Spatial characteristic evaluation and port configuration method and system for low-altitude flexible HMIMO

Abstract

The invention provides a low-altitude flexible HMIMO-oriented spatial characteristic evaluation and port configuration method and system, and the method comprises the steps: constructing the array geometry of a flexible HMIMO array, and setting a user position and an electromagnetic propagation environment model; secondly, visibility judgment and gating processing are carried out on the sight distance model; then, the whole array is divided into sub-arrays, and available sub-arrays are screened out; calculating an autocorrelation matrix and quantizing a channel statistical difference distance between any two sub-arrays to generate a spatial non-stationary heat map; meanwhile, the full-aperture space freedom degree is calculated; and finally, obtaining an average achievable port mode number by taking a statistical expectation from a target direction domain, and obtaining a port configuration engineering upper bound by integrating a theoretical degree of freedom and hardware constraints. According to the method, the problems of spatial non-stationary quantization, sub-array availability judgment and port-level realizable mode number determination of the flexible curved surface array under near-field and shielding conditions are solved, and a direct basis is provided for engineering design and resource allocation of flexible HMIMO in low-altitude communication.

Description

Technical Field

[0001] This invention relates to wireless communication and array signal processing technology, specifically to a method and system for spatial characteristic evaluation and port configuration of low-altitude flexible HMIMO. Background Technology

[0002] As 6G mobile communication technology evolves towards an integrated air-space-ground system, low-altitude economic scenarios, represented by drones, low-altitude aircraft, and near-ground terminals, urgently demand high capacity, high reliability, and three-dimensional wide coverage for wireless communication. Against this backdrop, holographic massive MIMO (HMIMO) technology, employing large physical apertures and ultra-high element density, is considered a key approach to improving beam focusing capabilities, spatial resolution, and spectral efficiency. However, in actual low-altitude base station deployments, limitations such as curved carrier installation, flexible substrate materials, structural deformation, and assembly tolerances mean that HMIMO arrays often exhibit bent, warped, continuous curved surface shapes, forming flexible or conformal arrays. This poses a significant challenge to the classical assumptions upon which traditional MIMO system analysis and design rely.

[0003] Existing technologies have the following four main shortcomings when dealing with low-altitude flexible HMIMO scenarios:

[0004] Firstly, regarding the "self-occlusion" phenomenon of curved arrays where some array elements are not visible to the user due to their own curvature, i.e., the Visibility Region (VR) problem, existing research mostly relies on empirical rules or specific measurement data to fit VR, lacking universal and clear geometric determination methods, making it difficult to perform stable and reusable modeling when array curvature, user distance, and orientation change.

[0005] Secondly, under large aperture and occlusion conditions, sub-apertures at different locations within the array face significant spatial non-stationarity (SnS). Existing common metrics for quantifying SnS, such as Correlation Matrix Distance (CMD), typically eliminate the impact of overall power scaling by normalizing the correlation matrix, thus focusing on comparing differences in the correlation "structure." However, when VR causes some sub-arrays to become completely invisible or experience severe power attenuation, huge power differences (i.e., power imbalances) emerge between sub-arrays. In this case, traditional CMD metrics may severely underestimate the actual degree of non-stationarity because they "cannot see" this power difference, leading to distorted evaluations.

[0006] Third, in hardware architectures employing hybrid beamforming or based on subarrays (ports), each subarray needs to be treated as a locally stable unit. However, existing work typically pre-determines the subarray size, lacking a calculable determination of whether the spatial correlation characteristics of the channel within the subarray are sufficiently stable under a given partition. When the near-field amplitude gradient is drastic or the VR boundary crosses the interior of the subarray, the subarray cannot be used as a stable unit, directly affecting beam calibration and signal processing performance.

[0007] Fourth, spatial degrees of freedom (DoF) characterize the theoretical upper limit of the array's multiplexing capability, but the practical engineering implementation of flexible HMIMO is limited by the number of ports and RF link resources. Existing technologies often analyze the full-aperture DoF or differences between subarrays in isolation, lacking a method to further map the quantification results of spatial nonstationarity into "the number of practically achievable, non-redundant port modes under port partitioning and hardware constraints." This makes it difficult to directly translate theoretical analysis into an effective basis for guiding hardware design decisions such as port merging / splitting and RF link configuration.

[0008] A patent search revealed invention patent CN118300927A, which discloses a knowledge-driven deep learning-based fast estimation method for high-dimensional TSN channels, belonging to the field of wireless communication channel estimation technology. This invention designs a knowledge-driven GMMV-LAMP high-dimensional channel estimation network and a frequency-selective broadband redundancy dictionary design method for channel estimation. The GMMV-LAMP network can perform fast and accurate broadband high-dimensional channel estimation. The frequency-selective broadband redundancy dictionary can accurately obtain the sparse domain representation of the channel in millimeter-wave UM-MIMO pure far-field, near-field, and mixed far-near-field scenarios, and overcomes the beam squint effect caused by the frequency flatness dictionary. However, this patent does not consider the flexible array morphology and self-occlusion effects, lacks spatial characteristic evaluation and port configuration guidance, and only addresses channel estimation, without addressing the determination of core parameters related to system resource configuration.

[0009] In summary, given the problems of the existing technologies, researching a method and system for evaluating the spatial characteristics and configuring ports for low-altitude flexible HMIMO has become a critical task that urgently needs to be addressed. Summary of the Invention

[0010] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for evaluating the spatial characteristics and configuring ports of low-altitude flexible HMIMOs.

[0011] A method for evaluating the spatial characteristics and configuring ports of a low-altitude flexible HMIMO according to the present invention includes the following steps: Step S1: Construct the array geometry of the flexible HMIMO array; Step S2: Set the user's position in three-dimensional space and select the electromagnetic propagation environment model; Step S3: If the selected model is a line-of-sight propagation model, then based on the array geometry and user location, the visibility of each array element is determined one by one using a geometric method. A binary visibility mask is generated according to the determination result, and the line-of-sight channel is gated to obtain the visible area gated channel as channel data. If the selected model is a non-line-of-sight propagation model, then a channel vector containing multipath clusters is generated as the full array channel data. If the selected model is an isotropic scattering model, then the channel spatial correlation characteristics are generated using a closed correlation kernel as the full array channel data. Step S4: Based on the full array channel data, the flexible HMIMO array is divided into multiple sub-arrays of equal size. The received power of each element in each sub-array is calculated to form the received power sequence of the sub-array. The relative variance of each received power sequence is calculated, and it is determined whether the relative variance meets the preset criteria. Sub-arrays that meet the preset criteria are used as usable sub-arrays. Step S5: Calculate the autocorrelation matrix of each available subarray, combine all available subarrays in the whole array in pairs to obtain multiple available subarray pairs, calculate the channel statistical difference distance of each available subarray pair in the user direction, and take the average value to obtain the average spatial nonstationarity index in the user direction. Traverse all user directions, calculate the corresponding average spatial nonstationarity index, and visualize it to form a spatial nonstationarity heat map. Step S6: Based on the full array channel data, calculate the full aperture spatial correlation matrix and calculate the full aperture spatial degrees of freedom using the Rényi-2 effective rank formula; Step S7: If the selected model is a line-of-sight propagation model, then based on the channel statistical difference distance, construct a port similarity matrix, calculate the effective rank using the Rényi-2 effective rank formula, take the statistical expectation of the effective rank in the target direction domain to obtain the average number of realizable port modes, and based on the average number of realizable port modes and the full aperture space degrees of freedom, derive the final engineering upper bound for the number of ports, which is used to guide port configuration and RF link planning.

[0012] Preferably, step S1 includes the following sub-steps: Step S1.1: Based on preset physical parameters, calculate the bending half-angle that describes the overall curvature of the array; the physical parameters include the total length of the array, the radius of curvature, and the total number of array elements; Step S1.2: Based on the total number of array elements and the bending half-angle in the physical parameters, calculate the central angle position corresponding to each array element when it is uniformly distributed on the arc array; Step S1.3: Combining physical parameters, bending half-open angle, and the center angle position of each array element, calculate the absolute position of the array element in the preset coordinate system using three-dimensional coordinate formulas to form the array geometry.

[0013] Preferably, step S2 includes the following sub-steps: Step S2.1: Set the user's position in three-dimensional space, using a spherical coordinate system for description; Step S2.2: Select one of the following three electromagnetic propagation environment models: A. Line-of-sight propagation model; B. Non-line-of-sight propagation model; C. Isotropic scattering model.

[0014] Preferably, if the selected model is a line-of-sight propagation model, step S3 includes the following sub-steps: Step S3.1-LoS: Based on the array geometry and user location, calculate the straight-line distance from each array element to the user, and substitute it into the free space propagation formula to calculate the complex baseband channel coefficients; Step S3.2-LoS: Use the tangent plane method or normal vector method to determine whether each array element is visible to the user, and generate a binary visibility mask. Step S3.3-LoS: The complex baseband channel coefficients are gated using a binary visibility mask to obtain the visible area gated channel, which is used as the full array channel data.

[0015] Preferably, step S3.2-LoS includes the following sub-steps: Step S3.2.1: Based on the array geometry, define the center of the arc array and calculate the outward normal unit vector for each array element; Step S3.2.2: Using the user's position and the outward normal unit vector, determine whether the user is located in the front half space of the array element. If so, the array element is determined to be visible; otherwise, the array element is determined to be invisible. Step S3.2.3: Convert the judgment result of each array element into a mathematical inequality and generate a binary visibility mask.

[0016] Preferably, step S4 includes the following sub-steps: Step S4.1: Divide the entire array into K subarrays of equal size; Step S4.2: Extract the channel sub-vectors corresponding to each sub-array from the full array channel data in sequence; Step S4.3: For the predetermined user direction, based on the channel sub-vector, calculate the received power of each element in each sub-array to form the received power sequence of the sub-array, and then calculate the power mean and variance of the received power sequence. Step S4.4: Based on the power mean and variance, calculate the relative variance of each received power sequence in the user direction, determine whether the relative variance meets the preset criteria, and select the subarrays that meet the preset criteria as usable subarrays.

[0017] Preferably, step S5 includes the following sub-steps: Step S5.1: Calculate the autocorrelation matrix of the channel subvectors for each available subarray; Step S5.2: For any two available subarrays, use the autocorrelation matrices corresponding to the two available subarrays to calculate the structural consistency coefficient and power ratio of the two available subarrays.

[0018] Step S5.3: Equalize the power ratio by introducing a power balance function.

[0019] Step S5.4: Combine the structural consistency coefficient and power balance function to calculate the channel statistical difference distance between two available subarrays.

[0020] Preferably, step S6 includes the following sub-steps: Step S6.1: Calculate the full aperture spatial correlation matrix based on the full array channel data; Step S6.2: Apply the Rényi-2 effective rank formula to the correlation matrix of the full aperture space to calculate the degrees of freedom of the full aperture space.

[0021] Preferably, step S7 includes the following sub-steps: Step S7.1: Using the channel statistical difference distance in each direction, construct a port similarity matrix for each user direction under the line-of-sight channel; Step S7.2: For the port similarity matrix under each user direction, calculate the effective rank using the Rényi-2 effective rank formula; Step S7.3: Statistically expect the effective rank within the target service direction domain to obtain the average number of achievable port modes. Take the minimum value of the average number of achievable port modes, the full aperture spatial degrees of freedom, and the preset number of available RF links to obtain the final engineering upper bound of the number of ports.

[0022] This invention also provides a space characteristic evaluation and port configuration system for low-altitude flexible HMIMO, comprising: Module M1 constructs the array geometry of the flexible HMIMO array; Module M2 sets the user's position in three-dimensional space and selects the electromagnetic propagation environment model; Module M3, if the selected model is a line-of-sight propagation model, then based on the array geometry and user location, performs visibility determination on each array element one by one using a geometric method, generates a binary visibility mask based on the determination result, and performs gating processing on the line-of-sight channel to obtain the visible area-gated channel as channel data; if the selected model is a non-line-of-sight propagation model, then generates a channel vector containing multipath clusters as the full array channel data; if the selected model is an isotropic scattering model, then uses a closed correlation kernel to generate channel spatial correlation characteristics as the full array channel data. Module M4, based on full array channel data, divides the flexible HMIMO array into multiple subarrays of equal size, calculates the received power of each element within each subarray to form a received power sequence of the subarray, calculates the relative variance of each received power sequence, determines whether the relative variance meets a preset criterion, and selects the subarrays that meet the preset criterion as usable subarrays. Module M5 calculates the autocorrelation matrix of each available subarray, pairs all available subarrays in the full array to obtain multiple available subarray pairs, calculates the channel statistical difference distance of each available subarray pair in the user direction, takes the average value to obtain the average spatial nonstationarity index in the user direction, traverses all user directions, calculates the corresponding average spatial nonstationarity index, and visualizes it to form a spatial nonstationarity heatmap. Module M6 calculates the full aperture spatial correlation matrix based on full array channel data and calculates the full aperture spatial degrees of freedom using the Rényi-2 effective rank formula; Module M7, if the selected model is the line-of-sight propagation model, constructs a port similarity matrix based on the channel statistical difference distance, calculates the effective rank using the Rényi-2 effective rank formula, takes the statistical expectation of the effective rank in the target direction domain, and obtains the average number of realizeable port modes. Based on the average number of realizeable port modes and the full aperture space degrees of freedom, the final engineering upper bound of the number of ports is obtained, which is used to guide port configuration and RF link planning.

[0023] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention addresses the self-occlusion problem of flexible arc arrays by using explicit geometric inequalities to determine the visibility of array elements, avoiding reliance on empirical thresholds or measurement fitting, and achieving stable and rapid determination under different curvatures, distances, and directions.

[0024] 2. This invention introduces a power balance function to explicitly quantize the power difference between subarrays. Even when VR causes the power of some subarrays to be significantly reduced or invisible, it can still reliably reflect the overall non-stationarity and avoid the problem of underestimating the difference due to normalization.

[0025] 3. This invention first selects usable subarrays with sufficiently stable internal statistical characteristics by calculating the relative variance of the received power sequence of the subarray and setting criteria, thus ensuring the reliability of the port partitioning basis; then, based on these usable subarrays, it performs global non-stationarity quantification and heatmap visualization, so that the port partitioning scheme and subsequent calibration design have a clear basis.

[0026] 4. This invention calculates the spatial degrees of freedom of the entire array and the effective rank based on the port similarity matrix using the Rényi-2 effective rank. These two methods complement each other, jointly characterizing the complete dimensional features of the array from its physical potential to its engineering implementation, avoiding misjudgments caused by a single indicator.

[0027] 5. This invention maps the PoVi-CMD distance to a port similarity matrix and calculates its effective rank to obtain the average number of non-redundant ports that can be realized in the target spatial domain. This value, together with the theoretical degrees of freedom and the number of hardware RF links, constrains the final engineering configuration, providing a direct quantitative decision-making basis for port merging / splitting, RF link planning, and beam resource allocation. Attached Figure Description

[0028] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of a low-altitude flexible HMIMO communication system in an embodiment of the present invention (including base station flexible aperture and low-altitude user / UAV link). Figure 2 This is a schematic diagram illustrating the relationship between the geometry of the flexible 1D arc array and the user's three-dimensional position in an embodiment of the present invention. Figure 3 This is a geometric schematic diagram of the flexible 2D array (stacked arc array) in an embodiment of the present invention; Figure 4-5 This is the SnS heatmap of the flexible linear array under LoS in this embodiment of the invention; Figure 6-8 This is a comparison diagram of the SnS heatmap slicing method under LoS in the embodiments of the present invention; Figure 9-12 This is a SnS heatmap of a flexible planar array under LoS in an embodiment of the present invention. Figure 13-16 This is a SnS heatmap of a flexible linear array under NLoS in an embodiment of the present invention. Figure 17-24 This is a SnS heatmap of a flexible surface array under NLoS in an embodiment of the present invention. Figure 25-28 This refers to the eigenvalue spectrum of the spatial correlation matrix of the flexible linear array under LoS in this embodiment of the invention. Figure 29-32This is the eigenvalue spectrum of the spatial correlation matrix of the flexible linear array under NLoS in this embodiment of the invention; Figure 33 This refers to the eigenvalue spectrum of the spatial correlation matrix of the isotropic flexible linear array in this embodiment of the invention. Figure 34 This refers to the eigenvalue spectrum of the spatial correlation matrix of the isotropic flexible surface array in this embodiment of the invention. Figures 35-37 This is a schematic diagram of the curve showing the change in the number of achievable port modes with curvature in an embodiment of the present invention. Detailed Implementation

[0029] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0030] Definitions of abbreviations and key terms:

[0031] This invention discloses a method and system for spatial characteristic evaluation and port configuration of low-altitude flexible large-scale multiple-input multiple-output (HMIMO) arrays. The method first constructs the array geometry of the flexible HMIMO array and sets user location and electromagnetic propagation environment models. Next, channel data is generated based on the selected model, and visibility determination and gating are performed using the tangent plane method for the line-of-sight model. Then, the entire array is divided into subarrays, the relative variance of the received power sequence is calculated, and usable subarrays with internal stationarity are selected. Based on the usable subarrays, the autocorrelation matrix is ​​calculated, and the channel statistical difference distance between any two subarrays is quantified to generate a spatial non-stationarity heatmap. Simultaneously, the full aperture spatial degrees of freedom are calculated. Finally, a port similarity matrix is ​​constructed using the channel difference distance, its effective rank is calculated, and the average number of realizeable port modes is obtained by taking the statistical expectation over the target direction domain. The upper bound for port configuration engineering is derived by combining theoretical degrees of freedom and hardware constraints. This invention solves the problems of spatial non-stationarity quantification, subarray availability judgment, and port-level realizeable mode determination for flexible curved arrays under near-field and obstruction conditions, providing a direct basis for the engineering design and resource allocation of flexible HMIMO in low-altitude communication.

[0032] Example 1: This embodiment provides a spatial characteristic evaluation and port configuration method for low-altitude flexible HMIMO. This method prioritizes geometry and, starting from the physical morphology of the array, sequentially and uniformly characterizes the following key aspects: geometric modeling of the flexible array (including 1D arc arrays and 2D stacked arc arrays); visibility zone (VR) determination based on self-occlusion under LoS and VR-gated channels; introducing the PoVi-CMD spatial nonstationarity index with power balancing and visibility gating; full-aperture spatial DoF calculation based on Rényi-2 effective rank; constructing a port similarity matrix using PoVi-CMD and extracting its effective rank to obtain the number of achievable port modes; achieving reproducible evaluation in NLoS scenarios using the 3GPP TR 38.901 CDL ​​model; and employing closed-form correlation expression in isotropic scattering scenarios to improve computational efficiency and result interpretability.

[0033] Figure 1 This is a schematic diagram of a low-altitude flexible HMIMO communication system (including base station flexible aperture and low-altitude user / UAV link) in an embodiment of the present invention. Figure 1 The typical application of flexible arrays in low-altitude communication scenarios is described.

[0034] Specifically, the method for evaluating the spatial characteristics and configuring ports of low-altitude flexible HMIMO includes the following steps: Step S1: Construct the array geometry of the flexible HMIMO array.

[0035] Specifically, based on the preset physical shape and physical parameters of the flexible HMIMO array, the position of each antenna element (array element) in the three-dimensional space is calculated to obtain the array geometry.

[0036] In this embodiment, the physical form of the flexible HMIMO array is a flexible 1D arc array or a flexible 2D array, and the physical parameters include the total array length, radius of curvature, number of array elements, and element spacing. The flexible 2D array is formed by stacking multiple 1D arc arrays along the x-direction. Figure 2 and Figure 3 The schematic diagrams of the 1D / 2D flexible array geometry in this embodiment are shown respectively.

[0037] Step S1 includes the following sub-steps: Step S1.1: Based on the preset physical parameters: total array length L (unit: meters) and radius of curvature R (unit: meters), calculate the key dimensionless parameter describing the overall bending degree of the array: bending half-open angle β.

[0038] The calculation formula is:

[0039] in: The time array is approximately a straight line. The time array is bent into a semicircle.

[0040] Step S1.2: Based on the total number of array elements in the physical parameters and the bending half-angle, calculate the position of the central angle corresponding to the uniform distribution of array elements on the arc array.

[0041] Specifically, let the flexible 1D arc array in this embodiment contain a total of There are several array elements (antenna elements), and the array elements are evenly distributed along the arc. When the array elements are uniformly distributed on the arc-shaped array, the corresponding central angle positions are:

[0042] in: Describes the relative angular position of the array elements in the arc physical form; when With the increase in size and the decrease in element spacing, the array gets closer to a continuous aperture (HMIMO dense sampling limit).

[0043] Step S1.3: Taking into account physical parameters, bending half-open angle, and the center angle position of each array element, calculate the absolute position of the array element in the preset coordinate system (e.g., deployed in the YZ plane) using three-dimensional coordinate formula.

[0044] Specifically, the array is deployed in a three-dimensional Cartesian coordinate system. In the plane, the first The position vector of each array element (Unit: m) is defined as: , Among them, the triples correspond to the three-dimensional rectangular coordinates of the array elements. Because the array is in Y In the plane, therefore all array elements .

[0045] all The set of elements constitutes the array geometry. Step S2: Set the user's position in three-dimensional space and select the electromagnetic propagation environment model; To prepare for subsequent channel modeling and analysis, the spatial location of the user is set, and the physical model that electromagnetic wave propagation follows is selected. This is the premise for all subsequent calculations.

[0046] Step S2 includes the following sub-steps: Step S2.1: Set the user's position in three-dimensional space, using a spherical coordinate system for description.

[0047] Define a user in three-dimensional space, where the user is located in three-dimensional spherical coordinates. The corresponding rectangular coordinate position vector (unit: )for:

[0048] in: The distance from the user to the array reference origin (the center or starting point of the reference array). ); pitch angle (rad or From the positive (Measured from the axial direction downwards) Azimuth (rad or ,exist From positive in the plane (Measured counterclockwise on the axis).

[0049] Step S2.2: Select one of the following three electromagnetic propagation environment models for subsequent channel generation.

[0050] A. The line-of-sight (LoS) propagation model describes the unobstructed direct wave propagation between the transmitter and receiver, and is the core scenario for evaluating near-field and self-occlusion effects.

[0051] B. Non-line-of-sight propagation model (NLoS model): This embodiment adopts the international standard 3GPP TR 38.901 CDL ​​(cluster delay line) model (such as CDL-A). This model uses multipath clusters to simulate complex environments with scattering and reflection, ensuring the reproducibility of the evaluation is aligned with the standard.

[0052] C. Isotropic scattering model (theoretical closed model): It assumes that the incident wave is uniformly distributed in half of the space and that its spatial correlation matrix has a closed solution of the sinc function. It is suitable for rapid performance baseline calculation of large-scale apertures to distinguish the contribution of environmental and geometric factors to nonstationarity.

[0053] Step S3: If the selected model is a line-of-sight propagation model, then based on the array geometry and user position, the visibility of each array element is determined one by one using the tangent plane method or the normal vector method. A binary visibility mask is generated according to the determination result, and the line-of-sight channel is gated to obtain the visible area gated channel as channel data. If the selected model is a non-line-of-sight propagation model, then a channel vector containing multipath clusters is generated as the full array channel data. If the selected model is an isotropic scattering model, then the channel spatial correlation characteristics are generated using a closed correlation kernel as the full array channel data.

[0054] Local filtering (generating a binary visibility mask and performing gating processing) and visibility determination are only applicable to scenarios where the full array channel data obtained in step S3 is a visible area (VR) gated channel under line-of-sight (LoS) conditions; in NLoS and isotropic environments, since there is no clear visible area, local filtering and visibility determination are skipped.

[0055] Specifically, if the selected model is the line-of-sight propagation model, step S3 includes the following sub-steps: Step S3.1-LoS: Based on the array geometry and user location, calculate the straight-line distance from each array element to the user, and substitute it into the free space propagation formula to calculate the complex baseband channel coefficients without considering obstruction.

[0056] Specifically, no. The straight-line distance from each element to the user for: , in, For user location, This refers to the position of the nth array element. When explicitly expanded, the distance is written as the square root of the sum of the squares of the three terms (the expanded form is omitted here; in engineering implementation, it is directly calculated based on the coordinate difference).

[0057] No. Complex baseband channel coefficients corresponding to each array element for:

[0058] in: The equivalent gain of the transmitter (array element) is dimensionless; in the embodiment, it can be taken as 1 or given by the antenna pattern. The equivalent gain (dimensionless) of the receiving end (user). The carrier wavelength (m) and carrier frequency The relationship is The speed of light; The magnitude term describing the free-space path loss; Describes the phase term caused by the propagation distance; It is the imaginary unit.

[0059] Step S3.2-LoS: To address the self-occlusion phenomenon of the flexible arc array, the tangent plane method or normal vector method is used to determine whether each array element is visible to the user, and a binary visibility mask is generated.

[0060] A method for constructing the VR visibility region based on tangent plane determination under LoS conditions. Flexible arc-shaped arrays may experience self-occlusion in certain directions: for some array elements, if the user's direction is located in the half-space behind the element, then that element is not visible to the user. This embodiment presents a geometric visibility determination method that does not rely on empirical values, used to generate VR masks and form VR-gated channels.

[0061] This embodiment uses the tangent plane method. Step S3.2-LoS includes the following sub-steps: Step S3.2.1, based on the array geometry, define the center of the arc array and calculate the outward normal unit vector for each array element.

[0062] Specifically, the center of the arc array for:

[0063] No. The outward normal unit vector of each array element (Dimensionless) is:

[0064] in: Description of the The local normal direction angle corresponding to the array element; This represents the unit normal of the array element facing outwards.

[0065] Step S3.2.2: Using the user's position and the outward normal unit vector, determine whether the user is located in the front half space of the array element. If so, the array element is determined to be visible; otherwise, the array element is determined to be invisible.

[0066] Specifically, for the nth array element, the user position Define the vector pointing from the array element to the user as... When the angle between the vector and the external normal of the array element does not exceed... When the dot product is non-negative, the array elements are considered visible.

[0067] The visibility condition is:

[0068] For ease of calculation, it is written in an equivalent form related to the center of the circle:

[0069] The two equations above are equivalent under arc geometry, and either one can be chosen for engineering implementation.

[0070] Step S3.2.3: Convert the judgment result of each array element into a mathematical inequality and generate a binary visibility mask.

[0071] Compare the user's spherical coordinates with Substitute, and write visibility as: ,in, And define the threshold term: .

[0072] Therefore, the VR criterion is written as: , Among them, the left side It is the incident direction projection quantity related to the direction; right side With distance Inversely proportional: the farther the distance (closer to the far field), the smaller the right side, and the easier it is to satisfy visibility; but even The conditions for the front half of the space still need to be met.

[0073] Define a binary visibility mask for the nth element: : When the visibility inequality is satisfied, then Take 1, otherwise Take 0.

[0074] Step S3.3-LoS: The complex baseband channel coefficients are gated using a binary visibility mask to obtain the visible area gated channel, which is used as the full array channel data.

[0075] Specifically, the LosS channel after VR gating is generated as follows:

[0076] in, is the complex baseband channel coefficient in this embodiment; the invisible array element is set to zero. This VR-gated channel is the key source of power imbalance and statistical structure difference in the subsequent SnS metric.

[0077] Optionally, far-field approximation (optional) and array steering vector: when the user distance satisfies the far-field condition. When this happens, a first-order approximation can be used to simplify the distance calculation, which can be written as: , obtain the array steering vector In this embodiment, the far-field approximation is only used for comparative analysis; in low-altitude, short-range links, to preserve the near-field effect, the accurate distance using the above formula is usually still used. The above model.

[0078] If the selected model is a non-line-of-sight propagation model, then according to the 3GPP TR 38.901 standard, channel vectors containing multipath clusters are generated as full array channel data. Specifically, the angle / power / delay and angular spread parameters of the clusters are given using models such as 3GPP CDL-A, and channels are generated by superimposing multipath rays.

[0079] If an isotropic scattering model is selected, the channel spatial correlation characteristics are generated as full-array channel data using a closed-form correlation kernel (such as the sinc function). Specifically, the elements of the spatial correlation matrix can be obtained by angular domain integration and can be approximated as a sinc-type closed-form expression; the coverage spread caused by bending can be corrected by introducing a one-dimensional integral term, and diagonal normalization is used to maintain unity power. This method avoids high-dimensional numerical integration and is suitable for rapid calculation of DoF and SnS baselines for large-scale apertures, used to determine the contribution of environmentally driven nonstationarity to geometrically driven nonstationarity.

[0080] Step S4: Based on the full array channel data, the flexible HMIMO array is divided into multiple sub-arrays of equal size. The received power of each element in each sub-array is calculated to form the received power sequence of the sub-array. The relative variance of each received power sequence is calculated, and it is determined whether the relative variance meets the preset criteria. Sub-arrays that meet the preset criteria are used as usable sub-arrays. Specifically, before calculating the differences between subarrays, it is necessary to ensure that the channels within each subarray are sufficiently stable. Relying solely on globally non-stationary SnS heatmaps is insufficient to provide reliable guidance for hardware port partitioning, because even if the differences between subarrays are small, their internal channels may experience severe fluctuations due to near-field effects (amplitude gradients) or crossing of the visible region (VR) boundary, rendering the subarray unusable. Therefore, this embodiment introduces a local screening step to first identify usable subarrays with internal stability before proceeding with subsequent SnS evaluations between subarrays.

[0081] The substructure analysis of the entire array, specifically, step S4 includes the following sub-steps: Step S4.1: Divide the entire array into K subarrays of equal size.

[0082] Specifically, let the entire array have Each array element (1D time) hour ), where N represents the number of array elements in the bending direction, and M represents the number of stacked flexible array layers, dividing the flexible array into equal-sized subarrays Each subarray contains the following number of array elements: Define the full array channel data (the channel vector of the full array) as follows: :

[0083] in Indicates the first The complex channel coefficients from each array element to the user.

[0084] Step S4.2: Extract the channel sub-vectors corresponding to each sub-array from the full array channel data in sequence.

[0085] Specifically, no. The channel subvectors corresponding to each subarray are denoted as follows: That is, from By index set I won it.

[0086] Step S4.3: Based on the user direction determined by the azimuth and elevation angles, and combined with the straight-line distance from the array element to the user, the received power of each array element in each subarray is calculated using the channel subvectors to form a received power sequence; then the power mean and variance of the sequence are calculated.

[0087] Specifically, define the first The received power of each array element is:

[0088] in: For the user The complex channel coefficients (including VR gating) are below. It is a non-negative real number, representing the received power intensity. The received power sequence that constitutes this subarray.

[0089] Calculate the first Subarrays power average With variance :

[0090] Step S4.4: Based on the power mean and variance, calculate the relative variance of each received power sequence in the user direction, determine whether the relative variance meets the preset criteria, and select the subarrays that meet the preset criteria as usable subarrays.

[0091] Specifically, relative variance is defined as follows:

[0092] like This indicates that the entire subarray is invisible in the user's direction (VR is all 0), and the user's direction is not included in the statistics.

[0093] In this embodiment, the criterion for sufficiently flat power within the subarray is defined as follows: ,in It is a natural constant.

[0094] Sampling in multiple directions The set of visible directions of the statistical subarray:

[0095] And calculate the probability of passing:

[0096] in, This is an indicator function.

[0097] The local stationarity criterion is set as follows: when When determining the subarray To achieve local stability, the percentage of subarrays that pass through can be statistically analyzed to assess whether a certain partitioning is usable.

[0098] Based on the evaluation results of all subarrays, the system assesses and outputs which number of subarrays and their partitioning methods (e.g., 1D continuous, 2D mesh) can ensure that most subarrays meet the local stationarity requirements under the current system parameters (frequency, array size, distance, curvature, etc.). This output is directly used for subsequent port implementation. If a partitioning is locally non-stationary in most directions, then that port size is not suitable.

[0099] Step S5: Calculate the autocorrelation matrix of each available subarray, combine all available subarrays in the whole array in pairs to obtain multiple available subarray pairs, calculate the channel statistical difference distance (PoVi-CMD distance) of each available subarray pair in the user direction, and take the average value to obtain the average spatial nonstationarity index in the user direction. Traverse all user directions, calculate the corresponding average spatial nonstationarity index, and visualize it on the direction grid to form a spatial nonstationarity heat map. A measure of spatial nonstationarity of the correlation matrix between power equalization and visibility perception, and its array domain visualization (SnSheatmap).

[0100] Based on the available subarrays, the spatial nonstationarity of the flexible HMIMO array is further evaluated. To address the problem of significant power imbalance in some subarrays caused by the visible region (VR), this embodiment proposes the Power Balanced and Visibility-Aware Correlation Matrix Distance (PoVi-CMD) method to reliably quantify the statistical differences between subarrays.

[0101] Specifically, step S5 includes the following sub-steps: Step S5.1: Calculate the autocorrelation matrix of the channel subvectors for each available subarray. If VR gating has been applied to the element-level channels, the formula for calculating the autocorrelation matrix of the available subarrays is:

[0102] in It is the conjugate transpose; For statistical expectation; This is the channel subvector of the kth available subarray after VR gating; .

[0103] Step S5.2: For any two available subarrays, use the autocorrelation matrices corresponding to the two available subarrays to calculate the structural consistency coefficient and power ratio of the two available subarrays.

[0104] Specifically, PoVi-CMD defines that for any two available subarrays... and First, define the structural consistency coefficients of the two available subarrays. :

[0105] in: The trace of the matrix; It is the Frobenius norm; The larger the value, the more similar the correlation structure of the signals inside the two available subarrays.

[0106] Define the power ratio of the two available subarrays. :

[0107] in: Characterizes the relative strength of the overall received power of two available subarrays. express The visible power / correlation strength is generally stronger than that of the available subarrays. on the contrary.

[0108] Step S5.3: Equalize the power ratio by introducing a power balance function.

[0109] To quantify the impact of power imbalance on statistical differences, a symmetric power balance function is introduced. :

[0110] in, It is an exponential parameter (dimensionless). The larger the value, the more sensitive it is to power imbalance; when hour, , indicating power balance; when or hour .

[0111] Step S5.4: Combine the structural consistency coefficient and power balance function to calculate the channel statistical difference distance (PoVi-CMD distance) between two available subarrays.

[0112] Specifically, the PoVi-CMD distance formula is defined as follows:

[0113]

[0114] When two available subarrays have identical related structures and similar power hour, This indicates weak spatial stability; when structural differences or power differences are large (especially when VR causes some subarrays to be semi-visible / invisible), As the amplitude increases, spatial non-stationarity becomes more pronounced. Compared to traditional CMD (which is insensitive to overall power scaling), PoVi-CMD can explicitly reflect the amplitude inconsistencies brought about by VR.

[0115] For the user direction, calculate the channel statistical difference distance between each pair of available subarrays and take the average value to obtain the average spatial nonstationarity index in the user direction. Traverse all user directions, calculate the corresponding average spatial nonstationarity index, and visualize it on the direction grid to obtain the spatial nonstationarity heat map.

[0116] Specifically, for each user direction Calculate all available subarray pairs And by averaging, we get: , Will A spatial nonstationarity (SnS) heatmap can be obtained by plotting on a half-space directional grid, which can be used to visually identify "which directions / distances / curvatures have the strongest statistical differences in the subarray".

[0117] like Figures 4-5 Showing the SnS heatmap of a flexible linear array under LoS. Figures 6-8 This chart compares the performance of different methods for measuring spatial non-stationarity in the SnS heatmap under LoS at a 90° azimuth angle. Figures 9-12 This demonstrates the SnS heatmap of a flexible planar array under LoS conditions. Furthermore, for the NLoS scenario, Figures 13-16 This displays SnS heatmaps of a flexible linear array under NLoS with different subarray separation degrees. Figures 17-24 This corresponds to the SnS heatmap of flexible surface arrays under different subarray separation degrees in NLoS.

[0118] Step S6: Based on the full array channel data, calculate the full aperture spatial correlation matrix, and calculate the full aperture spatial degrees of freedom using the Rényi-2 effective rank formula. The full aperture spatial degrees of freedom represent the theoretical upper limit of the independent signal spatial dimensions that the array can physically support. This step aims to calculate the physical maximum independent signal spatial dimension of the flexible HMIMO array, i.e., the full aperture spatial degrees of freedom (DoF). This metric provides a theoretical performance upper limit for subsequent port configuration and hardware planning.

[0119] Step S6 includes the following sub-steps: Step S6.1: Based on the full array channel data (channel vectors of the full array) obtained in step S3, calculate the full aperture spatial correlation matrix.

[0120] Specifically, the formula for calculating the full aperture spatial correlation matrix is ​​as follows: , Step S6.2: Apply the Rényi-2 effective rank formula to the correlation matrix of the full aperture space to calculate the degrees of freedom of the full aperture space.

[0121] Specifically, let the eigenvalue be... (Non-negative real numbers), and define normalized weights:

[0122] The effective rank of Rényi-2 is defined as:

[0123] in, For effective spatial degrees of freedom (dimensionless); Indicates total power; This indicates the degree of energy concentration on eigenvalues; when energy is concentrated on a few modes, Smaller; when energy is distributed across more modes, Increase.

[0124] The normalized DoF can also be provided: , Among them, such as Figures 25-28 The spatial correlation matrix eigenvalue spectrum of the flexible linear array under LoS and 3GPP CDL-D channel models is shown. Figures 29-32 The spatial correlation matrix eigenvalue spectrum of the flexible array under the NLoS 3GPP CDL-A channel model is described. Figure 33 This represents the eigenvalue spectrum of the spatial correlation matrix of an isotropic flexible linear array. Figure 34 The eigenvalue spectrum represents the spatial correlation matrix of an isotropic flexible surface array.

[0125] Step S7: If the selected model is the line-of-sight propagation model, then based on the channel statistical difference distance, construct a K×K port similarity matrix, calculate the effective rank using the Rényi-2 effective rank formula, take the statistical expectation of the effective rank in the target direction domain, and obtain the average number of realized port modes. Based on the average number of realized port modes and the full aperture space degrees of freedom, derive the final engineering upper bound of the number of ports, which is used to guide the configuration of port merging and separation and the planning of radio frequency links.

[0126] Based on the evaluation results of statistical differences between subarrays, the actual number of non-redundant ports that the array can provide is calculated under realistic constraints such as port partitioning and visibility, and power imbalance. Combining physical limits and hardware resources, an engineering upper bound for the final port configuration is given.

[0127] Step S7 includes the following sub-steps: Step S7.1: Using the PoVi-CMD distances in each direction calculated in step S5, a port similarity matrix is ​​constructed for each user direction under the line-of-sight channel.

[0128] In port-constrained hardware, arrays are often formed as subarrays / tiles. There are several ports. To compress the SnS heatmap into a usable port-dimensional budget, in this embodiment, a port similarity matrix is ​​constructed. Among them, diagonal elements Off-diagonal elements .

[0129] in, PoVi-CMD distance; The closer to 1, the more similar the two ports are in that direction (stronger redundancy); the closer to 0, the less similar they are (stronger parallelism).

[0130] Step S7.2: For the port similarity matrix under each user direction, calculate the effective rank using the Rényi-2 effective rank formula. This is to evaluate the actual number of independent ports among the K ports in a specific user direction.

[0131] Specifically, for the port similarity matrix Define the number of port modes (effective rank):

[0132] because This is also equivalent to:

[0133] If all ports have similar heights (SnS is weak), ),but This indicates that the ports are basically redundant, and port merging should be considered for robust focusing; if the port differences are significant (SnS strong), (large), then This indicates that the port can provide more independent modes, which is beneficial for multi-beam / multi-user parallel operation.

[0134] Step S7.3: Calculate the statistical expectation (average) of the effective rank within the target service direction domain to obtain the average number of achievable port modes. Take the minimum value of the average number of achievable port modes, the full aperture spatial degrees of freedom (physical theoretical upper limit) calculated in step S6, and the number of available RF links predetermined by the system hardware to obtain the final engineering upper bound of the number of ports to guide the hardware design.

[0135] Specifically, for the target service direction domain (For example, in the first half of the low-altitude space) take the average to obtain the average number of achievable port modes in this scenario:

[0136] Final port number upper bound (engineering constraint fusion):

[0137] in: The ratio of available RF links to baseband data streams (dimensionless) is determined by the hardware. This formula directly sets the upper limit of the physical aperture. Port redundancy Hardware RF data Unify them under the same constraint.

[0138] Under NLoS, the angle / power / delay and angular spread parameters of the clusters are given using models such as 3GPP CDL-A. Channels are generated by superimposing multipath rays, and PoVi-CMD and DoF are calculated according to steps S4 to S6. This ensures that the evaluation is reproducible, aligned with standards, and can reflect the phenomenon of DoF being limited by scattering under sparse multi-cluster scattering.

[0139] Under isotropic scattering half-space conditions, the spatial correlation matrix elements can be obtained by angular domain integration and can be approximated as a sinc-type closed expression; the coverage expansion caused by bending can be corrected by introducing a one-dimensional integral term, and diagonal normalization is used to maintain unity power. This method avoids high-dimensional numerical integration and is suitable for rapid calculation of DoF and SnS baselines for large-scale apertures, used to determine the contribution of environmentally driven nonstationarity to geometrically driven nonstationarity.

[0140] Example 2: The present invention also provides a spatial characteristic evaluation and port configuration system for low-altitude flexible HMIMO. The spatial characteristic evaluation and port configuration system for low-altitude flexible HMIMO can be implemented by executing the process steps of the spatial characteristic evaluation and port configuration method for low-altitude flexible HMIMO. That is, those skilled in the art can understand the spatial characteristic evaluation and port configuration method for low-altitude flexible HMIMO as a preferred embodiment of the spatial characteristic evaluation and port configuration system for low-altitude flexible HMIMO.

[0141] Figures 35-37 This diagram illustrates the curve showing the change in the number of port modes as a function of curvature for a flexible array under a given subarray partitioning scheme.

[0142] Specifically, this space characteristic evaluation and port configuration system for low-altitude flexible HMIMO includes: Module M1 constructs the array geometry of the flexible HMIMO array; Module M2 sets the user's position in three-dimensional space and selects the electromagnetic propagation environment model; Module M3, if the selected model is a line-of-sight propagation model, then based on the array geometry and user location, performs visibility determination on each array element one by one using a geometric method, generates a binary visibility mask based on the determination result, and performs gating processing on the line-of-sight channel to obtain the visible area-gated channel as channel data; if the selected model is a non-line-of-sight propagation model, then generates a channel vector containing multipath clusters as the full array channel data; if the selected model is an isotropic scattering model, then uses a closed correlation kernel to generate channel spatial correlation characteristics as the full array channel data. Module M4, based on full array channel data, divides the flexible HMIMO array into multiple subarrays of equal size, calculates the received power of each element within each subarray to form a received power sequence of the subarray, calculates the relative variance of each received power sequence, determines whether the relative variance meets a preset criterion, and selects the subarrays that meet the preset criterion as usable subarrays. Module M5 calculates the autocorrelation matrix of each available subarray, pairs all available subarrays in the full array to obtain multiple available subarray pairs, calculates the channel statistical difference distance of each available subarray pair in the user direction, takes the average value to obtain the average spatial nonstationarity index in the user direction, traverses all user directions, calculates the corresponding average spatial nonstationarity index, and visualizes it to form a spatial nonstationarity heatmap. Module M6 calculates the full aperture spatial correlation matrix based on full array channel data and calculates the full aperture spatial degrees of freedom using the Rényi-2 effective rank formula; Module M7, if the selected model is the line-of-sight propagation model, constructs a port similarity matrix based on the channel statistical difference distance, calculates the effective rank using the Rényi-2 effective rank formula, takes the statistical expectation of the effective rank in the target direction domain, and obtains the average number of realizeable port modes. Based on the average number of realizeable port modes and the full aperture space degrees of freedom, the final engineering upper bound of the number of ports is obtained, which is used to guide port configuration and RF link planning.

[0143] Example 1: Module M1 includes the following sub-modules: Module M1.1, based on preset physical parameters: total array length L (unit: meters) and radius of curvature R (unit: meters), calculates the key dimensionless parameter describing the overall bending degree of the array: bending half-open angle β.

[0144] The calculation formula is:

[0145] in: The time array is approximately a straight line. The time array is bent into a semicircle.

[0146] Module M1.2 calculates the central angle position corresponding to the uniform distribution of array elements on the arc array based on the total number of array elements in the physical parameters and the bending half-angle.

[0147] Specifically, let the flexible 1D arc array in this embodiment contain a total of There are several array elements (antenna elements), and the array elements are evenly distributed along the arc. When the array elements are uniformly distributed on the arc-shaped array, the corresponding central angle positions are:

[0148] in: Describes the relative angular position of the array elements in the arc physical form; when With the increase in size and the decrease in element spacing, the array gets closer to a continuous aperture (HMIMO dense sampling limit).

[0149] Module M1.3, taking into account physical parameters, bending half-open angle, and the center angle position of each array element, calculates the absolute position of the array element in a preset coordinate system (e.g., deployed in the YZ plane) using a three-dimensional coordinate formula.

[0150] Specifically, the array is deployed in a three-dimensional Cartesian coordinate system. In the plane, the first The position vector of each array element (Unit: m) is defined as: , Among them, the triples correspond to the three-dimensional rectangular coordinates of the array elements. Because the array is in Y In the plane, therefore all array elements .

[0151] all The set of elements constitutes the array geometry. Module M2 includes the following sub-modules: Module M2.1 sets the user's position in three-dimensional space, described using a spherical coordinate system.

[0152] Define a user in three-dimensional space, where the user is located in three-dimensional spherical coordinates. The corresponding rectangular coordinate position vector (unit: )for:

[0153] in: The distance from the user to the array reference origin (the center or starting point of the reference array). ); pitch angle (rad or From the positive (Measured from the axial direction downwards) Azimuth (rad or ,exist From positive in the plane (Measured counterclockwise on the axis).

[0154] Module M2.2 selects one of the following three electromagnetic propagation environment models for subsequent channel generation.

[0155] A. The line-of-sight (LoS) propagation model describes the unobstructed direct wave propagation between the transmitter and receiver, and is the core scenario for evaluating near-field and self-occlusion effects.

[0156] B. Non-line-of-sight propagation model (NLoS model): This embodiment adopts the international standard 3GPP TR 38.901 CDL ​​(cluster delay line) model (such as CDL-A). This model uses multipath clusters to simulate complex environments with scattering and reflection, ensuring the reproducibility of the evaluation is aligned with the standard.

[0157] C. Isotropic scattering model (theoretical closed model): It assumes that the incident wave is uniformly distributed in half of the space and that its spatial correlation matrix has a closed solution of the sinc function. It is suitable for rapid performance baseline calculation of large-scale apertures to distinguish the contribution of environmental and geometric factors to nonstationarity.

[0158] Specifically, if the selected model is the line-of-sight propagation model, module M3 includes the following sub-modules: Module M3.1-LoS calculates the straight-line distance from each array element to the user based on array geometry and user location, and substitutes it into the free space propagation formula to calculate the complex baseband channel coefficients without considering obstruction.

[0159] Specifically, no. The straight-line distance from each element to the user for: , in, For user location, This refers to the position of the nth array element. When explicitly expanded, the distance is written as the square root of the sum of the squares of the three terms (the expanded form is omitted here; in engineering implementation, it is directly calculated based on the coordinate difference).

[0160] No. Complex baseband channel coefficients corresponding to each array element for:

[0161] in: The equivalent gain of the transmitter (array element) is dimensionless; in the embodiment, it can be taken as 1 or given by the antenna pattern. The equivalent gain (dimensionless) of the receiving end (user). The carrier wavelength (m) and carrier frequency The relationship is The speed of light; The magnitude term describing the free-space path loss; Describes the phase term caused by the propagation distance; It is the imaginary unit.

[0162] Module M3.2-LoS addresses the self-occlusion phenomenon of flexible arc arrays by using the tangent plane method or normal vector method to determine whether each array element is visible to the user and generates a binary visibility mask.

[0163] A method for constructing the VR visibility region based on tangent plane determination under LoS conditions. Flexible arc-shaped arrays may experience self-occlusion in certain directions: for some array elements, if the user's direction is located in the half-space behind the element, then that element is not visible to the user. This embodiment presents a geometric visibility determination method that does not rely on empirical values, used to generate VR masks and form VR-gated channels.

[0164] This embodiment uses the tangent plane method. Module M3.2-LoS includes the following sub-modules: Module M3.2.1, based on array geometry, defines the center of the arc array and calculates the outward normal unit vector for each array element.

[0165] Specifically, the center of the arc array for:

[0166] No. The outward normal unit vector of each array element (Dimensionless) is:

[0167] in: Description of the The local normal direction angle corresponding to the array element; This represents the unit normal of the array element facing outwards.

[0168] Module M3.2.2 uses the user's position and the outward normal unit vector to determine whether the user is located in the front half space of the array element. If so, the array element is determined to be visible; otherwise, the array element is determined to be invisible.

[0169] Specifically, for the nth array element, the user position Define the vector pointing from the array element to the user as... When the angle between the vector and the external normal of the array element does not exceed... When the dot product is non-negative, the array elements are considered visible.

[0170] The visibility condition is:

[0171] For ease of calculation, it is written in an equivalent form related to the center of the circle:

[0172] The two equations above are equivalent under arc geometry, and either one can be chosen for engineering implementation.

[0173] Module M3.2.3 converts the judgment result of each array element into a mathematical inequality and generates a binary visibility mask.

[0174] Compare the user's spherical coordinates with Substitute, and write visibility as: ,in, And define the threshold term: .

[0175] Therefore, the VR criterion is written as: , Among them, the left side It is the incident direction projection quantity related to the direction; right side With distance Inversely proportional: the farther the distance (closer to the far field), the smaller the right side, and the easier it is to satisfy visibility; but even The conditions for the front half of the space still need to be met.

[0176] Define a binary visibility mask for the nth element: : When the visibility inequality is satisfied, then Take 1, otherwise Take 0.

[0177] The M3.3-LoS module uses a binary visibility mask to perform gating on the complex baseband channel coefficients to obtain the visible area gated channel, which is used as the full array channel data.

[0178] Specifically, the LosS channel after VR gating is generated as follows:

[0179] in, is the complex baseband channel coefficient in this embodiment; the invisible array element is set to zero. This VR-gated channel is the key source of power imbalance and statistical structure difference in the subsequent SnS metric.

[0180] Optionally, far-field approximation (optional) and array steering vector: when the user distance satisfies the far-field condition. When this happens, a first-order approximation can be used to simplify the distance calculation, which can be written as: , obtain the array steering vector In this embodiment, the far-field approximation is only used for comparative analysis; in low-altitude, short-range links, to preserve the near-field effect, the accurate distance using the above formula is usually still used. The above model.

[0181] If the selected model is a non-line-of-sight propagation model, then according to the 3GPP TR 38.901 standard, channel vectors containing multipath clusters are generated as full array channel data. Specifically, the angle / power / delay and angular spread parameters of the clusters are given using models such as 3GPP CDL-A, and channels are generated by superimposing multipath rays.

[0182] If an isotropic scattering model is selected, the channel spatial correlation characteristics are generated as full-array channel data using a closed-form correlation kernel (such as the sinc function). Specifically, the elements of the spatial correlation matrix can be obtained by angular domain integration and can be approximated as a sinc-type closed-form expression; the coverage spread caused by bending can be corrected by introducing a one-dimensional integral term, and diagonal normalization is used to maintain unity power. This method avoids high-dimensional numerical integration and is suitable for rapid calculation of DoF and SnS baselines for large-scale apertures, used to determine the contribution of environmentally driven nonstationarity to geometrically driven nonstationarity.

[0183] The substructure analysis of the entire array, specifically, module M4 includes the following submodules: Module M4.1 divides the entire array into K subarrays of equal size.

[0184] Specifically, let the entire array have Each array element (1D time) hour ), where N represents the number of array elements in the bending direction, and M represents the number of stacked flexible array layers, dividing the flexible array into equal-sized subarrays Each subarray contains the following number of array elements: Define the full array channel data (the channel vector of the full array) as follows: :

[0185] in Indicates the first The complex channel coefficients from each array element to the user.

[0186] Module M4.2 extracts the channel sub-vectors corresponding to each subarray sequentially from the full array channel data.

[0187] Specifically, no. The channel subvectors corresponding to each subarray are denoted as follows: That is, from By index set I won it.

[0188] Module M4.3, based on the user direction determined by the azimuth and elevation angles, and combined with the straight-line distance from the array element to the user, uses channel sub-vectors to calculate the received power of each array element in each subarray, forming a received power sequence; then the power mean and variance of this sequence are calculated.

[0189] Specifically, define the first The received power of each array element is:

[0190] in: For the user The complex channel coefficients (including VR gating) are below. It is a non-negative real number, representing the received power intensity. The received power sequence that constitutes this subarray.

[0191] Calculate the first Subarrays power average With variance :

[0192] Module M4.4 calculates the relative variance of each received power sequence in the user direction based on the power mean and variance, determines whether the relative variance meets the preset criteria, and selects the subarrays that meet the preset criteria as usable subarrays.

[0193] Specifically, relative variance is defined as follows:

[0194] like This indicates that the entire subarray is invisible in the user's direction (VR is all 0), and the user's direction is not included in the statistics.

[0195] In this embodiment, the criterion for sufficiently flat power within the subarray is defined as follows: ,in It is a natural constant.

[0196] Sampling in multiple directions The set of visible directions of the statistical subarray:

[0197] And calculate the probability of passing:

[0198] in, This is an indicator function.

[0199] The local stationarity criterion is set as follows: when When determining the subarray To achieve local stability, the percentage of subarrays that pass through can be statistically analyzed to assess whether a certain partitioning is usable.

[0200] Based on the evaluation results of all subarrays, the system assesses and outputs which number of subarrays and their partitioning methods (e.g., 1D continuous, 2D mesh) can ensure that most subarrays meet the local stationarity requirements under the current system parameters (frequency, array size, distance, curvature, etc.). This output is directly used for subsequent port implementation. If a partitioning is locally non-stationary in most directions, then that port size is not suitable.

[0201] Specifically, module M5 includes the following sub-modules: Module M5.1 calculates the autocorrelation matrix of the channel subvectors for each available subarray. If element-wise channel gating has been applied, the formula for calculating the autocorrelation matrix of the available subarray is:

[0202] in It is the conjugate transpose; For statistical expectation; This is the channel subvector of the kth available subarray after VR gating; .

[0203] Module M5.2 calculates the structural consistency coefficient and power ratio of any two available subarrays using the autocorrelation matrices of the two available subarrays.

[0204] Specifically, PoVi-CMD defines that for any two available subarrays... and First, define the structural consistency coefficients of the two available subarrays. :

[0205] in: The trace of the matrix; It is the Frobenius norm; The larger the value, the more similar the correlation structure of the signals inside the two available subarrays.

[0206] Define the power ratio of the two available subarrays. :

[0207] in: Characterizes the relative strength of the overall received power of two available subarrays. express The visible power / correlation strength is generally stronger than that of the available subarrays. on the contrary.

[0208] Module M5.3 performs power ratio equalization processing by introducing a power balance function.

[0209] To quantify the impact of power imbalance on statistical differences, a symmetric power balance function is introduced. :

[0210] in, It is an exponential parameter (dimensionless). The larger the value, the more sensitive it is to power imbalance; when hour, , indicating power balance; when or hour .

[0211] Module M5.4 integrates the structural consistency coefficient and power balance function to calculate the channel statistical difference distance (PoVi-CMD distance) between two available subarrays.

[0212] Specifically, the PoVi-CMD distance formula is defined as follows:

[0213]

[0214] When two available subarrays have identical related structures and similar power hour, This indicates weak spatial stability; when structural differences or power differences are large (especially when VR causes some subarrays to be semi-visible / invisible), As the amplitude increases, spatial non-stationarity becomes more pronounced. Compared to traditional CMD (which is insensitive to overall power scaling), PoVi-CMD can explicitly reflect the amplitude inconsistencies brought about by VR.

[0215] For the user direction, calculate the channel statistical difference distance between each pair of available subarrays and take the average value to obtain the average spatial nonstationarity index in the user direction. Traverse all user directions, calculate the corresponding average spatial nonstationarity index, and visualize it on the direction grid to obtain the spatial nonstationarity heat map.

[0216] Specifically, for each user direction Calculate all available subarray pairs And by averaging, we get: , Will A spatial nonstationarity (SnS) heatmap can be obtained by plotting on a half-space directional grid, which can be used to visually identify "which directions / distances / curvatures have the strongest statistical differences in the subarray".

[0217] like Figures 4-5 Showing the SnS heatmap of a flexible linear array under LoS. Figures 6-8 This chart compares the performance of different methods for measuring spatial non-stationarity in the SnS heatmap under LoS at a 90° azimuth angle. Figures 9-12 This demonstrates the SnS heatmap of a flexible planar array under LoS conditions. Furthermore, for the NLoS scenario, Figures 13-16This displays SnS heatmaps of a flexible linear array under NLoS with different subarray separation degrees. Figures 17-24 This corresponds to the SnS heatmap of flexible surface arrays under different subarray separation degrees in NLoS.

[0218] Module M6 includes the following sub-modules: Module M6.1 calculates the full-aperture spatial correlation matrix based on the full array channel data (the full array channel vector h) obtained from module M3.

[0219] Specifically, the formula for calculating the full aperture spatial correlation matrix is ​​as follows: , Module M6.2 calculates the degrees of freedom in the full aperture space by applying the Rényi-2 effective rank formula to the correlation matrix of the full aperture space.

[0220] Specifically, let the eigenvalue be... (Non-negative real numbers), and define normalized weights:

[0221] The effective rank of Rényi-2 is defined as:

[0222] in, For effective spatial degrees of freedom (dimensionless); Indicates total power; This indicates the degree of energy concentration on eigenvalues; when energy is concentrated on a few modes, Smaller; when energy is distributed across more modes, Increase.

[0223] The normalized DoF can also be provided: , Among them, such as Figures 25-28 The spatial correlation matrix eigenvalue spectrum of the flexible linear array under LoS and 3GPP CDL-D channel models is shown. Figures 29-32 The spatial correlation matrix eigenvalue spectrum of the flexible array under the NLoS 3GPP CDL-A channel model is described. Figure 33 This represents the eigenvalue spectrum of the spatial correlation matrix of an isotropic flexible linear array. Figure 34 The eigenvalue spectrum represents the spatial correlation matrix of an isotropic flexible surface array.

[0224] Module M7 includes the following sub-modules: Module M7.1 uses the PoVi-CMD distances in each direction calculated by module M5 to further construct a port similarity matrix for each user direction under the line-of-sight channel.

[0225] In port-constrained hardware, arrays are often formed as subarrays / tiles. There are several ports. To compress the SnS heatmap into a usable port-dimensional budget, in this embodiment, a port similarity matrix is ​​constructed. Among them, diagonal elements Off-diagonal elements .

[0226] in, PoVi-CMD distance; The closer to 1, the more similar the two ports are in that direction (stronger redundancy); the closer to 0, the less similar they are (stronger parallelism).

[0227] Module M7.2 calculates the effective rank of the port similarity matrix for each user direction using the Rényi-2 effective rank formula. This is used to evaluate the actual number of independent ports among the K ports in a specific user direction.

[0228] Specifically, for the port similarity matrix Define the number of port modes (effective rank):

[0229] because This is also equivalent to:

[0230] If all ports have similar heights (SnS is weak), ),but This indicates that the ports are basically redundant, and port merging should be considered for robust focusing; if the port differences are significant (SnS strong), (large), then This indicates that the port can provide more independent modes, which is beneficial for multi-beam / multi-user parallel operation.

[0231] Module M7.3 calculates the statistical expectation (average) of the effective rank within the target service direction domain to obtain the average number of realizeable port modes. The minimum value of the average number of realizeable port modes, the full aperture space degrees of freedom calculated by module M6 (the upper limit of physical theory), and the number of available RF links predetermined by the system hardware is taken to obtain the final engineering upper bound of the number of ports to guide the hardware design.

[0232] Specifically, for the target service direction domain (For example, in the first half of the low-altitude space) take the average to obtain the average number of achievable port modes in this scenario:

[0233] Final port number upper bound (engineering constraint fusion):

[0234] in: The ratio of available RF links to baseband data streams (dimensionless) is determined by the hardware. This formula directly sets the upper limit of the physical aperture. Port redundancy Hardware RF data Unify them under the same constraint.

[0235] Under NLoS, the angle / power / delay and angular spread parameters of the clusters are given using models such as 3GPP CDL-A. Channels are generated by superimposing multipath rays, and PoVi-CMD and DoF are calculated according to modules M4 to M6. This ensures that the evaluation is reproducible, aligned with standards, and can reflect the phenomenon of DoF being limited by scattering under sparse multi-cluster scattering.

[0236] Under isotropic scattering half-space conditions, the spatial correlation matrix elements can be obtained by angular domain integration and can be approximated as a sinc-type closed expression; the coverage expansion caused by bending can be corrected by introducing a one-dimensional integral term, and diagonal normalization is used to maintain unity power. This method avoids high-dimensional numerical integration and is suitable for rapid calculation of DoF and SnS baselines for large-scale apertures, used to determine the contribution of environmentally driven nonstationarity to geometrically driven nonstationarity.

[0237] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0238] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for evaluating the spatial characteristics and configuring ports of a low-altitude flexible HMIMO, characterized in that, Includes the following steps: Step S1: Construct the array geometry of the flexible HMIMO array; Step S2: Set the user's position in three-dimensional space and select the electromagnetic propagation environment model; Step S3: If the selected model is a line-of-sight propagation model, then based on the array geometry and the user position, the visibility of each array element is determined one by one using a geometric method. A binary visibility mask is generated according to the determination result, and the line-of-sight channel is gated to obtain a visible area-gated channel as channel data. If the selected model is a non-line-of-sight propagation model, then a channel vector containing multipath clusters is generated as the full array channel data. If the selected model is an isotropic scattering model, then the channel spatial correlation characteristics are generated using a closed correlation kernel as the full array channel data. Step S4: Based on the full array channel data, the flexible HMIMO array is divided into multiple sub-arrays of equal size. The received power of each element in each sub-array is calculated to form the received power sequence of the sub-array. The relative variance of each received power sequence is calculated, and it is determined whether the relative variance meets the preset criterion. Sub-arrays that meet the preset criterion are used as available sub-arrays. Step S5: Calculate the autocorrelation matrix of each available subarray, combine all available subarrays in the full array in pairs to obtain multiple available subarray pairs, calculate the channel statistical difference distance of each available subarray pair in the user direction, and take the average value to obtain the average spatial nonstationarity index in the user direction. Traverse all user directions, calculate the corresponding average spatial nonstationarity index, and visualize it to form a spatial nonstationarity heat map. Step S6: Based on the full array channel data, calculate the full aperture spatial correlation matrix and calculate the full aperture spatial degrees of freedom using the Rényi-2 effective rank formula; Step S7: If the selected model is the line-of-sight propagation model, then based on the channel statistical difference distance, construct the port similarity matrix, calculate the effective rank using the Rényi-2 effective rank formula, take the statistical expectation of the effective rank in the target direction domain, and obtain the average number of realizeable port modes. Based on the average number of realizeable port modes and the full aperture space degrees of freedom, derive the final engineering upper bound of the number of ports, which is used to guide port configuration and RF link planning.

2. The method for spatial characteristic evaluation and port configuration of low-altitude flexible HMIMO according to claim 1, characterized in that, Step S1 includes the following sub-steps: Step S1.1: Based on preset physical parameters, calculate the bending half-angle describing the overall curvature of the array; the physical parameters include the total length of the array, the radius of curvature, and the total number of array elements; Step S1.2: Based on the total number of array elements and the bending half-angle in the physical parameters, calculate the central angle position corresponding to each array element when it is uniformly distributed on the arc array; Step S1.3: Combining the physical parameters, the bending half-open angle, and the center angle position of each array element, calculate the absolute position of the array element in the preset coordinate system using the three-dimensional coordinate formula to form the array geometry.

3. The method for spatial characteristic evaluation and port configuration of low-altitude flexible HMIMO according to claim 1, characterized in that, Step S2 includes the following sub-steps: Step S2.1: Set the user's position in three-dimensional space, using a spherical coordinate system for description; Step S2.2: Select one of the following three electromagnetic propagation environment models: A. Line-of-sight propagation model; B. Non-line-of-sight propagation model; C. Isotropic scattering model.

4. The method for evaluating the spatial characteristics and configuring ports for low-altitude flexible HMIMO according to claim 1, characterized in that, If the selected model is the line-of-sight propagation model, step S3 includes the following sub-steps: Step S3.1-LoS: Based on the array geometry and user location, calculate the straight-line distance from each array element to the user, and substitute it into the free space propagation formula to calculate the complex baseband channel coefficients; Step S3.2-LoS: Use the tangent plane method or normal vector method to determine whether each array element is visible to the user, and generate a binary visibility mask. Step S3.3-LoS: The binary visibility mask is used to perform gating processing on the complex baseband channel coefficients to obtain the visible area gated channel, which is used as the full array channel data.

5. The method for evaluating the spatial characteristics and configuring ports for low-altitude flexible HMIMO according to claim 4, characterized in that, Step S3.2-LoS includes the following sub-steps: Step S3.2.1: Based on the array geometry, define the center of the arc array and calculate the outward normal unit vector for each array element; Step S3.2.2: Using the user's position and the outward normal unit vector, determine whether the user is located in the front half space of the array element. If so, the array element is determined to be visible; otherwise, the array element is determined to be invisible. Step S3.2.3: Convert the judgment result of each array element into a mathematical inequality and generate a binary visibility mask.

6. The method for space characteristic evaluation and port configuration of low-altitude flexible HMIMO according to claim 1, characterized in that, Step S4 includes the following sub-steps: Step S4.1: Divide the full array into K sub-arrays of equal size; Step S4.2: Extract the channel sub-vector corresponding to each sub-array sequentially from the full array channel data; Step S4.3: Based on the user direction determined by the azimuth and elevation angles, and combined with the straight-line distance from the array element to the user, the received power of each array element in each subarray is calculated using the channel subvectors to form a received power sequence; then the power mean and variance of the sequence are calculated. Step S4.4: Based on the power mean and the variance, calculate the relative variance of each received power sequence in the user direction, determine whether the relative variance meets the preset criterion, and select the subarray that meets the preset criterion as the usable subarray.

7. The method for space characteristic evaluation and port configuration of low-altitude flexible HMIMO according to claim 1, characterized in that, Step S5 includes the following sub-steps: Step S5.1: Calculate the autocorrelation matrix of the channel subvectors for each available subarray; Step S5.2: For any two available subarrays, use the autocorrelation matrix corresponding to the two available subarrays to calculate the structural consistency coefficient and power ratio of the two available subarrays; Step S5.3: Equalize the power ratio by introducing a power balance function; Step S5.4: Combine the structural consistency coefficient and the power balance function to calculate the channel statistical difference distance between the two available subarrays.

8. The method for space characteristic evaluation and port configuration of low-altitude flexible HMIMO according to claim 1, characterized in that, Step S6 includes the following sub-steps: Step S6.1: Calculate the full aperture spatial correlation matrix based on the full array channel data; Step S6.2: Apply the Rényi-2 effective rank formula to the full aperture space correlation matrix to calculate the full aperture space degrees of freedom.

9. The method for evaluating the spatial characteristics and configuring ports for low-altitude flexible HMIMO according to claim 1, characterized in that, Step S7 includes the following sub-steps: Step S7.1: Using the channel statistical difference distance in each direction, construct a port similarity matrix for each user direction under the line-of-sight channel; Step S7.2: For the port similarity matrix under each user direction, calculate the effective rank using the Rényi-2 effective rank formula; Step S7.3: Statistically expect the effective rank within the target service direction domain to obtain the average number of achievable port modes. Take the minimum value of the average number of achievable port modes, the full aperture spatial degrees of freedom, and the preset number of available RF links to obtain the final engineering upper bound of the number of ports.

10. A space characteristic evaluation and port configuration system for low-altitude flexible HMIMO, employing the space characteristic evaluation and port configuration method for low-altitude flexible HMIMO as described in any one of claims 1-9, characterized in that, include: Module M1 constructs the array geometry of the flexible HMIMO array; Module M2 sets the user's position in three-dimensional space and selects the electromagnetic propagation environment model; Module M3, if the selected model is a line-of-sight propagation model, then based on the array geometry and the user position, performs visibility determination on each array element one by one using a geometric method, generates a binary visibility mask according to the determination result, and performs gating processing on the line-of-sight channel to obtain a visible area-gated channel as channel data; if the selected model is a non-line-of-sight propagation model, then generates a channel vector containing multipath clusters as full array channel data; if the selected model is an isotropic scattering model, then uses a closed correlation kernel to generate channel spatial correlation characteristics as full array channel data. Module M4, based on the full array channel data, divides the flexible HMIMO array into multiple sub-arrays of equal size, calculates the received power of each element within each sub-array to form the received power sequence of the sub-array; calculates the relative variance of each received power sequence, determines whether the relative variance meets a preset criterion, and designates the sub-arrays that meet the preset criterion as usable sub-arrays. Module M5 calculates the autocorrelation matrix of each available subarray, pairs all available subarrays in the full array to obtain multiple available subarray pairs, calculates the channel statistical difference distance of each available subarray pair in the user direction, takes the average value to obtain the average spatial nonstationarity index in the user direction, traverses all user directions, calculates the corresponding average spatial nonstationarity index, and visualizes it to form a spatial nonstationarity heatmap. Module M6 calculates the full aperture spatial correlation matrix based on the full array channel data, and calculates the full aperture spatial degrees of freedom using the Rényi-2 effective rank formula; Module M7, if the selected model is the line-of-sight propagation model, constructs a port similarity matrix based on the channel statistical difference distance, calculates the effective rank using the Rényi-2 effective rank formula, takes the statistical expectation of the effective rank in the target direction domain, and obtains the average number of realizeable port modes. Based on the average number of realizeable port modes and the full aperture space degrees of freedom, the final engineering upper bound of the number of ports is obtained, which is used to guide port configuration and RF link planning.

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