Quasi-static intelligent reflecting surface three-dimensional forming beam forming design method based on subarray activation

Abstract

The invention discloses a quasi-static intelligent reflecting surface three-dimensional forming beam forming design method based on subarray activation, and relates to wireless communication. For a broadband multipath communication scene assisted by the QS-IRS, maximization of the minimum average RSRP of users in a target area is taken as an optimization target, subarray division and arrangement are carried out on the QS-IRS by adopting an OFDM-like mode, multipath parameter information of each user in the target area needing beam coverage is acquired through a ray tracing method, and the multipath parameter information of each user in the target area needing beam coverage is acquired. And designing a two-stage iterative equalization forming beamforming algorithm based on sub-array activation. The minimum average RSRP of the users in the specific target area is improved, and the minimum average RSPR close to the exhaustion search algorithm is achieved. And the complexity is greatly reduced. And obtaining sub-array combination configuration parameters based on the algorithm, including the beam direction # imgabs0 # of each sub-array and the common phase factor epsilon n, and completing the phase design of the whole QS-IRS reflection unit. And a new method is provided for QS-IRS three-dimensional forming beam design.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a quasi-static intelligent reflecting surface three-dimensional forming beam synthesis design method based on sub-array activation. Background Art

[0002] With the rapid development of mobile communication, users' pursuit of larger communication capacity, higher communication rate, smaller transmission delay, and better communication services has driven the mobile communication technology into an era of rapid update and iteration. Since the 1970s, communication technologies have gradually evolved from the technologies initially used for voice analog signal transmission to new communication technologies such as fifth-generation (5G) multi-input multi-output (MIMO) and millimeter-wave communication. At the same time, the large-scale commercial use of 5G wireless communication networks and the demand for wide-area three-dimensional coverage anytime and anywhere in practice are constantly inspiring people to innovate wireless communication technologies.

[0003] In recent years, intelligent reflecting surface (IRS) technology, also known as reconfigurable intelligent surface (RIS) or large intelligent surface (LIS), etc., has been regarded as an emerging technology that can be integrated with high-frequency bands in sixth-generation (6G) wireless communication networks to achieve ultra-high spectral efficiency, while effectively reducing costs and system energy consumption. The research on IRS-assisted wireless communication has been widely carried out and has been proven to be applicable to assist in improving the communication performance of various systems such as unmanned aerial vehicle communication, communication and sensing integration, and millimeter-wave communication (Z. Wang, et al., "Massive MIMO Communication with Intelligent Reflecting Surface," IEEE Transactions on Wireless Communications, vol. 22, no. 4, pp. 2566-2582, 2023). In addition, IRS reflection units can independently control the amplitude and phase of reflected signals through dynamic tuning and reconstruct the spatial wireless environment through an external controller; at the same time, IRS can construct a virtual line-of-sight (LoS) link when the communication link is blocked to achieve effective indirect communication. Therefore, IRS stands out among many 6G wireless communication technologies with its characteristics of low cost, low energy consumption, high spectral efficiency, programmable control, and high flexibility.

[0004] To meet the requirements of wide-area three-dimensional space beam coverage in 6G communication scenarios, some existing literature has conducted research on using IRS to enhance the three-dimensional beam coverage of the target area. For example, the literature (X. Lin, et al., “On the design of broadbeam of reconfigurable intelligent surface,” IEEE Trans. Commun., vol. 72, no. 5, pp. 3079–3094, 2024) uses a semidefinite programming algorithm based on Difference of Convex (DC) to achieve a wide beam with the maximum and equal power gain within a predefined angular region; 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) proposes a three-dimensional beam coverage design based on matrix lifting and linear matrix inequality techniques, and uses the methods of DC and Successive Convex Approximation (SCA) to transform the constant modulus non-convex constraint of IRS reflection units into convex constraints, and then uses a convex optimization toolbox to solve it, achieving the maximization of the minimum coverage beam gain of the target area; in 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), a low-overhead quasi-static millimeter-wave wide-area coverage based on statistical CSI is proposed without obtaining the instantaneous Channel State Information (CSI).

[0005] However, the performance of IRS-assisted communication systems is severely degraded by the double-segment path loss. Therefore, to effectively improve the communication quality of users in the coverage area, it is usually necessary to deploy a large number of IRSs to provide higher gains, which will also result in higher deployment and manufacturing costs and greater complexity overhead. To better balance the manufacturing cost of IRS, system deployment cost, implementation complexity, and adjustment flexibility, the concept of Quasi-Static IRS (QS-IRS) and the method of unit segmentation multiplexing and large-scale splicing are proposed in the literature (Lv Jiangbin. A broadband three-dimensional shaped beam coverage design method based on quasi-static intelligent reflecting surface: 202411191858.0 [P]. 2024-12-06). Specifically, QS-IRS is composed of units with different patch shapes or sizes. Rotating or mirroring the patch units can achieve different discrete phases. Therefore, different compensation phases can be achieved with as few unit styles as possible, which is beneficial to the large-scale mass production of units. Subsequently, according to the phase arrangement requirements for enhancing the coverage of a specific target area, the patch units are manually spliced and assembled to form a large-scale reflection array, thereby achieving a specific three-dimensional beam coverage. This design and method not only retain the lowest degree of adjustability but also achieve low-cost unit multiplexing and mass production, greatly reducing costs and the failure rate of the overall panel.

[0006] On the other hand, since the channel information at different positions in the spatial environment is usually different, and users at different positions have different requirements for communication quality, and the anisotropic radiation pattern of QS-IRS units has different electromagnetic power responses to signals incident and emitted at different angles, which will significantly affect the coverage performance of QS-IRS in different three-dimensional directions. Therefore, in an actual communication system, it is particularly important to design a three-dimensional beam with a certain spatial shape according to the gain requirements of different users in the target area, that is, the design of a shaped beam needs to be considered. Therefore, the literature (Lv Jiangbin. A broadband three-dimensional shaped beam coverage design method based on quasi-static intelligent reflecting surface: 202411191858.0 [P]. 2024-12-06) also designs a low-complexity alternating iterative optimization algorithm based on DC-SCA, considering the anisotropic radiation pattern of QS-IRS units and the different beam gain requirements of users at different positions in the target area, to achieve the three-dimensional shaped beam coverage design of ultra-large-scale QS-IRS.

[0007] It is worth noting that the above research has not yet addressed the three-dimensional shaped beam design for broadband systems in multipath scenarios. Against this backdrop, this invention will build on the relevant work of a previous literature (Lv Jiangbin. A broadband three-dimensional shaped beam coverage design method based on a quasi-static intelligent reflecting surface: 202411191858.0[P]. 2024-12-06), and further consider using QS-IRS to achieve three-dimensional shaped beam coverage for a specific target area in a multipath scenario, such that the formed shaped beam can match and enhance multipath signals in different spatial angular directions. It should be noted that the large-scale multipath parameters in an actual communication system are mainly determined by the buildings in the environment, and they play a dominant role in the system. Even though it may be affected by the dynamic influence of pedestrians, vehicles, or other moving objects, since the building distribution is relatively fixed, its dominant path is relatively stable. In recent years, thanks to the development and application of ray tracing technology, the channel parameters of each path, including path loss (PL), propagation delay (PD), angle of arrival (AOA), angle of departure (AOD), and power angular profile (PAP), etc., can be obtained through ray tracing. Therefore, based on the obtained multipath parameter information, it is effective and reasonable to use QS-IRS to achieve long-term beam coverage for a specific target area.

[0008] However, how to design the shaped beam to meet the matching enhancement of different users at different multipath spatial angles has become one of the urgent problems to be solved. In recent years, the research on the antenna array partitioning (Subarray Partition, SP) technology has provided new ideas and methods for solving this problem. Among them, the literature (W. Jiang and H. D. Schotten, "Beam-Based Multiple Access for IRS-Aided Millimeter-Wave and Terahertz Communications," 2024 IEEE Wireless Communications and Networking Conference (WCNC), IEEE, 2024) proposed to use multiple subarrays on the hybrid digital-analog array to form independent beams, so that each beam is directed towards its own direction, which can effectively reduce the interference between users and suppress the reflection of unwanted signals; in 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), the authors divided the IRS passive reflection array into multiple subarrays with appropriate sizes and adjustable beam widths, and adjusted the beam directions and their common phase shifts of each subarray according to needs to achieve flat beam coverage in a given area range.

[0009] Based on the above research and analysis, the present invention considers using the SP technology to divide the QS-IRS into multiple subarrays in a broadband multipath scenario, and reasonably designs the beam directions and phases of each subarray, so that the shaped beam synthesized by the subarrays can cover the users in a specific target area and match and enhance the multipath signals at different spatial angles, thereby improving the received signal gain of the users. Summary of the Invention

[0010] The object of the present invention is that there is no relevant research on shaped beam coverage for broadband multipath scenarios in the prior art; at the same time, in order to make the synthesized shaped beam cover the users in a specific target area and match and enhance the multipath signals at different spatial angles, the common method is to implement the shaped beam under all subarray combinations through an exhaustive search algorithm, and analyze the gain performance of the users in the target area under the action of each shaped beam, and compare to obtain the optimal shaped beam configuration. However, the complexity of this algorithm is Where N represents the number of sub-arrays, which will show an exponential increase as the number of sub-arrays increases. To address the above problems, the present invention considers using a technology similar to Orthogonal Frequency-Division Multiplexing (OFDM) to divide and arrange the sub-arrays of the QS-IRS, and proposes a three-dimensional shaping beam synthesis design method for the quasi-static intelligent reflecting surface based on sub-array activation.

[0011] To achieve the above object of the invention, the present invention provides the following technical solutions.

[0012] A three-dimensional shaping beam synthesis design method for the quasi-static intelligent reflecting surface based on sub-array activation, comprising the following steps:

[0013] 1) System model establishment and channel analysis: Construct a QS-IRS communication system model in a broadband multipath scenario and perform channel analysis to obtain the line-of-sight channel from the base station to the QS-IRS and the multipath channel parameters of the user.

[0014] 2) Performance index analysis and optimization problem construction: Analyze the average RSRP expression of the user and use it as an index to evaluate the system performance, and construct an optimization problem with the goal of maximizing the minimum average RSRP of the user.

[0015] 3) OFDM-like sub-array division and arrangement: Based on the grid division strategy of Orthogonal Frequency-Division Multiplexing (OFDM)-like, divide and arrange the sub-arrays of the QS-IRS, and determine the beam coverage angle of each sub-array.

[0016] 4) Design of a two-stage iterative equalization shaping beam synthesis algorithm based on sub-array activation: Adopt a two-stage iterative equalization algorithm based on sub-array activation to dynamically adjust the activation state, beam direction and phase of the sub-arrays, generate a three-dimensional shaping beam that matches the multipath spatial angle, and complete the optimal allocation of the sub-arrays; output the beam directions of each sub-array under this configuration and the common phase factor ε n , and complete the phase design of the overall QS-IRS.

[0017] In step 1), the specific methods for system model establishment and channel analysis are as follows: A QS-IRS uniform linear array is constructed and deployed on the surface of a tall building or an aerial vehicle to achieve a far-field communication scenario where the beam covers users in a specific target area on the ground. It is assumed that the direct link between the base station BS and the users in the target area is severely blocked and ignored, and communication is carried out only through the cascaded link constructed by the QS-IRS. To reduce the impact of the double-path loss of the QS-IRS, the QS-IRS is usually deployed close to the BS to ensure receiving most of the energy of the transmitted signal. On the other hand, it is assumed that the QS-IRS is deployed at a high altitude so that a LoS link is formed between it and the BS. The signals reflected by the QS-IRS are affected by factors such as dense buildings or obstacles, high and low terrain, and atmospheric environment, and will undergo different degrees of reflection, refraction, or scattering, thus forming multiple different propagation paths. It is assumed that the BS is equipped with a single directional antenna, and the direction of its maximum power gain points to the QS-IRS, with a maximum power gain of G t ; the user is equipped with a single omnidirectional antenna; the QS-IRS uniform linear array consists of M reflection units, and the maximum power gain of each unit is G.

[0018] First, the system model of three-dimensional shaping beam coverage of the QS-IRS in a broadband multipath scenario is as Figure 1 shown. A three-dimensional Cartesian coordinate system is established with the first unit of the QS-IRS as the origin, and the QS-IRS is placed in the yoz plane. It is assumed that the horizontal angle of the incident signal is and the elevation angle is θ i , denoted as The horizontal angle of the reflected signal is and the elevation angle θ r , denoted as It is assumed that the considered broadband system has a total of K sub-bands, each sub-band has a bandwidth of Δf, and the initial frequency point is f0. Then the frequency point of the k-th sub-band can be expressed as:

[0019] f k = f0 + kΔf, k = 1,..., K - 1

[0020] Therefore, according to the three-dimensional space angle relationship, the incident steering vector a k of the signal with sub-band frequency f i (Π i , f k ) on the QS-IRS can be calculated. Then the channel between the BS and the QS-IRS can be expressed as:

[0021] h = η(Π i )β i (f k )a i (Π i , f k )

[0022] where, η(Π i ) represents the radiation pattern gain generated by the QS-IRS reflection unit and the BS transmitting antenna, and β i (f k ) represents the large-scale path loss of the LoS link. Since the relevant channel information of the LoS link is available, the fixed-value part in the above formula is defined as Assume that a user in the target area has a total of L multipaths. Therefore, the steering vector of the l-th reflected path on the QS-IRS can also be defined as a rl (Π il , f k ). Then, the channel of the l-th reflected path can be expressed as:

[0023]

[0024] where, η(∏ rl ) represents the radiation pattern gain of the QS-IRS unit for the l-th reflected path. Since the gain it provides for the signal reflected at a certain angle is determined, the equivalent channel complex gain of the l-th reflected path can be defined as α l represents the large-scale path loss of the l-th reflected path; represents the phase of the l-th reflected path; τ l represents the propagation delay of the l-th reflected path. Assume that the phase shift matrix of the QS-IRS is m = 1,..., M, where represents the compensation phase of the m-th unit, and it can be vectorized as Based on this, the cascaded multipath channel can be expressed as:

[0025]

[0026] where, (·) T represents the transpose, a l (Π i , Π rl , f k ) = a i (Π i , f k ) ⊙ a rl (Π rl , f k ), and ⊙ represents the Hadamard product.

[0027] In step 2), the specific steps for the performance index analysis and optimization problem construction can be:

[0028] To effectively evaluate the system performance, the present invention uses the average reference signal received power (RSRP) of users as an indicator. First, define the amplitude spectral density of the BS transmitting antenna as S t (f k ). Then, the received signal amplitude spectral density S r (f k ) of a certain user in a specific target area under the broadband multipath scenario (T.Zugno, et al., "Implementation of a spatial channel model for ns-3." Proceedings of the 2020 Workshop on ns-3. 2020) can be expressed as the following formula:

[0029]

[0030] In the formula, Δ l represents the spatial frequency angle of the l-th reflected ray, To enhance the multipath signals at different spatial frequency angles through beam matching, the present invention plans to use the SP technology to divide the QS-IRS into N sub-arrays, and each sub-array contains reflecting units. For the convenience of subsequent mathematical derivation and proof, it is assumed in the present invention that the number of reflecting units M s of the sub-array is an integer, that is, there is a multiple relationship between the number of QS-IRS units and the number of sub-arrays. Define that each sub-array can be directed to a certain spatial angle direction Then, the beamforming vector of the n-th sub-array can be expressed as:

[0031]

[0032] Among them, represents the common phase of the n-th sub-array. Therefore, the compensation phase of each reflecting unit can be rewritten as:

[0033]

[0034] Substitute the above compensation phase into the received signal amplitude spectral density expression, and it can be further rewritten as:

[0035]

[0036] The summation term related to the sub - array elements in the above formula is transformed using the Array Factor (AF) (S. Rajagopal, "Beam broadening for phased antenna arrays using multi - beam subarrays," 2012 IEEE International Conference on Communications (ICC), IEEE, pp. 3637 - 3642, 2012). Then, the received amplitude spectral density of the user can be rewritten as:

[0037]

[0038] Assume that the beam directions of each sub - array and the common phase factor ε n are given. Therefore, the formed beam pattern factor A(Δ l ) after sub - array synthesis can be defined as:

[0039]

[0040] It should be noted that the beam pattern factor A(Δ l ) is a complex number, which represents the vector superposition generated by multiple sub - arrays at the spatial frequency angle Δ l . Since the beam direction and the common phase factor ε n are both assumed to be given, the magnitude part of A(Δ l ) is defined as and the phase part is Therefore, we have Then the received power spectral density |S r (f k )| 2 can be expressed as:

[0041]

[0042] Assume that the power distribution of the transmitting antenna on each sub - band is uniform, that is, the transmitting antenna amplitude spectral density S t (f k ) is independent of the frequency point. In addition, for the convenience of subsequent derivation and analysis, the present invention assumes that the bandwidth Δf of each sub - band is small relative to the coherence bandwidth of the channel, and the channels where the sub - band signals are located can be approximately regarded as flat fading, that is, the channel response does not change significantly within this bandwidth. Define the long - term fading part of the channel as Therefore, the total received power P total of the user can be obtained from the received power spectral density |S r (f k )|2 Integrating over the entire frequency spectrum gives:

[0043]

[0044] Due to the flat fading assumption of the channels where the sub - band signals are located, the summation term with respect to frequency only acts on the path delay parts. Observing the above formula, it can be seen that the first summation term represents the correlation between multipaths, and the second summation term represents the influence of each path delay at different frequencies. For the summation term with respect to frequency, the AF formula can also be used for transformation, that is:

[0045]

[0046] Substituting the above formula into the total received power expression, the received power P of the user total can be rewritten as:

[0047]

[0048] Since Therefore, first analyze L i L j and we have:

[0049]

[0050] Therefore, the received power P of the user total can be further expressed as:

[0051]

[0052] Assume that the phase factors Φ l of each path are relatively independent and follow a uniform distribution on [0, 2π]. Therefore, for this user, its average RSRP can be expressed as:

[0053]

[0054] When i = j, we have:

[0055]

[0056] When i ≠ j, then we have:

[0057]

[0058] Among them, it is defined that Since the parameter information of each link in the multipath scenario can be measured and obtained through ray - tracing technology, including the large - scale path loss |α′ l |, propagation delay τ l , the reflection angles of each path and θ rland power information. Based on this, for the trigonometric function expectation composed of independent and identically distributed variables Φ in the above formula l the result is as follows:

[0059]

[0060] Combined with the above analysis, it can be known that the average RSRP of this user can be expressed as:

[0061]

[0062] Observing the above formula, it can be seen that the average RSRP of the user is only determined by the average power of each path and the corresponding beam pattern factor A(Δ l ). Therefore, by reasonably designing the arrangement and synthesis of the sub-arrays, the average RSRP of this user can be maximized. However, the present invention considers multiple users within the target area covered by the beam. Therefore, the designed shaped beam needs to take into account the communication quality of each user, that is, the average RSRP of each user. Based on this, the present invention will maximize the minimum average RSRP of users within the target area by designing the beam directions and the common phase factor ε n of each sub-array. The optimization problem can be constructed as the following formula:

[0063]

[0064] where s represents the user index and S represents the set of all users within the target area.

[0065] In step 3), the specific steps of the class OFDM sub-array division and arrangement can be:

[0066] Since the multipath parameter information of different users within the target area can be obtained by ray tracing technology, therefore, define the minimum and maximum multipath spatial frequency angles as Δ min and Δ max respectively, then the spatial frequency angle range of the multipath is [Δ min , Δ max , It is worth noting that the first null beam width of a single sub-array is and its effective gain coverage range (Z. Xiao, et al., "Hierarchical Codebook Design for Beamforming Training in Millimeter-Wave Communication," IEEE Trans. Wireless Commun., vol. 15, no. 5, pp. 3380-3392, 2016) is The effective coverage width of the array beam is Therefore, if the number of sub-arrays divided is small, the total coverage width of each sub-array may be much smaller than the multipath spatial frequency angle range, making the shaped beam only able to match and enhance the multipath signals at only a few angles, thus seriously affecting the performance gain of users in the target area; if the number of sub-arrays divided is too large, causing each sub-array to be densely arranged within the considered multipath spatial frequency angle range, the coverage widths of each sub-array overlap and interfere with each other, thus greatly increasing the complexity of the phase design of each sub-array and the synthesis of sub-arrays. The present invention considers dividing the QS-IRS into N * sub-arrays based on the orthogonality of OFDM, specifically expressed as:

[0067]

[0068] Through the above method, the multipath spatial frequency angle range can be divided into N * grid points, and the interval of each grid point is set to And the spatial frequency angle corresponding to each grid point represents the peak beam direction of a sub-array. When performing sub-array synthesis, it also means that each sub-array can choose to direct its beam to the spatial frequency angle corresponding to any one of the grid points.

[0069] In step 4), the specific method for designing the two-stage iterative equalization shaped beam synthesis algorithm based on sub-array activation may be:

[0070] To achieve the shaped beam coverage design for a specific target area, considering combining and synthesizing different sub-arrays, a relatively common synthesis algorithm is the exhaustive search algorithm, whose complexity is and will increase exponentially with the increase in the number of sub-arrays, thus generating extremely high complexity. To effectively reduce the algorithm complexity, the present invention proposes a two-stage iterative equalization shaped beam synthesis algorithm based on sub-array activation. Specifically, in the first stage, first divide and arrange each sub-array in the OFDM-like manner in step 3); then, judge the activation situation of each sub-array according to the different multipath spatial frequency angles of different users, that is, when the spatial frequency angle Δ l of a certain path is within the coverage width of the nth sub-array, satisfying:

[0071]

[0072] It means that the nth sub-array is activated, and the spatial frequency angle corresponding to the currently activated sub-arrays will also be used as the reference angle for the subsequent sub-array arrangement and synthesis. Then, all permutations of the activated sub-arrays are performed, and through comparison and analysis, the permutation method that maximizes the minimum average RSRP of each user in the target area is obtained. Then, on this basis, one of the unactivated sub-arrays is selected and synthesized at the reference angle of the activated sub-arrays. After comparison and analysis, the combination method that also maximizes the minimum average RSRP of each user can be obtained. Repeat the above operations until all unactivated sub-arrays are reallocated and combined. At this time, the corresponding sub-array permutation and combination scheme is obtained, which is used as the initial parameter for the iterative equalization method in the next stage. It should be noted that to synthesize different sub-arrays at a certain same spatial frequency angle direction In addition to steering the beams of each sub-array to the direction, it is also necessary to carefully design the common phase factor ε n of each sub-array so that its phase satisfies in-phase superposition to obtain the maximum gain effect. Therefore, the common phase factor ε n of each sub-array can be set according to different beam directions as follows:

[0073]

[0074] Subsequently, it enters the second stage. First, the sub-array combination obtained in the first stage is used as the initial parameter, and the average RSRP of each user is calculated under the weighting of the formed beam pattern. At this time, the user with the minimum average RSRP is obtained. Then, the method of iterative balancing (J.Lyu, et al., "Cyclical Multiple Access in UAV-Aided Communications: A Throughput-Delay Tradeoff," IEEE Wireless Communications Letters, vol.5, no.6, pp.600-603, 2016) is used to finely adjust the sub-array combination. Specifically, in each round of iterative balancing process, the sub-array serving the current user with the maximum or the second maximum average RSRP is selected and redirected to the directions of each reference spatial frequency angle. At this time, the average RSRP of each user is calculated under the weighting of the corresponding formed beam pattern. If the current minimum average RSRP is larger than that of the initial parameter configuration in the previous round, the allocation is successful, and the current sub-array combination configuration is retained and used as the initial parameter configuration for the next round of iterative balancing; otherwise, if the current minimum average RSRP is smaller than that of the initial parameter configuration in the previous round, this reallocation scheme is not adopted, and the previous step is returned to reselect other sub-arrays for allocation. The above operations are repeated until all sub-arrays of the user with the maximum or the second maximum RSRP are reallocated in a certain round of iterative balancing, and the minimum average RSRP value is still not improved, then the algorithm ends. At this time, the combined configuration parameters of each current sub-array are output, including the beam directions of each sub-array and the common phase factor ε n , and then the phase setting of the overall QS-IRS can be obtained. The computational complexity of this algorithm is where N1 represents the number of activated sub-arrays and K represents the number of rounds of iterative balancing. Based on this, the two-stage iterative balancing formed beam synthesis algorithm based on sub-array activation proposed in the present invention is greatly reduced compared with the exponential complexity of the traditional exhaustive search algorithm.

[0075] The present invention proposes a quasi-static intelligent reflecting surface three-dimensional formed beam synthesis design method based on sub-array activation. First, a system model in a broadband multipath scenario is established and channel analysis is carried out. Secondly, the average RSRP expression of the user is analyzed and used as an index to evaluate the system performance. Subsequently, an optimization problem is constructed with the goal of maximizing the minimum average RSRP of the user. Then, the QS-IRS is divided and arranged into sub-arrays in an OFDM-like manner. Then, a two-stage iterative balancing formed beam synthesis algorithm based on sub-array activation is adopted to form the corresponding formed beam and complete the optimal allocation of the sub-arrays. Finally, the beam directions of each sub-array under this configuration are output and the common phase factor ε n , thus completing the phase design of the overall QS-IRS.

[0076] Compared with the prior art, the present invention has the following outstanding advantages:

[0077] 1. The two-stage iterative equalization shaping beam synthesis algorithm based on subarray activation proposed by the present invention reduces the complexity of subarray synthesis from the exponential level of the exhaustive search algorithm to , greatly reducing the computational complexity.

[0078] 2. The present invention is applicable to the long-term beam coverage of multipath scenarios. For the scatterers with fixed distribution in a specific environment, their large-scale multipath information is relatively stable. Therefore, all multipath information at each position within the target area can be obtained through a single ray tracing. To achieve beam coverage for users at different positions within the target area, only the subarray division needs to be determined according to the number of QS-IRS units and the specific multipath angle range, and the QS-IRS shaping beam design can be completed by using the two-stage iterative equalization shaping beam synthesis algorithm based on subarray activation. Even if the users to be beam-covered change, only by repeating the algorithm according to the previously obtained user multipath information, the corresponding QS-IRS shaping beam design can be achieved, which has a certain degree of flexibility.

[0079] 3. The present invention realizes the three-dimensional shaping beam design and the beam matching enhancement of multipath signals in different spatial frequency angle directions by combining and synthesizing different subarrays.

[0080] 4. Based on the concept of quasi-static intelligent reflecting surface, the present invention can effectively reduce the manufacturing cost and implementation complexity through unit segmentation multiplexing and manual assembly and splicing methods, and also has a certain degree of adjustability. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a system model diagram of a QS-IRS-assisted broadband multipath scenario three-dimensional beam coverage according to an embodiment of the present invention.

[0082] Figure 2 is a schematic diagram of the power gain of a single subarray.

[0083] Figure 3 is a schematic diagram of the division and arrangement of subarrays similar to OFDM.

[0084] Figure 4 is the shaping beam pattern under different subarray combination modes.

[0085] Figure 5 is the shaping beam pattern synthesized at the angles corresponding to the unactivated subarrays.

[0086] Figure 6 It is the design flow chart of the embodiment of the present invention.

[0087] Figure 7 It is the average RSRP value of each user in the target area under different schemes of the embodiment of the present invention. Detailed implementation manners

[0088] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, 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.

[0089] The present invention aims at the QS-IRS-assisted broadband multipath communication scenario, and takes maximizing the minimum average RSRP of users in the target area as the optimization objective. It proposes to use a method similar to OFDM to divide and arrange the sub-arrays of QS-IRS. Subsequently, the multipath parameter information of each user in the target area to be covered by the beam is obtained through the ray tracing method, and a two-stage iterative equalization shaping beam synthesis algorithm based on sub-array activation is designed. Compared with other benchmark schemes, this algorithm can effectively improve the minimum average RSRP of users in a specific target area, and can achieve a minimum average RSPR close to that of the exhaustive search algorithm. In addition, the complexity of this algorithm is greatly reduced compared with the traditional exhaustive search algorithm. Finally, based on the sub-array combination configuration parameters obtained by this algorithm, including the beam directions of each sub-array and the common phase factor ε n , the phase design of the overall QS-IRS reflection unit can be completed.

[0090] The embodiment of the method for designing a quasi-static intelligent reflecting surface three-dimensional shaping beam synthesis based on sub-array activation according to the present invention specifically includes the following steps:

[0091] 1. Establish a system model:

[0092] Consider a QS-IRS uniform linear array deployed on the surface of a tall building or an aerial vehicle to achieve far-field communication scenarios where the beam covers users in a specific target area on the ground. Assume that the direct link between the base station BS and the users in the target area is severely blocked and ignored, and communication is only carried out through the cascaded link constructed by the QS-IRS. To reduce the impact of the double-segment path loss of the QS-IRS, the QS-IRS is usually deployed close to the BS to ensure receiving most of the energy of the transmitted signal. On the other hand, assume that the QS-IRS is deployed at a high altitude so that a LoS link is formed between it and the BS. The signals reflected by the QS-IRS are affected by factors such as dense buildings or obstacles, high and low terrain, and atmospheric environment, and will undergo different degrees of reflection, refraction, or scattering, thus forming multiple different propagation paths. Assume that the BS is equipped with a single directional antenna, and its maximum power gain direction points to the QS-IRS; the user is equipped with a single omnidirectional antenna; the QS-IRS uniform linear array consists of M reflection units. A three-dimensional Cartesian coordinate system is established with the first unit of the QS-IRS as the coordinate origin, and the QS-IRS is placed in the yoz plane. Define the horizontal angle and elevation angle of the incident signal as and θ i , denoted as The distance between the BS and the QS-IRS is d1. Similarly, define the horizontal angle and elevation angle θ r of the reflected signal, denoted as Assume that the maximum power gain of the 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 reflection 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):

[0093]

[0094] 2. Objectives to be achieved:

[0095] The objective of the present invention is to maximize the minimum average RSRP of users in the target area in a multipath scenario. Specifically, it is achieved by dividing and arranging the QS-IRS into sub-arrays in a manner similar to OFDM, and then forming the corresponding optimal shaping beam through a two-stage iterative equalization and shaping beam synthesis algorithm based on sub-array activation to complete the optimal allocation of sub-arrays. Finally, the beam directions of each sub-array under this optimal configuration are output and the common phase factor ε n , thus completing the phase setting of the overall QS-IRS array.

[0096] 3. Specific implementation process:

[0097] A) Channel analysis

[0098] First, analyze the QS-IRS three-dimensional shaped beam coverage system in the broadband multipath scenario as Figure 1 shown. Establish a three-dimensional Cartesian coordinate system with the first unit of the QS-IRS as the origin, and place the QS-IRS in the yoz plane. Assume the horizontal angle of the incident signal is the elevation angle is θ i , denoted as the horizontal angle of the reflected signal and the elevation angle θ r , denoted as Assume that the considered broadband system has a total of K sub-bands, each sub-band has a bandwidth of Δf, and the initial frequency point is f0. Then the frequency point of the k-th sub-band can be expressed as:

[0099] f k = f0 + kΔf, k = 1,..., K - 1 (1)

[0100] Therefore, according to the three-dimensional space angle relationship, the steering vector a k of the incident signal with the sub-band frequency point f i (Π i , f k ) can be obtained as:

[0101]

[0102] Then the LoS link channel between the BS and the QS-IRS can be expressed as:

[0103] h = η(Π i )β(f k )a i (Π i , f k ) (3)

[0104] where η(Π i ) represents the radiation pattern gain generated by the QS-IRS reflection unit and the BS transmitting antenna, β i (f k ) represents the large-scale path loss of the LoS link, Since all the relevant channel information of the LoS link can be obtained, the fixed value part is defined as Assume that there are L multipaths between the QS-IRS and a certain user in the target area. Therefore, the steering vector of the l-th reflected path on the QS-IRS can also be defined as a rl (Π rl ,f k ):

[0105]

[0106] Then the channel of the l-th reflected path can be expressed as:

[0107]

[0108] Where η(Π rl ) represents the radiation pattern gain of the QS-IRS unit for the l-th reflected path. Since the gain it provides for the signal reflected at a certain angle is determined, the equivalent channel complex gain of the l-th reflected path can be defined as α l represents the large-scale path loss of the l-th reflected path. represents the phase of the l-th reflected path, and τ l represents the time delay of the l-th reflected path. Assume that the phase shift matrix of the QS-IRS is m = 1,..., M, where represents the compensation phase of the m-th reflection unit, which can be vectorized as Therefore, the multipath cascaded channel can be expressed as:

[0109]

[0110] Where (·)T represents the transpose, and a l (∏ i ,∏ rl ,f k ) = a i (∏ i ,f k )⊙a rl (∏ rl ,f k ), and ⊙ represents the Hadamard product.

[0111] B) Performance Index Analysis and Optimization Problem Construction

[0112] To effectively evaluate the system performance, the present invention will use the average reference signal received power (RSRP) of the user as an index. First, define the amplitude spectral density of the BS transmitting antenna as S t (f k ), then the received signal amplitude spectral density S of a certain user in a specific target area under the broadband multipath scenarior (f k ) can be expressed as:

[0113]

[0114] In the formula, Δ l represents the spatial frequency angle of the l-th reflection path, In order to enhance the multipath signals of different spatial frequency angles through beam matching, the present invention plans to divide the QS-IRS into N sub-arrays by using the SP technology, and each sub-array contains reflection units. For the convenience of subsequent mathematical derivation and proof, it is assumed in the present invention that the number M of reflection units in the sub-array s is an integer, that is, there is a multiple relationship between the number of QS-IRS units and the number of sub-arrays. It is defined that each sub-array can be directed to a certain spatial angle direction Then the beamforming vector of the n-th sub-array can be expressed as:

[0115]

[0116] Among them, represents the common phase of the n-th sub-array. Therefore, the compensation phase of each reflection unit can be rewritten as:

[0117]

[0118] Substituting Equation (9) into Equation (7), the received amplitude spectral density of this user in the target area can be further obtained:

[0119]

[0120] The above formula is disassembled and analyzed. First, for term, there is:

[0121]

[0122] And the first exponential term in the above formula can be written as:

[0123]

[0124] Secondly, the second exponential term in Equation (11) can be transformed by using the array factor AF formula into:

[0125]

[0126] Therefore, substituting Equations (12) and (13) into Equation (11), the final expression of the received amplitude spectral density of the user can be obtained:

[0127]

[0128] Assume the beam directions of each sub - array and the common phase factor ε n are given. Therefore, the shaped beam pattern factor A(Δ l ) after sub - array synthesis can be defined as:

[0129]

[0130] It should be noted that the beam pattern factor A(Δ l ) is a complex number, which represents the vector superposition generated by multiple sub - arrays at the spatial frequency angle Δ l . Since the beam direction and the common phase factor ε n are both assumed to be given, the magnitude part of A(Δ l ) is defined as and the phase part is Therefore, there is Based on equations (14) and (15), the received power spectral density |S r (f k )| 2 of the user can be expressed as:

[0131]

[0132] Assume that the power distribution of the transmitting antenna on each sub - band is uniform, that is, the amplitude spectral density S t (f k ) is independent of the frequency point. In addition, for the convenience of subsequent derivation and analysis, the present invention assumes that the bandwidth Δf of each sub - band is small relative to the coherence bandwidth of the channel, and the channels where the sub - band signals are located can be approximately regarded as flat - fading channels, that is, the channel response does not change significantly within this bandwidth. Define the long - term fading part of the channel as Therefore, the total received power P total of the user can be obtained by integrating the received power spectral density |S r (f k )| 2 over the entire frequency spectrum:

[0133]

[0134] Due to the flat - fading assumption of the channels where the sub - band signals are located, the summation term for frequency only acts on the parts of each path delay. Observing the above formula, the first summation term represents the correlation between multipaths, and the second summation term represents the influence of each path delay at different frequencies. For the summation term of frequency, it can also be transformed using the AF formula, that is, there is:

[0135]

[0136] Substitute Equation (18) into (17), and the received power P of the user can be total rewritten as:

[0137]

[0138] Since Therefore, first analyze L i L j and we have:

[0139]

[0140] Substitute the above equation into Equation (19), then the received power P of the user total can be further expressed as:

[0141]

[0142] Assume that the phase factors Φ l of each path are relatively independent and follow a uniform distribution on [0, 2π]. Therefore, for this user, its average RSRP can be expressed as:

[0143]

[0144] When i = j, we have:

[0145]

[0146] When i ≠ j, then we have:

[0147]

[0148] where, it is defined that Since the parameter information of each link in the multipath scenario can be measured and obtained through ray tracing technology, including the large-scale path loss |α′ l |, the propagation delay τ l , the reflection angle of each path and θ rl as well as the power information. Based on this, the result of the trigonometric function expectation l formed by the independent and identically distributed variables Φ in Equation (24) is:

[0149]

[0150] Combining Equations (22) - (25), it can be known that the average RSRP of this user can be expressed as:

[0151]

[0152] It can be seen from the above formula that the average RSRP of the user is only determined by the average power of each path and the corresponding beam pattern factor A(Δ l ). Therefore, by reasonably designing the arrangement and synthesis of sub-arrays, the average RSRP of this user can be maximized. However, the present invention considers multiple users within the target area covered by the beam. Therefore, the designed shaped beam needs to take into account the communication quality of each user, that is, the average RSRP of each user. Based on this, the present invention will maximize the minimum average RSRP of users within the target area by designing the beam directions and the common phase factor ε n . The optimization problem can be constructed as the following formula:

[0153]

[0154] where S represents the user index, and S represents the set of all users within the target area.

[0155] C) OFDM Sub-array Partitioning and Arrangement

[0156] The present invention considers partitioning and arranging sub-arrays for the QS-IRS. Therefore, reasonable sub-array partitioning may affect the effect of the shaped beam and the complexity of subsequent sub-array synthesis, and may further affect the performance of the overall system. It can be seen from Equation (15) that the influence of the sub-array on the average RSRP of the user involves the amplitude and phase of its synthesized beam. First, the amplitude part of a single sub-array can be expressed as:

[0157]

[0158] Figure 2 shows the power gain curve of the sub-array with the number of elements M = 8 when s . It can be observed that the sub-array achieves the peak gain when Δ l = 0, and the value is 0 when k = 1,..., N - 1. The beam width formed by its first zero point is This also shows that the beam width of the array is inversely proportional to the array aperture . Secondly, the effective gain coverage range of the beam is defined as . Therefore, the effective coverage width of the array beam is In other words, if the number of divided sub-arrays is smaller and the number of elements in each sub-array is larger, then its effective coverage width is narrower. In addition, since the multipath parameter information of different users within the target area in the broadband multipath scenario can be obtained through ray tracing technology. Therefore, the minimum and maximum spatial multipath spatial frequency angles can be defined according to the measured multipath angle information, which are Δ min and Δ max, the spatial frequency angular range of the multipath is

[0159] To achieve the shaped beam coverage for users within a specific target area, the present invention will arrange sub-arrays within the measured spatial frequency angular range. Therefore, if the number of divided sub-arrays is small, even when considering that the beam coverage widths of each sub-array do not overlap with each other, and the total coverage width of the array is still much smaller than the spatial frequency angular range, that is it may lead to the formed beam being unable to take into account the multipath signals at each spatial frequency angle within the range, that is, the synthesized shaped beam can only match and enhance the multipath signals at a few multipath angles, thus seriously affecting the received signal performance of other users in the area. On the other hand, if the number of divided sub-arrays is too large, such that they are densely arranged within the considered spatial frequency angular range and the coverage widths of each sub-array overlap with each other, at this time, the beams of each sub-array will interfere with each other, further greatly increasing the complexity of the phase design of each sub-array and the sub-array synthesis algorithm. Therefore, in order to make the beam coverage width of the sub-array adapt to the multipath spatial frequency angular range as much as possible, while effectively reducing the complexity of the sub-array phase design and synthesis, the present invention considers designing the division and arrangement of the sub-arrays by referring to the orthogonality property of OFDM sub-carriers. Specifically, design the beam direction of each sub-array to satisfy the effective coverage width of the interval, such as Figure 3 shown. At this time, only the current sub-array provides beam gain at the peak, and the multipath signals at other spatial frequency angles can be approximately considered to be provided with beam gain only by the two adjacent sub-arrays. Therefore, the complexity of the phase design will be effectively reduced. At the same time, the sub-array division will be related to the number M of QS-IRS units and the spatial frequency angular range Δ spec , and can be specifically expressed as:

[0160]

[0161] Through the above method, the spatial frequency angular range can be divided into N * grid points, and the spatial frequency angle corresponding to each grid point represents the peak beam direction of a sub-array. And when performing sub-array synthesis, it also means that each sub-array can choose to direct its beam to the spatial frequency angle corresponding to any one of the grid points.

[0162] D) Design of a two-stage iterative equalization shaped beam synthesis algorithm based on sub-array activation

[0163] The traditional sub-array synthesis algorithm is an exhaustive search algorithm, that is, for N sub-arrays directed to N spatial frequency angle directions for permutation and combination, its complexity is To reduce the exponential complexity of traditional exhaustive search algorithms, the present invention proposes a two-stage iterative equalization shaping beam synthesis algorithm based on sub-array activation. Specifically, in the first stage, each sub-array is first divided and arranged in the OFDM-like manner in step C); subsequently, according to the different multipath spatial frequency angles of different users, the activation status of each sub-array is judged. That is, when the spatial frequency angle Δ l of a certain path is within the coverage width of the nth sub-array and satisfies:

[0164]

[0165] it indicates that the nth sub-array is activated, and the spatial frequency angle corresponding to the currently activated sub-array will also be used as the reference angle for subsequent sub-array arrangement and synthesis; then, the activated sub-arrays are fully arranged, and through comparison and analysis, the arrangement method that maximizes the minimum average RSRP of each user in the target area is obtained; then, on this basis, one of the unactivated sub-arrays is selected and synthesized to the reference angle of the activated sub-arrays, and through comparison and analysis, the combination method that maximizes the minimum average RSRP of each user can also be obtained. The above operations are repeated until all unactivated sub-arrays are reallocated and combined, and at this time, the corresponding sub-array arrangement and combination scheme will be obtained, which is used as the initial parameter for the iterative equalization method in the next stage.

[0166] It should be noted that in order to synthesize different sub-arrays in a certain same direction in addition to directing the beams of each sub-array towards the direction, it is also necessary to carefully design the common phase factor ε n of each sub-array so that its phase satisfies in-phase superposition, thereby obtaining the maximum gain effect. Define the phase offset of a certain sub-array as:

[0167]

[0168] According to Equation (15), it can be seen that if the first Q sub-arrays are all directed towards the direction, the synthesized beam pattern factor can be expressed as:

[0169]

[0170] In order to achieve in-phase superposition of phases at , the phase of each sub-array needs to satisfy the following formula:

[0171]

[0172] Substituting Equation (31) into it, we can get:

[0173]

[0174] Let k = 0, then the common phase factor ε of each sub-array n can be expressed as:

[0175]

[0176] To simplify the analysis, set the common phase factor of the reference array to zero when synthesizing the sub-arrays, then we have:

[0177]

[0178] Through the above design of the sub-array beam direction and the common phase factor, corresponding shaped beams can be formed for different sub-array combinations. Figure 4 Shows the shaped beams formed by combining four sub-arrays at the corresponding activation angles. The dotted lines in the figure represent different multipath spatial frequency angles. Define the beam directions of each sub-array as {-0.25, -0.125, 0, 0.125}. Assume that the sub-arrays in the directions of {-0.25, 0.125} are activated. Therefore, the unactivated sub-arrays in the directions of {-0.125, 0} will be reallocated and combined, and then different shaped beams can be formed under different combination methods, as Figure 4 shown. Figure 5 Shows the shaped beam pattern synthesized by each sub-array at the unactivated angles. It can be observed that compared with the schemes of combining and synthesizing at the sub-array activation angles, this shaped beam pattern has a very low beam gain at the corresponding multipath spatial frequency angles. Therefore, it is reasonable and effective to only consider synthesizing the beam at the spatial frequency angles corresponding to the activated sub-arrays.

[0179] Subsequently, it enters the second stage. First, the sub-array combination obtained in the first stage is used as the initial parameter, and the average RSRP of each user is calculated under the weighted formed beam pattern. At this time, the user with the minimum average RSRP will be obtained. Then, the method of iterative balancing is used to finely adjust the sub-array combination. Specifically, in each round of iterative balancing process, the sub-array serving the user with the maximum or the second maximum current average RSRP is selected and redirected to the direction of each reference spatial frequency angle. At this time, the average RSRP of each user is calculated under the weighted formed beam pattern corresponding to the obtained result. If the current minimum average RSRP is larger than that of the initial parameter configuration in the previous round, the allocation is successful, and the current sub-array combination configuration is retained and used as the initial parameter configuration for the next round of iterative balancing; otherwise, if the current minimum average RSRP is smaller than that of the initial parameter configuration in the previous round, this reallocation scheme is not adopted, and the previous step is returned to reselect other sub-arrays for allocation. The above operations are repeated until all sub-arrays of the user with the maximum or the second maximum RSRP are reallocated in a certain round of iterative balancing, and the minimum average RSRP value is still not improved, then the algorithm ends. At this time, the configuration parameters of the current sub-array combination are output, including the beam direction of each sub-array and the common phase factor ε n , and substituting them into Equation (9), the phase setting of the overall QS-IRS can be obtained. The specific flow steps of the two-stage iterative balancing formed beam synthesis algorithm based on sub-array activation are shown in Figure 6 .

[0180] 4. Analysis of experimental results:

[0181] First, for the multipath information of different users within a specific target area, it can be obtained through simulation using the Quasi-Deterministic Radio channel Generator (QuaDRiGa) (I. Burtakov, et al., "QRIS: A QuaDRiGa-Based Simulation Platform for Reconfigurable Intelligent Surfaces," IEEE Access, vol. 11, pp. 90670-90682, 2023). This platform is a geometry-based stochastic channel modeling method that can create arbitrary two-way radio channels, and different antenna configurations and element radiation patterns can be inserted according to actual needs. It uses object-oriented programming and object handles, greatly reducing memory usage, effectively improving performance, and can be directly implemented using MATLAB. The method of obtaining channel parameters based on QuaDRiGa can be approximately regarded as a "statistical ray tracing method", that is, scatterers with statistical distributions are randomly generated in space, and the departure and arrival angles, propagation delay, and power of each path are simulated and deduced according to the positions of the transmitting antenna and different user receivers.

[0182] In this embodiment, the center frequency is set to 5 GHz, the sub-band bandwidth is 20 MHz, the maximum power gain G of the QS-IRS unit is 4, the unit is half-wavelength spacing, the 3GPP TR 38.901 urban macrocell model is adopted, and four users in a specific target area are selected. Receivers are placed at the user positions, and then the multipath information of each user is obtained through QuaDRiGa. To simplify subsequent processing and analysis, the present invention will select the two paths with dominant multipath power among each user as experimental parameters and perform power normalization. The multipath parameter information of each user is shown in Table 1.

[0183] Table 1 User multipath-related parameters obtained based on QuaDRiGa

[0184]

[0185] Based on the above multipath parameter information, it can be known that Δ min =-0.1208, Δ max =0.3607, then the multipath spatial frequency angle range Δ spec =0.4815. Assuming the number of QS-IRS units M = 200, according to Equation (29), the number of QS-IRS subarrays N = 8 can be calculated, and the number of units in each subarray is M s =25, and the coverage width of each subarray is Therefore, set the beam direction of each subarray They are respectively represented as:

[0186]

[0187] Subsequently, the shaping beam design is carried out by using the two-stage iterative equalization algorithm based on sub-array activation proposed in the present invention. At the same time, two benchmark schemes are set for simulation comparison analysis, namely, the random phase setting of QS-IRS and the flat beam design of QS-IRS (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). In addition, the gain performance of the traditional exhaustive algorithm is also analyzed. From Figure 7 It can be seen that the scheme based on the random phase setting of QS-IRS has the worst gain performance, while the two-stage iterative equalization algorithm based on sub-array activation proposed in the present invention has higher gain performance compared with the QS-IRS flat beam scheme. In addition, the algorithm proposed in the present invention can make the minimum average RSRP of the users in the target area approximately equal to the minimum average RSRP of the users under the exhaustive search algorithm. On the other hand, the solution time of the two-stage iterative equalization algorithm based on sub-array activation proposed in the present invention is 11.4019 s, and the solution time of the traditional exhaustive search algorithm is 3.2676×10 5 s. The algorithm proposed in the present invention has greatly reduced the solution complexity. Therefore, the shaping beam synthesis algorithm based on two-stage iterative equalization with sub-array activation proposed in the present invention has good effectiveness.

[0188] The above embodiments are only preferred embodiments of the present invention and cannot be considered as limiting the scope of implementation of the present invention. All equivalent changes and improvements made according to the scope of the present invention application should still fall within the scope covered by the patent of the present invention.

Claims

1. A three-dimensional forming beam synthesis design method for quasi-static intelligent reflecting surfaces based on sub-array activation, characterized in that It includes the following steps: 1) System model establishment and channel analysis: Construct a QS-IRS communication system model in a broadband multipath scenario and conduct channel analysis to obtain the line-of-sight channel from the base station to the QS-IRS and the multipath channel parameters of the user; 2) Performance metric analysis and optimization problem construction: Analyze the average RSRP expression of the user and use it as an index to evaluate the system performance, and construct an optimization problem with the goal of maximizing the minimum average RSRP of the user; 3) OFDM-like subarray division and arrangement: Based on the grid division strategy of OFDM-like, divide and arrange the QS-IRS into subarrays, and determine the beam coverage angle of each subarray; 4) Design of a Two-Stage Iterative Equalization Shaped Beam Synthesis Algorithm Based on Subarray Activation: The two-stage iterative equalization algorithm based on subarray activation is adopted to dynamically adjust the activation state, beam direction, and phase of the subarrays, generate a three-dimensional shaped beam that matches the multipath spatial angles, and complete the optimal allocation of the subarrays; the beam directions of each subarray under this configuration are output and the common phase factor ε n , and the phase design of the overall QS-IRS is completed.

2. The three-dimensional forming beam synthesis design method of the quasi-static intelligent reflecting surface based on sub-array activation according to claim 1, characterized in that In step 1), the specific methods for system model establishment and channel analysis are as follows: Construct a QS-IRS uniform linear array deployed on the surface of a tall building or an aerial vehicle to achieve the far-field communication scenario of beam covering users in a specific target area on the ground; Assume that the direct link between the base station BS and the users in the target area is severely blocked and ignored, and communication is only carried out through the cascaded link constructed by the QS-IRS; To reduce the influence of the double-segment path loss of the QS-IRS, the QS-IRS is deployed close to the BS to ensure receiving the energy of most of the transmitted signals; On the other hand, assume that the QS-IRS is deployed at a high altitude so that a LoS link is formed between it and the BS, and the signals reflected by the QS-IRS are affected by factors such as dense buildings or obstacles, high and low terrain, and atmospheric environment, and will undergo different degrees of reflection, refraction, or scattering, thus forming multiple different propagation paths; Assume that the BS is equipped with a single directional antenna, and the direction of its maximum power gain points to the QS-IRS, and the maximum power gain is G t ; The user is equipped with a single omnidirectional antenna; The QS-IRS uniform linear array consists of M reflection units, and the maximum power gain of each unit is G; A three-dimensional Cartesian coordinate system is established with the first unit of QS-IRS as the origin, and the QS-IRS is placed in the yoz plane; assume that the horizontal angle of the incident signal is and the elevation angle is θ i , denoted as The horizontal angle of the reflected signal and the elevation angle θ r , denoted as Assume that the considered broadband system has a total of K sub-bands, each sub-band has a bandwidth of Δf, and the initial frequency point is f0. Then the frequency point of the k-th sub-band is expressed as: f k = f0 + kΔf, k = 1, …, K - 1 Therefore, according to the three-dimensional spatial angle relationship, the calculated sub-band frequency point is f k The incident steering vector a of the signal on the QS-IRS i (Π i , f k ), then the channel between the BS and the QS-IRS is expressed as: h = η(Π i )β i (f k )a i (Π i ,f k ) where, η(∏ i ) represents the radiation pattern gain generated by the QS-IRS reflection unit and the BS transmitting antenna, and β i (f k ) represents the large-scale path loss of the LoS link; since all the relevant channel information of the LoS link can be obtained, the fixed-value part in the above formula is defined as Suppose a user in the target area has a total of L multipaths. Therefore, the steering vector of the l-th reflected path on the QS-IRS is also defined as a rl (∏ rl , f k ), then the channel of the l-th reflected path is expressed as: where, η(∏ rl ) represents the radiation pattern gain of the QS-IRS unit for the l-th reflected path; since the gain it provides for the signal reflected at a certain angle is determined, the equivalent channel complex gain of the l-th reflected path is defined as α l represents the large-scale path loss of the l-th reflected path; represents the phase of the l-th reflected path; τ l represents the propagation delay of the l-th reflected path; assume the phase shift matrix of the QS-IRS is where represents the compensation phase of the m-th unit, and its vectorization is Based on this, the multipath cascaded channel is expressed as: Among them, (·) T denotes transpose, a l (Π i , Π rl , f k ) = a i (Π i , f k ) ⊙ a rl (Π rl , f k ), where ⊙ denotes the Hadamard product.

3. The three-dimensional shaping beam synthesis design method of the quasi-static intelligent reflecting surface based on sub-array activation according to claim 1, characterized in that In step 2), the specific steps of the performance metric analysis and optimization problem construction are as follows: Taking the average reference signal received power (RSRP) of the user as an index, first define the amplitude spectral density of the BS transmitting antenna as S t (f k ). Then, the amplitude spectral density S r (f k ) of the received signal of a certain user in a specific target area under the broadband multipath scenario is expressed as follows: where, Δ l represents the spatial frequency angle of the l-th reflected path, To enhance the multipath signals with different spatial frequency angles by beam matching, the QS-IRS is divided into N sub-arrays by using the SP technique, and each sub-array contains reflecting elements; for the convenience of subsequent mathematical derivation and proof, it is assumed that the number of reflecting elements M of the sub-array s is an integer, that is, there is a multiple relationship between the number of QS-IRS elements and the number of sub-arrays; it is defined that each sub-array is directed to a certain spatial angle direction Then the beamforming vector of the n-th sub-array is expressed as: wherein, represents the common phase of the nth sub-array; thus, the compensation phase of each reflection unit is rewritten as: Substitute the above compensation phase into the received signal amplitude spectral density expression and further rewrite it as: Convert the summation term about the subarray elements in the above formula using the array factor AF, then the received amplitude spectral density of the user is rewritten as: Assume the beam direction of each sub-array and the common phase factor ε n are given; thus, the shaped beam direction pattern factor A(Δ l ) after sub-array synthesis is defined as: The beam pattern factor A(Δ l ) is a complex number, which represents the vector superposition generated by multiple sub-arrays at the spatial frequency angle Δ l ; Since the beam direction and the common phase factor ε n are both assumed to be given, the amplitude part of A(Δ l ) is defined as and the phase part is Therefore, there is Then the received power spectral density |S r (f k )| 2 is expressed as: Assume that the power allocation of the transmitting antenna on each sub-band is uniform, that is, the amplitude spectral density S of the transmitting antenna t (f k ) is independent of the frequency point; for the convenience of subsequent derivation and analysis, assume that the bandwidth Δf of each sub-band is small relative to the coherence bandwidth of the channel, and the channels where the sub-band signals are located are approximately regarded as flat fading, that is, the channel response does not change significantly within this bandwidth; define the long-term fading part of the channel as Therefore, the total received power P of the user total From the received power spectral density |S r (f k )| 2 Integrating over the entire frequency spectrum gives: Due to the flat fading assumption of the channels where each subband signal is located, the summation term for frequency only acts on the path delay part; the first summation term represents the correlation between multipaths, and the second summation term represents the influence of each path delay at different frequencies; for the summation term for frequency, it is also transformed using the AF formula, that is: Substitute the above equation into the total received power expression, and rewrite the received power \(P\) of the user as: total as follows: Since Therefore, first analyze L i L j to get: Therefore, the received power P of the user total is further expressed as: Assume that the phase factors Φ of each path l are relatively independent and follow a uniform distribution on [0, 2π]; thus, for this user, its average RSRP is expressed as: When i = j, there is: When i ≠ j, then there is: Among them, it is defined that Since the parameter information of each link in the multipath scenario is measured and obtained through ray tracing technology, including large-scale path loss |α′ l |, propagation delay τ l , reflection angles of each path and θ rl as well as power information; based on this, for the trigonometric function expectation l formed by the independent and identically distributed variables Φ in the above formula, the result is: Combined with the above analysis, the average RSRP of this user is expressed as: The average RSRP of the user is determined only by the average power of each path and the corresponding beam pattern factor A(Δ l ); by designing the arrangement and synthesis of the sub-arrays, the average RSRP of this user is maximized; multiple users within the beam coverage target area are considered; the designed shaped beam needs to take into account the communication quality of each user, that is, the average RSRP of each user; based on this, by designing the beam directions of each sub-array and the common phase factor ε n , the minimum average RSRP of the users within the target area is maximized; the optimization problem is formulated as follows: where s represents the user index and S represents the set of all users in the target area.

4. The three-dimensional forming beam synthesis design method of the quasi-static intelligent reflecting surface based on sub-array activation according to claim 1, wherein In step 3), the specific steps of the OFDM-like subarray division and arrangement are as follows: Since the multipath parameter information of different users in the target area is obtained through ray tracing technology, the minimum and maximum multipath spatial frequency angles are defined as Δ min and Δ max , then the range of the spatial frequency angle of the multipath is [Δ min , Δ max . The first null beamwidth of a single subarray is Its effective gain coverage range is The effective coverage width of the array beam is Consider dividing the QS-IRS into N sub-arrays based on the orthogonal property of OFDM, specifically expressed as: * ​ In the above manner, the multi-path spatial frequency angle range is divided into N * grid points, and the interval between each grid point is set to Moreover, the spatial frequency angle corresponding to each grid point represents the peak beam direction of a sub-array; when performing sub-array synthesis, it also means that each sub-array selects to direct its beam to the spatial frequency angle corresponding to any one of the grid points.

5. The three-dimensional forming beam synthesis design method of a quasi-static intelligent reflecting surface based on sub-array activation according to claim 1, characterized in that In step 4), the specific method of the two-stage iterative equalization shaping beam synthesis algorithm design based on subarray activation is as follows: In the first stage, each sub-array is divided and arranged in the OFDM-like manner in step 3); subsequently, the activation status of each sub-array is determined according to the different multi-path spatial frequency angles of different users, that is, when the spatial frequency angle Δ of a certain path l is within the coverage width of the th sub-array, satisfying: It means activating the nth subarray, and the spatial frequency angle corresponding to the currently activated subarray will also be used as the reference angle for subsequent subarray arrangement and synthesis. Then, perform a full permutation of the activated subarrays, compare and analyze to obtain the permutation method that maximizes the minimum average RSRP of each user in the target area. Select one of the unactivated subarrays and synthesize it at the reference angle of the activated subarrays. After comparison and analysis, also obtain the combination method that maximizes the minimum average RSRP of each user. Repeat the above operations until all unactivated subarrays are reallocated and combined. At this time, the corresponding subarray arrangement and combination scheme will be obtained, which will be used as the initial parameter for the iterative equalization method in the next stage. To synthesize different subarrays at a certain same spatial frequency angle direction In addition to directing the beams of each subarray to the direction, it is also necessary to carefully design the common phase factor ε n of each subarray so that its phases satisfy in-phase superposition to obtain the maximum gain effect. Therefore, the common phase factor ε n of each subarray is set according to different beam directions as follows: In the second stage, first use the subarray combination obtained in the first stage as the initial parameter, and calculate the average RSRP of each user under the weighting of the shaping beam pattern. At this time, the user with the minimum average RSRP will be obtained; then, use the method of iterative equalization to fine-tune the subarray combination; Specifically, in each round of iterative equalization process, select the subarray serving the user with the maximum or second maximum average RSRP at present and direct it to each reference spatial frequency angle direction again. At this time, calculate the average RSRP of each user under the weighting of the corresponding obtained shaping beam pattern; if the current minimum average RSRP is larger than the initial parameter configuration of the previous round, the allocation is successful, and the current subarray combination configuration is retained and used as the initial parameter configuration for the next round of iterative equalization; Conversely, if the current minimum average RSRP is smaller than the initial parameter configuration in the previous round, then this reallocation scheme is not adopted, and the previous step is returned to reselect other sub-arrays for allocation; the above operations are repeated until all sub-arrays of the user with the largest or second largest RSRP are reallocated in a certain round of iterative equilibrium, and the minimum average RSRP value is still not improved, then the algorithm ends; at this time, the combined configuration parameters of each current sub-array are output, including the beam direction of each sub-array and the common phase factor ε n , and then the phase setting of the overall QS-IRS is obtained; the computational complexity of this algorithm is where N1 represents the number of active sub-arrays and K represents the number of iterative equilibrium rounds.

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