under different minimum transmission rate conditions in an embodiment.

Detailed Description

The invention is further described below with reference to the drawings and examples. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.

In the description of the present invention, the meaning of a number is one or more, the meaning of a number is two or more, and greater than, less than, exceeding, etc. are understood to exclude the present number, and the meaning of a number is understood to include the present number. The description of the first and second is for the purpose of distinguishing between technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.

In the description of the present invention, the descriptions of the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Example 1

In some embodiments, the present invention contemplates uplink transmissions for multiple sets of NOMA systems, where the transmissions for each cell-edge user are aided by a RIS. The number of antennas provided by the Base Station (BS) and the user are a and 1, respectively. The number of reflective elements on the RIS is N. Let the number of concurrent transmissions of the cell center user and the edge user be U. To ensure parallel detection of each set of BSs, u+.a needs to be satisfied. We consider the distance between the intelligent reflective surfaces well separated. Thus, signals received by uncorrelated RIS are ignored at the BS due to obstruction of obstacles and double-loss of cascaded channels. A schematic diagram of the system model of the present invention is shown in FIG. 1. The invention aims to research a multi-intelligent reflecting surface-assisted non-orthogonal multiple access system uplink transmission method based on group serial interference deletion, which comprises the following specific implementation steps:

s1, obtaining a mathematical expression of the total received signal of the receiving end of the base station.

In NOMA mode, each user transmits a signal to a base station on the same time-frequency resource, signal z received at the base station _B Is modeled as

Where i represents the ith center user, j represents the jth edge user, h _C，i And h _E，j Representing direct channel parameters, alpha, between user i in the cell center group and user j in the cell edge group and the base station BS, respectively _C，i And alpha _E，j Transmission coefficients, x, representing cell center user i and cell edge user j, respectively _C，i And x _E，j The transmission data of the cell center user i and the transmission data of the cell edge user j are respectively,representing the channel vector, G, between user j of a cell edge group and the RIS it serves _j Representing the channel matrix, Φ, between the jth RIS and the base station BS _j The phase shift matrix representing the jth intelligent reflection surface RIS, denoted +.>Wherein τ _j，n Represents the jth cell edgeA phase shift of an nth reflective element in the user, N representing the number of reflective elements in each IRS, n= {1,2,3,., N };

due to practical circuit limitations, the RIS phase offset is set to be uniformly discrete, τ _j，n Is defined asWherein B is the number of resolution bits, that is, < +.>

S2, establishing channel models between users and base stations, between RIS and base stations and between users and RIS required in the system.

The channel has small scale fading and distance-based path loss characteristics. Thus, the base station

Wherein h is _C，i And h _E，j Representing direct channel parameters, d, between user i in the cell center group and user j and Base Station (BS) in the cell edge group, respectively _C，i And d _E，j Respectively representing the ith cell center user and the ith cell center userPropagation distance between j cell edge users and BS, ρ _B，C Is the path loss index between the central user and the BS,and->Represents the line-of-sight path gain (LoS), ρ, between the ith cell center user and the jth cell edge user and the BS, respectively _B，E Refers to the path loss index, K, between the edge user and the BS _B，U Refers to the rice K factor of the channel between the user and BS, the small scale fading vector q _C，i And q _E，j Is subject to +.>

The user-RIS-related channel is also modeled as rice fading, denoted as

S3, according to NOMA uplink demodulation principle, the propagation distances are sequenced from small to large, the user signals of the cell center group and the user signals of the cell edge group are demodulated in sequence, after the user signals of the center group are demodulated, the user signals of the edge group are deleted from the total received signals, the user signals of the edge group are demodulated continuously, and the data recovered by each user and the expression of the signal to noise ratio are obtained respectively.

And carrying out data detection of the users, wherein the detection scheme is realized group by group. The reason is that the later decoded group is not interfered with by the user signal of the previous group with the help of Group Serial Interference Cancellation (GSIC). Specifically, the signals of each user in the cell center group are designed first, then the signals of the cell center group are deleted, and then the cell edge group is detected.

In decoding the signals of the cell center users, the signals of the cell edge users are regarded as noise. Let w be _C，i Is the equalizer of the i-th cell center user, the recovered data is expressed as

/>

signal to interference plus noise ratio (SINR) gamma for the i-th cell center user _C，i ：

Signal-to-interference-and-noise ratio (SINR) gamma for jth cell-edge user _E，j Expressed as

Wherein the method comprises the steps ofIs the noise power.

And S4, on the premise of meeting the minimum transmission rate requirement of each user, establishing an optimization problem P1 of the phase offset design of the user transmitting power, the equalizer and the RIS, wherein the optimization target is the minimization of the total transmitting power of the system, and the optimization variables are the phase offsets of the transmitting power, the equalizer and the intelligent reflecting surface of each user.

Establishing an optimization problem P1, wherein an optimization variable is the transmitting power of a user, the phase offset of an equalizer and RIS, and an optimization target is to minimize the total transmitting power consumption of a system, and the method comprises the following steps:

s.t.Q1：log ₂ (1+γ _C，i )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j )≥r _E，j ^(th) ，1≤j≤U

wherein P is the total transmission power of the system; w (w) _C，i And w _E，j Equalizer representing the ith center user and equalizer of the jth edge user, respectively, r _C，i ^(th) And r _E，j ^(th) Minimum data rates representing user i in the cell center group and user j in the cell edge group, respectively; constraints Q1 and Q2 guarantee the quality of service for the user, constraint Q3 is used to ensure that each phase shifter belongs to a predefined set.

S5, obtaining an expression of the optimal equalizer of each user, and further obtaining an expression of the signal to noise ratio of the user, so that the optimization problem P1 is converted into a joint optimization problem P2 of transmission power and phase offset of RIS.

We use MMSE equalizer here because MMSE equalizer is the best equalizer for each user's SINR. Thus, the optimal equalizer can be expressed as a function of the transmit power, expressed as

Wherein I represents an identity matrix of a×a, a refers to the number of antennas at the base station; by substituting the equalizer into the SINR expression, the signal-to-interference-and-noise ratio (SINR) gamma of the ith cell center user is retrieved _C，i ⁽¹⁾ And the SINR gamma of the jth cell edge user _E，j ⁽¹⁾ The method comprises the following steps:

s.t.Q1：log ₂ (1+γ _C，i ⁽¹⁾ )≥r _c，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽¹⁾ )≥r _E，j ^(th) ，1≤j≤U

S6, according to the characteristics of the optimization problem P2, the method can be used, when the optimization problem P2 takes an optimal value, constraint conditions on the minimum rate requirement in the optimization problem P2 take equal signs, meanwhile, the parallel iteration method is used for optimizing the transmitting power of a user, and the transmitting power is substituted into an expression of the equalizer, so that the equalizer can be further optimized.

By using the back-proving method, we can know the condition that the constraint conditions Q1 and Q2 are satisfied to take the equation when the optimization problem P2 obtains the optimal solution. Then we have

Wherein,,transmit power for the ith central user, < >>The transmission power of the jth edge user is the optimal transmission power of different users is interactive; that is, the transmit power of each user is optimizedInfluence of transmit power to other users; therefore, a parallel iteration method is adopted, and when the ith user is optimized for the t time, the transmission power of other users takes the iteration result of the (t-1); obtain the transmission power of the ith center user after the t-th iteration +.>And the transmission power of the jth edge user after the t iteration +.>Namely expressed as:

S7, converting the optimization problem P2 into a pure phase shift optimization problem P3, and designing the phase shift of the RIS by adopting a parallel iteration method so as to further simplify the expression of the user SINR.

Each RIS for a givenAnd->And +.>And->To design an optimal phase shift; the optimization problem P2 is converted into a pure phase shift optimization problem P3:

(P3)Find：{Φ _i }

s.t.Q1：log ₂ (1+γ _C，i ⁽¹⁾ )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽¹⁾ )≥r _E，j ^(th) ，1≤j≤U

Wherein parameter M is defined ₁ And M ₂ ，

Wherein parameter M is defined ₃ 、M ₄ And M ₅ ，

S8, representing the SINR in a compact form, inserting an objective function to maximize the sum of SINR of all users, and thus converting the optimization problem P3 into the optimization problem P4.

Expressing the signal-to-noise ratio SINR of the user in a compact form, defining the parameter T _C，i，k 、v _k And q _C，i，k ^H The method comprises the following steps:

thus, SINR gamma of the ith center user _C，i ⁽³⁾ Further converted into:

/>

thus SINR gamma of the jth edge user _E，j ⁽³⁾ Further converted into:

s.t.Q1：log ₂ (1+γ _C，i ⁽³⁾ )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽³⁾ )≥r _E，j ^(th) ，1≤j≤U

s9, optimizing the phase shift by using a sequential rotation method, and further obtaining an expression of the user SINR.

Wherein the rotation matrix of the phase shift of the nth reflective element of the kth RIS is givenWherein θ is _k，n Nth reflection representing kth RISThe twiddle factor of the elemental phase shift can prove that if +.>The rotational phase shift modulo 2 pi still belongs to the set +.>The phase shift solution for the nth rotation of the kth RIS in the nth iteration is defined as +.>

Thus, a result is obtained

Rotation matrix Ω of the nth reflective element at the kth RIS _k，n In the design of (2), the phase shift vector of the last rotation is givenThus, the SINR gamma of the i-th cell center user _C，i ⁽⁴⁾ And SINR gamma of jth cell edge user _E，j ⁽⁴⁾ Is rewritten as:

/>

S10, further converting the optimization problem P4 into a problem P5, and obtaining an optimal solution of phase shift by using a penalty function method;

/>

definition of parameter y ₁ (θ _k，n )、y ₂ (θ _k，n ) And y ₃ (θ _k，n ) Wherein, the method comprises the steps of, wherein, in question P5 there is only one optimization variable；

The performance of the multi-intelligent reflector auxiliary NOMA system based on group serial interference deletion, which is provided by the invention, is illustrated by a simulation experiment. The system parameters are as follows: coverage radius R of cell _B The number of antennas per user a=4, the number of center and edge users are both U, u=2, noise powerThe channel is modeled as the product of the path loss and the small-scale fading, where the path loss index ρ of the center user to the base station _B，C =2.5, the path loss index of the edge user to the base station is ρ _B，E =3.5, ris to base station pathloss index ρ _B，I =3, path loss index ρ of edge user to RIS _I，U Small-scale fading obeys rice fading, the rice K factor of each channel is 3, the penalty parameter l=10000, the propagation distance L between the jth cell edge user and the corresponding jth RIS _j ∈[5，50]Distance d of jth RIS from base station _j Distance d from ith center user to base station =300 _C，i ∈[20，70]The resolution bit number b=4.

FIG. 2 shows the effect of different numbers of RIS reflective elements on total transmit power consumption, minimum transmission rates for cell center users and cell edge usersFour cases are considered simultaneously: an uplink transmission method of a NOMA system without RIS assistance, an uplink transmission method of a NOMA system with RIS assistance under the condition of random phase shift, an uplink transmission method of an OMA system with RIS assistance, and an uplink transmission method of a NOMA system with RIS assistance after optimizing phase shift. It is not difficult to find that as the number of reflective elements in the RIS increases, the total transmit power of the three conditions with the assistance of the RIS tends to decrease, and the advantage of the RIS in reducing the power consumption of the system can also be demonstrated. The reason for this is that the system performance is significantly improved, since a large number of reflective elements can enhance the received useful signal power. Under the condition of different numbers of reflecting elements, the total emission power consumption of the method is lower than that of other various reference methods, and the method also proves the advantages of the method in the aspect of reducing the system power consumption.

Fig. 3 shows a graph of the total transmit power consumption for different minimum user transmission rate conditions, where the number of RIS reflection elements n=100, and considers four cases: an uplink transmission method of a NOMA system without RIS assistance, an uplink transmission method of a NOMA system with RIS assistance under the condition of random phase shift, an uplink transmission method of an OMA system with RIS assistance, and an uplink transmission method of a NOMA system with RIS assistance after optimizing phase shift. It can be seen that the total transmission power after the phase shift is optimized is significantly improved. In addition, the total transmission power under the OMA scheme is always larger than NOMA, and the NOMA system performance can be proved to be more perfect. Under the condition of random phase shift, the power consumption of the RIS-assisted NOMA system is obviously higher than the total power consumption after the phase shift design of the RIS-assisted NOMA system, and the scientific rationality of the scheme of the RIS-assisted NOMA system can be proved. Finally, it can be seen from the figure that the performance of the system without deployed RIS is significantly worse, and the advantages of the RIS-assisted NOMA system are fully demonstrated.

Example 2

In a second aspect, the present embodiment provides an intelligent reflection-surface-assisted NOMA uplink transmission device under a non-ideal serial interference deletion condition, including a processor and a storage medium;

the storage medium is used for storing instructions;

the processor is operative according to the instructions to perform the steps of the method according to embodiment 1.

It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.

Claims

1. A multi-intelligent reflecting surface-assisted non-orthogonal multiple access system design method based on group serial interference deletion is characterized by comprising the following steps:

s10, further converting the optimization problem P4 into an optimization problem P5, and obtaining an optimal solution of phase shift by using a penalty function method;

wherein in S1, the total received signal z at the base station _B Expressed as:

where i represents the ith center user, j represents the jth edge user, h _C,i And h _E,j Representing direct channel parameters, alpha, between user i in the cell center group and user j in the cell edge group and the base station BS, respectively _C，i And alpha _E，j Transmission coefficients, x, representing cell center user i and cell edge user j, respectively _C,i And x _E,j The transmission data of the cell center user i and the transmission data of the cell edge user j are respectively,representing the channel vector, G, between user j of a cell edge group and the RIS it serves _j Representing the channel matrix, Φ, between the jth RIS and the base station BS _j The phase shift matrix representing the jth intelligent reflection surface RIS, denoted +.>Wherein τ _j，n Representing the phase shift of the nth reflective element in the jth cell edge user, N representing the reflective element in each IRSNumber of elements, n= {1,2,3,..n };

p represents Gaussian noise at the base stationWherein->Is the noise power; the number of users of the cell center group and the number of users of the cell edge group are U; and each edge user is equipped with a separate RIS, so the jth edge user is assisted in communication by the jth RIS;

wherein S2 comprises:

the direct channel between the user and the base station BS is modeled as rice fading, expressed as:

wherein h is _C,i And h _E,j Representing direct channel parameters, d, between user i in the cell center group and user j and Base Station (BS) in the cell edge group, respectively _C,i And d _E,j Respectively representing the propagation distances between the ith cell center user and the jth cell edge user and the BS, ρ _B，C Is a path loss finger between the central user and the BSThe number of the product is the number,and->Represents the line-of-sight path gain (LoS), ρ, between the ith cell center user and the jth cell edge user and the BS, respectively _B，E Refers to the path loss index, K, between the edge user and the BS _B,U Refers to the rice K factor of the channel between the user and BS, the small scale fading vector q _C,i And q _E,j Is subject to +.>

The user-RIS related channel is also modeled as rice fading, expressed as:

g _j is the channel parameter between the jth cell edge user and the corresponding jth RIS, G _j Is the channel parameter between BS and jth RIS, L _j Is the propagation distance, ρ, between the jth cell edge user and the corresponding jth RIS _I，U Is the path loss index between the user and the RIS,is the LoS gain, K between the jth cell edge user and the jth RIS _I,U Refers to the rice K factor of the channel between the RIS and the user, the small scale fading vector q _j Is subject to +.>d _j Is the propagation distance between BS and jth RIS, ρ _B，I Is the path loss index between BS and RIS, < >>Is the LoS gain, K, between BS and the jth RIS _B,I Refers to the rice K factor of the channel between BS and RIS, fading vector Q in small scale _j Each element of (a) follows +.>

2. The multiple intelligent reflector-assisted non-orthogonal multiple access system design method based on group serial interference cancellation as claimed in claim 1, wherein S3 comprises:

when decoding the signals of the cell center users, the signals of the cell edge users are regarded as noise; let w be _C,i Is the equalizer of the i-th cell center user, the recovered data is expressed as

Wherein the method comprises the steps ofData recovered for the ith central user; />Is w _C,i Is a conjugate transpose of (2);

when the signals of the cell edge users are decoded, deleting the decoded signals of the cell center users; let w be _E,j Equalizer for jth cell edge user, the recovered data is expressed as

Wherein the method comprises the steps ofData recovered for the jth edge user; />Is w _E,j Is a conjugate transpose of (2);

signal-to-interference-and-noise ratio gamma of ith cell center user _C，i ：

Wherein the method comprises the steps ofIs the noise power.

3. The method for designing a multiple intelligent reflector-assisted non-orthogonal multiple access system based on group serial interference cancellation according to claim 1, wherein in S4, the optimization problem P1 is expressed as:

(P1)

s.t.Q1：log ₂ (1+γ _C，i )≥r _C,i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j )≥r _E,j ^(th) ，1≤j≤U

wherein P is the total transmission power of the system; w (w) _C,i And w _E,j Equalizer representing the ith center user and equalizer of the jth edge user, respectively, r _C,i ^(th) And r _E,j ^(th) Minimum data rates representing user i in the cell center group and user j in the cell edge group, respectively; constraints Q1 and Q2 guarantee the quality of service for the user, constraint Q3 is used to ensure that each phase shifter belongs to a predefined set.

4. The multiple intelligent reflector-assisted non-orthogonal multiple access system design method based on group serial interference cancellation as claimed in claim 3, wherein S5 comprises:

wherein I represents an identity matrix of a×a, a refers to the number of antennas at the base station; by substituting the equalizer into the SINR expression, the signal-to-interference-and-noise ratio (SINR) gamma of the ith cell center user is retrieved _C，i ⁽¹⁾ And the SINR sINRgamma of the jth cell edge user _E，j ⁽¹⁾ The method comprises the following steps:

converting the optimization problem P1 into a joint optimization problem P2 of the user transmit power and the phase offset of the RIS: (P2)

s.t.Q1：log ₂ (1+γ _C，i ⁽¹⁾ )≥r _C，i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽¹⁾ )≥r _E，j ^(th) ，1≤j≤U

5. The multi-intelligent reflector-assisted non-orthogonal multiple access system design method based on group serial interference deletion as claimed in claim 4, wherein in S6, as known from the countercheck method, the condition that the constraint conditions Q1 and Q2 are satisfied when the optimization problem P2 gets the optimal solution is taken as an equation; thus there is

In S7, each RIS is for a givenAnd->And +.>And->To design an optimal phase shift; the optimization problem P2 is converted into a pure phase shift optimization problem P3:

(P3)Find：{Φ _i }

s.t.Q1：log ₂ (1+γ _C，i ( ¹ ))≥r _C,i (th)，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽¹⁾ )≥r _E,j ^(th) ，1≤j≤U

Wherein parameter M is defined ₁ And M ₂ ，

Wherein parameter M is defined ₃ 、M ₄ And M ₅ ，

6. The multiple intelligent reflector-assisted non-orthogonal multiple access system design method based on group serial interference cancellation as claimed in claim 5, wherein S8 comprises:

defining parameter T _C，i，k 、v _k And q _C,i,k ^H The method comprises the following steps:

thus, SINR gamma of the ith center user _C，i ⁽³⁾ Further converted into:

to obtain SINR of edge users, a parameter T is defined _E，j，k And q _E,j,k ^H The method comprises the following steps:

thus SINR gamma of the jth edge user _E，j ⁽³⁾ Further converted into:

(P4)

s.t.Q1：log ₂ (1+γ _C，i ⁽³⁾ )≥r _C,i ^(th) ，1≤i≤U

Q2：log ₂ (1+γ _E，j ⁽³⁾ )≥r _E,j ^(th) ，1≤j≤U

7. the multiple intelligent reflector-assisted non-orthogonal multiple access system design method based on group serial interference cancellation as claimed in claim 6, wherein S9 comprises:

Wherein the rotation matrix of the phase shift of the nth reflective element of the kth RIS is given Wherein θ is _k，n A twiddle factor representing the phase shift of the nth reflective element of the kth RIS, if +.>The rotational phase shift modulo 2 pi still belongs to the set +.>The phase shift solution for the nth rotation of the kth RIS in the nth iteration is defined as +.>

Thus, a result is obtained

Rotation matrix Ω of the nth reflective element at the kth RIS _k,n In the design of (2), the phase shift vector of the last rotation is givenThus, the SINR gamma of the i-th cell center user _C，i ⁽⁴⁾ And SINR gamma of jth cell edge user _E，j ⁽⁴⁾ Is rewritten as:

definition of parameter f _C，i，kn (θ _k，n )、ρ _{C，i，k，n} 、ω _{C，i，k，n} 、f _{E，j，k，n} (θ _k，n )、ρ _{E，j，k，n} 、ω _{E，j，k，n} 、/>And->Wherein the method comprises the steps of

8. The multiple intelligent reflector-assisted non-orthogonal multiple access system design method based on group serial interference cancellation as claimed in claim 1, wherein S10 comprises:

(P5)