A physical layer control method for a multi-user communication system under non-ideal hardware conditions

Abstract

The present application relates to a kind of non-ideal hardware conditions under the physical layer control method of multi-user communication system, comprising: establishing non-ideal hardware model at base station, intelligent super surface and user terminal;Establish the signal-to-interference-and-noise ratio model at user terminal and eavesdropper;According to two signal-to-interference-and-noise ratio models, the downlink security rate of each user terminal is obtained;According to the non-ideal hardware model at base station, intelligent super surface and user terminal and the downlink security rate of each user terminal, the optimization problem of maximum security transmission fairness between user terminals is established, the optimization problem is solved, and the optimal base station precoding matrix for base station operation and the optimal intelligent super surface reflection coefficient matrix for intelligent super surface operation are obtained.Compared with prior art, the present application solves the inter-user fairness problem of intelligent super surface assisted multi-user communication system under non-ideal hardware conditions, and has wide application scenarios, good applicability, lower hardware cost and higher energy efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and in particular to a physical layer control method for a multi-user communication system under non-ideal hardware conditions. BACKGROUND

[0002] With the increasing popularity of mobile devices, the capacity of global wireless networks is continuously increasing. In addition, emerging applications, such as industrial Internet of Things, virtual reality and augmented reality, have ultra-high quality of service requirements, such as ultra-low latency, ultra-high reliability and extremely high data rate. Some potential technologies, such as massive multiple-input multiple-output arrays, millimeter waves and terahertz communication, have been proposed to meet the above requirements. However, these technologies usually increase the cost of network deployment and the power consumption of the network.

[0003] With the development of micro-electro-mechanical systems and programmable metamaterials, smart metasurfaces have attracted widespread attention as a technology that can simultaneously improve the spectral and energy efficiency of wireless systems. It is believed that smart metasurfaces can well meet the ultra-high quality of service requirements of future networks.

[0004] A smart metasurface is a thin layer of metamaterials composed of a series of low-cost reflective elements integrated with low-power and controllable electronics. Due to the absence of power amplifiers, digital signal processing units and multiple radio frequency chains, smart metasurfaces have the characteristics of low implementation cost, low power consumption and easy deployment. Broadly speaking, a smart metasurface is a dynamic metasurface whose electromagnetic properties can be dynamically adjusted by control signals. For example, by simply optimizing the phase response of each component of the scattering element, electromagnetic waves impinging on the smart metasurface can be directed in different directions. Therefore, by properly adjusting the phase shift, the smart metasurface can achieve directional enhancement or suppression of signals, while achieving fine-grained three-dimensional beamforming, thereby improving the radio propagation environment. Smart metasurfaces can also be used to increase the required signal power to mitigate network interference and reduce electromagnetic pollution caused by not generating additional signals. Compared with traditional active antenna arrays equipped with multiple active radio frequency transceivers, smart metasurfaces only need to re-radiate incident signals by simply adjusting the amplitude and phase shift of the reflective elements, which can be achieved by controlling the junction voltage of PIN diodes or varactors, so the structure is simple and the hardware overhead is low. In addition, since the working mode is passive reflection, the energy consumption of the smart metasurface is negligible, and it itself does not generate new signals and thermal noise.

[0005] In order to improve the security performance of a wireless communication system, it is considered an effective method to combine an intelligent metasurface with a physical layer security design. The physical layer security design is a key aspect of an alternative solution to achieve secure communication by utilizing the characteristics of the hardware of the wireless communication medium and the transceiver. However, the traditional physical layer security design only focuses on the beamforming design on the transceiver, and in some cases may not provide good performance, for example, when the legitimate user and the eavesdropper have a highly correlated channel, the gain brought by the physical layer security design is very limited. Since the intelligent metasurface can change the reflection direction of the incident signal according to the needs of the propagation environment, it can enhance the signal received by the legitimate user while suppressing the signal received by the eavesdropper. Therefore, the combination of the intelligent metasurface and the physical layer security design can effectively make up for the shortcomings of the traditional physical layer security design. Existing solutions combining the intelligent metasurface and the physical layer security design are all based on the assumption that the transceiver is built by ideal and perfect hardware components. In actual communication systems, low-cost hardware is usually the first choice, even if these hardware may be subject to hardware impairments such as amplifier nonlinearity, quantization error and phase noise, etc. If these hardware impairments are ignored in the design stage, the performance will usually be reduced. In addition, the communication system usually needs to solve the problem of security transmission fairness among users. In summary, there is currently no solution to the security transmission fairness problem of a communication system formed by combining an intelligent metasurface with a multi-user communication system under non-ideal hardware conditions. SUMMARY

[0006] The purpose of the present application is to provide a multi-user communication system physical layer control method under non-ideal hardware conditions that can solve the problem of security transmission fairness among users.

[0007] The purpose of the present application can be achieved by the following technical solutions:

[0008] A multi-user communication system physical layer control method under non-ideal hardware conditions, for controlling an intelligent metasurface-assisted multi-user communication system under non-ideal hardware conditions, the intelligent metasurface-assisted multi-user communication system comprising a base station, an intelligent metasurface, a plurality of user terminals and a single eavesdropper, the non-ideal hardware conditions being that there are hardware impairments at the base station, the intelligent metasurface and the plurality of user terminals, and there is no hardware impairment at the eavesdropper;

[0009] The method comprises:

[0010] establishing a non-ideal hardware model at the base station;

[0011] establishing a non-ideal hardware model at the intelligent metasurface;

[0012] establishing a non-ideal hardware model at the user terminal;

[0013] establishing a signal-to-interference-plus-noise ratio model at the user terminal;

[0014] establishing a signal-to-interference-plus-noise ratio model at the eavesdropper;

[0015] obtaining a downlink security rate of each user terminal according to the signal-to-interference-plus-noise ratio models at the user terminal and the eavesdropper;

[0016] establishing an optimization problem of maximizing security transmission fairness among user terminals according to non-ideal hardware models at the base station, the intelligent metasurface and the user terminal and the downlink security rate of each user terminal, solving the optimization problem, and obtaining an optimal base station precoding matrix and an optimal intelligent metasurface reflection coefficient matrix;

[0017] controlling the base station to operate according to the optimal precoding matrix and controlling the intelligent metasurface to operate according to the optimal intelligent metasurface reflection coefficient matrix.

[0018] Further, the base station has N transmit antennas, the intelligent metasurface has M reflecting elements, the multi-user communication system includes K user terminals, the user terminal has a single receive antenna, and the eavesdropper has a single receive antenna.

[0019] Further, the non-ideal hardware model at the base station is η t ; η t is an independent zero-mean Gaussian random variable, and the corresponding distribution is where γ t = κ t diag(WW H ), κ t is the ratio of the transmit distortion noise power to the transmit signal power, is the precoding matrix of the base station, and satisfies Tr(W H W)≤P, P represents the maximum transmit power.

[0020] Further, the non-ideal hardware model at the intelligent metasurface is Λ; Λ is specifically Λ = diag(ψ), ψ = [ψ1, …, ψ M ] T , where ψ r，k m is the phase noise of the mth reflecting element caused by the hardware damage at the intelligent metasurface, and is uniformly distributed on the definition domain [-π / 2, π / 2].

[0021] Further, the non-ideal hardware model at the user terminal is that the added distortion noise item at the kth user terminal is η k , which is related to the kth user terminal UE r，k .The received information is irrelevant; η r，k The distribution satisfying γ r，k Specifically,

[0022]

[0023] where κ r，k is the ratio between the power of the distortion noise and the power of the received signal without distortion, h RU，k is the channel vector from the intelligent surface to the UE k , A is the random phase noise matrix, Φ is the reflection coefficient matrix of the intelligent surface, H BR is the channel matrix from the base station to the intelligent surface, h BU，k is the channel vector from the base station to the UE k , x is the information transmitted by the base station, n U，k is the additive white Gaussian noise satisfying the distribution , and is the total average power of other interference in the received signal of the UE k .

[0024] Further, the signal-to-interference-and-noise ratio model at the user terminal is: the signal-to-interference-and-noise ratio model γ k at the kth user terminal UE k ; γ k Specifically,

[0025]

[0026] wherein, h RU，k is the channel vector from the intelligent surface to the UE k , Φ is the reflection coefficient matrix of the intelligent surface, H BR is the channel matrix from the base station to the intelligent surface, h BU，k is the channel vector from the base station to the UE k , I M is the unit matrix with dimension M, w k is the precoding vector of the base station for the UE k , γ t is the power of the distortion noise in the signal transmitted by the base station, γ r，k is the power of the distortion noise at the UE k , is the total average power of other interference in the received signal of the UE k .

[0027] Further, the signal-to-interference-and-noise ratio model at the eavesdropper is: the signal-to-interference-and-noise ratio model γ k of the eavesdropper eavesdropping the kth user terminal UE E，k; gamma E，k Specifically,

[0028]

[0029] wherein, h RE is a channel vector from the intelligent metasurface to the eavesdropper, Phi is a reflection coefficient matrix of the intelligent metasurface, H BR is a channel matrix from the base station to the intelligent metasurface, h BE is a channel vector from the base station to the eavesdropper, I M is a unit matrix with a dimension of M, w k is a precoding vector of the base station for the UE k , gamma t is a power of distortion noise in a signal transmitted by the base station, is a total average power of other interference in a signal received by the eavesdropper.

[0030] Further, the downlink security rate of the user terminal is: the downlink security rate of the kth user terminal UE k is R k (W, Phi); R k (W, Phi) is specifically:

[0031]

[0032] wherein, is a precoding matrix of the base station, w k is a precoding vector of the base station for the UE k , Phi is a reflection coefficient matrix of the intelligent metasurface, R U，k (W, Phi) = log(1 + gamma k ), R E，k (W, Phi) = log(1 + gamma E，k ), gamma k is a signal-to-interference-and-noise ratio model at the UE k , gamma E，k is a signal-to-interference-and-noise ratio model of the eavesdropper eavesdropping the UE k .

[0033] Further, the optimization problem is:

[0034]

[0035] s.t. Tr(W H W) <= P,

[0036]

[0037] wherein, omega k is the kth user terminal UEk The reciprocal of the downside weight, R k (W, Φ) represents UE k The downlink security rate is given by P, where P is the maximum transmit power of the base station, and Φ is the smart metasurface reflection coefficient matrix. It is the precoding matrix of the base station, w k For base station targeting UE k The precoding vector, φ m，m Let be the reflection coefficient of the m-th reflective element of the smart metasurface.

[0038] Furthermore, the solution process for the optimization problem is as follows:

[0039] The optimization problem is transformed into an equivalent optimization problem.

[0040] Solve the equivalent optimization problem to obtain the optimal base station precoding matrix and the optimal smart metasurface reflection coefficient matrix;

[0041] The equivalent optimization problem is:

[0042]

[0043] Where, ω k For the k-th user terminal (UE) k The reciprocal of the downside weight, For UE k The lower bound function of the downlink safety rate, where Φ is the reflection coefficient matrix of the smart metasurface. It is the precoding matrix of the base station, w k For base station targeting UE k The precoded vector, P represents a set of different downlink security rate auxiliary variables. max φ is the maximum transmit power of the base station. m，m Let be the reflection coefficient of the m-th reflective element of the smart metasurface;

[0044] Solving equivalent optimization problems using the BCD-MM algorithm involves the following steps:

[0045] The optimization variables of the equivalent optimization problem are considered as five sets, among which... As a group, As a group, As a group, As a group, , W is a group, Φ is a group;

[0046] Five sets of variables are iteratively optimized using the block coordinate descent method: In each iteration, four sets of variables are fixed to solve for the other set, and the newly solved variables are substituted into the next iteration.

[0047] where the solution of is obtained by using the quadratic transformation method in fractional programming;

[0048] the solution of is obtained by using Lemma 1, which is: for any function has the optimal solution if and only if

[0049] the solution of is obtained by using Lemma 2, which is: for any function has the optimal solution if and only if

[0050] the solution of and is obtained by using Lemma 2 and Lemma 3, which is: given a complex vector for the function there is always has the optimal solution if and only if

[0051] MM method is used to solve W and Φ respectively, the objective function value of the original optimization problem is calculated after each iteration, and the iteration process is terminated when the difference between the objective functions of adjacent two iterations is less than a given threshold, and the solution obtained at this time is the solution of the base station precoding matrix and the intelligent metasurface reflection coefficient matrix under the maximum fairness criterion of inter-user secure transmission.

[0052] Compared with the prior art, the present application has the following advantages:

[0053] (1) The intelligent metasurface is introduced into the multi-user communication network under non-ideal hardware, the intelligent metasurface and the physical layer security technology are combined to assist communication, the minimum weighted security rate of all users is maximized through joint optimization of the base station and the intelligent metasurface, the fairness problem between users is solved, the low-cost hardware and the inequality of user priority that may exist in the actual communication system can be adapted, and the overall security performance of the communication system is improved.

[0054] (2) The present application establishes an optimization problem of maximizing the transmission fairness between user terminals, obtains the equivalent optimization problem of the problem and solves the optimization problem by using the BCD-MM algorithm, can obtain an approximate optimal solution close to the global optimal solution with very low computational overhead, improves the computational efficiency, and can accurately obtain the optimal base station precoding matrix and the optimal intelligent metasurface reflection coefficient matrix.

[0055] ​​​​​(3) The communication system of the present application is a multi-user communication system under non-ideal hardware, which has a wider application scenario and better applicability compared with the single-user communication system assisted communication scheme combining the existing ideal hardware intelligent metasurface and physical layer security technology.

[0056] (4) The communication system of the present application adopts intelligent metasurface assisted communication, which can suppress interference signals and enhance useful signals at the user, and has simple structure, does not produce new signals and almost does not consume energy, so the hardware cost is lower and the energy efficiency is higher. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 A flowchart of a physical layer control method for a multi-user communication system under non-ideal hardware conditions provided in an embodiment of the present application is shown.

[0058] Figure 2 A structure diagram of a multi-user communication system assisted by intelligent metasurface under non-ideal hardware conditions provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme of the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0060] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor are within the scope of protection of the present application.

[0061] It should be noted that: similar numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0062] Embodiment 1

[0063] The embodiment provides a physical layer control method of a multi-user communication system under non-ideal hardware conditions, and the method is used for controlling an intelligent metasurface assisted multi-user communication system, the non-ideal hardware conditions refer to that hardware impairments exist at a base station, an intelligent metasurface and a plurality of user terminals, and no hardware impairment exists at an eavesdropper, the intelligent metasurface assisted multi-user communication system comprises the base station, the intelligent metasurface, the plurality of user terminals and the single eavesdropper, the base station has a plurality of transmitting antennas, the intelligent metasurface has a plurality of reflecting elements, the user terminal has a single receiving antenna, and the eavesdropper has a single receiving antenna, most of noises except the hardware distortion noise of the base station and interference from other users can be eliminated, and the base station and a received signal are misled during channel estimation by sending a pilot signal to the base station by disguising as a legal user, as shown in the following formula. Figure 2

[0064] In the embodiment, the base station has N transmitting antennas, the intelligent metasurface has M reflecting elements, and the multi-user communication system comprises K user terminals.

[0065] The channel state of the multi-user communication system is quasi-static, and the channel state information can be completely acquired by the base station; the base station calculates an optimal base station precoding matrix and an optimal intelligent metasurface reflection coefficient matrix for transmitting information symbols of the multi-user terminal in real time, and sends control information to the intelligent metasurface through a dedicated channel. In the scene that the base station and the multi-user terminal exchange information on the same carrier frequency at the same time, a signal transmission model is established. In order to maximize the security transmission fairness among users, an optimization model of jointly optimizing the base station precoding matrix and the intelligent metasurface reflection coefficient is established under the constraint condition of the maximum transmission power of the base station and the unit modulus of the intelligent metasurface reflection coefficient, and the optimization problem is solved through an efficient algorithm.

[0066] As shown in the following formula, Figure 1 the physical layer control method of the intelligent metasurface assisted multi-user communication system under non-ideal hardware conditions comprises the following specific steps.

[0067] S1: a non-ideal hardware model at the base station is established; a non-ideal hardware model at the intelligent metasurface is established; and a non-ideal hardware model at the user terminal is established;

[0068] S2: a signal-to-interference-and-noise ratio model at the user terminal is established; a signal-to-interference-and-noise ratio model at the eavesdropper is established; and the downlink security rate of each user terminal is acquired according to the two signal-to-interference-and-noise ratio models;

[0069] S3: an optimization problem of maximizing the security transmission fairness among user terminals is established according to the three non-ideal hardware models and the downlink security rate, the optimization problem is solved, and an optimal base station precoding matrix and an optimal intelligent metasurface reflection coefficient matrix are acquired;

[0070] ​S4: the base station operates according to the optimal precoding matrix, and the intelligent metasurface operates according to the optimal intelligent metasurface reflection coefficient matrix.

[0071] Specifically, the non-ideal hardware model at the base station is η t ; η t is an independent zero-mean Gaussian random variable, and its distribution is where γ t = κ t diag(WW H ), κ t is the ratio between the transmit distortion noise power and the transmit signal power, is the precoding matrix of the base station, and satisfies Tr(W H W)≤P, P represents the maximum transmit power.

[0072] And in this embodiment, w k is an N-row column vector.

[0073] Specifically, the non-ideal hardware model Λ; A at the intelligent metasurface is A = diag(ψ), ψ = [ψ1, …, ψ M ]T, where ψ m is the phase noise of the mth reflecting element caused by the hardware damage at the intelligent metasurface, and is uniformly distributed on the domain [-π / 2, π / 2].

[0074] And in this embodiment, A is an M-row M-column diagonal matrix, where is the phase shift error.

[0075] Specifically, the non-ideal hardware model at the user terminal is: the distortion noise term η r，k added at the kth user terminal is independent of the information received at the kth user terminal UE k ; η r，k satisfies the distribution γ r，k is specifically

[0076]

[0077] where κ r，k is the ratio between the distortion noise power and the undistorted received signal power, h RU，k is the channel vector from the intelligent metasurface to the UE k , A is the random phase noise matrix, Φ is the intelligent metasurface reflection coefficient matrix, H BR is the channel matrix from the base station to the intelligent metasurface, and h BU，k is the channel vector from the base station to the UE kh is a channel vector from the smart surface to the UE, x is information transmitted by the base station, and n is additive white Gaussian noise U，k To meet the distribution of the received signal, the base station needs to know the channel vector h from the smart surface to the UE k , the total average power of other interference in the received signal, and the total average power of the distortion noise in the received signal.

[0078] In this embodiment, h RU，k is a column vector of M rows, A and Φ are both diagonal matrices of M rows and M columns, the reflection coefficient matrix Φ of the smart surface is diag(φ 1，1 , φ 2，2 , …, φ M，M ), φ m is the reflection coefficient of the mth reflection element of the smart surface, θ BR is a phase shift, H BU，k is a matrix of M rows and N columns, h k and x are both column vectors of N rows,

[0079] Specifically, the signal-to-interference-and-noise ratio model at the user terminal is: the signal-to-interference-and-noise ratio model γ k at the kth user terminal UE k ; γ RU，k is specifically:

[0080]

[0081] wherein, h k is a channel vector from the smart surface to the UE BR , Φ is a reflection coefficient matrix of the smart surface, H BU，k is a channel matrix from the base station to the smart surface, h k is a channel vector from the base station to the UE M , I k is a unit matrix with a dimension of M, w k is a precoding vector of the base station for the UE t , γ r，k is the power of the distortion noise in the signal sent by the base station, γ k is the power of the distortion noise at the UE k , and γ RU，k is the total average power of other interference in the received signal of the UE

[0082] In this embodiment, h BR is a column vector of M rows, Φ is a diagonal matrix of M rows and M columns, H BU，k is a matrix of M rows and N columns, h k is a column vector of N rows, and T is a diagonal matrix of M rows and M columns, is a column vector of N rows, is a matrix of M rows and N columns, is a matrix of M rows and N+1 columns.

[0083] Specifically, the signal-to-interference-and-noise ratio model at the eavesdropper is: the signal-to-interference-and-noise ratio model γ k of the kth user terminal UE E，k eavesdropped by the eavesdropper; γ E，k is specifically:

[0084]

[0085] wherein, h RE is a channel vector from the intelligent metasurface to the eavesdropper, Φ is a reflection coefficient matrix of the intelligent metasurface, H BR is a channel matrix from the base station to the intelligent metasurface, h BE is a channel vector from the base station to the eavesdropper, I M is a unit matrix with a dimension of M, w k is a precoding vector of the base station for the UE k , γ t is the power of the distortion noise in the signal transmitted by the base station, is the total average power of other interference in the signal received by the eavesdropper.

[0086] And in this embodiment, h RE is a column vector of M rows, Φ is a diagonal matrix of M rows and M columns, H BR is a matrix of M rows and N columns, h BE is a column vector of N rows, T is a diagonal matrix of M rows and M columns, is a column vector of N rows, is a matrix of M rows and N columns, is a matrix of M rows and N+1 columns.

[0087] According to the signal-to-interference-and-noise ratio model γ k at the kth user terminal UE k obtained above and the signal-to-interference-and-noise ratio model γ k of the kth user terminal UE E，k eavesdropped by the eavesdropper, the downlink security rate of each user terminal is obtained by using the Shannon formula, that is, the downlink security rate of the kth user terminal UE k is R k (W, Φ); R k (W, Φ) is specifically:

[0088]

[0089] wherein, is a precoding matrix of the base station, w ka precoding vector of the base station for the UE k , Φ is a reflection coefficient matrix of the intelligent metasurface, R U，k (W, Φ) = log (1 + γ k ), R E，k (W, Φ) = log (1 + γ E，k ), γ k is a signal-to-interference-and-noise ratio model at the UE k , γ E，k is a signal-to-interference-and-noise ratio model of a eavesdropper eavesdropping the UE k .

[0090] According to the signal-to-interference-and-noise ratio model γ k at the kth user terminal UE k , the signal-to-interference-and-noise ratio model γ k of the eavesdropper eavesdropping the kth user terminal UE E，k , and the downlink security rate R k of the kth user terminal UE k , an optimization problem of maximizing the fairness of inter-user secure transmission is established:

[0091]

[0092] s.t. Tr (W H W) ≤ P,

[0093]

[0094] where ω k is the reciprocal of the downlink weight of the kth user terminal UE k , R k (W, Φ) is the downlink security rate of the UE k , P is the maximum transmission power of the base station, Φ is a reflection coefficient matrix of the intelligent metasurface, is a precoding matrix of the base station, w k is a precoding vector of the base station for the UE k , φ m , m is the reflection coefficient of the mth reflection element of the intelligent metasurface.

[0095] The steps of solving the optimization problem include: converting the optimization problem into an equivalent optimization problem; solving the equivalent optimization problem to obtain the optimal base station precoding matrix and the optimal intelligent metasurface reflection coefficient matrix.

[0096] Specifically, the downlink security rate R k of the kth user terminal UE k (W, Φ) can be equivalently rewritten as R k (W, Φ) = f 1，k(W, Φ) + f 2，k (W, Φ) + f3(W, Φ), where Next, we introduce three lemmas, based on which we derive the lower bound functions for f 1，k (W, Φ), f 2，k (W, Φ) and f3(W, Φ) and where, are the introduced auxiliary variable sets.

[0097] For f 1，k (W, Φ), we first use Lemma 1 to process, i.e., for any function has iff achieves the optimal solution. Thus, we can get where, is the introduced auxiliary variable set. Next, by the quadratic transformation method in fractional programming, we can further get the lower bound function of f 1，k (W, Φ)

[0098]

[0099] where, h RU，k is the channel vector from the intelligent metasurface to UEk, Φ is the reflection coefficient matrix of the intelligent metasurface, H BR is the channel matrix from the base station to the intelligent metasurface, h BU，k is the channel vector from the base station to UE k , I M is the unit matrix with dimension M, w k is the precoding vector of the base station for UE k , is the total average power of other interference in the received signal of UE k , κ r，k is the ratio between the noise power of distortion and the received signal power without distortion, κ t is the ratio between the transmitted noise power of distortion and the transmitted signal power. is the introduced auxiliary variable set.

[0100] For f 2，k (W, Φ), we introduce Lemma 2, i.e., for any function has iff The optimal solution is obtained when and only when f 2，k The lower bound function of f(W, Φ)

[0101]

[0102] where, hR E is the channel vector from the intelligent metasurface to the eavesdropper, Φ is the reflection coefficient matrix of the intelligent metasurface, H BR is the channel matrix from the base station to the intelligent metasurface, h BE is the channel vector from the base station to the eavesdropper, I M is the identity matrix with dimension M, w k is the precoding vector of the base station for the UE k , γ t is the power of the distortion noise in the signal sent by the base station, is the total average power of other interference in the signal received by the eavesdropper, is the set of auxiliary variables introduced.

[0103] For f3(W, Φ), Lemma 2 and Lemma 3 are used for processing. Lemma 3 is specifically that given a complex vector For the function there is always The optimal solution is obtained when and only when Therefore, the lower bound function of f3(W, Φ) can be obtained as

[0104]

[0105] where, and is the set of auxiliary variables introduced.

[0106] Specifically, when W is the only optimization variable:

[0107]

[0108] where,

[0109] Specifically, when Φ is the only optimization variable:

[0110]

[0111] where, Φ = diag(φ), h REis the channel vector from the smart metasurface to the eavesdropper, is the reflection coefficient matrix of the smart metasurface, H BR is the channel matrix from the base station to the smart metasurface, h BE is the channel vector from the base station to the eavesdropper, I M is the identity matrix with dimension M, w k is the precoding vector of the base station for the UE k , γ t is the power of the distortion noise in the signal sent by the base station, is the total average power of other interference in the signal received by the eavesdropper.

[0112] According to and , for , the condition that makes hold is:

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] and any variable is a concave function.

[0120] By , the optimization problem is converted into an equivalent optimization problem:

[0121]

[0122] s.t.Tr(W H W)≤P,

[0123]

[0124] In this embodiment, the BCD-MM algorithm is used to solve the equivalent optimization problem, and the optimal base station precoding matrix and the optimal smart reflection surface reflection coefficient matrix are obtained.

[0125] The steps of solving the equivalent optimization problem by the BCD-MM algorithm include:

[0126] (1) The optimization variables of the equivalent optimization problem are regarded as seven groups, where is a group, is a group, is a set of is a set of is a set of

[0127] (2) Iterative optimization of seven groups of variables by block coordinate descent method: in each iteration, fix six groups of variables to solve another group of variables, and substitute the newly solved variables into the next iteration, where the solution of Using the quadratic transformation method in fractional programming; solving Using Lemma 1, that is, for any The function has iff achieves the optimal solution; solving Using Lemma 2, that is, for any The function has iff achieves the optimal solution; solving and Using Lemma 2 and Lemma 3, where Lemma 3 is specifically given a complex vector For the function There is always iff achieves the optimal solution; solving W and Φ respectively uses the MM method, and the objective function value of the original optimization problem is calculated after each iteration. The iteration process is terminated when the difference between the objective functions of the adjacent two iterations is less than a given threshold value, and the solution obtained at this time is the solution of the base station precoding matrix and the intelligent metasurface reflection coefficient matrix under the criterion of maximizing the fairness of inter-user secure transmission.

[0128] The inner iteration method for solving the precoding matrix and the intelligent metasurface reflection coefficient matrix based on the MM method includes:

[0129] In the block coordinate descent method, when solving the precoding matrix by regarding other variables as constants, the objective function is a segmented function of the precoding matrix, which is iteratively solved by using the MM method;

[0130] In the block coordinate descent method, when solving the reflection coefficient matrix by regarding other variables as constants, the objective function is a segmented function of the reflection coefficient matrix, which is iteratively solved by using the MM method;

[0131] When using the MM method for iterative solution, in each iteration, a smooth concave function is used to approximate the objective function, and then the smooth concave function is replaced with its lower bound function to give a closed expression of the solution to the problem after transformation. This solution is used to update the objective function of the next iteration, and the value of the objective function of the original optimization problem is calculated. The process terminates when the difference between the objective functions of two adjacent iterations is less than a certain given threshold. The precoding matrix at the time of termination is the solution to the mean square error minimization problem when other variables are given.

[0132] Specifically, the optimal The following are given by equations (1), (2), (3), (4), and (5):

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] Once determined, we can obtain the subproblems of the equivalent optimization problem with respect to W:

[0140]

[0141] Once determined, the subproblems of the equivalent optimization problem with respect to Φ can be obtained:

[0142]

[0143] definition The steps for solving equivalent optimization problems using the BCD-MM algorithm are as follows:

[0144] BCD-MM algorithm flow:

[0145] 1. Initialize the current loop number l = 0, and initialize the feasible solution W. 0 and Φ 0 Calculate Obj(W) 0 , Φ 0 Set the maximum number of loops l max and error tolerance ε;

[0146] 2. Given W l and Φ l Update the auxiliary variable set using equation (1)

[0147] 3. Given W l , Φ l , Update the set of auxiliary variables using equation (2)

[0148] 4. Given W l , Φ l , and Update the set of auxiliary variables using equation (3)

[0149] 5. Given W l , Φ l , and Update the set of auxiliary variables using equation (4)

[0150] 6. Given W l , Φ l , and Update the set of auxiliary variables using equations (5) and (6)

[0151] 7. Given Φ l , and Take W l as the initial feasible solution, and solve problem (7) iteratively using the MM algorithm to update the precoding matrix W l+1 ;

[0152] 8. Given W l+1 , and Take Φ l as the initial feasible solution, and solve problem (8) iteratively using the MM algorithm to update the reflection coefficient matrix Φ l+1 ;

[0153] 9. Compute Obj(W l+1 , Φ l+1 )

[0154] 10. If |Obj(W l+1 , Φ l+1 )| - Obj(W l , Φ l ) < εObj(W l , Φ l )| or l ≥ l max , the algorithm ends; otherwise, l = l + 1 and go to step 2.

[0155] The flow of solving the sub-problems (7) and (8) by using the MM algorithm is the same. Taking solving the sub-problem (7) as an example, the flow of solving the sub-problem (7) by using the MM algorithm is as follows:

[0156] Defining Obj MM (W)=Obj(W,Φ l ), the flow of solving the sub-problem (7) by using the MM algorithm is as follows:

[0157] 1. Setting an initial feasible solution the maximum number of loops l max and the error tolerance ε;

[0158] 2. Using a derivable smoothing function f(W) to approximate the objective function of the sub-problem (7);

[0159] 3. Constructing a lower bound function of the smoothing function at

[0160] 4. Replacing the objective function of the sub-problem with the lower bound function to obtain a substitute problem;

[0161] 5. Solving the substitute problem to update the solution

[0162] 6. If or l≥l max , the algorithm ends; otherwise, l=l+1 and jumping to step 2.

[0163] When the optimal base station precoding matrix and the optimal intelligent metasurface reflection coefficient matrix are obtained by using the BCD-MM algorithm, the base station operates according to the optimal precoding matrix, and the intelligent metasurface operates according to the optimal intelligent metasurface reflection coefficient matrix. In this embodiment, an intelligent metasurface controller is arranged in the intelligent metasurface, and specifically:

[0164] The base station adjusts the transmission beamforming according to the optimal precoding matrix, and transmits a control signal to the intelligent metasurface through a dedicated channel according to the optimal reflection coefficient matrix;

[0165] The intelligent metasurface controller adjusts the phase shift of each reflection element of the intelligent metasurface according to the received control signal;

[0166] The user terminal receives the reflected signal of the intelligent metasurface.

[0167] The preferred embodiments of the application are described in detail above. It should be understood that those skilled in the art can make many modifications and changes without creative labor based on the concept of the application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment based on the prior art according to the concept of the application should be within the protection scope determined by the claims.​

Claims

1. A method for physical layer control of a multi-user communication system under non-ideal hardware conditions, for controlling an intelligent metasurface-assisted multi-user communication system under non-ideal hardware conditions, characterized in that, The intelligent metasurface-assisted multi-user communication system includes a base station, an intelligent metasurface, a plurality of user terminals and a single eavesdropper, the non-ideal hardware condition is that there is hardware impairment at the base station, the intelligent metasurface and the plurality of user terminals and there is no hardware impairment at the eavesdropper; The method comprises: establishing a non-ideal hardware model at the base station; establishing a non-ideal hardware model at the intelligent metasurface; establishing a non-ideal hardware model at the user terminal; establishing a signal-to-interference-and-noise ratio model at the user terminal; establishing a signal-to-interference-and-noise ratio model at the eavesdropper; obtaining the downlink security rate of each user terminal according to the signal-to-interference-and-noise ratio models at the user terminal and the eavesdropper; establishing an optimization problem of maximizing the security transmission fairness among user terminals according to the non-ideal hardware models at the base station, the intelligent metasurface and the user terminal and the downlink security rate of each user terminal, solving the optimization problem, and obtaining an optimal base station precoding matrix and an optimal intelligent metasurface reflection coefficient matrix; controlling the base station to operate according to the optimal precoding matrix and controlling the intelligent metasurface to operate according to the optimal intelligent metasurface reflection coefficient matrix; The base station has N transmit antennas, the intelligent metasurface has M reflecting elements, the multi-user communication system includes K user terminals, the user terminal has a single receive antenna, and the eavesdropper has a single receive antenna; The non-ideal hardware model at the base station is ; are independent zero-mean Gaussian random variables with the corresponding distribution , where , is the ratio of the transmit distortion noise power to the transmit signal power, is the precoding matrix of the base station and satisfies , denotes the maximum transmit power; The non-ideal hardware model at the intelligent metasurface is: ; Specifically , , ,in The first is caused by hardware damage at the smart metasurface. Phase noise of each reflective element, and In the domain Evenly distributed on the top; The non-ideal hardware model at the user terminal is: (The first...) The distortion noise term added at each user terminal is It is related to the first User terminals The information received is irrelevant. The distribution that satisfies this is ; Specifically: in, It is the ratio between the power of the distorted noise and the power of the undistorted received signal. For intelligent metasurfaces to The channel vector, The random phase noise matrix, The reflection coefficient matrix of the intelligent metasurface. The channel matrix from the base station to the smart metasurface. For base station to The channel vector, Information transmitted to the base station To satisfy the distribution Additive white Gaussian noise, for Total average power of other interference in the received signal.

2. The method of claim 1, wherein, The signal-to-interference-noise ratio model at the user terminal is: the signal-to-interference-noise ratio model at the first user terminal ; Specifically, wherein , , , , is a channel vector from the intelligent metasurface to the user equipment, , is a reflection coefficient matrix of the intelligent metasurface, is a channel matrix from the base station to the intelligent metasurface, is a channel vector from the base station to the user equipment, is an identity matrix of dimension , is a precoding vector of the base station for the user equipment, is a power of the distortion noise in the signal transmitted by the base station, is a power of the distortion noise at , is a total average power of other interferences in the received signal at , is a diagonal matrix of size , .

3. The method of claim 1, wherein, The signal-to-interference-noise ratio model at the eavesdropper is: the eavesdropper eavesdrops on the signal-to-interference-noise ratio model of the first user terminal Specifically:​​​ wherein , , , , is the channel vector from the intelligent meta-surface to the eavesdropper, is the reflection coefficient matrix of the intelligent meta-surface, is the channel matrix from the base station to the intelligent meta-surface, is the channel vector from the base station to the eavesdropper, is the identity matrix of dimension , is the precoding vector of the base station for , is the power of the distortion noise in the signal transmitted by the base station, is the total average power of other interferences in the signal received by the eavesdropper.

4. The method of claim 1, wherein, The downlink security rate of the user terminal is: the first user terminal is ; Specifically: wherein is a precoding matrix of the base station, is a precoding vector of the base station for is an intelligent meta-surface reflection coefficient matrix, , , is a signal-to-interference-and-noise ratio model at is a signal-to-interference-and-noise ratio model of the eavesdropper eavesdropping on .​​ 5. The method of claim 1, wherein, The optimization problem is: wherein, is the inverse of the downlink weight of the th user terminal , is the downlink safety rate of the th user terminal, is the maximum transmit power of the base station, is the reflection coefficient matrix of the intelligent meta-surface, is the precoding matrix of the base station, is the precoding vector of the base station for the th user terminal, is the reflection coefficient of the reflection element of the th intelligent meta-surface.

6. The method of claim 5, wherein, The solving process of the optimization problem is: transforming the optimization problem into an equivalent optimization problem; solving the equivalent optimization problem to obtain the optimal base station precoding matrix and the optimal intelligent metasurface reflection coefficient matrix; The equivalent optimization problem is: wherein, is the inverse of the downlink weight of the user terminal , is a lower bound function of the downlink safety rate of the UE k , is the reflection coefficient matrix of the intelligent metasurface, is the precoding matrix of the base station, is the precoding vector of the base station for , are sets of different downlink safety rate auxiliary variables, respectively, is the maximum transmit power of the base station, is the reflection coefficient of the reflective element of the intelligent metasurface The BCD-MM algorithm is used to solve the equivalent optimization problem, and the steps of using the BCD-MM algorithm to solve the equivalent optimization problem include: The optimization variables of the equivalent optimization problem are considered as seven groups, where is a group, is a group, is a group, is a group, is a group, is a group, is a group; Seven groups of variables are iteratively optimized by block coordinate descent method: in each iteration, the other group of variables is solved by fixing six groups of variables, and the newly solved variables are substituted into the next iteration, where the solution is sought Using the quadratic transformation method in fractional programming; solving By Lemma 1, Lemma 1 is: for any function , has , if and only if the optimal solution is obtained; solving By Lemma 2, Lemma 2 is: for any function , has , if and only if the optimal solution; solving and Using Lemma 2 and Lemma 3, Lemma 3 specifically that given a complex vector , for the function , there is always , if and only if takes the optimal solution; solving , The MM method is used at each iteration, and the objective function value of the original optimization problem is calculated after each iteration. The iteration process is terminated when the difference between the objective functions of the adjacent two iterations is less than a given threshold value, and the solution obtained at this time is the solution of the base station precoding matrix and the intelligent metasurface reflection coefficient matrix under the fairness maximization criterion of inter-user safe transmission.

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