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CN116388825B - Beam design method for maximizing user and rate - Google Patents

Beam design method for maximizing user and rate

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Publication number
CN116388825B
CN116388825B CN202310418099.6A CN202310418099A CN116388825B CN 116388825 B CN116388825 B CN 116388825B CN 202310418099 A CN202310418099 A CN 202310418099A CN 116388825 B CN116388825 B CN 116388825B
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intelligent
phase shift
user
irs
sum rate
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CN116388825A (en
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刘刚
潘澄
郭漪
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Xidian 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
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/0082—Monitoring; Testing using service channels; using auxiliary channels
    • H04B17/0087—Monitoring; Testing using service channels; using auxiliary channels using auxiliary channels or channel simulators
    • H—ELECTRICITY
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    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H04B17/3912—Simulation models, e.g. distribution of spectral power density or received signal strength indicator [RSSI] for a given geographic region
    • 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
    • H04B7/0619—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 using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]
    • 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
    • H04B7/0619—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 using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0632—Channel quality parameters, e.g. channel quality indicator [CQI]
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0857—Joint weighting using maximum ratio combining techniques, e.g. signal-to- interference ratio [SIR], received signal strenght indication [RSS]
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • 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
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    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

本发明公开了一种最大化用户和速率的波束设计方法，主要解决现有单智能反射面的和速率增益低，双智能反射面元素数目大的问题，其实现方案是：基站通过信道估计得到等效信道模型，并对其最大和速率进行拉格朗日和二次变换，得到最大和速率的多项式表示；通过加权最小均方误差设计发射波束形成矩阵，且分别固定两个智能反射面相移系数并松弛非凸约束，得到最大和速率的半正定规划形式，并对其求解得到单次迭代的发射波束成型矩阵及两个智能反射面的相移系数；在设定的迭代约束下得到最终的发射波束成型矩阵及两个智能反射面相移系数的最优值。本发明能在智能反射面元素数目相同且较小的情况下获得明显的和速率增益，可用于蜂窝小区或局域网通信系统。

The present invention discloses a beam design method for maximizing user sum rates, primarily addressing the low sum rate gain of existing single-intelligent reflector systems and the large number of elements in dual-intelligent reflector systems. The implementation scheme comprises the following steps: a base station obtains an equivalent channel model through channel estimation and performs a Lagrangian and quadratic transform on its maximum sum rate to obtain a polynomial representation of the maximum sum rate; a transmit beamforming matrix is designed using weighted minimum mean square error, and the phase shift coefficients of the two intelligent reflectors are fixed and non-convex constraints are relaxed to obtain a semi-positive definite programming form for the maximum sum rate. This is then solved to obtain a single-iteration transmit beamforming matrix and the phase shift coefficients of the two intelligent reflectors; and the final transmit beamforming matrix and the optimal values of the phase shift coefficients of the two intelligent reflectors are obtained under the set iterative constraints. The present invention can achieve significant sum rate gain while maintaining a constant and small number of intelligent reflector elements, and can be used in cellular cell or local area network communication systems.

Description

Beam design method for maximizing user and rate
Technical Field
The invention belongs to the technical field of electronic circuits, and further relates to a sum-rate wave beam design method which can be used for a cellular cell or a local area network communication system.
Background
It is expected that the capacity of communication networks will increase 1000 times in the next decade and ubiquitous wireless connectivity will become a reality. However, highly complex networks, high cost hardware and ever-increasing energy consumption will be critical issues facing future wireless communications. For example, in ultra dense network UDNs, a large number of base stations increase hardware and maintenance costs and face severe network interference. The spectrum extends from sub-6GHz to millimeter waves, terahertz requires more complex signal processing and more expensive power consuming hardware. Research on innovative, efficient, spectrum and resource saving future wireless network solutions is imperative. The intelligent reflection surface IRS is a novel technology, is an artificial electromagnetic surface structure with programmable electromagnetic characteristics, and can independently control the electromagnetic characteristics of each element on the IRS through programming, so that the phase or amplitude of an incident signal is changed, and the IRS is utilized to have the capability of reconstructing a wireless transmission environment, so that signal transmission can be enhanced.
Currently, IRSs have been integrated into various communication systems, such as orthogonal frequency division multiplexing OFDM, non-orthogonal multiple access NOMA, with their unique low cost, low power consumption, programmability, and ease of deployment. Beamforming in IRS assisted communication systems is a technique for transmitting signals in a specific direction to enhance the signal, which directly affects the signal quality received by the receiving end user, and if no beamforming is performed, the base station will transmit the transmission signal in all directions, which weakens the signal power received by the receiving user and thus reduces the performance of the system.
HuayanGuo et al, in Weighted Sum-Rate Maximization for Reconfifigurable Intelligent Surface AIDED WIRELESS Networks, for the first time propose a beam design method for maximizing the Weighted Sum rate applied to a single IRS system, which first uses a split-type programming to obtain a smooth solution to the joint design problem, and then uses a random continuous convex approximation technique to achieve beam design with maximized Weighted Sum rate in the single IRS system. The method only considers the scene of single IRS auxiliary communication, so that the established system model and the method for designing the corresponding wave beam can only improve the power of the signal received by the receiving end by 2dB at most under the condition that the number of IRS elements is increased by two times.
For a communication system with a larger communication capacity requirement, the power gain provided by a single IRS under the method cannot meet the requirement of a large-capacity communication system due to the limitation of the IRS on the area and the volume.
YitaoHan et al, cooperative Double-IRS Aided Communication, beamforming DESIGN AND Power Scaling, propose a joint passive Beamforming design approach for two IRS. The method is based on the geometric relation of two IRSs, and obtains a passive beam matrix under the system by simulating a line-of-sight propagation LoS channel and a conjugate zero forcing method, so that the receiving signal-to-noise ratio of a user is improved. However, the beam design algorithm proposed by the method can only show performance advantages under the condition of larger IRS element number, and when the IRS element number is smaller, the performance gain provided by two IRS is lower than that provided by a single IRS. Therefore, the method can only show the performance advantage of double IRS compared with single IRS under the condition of larger IRS area and volume.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a sum rate beam design method suitable for users in a double IRS system, so as to realize higher power gain than that of a single IRS under the condition of smaller IRS element number.
The method comprises the technical ideas of the method, aiming at the sum rate optimization problem of a double IRS (information processing system), converting the optimization problem into a polynomial summation problem through Lagrangian dual transformation and secondary transformation, aiming at the converted polynomial and optimization problem, carrying out beam design of a transmitting end through a traditional weighted minimum mean square error WMMSE, aiming at a converted optimization model, decoupling the multivariable problem into a univariate problem through an alternative optimization algorithm, relaxing the original optimization problem into a convex problem through relaxation of non-convex constraint, converting the problem into a classical semi-positive optimization problem through matrix Shull compensation, solving IRS phase shift coefficients through an optimization tool of a computer, and obtaining optimal values of the beam and the phase shift coefficients under the appointed iteration times and the iteration difference value through alternative optimization of three variables in the optimization problem in each iteration process.
According to the above idea, the implementation steps of the invention include the following:
(1) Constructing a baseband equivalent channel model, and carrying out Lagrange dual conversion and secondary conversion on the maximum sum rate under the model:
1a) The transmitting terminal base station obtains Channel State Information (CSI) through channel estimation, obtains initial phase shift coefficients phi 1 (0) and phi 2 (0) of two IRS through complex normal distribution, and obtains a baseband equivalent channel model through the Channel State Information (CSI) and the phase shift coefficients of the two IRS
1B) Substituting the baseband equivalent channel model into a signal-to-interference-plus-noise ratio (SINR) formula to obtain a signal-to-interference ratio gamma k of a user, obtaining a user rate R according to gamma k through a shannon formula, and summing the user rates to obtain an expression form of the maximum sum rate;
1c) Carrying out Lagrange dual conversion on the representation form of the maximum sum rate by introducing an auxiliary variable alpha so as to convert the logarithmic sum into a partial sum;
(2) Fixing phase shift coefficients of the two intelligent reflection surfaces IRS, and obtaining a transmitting beam forming matrix W through a minimum mean square error beam design method;
(3) The maximum sum rate of the phase shift coefficients Φ 1 and Φ 2 and the beamforming matrix W, which contain the two intelligent reflection planes IRS, is converted into a semi-positive programming SDP form:
3a) On the basis of a beam forming matrix W, respectively fixing two intelligent reflection surface IRS phase shift coefficients phi 1 and phi 2, and converting the maximum sum rate with the non-convex constraint into the maximum sum rate with the convex constraint by relaxing non-convex constraint I phi i I to I i I;
3b) Introducing a dual variable mu for the maximum sum rate with convex constraint, and performing Lagrange dual decomposition to obtain a closed solution of a phase shift angle theta * of each element on two IRS;
3c) Bringing θ * into the maximum sum rate form with convex constraints and simultaneously converting this form into the classical semi-positive-definite programming SDP form using the matrix sulf;
(4) Optimizing the semi-positive setting programming SDP form through a computer optimization tool CVX tool box to obtain an optimal solution of the first intelligent reflection surface IRS1 phase shift coefficient phi 1, the second intelligent reflection surface IRS2 phase shift coefficient phi 2 and the beam forming matrix W in a single iteration process;
(5) Setting the maximum iteration number i max and the maximum iteration difference epsilon, and judging whether the iteration termination condition is met or not:
When the iteration number i exceeds the set iteration number i max or the difference between the optimal values of the objective functions formed by phi 1,Φ2 and W in two adjacent iteration processes is smaller than the maximum iteration difference epsilon, ending the iteration to obtain final optimization results W *,Φ1 * and phi 2 *;
otherwise, let iteration number i=i+1, return to step (2).
Compared with the prior art, the invention has the following advantages:
First, the invention aims at the maximum optimization problem of the sum rate of users under the dual intelligent reflection surface IRS model, uses WMMSE to calculate the transmission beam matrix, respectively fixes the phase shift coefficients of the two intelligent reflection surfaces IRS, and iteratively optimizes the transmission beam matrix and the phase shift coefficients of the two intelligent reflection surfaces IRS. Compared with a single communication system based on intelligent reflection surface IRS assistance, under the condition of the same number of intelligent reflection surface IRS elements, the dual intelligent reflection surface IRS wave beam designed by the invention can provide higher system gain.
Second, the invention uses Lagrangian dual transform and quadratic transform to transform the sum rate form from logarithmic sum form to polynomial sum form, which aims at the maximum optimization problem of the sum rate of users under the dual intelligent reflector IRS model. The method has a lower complexity than a single intelligent reflector IRS-assisted communication system.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a prior art dual intelligent reflector IRS-based auxiliary communication system used in the present invention;
FIG. 3 is a graph of the sum rate comparison of a dual intelligent reflector IRS of the present invention and a prior art single intelligent reflector IRS.
Detailed Description
Embodiments and effects of the present invention are described in further detail below with reference to the accompanying drawings.
Referring to fig. 2, the dual intelligent reflector IRS-based auxiliary communication system used in the present invention includes an access point AP, L user receivers, a first intelligent reflector IRS1 and a second intelligent reflector IRS2. The second intelligent reflection surface IRS2 is disposed in the vicinity of the access point AP and the first intelligent reflection surface IRS1 is disposed in the vicinity of the user. The direct link between the AP and the user is blocked and the signal can only be transmitted through the two distributed intelligent reflection surfaces IRS, the system not only has a link from each intelligent reflection surface IRS to the user, but also has a reflective link between the two intelligent reflection surfaces IRS1 and IRS2. The two intelligent reflecting surfaces IRS1 and IRS2 have the same structure, the access point AP adopts a uniform linear array ULA, the reflection coefficients of each unit of the two intelligent reflecting surfaces are controlled by an intelligent controller, and the passive beam design of the system is realized, so that the propagation environment between a user and the access point AP is reconstructed.
Referring to fig. 1, the beam design method based on the present example of the system includes the following implementation steps:
Step 1, constructing a baseband equivalent channel model by acquiring channel state information and initial phase shift coefficients of two intelligent reflection surfaces IRS.
1.1 The base station obtains channel state information CSI through channel estimation. Obtaining initial phase shift coefficients of two intelligent reflecting surfaces IRS through complex normal distribution, namely initial phase shift coefficient phi 1 (0) of a first intelligent reflecting surface IRS1 and initial phase shift coefficient phi 2 (0) of a second intelligent reflecting surface IRS2, and obtaining a baseband equivalent channel model through channel state information CSI and the phase shift coefficients of the two intelligent reflecting surfaces
Wherein the method comprises the steps ofRepresenting the channel from the first intelligent reflective surface IRS1 to user k,Representing the channel from the second intelligent reflective surface IRS2 to user k,Representing the channel of the second intelligent reflector IRS2 to the first intelligent reflector IRS1,Representing the channel of the access point AP to the first intelligent reflective surface IRS1,Representing the channel from the access point AP to the second intelligent reflective surface IRS2, M 1 representing the maximum number of elements of the first intelligent reflective surface IRS1, M 2 representing the maximum number of elements of the second intelligent reflective surface IRS2, N representing the number of antennas of the access point AP, [ · ] H representing the conjugate transpose of the matrix.
1.2 According to the baseband equivalent channel modelObtaining a signal y k received by a user k:
Wherein the method comprises the steps of Is the beamforming vector for user k,Is the beamforming vector for interfering user j, u k is subject toIs a complex gaussian noise of (a) and (b),Is the data symbol received by user k from access point AP, t kωksk receives the signal for user k,Interference is received for user k for other users.
And 2, constructing a maximum sum rate expression form through a baseband equivalent channel model.
2.1 According to the baseband equivalent channel modelThe signal-to-interference ratio gamma k for user k in the system is expressed as:
wherein σ 0 2 represents the noise power following the complex symmetric complex gaussian CSCG distribution;
2.2 According to the signal-to-interference ratio gamma k of the user k, obtaining a user rate R by a shannon formula:
R=log2(1+γk)
2.3 Based on the weights w k for user rate R and user k, a representation of the system and rate R sum is obtained:
2.4 According to the characteristic that the intelligent reflection surface IRS only changes the phase and does not change the amplitude and the characteristic of the limit of the transmitting power, the system and the rate R sum are utilized to obtain the representation P1 of the original maximum sum rate form:
P1:
W= [ ω 1,ω2,…,ωk,…,ωL ] is a transmit beamforming matrix, L is the total number of users in the system, P T represents the transmit power constraint of the AP, Φ 1 is the phase shift coefficient of the first intelligent reflective surface IRS1, Φ 1＝diag(θ1), Representing the phase shift angle of each reflective element on the first intelligent reflective surface IRS1, M 1 representing the maximum number of elements on the first intelligent reflective surface IRS 1; Φ 2＝diag(θ2) being the phase shift coefficient of the second intelligent reflective surface IRS2,Representing the phase shift coefficient of each reflective element on the second intelligent reflective surface IRS2, and M 2 represents the maximum number of elements on the second intelligent reflective surface IRS 2.
And step 3, carrying out Lagrange transformation and secondary transformation on the original maximum sum rate form to obtain a transformed maximum sum rate form P1".
3.1 Introducing an auxiliary variable alpha= [ alpha 1,α2,…,αk,…,αL]T to perform Lagrange dual transformation on P1 to obtain a maximum sum rate form P1' after Lagrange transformation:
P1':
Wherein the method comprises the steps of The representation and rate, L represents the total number of system users, k represents the current user index, [. Cndot. ] T represents the transpose of the matrix;
3.2 Pair and rate Regarding alpha k, the bias is determined and is set to 0, i.eObtainingAnd then will beCarry-inFormula, rate of sumIs simplified into
Wherein the method comprises the steps ofAlpha k is an auxiliary variable introduced by Lagrangian transformation;
3.3 For the simplified sum rate) Introducing an auxiliary variable beta to perform secondary transformation to obtain a sum rate after secondary transformation
Wherein the auxiliary variable beta= [ beta 1,β2,…,βk,…,βL]T,As the auxiliary variable of the kth user, L is the total number of users of the system, and alpha k is the auxiliary variable introduced by Lagrange transformation;
3.4 F y1(W,Φ1,Φ2, β) into the original maximum sum rate form P1, resulting in a maximum sum rate form P1 "after lagrangian transformation and secondary transformation:
P1′′:
And 4, fixing the phase shift coefficients phi 1 and phi 2 of the two intelligent reflecting surfaces to obtain a transmitting beam omega k closed form of the user k.
4.1 Fix the phase shift coefficient Φ 1 of the first intelligent reflective surface IRS1 and the phase shift coefficient Φ 2 of the second intelligent reflective surface IRS2 to be constant such that the maximum sum rate form P1″ after the secondary transformation is degenerated to a sum rate form P2 only with respect to the transmit beamforming matrix W, which is of the form:
P2:
4.2 Using the lagrangian multiplier method, introducing a lagrangian dual variable λ, giving a closed form of ω k:
Wherein, the For the equivalent baseband model of interfering user I, I N represents an identity matrix of size nxn.
And 5, solving a transmitting beam forming matrix W.
5.1 Using a dichotomy to obtain an optimal solution of the Lagrangian dual variable lambda as lambda * for the transmission beam omega k of the user k, and bringing lambda * back to the closed solution of the transmission beam omega k of the user k to obtain an optimal value of the transmission beam omega k of the user k in single optimization;
5.2 The transmission beams omega 1～ωL of the L users are cascaded to obtain a transmission beam forming matrix W.
And 6, fixing the phase shift coefficient phi 1 of the first intelligent reflecting surface IRS1 to obtain a quadratic constraint and quadratic programming QCQP form P3) of the phase shift coefficient vector theta 2 of the reflecting unit of the second intelligent reflecting surface IRS2 under convex constraint.
6.1 Fix the phase shift coefficient Φ 1 of the second intelligent reflection surface IRS1, rewrite the maximum sum rate form P1 "after the secondary transformation to the maximum sum rate form P3 of the second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector θ 2:
P3:
wherein (-) * represents the conjugate of the complex number.
6.2 Mathematical transformation is carried out on the baseband equivalent model obtained in the step 1, and the following form of the baseband equivalent channel t k' based on the second intelligent reflection surface IRS2 is obtained:
Wherein the method comprises the steps of R denotes the index of the current intelligent reflector IRS, diag (·) denotes the matrix diagonalization of vectors, M r is the number of elements of the r-th intelligent reflector IRS,Representing the value updated last time in the iterative process;
6.3 A baseband equivalent channel t k' based on the second intelligent reflection surface IRS2 is brought into a maximum sum rate form P3 of the second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector θ 2, resulting in a maximum sum rate function f b1(θ2 of the second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector θ 2):
Wherein the method comprises the steps of
6.4 Maximum sum rate function for second intelligent reflector IRS2 reflection unit phase shift coefficient vector theta 2 Variable replacement is carried out, irrelevant constant items are deleted, and then the maximum sum rate form P3 of the phase shift coefficient vector theta 2 of the second intelligent reflection surface IRS2 reflection unit is rewritten into a quadratic constraint quadratic programming QCQP form P3' of the phase shift coefficient vector theta 2 of the second intelligent reflection surface IRS2 reflection unit:
P3′:
Wherein the method comprises the steps of
Q 2 is a first order coefficient in the maximum sum rate form of variable θ 2, F 2 is a second order coefficient in the maximum sum rate form of variable θ 2, k is a current user index, r is an index of a current IRS, θ 1 is a first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector, ω k is a beamforming vector of user k, ω j is a beamforming vector of interference user j, α is an auxiliary variable introduced by Lagrange transformation, β is an auxiliary variable introduced by secondary transformation,A quadratic form of the system and the velocity representing the second intelligent reflector IRS2 reflection unit phase shift coefficient vector θ 2 as a variable;
6.5 Non-convex constraint in the quadratic programming form P3 'of the quadratic constraint of the univariate θ 2 is relaxed, and the P3' is converted into a form P3″ of QCQP of the second intelligent reflector IRS2 reflection unit phase shift coefficient vector θ 2 under the convex constraint:
P3′′:
Where e m is the initial vector of 1 on the mth bit, M represents the element index on the intelligent reflector IRS, r represents the index of the current intelligent reflector IRS, and M r is the number of elements of the r-th intelligent reflector IRS.
And 7, fixing the phase coefficient phi 2 of the second intelligent reflection surface IRS2 to obtain a quadratic constraint quadratic programming QCQP form P4 "of the phase shift coefficient vector theta 1 of the reflection unit of the first intelligent reflection surface IRS1 under convex constraint.
7.1 Fix the phase shift coefficient Φ 2 of the second intelligent reflection surface IRS2, rewrite the maximum sum rate form P1 "after the secondary transformation to the maximum sum rate form P4 of the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1:
P4:
wherein f c1(θ1) is the maximum sum rate function of the first intelligent reflector IRS1 reflecting unit phase shift coefficient vector θ 1.
7.2 Mathematical transformation is carried out on the baseband equivalent model obtained in the step 1, and the following form of a baseband equivalent channel t k' based on the first intelligent reflection surface IRS1 is obtained:
Wherein the method comprises the steps of AndR represents the index of the current intelligent reflection surface IRS, and M r is the element number of the r intelligent reflection surface IRS;
7.3 A baseband equivalent channel t k 'based on the first intelligent reflection surface IRS1 is brought into a maximum sum rate form P4 of the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1, variable substitution is performed and uncorrelated constant terms are deleted, and the maximum sum rate form P4 of the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1 is rewritten into a quadratic constraint quadratic programming QCQP form P4' of the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1:
P4':
Wherein the method comprises the steps of
Q 1 is the first order coefficient in the maximum sum rate form of variable θ 1, F 1 is the second order coefficient in the maximum sum rate form of variable θ 1,A quadratic form of the system and the velocity representing the first intelligent reflector IRS1 reflection unit phase shift coefficient vector θ 1 as a variable;
7.4 Non-convex constraint in a quadratic programming form P4 'of the secondary constraint of the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1 is relaxed, and the P4' is converted into a QCQP form P4″ of the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1 under the convex constraint:
P4”:
Where e m is the initial vector of 1 at bit m, which represents the element index on the intelligent reflective surface IRS.
And 8, obtaining closed solutions of the phase shift coefficient vector theta * of the reflecting unit on the two intelligent reflecting surfaces IRS through Lagrange dual decomposition.
8.1 A Lagrangian dual decomposition is performed on QCQP form P3' ' of a second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector theta 2 under convex constraint to obtain QCQP form P3' ' ') of a second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector theta 2 after the Lagrangian dual decomposition:
P3”':
Wherein the method comprises the steps of A lagrangian function in the form of QCQP representing the second intelligent reflector IRS2 reflecting element phase shift coefficient vector theta 2,Represents the second intelligent reflection surface pair even variable, mu 2,m is the pair even variable of the m-th element on the second intelligent reflection surface, m represents the element index on the intelligent reflection surface IRS,Representing the second intelligent reflector IRS2 reflection element phase shift coefficient vector θ 2 under convex constraints as a quadratic form of the system and rate of the variables.
8.2 A) performing Lagrangian dual decomposition on QCQP form P4 'of a first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector theta 1 under convex constraint, wherein QCQP form P4', of theta 1 after Lagrangian dual decomposition:
P4”':
Wherein the method comprises the steps of A lagrangian function in QCQP form representing a first smart reflective surface IRS1 reflective element phase shift coefficient vector θ 1, whereRepresents the first intelligent reflection surface pair even variable, mu 1,m is the pair even variable of the mth element on the first intelligent reflection surface, m represents the element index on the intelligent reflection surface IRS,A quadratic form of the system and the velocity representing the first intelligent reflector IRS1 reflection unit phase shift coefficient vector θ 1 as a variable;
8.3 For the second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector θ 2, the lagrangian function Λ (θ 2,μ2) in QCQP form is used for performing partial derivative on μ 2 to obtain an optimal closed solution θ 2 * of θ 2, which is:
8.4 For the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector theta 1, the Lagrange function lambda (theta 1,μ1) in QCQP form is used for carrying out partial derivative on mu 1 to obtain the optimal closed solution of theta 1
And 9, obtaining the maximized and speed half-positive planning SDP form of the IRS of the two intelligent reflecting surfaces through matrix Shu' er compensation.
9.1 Any one of the aboveIs brought into QCQP form P3' of phase shift coefficient vector theta 2 of the reflection unit of the second intelligent reflection surface IRS2 after being subjected to Lagrangian dual decomposition, and is carried outAnd (3) carrying out the phase shift of the first intelligent reflecting surface IRS1 reflecting unit after the Lagrange dual decomposition in a QCQP form P4' of a phase shift coefficient vector theta 1 to obtain a sum speed tau r under the semi-positive rule of the r intelligent reflecting surface:
τr＝qr H(Fr+diag(μr))q+tr(diag(μr)),
wherein r represents an index of the current IRS;
9.2 The sum rate tau r under the semi-positive programming is deformed by using a matrix sulf form and is brought into a QCQP form P3', of a second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector theta 2 after being subjected to Lagrange dual decomposition, and the maximized sum rate semi-positive programming SDP 3 final of the second intelligent reflection surface IRS2 is obtained:
P3final:
Wherein τ 2 is the sum rate under the semi-positive rule of the 2 nd intelligent reflecting surface;
9.3 The sum rate τ r under the semi-positive programming is deformed by using a matrix sulf form and is brought into a QCQP form P4' "of a first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector θ 1 after lagrange dual decomposition, resulting in a maximized sum rate semi-positive programming SDP form P4 final representation of the first intelligent reflection surface IRS 1:
P4final:
where τ 1 is the sum rate under the semi-positive schedule for the 1 st intelligent reflecting surface.
And step 10, obtaining a second intelligent reflection surface IRS2 phase shift coefficient optimal solution phi 2 and a first intelligent reflection surface IRS1 phase shift coefficient optimal solution phi 1 by using a computer optimization tool CVX tool box.
10.1 Optimizing the maximized second intelligent reflection surface IRS2 and the semi-positive setting SDP form P3 final of the speed through a computer optimization tool CVX tool box to obtain an optimal solution phi 2 of the phase shift coefficient of the second intelligent reflection surface IRS2 in a single iteration process;
10.2 The maximized second intelligent reflection surface IRS2 and the semi-positive setting SDP form P4 final of the speed are optimized through a CVX tool box of the optimization tool of the computer, and the optimal solution phi 1 of the phase shift coefficient of the first intelligent reflection surface IRS1 in the single iteration process is obtained.
And step 11, judging iteration termination conditions to obtain final optimization results W *,Φ1 * and phi 2 *.
11.1 Setting a maximum iteration number i max and a maximum iteration difference epsilon;
11.2 A first intelligent reflection surface IRS1 phase shift coefficient optimal solution phi 1, a second intelligent reflection surface IRS2 phase shift coefficient optimal solution phi 2 and a transmission beam forming matrix W are brought into an objective function Obtaining the sum rate in the iterative process;
11.3 When the iteration number i exceeds the set iteration number i max or in two adjacent iteration processes, the objective function formed by phi 1,Φ2 and W If the difference between the sum rates of (a) is smaller than the maximum iteration difference epsilon, ending the iteration to obtain final optimization results W *,Φ1 * and phi 2 *, and completing the beam design of the maximized user and rate;
11.4 Otherwise, let iteration number i=i+1, return to step 4.
The effects of the present invention can be further illustrated by the following simulation results
Simulation conditions
Setting the coordinate position of an access point AP as (0 m,0 m), the central coordinate position of a user cluster as (40 m,1 m), the radius r=0.5 m of the user cluster, the coordinate position of a second intelligent reflection surface IRS2 as (1 m,1 m), and the coordinate position of a first intelligent reflection surface IRS1 as (39 m,1 m);
Setting the number of AP antennas of an access point to be N=32, wherein the total transmitting power is P T =0 dBm, and the noise power of a user receiver is sigma 0 = -85dBm;
the weights w k of all users are set equal.
Second, simulation content
Under the above simulation conditions, the sum rate of the maximum systems achieved by the present invention and the existing method for designing beams are simulated, respectively, and the result is shown in figure 3,
As can be seen from fig. 3, in the case that the number of elements of the intelligent reflection surface IRS is the same, the dual intelligent reflection surface IRS of the present invention has an obvious sum rate gain with respect to the existing single intelligent reflection surface IRS, and as the number of elements of the intelligent reflection surface IRS increases, the sum rate gain of the dual intelligent reflection surface IRS with respect to the single intelligent reflection surface IRS becomes more obvious.
The above description is only one specific example of the invention and does not constitute any limitation of the invention, and it will be apparent to those skilled in the art that various modifications and changes in form and details may be made without departing from the principles, construction of the invention, but these modifications and changes based on the idea of the invention are still within the scope of the claims of the invention.

Claims (7)

1. A method of beam design to maximize user and rate comprising the steps of:
(1) Constructing a baseband equivalent channel model, and carrying out Lagrange dual conversion and secondary conversion on the maximum sum rate under the model:
1a) The transmitting terminal base station obtains Channel State Information (CSI) through channel estimation, obtains initial phase shift coefficients (phi 1 (0) and phi 2 (0)) of two Intelligent Reflection Surfaces (IRS) through complex normal distribution, and obtains a baseband equivalent channel model through the Channel State Information (CSI) and the phase shift coefficients of the two IRS
1B) Substituting the baseband equivalent channel model into a signal-to-interference-plus-noise ratio (SINR) formula to obtain a signal-to-interference ratio gamma k of a user, obtaining a user rate R according to gamma k through a shannon formula, and summing the user rates to obtain an expression form of the maximum sum rate;
1c) The Lagrange's dual transformation is performed on the representation of the maximum sum rate by introducing an auxiliary variable alpha to convert the logarithmic sum into a polynomial sum, and then the quadratic transformation QT is performed by introducing an auxiliary variable beta to convert the polynomial sum, as follows:
Wherein β= [ β 1,β2,…,βk,…,βL]T ] is the auxiliary variable introduced by the secondary transformation in step 1 c), L is the total number of users of the system, and Gamma k denotes the signal-to-interference ratio of user k, alpha k is an auxiliary variable introduced by the lagrangian transformation,For the equivalent baseband model of user k, ω k is the beamforming vector for user k, ω j is the beamforming vector for interfering user j, σ 0 2 is the noise power, [ · ] T represents the transpose of the matrix;
(2) The phase shift coefficients of the two intelligent reflection surfaces IRS are fixed, and a transmitting beam forming matrix W is obtained through a minimum mean square error beam design method, so that the following steps are realized:
7a) Setting the initial phase shift coefficient of the first intelligent reflecting surface IRS1 as phi 1 (0), setting the initial phase shift coefficient of the second intelligent reflecting surface IRS2 as phi 2 (0), fixing the initial phase shift coefficient as a constant, introducing a Lagrangian dual variable lambda, and obtaining a closed solution of a transmitting wave beam omega k containing lambda of a user k by a Lagrangian multiplier method;
Wherein the method comprises the steps of Alpha k is the auxiliary variable introduced by the Lagrangian transformation of step 1 c), beta k is the auxiliary variable introduced by the quadratic transformation of step 1 c),For the equivalent baseband model of user k,For the equivalent baseband model of the interference user I, I N represents an identity matrix with a size of nxn;
7b) Obtaining an optimal solution lambda * by using a dichotomy for the closed solution of the obtained user k transmitting beam omega k in 7 a), bringing lambda * back to the closed solution of the user k transmitting beam omega k, and cascading transmitting beams of L users to obtain a transmitting beam forming matrix W;
(3) The maximum sum rate of the phase shift coefficients Φ 1 and Φ 2 and the beamforming matrix W, which contain the two intelligent reflection planes IRS, is converted into a semi-positive programming SDP form:
3a) On the basis of a beam forming matrix W, two intelligent reflection surface IRS phase shift coefficients phi 1 and phi 2 are respectively fixed, and the maximum sum rate with non-convex constraint is converted into the maximum sum rate with convex constraint by relaxing non-convex constraint I phi i I to I i I, which is expressed as follows:
Where q 1 is the first order coefficient in the maximum sum rate form of variable θ 1, q 2 is the first order coefficient in the maximum sum rate form of variable θ 2, F 1 is the second order coefficient in the maximum sum rate form of variable θ 1, F 2 is the second order coefficient in the maximum sum rate form of variable θ 2, e m is the initial vector of 1 at the mth bit,
Diag (·) represents the matrix diagonalization of vectors, k is the current user index, r represents the index of the current intelligent reflection surface IRS, M r is the number of elements of the r-th intelligent reflection surface IRS, θ 2 represents the second intelligent reflection surface IRS2 reflection unit phase shift coefficient vector, θ 1 represents the first intelligent reflection surface IRS1 reflection unit phase shift coefficient vector, α is the auxiliary variable introduced by the lagrangian transformation, β is the auxiliary variable introduced by the quadratic transformation,Representing the value updated last time in the iterative process;
3b) Introducing a dual variable mu for the maximum sum rate with convex constraint, and performing Lagrange dual decomposition to obtain a closed solution of a phase shift coefficient vector theta * of a reflection unit on two intelligent reflection surfaces IRS;
3c) Bringing θ * into the maximum sum rate form with convex constraints and simultaneously converting this form into the classical semi-positive-definite programming SDP form using the matrix sulf;
(4) Optimizing the semi-positive setting SDP form through a computer optimization tool CVX tool box to obtain a first intelligent reflection surface IRS1 phase shift coefficient phi 1 and a second intelligent reflection surface IRS2 phase shift coefficient phi 2 in a single iteration process;
(5) Setting the maximum iteration number i max and the maximum iteration difference epsilon, and judging whether the iteration termination condition is met or not:
When the iteration number i exceeds the set iteration number i max or the difference between the sum rates formed by phi 1,Φ2 and W in two adjacent iteration processes is smaller than the maximum iteration difference epsilon, the iteration is ended, the final optimization result W * is obtained, And
Otherwise, let iteration number i=i+1, return to step (2).
2. The method of claim 1, wherein the baseband equivalent channel model obtained in step 1 a)The expression is as follows:
Wherein the method comprises the steps of Representing the channel from the first intelligent reflective surface IRS1 to user k,Representing the channel from the second intelligent reflective surface IRS2 to user k,Representing the channel of the second intelligent reflector IRS2 to the first intelligent reflector IRS1,Representing the channel of the access point AP to the first intelligent reflective surface IRS1,Represents the channel from the access point AP to the second intelligent reflection surface IRS2, phi 1 is the phase shift coefficient of the first intelligent reflection surface IRS1, phi 2 is the phase shift coefficient of the second intelligent reflection surface IRS2, and [ (H ] represents the conjugate transpose of the matrix.
3. The method according to claim 1, wherein the signal-to-interference ratio γ k and the user rate R obtained in step 1 b) are respectively expressed as follows:
R=log2(1+γk)
Wherein the method comprises the steps of Is the beamforming vector for user k,Is the beamforming vector of interfering user j,Σ 0 2 represents the noise power following a Complex Symmetric Complex Gaussian (CSCG) distribution for the equivalent baseband model of user k obtained in step 1 a).
4. The method according to claim 1, characterized in that the expression of the maximum sum rate obtained in step 1 b) is expressed as follows:
Where ω k is the beamforming vector for user k, w= [ ω 1,ω2,…,ωk,…,ωL ] is the transmit beamforming matrix, L is the total number of users in the system, W k is the weight of user k, γ k is the signal-to-interference ratio for user k, P T is the transmit power constraint for AP, Φ 1 is the phase shift coefficient for IRS1, Φ 1＝diag(θ1), Representing the phase shift angle of each reflective element on IRS1, M 1 representing the maximum number of elements on IRS 1; Φ 2＝diag(θ2) being the phase shift coefficient of IRS2,Representing the phase shift coefficient of each reflective element on IRS2, and M 2 represents the maximum number of elements on IRS 2.
5. The method according to claim 1, characterized in that the logarithmic sum is converted into a partial sum by lagrangian transformation in step1 c) as follows:
Wherein the method comprises the steps of Alpha k is the auxiliary variable introduced by the lagrangian transformation of step 1 c),For the equivalent baseband model for user k, ω k is the beamforming vector for user k, ω j is the beamforming vector for interfering user j, w k is the weight, σ 0 2 is the noise power, and γ k represents the signal-to-interference ratio for user k.
6. The method according to claim 1, wherein a closed-form solution of the reflection unit phase shift coefficient vector θ * on the two intelligent reflection surfaces IRS is obtained in step 3 b), expressed as follows:
Wherein theta 1 * is a phase shift coefficient vector of the first intelligent reflection surface IRS1 reflection unit, E m is an initial vector of 1 on the M-th bit, M represents an element index on the intelligent reflection surface IRS, mu 2,m is a dual variable of the M-th element on the second intelligent reflection surface, mu 1,m is a dual variable of the M-th element on the first intelligent reflection surface, M 2 represents the maximum number of elements on the IRS2, M 1 is the number of elements of IRS1, M 2 is the number of elements of IRS2, q 1 is a first-order coefficient in the maximum sum rate form of variable theta 1, q 2 is a first-order coefficient in the maximum sum rate form of variable theta 2, F 1 is a second-order coefficient in the maximum sum rate form of variable theta 1, and F 2 is a second-order coefficient in the maximum sum rate form of variable theta 2.
7. The method according to claim 1, characterized in that in step 3 c) a classical semi-positive programming SDP form is obtained, expressed as follows:
τr＝qr H(Fr+diag(μr))qr+tr(diag(μr));
Where τ r is the sum rate under the semi-positive rule of the r-th intelligent reflector IRS, Representing the dual variables introduced in the Lagrangian dual decomposition, r representing the index of the current intelligent reflection surface IRS, M r representing the number of elements on the r-th intelligent reflection surface IRS, M representing the index of elements on the intelligent reflection surface IRS, q r representing the first order coefficient in the maximum sum rate form of the variable θ r, F r representing the second order coefficient in the maximum sum rate form of the variable θ r, [. Cndot. T representing the transpose of the matrix.
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