CN114124172B - Intelligent reflector wave beam shaping and phase shift design method based on alternate direction - Google Patents

Intelligent reflector wave beam shaping and phase shift design method based on alternate direction Download PDF

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CN114124172B
CN114124172B CN202111500717.9A CN202111500717A CN114124172B CN 114124172 B CN114124172 B CN 114124172B CN 202111500717 A CN202111500717 A CN 202111500717A CN 114124172 B CN114124172 B CN 114124172B
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phase shift
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ris
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牛鸿
蒋伟
雷霞
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission

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Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to an intelligent reflector beam forming and phase shift design method based on alternate directions. The invention provides an intelligent reflecting surface wave beam forming and phase shifting design scheme with low complexity in alternate directions based on a RIS auxiliary MIMO transmission communication system, wherein in the LAD scheme, different from the AD scheme, the problem is solved by only optimizing phase shifting under the condition of not considering the wave beam forming vector, thereby greatly reducing the complexity and improving the convergence speed.

Description

Intelligent reflector wave beam shaping and phase shift design method based on alternate direction
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to an intelligent reflector beam forming and phase shift design method based on alternate directions.
Background
Intelligent Reflector (RIS) technology is a completely new and revolutionary technology that can intelligently reconfigure the wireless propagation environment by integrating a large number of low-cost passive reflective elements on a flat surface, thereby significantly improving the performance of wireless communication networks.
By varying the reflection coefficient using the RIS controller, the elements can independently adjust the phase shift of the wireless signal by optimizing the beam forming and phase shift to cooperatively provide multipath diversity gain, resulting in extensive research
In order to solve the non-convex problem of joint optimization of beam forming and phase shift design in the MIMO system, the conventional RIS solution often generates performance loss and high complexity.
Disclosure of Invention
In order to solve the problems, the invention provides a Low-complexity Alternating Direction (LAD) scheme, and provides a Low-complexity Alternating Direction (LAD) scheme, which is different from the AD scheme in that the overall received signal-to-noise ratio is improved to the maximum extent, and the LAD greatly reduces the calculation complexity and improves the convergence speed by maximizing the lower bound of the overall received signal-to-noise ratio.
The technical scheme adopted by the invention is the intelligent reflector beam forming and phase shift design based on low-complexity alternating direction: the system model is shown in fig. 1, and considers a communication system for RIS assisted MIMO transmission, where the sender is BS and the Receiver is Receiver. Wherein the sender BS is deployed with N t Root antenna, RIS with N reflection units and Receiver with N r A root antenna. The sender communicates with the receiver through the RIS. Each reflection unit in the RIS can adjust the Phase Shift (PS) of the incident signal independently using the reflection coefficient.
Figure GDA0003858308480000011
And
Figure GDA0003858308480000012
respectively representing a channel of a BS-RIS link, a channel of a RIS-Receiver link and a channel of a BS-Receiver link, wherein
Figure GDA0003858308480000013
Representing a complex field.
The working principle of the intelligent reflector beamforming and phase shift design based on the alternate direction is as follows: defining the base band transmitting signal as s, and satisfying the power constraint of s H s＝E s Vector formed by beam
Figure GDA0003858308480000014
Precoding is performed such that the overall signal at the receiver can be modeled as
Figure GDA0003858308480000015
Wherein y is the received signal, Θ is the phase shift matrix of RIS,
Figure GDA0003858308480000021
is complex additive white Gaussian noise, sigma 2 Represents variance, I represents identity matrix, H = R Θ T + D is channel;
thus, this problem can be expressed as:
Figure GDA0003858308480000022
s.t.||w|| 2 ＝1,
θ i ∈[0,2π),i＝1,2,…,N
where R is the objective function, θ i For the ith element of the phase shift matrix theta, the objective function of the problem is, according to the expression of the received signal
R＝log(1+γ SNR )
Wherein gamma is SNR For received signal-to-noise ratio, it is expressed as:
Figure GDA0003858308480000023
then the problem is
Figure GDA0003858308480000024
Can be converted into:
Figure GDA0003858308480000025
s.t.||w|| 2 ＝1,
θ i ∈[0,2π),i＝1,2,…,N
the problem is that because the high coupling of w and theta is difficult to solve by a conventional method, the invention designs an intelligent reflecting surface beam forming and phase shifting design scheme based on a low-complexity alternating direction, which specifically comprises the following steps:
regardless of the information of the beamforming vector w, will be a problem
Figure GDA0003858308480000026
The transformation is:
Figure GDA0003858308480000027
s.t.θ i ∈[0,2π),i＝1,2,…,N
according to the theorem
Figure GDA0003858308480000028
Maximization
Figure GDA0003858308480000031
Wherein | · | non-woven phosphor 2 Represents the 2-norm of the matrix, | | · |. Non-woven phosphor F Representing the F-norm of the matrix, converting the problem into
Figure GDA0003858308480000032
s.t.θ i ∈[0,2π),i＝1,2,…,N
Will be provided with
Figure GDA0003858308480000033
Decomposing into N sub-problems, each sub-problem being used to optimize one reflection unit:
Figure GDA0003858308480000034
s.t.θ n ∈[0,2π)
wherein
Figure GDA0003858308480000035
For the nth sub-problem, define
Figure GDA0003858308480000036
Wherein
Figure GDA0003858308480000037
Figure GDA0003858308480000038
Order to
Figure GDA0003858308480000039
Fang Cheng
Figure GDA00038583084800000310
There are two roots, denoted:
Figure GDA00038583084800000311
Figure GDA00038583084800000312
wherein
Figure GDA00038583084800000313
Figure GDA00038583084800000314
Figure GDA00038583084800000315
Figure GDA00038583084800000316
By making a judgment
Figure GDA00038583084800000317
And
Figure GDA00038583084800000318
which one can enable
Figure GDA00038583084800000319
Is an objective function of
Figure GDA00038583084800000320
Becomes large to determine its solution, in order toGet an overall solution, must be from θ 1 Repeat to theta n Until all elements are converged to obtain the optimal theta, utilizing the obtained theta to pass through the problem
Figure GDA00038583084800000321
Obtaining the optimal w, and finally obtaining the optimal theta and w.
The invention has the advantages that based on a RIS auxiliary MIMO transmission communication system, a low-complexity alternative-direction intelligent reflector wave beam shaping and phase shift design scheme is provided, and in the LAD scheme, different from the AD scheme, the problem is solved by only optimizing the phase shift under the condition of not considering the wave beam shaping vector, thereby greatly reducing the complexity and improving the convergence speed.
Drawings
FIG. 1 is a schematic diagram of the logic structure of the system of the present invention.
FIG. 2 is a comparison graph of the LAD algorithm simulation result and the theoretical boundary.
FIG. 3 is a drawing showing
Figure GDA0003858308480000041
Objective function with theta n And (5) a variation graph.
Fig. 4 shows a convergence comparison between the AD algorithm and the LAD algorithm.
Fig. 5 is a comparison of the performance of the AD algorithm and the LAD algorithm.
Detailed Description
The following detailed description of embodiments of the invention is provided in connection with the accompanying drawings.
The AD algorithm is computationally very complex due to two-layer iteration. More specifically, when w is updated, the Θ of the inner layer must be iteratively updated again. Furthermore, the updated Θ requires w to be updated again in the outer iteration. Therefore, the cross-iteration introduces excessive complexity, which is detrimental to the actual scenario. LAD optimizes only the design phase matrix Θ without considering the beamforming vector w. The specific scheme is as follows.
Information without considering the beamforming vector w, problem
Figure GDA0003858308480000042
Can be changed into
Figure GDA0003858308480000043
s.t.θ i ∈[0,2π),i＝1,2,…,N
Direct solution
Figure GDA0003858308480000044
Is very difficult, so according to the theorem
Figure GDA0003858308480000045
Can maximize
Figure GDA0003858308480000046
Lower bound of (2), then the problem translates into
Figure GDA0003858308480000047
s.t.θ i ∈[0,2π),i＝1,2,…,N
Likewise, when other variables are unchanged, θ can be derived n Closed-form solution of (1). Therefore, the temperature of the molten metal is controlled,
Figure GDA0003858308480000048
can be decomposed into N subproblems
Figure GDA0003858308480000051
s.t.θ n ∈[0,2π)
Likewise, define
Figure GDA0003858308480000052
Wherein
Figure GDA0003858308480000053
Figure GDA0003858308480000054
Order to
Figure GDA0003858308480000055
The equation has two roots, expressed as:
Figure GDA0003858308480000056
Figure GDA0003858308480000057
wherein
Figure GDA0003858308480000058
Figure GDA0003858308480000059
Figure GDA00038583084800000510
Figure GDA00038583084800000511
By making a judgment
Figure GDA00038583084800000512
And
Figure GDA00038583084800000513
which one can enable
Figure GDA00038583084800000514
Is an objective function of
Figure GDA00038583084800000515
Becomes larger to determine its solution.
To illustrate the superiority of this scheme in power performance, the beneficial effects of the present invention are verified by simulation below.
Firstly, comparing a theoretical boundary with a simulation result, and verifying the accuracy of the theoretical result through Monte Carlo simulation. In conjunction with Monte Carlo simulations, FIG. 2 reveals the number of BS antennas N t And the number N of RIS units influences the error rate of the LAD scheme. The solid line and the dotted line represent the computer simulation result and the theoretical analysis result, respectively. According to the results shown in fig. 1, the larger the number of BS antennas is, the better the error rate performance is, and the more excellent the error rate performance can be obtained by increasing the number of RIS units. For example, at BER =10 -3 ，N t =2 to N t The snr loss of =4 is about 3dB, while the snr gain for N =32 is about 5dB compared to N = 16.
FIG. 3 depicts the objective function for a single channel as a function of a particular RIS unit θ n At [0,2 π]The value of the change. The three results of the graph show that
Figure GDA0003858308480000061
In order to be the objective function of the target,
Figure GDA0003858308480000062
and
Figure GDA0003858308480000063
one reaches a maximum value and the other reaches a minimum value. The optimality of the scheme is proved.
In fig. 4, the convergence of the AD algorithm and the LAD algorithm was evaluated and compared. Wherein the simulation parameter is set to N t ＝4,N r And =4. The maximum number of iterations of the AD algorithm is set to I =1. It can be seen that 1) the performance of AD and LAD is almost the same over multiple iterations. 2) LAD is superior to AD in convergence speed because the boundary of LAD is always higher than the boundary of AD。
FIG. 5 compares at N t ＝4、N r Information reachability performance of AD algorithm and LAD algorithm under =2,4 and N =16 × 1 to 16 × 8. Not expected, the AD and LAD properties were identical. In addition, a larger number of RIS units contributes to an increase in information reachability, and a larger number of receive antennas also provides performance gain. Thus, LAD has lower complexity and almost the same performance compared to AD.

Claims (1)

1. An intelligent reflector beamforming and phase shift design method based on low-complexity alternate direction is used for a communication system for RIS auxiliary MIMO transmission, and a sender BS in the system is deployed with N t A root antenna, a RIS is provided with N reflection units, and a Receiver is provided with N receivers r The receiver comprises a root antenna, a receiver and a receiver, wherein the transmitter communicates with the receiver through an RIS, and each reflecting unit in the RIS can independently utilize a reflection coefficient to adjust the phase shift of an incident signal; definition of
Figure FDA0003858308470000011
And
Figure FDA0003858308470000012
respectively represent a channel of a BS-RIS link, a channel of an RIS-Receiver link and a channel of a BS-Receiver link, wherein
Figure FDA0003858308470000013
Representing a complex field, defining a baseband transmission signal as s, whose power constraint satisfies s H s＝E s Vector formed by beam
Figure FDA0003858308470000014
Carrying out pre-coding; the receiver signal model is:
Figure FDA0003858308470000015
where y is the received signal and Θ is the phase shift of the RISThe matrix is a matrix of a plurality of matrices,
Figure FDA0003858308470000016
is complex additive white Gaussian noise, sigma 2 Represents variance, I represents identity matrix, H = R Θ T + D is channel;
the method is characterized in that the method for designing the beam forming and the phase shift comprises the following steps of firstly establishing an optimization model:
Figure FDA0003858308470000017
s.t.||w|| 2 ＝1,
θ i ∈[0,2π),i＝1,2,…,N
wherein R is an objective function, θ i For the ith element of the phase shift matrix Θ, the objective function of the problem is expressed as:
R＝log(1+γ SNR )
wherein gamma is SNR For received signal-to-noise ratio, it is expressed as:
Figure FDA0003858308470000018
then the problem is
Figure FDA0003858308470000019
Can be converted into:
Figure FDA00038583084700000110
s.t.||w|| 2 ＝1,
θ i ∈[0,2π),i＝1,2,…,N
the problem is difficult to solve by a conventional method due to high coupling of w and theta, so that an intelligent reflector beamforming and phase shift design method based on a low-complexity alternating direction is adopted, and the method specifically comprises the following steps:
regardless of the information of the beamforming vector w, will be a problem
Figure FDA0003858308470000021
The transformation is:
Figure FDA0003858308470000022
s.t.θ i ∈[0,2π),i＝1,2,…,N
according to the theorem
Figure FDA0003858308470000023
Maximization
Figure FDA0003858308470000024
Wherein | · | non-woven phosphor 2 Represents the 2-norm of the matrix, | | without calculation F Representing the F-norm of the matrix, converting the problem into
Figure FDA0003858308470000025
s.t.θ i ∈[0,2π),i＝1,2,…,N
Will be provided with
Figure FDA0003858308470000026
Decomposing into N sub-problems, each sub-problem being used to optimize one reflection unit:
Figure FDA0003858308470000027
s.t.θ n ∈[0,2π)
wherein
Figure FDA0003858308470000028
For the nth sub-problem, define
Figure FDA0003858308470000029
Wherein
Figure FDA00038583084700000210
Figure FDA00038583084700000211
Order to
Figure FDA00038583084700000212
Fang Cheng
Figure FDA00038583084700000213
There are two roots, denoted:
Figure FDA00038583084700000214
Figure FDA00038583084700000215
wherein
Figure FDA0003858308470000031
Figure FDA0003858308470000032
Figure FDA0003858308470000033
Figure FDA0003858308470000034
By making a judgment
Figure FDA0003858308470000035
And
Figure FDA0003858308470000036
which can enable
Figure FDA0003858308470000037
Is an objective function of
Figure FDA0003858308470000038
Becomes larger to determine its solution, and must be determined from θ in order to obtain the overall solution 1 Repeat to theta n Until all elements are converged to obtain the optimal theta, the obtained theta is utilized to pass through the problem
Figure FDA0003858308470000039
Obtaining the optimal w, and finally obtaining the optimal theta and w.
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CN113037349A (en) * 2021-03-12 2021-06-25 重庆邮电大学 Physical layer security design method based on alternate iteration in IRS-assisted MISO system
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