CN116366109B - A multilayer intelligent metasurface device and a beamforming method - Google Patents

A multilayer intelligent metasurface device and a beamforming method

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Publication number
CN116366109B
CN116366109B CN202111623669.2A CN202111623669A CN116366109B CN 116366109 B CN116366109 B CN 116366109B CN 202111623669 A CN202111623669 A CN 202111623669A CN 116366109 B CN116366109 B CN 116366109B
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metasurface
layer
intelligent
user
smart
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CN116366109A (en
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吴秋岑
林田
朱宇
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Fudan University
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Fudan University
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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
    • H04B7/06—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
    • 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
    • H04B7/0615—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 of weighted versions of same signal
    • H04B7/0617—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 of weighted versions of same signal for beam forming
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Aerials With Secondary Devices (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

本发明提供了一种多层智能超表面装置，用于对入射的无线信号进行调制，并通过反射和透射同时向反射端用户和透射端用户辐射，包括：两层或多层智能超表面。本发明还提供了一种多层智能超表面装置辅助下的下行多用户通信系统的波束成形方法，包括以下步骤：步骤1，对多层智能超表面装置辅助下的下行多用户通信系统进行建模，并对多用户和速率最大的优化问题进行建模；步骤2，将多用户和速率最大的优化问题转换为最小化加权均方误差问题，针对最小化加权均方误差问题，交替优化接收端系数矩阵和辅助权重系数矩阵、基站端数字波束成形设计和不同层的智能超表面的模拟波束成形，最终得到基站端数字波束成形和不同层的智能超表面的模拟波束成形。

This invention provides a multilayer smart metasurface device for modulating incident wireless signals and radiating them simultaneously to both reflecting and transmitting users, comprising two or more layers of smart metasurfaces. This invention also provides a beamforming method for a downlink multi-user communication system assisted by a multilayer smart metasurface device, comprising the following steps: Step 1, modeling the downlink multi-user communication system assisted by the multilayer smart metasurface device and modeling an optimization problem for maximizing multi-user sum and rate; Step 2, transforming the optimization problem for maximizing multi-user sum and rate into a problem of minimizing weighted mean square error, and for minimizing the weighted mean square error problem, alternately optimizing the receiver coefficient matrix and auxiliary weight coefficient matrix, the base station digital beamforming design, and the simulated beamforming of different layers of smart metasurfaces, ultimately obtaining the base station digital beamforming and the simulated beamforming of different layers of smart metasurfaces.

Description

Multilayer intelligent super-surface device and beam forming method
Technical Field
The invention belongs to the technical field of wireless technology, and particularly relates to a multilayer intelligent super-surface device and a beam forming method.
Background
In recent years, with the popularity of commercial fifth generation (5G) wireless communication networks worldwide, more and more scientists are working on studying upcoming super-fifth generation (B5G) and sixth generation (6G) wireless communication network technologies, including higher carrier frequencies, lower energy consumption, microsecond-level delays and full-dimensional network coverage. To achieve these stringent specifications, many new technologies have been proposed in recent years, including ultra-large-scale multiple-input multiple-output (UM-MIMO), ultra-dense networks (UDNs) and terahertz (THz) communication technologies. However, the increased number of base station antennas will result in higher energy consumption and hardware costs, while the high path loss resulting from the increased carrier frequency will result in further increases in energy consumption, making these techniques difficult to use in next generation wireless communication networks.
Due to the rapid development of the super-surface related technology, reconfigurable Intelligent Surfaces (RIS) are receiving extensive attention from the scientific and industrial world, and become a promising and important solution in 6G wireless network technology. The smart supersurface consists of a number of passive sub-wavelength scattering elements, the surface of which is distributed with PIN junctions. By controlling the on-off of these PIN junctions, the scattering unit can control the amplitude and phase of the signal. Therefore, if the states of different scattering units can be properly controlled, the reconfiguration of the wireless environment can be realized, and the system performance is improved. Compared with the traditional relay communication, the intelligent reflection surface scattering unit is a passive device, and a radio frequency chain is not needed, so that the intelligent reflection surface scattering unit has lower energy consumption and cost.
In previous studies, the most well known RIS model was the Intelligent Reflective Surface (IRS), which consists of a three-layer arrangement of a scattering cell layer, a metal back plane and a control circuit board, which only reflects the incoming signal to the corresponding user. Thus, if the user and base station are on either side of the IRS, the IRS will no longer be able to service the user.
To address this problem, a new RIS model, known as an Intelligent Omnidirectional Subsurface (IOS), has recently been proposed that can serve users on both sides of the subsurface simultaneously. Specifically, the following behavior examples, signals incident on both sides of the IOS may be reflected and refracted simultaneously onto users at both the reflective and transmissive ends. This dual function of reflecting and refracting signals simultaneously allows the IOS to extend wireless coverage throughout the space, thereby significantly improving quality of service.
Despite the above advantages, one major drawback of existing IOS designs is that the scattering unit is not able to independently control the phase shift of the reflected and transmitted signals. Thus, the beam forming of the IOS for users on both sides of the smart reflective surface is inevitably coupled together, which will significantly affect the performance of the communication system. Therefore, the IOS design with the independent transmission control and reflection signal freedom degree has great significance.
Disclosure of Invention
The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a multi-layer intelligent super-surface device and a beam forming method.
The present invention provides a multi-layer intelligent subsurface device for modulating an incoming wireless signal and radiating simultaneously by reflection and transmission to both a reflective end user and a transmissive end user, having the features of comprising: and the wireless signals sent by the base station are communicated with the transmitting end user after being transmitted for multiple times through all the intelligent super surfaces, and the formed wave beams of the reflecting end user and the transmitting end user are independently controlled by controlling the states of different scattering units.
The invention also provides a beam forming method of the downlink multi-user communication system assisted by the multi-layer intelligent super-surface device, which has the characteristics that the method comprises the following steps:
Step 1, modeling a downlink multi-user communication system assisted by a multi-layer intelligent super-surface device, and modeling an optimization problem with maximum multi-user and rate;
Step 2, converting the optimization problem of maximum multi-user and velocity into the minimization of weighted mean square error, alternately optimizing a receiving end coefficient matrix and an auxiliary weight coefficient matrix, a digital beam forming design of a base station end and the analog beam forming of intelligent super surfaces of different layers aiming at the minimization of weighted mean square error, finally obtaining the digital beam forming of the base station end and the analog beam forming of the intelligent super surfaces of different layers,
The downlink multi-user communication system assisted by the multi-layer intelligent super-surface device comprises a base station provided with a plurality of antennas, the multi-layer intelligent super-surface device for receiving wireless signals of the base station and simultaneously reflecting and transmitting, and a plurality of users, including a reflecting end user and a transmitting end user, wherein the optimization of the analog beam forming is performed based on a coordinate iteration descent algorithm.
The beam forming method of the downlink multi-user communication system assisted by the multi-layer intelligent super-surface device provided by the invention can also be characterized in that the step 1 comprises the following substeps:
Step 1-1, the coefficient matrix expression form of the intelligent super surface of the single layer is as follows:
Step 1-2, obtaining an equivalent coefficient matrix expression form of the multi-layer intelligent super surface based on the coefficient matrix of the single-layer intelligent super surface, wherein the equivalent coefficient matrix expression form is as follows:
Step 1-3, the mathematical expression form of the base station transmitting signal is as follows:
x=Vs (3);
step 1-4, the mathematical expression of the received signal of the user is as follows:
step 1-5, the mathematical form of the user side rate is as follows:
step 1-6, modeling the mathematical form of the multi-user and rate-maximised optimisation problem as follows:
subject to Tr(VVH)≤Pb
In equation (1), M represents the number of scattering units in the intelligent subsurface of the monolayer, and ε μ represents the intensity coefficients of the reflected and transmitted signals of the intelligent subsurface of the monolayer. When μ=r, reflection, transmission, e t+∈r＝1,φm, phase shift of the incident signal by the mth scattering element,
In the formula (2),The diagonal coefficient matrixes corresponding to the first intelligent super-surface layer and the second intelligent super-surface layer respectively, the E μ,ξμ is the intensity coefficient of the reflected and transmitted signals of the first intelligent super-surface layer and the second intelligent super-surface layer respectively,For a channel matrix between two layers of intelligent subsurface,
In the formula (3),Representing the pre-coding matrix and,Indicating information symbols transmitted to each user, N indicating the number of base station antennas, K indicating the number of users,
In equation (4), when k=1,..k r, μ (K) =r, when k=k r+1,...,Kr+Kt, μ (K) =t,The channel coefficient vectors from the base station to the multi-layer intelligent subsurface device and from the multi-layer intelligent subsurface device to the kth user are respectively represented, nk represents Gaussian noise of the kth user, the average value of the Gaussian noise is 0, and the variance of the Gaussian noise is sigma 2.
In the formula (5) of the present invention,Representing the total power of equivalent noise and interference at the kth user,
In the formula (6), the first constraint condition indicates that the total transmission power of the base station must not be greater than P b, and the second constraint condition and the third constraint condition indicate constant mode constraint of a scattering unit in the multi-layer intelligent super-surface device, the scattering unit only changes the phase of an incident signal and does not change the amplitude of the incident signal.
The beam forming method of the downlink multi-user communication system assisted by the multi-layer intelligent super-surface device provided by the invention can also be characterized in that the step 2 comprises the following substeps:
step 2-1, converting the maximum optimization problem of the multiuser sum rate into an equivalent minimum weighted mean square error problem by using the relation between the mean square error and the sum rate, wherein the mathematical form of the minimum weighted mean square error problem is as follows:
subject to Tr(VVH)≤Pb
in the formula (7) of the present invention, Representing the magnitude of the MSE value, w k represents the receiver coefficient of the kth user terminal, ψ k is an auxiliary weighting coefficient for establishing the equivalence between the MSE and the rate, and the closed solutions are respectively: And is k＝ek -1, wherein,
Further, a receiving end coefficient matrix ψ=diag (ψ 1,...,ψK) is defined, an auxiliary weight coefficient matrix w=diag (W 1,...,wK),E＝diag(e1,...,eK) is substituted into a closed-form solution of ψ, W, and then the mathematical form of minimizing the weighted mean square error problem is converted into:
subject to Tr(VVH)≤Pb
step 2-2, optimizing beam forming at a base station end, optimizing digital precoding V by fixing phi and theta, and under the power constraint according to a KKT condition, solving a closed solution of the V optimal solution as follows:
step 2-3, optimizing the intelligent super surface of the first layer, and defining the phase shift coefficient matrix phi of the intelligent super surface of the first layer by fixing other variables Phi=diag (phi), and applying identities Tr (C HACB)＝cH(A⊙BT) C and Tr (AC) =a T C, the objective function is reduced to:
f=φHPφ-qHφ-φHq (11)
to extract out The contribution to f, the objective function is further transformed into:
Obtaining Is the optimal solution of (a): Wherein the method comprises the steps of Each element is optimized alternately through a coordinate iteration descent algorithm, and a local optimal solution of phi is obtained;
step 2-4, optimizing the intelligent super surface of the second layer, and optimizing a phase shift coefficient matrix Θ of the intelligent super surface of the second layer by fixing other variables to split H into two parts related to a reflection user and a transmission user: Wherein, the After ignoring the constant independent of Θ, the objective function f is reduced to:
f=θHP′θ-q′Hθ-θHq′ (13)
in the formula (13) of the present invention, θ=diag(Θ), Obtaining a local optimal solution of theta through a coordinate iteration descent algorithm;
Step 2-5, alternately optimizing the receiving end coefficient matrix W, the auxiliary weight coefficient matrix psi, the digital pre-coding matrix V of the base station, the phase shift coefficient matrix phi of the intelligent super-surface of the first layer and the phase shift coefficient matrix theta of the intelligent super-surface of the second layer, outputting digital beam forming at the base station end and analog beam forming of the intelligent super-surface of different layers if the termination requirement is met, repeating the steps 2-2 to 2-4 if the termination requirement is not met,
In the formula (10) of the present invention,
Effects and effects of the invention
According to the multilayer intelligent super-surface device, incident wireless signals are modulated, radiation is emitted to a reflecting end user and a transmitting end user through reflection and transmission, and each intelligent super-surface can adjust the phase of the wireless signals through the scattering unit, so that beam forming of the reflecting end and the transmitting end can be independently controlled. In addition, according to the beam forming method of the downlink multi-user communication system assisted by the multi-layer intelligent super-surface device, the original problems of maximization and spectrum efficiency optimization in a complex form are equivalently converted into the problems of minimizing weighted mean square error, then the receiving end coefficient matrix and the auxiliary weight coefficient matrix, the digital beam forming design of the base station end and the analog beam forming of the intelligent super-surface of different layers are alternately optimized according to the converted problems, and finally the digital beam forming of the base station end and the analog beam forming of the intelligent super-surface of different layers are obtained.
Drawings
FIG. 1 is a schematic diagram of the architecture of a multi-layer intelligent subsurface device in an embodiment of the invention;
FIG. 2 is a flow chart of a method of beamforming for a downlink multi-user communication system with the assistance of a multi-layer intelligent subsurface device in an embodiment of the invention;
FIG. 3 is a beam forming schematic of a single layer intelligent subsurface in an embodiment of the invention;
FIG. 4 is a beam forming schematic of a dual-layer smart subsurface in an embodiment of the invention;
FIG. 5 is a schematic diagram of a downstream multi-user communication system aided by a multi-layer intelligent subsurface device in an embodiment of the invention;
FIG. 6 is a graph showing the relationship between the transmitting power and the user and the velocity in the case of the number of scattering units, the number of transmitted users, and the number of reflected users of the fixed intelligent supersurface in the embodiment of the invention;
FIG. 7 is a graph showing the relationship between the number of scattering units and the user and the rate for an intelligent supersurface in the case of a fixed emission rate, a number of transmitted users, and a number of reflected users in an embodiment of the invention;
fig. 8 is a graph of the relationship between the number of transmitted users and the user and rate for the case of a fixed transmission rate, the total number of users and the number of scattering units on the intelligent supersurface in an embodiment of the invention.
Detailed Description
In order to make the technical means and effects of the present invention easy to understand, the present invention will be specifically described with reference to the following examples and the accompanying drawings.
< Example >
FIG. 1 is a schematic diagram of the architecture of a multi-layer intelligent subsurface device in an embodiment of the invention.
As shown in FIG. 1, the multi-layer intelligent subsurface device of the present embodiment is used for modulating an incident wireless signal and radiating to a reflecting end user and a transmitting end user simultaneously through reflection and transmission, and comprises two or more layers of intelligent subsurface.
A dual-layer multi-layer intelligent subsurface device (BIOS) is used in this embodiment, having a dual-layer intelligent subsurface, including a first layer intelligent subsurface (IOS 1) and a second layer intelligent subsurface (IOS 2).
Each layer of intelligent super surface consists of a plurality of scattering units and a digital control module connected with the scattering units,
The wireless signal sent by the base station is communicated with the reflecting end user through the reflection of the first layer of intelligent super surface, the wireless signal sent by the base station is communicated with the transmitting end user after being transmitted for a plurality of times through all intelligent super surfaces,
The shaped beams of the reflective end-user and the transmissive end-user are independently controlled by controlling the states of the different scattering elements.
In this embodiment, each scattering element may phase shift the incoming wireless signal and transmit at both the transmissive and reflective ends. The distance between the two layers of intelligent super surfaces is very short and the two layers of intelligent super surfaces are fixed when leaving the factory, so that a communication channel between the two layers of intelligent super surfaces only has a direct path and no scattering path. For the reflecting end, the user signal is only reflected by the first layer of intelligent super-surface, and for the transmitting end, the user signal is transmitted through the two layers of intelligent super-surfaces, so that the PIN junction on-off condition of all scattering units on the two layers of intelligent super-surfaces is properly set, and the independent design of beam forming of the transmitting end and the reflecting end can be realized.
Fig. 2 is a flow chart of a beam forming method of a downlink multi-user communication system with the assistance of a multi-layer intelligent subsurface device in an embodiment of the invention.
As shown in fig. 2, a beam forming method of a downlink multi-user communication system assisted by a multi-layer intelligent super-surface device in this embodiment includes the following steps:
step 1, modeling a downlink multi-user communication system assisted by a multi-layer intelligent super-surface device, and modeling an optimization problem with maximum multi-user and rate.
Step 1 comprises the following sub-steps:
Step 1-1, for a single-layer intelligent subsurface, it can be expressed as a pair of corner matrices in a communication system. For a smart subsurface having M scattering elements, the coefficient matrix for a single layer smart subsurface is expressed as follows:
For the double-layer multi-layer intelligent super-surface device, as the signal received by the reflecting end user is reflected only by the first layer intelligent super-surface, and the signal received by the transmitting end user is modulated by the transmission of the two layers intelligent super-surfaces, the equivalent coefficient matrix expression form of the multi-layer intelligent super-surface is obtained based on the coefficient matrix of the single-layer intelligent super-surface as follows:
In this embodiment, N antennas are deployed at a base station in a downlink multi-user communication system under the assistance of a multi-layer intelligent super-surface device (BIOS), and the total number of users is K, which includes K r reflective end users and K t transmissive end users, respectively. In this embodiment, number 1,..k r is assigned to the reflective user, and number K r+1,...,Kr+Kt is assigned to the transmissive user.
Step 1-3, from the perspective of equivalent baseband representation, the mathematical expression form of the base station transmitting signal is as follows:
x=Vs (3);
step 1-4, the mathematical expression of the received signal of the user is as follows:
in steps 1-5, the direct channel between the user and the base station is negligible due to severe blocking. Thus, the mathematical form of the reception rate of the kth user is as follows:
Step 1-6, modeling the mathematical form of the optimal problem of multi-user and maximum rate as the magnitude of the receiving rate, the coefficient matrix phi, theta of the multi-layer intelligent super-surface device and the precoding matrix V of the base station end is as follows:
subject to Tr(VVH)≤Pb
In equation (1), M represents the number of scattering units in the intelligent subsurface of the monolayer, and ε μ represents the intensity coefficients of the reflected and transmitted signals of the intelligent subsurface of the monolayer. When μ=r, reflection and transmission, when μ=t, the sum of the energies of the transmitted and reflected signals is equal to the incident signal (ignoring the energy loss of the scattering element), since the smart supersurface is a passive element, which is to satisfy the constraint of energy conservation, i.e. e t+∈r＝1,φm represents the phase shift of the incident signal by the mth scattering element, assuming in this embodiment that the phase shift of the transmitted and reflected signals by the scattering element is the same
In the formula (2),The diagonal coefficient matrixes corresponding to the first intelligent super-surface layer and the second intelligent super-surface layer respectively, the E μ·ξμ is the intensity coefficient of the reflected and transmitted signals of the first intelligent super-surface layer and the second intelligent super-surface layer respectively,For a channel matrix between two layers of intelligent subsurface, the multi-layer intelligent subsurface device is different for the transmissive side and reflective side beamforming matrices, which can enable separate control of transmissive side and reflective side beamforming.
In the formula (3),Representing the pre-coding matrix and,Indicating information symbols transmitted to each user, N indicating the number of base station antennas, K indicating the number of users,
In equation (4), when k=1,..k r, μ (K) =r, when k=k r+1,...,Kr+Kt, μ (K) =t,The channel coefficient vectors from the base station to the multi-layer intelligent subsurface device and from the multi-layer intelligent subsurface device to the kth user are respectively represented, n k represents Gaussian noise of the kth user, the average value of the Gaussian noise is 0, and the variance of the Gaussian noise is sigma 2.
In the formula (5) of the present invention,Representing the total power of equivalent noise and interference at the kth user,
In the formula (6), the first constraint condition indicates that the total transmission power of the base station must not be greater than P b, and the second constraint condition and the third constraint condition indicate constant mode constraint of a scattering unit in the multi-layer intelligent super-surface device, the scattering unit only changes the phase of an incident signal and does not change the amplitude of the incident signal.
And 2, because the optimization problem is highly non-convex and comprises coupling of multiple optimization variables, the method has great difficulty in directly solving the original problem, converts the optimization problem with maximum multi-user and velocity into a minimum weighted mean square error problem, and alternately optimizes a receiving end coefficient matrix and an auxiliary weight coefficient matrix, a digital beam forming design of a base station end and analog beam forming of intelligent super surfaces of different layers aiming at the minimum weighted mean square error problem, and finally obtains digital beam forming of the base station end and analog beam forming of the intelligent super surfaces of different layers.
The optimization of the analog beamforming is based on a coordinate iterative descent algorithm.
Step 2 comprises the following sub-steps:
step 2-1, converting the maximum optimization problem of the multiuser sum rate into an equivalent minimum weighted mean square error problem by using the relation between the mean square error and the sum rate, wherein the mathematical form of the minimum weighted mean square error problem is as follows:
subject to Tr(VVH)≤Pb
in the formula (7) of the present invention, Representing the magnitude of the MSE value, w k represents the receiver coefficient of the kth user terminal, ψ k is an auxiliary weighting coefficient for establishing the equivalence between the MSE and the rate, and the closed solutions are respectively: and is k=ek -1, wherein,
Further, a receiving end coefficient matrix ψ=diag (ψ 1,..,ψK) is defined, an auxiliary weight coefficient matrix w=diag (W 1,...,wK),E＝diag(e1,...,eK) is substituted into a closed-form solution of ψ, W, and then the mathematical form of minimizing the weighted mean square error problem is converted into:
subjectto Tr(VVH)≤Pb
step 2-2, optimizing beam forming at a base station end, optimizing digital precoding V by fixing phi and theta, and under the power constraint according to a KKT condition, solving a closed solution of the V optimal solution as follows:
and 2-3, optimizing the intelligent super surface of the first layer, and optimizing a phase shift coefficient matrix phi of the intelligent super surface of the first layer by fixing other variables. Because the elements thereof meet the constant modulus constraint, the problem is still not convex, so that the global optimal solution is difficult to obtain. However, since the constraint is decoupled for different matrix elements, a coordinate iterative descent algorithm can be used to solve for the local optimal solution. Definition of the definition Phi=diag (phi), and applying identities Tr (C HACB)＝cH(A⊙BT) C and Tr (AC) =a T C (a, B is any matrix, C is any diagonal matrix, a=diag (a), c=diag (C)), the objective function is reduced to:
f=φHPφ-qHφ-φHq (11)
to extract out The contribution to f, the objective function is further transformed into:
Obtaining Is the optimal solution of (a): Wherein the method comprises the steps of Each element is optimized alternately through a coordinate iteration descent algorithm, and a local optimal solution of phi is obtained;
step 2-4, optimizing the intelligent super-surface of the second layer, and optimizing the phase shift coefficient matrix Θ of the intelligent super-surface of the second layer by fixing other variables, wherein only the speed of the transmitting end user is related to the intelligent super-surface of the second layer, and splitting H into two parts related to the reflecting user and the transmitting user: Wherein, the After ignoring the constant independent of Θ, the objective function f is reduced to:
f=θHP′θ-q′Hθ-θHq′ (13)
in the formula (13) of the present invention, θ=diag(Θ), Obtaining a local optimal solution of theta through a coordinate iteration descent algorithm;
Step 2-5, alternately optimizing the receiving end coefficient matrix W, the auxiliary weight coefficient matrix psi, the digital pre-coding matrix V of the base station, the phase shift coefficient matrix phi of the intelligent super-surface of the first layer and the phase shift coefficient matrix theta of the intelligent super-surface of the second layer, outputting digital beam forming at the base station end and analog beam forming of the intelligent super-surface of different layers if the termination requirement is met, repeating the steps 2-2 to 2-4 if the termination requirement is not met,
In the formula (10) of the present invention,
In this embodiment, the beam forming method of the downlink multi-user communication system under the assistance of the multi-layer intelligent omni-directional surface can be simply derived according to the beam forming method of the downlink multi-user communication system under the assistance of the multi-layer intelligent omni-directional surface.
In this embodiment, beam forming on both sides of a single-layer smart subsurface (IOS) and a double-layer smart subsurface (BIOS) is analyzed, and fig. 3 is a schematic diagram of beam forming of a single-layer smart subsurface in an embodiment of the present invention.
As shown in fig. 3, for a single-layer smart subsurface, the beamforming on both sides is highly correlated, since each scattering element is coupled for the phase shift of the transmitted and reflected signals. In particular, a typical smart subsurface model is one in which the phase shift of the scattering element to the reflected and transmitted signals is uniform, and in which the beams on both sides of the smart subsurface will be identical. When users are randomly distributed on both sides of the intelligent subsurface, this is likely to result in some beams not pointing to any user, resulting in a large energy loss.
FIG. 4 is a beam forming schematic of a dual-layer smart subsurface in an embodiment of the invention.
As shown in fig. 4, for a dual-layer intelligent subsurface, since the signal received by the reflective end user is reflected by the first layer of intelligent subsurface, and the signal received by the transmissive end user is transmitted through the two layers of intelligent subsurface, the dual-layer intelligent subsurface can implement different beam forming on both sides, reducing energy loss.
Fig. 5 is a schematic diagram of a downlink multi-user communication system with the assistance of a multi-layer intelligent subsurface device in an embodiment of the invention.
As shown in FIG. 5, the two intelligent super-surfaces are both uniform square planar arrays, and the number of scattering units is M. The first layer of intelligent supersurface (IOS 1) has a transmission (∈ r) and a reflection intensity coefficient (∈ t) of 0.5, and the second layer of intelligent supersurface (IOS 2) is set to total transmission (ζ r＝0,ξt =1). The base station end is configured with a uniform linear antenna array of 8 antennas, and the user end is a single antenna node. The cell spacing of all antenna arrays and scattering cell arrays is half wavelength, and there is no gap between the cells. The heights of the base station and the double-layer multi-layer intelligent super-surface device (BIOS) are 5m, and the interval between the base station and the double-layer multi-layer intelligent super-surface device is 20m. The interval between the two-layer intelligent super-surface of the multi-layer intelligent super-surface device is 0.015m. The users are randomly distributed in the range of 3 m-10 m away from the multi-layer intelligent super-surface device, wherein the height of the users is 1.5 m. The gaussian noise variance σ 2 = -80dBm at the user end.
Base station to multi-layer intelligent subsurface device channel (G) and multi-layer intelligent subsurface device to user channelAll adopt rice channel model. For a channel (F) between two layers of intelligent super surfaces, because the distance between the two layers of intelligent super surfaces is extremely small, a near-field channel model dominated by a direct path is adopted for the channel between each scattering unit. In addition, in numerical simulations, it is assumed that the base station to user direct path is negligible due to strong blocking.
To compare the performance of different intelligent subsurface, the present embodiment performs numerical simulations on a dual-layer multi-layer intelligent subsurface device (BIOS), intelligent reflector IRS, and single-layer intelligent subsurface (IOS). The positions and the number of scattering units of the intelligent reflection surface IRS are the same as those of the first layer IOS in the BIOS. IRSs can only reflect signals and therefore cannot serve transmitting end users. The transmission and reflection intensities of the single layer IOS were set to 0.5, as follows:
When the number of the scattering units on the intelligent super surface is fixed When the number of transmitted users (K t) is 3 and the number of reflected users (K r) is 2, the relation between the transmitting power and the user and the speed in the three systems is obtained through numerical simulation. Fig. 6 is a graph showing the relationship between the transmission power and the user and the rate in the case of fixing the number of scattering units, the number of transmitted users, and the number of reflected users on the intelligent super surface in the embodiment of the present invention.
As shown in FIG. 6, for three systems, both user and rate increase with increasing transmit power, while BIOS and IOS systems offer significant performance advantages over IRS systems. This is because the BIOS and IOS can serve users on both sides at the same time, while the IRS can only serve reflector users. Further, since the BIOS can implement different beamforming on both sides, its performance is more advantageous than IOS.
When the fixed emission rate (P b =30 dBm), the number of transmission users (K t) and the number of reflection users (K r) are 3 and 2, the number of scattering units of the intelligent super surface in the three systems is obtained through numerical simulationRelationship to user and rate. Fig. 7 is a relationship between the number of scattering units and the user and the rate of the intelligent super-surface in the case of a fixed emission rate, a number of transmitted users, and a number of reflected users in an embodiment of the present invention.
As shown in fig. 7, as the scattering elements of the smart subsurface increase, the beamforming gain will increase, resulting in an increase in both the user and rate of the three systems. At the same time, BIOS performance is significantly advantageous over IOS and IRS.
When the transmission rate is fixed (P b =20 dBm), the total number of users (K=5), and the number of scattering units on the intelligent super surfaceUnder the condition, the relation between the transmission user number (K t) in the three systems and the user and the speed is obtained through numerical simulation. Fig. 8 is a graph of the relationship between the number of transmitted users and the user and rate for the case of a fixed transmission rate, the total number of users and the number of scattering units on the intelligent supersurface in an embodiment of the invention.
As shown in fig. 8, for IRS systems, since they can only serve reflective end users, their performance will drop monotonically to 0 as more users are distributed on the transmissive end. For the IOS system, since the transmission and reflection intensity coefficients are both 0.5, the capacities of users on both sides of the IOS service are completely consistent, so that the performance of the IOS system hardly changes with the change of the number of transmitted users. For BIOS systems, BIOS can control beamforming on both sides almost independently due to the presence of the second layer IOS, thus providing better performance over the other two systems. Since the first layer IOS has a transmission and reflection coefficient of 0.5, the power allocated to the reflection and transmission ends is almost uniform, and thus, the user and the speed of the BIOS system reach the maximum when the user is uniformly distributed on both sides of the BIOS (K t =2 or 3). In addition, when the number of transmissive end users is large (K t =4 or 5), the users and rates of the BIOS system still have significant advantages over IOS because for transmissive end users, their signals can be transmitted through the two-layer IOS with better beamforming quality than for reflective ends.
In summary, in the embodiment, the multi-layer intelligent super surface device (BIOS) of the present invention is used for assistance in a multi-user multiple-input single-output scenario, so that better performance compared with the IOS and IRS systems is achieved, and when users are uniformly distributed on both sides of the BIOS, the performance gap is maximized.
Effects and effects of the examples
According to the multilayer intelligent super-surface device, incident wireless signals are modulated, radiation is emitted to a reflecting end user and a transmitting end user through reflection and transmission, and each intelligent super-surface can adjust the phase of the wireless signals through the scattering unit, so that beam forming of the reflecting end and the transmitting end can be independently controlled. In addition, according to the beam forming method of the downlink multi-user communication system assisted by the multi-layer intelligent super-surface device, firstly, the problems of maximization and spectrum efficiency optimization in the prior complex form are equivalently converted into the problems of minimizing weighted mean square error, then, aiming at the converted problems, a receiving end coefficient matrix and an auxiliary weight coefficient matrix, a base station end digital beam forming design and the analog beam forming of intelligent super-surfaces of different layers are alternately optimized, and finally, the base station end digital beam forming and the analog beam forming of the intelligent super-surfaces of different layers are obtained.
The above embodiments are preferred examples of the present invention, and are not intended to limit the scope of the present invention.

Claims (3)

1.一种多层智能超表面装置辅助下的下行多用户通信系统的波束成形方法，其特征在于，1. A beamforming method for a downlink multi-user communication system assisted by a multilayer intelligent metasurface device, characterized in that, 所述多层智能超表面装置用于对入射的无线信号进行调制并通过反射和透射同时向反射端用户和透射端用户辐射，所述多层智能超表面装置包括两层或多层智能超表面，The multilayer smart metasurface device is used to modulate incident wireless signals and radiate them simultaneously to both the reflecting and transmitting users. The multilayer smart metasurface device comprises two or more smart metasurfaces. 每层所述智能超表面均由多个散射单元以及与所述散射单元相连的数字控制模块组成，Each layer of the intelligent metasurface consists of multiple scattering units and a digital control module connected to the scattering units. 基站发出的所述无线信号通过第一层所述智能超表面反射与所述反射端用户通信，The wireless signal emitted by the base station communicates with the user at the reflecting end through reflection via the first layer of the smart metasurface. 基站发出的所述无线信号通过所有所述智能超表面多次透射后与所述透射端用户通信，The wireless signal emitted by the base station communicates with the user at the transmission end after being transmitted multiple times through all the smart metasurfaces. 所述反射端用户和所述透射端用户的成形波束通过控制不同所述散射单元的状态进行独立控制，The shaping beams of the reflecting end user and the transmitting end user are independently controlled by controlling the state of different scattering units. 其中，所述方法包括以下步骤：The method includes the following steps: 步骤1，对所述多层智能超表面装置辅助下的下行多用户通信系统进行建模，并对多用户和速率最大的优化问题进行建模；Step 1: Model the downlink multi-user communication system assisted by the multi-layer intelligent metasurface device, and model the optimization problem of maximizing multi-user and speed. 步骤2，将所述多用户和速率最大的优化问题转换为最小化加权均方误差问题，针对所述最小化加权均方误差问题，交替优化接收端系数矩阵和辅助权重系数矩阵、基站端数字波束成形设计和不同层的所述智能超表面的模拟波束成形，最终得到所述基站端数字波束成形和不同层的所述智能超表面的模拟波束成形，Step 2: The optimization problem of maximizing the number of users and the maximum rate is transformed into a problem of minimizing the weighted mean square error. For the problem of minimizing the weighted mean square error, the receiver coefficient matrix and auxiliary weight coefficient matrix, the digital beamforming design at the base station, and the simulated beamforming of the smart metasurface at different layers are alternately optimized to finally obtain the digital beamforming at the base station and the simulated beamforming of the smart metasurface at different layers. 其中，所述多层智能超表面装置辅助下的下行多用户通信系统包括部署有多个天线的基站、用于接收所述基站的无线信号并同时进行反射与透射的所述多层智能超表面装置以及多个用户，包括反射端用户和透射端用户，The downlink multi-user communication system assisted by the multi-layer intelligent metasurface device includes a base station with multiple antennas, the multi-layer intelligent metasurface device for receiving wireless signals from the base station and simultaneously reflecting and transmitting them, and multiple users, including reflecting end users and transmitting end users. 所述模拟波束成形的优化基于坐标迭代下降算法进行。The optimization of the simulated beamforming is based on the coordinate iterative descent algorithm. 2.根据权利要求1所述的多层智能超表面装置辅助下的下行多用户通信系统的波束成形方法，其特征在于：2. The beamforming method for a downlink multi-user communication system assisted by a multi-layer intelligent metasurface device according to claim 1, characterized in that: 其中，步骤1包括以下子步骤：Step 1 includes the following sub-steps: 步骤1-1，单层的所述智能超表面的系数矩阵表达形式如下：Step 1-1, the coefficient matrix of the single-layer smart metasurface is expressed as follows: ， , 上式中，表示单层的所述智能超表面的系数矩阵，表示第一层的所述智能超表面的对角系数矩阵，表示单层的所述智能超表面的反射和透射信号的强度系数，当时表示反射，当时表示透射，，表示第个散射单元对入射信号产生的相位移动，表示单层的所述智能超表面中散射单元的数目，，表示虚数单位；In the above formula, This represents the coefficient matrix of the single-layer intelligent metasurface. This represents the diagonal coefficient matrix of the intelligent metasurface in the first layer. Indicates the intensity coefficients of the reflected and transmitted signals of the single-layer smart metasurface, when Time indicates reflection, when Time indicates transmission. , Indicates the first The phase shift of the incident signal by each scattering unit This indicates the number of scattering units in the single-layer intelligent metasurface. , Represents the imaginary unit; 步骤1-2，基于单层的所述智能超表面的系数矩阵得到多层智能超表面的等效系数矩阵表达形式如下：Steps 1-2: Based on the coefficient matrix of the single-layer smart metasurface, the equivalent coefficient matrix expression of the multilayer smart metasurface is obtained as follows: ，， , , 上式中，表示所述多层智能超表面在反射模式下的等效系数矩阵，表示所述多层智能超表面在透射模式下的等效系数矩阵，为第二层智能超表面对应的对角系数矩阵，、分别表示第一层的所述智能超表面的反射和透射信号的强度系数，表示第二层的所述智能超表面的透射信号的强度系数，为两层智能超表面之间的信道矩阵，表示复数集；In the above formula, This represents the equivalent coefficient matrix of the multilayer smart metasurface in reflection mode. This represents the equivalent coefficient matrix of the multilayer smart metasurface in transmission mode. This is the diagonal coefficient matrix corresponding to the second layer of intelligent metasurface. , These represent the intensity coefficients of the reflected and transmitted signals of the intelligent metasurface in the first layer, respectively. This represents the intensity coefficient of the transmitted signal of the intelligent metasurface in the second layer. The channel matrix between the two smart metasurface layers. Represents the set of complex numbers; 步骤1-3，基站发送信号的数学表达形式如下：Steps 1-3, the mathematical expression of the base station's transmitted signal is as follows: ， , 上式中，表示数字预编码矩阵，表示向各用户发送的信息符号，表示基站天线数，表示用户数；In the above formula, Represents a digital precoding matrix. Symbols representing information sent to each user. Indicates the number of base station antennas. Indicates the number of users; 步骤1-4，用户的接收信号的数学表达形式如下：Steps 1-4, the mathematical expression of the user's received signal is as follows: ， , 上式中，表示第个用户接收到的信号，当时，，当时，，、分别表示基站到所述多层智能超表面装置和所述多层智能超表面装置到第个用户的信道系数向量，表示第个用户端的高斯噪声，其平均值为0，方差为；In the above formula, Indicates the first The signal received by each user, when hour, ,when hour, , , These respectively represent the connection from the base station to the multilayer intelligent metasurface device and the connection from the multilayer intelligent metasurface device to the first... Channel coefficient vectors for each user Indicates the first The user terminals have Gaussian noise with a mean of 0 and a variance of . ; 步骤1-5，用户端速率的数学形式如下：Steps 1-5, the mathematical form of the user-side speed is as follows: ， , 上式中，表示第个用户端速率，表示第个用户处的等效噪声与干扰总功率，表示第个用户对应的基站预编码向量；In the above formula, Indicates the first User terminal speed, Indicates the first Equivalent noise and total interference power at each user location Indicates the first The base station precoding vector corresponding to each user; 步骤1-6，建模多用户和速率最大的优化问题的数学形式如下：Steps 1-6, the mathematical form of the optimization problem of maximizing the sum of multiple users and the rate is as follows: ， , 上式中，第一个约束条件表示基站的发射总功率不得大于，第二、三个约束条件表示所述多层智能超表面装置中的所述散射单元的恒模约束，所述散射单元只改变入射信号的相位，不改变入射信号的振幅。In the above formula, the first constraint states that the total transmit power of the base station must not exceed [a certain value]. The second and third constraints represent the constant mode constraints of the scattering unit in the multilayer intelligent metasurface device. The scattering unit only changes the phase of the incident signal, but does not change the amplitude of the incident signal. 3.根据权利要求2所述的多层智能超表面装置辅助下的下行多用户通信系统的波束成形方法，其特征在于：3. The beamforming method for a downlink multi-user communication system assisted by a multi-layer intelligent metasurface device according to claim 2, characterized in that: 其中，步骤2包括以下子步骤：Step 2 includes the following sub-steps: 步骤2-1，运用均方误差和和速率之间的关系，将所述多用户和速率最大的优化问题转化为等价的所述最小化加权均方误差问题，所述最小化加权均方误差问题的数学形式如下：Step 2-1: Using the relationship between mean square error and rate, the optimization problem of maximizing the sum of multiple users and rates is transformed into the equivalent problem of minimizing the weighted mean square error. The mathematical form of the problem of minimizing the weighted mean square error is as follows: ， , 上式中，表示MSE值大小，表示第个用户端的接收机系数，为一个辅助加权系数，用于建立均方误差MSE和速率之间的等价性，闭式解分别为：，，其中，，In the above formula, Indicates the magnitude of the MSE value. Indicates the first Receiver coefficients at each user terminal An auxiliary weighting coefficient is used to establish the equivalence between the mean squared error (MSE) and the rate. The closed-form solutions are as follows: , ,in, , 定义所述接收端系数矩阵，辅助权重系数矩阵，，并代入，的闭式解后，所述最小化加权均方误差问题的数学形式转化为：Define the receiving end coefficient matrix Auxiliary weight coefficient matrix , and substitute , After obtaining the closed-form solution, the mathematical form of the problem of minimizing the weighted mean square error is transformed into: ， , ； ; 步骤2-2，优化所述基站端波束成形，通过固定和，优化数字预编码，根据KKT条件，在功率约束下，最优解有闭式解如下：Step 2-2, optimize the beamforming at the base station end by fixing and Optimize digital precoding According to the KKT conditions, under power constraints, The optimal solution has the following closed-form solution: ， , 上式中，，，表示维的单位矩阵；In the above formula, , , express An identity matrix of 3D; 步骤2-3，优化第一层的所述智能超表面，通过固定其他变量，优化第一层的所述智能超表面的对角系数矩阵，定义，，并运用恒等式及，目标函数简化为：Steps 2-3: Optimize the smart metasurface of the first layer by fixing other variables and optimizing the diagonal coefficient matrix of the smart metasurface of the first layer. ,definition , and use identities and The objective function simplifies to: ， , 为提取出对的贡献，目标函数进一步变换为：To extract right The objective function is further transformed into: ， , 得到的最优解：，其中，通过坐标迭代下降算法交替优化每一个元素，得到的局域最优解；get The optimal solution: ,in By alternately optimizing each element using a coordinate iterative descent algorithm, we obtain... The local optimal solution; 步骤2-4，优化第二层的所述智能超表面，通过固定其他变量，优化第二层的所述智能超表面的对角系数矩阵，将拆分成与反射用户和透射用户相关的两个部分：，其中，，，在忽略掉与无关的常数后，目标函数简化为：Steps 2-4: Optimize the smart metasurface of the second layer by fixing other variables and optimizing the diagonal coefficient matrix of the smart metasurface of the second layer. ,Will It can be broken down into two parts related to reflection users and transmission users: ,in, , ignoring After irrelevant constants, the objective function Simplified to: ， , 上式中，，，，，，，通过坐标迭代下降算法得到的局域最优解；In the above formula, , , , , , The coordinate iterative descent algorithm is used to obtain The local optimal solution; 步骤2-5，交替优化所述接收端系数矩阵、所述辅助权重系数矩阵、基站的数字预编码矩阵、第一层的所述智能超表面的对角系数矩阵以及第二层的所述智能超表面的相移系数矩阵，若达到终止要求，则输出所述基站端数字波束成形和不同层的所述智能超表面的模拟波束成形，若没有达到终止要求，则重复循环步骤2-2至步骤2-4。Steps 2-5: Alternately optimize the receiver coefficient matrix. The auxiliary weight coefficient matrix Digital precoding matrix of base station The diagonal coefficient matrix of the first layer of the intelligent metasurface and the phase shift coefficient matrix of the intelligent metasurface in the second layer. If the termination requirement is met, the digital beamforming of the base station and the simulated beamforming of the smart metasurface of different layers are output. If the termination requirement is not met, steps 2-2 to 2-4 are repeated.
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