CN112601242B - Intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method - Google Patents

Intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method Download PDF

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CN112601242B
CN112601242B CN202011491750.5A CN202011491750A CN112601242B CN 112601242 B CN112601242 B CN 112601242B CN 202011491750 A CN202011491750 A CN 202011491750A CN 112601242 B CN112601242 B CN 112601242B
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王鸿
刘陈
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses an intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method, which comprises the following steps: step a, obtaining the expression z of the received signal at the base station b b The method comprises the steps of carrying out a first treatment on the surface of the Step b, obtaining the signal-to-interference-and-noise ratio expression gamma of the central user C，b The method comprises the steps of carrying out a first treatment on the surface of the Step c, obtaining the signal-to-interference-and-noise ratio expression gamma of the edge user E The method comprises the steps of carrying out a first treatment on the surface of the Step d, constructing a constraint optimization problem P0; step e, converting the original constraint optimization problem P0 into a constraint optimization problem P1; step f, further converting the optimization problem P1 into an optimization problem P2; step g, obtaining an optimal solution of the optimization problem P2 by adopting eigenvalue decompositionStep h, obtaining the optimal phase offset meeting the limiting conditionAnd i, constructing an optimal phase shift matrix phi to obtain the transmitting power required by the central user and the edge user. The two-cell NOMA uplink low-power transmission method assisted by the intelligent reflecting surface can configure the wireless channel propagation environment in real time and reduce the total transmission power consumption of the system.

Description

Intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method
Technical Field
The invention particularly relates to a two-cell NOMA uplink low-power-consumption transmission method assisted by an intelligent reflecting surface, and belongs to the technical field of intelligent reflecting surfaces in wireless communication.
Background
Smart reflective surfaces (IRSs) are considered to be one of the key technologies for next generation mobile communications, being manufactured from configurable electromagnetic metamaterials, a low cost and energy efficient solution in future wireless communications. The intelligent reflecting surface can be deployed on the outer vertical surface of a building or the top of a house, and the randomness of the wireless electromagnetic propagation environment can be effectively resisted by adjusting the phase of an incident signal in real time. On the other hand, non-orthogonal multiple access (NOMA) techniques employ a serial interference cancellation receiver to distinguish between different user signals in a new power domain, and NOMA can achieve support of a greater number of concurrent connections over the same number of time-frequency resource blocks than orthogonal multiple access. The integration of the intelligent reflecting surface and the NOMA can more efficiently utilize the frequency spectrum and the power resource, and thus, the intelligent reflecting surface and the NOMA are widely paid attention to.
In a multi-cell intelligent reflection-assisted NOMA system, the advantages of an intelligent reflection surface and NOMA in the system cannot be combined by a traditional orthogonal multiple access transmission scheme and a NOMA scheme without intelligent reflection surface assistance, and for a simple intelligent reflection surface phase deviation design scheme, such as a random phase design and an equal phase design, a wireless transmission environment cannot be intelligently configured by fully utilizing instantaneous channel state information, therefore, the advantages of the intelligent reflection surface in the aspects of enhancing useful signals and inhibiting interference signals in the multi-cell system cannot be furthest exerted by the random phase design and the equal phase design method, and the power efficiency of the intelligent reflection-assisted NOMA system is affected.
Disclosure of Invention
The technical problem to be solved by the invention is to solve the defects in the prior art, and provide the intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method capable of configuring the wireless channel propagation environment in real time and reducing the total transmission power consumption of the system.
In order to solve the technical problems, the invention adopts the following technical scheme:
an intelligent reflection-assisted two-cell NOMA uplink low-power transmission method comprises the following steps:
step a, under NOMA transmission mode, the central user and the edge user work in the same time-frequency resource block to obtain the expression z of the received signal at the base station b b ；
Step b, according to the demodulation sequence of the users, firstly demodulating the signals of the central user at each base station to obtain a signal-to-interference-and-noise ratio table of the central userReach gamma C,b ；
C, after the demodulation of the central user is finished, each base station deletes the recovered central user signal from the received signal, and transmits the residual edge user signal to the central unit for joint detection, and the central unit processes the signals from the two base stations by adopting the maximum ratio combining technology to obtain the signal-to-interference-and-noise ratio expression gamma of the edge user E ；
Step d, center user transmitting power coefficient { beta } served by base station b C,b B=1, 2}, the transmit power coefficient β of the edge user E And the phase shift matrix phi is an optimization variable, the total transmission power consumption of the system is an objective function, and a constraint optimization problem P0 is constructed on the premise of meeting the signal-to-interference-and-noise ratio threshold of a central user and an edge user;
step e, according to the relation between the transmitting power of the central user and the edge user and the phase shift matrix, converting the original constraint optimization problem P0 into a constraint optimization problem P1, wherein the optimization variables of the converted problem P1 only comprise phase shift variables
Step f, further decomposing the low-rank matrix by using the low-rank characteristic of the matrix contained in the transformation problem P1 and adopting Schmidt orthogonalization to further transform the optimization problem P1 into an optimization problem P2;
step g, neglecting the constraint condition of the constraint optimization problem P2, and obtaining the optimal solution of the constraint optimization problem P2 by adopting eigenvalue decomposition according to the property of generalized Rayleigh entropy
Step h, adjusting the obtained optimal solution according to the principle that the included angle between the optimal solution of the optimization problem P2 and the adjusted feasible solution is minimum, so as to obtain the optimal phase offset meeting the limiting condition
Step i, according to step hIs the optimum phase offset of (a)And e, constructing an optimal phase shift matrix phi, and respectively obtaining the transmitting power required by the central user and the edge user according to the relation between the phase shift and the power distribution in the step e.
In step a, the base station b center subscriber transmits the signal x C,b Transmission signal x with edge user E Transmitted on the same time-frequency resource block, then the received signal at base station b can be expressed as
wherein ,βC,b Center user transmit power coefficient, beta, serving base station b E The transmission power coefficient for the edge user, h C,b Channel coefficient, h, between base station b and its serving central user E,b For the channel coefficients of the edge user to base station b,for the channel vector from the intelligent reflecting surface to the base station b, h E,I V is the channel vector between the intelligent reflecting surface and the edge user b Is an additive noise signal at base station b, subject to a mean of 0, variance +.>Phi is a diagonal matrix representing the phase shift of the intelligent reflecting surface; the phase shift matrix may be expressed as Φ=diag { w } 1 ,…,w N}, wherein ,0≤θ n < 2pi, diag {.cndot }, is the diagonalization operation, N is the number of reflective units deployed on the intelligent reflective surface, θ n For the phase offset of the nth reflection unit j is the imaginary unit, i.e +.>
In step b, when demodulating the central user signal, regarding the signal of the edge user as interference, the signal-to-interference-and-noise ratio of the central user of the base station b can be expressed as
In step c, the received signal-to-interference-and-noise ratio of the edge user can be expressed as
In step d, in order to minimize the total transmission power consumption of the system, the optimization problem P0 may be expressed as
P0：
s.t.C1：
C3：|w n |＝1,1≤n≤N，
wherein ,and->For the signal-to-interference-and-noise ratio threshold of the central user and the edge user of the base station b, the limiting conditions C1 and C2 are used for meeting the service quality of the central user and the edge user, and the limiting condition C3 is used for meeting the amplitude of each reflecting unit of the intelligent reflecting surface to be 1.
In step e, according to the contradictory method, the optimization problem P0 can be obtained to be the mostWhen the figure of merit is high, the constraint conditions C1 and C2 take equal signs, and then the required transmitting power of the edge user is
Accordingly, the transmit power required by the central user can be expressed as
Define a phase offset vector u= [ w ] 1 ,…,w N ] T Concatenating channel state information Then substituting the transmit power obtained by the constraints C1 and C2>And->The objective function of the optimization problem P0 can be expressed as
wherein ,
to further write the objective function into a compressed form, a phase offset augmentation vector is definedCascaded channel state information augmentation vector +> Representing the channel coefficient h E,b Conjugation of (C) and use ofThe objective function of the optimization problem P0 can be further expressed as
wherein ,here I N+1 Representing the identity matrix of (n+1) × (n+1);
based on the objective function, the optimization problem P0 may be further converted into an optimization problem P1 as follows: p1:
s.t.C4：w N+1 ＝1,|w n |＝1,1≤n≤N。
in step f, the cascade channel is augmented with vectorsThe Schmitt orthogonalization is performed to obtain
wherein ,II indicates the 2 norms of the vector,/> and />Respectively representing the cascade channel augmentation vectors in the cell 1 and the cell 2;
based on the orthogonal vector { q } 1 ,q 2 Construction of a quadrature matrix q= [ Q ] 1 ,q 2 ,q 3 ,…,q N+1 ]Wherein { q 3 ,…,q N+1 The { q } is 1 ,q 2 Orthogonal vector of }, then the matrix { B in problem P1 is optimized b B=1, 2} can be decomposed into
B b ＝QΛ b Q H ,b＝1,2，
wherein ,
Λ 1 ＝diag{A 1 ,0 N-1 }，
0 N-1 all-zero matrix, ρ, representing (N-1) × (N-1) * Represents the conjugation of ρ;
the optimization objective of the optimization problem P1 can be expressed as
Accordingly, the optimization problem P1 may be further converted into an optimization problem P2 as follows:
P2：
s.t.C4：w N+1 ＝1,|w n |＝1,1≤n≤N。
in step g, according to the generalized Rayleigh entropy property, the optimization problem P2 is knownIs matrix->A feature vector corresponding to the maximum feature value, wherein +.>Can be expressed as
To obtain a matrixIs characterized by the matrix->And (3) performing eigenvalue decomposition, wherein the eigenvalue decomposition comprises the following steps:
wherein ,δk The kth eigenvalue of the matrix is represented, and U represents the matrix formed by all eigenvectors; by one-dimensional search, the index number of the maximum eigenvalue is found, which can be expressed as k * ＝arg max k {δ k ,1≤k≤2}；
Thus, the first and second substrates are bonded together,corresponding to the maximum eigenvalue of (a)The sign vector is
wherein ,represents the mth row and kth row of the matrix * Columns correspond to elements.
In step h, the adjusted feasible solution is defined asThe goal of the adjustment is to minimize the angle between the optimal solution and the adjusted feasible solution, which can be expressed as
s.t.C5：θ N+1 ＝0,0≤θ n ＜2π,1≤n≤N；
wherein ,constraint C5 is equivalently transformed from constraint C4 of optimization problem P2;
and (c) carrying out optimal solution obtained in the step (g)The individual elements are expressed in terms of amplitude and phase as follows:
then the adjusted optimum phase offset can be obtained as
Where mod 2 pi represents modulo 2 pi.
The invention has the beneficial effects that: the invention provides a two-cell NOMA uplink low-power transmission method assisted by an intelligent reflecting surface, which establishes a joint optimization problem of user power distribution and intelligent reflecting surface phase shift on the premise of simultaneously guaranteeing service quality of cell center users and edge users; by utilizing the characteristic of the optimization problem, a conversion relation between the emission power required by a user and the phase offset of the intelligent reflecting surface is established, and the original joint optimization problem is converted into a pure phase offset optimization problem; the low-rank matrix in the optimization objective function is further decomposed by using the low-rank characteristic of the matrix and the Schmitt orthogonalization, so that the optimal phase offset of the unconstrained optimization problem is obtained; in order to enable each phase offset to meet the characteristic that the modulus is 1, adopting an included angle minimization principle to further adjust the obtained phase offset; and constructing an optimized phase shift matrix according to the adjusted phase shift amount, and respectively obtaining the transmitting power required by the central user and the transmitting power required by the edge user according to the optimized phase shift matrix. Compared with the traditional orthogonal multiple access transmission method, the intelligent reflection surface random phase shift method, the intelligent reflection surface equal phase shift method and the intelligent reflection surface-free transmission method, the method provided by the invention utilizes channel state information to jointly and optimally design the user power distribution and the intelligent reflection surface phase shift on the premise of meeting the signal-to-interference-plus-noise ratio of all users, and can obviously reduce the total transmission power consumption of the system.
Drawings
FIG. 1 is a two-cell uplink NOMA system model assisted by the intelligent reflecting surface of the present invention;
fig. 2 is a diagram of the total transmit power consumption of a two-cell NOMA system under different signal-to-interference-and-noise ratio threshold conditions;
FIG. 3 is an illustration of the effect of the number of reflective elements of a smart reflective surface on the total emitted power consumption of the system.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and the following examples are only for more clearly illustrating the technical aspects of the present invention, and are not to be construed as limiting the scope of the present invention.
The invention considers that both covering radii are R B Is located in the center of the hexagonal coverage area. Is thatThe coverage quality of the cell edge is improved, and the intelligent reflecting surface is arranged between two base stations. The base station and the user are single antenna devices, and the number of reflection units of the intelligent reflection surface is N. Each base station serves a "center user" near the center of the cell, which is randomly distributed around the base station with a radius R C At the same time, there is an "edge user" at the boundary of two cells, which is randomly distributed around the intelligent reflecting surface with radius R I Is within the circular hot spot area of (c). The central user and the edge users work in NOMA mode, i.e. the same time-frequency resource block is adopted for data transmission. In order to improve the transmission performance of the edge users, the method adopts a coordinated multi-point transmission technology to simultaneously communicate with two base stations, and transmits a received signal to a central unit for joint detection through the two base stations. The system model of the present invention is shown in fig. 1.
The invention provides an intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method, which comprises the following steps:
step one: in NOMA transmission mode, the central user and the edge user work in the same time-frequency resource block to obtain the expression z of the received signal at the base station b b 。
In NOMA transmission mode, base station b transmits signal x to central user C,b Transmission signal x with edge user E Transmitted on the same time-frequency resource block, then the received signal at base station b can be expressed as
wherein ,βC,b Center user transmit power coefficient, beta, serving base station b E The transmission power coefficient for the edge user, h C,b Channel coefficient, h, between base station b and its serving central user E,b For the channel coefficients of the edge user to base station b,for intelligent reflection to base station bLane vectors, h E,I V is the channel vector between the intelligent reflecting surface and the edge user b Is an additive noise signal at base station b, subject to a mean of 0, variance +.>Phi is a diagonal matrix representing the phase offset of the intelligent reflecting surface.
Further, the phase shift matrix may be expressed as Φ=diag { w } 1 ,…,w N}, wherein ,0≤θ n < 2pi, diag {.cndot }, is the diagonalization operation, N is the number of reflective units deployed on the intelligent reflective surface, θ n For the phase offset of the nth reflection unit j is the imaginary unit, i.e +.>
Step two: according to the user demodulation sequence, firstly demodulating signals of the central user at each base station to obtain a signal-to-interference-and-noise ratio expression gamma of the central user C,b 。
Because the central user has a larger average signal strength, the central user signal is demodulated first at the base station. When demodulating the central user signal, regarding the signal of the edge user as interference, the central user signal-to-interference-and-noise ratio of the base station b can be expressed as
Step three: after the demodulation of the central user is completed, each base station deletes the recovered central user signal from the received signal, and transmits the residual edge user signal to the central unit for joint detection. The central unit processes the signals from two base stations by using the maximum ratio combining technology to obtain the signal-to-interference-and-noise ratio expression gamma of the edge user E 。
Then the received signal-to-interference-and-noise ratio of the edge user can be expressed as
Step four: in { beta ] C,b ,b＝1,2}，β E And phi is an optimization variable, the total transmission power consumption of the system is an objective function, and the constraint optimization problem P0 is constructed on the premise of meeting the signal-to-interference-and-noise ratio threshold of the central user and the edge user.
To minimize the total system transmit power consumption, the optimization problem P0 can be expressed as:
P0：
s.t.C1：
C2：
C3：|w n |＝1,1≤n≤N，
wherein ,and->For the signal-to-interference-and-noise ratio threshold of the central user and the edge user of the base station b, the limiting conditions C1 and C2 are used for meeting the service quality of the central user and the edge user, and the limiting condition C3 is used for meeting the amplitude of each reflecting unit of the intelligent reflecting surface to be 1.
Step five: according to the relation between the transmitting power of the central user and the edge user and the phase shift matrix, the original constraint optimization problem P0 is converted into a constraint optimization problem P1, and the optimization variables of the converted problem P1 only comprise phase shift variables
According to the contradiction method, the constraint conditions C1 and C2 can be equal when the optimization problem P0 takes the optimal value. Then the required transmit power for the edge user is:
accordingly, the transmit power required by the central user can be expressed as:
further, a phase offset vector u= [ w ] is defined 1 ,…,w N ] T Concatenating channel state informationThen substituting the transmit power obtained by the constraints C1 and C2>And->Expressed, the objective function of the optimization problem P0 can be expressed as:
wherein ,
to further write the objective function into a compressed form, a phase offset augmentation vector is definedCascaded channel state information augmentation vector +>Representing the channel coefficient h E,b Conjugation of (C) and use ofThe objective function of the optimization problem P0 can be further expressed as
wherein ,here I N+1 Represents the identity matrix of (n+1) × (n+1).
Based on the objective function, the optimization problem P0 may be further converted into an optimization problem P1 as follows:
P1：
s.t.C4：w N+1 ＝1,|w n |＝1,1≤n≤N。
step six: and further decomposing the low-rank matrix by using the low-rank characteristic of the matrix contained in the transformation problem P1 and adopting Schmidt orthogonalization to further transform the optimization problem P1 into an optimization problem P2.
Augmentation vector for cascade channelsThe Schmitt orthogonalization is performed to obtain
wherein ,II indicates the 2-norm of the vector.
Based on the orthogonal vector { q } 1 ,q 2 Construction of a quadrature matrix q= [ Q ] 1 ,q 2 ,q 3 ,…,q N+1 ]Wherein { q 3 ,…,q N+1 The { q } is 1 ,q 2 Orthogonal vectors of }. Then, the matrix { B in the optimization problem P1 b B=1, 2} can be decomposed into
B b ＝QΛ b Q H ,b＝1,2，
wherein ,
Λ 1 ＝diag{A 1 ,0 N-1 }，
0 N-1 all-zero matrix, ρ, representing (N-1) × (N-1) * Representing the conjugate of p.
Further, the optimization objective of the optimization problem P1 can be expressed as
Accordingly, the optimization problem P1 may be further converted into an optimization problem P2 as follows:
P2：
s.t.C4：w N+1 ＝1,|w n |＝1,1≤n≤N。
step seven: ignoring the constraint condition of the constraint optimization problem P2, and obtaining the optimal solution of the optimization problem P2 by adopting eigenvalue decomposition according to the property of generalized Rayleigh entropy
From the generalized Rayleigh entropy property, the optimization problem P2 is knownIs matrix->A feature vector corresponding to the maximum feature value, wherein +.>Can be expressed as
Further, to obtain a matrixIs characterized by the matrix->And (3) performing eigenvalue decomposition, wherein the eigenvalue decomposition comprises the following steps:
wherein ,δk The kth eigenvalue of the matrix is represented, and U represents the matrix of all eigenvectors.
By one-dimensional search, the index number of the maximum characteristic value is found, which can be expressed as
k * ＝arg max k {δ k ,1≤k≤2}。
Thus, the first and second substrates are bonded together,the feature vector corresponding to the maximum feature value of (2) is
wherein ,represents the mth row and kth row of the matrix * Columns correspond to elements.
Step eight: the optimal solution obtained by the optimization in the step sevenThe elements in the optimization problem P2 do not necessarily meet the constraint condition of the constraint optimization problem P2, and the obtained optimal solution needs to be adjusted according to the adjustment principle that the included angle between the optimal solution of the optimization problem P2 and the adjusted feasible solution is minimum, so that the optimal phase offset which meets the constraint condition is obtained>
The adjusted feasible solution is defined asThe goal of the adjustment is to minimize the angle between the optimal solution and the adjusted feasible solution, which can be expressed as
s.t.C5：θ N+1 ＝0,0≤θ n ＜2π,1≤n≤N。
wherein ,constraint C5 is equivalently translated from constraint C4 of optimization problem P2.
The optimal solution obtained in the step seven is processedThe individual elements are expressed in terms of amplitude and phase as follows:
then the adjusted optimum phase offset can be obtained as
Where mod 2 pi represents modulo 2 pi.
Step nine: according to the optimal phase offset obtained in the step eightAnd (3) constructing an optimal phase shift matrix phi, and respectively obtaining the transmitting power required by the central user and the edge user according to the relation between the phase shift and the power distribution in the step five.
The performance of the intelligent reflection-surface-assisted two-cell NOMA uplink low-power-consumption transmission method is described below through Monte Carlo simulation experiments. The system parameters are as follows: coverage radius R of each cell B Circular area radius R of central user profile =500 m C Radius R of service area of intelligent reflecting surface =200m I =50m, variance of additive noiseModeling a channel in a system as a combination of path loss and small-scale fading, wherein the path loss index of the channel between a central user and a base station is 2.5, and the small-scale fading obeys complex Gaussian distribution with a mean value of 0 and a variance of 1; direct connection channel between edge user and base stationPath loss index is 3.5, and small-scale fading obeys complex Gaussian distribution with mean value of 0 and variance of 1; the path loss index of the channel vector from the intelligent reflecting surface to the base station is 3, and the small-scale fading is modeled as a related Rayleigh distribution, namely +.>Wherein the vector->Each element in the matrix obeys complex Gaussian distribution with 0 mean and 1 variance, and a transmission correlation matrix sigma T Item (i, k) of (1) is denoted as [ Σ ] T ] i,k ＝0.5 |i-k| The method comprises the steps of carrying out a first treatment on the surface of the The path loss index of the channel vector between the edge user and the intelligent reflecting surface is 2, and the small-scale fading is modeled as rice distribution in consideration of the line-of-sight path between the edge user and the intelligent reflecting surface, namely wherein ,t0 Representing the intensity of the line-of-sight path, each element of which is set to 1, the rice factor K 0 =3, vector t E,I Each element in the received correlation matrix sigma is subjected to complex Gaussian distribution with mean value of 0 and variance of 1 R Item (i, k) of (1) is denoted as [ Σ ] R ] i,k ＝0.5 |i-k| 。
Figure 2 gives the number of reflecting elements n=128,and the relation between the total transmission power consumption of the system and the signal-to-interference-and-noise ratio threshold value. It can be seen that, at different signal-to-interference-and-noise ratio thresholds, the transmission power consumption required by the method of the present invention is significantly smaller than that of the existing scheme, because the phase offset and the user transmission power are jointly optimized according to the channel state information in the present invention. Signal-to-interference-and-noise ratio threshold when edge user>When compared with the prior artThe method of the invention requires a reduction of about 10dBm in the transmit power, which is a random phase shift method, an equal phase shift method, an orthogonal multiple access method, a smart reflector-less method.
FIG. 3 showsAnd the relation between the total transmission power consumption of the system and the number of reflecting units. It can be seen that as the number of transmitting units increases, the power consumption of the transmission required by the method of the present invention decreases, because the increase in the number of reflecting units increases the strength of the useful signal. Under the condition of different reflecting unit configurations, compared with the existing random phase shift method, equal phase shift method and orthogonal multiple access method, the transmitting power consumption of the method is reduced by at least 8dBm. Compared with the method without the intelligent reflecting surface, the method provided by the invention has the advantage that the emission power consumption is reduced by at least 12dBm.
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 (9)

1. An intelligent reflection-assisted two-cell NOMA uplink low-power transmission method is characterized in that: the method comprises the following steps:
step a, under NOMA transmission mode, the central user and the edge user work in the same time-frequency resource block to obtain the expression z of the received signal at the base station b b ；
Step b, according to the demodulation sequence of the users, firstly demodulating signals of the central user at each base station to obtain a signal-to-interference-and-noise ratio expression gamma of the central user C，b ；
C, after the demodulation of the central user is finished, each base station deletes the recovered central user signal from the received signal, and transmits the residual edge user signal to the central unit for joint detection, and the central unit adopts the maximum ratio combining technology to process the signals from the two base stationsThe signal of the station, the signal-to-interference-and-noise ratio expression gamma of the edge user is obtained E ；
Step d, center user transmitting power coefficient { beta } served by base station b C，b B=1, 2}, the transmit power coefficient β of the edge user E And the phase shift matrix phi is an optimization variable, the total transmission power consumption of the system is an objective function, and a constraint optimization problem P0 is constructed on the premise of meeting the signal-to-interference-and-noise ratio threshold of a central user and an edge user;
step e, according to the relation between the transmitting power of the central user and the edge user and the phase shift matrix, converting the original constraint optimization problem P0 into a constraint optimization problem P1, wherein the optimization variables of the converted problem P1 only comprise phase shift variables
Step f, further decomposing the low-rank matrix by using the low-rank characteristic of the matrix contained in the transformation problem P1 and adopting Schmidt orthogonalization to further transform the optimization problem P1 into an optimization problem P2;
step g, neglecting the constraint condition of the constraint optimization problem P2, and obtaining the optimal solution of the constraint optimization problem P2 by adopting eigenvalue decomposition according to the property of generalized Rayleigh entropy
Step h, adjusting the obtained optimal solution according to the principle that the included angle between the optimal solution of the optimization problem P2 and the adjusted feasible solution is minimum, so as to obtain the optimal phase offset meeting the limiting condition
Step i, according to the optimal phase offset obtained in the step hConstructing an optimal phase shift matrix phi, and dividing according to the relation between the phase shift and the power distribution in the step eAnd respectively obtaining the transmitting power required by the central user and the edge user.
2. The method for transmitting the two-cell NOMA uplink with the assistance of the intelligent reflecting surface in low power consumption according to claim 1, wherein the method comprises the following steps:
in step a, the base station b center subscriber transmits the signal x C，b Transmission signal x with edge user E Transmitted on the same time-frequency resource block, then the received signal at base station b can be expressed as
wherein ,βC，b Center user transmit power coefficient, beta, serving base station b E The transmission power coefficient for the edge user, h C，b Channel coefficient, h, between base station b and its serving central user E，b For the channel coefficients of the edge user to base station b,for the channel vector from the intelligent reflecting surface to the base station b, h E，I V is the channel vector between the intelligent reflecting surface and the edge user b Is an additive noise signal at base station b, subject to a mean of 0, variance +.>Phi is a diagonal matrix representing the phase shift of the intelligent reflecting surface; the phase shift matrix may be expressed as Φ=diag { w } 1 ，...，w N }, wherein->0≤θ n < 2pi, diag {.cndot }, is the diagonalization operation, N is the number of reflective units deployed on the intelligent reflective surface, θ n For the phase offset of the nth reflection unit j is the imaginary unit, i.e +.>
3. The method for transmitting the two-cell NOMA uplink with the assistance of the intelligent reflecting surface in low power consumption according to claim 2, wherein the method comprises the following steps: in step b, when demodulating the central user signal, regarding the signal of the edge user as interference, the signal-to-interference-and-noise ratio of the central user of the base station b can be expressed as
4. The method for transmitting the two-cell NOMA uplink with the assistance of the intelligent reflecting surface in low power consumption according to claim 3, wherein the method comprises the following steps: in step c, the received signal-to-interference-and-noise ratio of the edge user can be expressed as
5. The intelligent reflector assisted two-cell NOMA uplink low power transmission method according to claim 4, wherein the method comprises the following steps: in step d, in order to minimize the total transmission power consumption of the system, the optimization problem P0 may be expressed as
P0：
s.t.C1：
C2：
C3：|w n |＝1，1≤n≤N，
wherein ,and->For the signal-to-interference-and-noise ratio threshold of the central user and the edge user of the base station b, the limiting conditions C1 and C2 are used for meeting the service quality of the central user and the edge user, and the limiting condition C3 is used for meeting the amplitude of each reflecting unit of the intelligent reflecting surface to be 1.
6. The intelligent reflector assisted two-cell NOMA uplink low power transmission method according to claim 5, wherein the method comprises the following steps: in step e, according to the contradiction method, when the optimization problem P0 takes the optimal value, the constraint conditions C1 and C2 take the equal sign, and then the transmitting power required by the edge user is
Accordingly, the transmit power required by the central user can be expressed as
Define a phase offset vector u= [ w ] 1 ，...，w N ] T Concatenating channel state information Then substituting the transmit power obtained by the constraints C1 and C2>And->The objective function of the optimization problem P0 can be expressed as
wherein ,
to further write the objective function into a compressed form, a phase offset augmentation vector is definedCascaded channel state information augmentation vector +> Representing the channel coefficient h E，b Conjugation of (2) and use->The objective function of the optimization problem P0 can be further expressed as
wherein ,here I N+1 Representing the identity matrix of (n+1) × (n+1);
based on the objective function, the optimization problem P0 may be further converted into an optimization problem P1 as follows:
P1：
s.t.C4：w N+1 ＝1，|w n |＝1，1≤n≤N。
7. the intelligent reflector assisted two-cell NOMA uplink low power transmission method according to claim 6, wherein the method comprises the following steps: in the step f of the process,
augmentation vector for cascade channelsBy performing Schmitt orthogonalization, +.>
wherein ,|·| represents the 2-norm of the vector, ++> and />Respectively representing the cascade channel augmentation vectors in the cell 1 and the cell 2;
based on the orthogonal vector { q } 1 ，q 2 Construction of a quadrature matrix q= [ Q ] 1 ，q 2 ，q 3 ，...，q N+1 ]Wherein { q 3 ，...，q N+1 The { q } is 1 ，q 2 Orthogonal vector of }, then the matrix { B in problem P1 is optimized b B=1, 2} can be decomposed into
B b ＝QΛ b Q H ，b＝1，2，
wherein ,
Λ 1 ＝diag{A 1 ，0 N-1 }，
0 N-1 all-zero matrix, ρ, representing (N-1) × (N-1) * Represents the conjugation of ρ;
the optimization objective of the optimization problem P1 can be expressed as
Accordingly, the optimization problem P1 may be further converted into an optimization problem P2 as follows:
P2：
s.t.C4：w N+1 ＝1，|w n |＝1，1≤n≤N。
8. the intelligent reflector assisted two-cell NOMA uplink low power transmission method according to claim 7, wherein the method comprises the following steps: in step g, according to the generalized Rayleigh entropy property, the optimization problem P2 is knownIs matrix of optimal solutionsA feature vector corresponding to the maximum feature value, wherein +.>Can be expressed as
To obtain a matrixIs characterized by the matrix->And (3) performing eigenvalue decomposition, wherein the eigenvalue decomposition comprises the following steps:
wherein ,δk The kth eigenvalue of the matrix is represented, and U represents the matrix formed by all eigenvectors;
by one-dimensional search, the index number of the maximum characteristic value is found, which can be expressed as
k * ＝arg max k {δ k ，1≤k≤2}；
Thus, the first and second substrates are bonded together,the feature vector corresponding to the maximum feature value of (2) is
wherein ,represents the mth row and kth row of the matrix * Columns correspond to elements.
9. The intelligent reflector assisted two-cell NOMA uplink low-power transmission method according to claim 8, wherein the method comprises the following steps: in step h, the adjusted feasible solution is defined asThe goal of the adjustment is to minimize the angle between the optimal solution and the adjusted feasible solution, which can be expressed as
s.t.C5：θ N+1 ＝0，0≤θ n ＜2π，1≤n≤N；
wherein ,constraint C5 is equivalently transformed from constraint C4 of optimization problem P2;
and (c) carrying out optimal solution obtained in the step (g)The individual elements are expressed in terms of amplitude and phase as follows:
then the adjusted optimum phase offset can be obtained as
Where mod 2 pi represents modulo 2 pi.
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