阅读说明：本技术 一种基于统计csi的智能反射面的相移设计方法 (Intelligent reflecting surface phase shift design method based on statistical CSI ) 是由 施政 杨光华 窦庆萍 李晓帆 马少丹 塞奥佐罗斯.特斯菲斯 屈挺 于 2021-07-05 设计创作，主要内容包括：本发明公开了一种基于统计CSI的智能反射面的相移设计方法,该方法包括以下步骤：首先,获取收发端与智能反射面(RIS)的参数配置、信道状态信息(CSI)的统计知识；然后利用统计CSI优化RIS的相位偏移使得中断概率最小；继而运用中断概率的渐近表达式简化优化问题；最后,使用数值优化方法如遗传算法迭代求解最佳相位偏移值。本发明利用CSI的统计知识进行RIS相位偏移的优化设计,从而避免了频繁的信道估计、信令交互等引起通信系统开销；此外,基于渐进中断概率实现的最佳设计方法具有极低复杂度。(The invention discloses a statistical CSI-based intelligent reflecting surface phase shift design method, which comprises the following steps: firstly, acquiring parameter configuration of a transmitting and receiving end and an intelligent reflecting surface (RIS) and statistical knowledge of Channel State Information (CSI); then, optimizing the phase offset of the RIS by utilizing statistical CSI to ensure that the interruption probability is minimum; then, simplifying the optimization problem by using an asymptotic expression of the interruption probability; finally, the optimal phase offset value is iteratively solved using a numerical optimization method, such as a genetic algorithm. The invention utilizes the statistical knowledge of the CSI to carry out the optimization design of the RIS phase deviation, thereby avoiding the communication system overhead caused by frequent channel estimation, signaling interaction and the like; furthermore, the optimal design method based on progressive outage probability implementation has very low complexity.)

1. A phase shift design method of an intelligent reflecting surface based on statistical CSI is characterized in that the implementation steps of the phase shift design method are as follows:

s1, initializing system parameters and determining the number N of antennas at the transmitting end_tAnd the number of receiving-end antennas N_rTotal transmitting power is P, and the number of reflecting units of the intelligent reflecting surface is N_sThe intelligent reflecting surface is abbreviated as RIS,a channel covariance matrix of a transmitting end is represented,receive covariance representing RISThe matrix is a matrix of a plurality of matrices,a transmit covariance matrix representing the RIS,representing the receive covariance matrix, δ, at the receiving end²Is the variance of additive white gaussian noise;

s2, constructing a problem of minimizing the interruption probability, wherein the expression formula is as follows:

wherein p is_outRepresenting outage probability, θ, of a RIS-assisted MIMO system_nRepresents the phase shift introduced by the nth reflecting element on the RIS;

s3, replacing the expression of the interruption probability minimization problem with progressive interruption probability to realize simplified optimization design, which is equivalent to the following optimization problem, and the expression is as follows:

where xi is expressed with N_s、N_tAnd N_rThe relationship between the three is as follows:

when N is present_s≥N_t+N_rWhen is expressed as xi

When N is present_s＜N_t+N_rIs a time of and N_t+N_r-N_sWhen the number is odd, xi is expressed as

When N is present_s＜N_t+N_rIs a time of and N_t+N_r-N_sWhen the number is even, the xi expression is

Wherein the content of the first and second substances,representation matrixIs used, Δ (x) represents the vandermonde determinant constructed by vector x, det (-) represents the determinant, | represents the absolute value sign,phase shift matrix, phi, representing the RIS_n＝exp(iθ_n)，θ_nRepresenting the phase shift introduced by the nth reflecting element,diag (, …,) denotes the diagonal matrix, N ∈ [1, N ∈_s]。

2. The method as claimed in claim 1, wherein the approximate equivalence problem in step S3 is based on the assumption that the transmitting antennas are uncorrelated, i.e. the method for designing phase shift of intelligent reflective surface based on statistical CSIWherein, I_mAn identity matrix of m × m dimensions is represented, and therefore the optimization problem solution in step S3 ignores the correlation between the transmit antennas.

3. The method as claimed in claim 1, wherein the method for designing phase shift of the intelligent reflective surface based on statistical CSICharacterised in that default N is used in the derivation of xi in step S3_t≥N_rCondition if N_t＜N_rBy interchanging the number of transmitting and receiving antennas, i.e. N_tAnd N_rInterchange while replacing b with a matrixAnd disregards the correlation between the receive antennas, i.e. the vector formed by the characteristic roots of (c)

4. The method as claimed in claim 1, wherein the non-convex optimization problem in step S3 is solved by numerical optimization, the numerical optimization is performed by genetic algorithm GA, and convergence can be achieved within 20 times by using genetic algorithm GA as an optimization tool.

5. The method of claim 1, wherein in step S3, if no correlation exists between reflection units of RIS, the phase shift is adjusted in any wayWill not affect interrupt performance.

Technical Field

The invention relates to the technical field of wireless communication, in particular to a phase shift design method of an intelligent reflecting surface based on statistical CSI.

Background

Intelligent Reflectors (RIS) have attracted extensive attention in academia and industry due to their ability to reconstruct the propagation environment and improve signal reception quality. The reconstruction feature of the RIS comes from the artificial plane being made up of many low cost passive electromagnetic metamaterials, which can be adjusted and programmed by an integrated microcontroller. Each reconfigurable reflector is capable of independently adjusting the amplitude or phase offset of an incident electromagnetic wave in accordance with a dynamic fading environment. Flexibly and intelligently reflects signals on a receiver actively or passively, thereby realizing enhancement of received signals and reduction of interference signals. Intelligent reflector-assisted communication networks can provide superior performance over traditional relay-assisted networks in terms of hardware cost and energy consumption. Due to the significant advantages of RIS, researchers have attempted to combine RIS with various wireless technologies to further enhance system performance, such as multiple-input multiple-output (MIMO), massive MIMO, millimeter-wave, orthogonal multiple access (NOMA), free-space optics, visible light communications, and so forth.

Most of the present findings assume that the RIS controller possesses perfect CSI, and in fact obtaining perfect CSI on RIS relies on frequent channel estimation, signaling interaction, and high energy consumption, which presents a huge challenge to the optimal design of passive RIS. Furthermore, channel estimation errors are somewhat unavoidable due to quantization errors and unpredictable noise. In order to greatly save bandwidth and energy consumption, it is urgently needed to provide an optimal phase offset design method of RIS on the premise that RIS only has statistical Channel State Information (CSI).

Disclosure of Invention

The invention aims to solve the defects in the prior art and provides a phase shift design method of an intelligent reflecting surface based on statistical CSI. The method comprises the steps of firstly, carrying out channel modeling on MIMO transmission by adopting a Kronecker channel model, then, deducing an accurate closed expression of the outage probability by utilizing Mellin transformation, and then, carrying out progressive analysis under the condition of high signal-to-noise ratio by the outage probability to obtain a simplified expression. Based on the asymptotic analysis result, the optimal design of the intelligent reflecting surface phase offset is realized by applying a genetic algorithm with the aim of minimizing the interruption probability of the RIS auxiliary MIMO system. The invention is not only independent of the instantaneous CSI, but also has low realization complexity.

The purpose of the invention can be achieved by adopting the following technical scheme:

a phase shift design method of an intelligent reflecting surface based on statistical CSI comprises the following implementation steps:

s1, initializing system parameters and determining the number N of antennas at the transmitting end_tAnd the number of receiving-end antennas N_rTotal transmitting power is P, and the number of reflecting units of the intelligent reflecting surface is N_sThe intelligent reflecting surface is abbreviated as RIS,a channel covariance matrix of a transmitting end is represented,a reception covariance matrix representing the RIS,a transmit covariance matrix representing the RIS,representing the receive covariance matrix, δ, at the receiving end²Is the variance of additive white gaussian noise;

s2, constructing a problem of minimizing the interruption probability, wherein the expression formula is as follows:

wherein p is_outRepresenting outage probability, θ, of a RIS-assisted MIMO system_nRepresents the phase shift introduced by the nth reflecting element on the RIS;

s3, replacing the expression of the interruption probability minimization problem with progressive interruption probability to realize simplified optimization design, which is equivalent to the following optimization problem, and the expression is as follows:

where xi is expressed with N_s、N_tAnd N_rThe relationship between the three is as follows:

when N is present_s≥N_t+N_rWhen is expressed as xi

When N is present_s＜N_t+N_rIs a time of and N_t+N_r-N_sWhen the number is odd, xi is expressed as

When N is present_s＜N_t+N_rIs a time of and N_t+N_r-N_sWhen the number is even, the xi expression is

Wherein the content of the first and second substances,representation matrixIs used, Δ (x) represents the vandermonde determinant constructed by vector x, det (-) represents the determinant, | represents the absolute value sign,phase shift matrix, phi, representing the RIS_n＝exp(iθ_n)，θ_nRepresenting the phase shift introduced by the nth reflecting element,representing a diagonal matrix, N ∈ [1, N_s]。

Further, the approximate equivalence problem in step S3 is based on the assumption that the transmit antennas are uncorrelated, i.e.Wherein, I_mAn identity matrix of m × m dimensions is represented, and therefore the optimization problem solution in step S3 ignores the correlation between the transmit antennas.

Further, default N is set for the derivation of ξ in step S3_t≥N_rCondition if N_t＜N_rBy interchanging the number of transmitting and receiving antennas, i.e. N_tAnd N_rInterchange while replacing b with a matrixAnd disregards the correlation between the receive antennas, i.e. the vector formed by the characteristic roots of (c)

Further, the non-convex optimization problem in step S3 is solved by numerical optimization, which is performed by genetic algorithm GA, and convergence can be achieved within 20 times by using genetic algorithm GA as an optimization tool.

Further, in the step S3, if it is assumed that there is no correlation between the reflection units of the RIS, the phase shift is adjusted in any wayWill not affect interrupt performance.

Compared with the prior art, the invention has the following advantages and effects:

1. different from the prior RIS system design, the design depends on frequent instantaneous channel estimation information, which puts high requirements on the accuracy of channel estimation, channel feedback and the like, and the invention utilizes the statistical knowledge of channel state information to carry out the optimization design of RIS phase shift, thereby avoiding the additional system overhead caused by frequent channel estimation, signaling interaction and the like;

2. because the asymptotic expression of the outage probability is simple in form and low in computational complexity compared with the accurate expression of the outage probability, the invention provides a low-complexity implementation method for the phase offset optimal design based on the asymptotic outage probability result.

Drawings

FIG. 1 is a flow chart of an implementation of a method for designing a phase shift of an intelligent reflective surface based on statistical CSI according to the present invention;

fig. 2 is a genetic algorithm convergence diagram when the channel correlation coefficient ρ is 0.1;

fig. 3 is a genetic algorithm convergence diagram when the channel correlation coefficient ρ is 0.5;

fig. 4 is a genetic algorithm convergence chart when the channel correlation coefficient ρ is 0.99.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Examples

The embodiment discloses a statistical CSI-based phase shift design method for an intelligent reflecting surface, and the phase shift design method is specifically analyzed below.

Model of MIMO communication system

The invention provides that the direct-view path is blocked in the process of signal propagation, and an intelligent reflecting surface is used(RIS) to facilitate MIMO communications. Then the signal is receivedCan be expressed as

Wherein N is_t、N_rRespectively, the number of transmit and receive antennas, P is the total transmit power,represents N_tThe modulation symbols transmitted on the root antenna,representing a complex space of dimension m x n, assuming the average power per symbol to be 1, i.e. It is shown that it is desirable to,representative dimension is N_r×N_tN denotes a mean value of zero and a variance of δ²Complex white gaussian noise. If signals reflected multiple times by the RIS are ignored, the channel matrix H can be modeled as

H＝H₂ΦH₁， (2)

Wherein the content of the first and second substances,respectively representing the channel matrix from the sender to the RIS and the channel matrix from the RIS to the receiver, N_sIndicating the number of passive reflecting elements on the RIS,representing the RIS-induced phase shift matrix, phi_n＝exp(iθ_n)，θ_nRepresenting the phase shift introduced by the nth reflecting element,representing a diagonal matrix, N ∈ [1, N_s]. Furthermore, assuming that the channel obeys Rayleigh distribution, the channel matrix H is modeled according to the Kronecker model as follows

Wherein the content of the first and second substances,andrepresents transmit-side and receive-side covariance matrices, respectively, and W_iA standard-compliant rayleigh distribution, i.e., a complex gaussian distribution with all its elements compliant with the zero-mean unit variance of the independent homography. According to the Kronecker channel model, there arevec (-) denotes the vectorization operator,representing the Kronecker matrix product, symbol A^TRepresenting the transpose of the a matrix. Furthermore, for the purpose of subsequent analysis, it is assumed that the transmit antennas are uncorrelated, i.e.Wherein, I_mAn identity matrix representing the dimension m x m.

Second, interruption probability analysis

The amount of mutual information of the RIS assisted MIMO channel can be expressed as

Wherein, γ_T＝P/(N_tδ²) Det (-) denotes a determinant, symbol A^HRepresenting the conjugate transpose of the a matrix. To avoid the rank reduction effect of the cascaded MIMO channel, the present invention assumes N_s≥max{N_t,N_r}. In addition, for convenience of handling, first consider N_t＝N_rN.

For (4), the outage probability for the RIS assisted MIMO system is given by

p_out＝Pr{I(x；y|H)＜R}＝F_G(2^R), (5)

Wherein G ═ det (I + gamma)_THH^H) R represents a predetermined transmission rate, F_G(x) Representing the cumulative distribution function of the random variable G.

Consider that the random variable G can be written as a random matrix HH^HSince the mellin transform is generally used to deal with the problem of distribution of multiple random variable products. Thus, by using the Mellin transform, the distribution function F is accumulated_G(x) Can be represented by the following formula

Where c ∈ (— ∞,0),is the mellin transform of the probability density function of the random variable G. Therefore, the temperature of the molten metal is controlled,can be expressed in the following forms

Wherein the content of the first and second substances,_mF_nthe matrix variable hyper-geometric function is represented. By using super tableThe nature of which function can change (7) to determinant form, as follows

Where Δ (x) represents the vandermonde determinant constructed by vector x, λ ═ λ₁,…,λ_N)、Respectively represent matricesAndthe vector of eigenvalues of. According to the assumption that the transmitting antennas are uncorrelated, i.e.(i.e. theWhere 1 represents a column vector with all elements 1), it can be deduced according to the generalized Cauchy-Binet formulaIs finally expressed as

Wherein a ═ a₁,…,a_N) (or)、Respectively representAndcharacteristic root vector of A^-1The inverse of the matrix a is represented by,representing the Meijer G function and Γ (·) the gamma function. Based on (9), the result of mellin transform can be further generalized to the case where the number of transmit and receive antennas is not equal. Specifically, if N is assumed to be N_t≥N_rBy utilizing the generalized Cauchy-Binet formula,can be further expressed as

Wherein the content of the first and second substances,

similarly, similar results can be extended to N ═ N_r＜N_tThe case (1). Specifically, G can be rewritten as G ═ det (I + γ) by the property of determinant_TH^HH) In that respect Thus, by interchanging the number of transmitting and receiving antennas, i.e. N_t、N_rTo satisfy the requirement of the formula (10), a and b in the formula are respectively replaced by matrixesSum matrixThe feature root vector of (2). Furthermore, for this case, the correlation between the receiving antennas needs to be ignored, i.e.

By combining (5), (6) and (10), the probability of interruption can be expressed as

Using variable substitution, equation (11) can be converted to an inverse Laplace transform, i.e.

Since the Meijer G function is involved in f(s), it is almost impossible to accurately calculate the probability of interruption. However, by using the Abate-Whitt method, the probability of outage can be approximated by a controlled computational accuracy

Wherein the content of the first and second substances,representing the real operator, M is the number of euler summation terms, and Q is the truncation order. Notably, the approximation error is composed of a discretization error and a truncation error. On one hand, the discretization error is subject to |. epsilon | < e |^-A/(1-e^-A) The limit of (2). For example, to control the dispersion error at 10^-10And a is set to a ≈ 23. On the other hand, the truncation error can also be flexibly configured by appropriately selecting M and Q, and typically M-11 and Q-15 are selected.

To further simplify the computational complexity of the outage probability, an asymptotic analysis is next performed on the outage probability. Only N will be discussed in the following analysis_t≥N_rCan be appropriately transformed to extend the similar result to N_t＜N_rBy substituting (10) into (11), the compound can be obtained

Applying the Lei-Bluetz formula to the determinant in (14), (14) can be written as a summation form

Wherein sgn (α) represents a symbol replacing α,denotes {1,2, …, N_sAll permutation sets of_iThe ith element representing α. At gamma by the Meijer G function_TAsymptotic expansion is performed at the position of → ∞ and a series of algebraic operations are performed, so that the asymptotic result is obtained as follows

Wherein the parametersIs given by the following expression

Wherein the content of the first and second substances,taking the maximum integer less than x and taking the integer less than x,is a set of integers. From the three cases in the formula, the asymptotic outage probability expressions for the three cases are discussed separately next.

1)N_s≥N_t+N_r: in this case, based on (17), there areAndthus, the asymptotic expression of the probability of interruption can be expressed as

Wherein the equation (18) is used in the certification process And

2)N_s＜N_t+N_randin this case, it is preferable that the air conditioner,this is true. Thus, can obtainAndaccordingly, an asymptotic expression of the probability of outage can be written as

3)N_s＜N_t+N_rAndin this kind ofIn the case, there is an equationThis is true. Thus can obtainAndthus, the asymptotic expression of the probability of interruption can be expressed as

Furthermore, it is found from (18), (20), and (21) that the interruption probability asymptotic forms can be unified into

Wherein the content of the first and second substances,representing the index function and d the diversity order, the specific calculation formula is as follows

Therefore, (22) answers how many reflecting elements should be provided on the RIS? MIMO system without RIS with diversity order d-N_tN_r. From this, RIS does not enhance the diversity order of the MIMO system. However, it can indeed improve the outage performance by diversity gain. Therefore, in order to make the MIMO system fully utilize RIS without reducing the spatial diversity gain of the MIMO system, the minimum requirement for the number of reflecting elements is N_s＝N_t+N_r。

Optimization design of three, RIS optimum phase shift

Phase shiftθ_n(n∈[1,N_s]) The interruption performance is influenced by the phase shift matrix Φ. Therefore, it is necessary to optimize the phase offset based on statistical knowledge of the channel state information to obtain the lowest outage probability. Here by N_s≥N_t+N_rFor example, the exact probability of interruption is replaced with an asymptotic probability of interruption. Consider onlyCharacteristic value ofOffset from phase by theta_n(n∈[1,N_s]) In connection therewith, the minimization problem of the probability of interruption is equivalent to

Where, | · | represents an absolute value. It is apparent that the fractional optimization problem (24) is a non-convex problem, eigenvalueAnd phase shift fromThere is an implicit relationship between them and therefore a closed solution cannot be solved. This would lead to excessive computational complexity if the search method is exhaustive. To solve the problem, a numerical optimization tool, such as a Genetic Algorithm (GA), may be introduced to solve the problem (24). Furthermore, spatial correlation theoretically adversely affects interrupt performance. It can therefore be concluded roughly that if there is no correlation between the RIS reflecting units, i.e.Due to phi^HAs I, it is clear that there areThus, the phase offset is adjusted regardless of howWill not affect interrupt performance.

In the simulation analysis of fig. 2 to 4, different correlation coefficients ρ ═ 0.1, ρ ═ 0.5, and ρ ═ 0.99 are considered, and a 3D map of the objective function value and the RIS phase offset is plotted, and a fitness function value variation curve of the GA algorithm with the number of iterations is also shown. It is clear from the figure that the larger the correlation coefficient, the larger the fluctuation range of the objective function value, and the larger the influence of the phase shift on the interrupt performance. I.e., at low spatial correlation, the phase offset does not have a significant impact on the interrupt performance. Therefore, in the event of high spatial correlation, the phase offset should be designed reasonably to achieve a minimum outage probability. Furthermore, it can also be seen that the genetic algorithm GA was converged in almost 20 times as an optimization tool, which further demonstrates the effectiveness of the algorithm.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.