Broadband three-dimensional forming beam coverage design method based on quasi-static intelligent reflecting surface

Abstract

The invention discloses a broadband three-dimensional forming beam coverage design method based on a quasi-static intelligent reflecting surface, and relates to the technical field of wireless communication. The low cost, low complexity and flexibility of the quasi-static intelligent reflecting surface are utilized to increase the adjustability which the static reflecting array does not have; according to the method, the target area angle range information of beam coverage is obtained, the beam coverage design is completed offline by using the alternating iterative optimization algorithm based on DC-SCA, real-time channel estimation is not needed, and the system overhead and the calculation complexity are reduced. And in combination with an IRS unit radiation pattern, forming beam coverage of differentiated gain requirements of a target area and balance of gains at different sub-band frequency points in a broadband communication scene are realized. In consideration of requirements of working frequency points, working bandwidth, quantization bits and the like, manual splicing is carried out by designing a proper QS-IRS unit pattern, and a large-scale reflection array is formed. The problems existing in the traditional communication technology are solved, actual factors are considered, and the method has important practical significance and application value.

Description

Technical Field

[0001] The invention relates to the technical field of wireless communications, and in particular to a broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflecting surface. Background Art

[0002] Intelligent Reflecting Surface (IRS), also known as Reconfigurable Intelligent Surface (RIS) or metasurface, is expected to improve communication coverage and quality in the next generation of mobile communication networks. Therefore, in recent years, IRS hardware and beamforming design, channel modeling and channel estimation, as well as network performance and deployment optimization analysis have received extensive attention and research. It is worth noting that IRS can establish a virtual line of sight (LoS) link when the base station and the user area are severely blocked to enhance communication coverage and communication quality. However, in order to compensate for the impact of double-segment path loss, a large number of IRS reflection units are usually required, which may bring greater cost and complexity overhead, and also put forward higher requirements for large-scale IRS deployment and optimization.

[0003] At present, IRS is usually composed of electronic components such as PIN diodes or MEMS switches and control circuits, and different state responses are achieved by connecting external controllers such as FPGA (B. Rana, et al., "Review paper on hardware of reconfigurable intelligent surfaces," IEEE Access, vol. 11, pp. 29614–29634, 2023). Its cost includes the manufacturing of reflective elements, control circuits and controllers, as well as the power supply required for system operation. Its overall cost is high, and the number of units in a single IRS panel is limited. On the other hand, in order to achieve dynamic adjustment of the beam, real-time channel estimation and fast optimization algorithms are required as support, so the hardware cost, system overhead and implementation complexity are high. In contrast, the traditional static reflect array is composed of fixedly arranged units to achieve fixed beam functions. It does not require an external controller for real-time beam adjustment, so its hardware implementation complexity and manufacturing cost are relatively low. However, due to the different environmental parameters covered by the beam, the required beamforming vectors are also different. In order to meet different coverage requirements, each time, it is necessary to independently open molds and design static reflective arrays that meet the requirements according to the respective environmental parameters. Once the design and manufacturing are completed, they cannot be reconstructed and adjusted, and the flexibility is poor, making it difficult to achieve large-scale mass production. Therefore, the overall manufacturing cost is still high. In particular, whether it is a dynamically adjustable IRS or a static reflective array, it is usually composed of a large number of units to form an overall panel, and is manufactured in an integrated mold, which has high requirements on the manufacturing process, and the overall failure rate and failure cost are high.

[0004] At present, some literature has studied the deployment of IRS to achieve beam coverage in the target area. For example, the literature (J.Wang,etal.,“Transparent RIS:Wireless coverage enhancement via region-oriented passive beamforming,”IEEE Trans.Wireless Commun.,pp.1–1,2024) introduces in detail the research status and representative achievements of coverage-oriented IRS, and proposes a transparent IRS design without changing the original system transmission protocol. The literature (X.Lin,et al.,“On the design of broad beam of reconfigurable intelligent surface,”IEEE Trans.Commun.,vol.72,no.5,pp.3079–3094,2024) realizes a wide beam with maximum and equal power gain in a predefined angle region through a semi-positive programming algorithm based on convex difference. The literature (W.Ma, L.Zhu, and R.Zhang, "Passive beamforming for 3-D coverage in IRS-assisted communications," IEEE Wireless Communications Letters, vol.11, no.8, pp.1763–1767, 2022) proposed a passive beamforming design based on matrix lifting and linear matrix inequality technology to achieve the minimum coverage beamforming gain of the target area. The literature (H.Lu, et al., "Aerial intelligent reflecting surface: Joint placement and passive beamforming design with 3D beam flattening," IEEE Trans. Wireless Commun., vol.20, no.7, pp.4128–4143, 2021) proposed a subarray-based beam broadening and flattening technology to achieve IRS phase shift design and three-dimensional beam coverage of the target area.The literature (M.He, et al., "RIS-assisted quasi-static broad coverage for wideband mmwave massive MIMO systems," IEEE Trans. Wireless Commun., vol. 22, no. 4, pp. 2551–2565, 2023) proposed a low-overhead quasi-static broad coverage based on statistical CSI and designed a framework to synthesize the power pattern of IRS. However, the above studies rarely pay attention to the design of beam shape.

[0005] QS-IRS is mainly used to improve the performance of wireless communication systems. Consider using large-scale QS-IRS to achieve broadband three-dimensional beamforming coverage of the target area. When there are multiple frequency components in the broadband system, it will cause serious changes in time delay and phase difference, resulting in the influence of broadband effects such as beam broadening and pointing deviation. In addition, due to the lack of digital signal processing capabilities, each IRS unit can only provide an adjustable phase shift for different frequency components, so how to achieve the phase shift trade-off between multiple frequency components is very challenging (Y.Chen, D.Chen, and T.Jiang, "Beam-squintmitigating in reconfigurable intelligent surface aided wideband mmwavecommunications," in 2021IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2021, pp. 1–6). On the other hand, since QS-IRS does not have power amplification function, its phase modulation capability is limited by constant modulus constraints. One of the common practices is to transform the non-convex problem with constant modulus constraints into a common semi-positive definite programming convex problem, and then solve it using CVX based on the interior point method, with a complexity of (M.Fu,et al.,“Reconfigurable intelligent surface empowered downlinknon-orthogonal multipleaccess,”IEEE Transactions on Communications,vol.69,no.6,pp.3802–3817,2021),where M represents the number of reflection units. Therefore, when the number of QS-IRS units increases to a certain scale, the computational complexity becomes very large, which is not conducive to the large-scale or ultra-large-scale integrated deployment of QS-IRS. Therefore, it is particularly important to design a low-complexity algorithm that can achieve large-scale or ultra-large-scale QS-IRS broadband three-dimensional shaping beam coverage. Summary of the invention

[0006] The purpose of the present invention is to provide a low-cost, low-complexity, flexible and adjustable broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflector, in view of the high complexity of the common algorithms for implementing broadband three-dimensional shaping beam coverage in the prior art due to large-scale or ultra-large-scale deployment of QS-IRS, and the problem that the influence of unit radiation pattern gain at different positions cannot be ignored. The present invention considers the influence of IRS unit radiation pattern gain at different user positions and proposes a low-complexity algorithm based on alternating iterative optimization. This algorithm reduces the computational complexity from Reduced to Where M = M y ×M z , achieving low-complexity beamforming optimization for large-scale QS-IRS. The proposed method also meets the broadband beam requirements in typical wireless communication scenarios.

[0007] The present invention provides a broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflecting surface, comprising the following steps:

[0008] 1) Establish a system model and calculate system-related parameters; construct a broadband far-field communication scenario in which a QS-IRS is deployed at a certain altitude to serve a ground target area, and calculate system-related parameters including direction vector, array steering vector, channel, and received power;

[0009] 2) Set up a reference system and derive the relative power gain γ of the QS-IRS array; Set up a reference system, analyze the changes in user received power, and calculate the relative power gain of the QS-IRS with respect to the reference system;

[0010] 3) Construct optimization objectives and optimization problems: Design a beamforming beam that meets the gain requirements at different locations in the target area, perform discrete sampling, define the mask of the beamforming beam in the target area, and maximize the common beam gain of the target area while keeping the difference between the beam gain in the target area and the beam gain in the non-target area constant, thus constructing an optimization problem;

[0011] 4) Design an alternating iterative optimization algorithm based on DC-SCA; upgrade the constant modulus constraint of the beamforming vector in the optimization problem to a semi-positive definite beamforming matrix with rank 1, use a DC-SCA-based method to solve the non-convex constraints in the optimization problem, and gradually approach the optimal solution of the problem through an alternating iterative method to obtain a beamforming vector that meets the requirements and achieve optimal control of the panel phase;

[0012] 5) Quantization selection and large-scale splicing: According to the system's operating frequency, operating bandwidth, and quantization bit requirements, the QS-IRS is quantized and selected. The unit and rotation angle are selected according to the phase distribution, and large-scale splicing is performed.

[0013] In step 1), the specific method of establishing the system model and calculating the system related parameters is as follows: construct a broadband far-field communication scenario in which a QS-IRS is deployed at a certain height to serve the ground target area; the deployment positions of the base station BS and the QS-IRS are fixed, and the BS is equipped with a single directional antenna, and its maximum power gain direction points to the QS-IRS, and the maximum power gain is G t ; Establish a three-dimensional Cartesian coordinate system with the first unit of QS-IRS as the origin. QS-IRS is placed in the yoz plane. The number of units is M = M y ×M z , M y and M z represents the number of cells along the y-axis and z-axis; it is assumed that the direct link between the BS and the target area is severely blocked and can be ignored, and communication is only carried out through the LoS link constructed by QS-IRS; it is assumed that the horizontal angle incident on the QS-IRS plane is The pitch angle is θ i , denoted as The horizontal angle of the reflected signal is obtained based on the angle range information of the target area covered by the QS-IRS beam and the pitch angle θ r , denoted as According to the angular relationship of the three-dimensional Cartesian coordinate system, the incident direction vector u is derived i and the reflection direction vector u r ; From this, the sub-band frequency can be calculated as f k The receiving array steering vector of the signal on the QS-IRS array is The reflect array steering vector is Therefore, the array steering vector generated by the signal passing through the QS-IRS array can be expressed as a(Ω i ,Ω r , f k )=a i (Ω i , f k )⊙a r (Ω r , f k ), where ⊙ represents the Hadamard product; on the other hand, the receiving array steering vector a of the QS-IRS array i (Ω i , f k ) can be decomposed into array steering vectors along the y-axis and z-axis and The Kronecker product of in represents the Kronecker product; similarly, the reflect array steering vector a r (Ω r , f k ) can also be decomposed and expressed as Therefore, the array steering vector generated by the linear array of the signal decomposed along the y-axis by QS-IRS can be expressed as a y (Ω i ,Ω r , f k )=a iy (Ω i , f k )⊙a ry (Ω r , f k ); Similarly, the array steering vector generated by the linear array decomposed along the z-axis is a z (Ω i ,Ω r , f k )=a iz (Ω i , f k )⊙a rz (Ω r , f k ); Assuming that the normalized radiation pattern of the QS-IRS unit is F(Ω), the radiation pattern gain of the QS-IRS unit can be calculated as G according to the angles of signal incidence and reflection. 2 F(Ω i )F(Ω r ); Assuming the channel is a free space path loss model, the channels from BS to QS-IRS and from QS-IRS to the target area can be expressed as and Assume that the phase shift matrix of QS-IRS is expressed as in represents the phase compensation of the mth reflection unit; assuming that the BS antenna transmit power is P t Therefore, the received power P of a user at a certain location in the target area r (Ω i ,Ω r , f k )for:

[0014]

[0015] in,(·) T represents transpose, represents the gain generated by the BS antenna and the QS-IRS unit radiation pattern, β represents the large-scale free space path loss of the cascaded channel; definition is the beamforming vector of the QS-IRS array, which can be expressed by the component along the y-axis and the z-axis component The Kronecker product is composed of

[0016] In step 2), the specific method is: set up a reference system, where the BS transmitting antenna is a single omnidirectional antenna, the QS-IRS is composed of only a single reflection unit, and the influence of the unit radiation pattern gain is not considered; under the same initialization parameters, the received power of the user at the same position in the reference system can be expressed as: P r0 (Ω i ,Ω r , f k )=P t β; The relative power gain of QS-IRS with respect to the reference system can be expressed as:

[0017]

[0018] In step 3), the specific method of constructing the optimization target and the optimization problem is: designing a shaped beam that meets the gain requirements at different positions in the target area; in order to facilitate the numerical realization of the problem, the horizontal angle and the pitch angle Ω of the reflected signal are r Discrete sampling is performed at equal intervals of every 10°; therefore, the continuous angles of the target area are discretely sampled as p∈P, where the set P contains all angle sampling combinations of the target area; the continuous angles of the non-target area are discretely sampled as q∈Q, where the set Q contains all angle sampling combinations of non-target areas; the mask of the beamforming in the target area is defined as d(Ω p , f k ); The problem requires that the difference between the beam gain in the target area and the beam gain in the non-target area is δ, and the common beam gain ρ in the target area is maximized; therefore, the optimization problem can be constructed as:

[0019]

[0020] |w y [m y ]|=1,m y =1,2,,M y

[0021] |w z [m z ]|=1,mz=1,2,,M z

[0022] Among them, m y and m z represents the cell index along the y-axis and z-axis, |w y [m y ]|=1 and |w z [m z ]|=1 indicates that the beamforming vectors along the y-axis and the z-axis satisfy the constant modulus constraint.

[0023] In step 4), the specific steps of designing the alternating iterative optimization algorithm based on DC-SCA can be as follows: observing the optimization problem constructed in step 3), it can be seen that the relative power gain components of the array along the y-axis and the z-axis are coupled with each other; at the same time, the unit radiation pattern gain obtained at different positions is also different, and it is impossible to decompose it into independent components along the y-axis and the z-axis for consideration; in order to reduce the complexity of problem solving, an alternating iterative optimization algorithm is used for solving; in step 4), the specific algorithm is:

[0024] 4.1) Transform the constant modulus non-convex constraints of the optimization problem in step 3)

[0025] In step 4.1), the specific method is: the beamforming vector w along the y-axis and the z-axis is y and w z Lifted to a rank-1 positive semidefinite matrix and in(·) H represents the conjugate transpose; therefore, the optimization problem in step 3) can be equivalently rewritten as:

[0026]

[0027] stn(Ω i ,Ω p )Re(Tr(A y (Ω i ,Ω p ,f k )W y ))Re(Tr(A z (Ω i ,Ωp ,f k )W z ))≥ρd(Ω p ,f k ), p∈P

[0028] η(Ω i ,Ω q )Re(Tr(A y (Ω i ,Ω q ,f k )W y ))Re(Tr(A z (Ω i ,Ωq,f k )W z ))≤ρ / δ,q∈Q

[0029] W y [m y , m y ]=1,m y =1,2,…,M y , rank(W y )=1,

[0030] W z [m z , m z ]=1,m z =1,2,…,M z , rank(W z )=1,

[0031] Among them, Tr(·) represents the trace, Re(·) represents the real part, (·) * It means taking conjugate;

[0032] 4.2) Process the coupling variable W in step 4.1) of the optimization problem y and W z

[0033] In step 4.2), the specific method is: given an initialized semi-positive definite matrix W that satisfies the constant modulus constraint z , at this time the optimization problem is only about the variable W y; Then, the rank(·)=1 non-convex constraint is converted into a convex constraint by using the method based on Difference of Convex (DC) and Successive Convex Approximation (SCA); CVX is then used to find the y-axis component beamforming matrix W of the QS-IRS approximation optimal at this time y ; Then the solved W y As a given value, the optimization problem is only about the variable W z , the DC-SCA-based method is used again to transform the non-convex constraints, and CVX is used to solve the z-axis component beamforming matrix W that is approximately optimal for QS-IRS at this time z ; At this point, the algorithm has achieved a round of alternating iterations;

[0034] 4.3) Repeat step 4.2); after the preset maximum number of alternating iterative optimization times N, observe the convergence of the target gain ρ, and finally solve the approximate optimal beamforming matrix W of the QS-IRS along the y-axis and z-axis that meets the requirements y and W z ; In order to obtain the beamforming vector w of the entire array, it is only necessary to replace W y and W z Make the Kronecker product and then perform eigenvalue decomposition, and take the eigenvector corresponding to the maximum eigenvalue as the approximate optimal beamforming vector w of the entire array, and then the phase arrangement of the entire panel can be obtained.

[0035] In step 5), the specific steps of the quantitative selection and large-scale splicing may be:

[0036] 5.1) Quantization selection: Design or select the unit style of QS-IRS according to the system's operating frequency, operating bandwidth and quantization bit requirements; ensure that the selected unit can provide the required phase control range and accuracy within the specified frequency band; for example, for a specific operating frequency and bandwidth, it may be necessary to select units with specific sizes and structures to ensure that they can exhibit good electrical performance within the frequency band;

[0037] 5.2) Selecting units and rotation angles according to phase distribution: According to the phase distribution obtained in step 4), select corresponding units and their rotation angles to achieve corresponding discrete phases; convert the continuous phase values ​​obtained by the optimization algorithm into actually achievable discrete phase values;

[0038] 5.3) Unit splicing and assembly: Attach the corresponding units to the wall or acrylic back panel. The acrylic back panel can be attached with copper film or aluminum film to enhance the reflective performance. In this way, a large-scale reflective array can be manually assembled and deployed to the corresponding position. During the splicing and assembly process, ensure that the units are arranged closely and according to the predetermined design layout to ensure the performance of the entire array.

[0039] The present invention designs a broadband three-dimensional shaping beam coverage scheme for a target area. First, a system model is established and the channel model and the relative power gain of a certain position in the target area are determined according to the angle range information of the target area and system-related parameters. Secondly, the beam shape is designed according to the gain requirements at each position and the corresponding optimization problem is constructed. Next, the constant modulus constraint of the beamforming vector in the optimization problem is promoted to a semi-positive definite beamforming matrix with a rank of 1. Then, a DC-SCA-based method is used to solve the non-convex constraints in the optimization problem. Finally, an alternating iterative optimization algorithm is used to achieve broadband three-dimensional shaping beam coverage of the target area. Compared with the prior art, the present invention has the following outstanding advantages:

[0040] 1. The present invention proposes the concept of QS-IRS and a method of unit segmentation, multiplexing, and large-scale splicing, aiming to take advantage of ultra-low-cost reflective units and manual splicing, rotate or mirror units of different patch shapes or sizes, and achieve different discrete phases with as few unit styles as possible, which is conducive to the mass production of units. Then, according to the array phase arrangement requirements, the corresponding patch units and their rotation angles are selected and manually spliced ​​into a large-scale reflective array. Therefore, the manufacturing cost and overall failure rate are greatly reduced, the beam coverage of a specific target area is achieved, and the flexibility of later adjustment is also achieved.

[0041] 2. The QS-IRS three-dimensional beam coverage design proposed in the present invention does not require real-time CSI acquisition, and is intended to cover a target area with a relatively fixed beam coverage position. Even if the target area changes, it only needs to obtain the latest target area angle information and calculate the beamforming vector at this time, and it can be reused, which has good flexibility.

[0042] 3. The present invention takes into account the actual broadband wireless communication scenario and the influence of the QS-IRS unit radiation pattern gain, and proposes a forming beam design that can meet a certain working bandwidth and meet the gain requirements of different positions in the target area.

[0043] 4. Based on the low cost and easy large-scale deployment of QS-IRS, the present invention proposes a low-complexity alternating iterative optimization algorithm suitable for large-scale beamforming. Reduced to BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 4 is a system model diagram of an embodiment of the present invention.

[0045] Figure 2 FIG. 4 is a schematic diagram of a beamforming according to an embodiment of the present invention.

[0046] Figure 3 The figure is a design flow chart of an embodiment of the present invention.

[0047] Figure 4 This is a diagram of the coverage gain effect of three-dimensional flat-shaped beam in a broadband system.

[0048] Figure 5 This is a diagram of the flat beamforming gain effect at different sub-band frequencies.

[0049] Figure 6 is the gain change at different sub-band frequencies.

[0050] Figure 7 Comparison of system gain performance under different schemes and scenarios.

[0051] Figure 8 The gain change curve for different scenarios as the number of units increases.

[0052] Fig. 9 It is the discrete phase quantization error analysis.

[0053] Fig.10 It is a 2-bit discrete phase distribution diagram. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0055] In order to balance cost, complexity and flexibility, the present invention proposes a quasi-static intelligent reflector (QuasiStatic IRS, QS-IRS) concept, which not only retains the minimum adjustability, but also can achieve low-cost unit reuse and mass production. Specifically, the QS-IRS proposed in the present invention is composed of units of different patch shapes or sizes. Different discrete phases can be achieved by rotating or mirroring the units, such as Figure 1 In particular, unlike typical integrated panel design and manufacturing, the present invention proposes a method of unit segmentation and multiplexing, which uses as few unit styles as possible to achieve a 360° full range of multi-bit discrete phases through rotation or mirroring operations. Figure 1As shown in the figure, a 90° phase difference can be achieved through different patch shapes (such as the size of the open loop), and a 180° phase difference can be achieved through mirroring, thereby achieving four phases (2 bits) of 0°, 90°, 180°, and 270°. Further, through unit segmentation and multiplexing, only two styles need to be mass-produced, such as Figure 1 As shown in Figure (a) and Figure (c) in the small figure in the upper right corner. Based on the designed unit style and the array phase arrangement requirements, the units are manually spliced ​​and pasted on the wall surface (or acrylic backplane) to form an ultra-large-scale reflective array. This unit segmentation and reuse method combined with the manual splicing solution enables unit mass production, greatly reducing costs and the failure rate of the overall panel. At the same time, because it is manually adjustable, simple to assemble, and can be adjusted later, the splicing method of the reflective unit can be flexibly changed according to different beam coverage requirements and the corresponding propagation environment to achieve beam coverage of specific target areas.

[0056] The embodiment of the present invention includes the following steps:

[0057] 1) Establish a system model and calculate system-related parameters; construct a broadband far-field communication scenario in which a QS-IRS is deployed at a certain height to serve a ground target area. The deployment locations of the fixed base station BS (Base Station) and the QS-IRS are fixed. The BS is equipped with a single directional antenna with its maximum power gain pointing to the QS-IRS. The maximum power gain is G t .like Figure 1 As shown, a three-dimensional Cartesian coordinate system is established with the first unit of QS-IRS as the origin. QS-IRS is placed in the yoz plane, and the number of units is M = M y ×M z , M y and M z represents the number of cells along the y-axis and z-axis. Assume that the direct link between the BS and the target area is severely blocked and can be ignored, and only the LoS link constructed by the QS-IRS is used for communication. Assume that the horizontal angle incident on the QS-IRS plane is The pitch angle is θ i , denoted as The horizontal angle of the reflected signal is obtained based on the angle range information of the target area covered by the QS-IRS beam and the pitch angle θ r , denoted as According to the angular relationship of the three-dimensional Cartesian coordinate system, the incident direction vector u is derived i and the reflection direction vector u r . From this, we can calculate the sub-band frequency as f k The receiving array steering vector of the signal on the QS-IRS array is The reflect array steering vector is Therefore, the array steering vector generated by the signal passing through the QS-IRS array can be expressed as a(Ω i ,Ω r , f k )=a i (Ω i , f k )⊙a r (Ω r , f k ), where ⊙ represents the Hadamard product. On the other hand, the receiving array steering vector a of the QS-IRS array i (Ω i , f k ) can be decomposed into array steering vectors along the y-axis and z-axis and The Kronecker product of in, represents the Kronecker product. Similarly, the reflect array steering vector a r (Ω r , f k ) can also be decomposed and expressed as Therefore, the array steering vector generated by the linear array of the signal decomposed along the y-axis by QS-IRS can be expressed as a y (Ω i ,Ω r , f k )=a iy (Ω i , f k )⊙a ry (Ω r , f k ). Similarly, the array steering vector generated by the linear array decomposed along the z-axis is a z (Ω i ,Ω r , f k )=a iz (Ω i , f k )⊙a rz (Ω r , f k ). Assuming that the normalized radiation pattern of the QS-IRS unit is F(Ω), the radiation pattern gain of the QS-IRS unit can be calculated as G according to the angles of signal incidence and reflection. 2 F(Ω i )F(Ω i ). Assuming the channel is a free space path loss model, the channels from BS to QS-IRS and from QS-IRS to the target area can be expressed as and Assume that the phase shift matrix of QS-IRS is expressed as in represents the phase compensation of the mth reflection unit. Assume that the BS antenna transmit power is P t Therefore, the received power P of a user at a certain location in the target area is r (Ω i ,Ω r , f k )for:

[0058]

[0059] in,(·) T represents transpose, represents the gain produced by the BS antenna and the QS-IRS unit radiation pattern, and β represents the large-scale free-space path loss of the cascaded channel. is the beamforming vector of the QS-IRS array, which can be expressed by the component along the y-axis and the z-axis component The Kronecker product is composed of

[0060] 2) Set up a reference system and derive the relative power gain γ of the QS-IRS array; Set up a reference system where the BS transmitting antenna is a single omnidirectional antenna, the QS-IRS consists of only a single reflection unit, and the influence of the unit radiation pattern gain is not considered. Therefore, under the same initialization parameters, the received power of the user at the same position in the reference system can be expressed as: P r0 (Ω i ,Ω r , f k )=P t β. Therefore, the relative power gain of QS-IRS with respect to the reference system can be expressed as:

[0061]

[0062] 3) Construct the optimization target and optimization problem; design a beamforming method that meets the gain requirements at different locations in the target area. In order to facilitate the numerical implementation of this problem, the horizontal angle and elevation angle Ω of the reflected signal are r Discrete sampling is performed at equal intervals of every 10°. Therefore, the continuous angles of the target area are discretely sampled as p∈P, where the set P contains all angle sampling combinations of the target area. The continuous angles of the non-target area are discretely sampled as q∈Q, where the set Q contains all angle sampling combinations of non-target areas. The mask of the beamforming in the target area is defined as d(Ω p , f k ). The problem requires that the difference between the beam gain in the target area and the beam gain in the non-target area is δ, while maximizing the common beam gain ρ in the target area; therefore, the optimization problem can be constructed as:

[0063]

[0064] |w y [m y ]|=1,m y =1,2,...,M y

[0065] |w z [m z ]|=1,m z =1,2,...,M z

[0066] Among them, m y and m z represents the cell index along the y-axis and z-axis, |w y [m y ]|=1 and |w z [m z ]|=1 indicates that the beamforming vectors along the y-axis and the z-axis satisfy the constant modulus constraint.

[0067] 4) Design an alternating iterative optimization algorithm based on DC-SCA; Observing the optimization problem constructed in step 3), it can be seen that the relative power gain components of the array along the y-axis and the z-axis are coupled with each other; at the same time, the unit radiation pattern gain obtained at different positions is also different, and it is impossible to decompose it into independent components along the z-axis and the z-axis for consideration. In order to reduce the complexity of problem solving, the present invention adopts an alternating iterative optimization algorithm for solution. In step 4), the specific algorithm is:

[0068] 4a) Convert the constant modulus non-convex constraints of the optimization problem in step 3)

[0069] In step 4a), the specific method is: the beamforming vector w along the y-axis and the z-axis is y and w z Lifted to a rank-1 positive semidefinite matrix and in(·) H represents the conjugate transpose. Therefore, the optimization problem in step 3) can be equivalently rewritten as:

[0070]

[0071] stη(Ω i ,Ω p )Re(Tr(A y (Ω i ,Ω p ,f k )W y ))Re(Tr(A z (Ωi ,Ω p ,f k )W z ))≥ρd(Ω px f k ), p∈P

[0072] η(Ω i ,Ω q )Re(Tr(A y (Ω i ,Ω q ,f k )W y ))Re(Tr(Az(Ω i ,Ω q ,f k )W z ))≤ρ / δ,q∈Q

[0073] W y [m y , m y ]=1,m y =1,2,…,M y , rank(W y )=1,

[0074] W z [m z , m z ]=1,m z =1,2,…,M z , rank(W z )=1,

[0075] Among them, Tr(·) represents the trace, Re(·) represents the real part, (·) * Indicates conjugation.

[0076] 4b) Processing step 4a) of the optimization problem of the coupled variable W y and W z

[0077] In step 4b), the specific method is: given an initialized semi-positive definite matrix W that satisfies the constant modulus constraint z , at this time the optimization problem is only about the variable W yThen, the non-convex constraint of rank(·)=1 is converted into a convex constraint using the method based on Difference of Convex (DC) and Successive Convex Approximation (SCA). Then, CVX is used to find the y-axis component beamforming matrix W of the QS-IRS approximation optimal at this time. y Then the solved W y As a given value, the optimization problem is only about the variable W z , the DC-SCA-based method is used again to transform the non-convex constraints, and CVX is used to solve the z-axis component beamforming matrix W that is approximately optimal for QS-IRS at this time z At this point, the algorithm has completed a round of alternating iterations.

[0078] 4c) Repeat step 4b). After the preset maximum number of alternating iterative optimization times N, observe the convergence of the target gain ρ, and finally solve the approximate optimal beamforming matrix W of the QS-IRS along the y-axis and z-axis that meets the requirements. y and W z In order to obtain the beamforming vector w of the entire array, it is only necessary to replace W y and W z Make the Kronecker product and then perform eigenvalue decomposition, and take the eigenvector corresponding to the maximum eigenvalue as the approximate optimal beamforming vector ω of the entire array, and then the phase arrangement of the entire panel can be obtained.

[0079] 5) Quantization selection and large-scale splicing: Design or select the QS-IRS unit style according to the requirements of working frequency, working bandwidth, and quantization bit. Then, according to the phase distribution obtained in step 4), select the corresponding unit and its rotation angle to achieve the corresponding discrete phase. Then attach the corresponding unit to the wall or acrylic backplane (the acrylic backplane can be attached with copper film or aluminum film to enhance the reflection performance), and manually assemble it into a large-scale reflection array and deploy it to the corresponding position.

[0080] A specific embodiment is given below.

[0081] 1. Establishment of system model:

[0082] Consider a broadband far-field communication scenario where a QS-IRS is deployed at a certain height to serve a ground target area. Assume that the base station BS and the QS-IRS are fixed in position, the BS is equipped with a single directional antenna with its maximum power gain pointing to the QS-IRS, and a single omnidirectional antenna is deployed in the target area. Consider a unit with M=M y ×M zThe passive QS-IRS serves a relatively fixed target area. Assume that the communication link between the BS and the target area is severely blocked by obstacles, so the communication between the BS and the target area is only supported by the cascade link constructed by the QS-IRS. Figure 1 As shown in the figure, a three-dimensional Cartesian coordinate system is established with the reflection unit at the lower left corner of the QS-IRS as the origin of the coordinates, and the QS-IRS is placed in the yoz plane. Since the positions of the BS and the QS-IRS are fixed and the incident signal is emitted along the direction of the maximum power gain of the BS antenna, the horizontal angle and elevation angle of the BS transmission signal reaching the QS-IRS plane are determined as follows: and θ i , denoted as The distance between BS and QS-IRS is d1. Similarly, according to the angle range information of the ground target area that QS-IRS needs to serve, the horizontal angle of the reflected signal is and pitch angle Recorded as The distance between QS-IRS and the target area user is d2. Assume that the maximum power gain of BS transmitting antenna is G t , the maximum power gain of the QS-IRS unit is G, and the normalized radiation pattern of the QS-IRS unit can be expressed as (W. Tang et al., "Wireless communications with reconfigurable intelligent surface: Path loss modeling and experimental measurement," IEEE Trans. Wireless Commun., vol. 20, no. 1, pp. 421–439, 2021):

[0083]

[0084] 2. Achieve goals:

[0085] like Figure 2 As shown in the figure, since the channels at different locations in the target area are usually different, the requirements for beam gain of users at different locations are also different. In addition, the unit radiation pattern gain obtained by IRS for users at different locations is also different. However, most of the existing literature on IRS beamforming does not consider the influence of the unit radiation pattern, that is, the unit radiation pattern will significantly affect the response of IRS to incident and outgoing signals at different locations and the three-dimensional coverage performance of the system. For this reason, it is of great practical significance to design a customized shaping beam coverage solution that can match the size of the target area and the gain intensity requirements at different locations in the area. In addition, in view of the needs of typical broadband wireless communication scenarios, the designed solution also needs to meet certain working bandwidth requirements.

[0086] The present invention aims to achieve large-scale QS-IRS three-dimensional beamforming coverage in broadband communication scenarios. Specifically, the unit radiation pattern gain at different positions is taken into account, and the formed beam can cover the entire target area while meeting the gain requirements at different positions in the target area. By setting a certain gain difference δ between the target area and the non-target area, the useless energy in the non-target area is suppressed, and the useful energy is concentrated in the target area as much as possible, thereby maximizing the common beam gain ρ at different positions in the target area.

[0087] 3. Specific implementation process:

[0088] To achieve the goal in step (2), this embodiment mainly controls three variables: the number of QS-IRS units, the angle range of the target area, and the working bandwidth of the broadband system.

[0089] A) Calculation system related parameters

[0090] Fixed the positions of BS and QS-IRS, it can be known that the horizontal angle and elevation angle of the signal incident on QS-IRS are and θ i (i.e., the angle range of the target area), denoted as The distance between BS and QS-IRS is d1. Similarly, according to the angle range information of the target area that QS-IRS needs to serve, the horizontal angle and elevation angle of the reflected signal are and θ r , denoted as The distance between QS-IRS and the target area is d2. According to the initialization parameters, a three-dimensional Cartesian coordinate system is established with the lower left corner unit of QS-IRS as the origin. According to the three-dimensional angle relationship, the direction vector of the incident signal can be derived as follows: The direction vector of the reflected signal is Therefore, the subband frequency in the broadband system is f k The receiving array steering vector of the signal on the QS-IRS array can be expressed as The reflect array steering vector can be expressed as in(·) T Indicates taking the transpose, r m , m = 1, ..., M represents the position vector of the mth reflection unit. Therefore, the array steering vector generated by the signal passing through the QS-IRS array can be expressed as a(Ω i ,Ω r , f k )=a i (Ω i , f k )⊙a r (Ω r , f k). In addition, the receiving array steering vector a of the QS-IRS array i (Ω i , f k ) can be decomposed into the receiving steering vector a along the y-axis and z-axis arrays iy (Ω i , f k ) and a iz (Ω i , f k ), where Similarly, the reflection guide vectors along the y-axis and z-axis arrays can be obtained: as well as Therefore, the array steering vector generated by the signal along the y-axis array through the QS-IRS can be expressed as a y (Ω i ,Ω r , f k )=a iy (Ω i , f k )⊙a ry (Ω r , f k ), the array steering vector generated along the z-axis can be expressed as a z (Ω i ,Ω r , f k )=a iz (Ω i , f k )⊙a rz (Ω r , f k ). Assume that the phase shift matrix of QS-IRS is expressed as in represents the phase compensation of the mth reflection unit. Assuming the channel is a free space path loss model, the channels from BS to QS-IRS and from QS-IRS to the target area can be expressed as follows:

[0091]

[0092] Assume that the BS transmit power is P t , then the received power P of the user at a certain position in the target area r (Ω i ,Ω r , f k )for:

[0093]

[0094] in, represents the gain produced by the BS antenna and the QS-IRS unit radiation pattern, Represents the large-scale free-space path loss of the concatenated channel. Definition is the beamforming vector of the QS-IRS array. It can be decomposed into components along the y-axis and z-axis, expressed as in Each satisfies the constant modulus constraint.

[0095] B) Setting up the reference system and deriving the relative power gain γ of the QS-IRS array

[0096] Set up the reference system: The BS transmitting antenna is a single omnidirectional antenna, the QS-IRS consists of only a single reflection unit, and the influence of the unit radiation pattern gain is not considered. Therefore, under the same initialization parameters, the received power of the user at the same position in the reference system can be expressed as: P r0 (Ω i ,Ω r , f k )=P t β. Therefore, the relative power gain of the QS-IRS array with respect to the reference system can be expressed as:

[0097]

[0098] C) Construct optimization objectives and optimization problems

[0099] The optimization goal is to make the formed beam cover the entire target area and meet the gain requirements of different positions in the target area, while suppressing the useless energy in the non-target area and concentrating the useful energy in the target area as much as possible. r Discrete sampling is performed at equal intervals of every 10°. Therefore, the continuous angles of the target area are discretely sampled as p∈P, where the set P contains all angle sampling combinations of the target area. The continuous angles of the non-target area are discretely sampled as q∈Q, where the set Q contains all angle sampling combinations of non-target areas. Assume that the mask of the beamforming in the target area is d(Ω p , f k ), the waveform formed by its value can be expressed as the shape of the required beam. By setting a certain gain difference δ between the target area and the non-target area, the energy of the non-target area can be suppressed as much as possible, while maximizing the common beam gain ρ at different positions in the target area. The specific optimization problem can be modeled as follows:

[0100]

[0101] |w y [m y ]|=1,my=1,2,...,My

[0102] |w z [m z ]|=1,m z =1,2,...,M z

[0103] D) Design of alternating iterative optimization algorithm based on DC-SCA

[0104] From the above optimization problem, we can see that the relative power gain components of the array along the y-axis and the z-axis are coupled with each other; at the same time, the unit radiation pattern gain obtained at different positions is also different, and it is impossible to decompose it into independent components along the y-axis and the z-axis for consideration. Therefore, in order to effectively reduce the complexity of problem solving, the present invention adopts an alternating iterative optimization algorithm for solving. In view of the constant modulus non-convex constraint in the optimization problem, the QS-IRS beamforming vector w is firstly y and w z Lifted to a rank-1 positive semidefinite matrix and in(·) H represents the conjugate transpose. Therefore, the optimization problem is equivalently rewritten as:

[0105]

[0106] stη(Ω i ,Ω p )Re(Tr(A y (Ω i ,Ω p ,f k )W y ))Re(Tr(A z (Ω i ,Ω p ,f k )W z ))≥ρd(Ω p ,f k ), p∈P

[0107] η(Ω i ,Ω q )Re(Tr(A y (Ω i ,Ω q ,f k )W y ))Re(Tr(A z (Ω i ,Ω q ,f k )W z ))≤ρ / δ,q∈Q

[0108] Wy [m y , m y ]=1,m y =1,2,…,M y , rank(W y )=1,

[0109] W z [m z , m z ]=1,m z =1,2,…,M z , rank(W z )=1,

[0110] Among them, Tr(·) represents the trace, Re(·) represents the real part, (·) * Then, for the rank-one non-convex constraint in the above optimization problem, the DC technique is used to convert it into:

[0111]

[0112] where ||·|| * represents the nuclear norm of the matrix, which is equal to the sum of all eigenvalues ​​of the matrix, and ||·||2 represents the spectral norm of the matrix, which is equal to the largest eigenvalue of the matrix. In addition, in order to deal with the coupling variable W y and W z , using an alternating iterative optimization algorithm, specifically given an initialized semi-positive definite matrix W that satisfies the diagonal elements to be 1 z , at this time the optimization problem is only about the variable W y Then, the DC method proposed above is used to transform the rank-one non-convex constraint, and then the SCA method is used to transform the convex difference expression in Perform a first-order Taylor expansion at , and then the optimization problem can be approximately rewritten as:

[0113]

[0114] stη(Ω i ,Ω p )Re(Tr(A y (Ω i ,Ω p ,f k )W y ))Re(Tr(A z (Ω i ,Ω p , f k )W z ))≥ρd(Ωp, f k ), p∈P

[0115] η(Ω i ,Ω q )Re(Tr(A y (Ω i ,Ω q , f k )W y ))Re(Tr(A z (Ω i ,Ω q ,f k )W z ))≤ρ / δ,q∈Q

[0116] W y [m y , m y ]=1,m y =1,2,…,M y ,

[0117] Among them, σ represents the introduced penalty factor, ||W y ||2 in The partial derivative at is expressed as s means For the above convex problem, CVX is used to find the y-axis component beamforming matrix W that is approximately optimal for QS-IRS. y Then the solved W y As a given value, the optimization problem is only about the variable W z , again using the DC and SCA methods, the optimization problem is approximately rewritten as:

[0118]

[0119] stη(Ω i ,Ω p )Re(Tr(A y (Ω i ,Ω p ,f k )W y ))Re(Tr(A z (Ω i ,Ω p , f k )W z ))≥ρd(Ω p , f k ), p∈P

[0120] η(Ω i ,Ω q)Re(Tr(A y (Ω i ,Ω q , f k )W y ))Re(Tr(A z (Ω i ,Ω q ,f k )W z ))≤ρ / δ,q∈Q

[0121] W z [m z , m z ]=1,m z =1,2,…,M z ,

[0122] For the above convex problem, CVX is used again to solve the z-axis component beamforming matrix W that is approximately optimal for QS-IRS at this time. z . So far, the algorithm has achieved one round of alternating iterations. The maximum number of iterations N of alternating optimization is preset in advance. After N rounds of alternating iterative optimization, the convergence of the target gain ρ is observed, and the QS-IRS approximate optimal beamforming semi-positive definite matrix W that meets the requirements is solved. y and W z In order to obtain the beamforming vector W of the entire array, it is only necessary to replace W y and W z Make the Kronecker product and then perform eigenvalue decomposition, and take the eigenvector corresponding to the maximum eigenvalue as the approximate optimal beamforming vector w of the entire array, and then the phase arrangement of the entire panel can be obtained.

[0123] E) Quantitative selection and large-scale splicing

[0124] Design or select the QS-IRS unit style according to the requirements of operating frequency, operating bandwidth, and quantization bit. Then, according to the phase distribution obtained in step D), select the corresponding unit and its rotation angle to achieve the corresponding discrete phase. Then attach the corresponding unit to the wall or acrylic backplane (the acrylic backplane can be attached with copper film or aluminum film to enhance the reflection performance), and manually assemble it into a large-scale reflection array and deploy it to the corresponding position. See the specific process steps of large-scale QS-IRS three-dimensional shaping beam coverage design in broadband communication scenarios. Figure 3 .

[0125] 4. Result analysis:

[0126] The simulation parameters are set as follows: The goal is to achieve flat three-dimensional beam coverage in the target area, that is, d(Ω p , f k)=1, set the broadband system center frequency to 2.4GHz, bandwidth to 10MHz, number of subbands to 5, subband spacing to 2MHz, number of QS-IRS units to 80×80, unit spacing to half wavelength, and BS transmitting antenna maximum power gain to G t =14.5dB, the maximum power gain of the QS-IRS unit is G=4dB, and the horizontal angle and elevation angle of the incident signal are θ i =144°, the target area angle is θ r ∈[110°, 140°], the angle sampling interval is 10°, the gain difference between the target area and the non-target area is δ = 10 dB, the penalty factor introduced by SCA is σ = 20, the SCA solution iteration stop threshold is 0.01, and the maximum number of alternating optimization iterations is N = 10. Unless otherwise specified, the above parameters are the default simulation configuration.

[0127] Figure 4 The flat beam coverage gain effect diagram of the target area under the broadband system is shown. As shown in the figure, the proposed algorithm achieves flat beam coverage in the target area, and the gain difference between the target area and the non-target area reaches the preset 10dB. Figure 5 The flat beam gain effect diagram of a broadband system with a bandwidth of 10MHz at different sub-band frequencies is shown. Observe the different sub-bands at angle θ r The gain in the domain, the right figure shows a fixed θ r , observe the different sub-bands at angles It can be observed that the proposed algorithm achieves flat beam coverage at different sub-band frequencies, which verifies the effectiveness of the proposed alternating iterative optimization algorithm based on DC-SCA.

[0128] Figure 6 The gain of different systems with a bandwidth of 100MHz at different sub-band frequencies is shown. It can be observed that the broadband multi-frequency optimization at a single location has a certain performance loss compared to the perfect phase alignment of a single frequency. The reason is that the intelligent reflector unit can only provide a common phase compensation for signals of different frequencies. In order to achieve the phase shift trade-off between multiple frequency components, it is necessary to sacrifice a certain gain performance in exchange for balanced gain at each frequency. The broadband system with a bandwidth of 100MHz is optimized to achieve flat gain over the entire working bandwidth. Although there are small fluctuations in the gain over the entire bandwidth, for systems with a gain difference of 10dB between the target area and the non-target area, this variation can be considered to be within the allowable range. Therefore, the proposed algorithm achieves the system's flat beam optimization goal in the frequency domain.

[0129] Figure 7The beamforming performances of three schemes, namely, optimization with non-target area gain constraint, optimization without non-target area gain constraint, and random phase optimization, are compared, considering the number of QS-IRS units to be 64×64. Among them, Case 1 is the default target area range. It can be observed that the flat beamforming gain value achieved by considering the non-target area gain constraint is higher than that of the scheme without considering the non-target area gain constraint, and is significantly better than the random phase optimization scheme. This is because after adding the non-target area gain constraint, the possible energy leakage in the area is effectively suppressed, thereby concentrating the energy in the target area. Therefore, the necessity of the proposed algorithm considering the non-target area gain constraint is verified. In addition, Case 2 indicates that the target area range is: θ r ∈[110°, 140°]. It can be observed that a flat beamforming in the target area is also achieved under this setting. Compared with Case 1, the gain value decreases as the target area expands.

[0130] Figure 8 The gain performance in different broadband scenarios is compared as the number of QS-IRS units increases. Case 1 to Case 4 represent the target area ranges as follows: θ r ∈[125°, 135°], θ r ∈[120°, 140°], θ r ∈[120°, 140°] and θ r ∈[12O°,140°]. θ r =130° as the center, as the target area gradually expands, the system gain performance decreases. This is because under the premise of constant total energy, the smaller the target area, the more concentrated the useful energy, and the greater the gain value. Conversely, the gain value will decrease after the target area is expanded. Further observation shows that the amplitude gain changes approximately linearly with the increase in the number of units, indicating that the power scaling law of the proposed broadband three-dimensional beamforming design method is In addition, it can be seen from the figure that the proposed algorithm realizes the QS-IRS broadband shaping beam optimization of large-scale reflection units (e.g., 100×100).

[0131] The proposed algorithm considers the continuous phase optimization of QS-IRS. However, in practical scenarios, QS-IRS usually implements discrete phase compensation. Therefore, practical applications require a trade-off between performance gain and complexity. Fig. 9 Displayed at the center frequency 2.4GHz, pitch angle θ r=140°, the gain curves of three discrete bit phases. It can be observed that the 4-bit discrete phase can achieve almost the same performance as the ideal continuous phase, while the 2-bit discrete phase will cause about 3dB of gain loss. Fig.10 The figure shows the compensation phase distribution diagram provided by each unit under 2-bit discrete phase. Therefore, the corresponding discrete phase QS-IRS can be designed according to the phase distribution diagram. Specifically, two unit styles (such as Figure 1 The patch units with two different open-loop sizes shown in the figure are rotated and mirrored to represent four different discrete phases. Fig.10 The panel phase distribution shown manually splices different units, so that the QS-IRS array with 80×80 units can achieve broadband shaping beam coverage of the given target area.

[0132] The present invention proposes the concept of a quasi-static intelligent reflector and a method for unit segmentation, multiplexing, and large-scale manual splicing, and designs a method for realizing large-scale quasi-static intelligent reflector beamforming. The design utilizes the low cost, low complexity, and flexibility of the quasi-static intelligent reflector to solve the problems of high overall cost, complex manufacturing and algorithm implementation, and difficulty in large-scale deployment of traditional dynamically adjustable IRS. On the other hand, it increases the adjustability that static reflector arrays do not have. By obtaining the angle range information of the target area covered by the beam, the beam coverage design of the quasi-static intelligent reflector is completed offline using an alternating iterative optimization algorithm based on DC-SCA, without the need for real-time channel estimation, which greatly reduces system overhead and computational complexity. And when the position of the target area changes, the beamforming design can be adjusted in time according to the angle range information of the target area to adapt to the coverage requirements, with good flexibility. In addition, the algorithm combines the radiation pattern of the IRS unit to not only achieve the beamforming coverage of the differentiated gain requirements of the target area, but also achieves the balance of gain at different sub-band frequency points in broadband communication scenarios, with good robustness and effectiveness. Finally, the QS-IRS unit style can be designed according to the requirements of working frequency, working bandwidth, quantization bit, etc., and the corresponding unit style can be selected according to the panel phase distribution for manual splicing to form a large-scale reflection array. Overall, this design has solved the problems existing in traditional communication technology and considered more practical factors in the design, which has important practical significance and application value.

[0133] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A broadband three-dimensional shaping beam coverage design method based on quasi-static intelligent reflector, Features The following steps are involved: 1) Establish a system model and calculate system-related parameters; construct a broadband far-field communication scenario in which a QS-IRS is deployed at a certain altitude to serve a ground target area, and calculate system-related parameters including direction vector, array steering vector, channel, and received power; 2) Set up a reference system and derive the relative power gain γ of the QS-IRS array; Set up a reference system, analyze the changes in user received power, and calculate the relative power gain of the QS-IRS with respect to the reference system; 3) Construct optimization objectives and optimization problems: Design a beamforming beam that meets the gain requirements at different locations in the target area, perform discrete sampling, define the mask of the beamforming beam in the target area, and maximize the common beam gain of the target area while keeping the difference between the beam gain in the target area and the beam gain in the non-target area constant, thus constructing an optimization problem; 4) Design an alternating iterative optimization algorithm based on DC-SCA; The constant modulus constraint of the beamforming vector in the optimization problem is promoted to a semi-positive definite beamforming matrix with rank 1. The DC-SCA-based method is used to solve the non-convex constraints in the optimization problem. Through the alternating iteration method, the optimal solution of the problem is gradually approached to obtain the beamforming vector that meets the requirements, and the optimal control of the panel phase is achieved. 5) Quantization selection and large-scale splicing: According to the system's operating frequency, operating bandwidth, and quantization bit requirements, the QS-IRS is quantized and selected. The unit and rotation angle are selected according to the phase distribution, and large-scale splicing is performed.

2. A broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflector as claimed in claim 1, Features In step 1), the specific method of establishing the system model and calculating the system related parameters is as follows: construct a broadband far-field communication scenario in which a QS-IRS is deployed at a certain height to serve the ground target area; the deployment positions of the base station BS and the QS-IRS are fixed, and the BS is equipped with a single directional antenna, and its maximum power gain direction points to the QS-IRS, and the maximum power gain is G t ; Establish a three-dimensional Cartesian coordinate system with the first unit of QS-IRS as the origin. QS-IRS is placed in the yoz plane. The number of units is M = M y ×M z , M y and M z represents the number of cells along the y-axis and z-axis; it is assumed that the direct link between the BS and the target area is severely blocked and can be ignored, and communication is only carried out through the LoS link constructed by QS-IRS; it is assumed that the horizontal angle incident on the QS-IRS plane is The pitch angle is θ i , denoted as The horizontal angle of the reflected signal is obtained based on the angle range information of the target area covered by the QS-IRS beam and the pitch angle θ r , denoted as According to the angular relationship of the three-dimensional Cartesian coordinate system, the incident direction vector u is derived i and the reflection direction vector u r ; From this, the sub-band frequency is calculated as f k The receiving array steering vector of the signal on the QS-IRS array is The reflect array steering vector is Therefore, the array steering vector generated by the signal passing through the QS-IRS array is expressed as a(Ω i ,Ω r , f k )=a i (Ω i , f k )⊙a r (Ω r , f k ), where ⊙ represents the Hadamard product; on the other hand, the receiving array steering vector a of the QS-IRS array i (Ω i , f k ) is decomposed into array steering vectors along the y-axis and z-axis and The Kronecker product of in represents the Kronecker product; similarly, the reflect array steering vector a r (Ω r , f k ) is also decomposed and expressed as Therefore, the array steering vector generated by the linear array decomposed by QS-IRS along the y-axis is expressed as a y (Ω i ,Ω r , f k )=a iy (Ω i , f k )⊙a ry (Ω r , f k ); Similarly, the array steering vector generated by the linear array decomposed along the z-axis is a z (Ω i ,Ω r , f k )=a iz (Ω i , f k )⊙a rz (Ω r , f k ); Assuming that the normalized radiation pattern of the QS-IRS unit is F(Ω), the radiation pattern gain of the QS-IRS unit is calculated based on the angles of signal incidence and reflection as G 2 F(Ω i )F(Ω r ); Assuming the channel is a free space path loss model, the channels from BS to QS-IRS and from QS-IRS to the target area are expressed as and Assume that the phase shift matrix of QS-IRS is expressed as in represents the phase compensation of the mth reflection unit; assuming that the BS antenna transmit power is P t Therefore, the received power P of a user at a certain location in the target area r (Ω i ,Ω r , f k )for: in,(·) T represents transpose, represents the gain generated by the BS antenna and the QS-IRS unit radiation pattern, β represents the large-scale free space path loss of the cascaded channel; definition is the beamforming vector of the QS-IRS array, which consists of the components along the y-axis and the z-axis component The Kronecker product is composed of 3. A broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflector as claimed in claim 1, Features In step 2), the specific method is: set up a reference system, where the BS transmitting antenna is a single omnidirectional antenna, the QS-IRS consists of only a single reflection unit, and the influence of the unit radiation pattern gain is not considered; under the same initialization parameters, the received power of the user at the same position in the reference system is expressed as: P r0 (Ω i ,Ω r , f k )=P t β; The relative power gain of QS-IRS with respect to the reference system is expressed as: Among them, P r (Ω i ,Ω r , f k ) is the received power of the user at a certain location in the target area, P r0 (Ω i ,Ω r , f k ) is the received power of the user at the same location in the reference system.

4. A broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflector as claimed in claim 1, Features In step 3), the specific method of constructing the optimization target and the optimization problem is: designing a shaped beam that meets the gain requirements at different positions in the target area; in order to facilitate the numerical realization of the problem, the horizontal angle and the pitch angle Ω of the reflected signal are r Discrete sampling is performed at equal intervals of every 10°; the continuous angles of the target area are discretely sampled as The set P contains all angle sampling combinations of the target area; the continuous angles of the non-target area are discretely sampled as The set Q contains all angle sampling combinations of non-target areas; the mask of the beamforming in the target area is defined as d(Ω p , f k ); The problem requires that the difference between the beam gain in the target area and the beam gain in the non-target area is δ, and the common beam gain ρ in the target area is maximized; therefore, the optimization problem is constructed as: Among them, m y and m z represents the cell index along the y-axis and z-axis, |w y [m y ]|=1 and |w z [m z ]|=1 indicates that the beamforming vectors along the y-axis and the z-axis satisfy the constant modulus constraint.

5. A broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflector as claimed in claim 1, Features In step 4), the specific steps of designing the alternating iterative optimization algorithm based on DC-SCA are as follows: observing the optimization problem constructed in step 3), it can be seen that the array relative power gain components along the y-axis and the z-axis are coupled with each other; at the same time, the unit radiation pattern gain obtained at different positions is also different, and it is impossible to decompose it into independent components along the y-axis and the z-axis for consideration; in order to reduce the complexity of problem solving, an alternating iterative optimization algorithm is used for solving; the specific algorithm is: 4.1) Transform the constant modulus non-convex constraints of the optimization problem in step 3) The specific method is: the beamforming vector w along the y-axis and z-axis y and w z Lifted to a rank-1 positive semidefinite matrix and in(·) H It means taking the conjugate transpose; Therefore, the optimization problem in step 3) is equivalently rewritten as: Among them, Tr(·) represents the trace, Re(·) represents the real part, (·) * It means taking conjugate; 4.2) Process the coupling variable W in step 4.1) of the optimization problem y and W z The specific method is: given an initialized semi-positive definite matrix W that satisfies the constant modulus constraint z , at this time the optimization problem is only about the variable W y ; Then, the rank(·)=1 non-convex constraint is converted into a convex constraint by using a method based on convex difference and successive convex approximation; Then, CVX is used to find the y-axis component beamforming matrix W of the QS-IRS approximation optimal at this time y ; Then the solved W y As a given value, the optimization problem is only about the variable W z , the DC-SCA-based method is used again to transform the non-convex constraints, and CVX is used to solve the z-axis component beamforming matrix W that is approximately optimal for QS-IRS at this time z ; At this point, the algorithm has achieved a round of alternating iterations; 4.3) Repeat step 4.2); after the preset maximum number of alternating iterative optimization times N, observe the convergence of the target gain ρ, and finally solve the approximate optimal beamforming matrix W of the QS-IRS along the y-axis and z-axis that meets the requirements y and W z ; In order to obtain the beamforming vector w of the entire array, it is only necessary to replace W y and W z Make the Kronecker product and then perform eigenvalue decomposition, and take the eigenvector corresponding to the maximum eigenvalue as the approximate optimal beamforming vector w of the entire array, and then get the phase arrangement of the entire panel.

6. A broadband three-dimensional shaping beam coverage design method based on a quasi-static intelligent reflector as claimed in claim 1, Features In step 5), the specific steps of the quantitative selection and large-scale splicing are: 5.1) Quantization selection: Design or select the unit style of QS-IRS according to the system's operating frequency, operating bandwidth and quantization bit requirements; Ensure that the selected unit can provide the required phase control range and accuracy within the specified frequency band; 5.2) Selecting units and rotation angles according to phase distribution: According to the phase distribution obtained in step 4), select corresponding units and their rotation angles to achieve corresponding discrete phases; convert the continuous phase values ​​obtained by the optimization algorithm into actually achievable discrete phase values; 5.3) Unit splicing and assembly: Attach the corresponding units to the wall or acrylic back panel, and the acrylic back panel is attached with copper film or aluminum film to enhance the reflective performance; in this way, manually assemble into a large-scale reflective array and deploy it to the corresponding position; during the splicing and assembly process, ensure that the arrangement between the units is tight and according to the predetermined design layout to ensure the performance of the entire array.

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