CN113596784A - Robustness transmission design method of intelligent reflection surface assisted D2D communication system - Google Patents

Robustness transmission design method of intelligent reflection surface assisted D2D communication system Download PDF

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CN113596784A
CN113596784A CN202110840449.9A CN202110840449A CN113596784A CN 113596784 A CN113596784 A CN 113596784A CN 202110840449 A CN202110840449 A CN 202110840449A CN 113596784 A CN113596784 A CN 113596784A
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徐齐钱
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Zhejiang Yizheng Communication Technology Co ltd
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Abstract

The invention discloses a robust transmission design method of an intelligent reflection surface auxiliary D2D communication system, which relates to the technical field of communication and comprises the steps of establishing an intelligent reflection surface auxiliary D2D communication system model and a non-perfect channel model, establishing a robust optimization problem based on the non-perfect scene of channel state information, processing the optimization problem containing channel parameter uncertainty by using matrix knowledge and a convex optimization theory, converting a semi-infinite constraint condition into a convex constraint, decomposing the robust problem of minimized power into two subproblems for solving by adopting a BCD algorithm and an S-procedure theorem, obtaining a robust power distribution scheme by iterating the two subproblems, establishing a resource distribution scheme of the intelligent reflection surface D2D communication system, effectively reducing user communication interruption and improving the robustness of the system.

Description

Robustness transmission design method of intelligent reflection surface assisted D2D communication system
Technical Field
The invention relates to the technical field of communication, in particular to a robust transmission design method of an intelligent reflection surface assisted D2D communication system.
Background
Currently, an intelligent reflective surface is a planar array of a large number of low-cost passive reflective elements placed between a transmitting end and a receiving end. By independently phasing the incident signal with each reflective element, the direction of signal propagation from end-to-end (D2D, Device-to-Device) is changed, allowing the user to better receive the signal transmitted by the base station. By adjusting the wave beam, the reflected signal of the intelligent reflecting surface and the signal of other paths are mutually offset, and the interference signal of other channels is eliminated. Compared with the traditional relay technology, the intelligent reflecting surface has the advantages of small size, easiness in deployment and low cost, avoids extra power consumption and expensive communication equipment, and is an economical and applicable high-speed communication technology with low power consumption.
D2D communication is a new technology for direct communication between users without relaying through the base station under the control of the base station, in which neighboring mobile terminals are allowed to directly use cellular communication resources, and D2D communication is also called terminal-through. Unlike other traditional wireless communication technologies, the D2D communication data transmission process does not need to be relayed by a base station, which can relieve the pressure of the base station and facilitate access to more users. In some multi-user network scenarios, neighboring users may establish D2D communication and reuse the Spectrum resources of cellular users, thereby greatly improving the Spectrum Efficiency (SE) of the system and reducing network energy consumption. The D2D communication has advantages in the aspects of cell coverage, energy consumption and the like, is widely applied in real life, conforms to the actual requirements of the application development of future communication technology, and meets the ever-increasing communication requirements.
However, in a lot of literature, the research is based on the case of perfect Channel State Information (CSI), but actually, since the signal processing capability of the reflection element of the intelligent reflection surface is limited, the intelligent reflection surface does not use any radio frequency link, and the passive beam forming of the intelligent reflection surface is highly dependent on the acquired CSI, so that in the wireless communication system assisted by the intelligent reflection surface, it is challenging to obtain accurate CSI, and most of the existing research focuses on the Channel estimation aspect of the Channel related to the intelligent reflection surface and the integration of the intelligent reflection surface as auxiliary communication into various wireless communication systems, and the research on the IRS-D2D communication system under imperfect CSI is less. And if the channel is considered as a perfect channel, this will result in some loss of system performance.
Due to the rapid development of a radio frequency electronic system and the large application of a programmable reconfigurable super surface, and in some emergency situations, the direct channel propagation between a base station and a user becomes poor, so that in order to reduce user communication interruption and improve the system robustness, it is an urgent problem to research how to perform robust transmission of an intelligent reflective surface assisted D2D communication system under imperfect CSI.
Disclosure of Invention
The invention aims to provide a robust transmission design method of an intelligent reflection surface auxiliary D2D communication system, which is characterized in that an intelligent reflection surface technology is applied to a D2D communication system, under the condition of imperfect CSI, a matrix knowledge, a convex optimization theory, a BCD algorithm and an S-procedure theorem are utilized, the robust problem of minimized power is decomposed into two subproblems to be solved, and a robust resource allocation scheme is obtained by iterating the two subproblems, so that communication interruption is reduced, power minimization is realized, and the robustness of the system is improved.
In a first aspect, the above object of the present invention is achieved by the following technical solutions:
a robust transmission design method of an intelligent reflection surface assisted D2D communication system is characterized by establishing an intelligent reflection surface assisted D2D communication system model and an imperfect channel model, constructing a robust optimization problem based on the imperfect scene of channel state information, processing the optimization problem containing channel parameter uncertainty by using matrix knowledge and a convex optimization theory, converting a semi-infinite constraint condition into a convex constraint, and establishing a resource allocation scheme of the intelligent reflection surface D2D communication system.
The invention is further configured to: the intelligent reflection surface assisted D2D communication system model comprises a base station, an intelligent reflection surface and a D2D communication system, wherein D2D users multiplex downlink spectrum resources of a cellular communication link; the base station is equipped with N antennas, the cellular user and D2D user pairs are each equipped with a single antenna, and the smart reflective surface has M reflective elements.
The invention is further configured to: an ellipsoid model is adopted to establish an imperfect channel model, interference channel gain and an uncertain region of each D2D user between a transmitting end and a cellular user are obtained, a base station assists cascade channel gain and an uncertain region of a D2D communication system and each D2D user at a receiving end through an intelligent reflection surface, and each D2D user assists cascade channel gain and an uncertain region of a D2D communication system and a cellular user at a transmitting end through an intelligent reflection surface.
The invention is further configured to: under imperfect channel state information, the optimization problem includes: transmission power minimization objective function, minimum rate requirements for cellular and D2D users, rank-one requirements, unit modulus requirements for reflection element coefficients, power requirements for cellular and D2D users, channel gain gC,k/Tk/RkUncertainty of the system and the requirement for system robustness.
The invention is further configured to: the worst case minimization of the transmission power optimization problem, the objective function is represented by:
Figure BDA0003178719200000041
the constraint conditions include:
Figure BDA0003178719200000042
RC≥RCmin (1b)；
rank(W)＝1 (1c)；
Figure BDA0003178719200000043
0≤trace(W)≤PCmax (1e)；
0≤PK,K≤PDmax (1f)；
Figure BDA0003178719200000044
Figure BDA0003178719200000045
Figure BDA0003178719200000046
wherein W is PCwwHW represents a beamforming vector associated with a cellular user, and H represents a matrix transposition; pk,kRepresenting the transmit power of the transmit end D2D-T of the kth pair D2D user pair to the receive end D2D-R of the kth pair D2D user pair,
Figure BDA0003178719200000047
representing the rate, R, of the kth pair D2D user pairsDminRepresents the minimum rate of the D2D user; rCminRepresents a minimum rate for a cellular user; | em|2Representing the unit mode, P, of the m-th reflecting element of the intelligent reflecting surfaceDmaxRepresents the maximum transmit power of the D2D user; pCmaxRepresents the maximum transmit power of the cellular user;
equation (1a) (1b) represents the minimum rate requirements for cellular users and D2D users;
equation (1c) represents a rank-one requirement;
equation (1d) represents the unit mode requirement for the coefficient of the reflective element;
equation (1e) (1f) represents the maximum power constraint for cellular users and D2D users;
equation (1g) represents the interference channel gain g between the kth pair of D2D users and the cellular userC,KThe uncertainty effect of (2);
the formula (1h) represents the cascade channel gain T of the base station and the k-th pair D2D user pair receiving end through the intelligent reflection surface auxiliary D2D communication systemkInfluence of uncertainty of；
Equation (1h) represents the cascade channel gain R of the k-th pair D2D user pair transmitting end and the cellular user through the intelligent reflection surface auxiliary D2D communication systemKThe uncertainty of (c).
The invention is further configured to: introducing relaxation parameters, performing equivalent transformation on constraint conditions by adopting S-procedure lemma, and processing the optimization problem containing channel parameter uncertainty; and (3) converting the channel parameter uncertainty problem into a convex optimization problem by adopting a block coordinate descent algorithm, iteratively optimizing a beam forming matrix W, D2D user transmission power P and a reflection unit matrix e of the base station, and directly stopping convergence to obtain the beam forming matrix W, D2D user transmission power P and the reflection unit matrix e of the base station.
The invention is further configured to: under the condition of fixing the reflecting unit matrix e, adopting a semi-positive definite relaxation method to obtain a beam forming matrix W, D2D user transmission power P distribution scheme of the base station; under the condition of giving a beam forming matrix W and user transmission power P of D2D, a reflection unit matrix e is obtained by adopting a punishment concave-convex process, so that the optimization problem of the beam forming matrix W, D2D user transmission power P and the reflection unit matrix e is simplified into a convex optimization problem.
The invention is further configured to: introducing a relaxation parameter rho, and rewriting the formula (1a) as:
Figure BDA0003178719200000051
Figure BDA0003178719200000052
and (3) carrying out mathematical formula conversion on the formula (6) by utilizing the S-procedure lemma to obtain:
Figure BDA0003178719200000053
the equation (1b) is equivalently transformed and rewritten as:
Figure BDA0003178719200000061
Figure BDA0003178719200000062
Figure BDA0003178719200000063
Figure BDA0003178719200000064
wherein, alpha, beta and gamma are relaxation parameters;
the approximate optimization problem after the channel parameter uncertainty is processed is as follows:
Figure BDA0003178719200000065
s.t.(5)，(8)，(9)，(14)，(15)，(16)，(1c)，(1d)，(1e)，(1f) (2)；
and converting the optimization problem containing the boundary channel parameters into a deterministic problem.
The invention is further configured to: for the case that the rank of the optimal solution of the beamforming matrix W of the base station is 1, given the matrix e of the reflection unit, the beamforming matrix W, D2D user transmission power P allocation scheme of the base station is solved,
Figure BDA0003178719200000066
s.t.(5)，(8)，(9)，(14)，(15)，(16)，(1c)，(1e)，(1f) (3)；
loosening the problem (18) by adopting an SDR technology to obtain a convex SDP problem, and solving by utilizing a convex optimization toolkit CVX;
for the case that the rank of the optimal solution of the beamforming matrix W of the base station is not 1, a Gaussian random method is adopted to obtain a rank 1 solution, then a reflection unit matrix e is given, and the beamforming matrix W, D2D user transmission power P distribution scheme of the base station is solved.
The invention is further configured to: for a given base station's beamforming matrix W, D2D user transmission power P allocation scheme, a relaxation variable χ ═ χ is introduced1,χ2]TAnd modifying the constraint (2) and the constraint (9) to obtain:
Figure BDA0003178719200000071
Figure BDA0003178719200000072
the sub-problem with the matrix of reflective elements e translates into:
Figure BDA0003178719200000073
s.t.(8)，(14)，(15)，(16)，(1d)，(19)，(20) (4)；
adopting punished concave-convex process, introducing relaxation variable b ═ b1,b2，...,b2M]TConstraint (1d) is equivalent to:
Figure BDA0003178719200000074
|em|2≤1+bM+m,1≤m≤M (23)；
solving the subproblem of the reflection unit matrix e, and converting into:
Figure BDA0003178719200000075
s.t.(8)，(14)，(15)，(19)，(20)，(22)，(23) (25)；
b≥0 (26)；
wherein | b | Y phosphor1A penalty term representing an objective function, | | b | | non-woven phosphor1By a regularization factor kappa[p]Scaling is performed to control the feasibility of the constraint.
In a second aspect, the above object of the present invention is achieved by the following technical solutions:
a robust transmission design terminal for a smart reflective surface assisted D2D communication system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor implementing the method of the present application when executing the computer program.
In a third aspect, the above object of the present invention is achieved by the following technical solutions:
a computer-readable storage medium, in which a computer program is stored, which, when being executed by a processor, carries out the method of the present application.
Compared with the prior art, the beneficial technical effects of this application do:
1. according to the method, under the condition of imperfect CSI, the advantages of the intelligent reflecting surface are combined, the intelligent reflecting surface is introduced into a D2D communication system, robustness transmission design is carried out, user communication interruption can be effectively reduced, and the robustness of the system is improved;
2. furthermore, the robustness of the system is effectively improved by optimizing the reflection unit matrix, the beam forming matrix of the base station and the D2D user transmission rate;
3. furthermore, the constraint conditions under the condition of imperfect CSI are set, equivalent transformation is carried out on the constraint conditions, the non-convex optimization problem is converted into deterministic convex constraint, optimization of a reflection unit matrix, a beam forming matrix of a base station and the transmission rate of a D2D user is achieved, system robustness is improved, and system reliability is improved.
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FIG. 1 is a schematic diagram of a smart reflective surface assisted D2D communication system configuration according to an embodiment of the present application;
FIG. 2 is a diagram illustrating the results of simulation verification under a first condition in accordance with an embodiment of the present application;
FIG. 3 is a diagram illustrating simulation verification results under a second condition in accordance with an exemplary embodiment of the present application;
FIG. 4 is a diagram illustrating simulation verification results under a third condition in accordance with an embodiment of the present application.
Detailed Description
The present invention will be described in further detail below.
Detailed description of the preferred embodiment
According to the robust transmission design method of the intelligent reflection surface auxiliary D2D communication system, firstly, an intelligent reflection surface auxiliary D2D communication system model is established, and research is conducted on the basis of the model.
An intelligent reflection surface assisted D2D communication system model, as shown in fig. 1, includes a base station, a Cellular User, and a K pair D2D User pair, with a MISO (Multiple Input Single Output) wireless communication and a D2D communication scenario, where the D2D User multiplexes downlink spectrum resources of a Cellular communication link in an underlay mode, the base station is equipped with N antennas, the Cellular User Equipment (CUE) and the K pair D2D User pair are respectively equipped with a Single antenna, and the intelligent reflection surface has M reflection elements. A controller is installed on the intelligent reflective surface to control the reflection coefficient of the intelligent reflective surface and to communicate through a separate wireless link.
In reality, the direct channel propagation condition between the Base Station (BS) and the user may be unfavorable due to some emergency situations, and therefore the direct channel between the BS and the user is ignored.
The analysis is performed based on a model of the intelligent reflective surface assisted D2D communication system, wherein,
channel gain between base station and intelligent reflective surface, expressed as
Figure BDA0003178719200000091
Channel enhancement between smart reflective surface and cellular subscriberYi, is represented as
Figure BDA0003178719200000092
Channel gain between the Intelligent reflective surface and the D2D User-to-receiving end (D2D User Receiver, D2D-R), denoted as
Figure BDA0003178719200000101
Channel gain between the D2D user pairs, denoted as
Figure BDA0003178719200000102
The channel gain between the D2D User pair Transmitter (D2D User Transmitter, D2D-T) and the smart reflective surface is expressed as
Figure BDA0003178719200000103
Then, the signal to interference plus noise ratio γ of the cellular userCAs shown in the following formula:
Figure BDA0003178719200000104
signal to interference plus noise ratio of D2D user pair
Figure BDA0003178719200000105
As shown in the following formula:
Figure BDA0003178719200000106
in the formula (I), the compound is shown in the specification,
pk,kdenoted as the transmission power, P, of the k-th pair D2D-T through the k-th pair D2D-RCIs the transmit power of the base station to the cellular user,
Figure BDA0003178719200000107
to noise power, w represents the beamforming vector associated with the cellular user.
Intelligent anti-theftThe passive beamforming matrix model of the emitting surface is as follows:
Figure BDA0003178719200000108
Figure BDA0003178719200000109
indicating that the intelligent reflective surface has M reflective elements, each element satisfying a unit modulus | -em|2＝1,1≤m≤M。
Figure BDA00031787192000001010
Represents the interference channel gain, D, of the k-th pair D2D-T with the cellular userk,jRepresenting the interference channel gain between the kth pair of D2D users and the jth pair of D2D users.
For simplicity, let only one pair of D2D users in the system, i.e., K ═ 1.
The rate R of the cellular userCAs shown in the following formula:
Figure BDA0003178719200000111
the rate R of the D2D userDAs shown in the following formula:
Figure BDA0003178719200000112
under the condition of an imperfect channel model, assuming that the CSI of an interference channel has uncertainty, the CSI of other channel links is completely known, and an ellipsoid model is adopted to establish a channel estimation error model.
Interference channel gain g between kth pair of D2D-T users and cellular usersC,kArea of uncertainty thereof
Figure BDA0003178719200000113
Is shown as
Figure BDA0003178719200000114
Base stationIntelligent reflective surface station-cascaded channel gain of D2D user to receiving end (BS-IRS-D2DR)
Figure BDA0003178719200000115
Its uncertainty region
Figure BDA0003178719200000116
Is shown as
Figure BDA0003178719200000117
Cascaded channel gain for D2D user to transmitting end-Intelligent reflective surface station-cellular user (D2DT-IRS-CUE)
Figure BDA0003178719200000118
Its uncertainty region
Figure BDA0003178719200000119
Is shown as
Figure BDA00031787192000001110
Wherein Δ gC,KRepresents the channel gain gC,KIs estimated error, Δ TKRepresents the channel gain TKIs estimated error of (1), Δ RKRepresents the channel gain RKEstimate error of, deltaKRepresenting an uncertain region
Figure BDA00031787192000001111
Upper bound of, tKRepresenting an uncertain region
Figure BDA00031787192000001112
Upper bound of rKRepresenting an uncertain region
Figure BDA00031787192000001113
Upper bound of (d)K、tKAnd rKA larger value of (a) means a larger uncertainty area and a larger uncertainty.
Controlling the transmission power level can reduce interference, and thus, the channel state information is not fully knownIn the case, the constraint conditions include: worst case minimum transmission power optimization problem, minimum rate requirements for cellular and D2D users, rank-one requirements, unit modulus requirements for reflection unit coefficients, power requirements for cellular and D2D users, channel gain gC,k/Tk/RkUncertainty of the system and the requirement for system robustness.
Based on the worst case minimization of the transmission power optimization problem, the objective function is expressed as:
Figure BDA0003178719200000121
the constraint conditions include:
Figure BDA0003178719200000122
RC≥RCmin (1b)；
rank(W)＝1 (1c)；
Figure BDA0003178719200000123
0≤trace(W)≤PCmax (1e)；
0≤PK,K≤PDmax (1f)；
Figure BDA0003178719200000124
Figure BDA0003178719200000125
Figure BDA0003178719200000126
wherein W is PCwwHConstraint (1a) and constraint (1b) represent the minimum rate requirements of cellular users and D2D users, respectively; constraint (1c) represents a rank 1 constraint; constraint (1d) represents the unit modulus requirement of the reflection cell coefficients; constraint (1e) and constraint (1f) represent the power requirements of cellular users and D2D users, respectively; constraint (1g) means that the channel gain g is taken into accountC,KUncertainty of (d) and requirements on system robustness; constraint (1h) indicates that the channel gain T is taken into accountKUncertainty of (d) and requirements on system robustness; constraint (1i) indicates that the channel gain R is taken into accountKUncertainty of the system and the requirement for system robustness.
Since the beamforming vector W and the reflection element coefficient matrix E are coupled in the constraint (1a) and the constraint (1b), and meanwhile, the imperfect CSI needs to be considered, the optimization problem at this time is a semi-infinite programming problem. These factors make the optimization problem non-convex and difficult to solve. Therefore, the semi-infinite constraint in the problem needs to be transformed into a deterministic convex constraint, which is described in detail below.
By using matrix knowledge and a convex optimization theory and combining mathematical theories such as an S-procedure theorem and the like, uncertainty of channel parameters under a bounded CSI error model is processed, constraint conditions are converted, a non-convex optimization problem is converted into a convex optimization problem, a robust transmission scheme is designed, the system robustness is increased, and the system reliability is improved.
The optimization problem objective function (1) is non-convex due to the influence of uncertainty of the channel parameters, so the uncertainty of the channel parameters is processed first.
Introducing a relaxation parameter ρ, constraint (1a) is rewritten as:
Figure BDA0003178719200000132
Figure BDA0003178719200000133
the existence of an ellipsoid uncertainty region in the formula (6)
Figure BDA0003178719200000134
And is
Figure BDA0003178719200000135
Considering the mathematical transformation formula trace (A)HB)＝vecH(A) vec, (B) and
Figure BDA0003178719200000136
so the left side of equation (6) is rewritten as:
Figure BDA0003178719200000131
the above formula (7) is substituted into the formula (6), and the S-procedure theory is used to convert the formula into the following equivalent formula:
Figure BDA0003178719200000141
similarly, constraint (1b) introduces relaxation parameters:
Figure BDA0003178719200000142
Figure BDA0003178719200000143
according to the application of the mathematical inequality | a + b + c-2≤3|a|2+3|b|2+3|c|2Where a, b, c are all complex numbers, the left side of equation (10) is rewritten as:
Figure BDA0003178719200000144
continuing to relax equation (11) can be expressed as:
Figure BDA0003178719200000145
Figure BDA0003178719200000146
Figure BDA0003178719200000147
it can be observed that equation (12) continues to translate into:
Figure BDA0003178719200000148
similarly, the conversion processing is performed on the formula (4-13):
Figure BDA0003178719200000151
in summary, after the conversion processing, the objective function of the approximate optimization problem of the uncertainty of the channel parameter is:
Figure BDA0003178719200000152
s.t.(5)，(8)，(9)，(14)，(15)，(16)，(1c)，(1d)，(1e)，(1f) (2)；
the number in parentheses in the formula (2) represents a corresponding expression.
Through a series of operations of the relaxation conversion, the optimization problem containing the boundary CSI is converted into a deterministic problem, but high coupling exists among variables, and the formula (17) is still a non-convex problem. For this purpose, an iterative algorithm based on the BCD algorithm is used to solve by iteratively optimizing two sub-problems with respect to the reflection element matrix e, with respect to the beamforming matrix W and the user transmission power P of D2D, until convergence.
Specifically, equation (17) is transformed into two subproblems, the first subproblem: giving a reflection unit matrix e, and solving a beam forming matrix W, D2D user transmission power P distribution scheme of a base station; the second sub-problem: given the beamforming matrix W, D2D user transmission power P of the base station, the matrix of reflection elements e is solved.
For the first sub-problem, solving by adopting a semi-positive definite relaxation method and utilizing a convex optimization tool package CVX; giving a reflection unit matrix e, and solving the following subproblems to obtain a beam forming matrix W, D2D user transmission power P distribution scheme of the base station:
Figure BDA0003178719200000153
s.t.(5)，(8)，(9)，(14)，(15)，(16)，(1c)，(1e)，(1f) (3)；
the non-convex rank 1 constraint (1c) is present in equation (18), and is still a non-convex problem.
For the case that the rank of the beamforming matrix W of the base station is 1, the SDR technology is adopted to relax the problem (18) to obtain a convex SDP problem, and then a convex optimization tool kit CVX is utilized to solve the problem. For the case that the rank of the beamforming matrix W of the base station is not 1, a gaussian random method is adopted to obtain a rank 1 solution, then a reflection unit matrix e is given, and a beamforming matrix W, D2D user transmission power P allocation scheme of the base station is solved.
For the second sub-problem, a penalty Concave-Convex process (CCP) method is adopted to convert the sub-problem into a Convex optimization problem, and a Convex optimization tool bag CVX is adopted to solve the problem.
At this time, the sub-problem regarding the reflection element matrix e is a feasibility checking problem.
Introducing relaxation variable chi ═ chi1,χ2]TThe constraint (5) and the constraint (9) are corrected, and the equations (5) and (9) are respectively rewritten as follows:
Figure BDA0003178719200000161
Figure BDA0003178719200000162
combining the above two equations, the sub-problem for the reflection element matrix e translates into:
Figure BDA0003178719200000163
s.t.(8)，(14)，(15)，(16)，(1d)，(19)，(20) (4)；
but the above problem is still non-convex due to the constraint of the unit mode (1 d). This non-convex constraint is handled using a penalty CCP method, introducing a slack variable b ═ b1,b2，...,b2M]TConstraint (1d) is equivalent to:
Figure BDA0003178719200000164
|em|2≤1+bM+m,1≤m≤M (23)；
and optimizing the subproblem of the reflecting unit matrix e, and further converting into:
Figure BDA0003178719200000173
s.t.(8)，(14)，(15)，(19)，(20)，(22)，(23) (25)；
b≥0 (26)；
wherein | b | purple1A penalty term representing an objective function, | | b | | non-woven phosphor1By a regularization factor kappa[p]Scaling is performed to control the feasibility of the constraint. The algorithm for finding the feasible solution e in the problem (24) is shown in table 1.
TABLE 1 penalty CCP Algorithm
Figure BDA0003178719200000171
For the solution of equation (1), the sub-problem is solved by iteration, and the specific steps are shown in algorithm table 2.
Table 2 robust transmission scheme design
Figure BDA0003178719200000172
Figure BDA0003178719200000181
Since only two convex optimization problems need to be solved in each iteration, the algorithm 2 is less complex and can converge quickly.
By adopting the method, the robustness of the intelligent reflection surface D2D communication system under the condition of considering the imperfect CSI is good, and the simulation verification is carried out, wherein the result is as follows:
assuming that the base station is located at (0m,0m), the intelligent reflective surface is fixed at (60m,10m), and the location of the cellular user and the location of the D2D user are randomly generated. The specific simulation parameter table is shown in table 3.
TABLE 3 simulation parameters
Figure BDA0003178719200000182
Figure BDA0003178719200000191
In the present simulation experiment, the non-robust solution means that the uncertainty of the channel parameters is not considered, i.e. the estimated values of these parameters are considered to be accurate. By the same algorithm as the robust algorithm, a solution to the non-robust optimization problem can be obtained. In this simulation, the channel uncertainty ∈G，∈T，∈RRespectively expressed as:
Figure BDA0003178719200000192
this indicates that the channel gain error does not exceed 1% of its estimated value when the channel uncertainty e is 0.01. If there are no other settings, e in this sectionG＝∈T＝∈R＝0.01。
FIG. 2 shows the difference in RDminThe variation of the transmission power with uncertainty e. In the figure, R corresponds to the line with triangleDminEqual to 3, R corresponding to the dotted line with a circleDminEqual to 2, R corresponding to the circled solid lineDminEqual to 1, the abscissa represents the uncertainty e, the larger e, the higher the transmission power increases, as can be seen from fig. 2. This is because more power needs to be consumed to counter the effects of increased uncertainty.
FIG. 3 shows the transmission power as a function of R at different ∈DminThe variation of (2). The corresponding uncertainty of the line with the triangle is equal to 0.02, the corresponding uncertainty of the line with the circle is equal to 0.03, the corresponding uncertainty of the line with the cross star is equal to 0.01, and the abscissa represents RDmin。
It can also be seen from fig. 3 that R is fixed with a fixed uncertaintyDminThe larger its transmission power. Because with RDminWith this increase, the range of feasible solutions to the optimization problem increases, i.e., more power is required to meet the minimum rate requirements of the user.
FIG. 4 shows transmission power as a function of R in a robust scheme and a non-robust schemeDminA change in (c). Robust algorithm corresponding to solid line with circle, non-robust algorithm corresponding to dotted line with circle, and abscissa represents RDmin。
As can be seen from the comparison scheme, the non-robust scheme requires less power than the robust scheme, because the robust scheme requires more transmission power to resist the influence of uncertainty. However, the non-robust scheme may not satisfy the constraint condition, so that the robust scheme has more robustness and better meets the actual requirement although the robust scheme requires relatively more power.
In summary, the present application applies the intelligent reflective surface technology to the D2D communication system to reduce communication interruption, and improve the robustness of the system while achieving the minimum power.
Detailed description of the invention
An embodiment of the present invention provides a terminal device for robust transmission design of an intelligent reflective surface assisted D2D communication system, where the terminal device includes: a processor, a memory and a computer program stored in the memory and executable on the processor, the processor implementing the method of embodiment 1 when executing the computer program.
Illustratively, the computer program may be partitioned into one or more modules/units that are stored in the memory and executed by the processor to implement the invention. The one or more modules/units may be a series of computer program instruction segments capable of performing specific functions for describing the execution of the computer program in a robust transmission design terminal device of the intelligent reflective surface assisted D2D communication system. For example, the computer program may be divided into a plurality of modules, each module having the following specific functions:
1. giving a reflection unit matrix e, solving a beamforming matrix W, D2D user transmission power P distribution scheme module of the base station, and obtaining a beamforming matrix W, D2D user transmission power P of the base station;
2. the beamforming matrix W, D2D user transmission power P for a given base station solves for the reflection element matrix e optimization scheme for the reflection element matrix e.
The robustness transmission design terminal device of the intelligent reflection surface assisted D2D communication system can be a desktop computer, a notebook computer, a palm computer, a cloud server and other computing devices. The terminal device for robust transmission design of the intelligent reflective surface assisted D2D communication system may include, but is not limited to, a processor, a memory. It will be appreciated by those skilled in the art that the above examples are merely examples of robust transmission design end devices for intelligent reflective surface assisted D2D communication systems and do not constitute a limitation on robust transmission design end devices for intelligent reflective surface assisted D2D communication systems, and may include more or less components than those shown, or some components in combination, or different components, e.g., the end devices may also include input output devices, network access devices, buses, etc.
The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, discrete hardware component, etc. The general purpose processor may be a microprocessor or the processor may be any conventional processor or the like, the processor being the control center of the robust transmission design end device of the intelligent reflective surface assisted D2D communication system, the various parts of the robust transmission design end device of the entire intelligent reflective surface assisted D2D communication system being connected by various interfaces and lines.
The memory may be used for storing the computer programs and/or modules, and the processor may be adapted to implement the various functions of the robust transmission design end device of the one intelligent reflective surface assisted D2D communication system by executing or executing the computer programs and/or modules stored in the memory and invoking the data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.
Detailed description of the preferred embodiment
The modules/units integrated by the robust transmission design terminal device of the intelligent reflective surface assisted D2D communication system can be stored in a computer readable storage medium if implemented in the form of software functional units and sold or used as independent products. Based on such understanding, all or part of the flow of the method according to the embodiments of the present invention may also be implemented by a computer program, which may be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the method embodiments may be implemented. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, etc. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals as is required by legislation and patent practice.
The embodiments of the present invention are preferred embodiments of the present invention, and the scope of the present invention is not limited by these embodiments, so: all equivalent changes made according to the structure, shape and principle of the invention are covered by the protection scope of the invention.

Claims (12)

1. A robust transmission design method of an intelligent reflecting surface auxiliary D2D communication system is characterized by comprising the following steps: establishing an intelligent reflecting surface assisted D2D communication system model and an imperfect channel model, establishing a robust optimization problem based on the imperfect scene of channel state information, processing the optimization problem containing channel parameter uncertainty by using matrix knowledge and a convex optimization theory, converting a semi-infinite constraint condition into a convex constraint, and establishing a resource allocation scheme of the intelligent reflecting surface D2D communication system.
2. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 1, wherein: the intelligent reflection surface assisted D2D communication system model comprises a base station, an intelligent reflection surface and a D2D communication system, wherein D2D users multiplex downlink spectrum resources of a cellular communication link; the base station is equipped with N antennas, the cellular user and D2D user pairs are each equipped with a single antenna, and the smart reflective surface has M reflective elements.
3. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 1, wherein: an ellipsoid model is adopted to establish an imperfect channel model, interference channel gain and an uncertain region of each D2D user between a transmitting end and a cellular user are obtained, a base station assists cascade channel gain and an uncertain region of a D2D communication system and each D2D user at a receiving end through an intelligent reflection surface, and each D2D user assists cascade channel gain and an uncertain region of a D2D communication system and a cellular user at a transmitting end through an intelligent reflection surface.
4. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 1, wherein: under imperfect channel state information, the optimization problem includes: transmission power minimization objective function, minimum rate requirements for cellular and D2D users, rank-one requirements, unit modulus requirements for reflection element coefficients, power requirements for cellular and D2D users, channel gain gC，k/Tk/RkUncertainty of the system and the requirement for system robustness.
5. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 4, wherein: the worst case minimization of the transmission power optimization problem, the objective function is represented by:
Figure FDA0003178719190000021
the constraint conditions include:
Figure FDA0003178719190000022
RC≥RCmin (1b)；
rank(W)＝1 (1c)；
Figure FDA0003178719190000023
0≤trace(W)≤PCmax (1e)；
0≤PK，K≤PDmax (1f)；
Figure FDA0003178719190000024
Figure FDA0003178719190000025
Figure FDA0003178719190000026
wherein W is PCwwHW represents a beamforming vector associated with a cellular user, and H represents a matrix transposition; pk，kRepresenting the transmit power of the transmit end D2D-T of the kth pair D2D user pair to the receive end D2D-R of the kth pair D2D user pair,
Figure FDA0003178719190000027
representing the rate, R, of the kth pair D2D user pairsDminRepresents the minimum rate of the D2D user; rCminRepresents a minimum rate for a cellular user; | em|2Representing the unit mode, P, of the m-th reflecting element of the intelligent reflecting surfaceDmaxRepresents the maximum transmit power of the D2D user; pCmaxRepresents the maximum transmit power of the cellular user;
equation (1a) (1b) represents the minimum rate requirements for cellular users and D2D users;
equation (1c) represents a rank-one requirement;
equation (1d) represents the unit mode requirement for the coefficient of the reflective element;
equation (1e) (1f) represents the maximum power constraint for cellular users and D2D users;
equation (1g) represents the interference channel gain g between the kth pair of D2D users and the cellular userC，KThe uncertainty effect of (2);
the formula (1h) represents the cascade channel gain T of the base station and the k-th pair D2D user pair receiving end through the intelligent reflection surface auxiliary D2D communication systemkThe uncertainty effect of (2);
equation (1h) represents the cascade channel gain R of the k-th pair D2D user pair transmitting end and the cellular user through the intelligent reflection surface auxiliary D2D communication systemKThe uncertainty of (c).
6. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 5, wherein: introducing relaxation parameters, performing equivalent transformation on constraint conditions by adopting S-procedure lemma, and processing the optimization problem containing channel parameter uncertainty; and (3) converting the channel parameter uncertainty problem into a convex optimization problem by adopting a block coordinate descent algorithm, iteratively optimizing a beam forming matrix W, D2D user transmission power P and a reflection unit matrix e of the base station, and directly stopping convergence to obtain the beam forming matrix W, D2D user transmission power P and the reflection unit matrix e of the base station.
7. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 6, wherein: under the condition of fixing the reflecting unit matrix e, adopting a semi-positive definite relaxation method to obtain a beam forming matrix W, D2D user transmission power P distribution scheme of the base station; under the condition of giving a beam forming matrix W and user transmission power P of D2D, a reflection unit matrix e is obtained by adopting a punishment concave-convex process, so that the optimization problem of the beam forming matrix W, D2D user transmission power P and the reflection unit matrix e is simplified into a convex optimization problem.
8. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 7, wherein: introducing a relaxation parameter rho, and rewriting the formula (1a) as:
Figure FDA0003178719190000041
Figure FDA0003178719190000042
and (3) carrying out mathematical formula conversion on the formula (6) by utilizing the S-procedure lemma to obtain:
Figure FDA0003178719190000043
the equation (1b) is equivalently transformed and rewritten as:
Figure FDA0003178719190000044
Figure FDA0003178719190000045
Figure FDA0003178719190000046
Figure FDA0003178719190000047
wherein, alpha, beta and gamma are relaxation parameters;
the approximate optimization problem after the channel parameter uncertainty is processed is as follows:
Figure FDA0003178719190000048
s.t.(5)，(8)，(9)，(14)，(15)，(16)，(1c)，(1d)，(1e)，(1f) (2)；
and converting the optimization problem containing the boundary channel parameters into a deterministic problem.
9. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 8, wherein: for the case that the rank of the optimal solution of the beamforming matrix W of the base station is 1, given the matrix e of the reflection unit, the beamforming matrix W, D2D user transmission power P allocation scheme of the base station is solved,
Figure FDA0003178719190000051
s.t.(5)，(8)，(9)，(14)，(15)，(16)，(1c)，(1e)，(1f) (3)；
loosening the problem (18) by adopting an SDR technology to obtain a convex SDP problem, and solving by utilizing a convex optimization toolkit CVX;
for the case that the rank of the optimal solution of the beamforming matrix W of the base station is not 1, a Gaussian random method is adopted to obtain a rank 1 solution, then a reflection unit matrix e is given, and the beamforming matrix W, D2D user transmission power P distribution scheme of the base station is solved.
10. The robust transmission design method of intelligent reflective surface assisted D2D communication system according to claim 8, wherein: a beamforming matrix W for a given base station,D2D user transmission power P distribution scheme, introducing relaxation variable χ ═ χ1，χ2]TAnd modifying the constraint (2) and the constraint (9) to obtain:
Figure FDA0003178719190000052
Figure FDA0003178719190000053
the sub-problem with the matrix of reflective elements e translates into:
Figure FDA0003178719190000054
s.t.(8)，(14)，(15)，(16)，(1d)，(19)，(20) (4)；
adopting punished concave-convex process, introducing relaxation variable b ═ b1，b2，...，b2M]TConstraint (1d) is equivalent to:
Figure FDA0003178719190000055
|em|2≤1+bM+m，1≤m≤M (23)；
solving the subproblem of the reflection unit matrix e, and converting into:
Figure FDA0003178719190000061
s.t.(8)，(14)，(15)，(19)，(20)，(22)，(23) (25)；
b≥0 (26)；
wherein | b | Y phosphor1A penalty term representing an objective function, | | b | | non-woven phosphor1By a regularization factor kappa[p]Scaling to control the contractFeasibility of the bundle.
11. A robust transmission design terminal for a smart reflective surface assisted D2D communication system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: the processor, when executing the computer program, implements the method of any of claims 1-10.
12. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1 to 10.
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