Underground space multi-ris cooperative deployment method and system based on improved weighted k-medoids

Abstract

The application provides an underground space multi-RIS cooperative deployment method and system based on improved weighted k-medoids, comprising: obtaining each node direct connection reference signal-to-noise ratio to divide weak direct connection nodes and generate a feasible candidate deployment point set; under the number of RISs currently attempted to be deployed, candidate positions meeting the second hop attenuation constraint are selected to deploy RISs, the weak direct connection nodes are allocated to each RIS to form a service cluster, and the first hop link quality penalty value of each node is determined; the penalty value is used to replace the Euclidean distance as the allocation basis, an inner layer cost function is constructed with an important node deployment guarantee index and a load balancing index, and node re-allocation and RIS position updating are alternately performed until convergence; all RIS numbers are traversed, a total optimization objective function value is calculated in combination with a deployment number penalty index, and a minimum value corresponding scheme is selected as an optimal deployment scheme. The application can realize joint optimization of the number, position and node service relationship of RISs in the underground space, guarantee the link quality of weak direct connection nodes and balance the service load of each RIS.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method and system for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids. Background Technology

[0002] As a crucial component of smart city infrastructure, underground spaces play a vital role in critical tasks such as environmental sensing, facility monitoring, and safety early warning. The reliability of their communication networks directly impacts the safety and efficiency of urban operations. However, underground spaces possess inherent physical characteristics such as strong enclosure, complex structure, dense obstacles, and numerous turns and corners. Wireless signals suffer severe path loss, shadowing fading, and multipath effects during propagation. Furthermore, many sensor nodes and data access points are not directly connected, resulting in communication coverage blind spots and insufficient link reliability. These issues have become prominent bottlenecks hindering the intelligent development of underground spaces.

[0003] Reconfigurable Intelligent Surfaces (RIS), as an emerging wireless communication enhancement technology, utilize a large number of low-cost, low-power tunable reflective elements to modulate the phase and amplitude of incident electromagnetic waves. This allows for the construction of additional reflected transmission paths without the need for extra radio frequency links, providing a new technical approach to improve the communication quality of non-directly connected nodes. However, in practical deployment of RIS in underground spaces, more RIS do not necessarily lead to better results. Increasing the number of RIS not only directly increases the costs of equipment procurement, installation, construction, and maintenance, but also significantly increases the complexity of scheduling and coordination among multiple surfaces. More importantly, in underground spaces with complex obstacle distribution and limited installation locations, blindly increasing the number of RIS often leads to unreasonable deployment locations and severely uneven service loads among the RIS, potentially reducing the overall system performance.

[0004] To address the aforementioned issues, existing research has made some progress in RIS deployment optimization, but most of these studies focus on open spaces or simple indoor scenarios. They typically only consider spatial distance as the primary basis for location selection, failing to fully consider the line-of-sight constraints unique to underground spaces, the differentiated transmission requirements of node service types, and load balancing factors among multiple RISs. Meanwhile, the real RIS deployment problem is essentially a mixed integer optimization problem that simultaneously involves quantity selection, candidate location selection, and determination of node service relationships. The strong coupling between discrete decision variables makes traditional optimization methods face the challenge of excessive computational complexity, making it difficult to promote and apply them in practical engineering. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a method and system for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids, in order to solve the problems of existing technologies, such as lack of reasonable basis for RIS deployment location selection under complex constraints of underground space, severe uneven service load among multiple RIS, and high computational complexity in solving mixed integer optimization problems, which makes it difficult to balance link guarantee and deployment cost control.

[0006] On one hand, this invention provides a method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids, the method comprising: The direct connection reference signal-to-noise ratio between each node and the central data access point in the underground space communication scenario is obtained. Nodes with a direct connection reference signal-to-noise ratio not greater than a preset weak threshold are classified as weak direct connection nodes. A set of feasible candidate deployment points is generated, consisting of multiple candidate locations that have line-of-sight links with the central data access point. Given the current number of RISs to be deployed, select candidate locations from the set of feasible candidate deployment points that satisfy the second-hop link attenuation constraint and whose number is equal to the current number of deployment attempts as the current RIS deployment locations. Assign each weakly directly connected node to one of the RISs to form a corresponding number of service clusters, and determine the first-hop link quality penalty value of each weakly directly connected node in its assigned service cluster. Using the first-hop link quality penalty value instead of Euclidean distance as the allocation basis, each weakly directly connected node is reallocated to the RIS that minimizes the penalty value, and each service cluster is updated; and, an inner cost function is constructed using the important node deployment guarantee index and the load balancing index, and with the goal of minimizing the inner cost function, the deployment position of each RIS is updated one by one by traversing the candidate positions in the feasible candidate deployment point set; the reallocation and position update operations are repeated until convergence, and the optimal deployment position and optimal service relationship under the current number of RISs to be deployed are obtained; wherein, the important node deployment guarantee index is calculated based on the direct connection gap of each weakly directly connected node and the first-hop link quality penalty value, and the load balancing index is calculated based on the sum of the transmission demand weights of the weakly directly connected nodes in each service cluster; Within the preset range of RIS quantity values, each possible value is traversed to obtain the optimal deployment location and optimal service relationship corresponding to each possible value. The total optimization objective function value under each possible value is calculated in combination with the deployment quantity penalty index. The possible value that minimizes the total optimization objective function value and its corresponding deployment location and service relationship are selected as the final output optimal RIS deployment scheme. The deployment quantity penalty index increases as the possible value increases.

[0007] In some embodiments of the present invention, determining the first-hop link quality penalty value for each weakly directly connected node within its assigned service cluster includes: Obtain the signal-to-noise ratio of the first-hop link between the weakly directly connected node and its assigned RIS; When the signal-to-noise ratio of the first hop link is less than the preset first hop minimum signal-to-noise ratio threshold, the quality penalty value of the first hop link increases linearly as the difference between the first hop link signal-to-noise ratio and the preset first hop minimum signal-to-noise ratio threshold increases. When the signal-to-noise ratio of the first hop link is not less than the preset first hop minimum signal-to-noise ratio threshold, the quality penalty value of the first hop link decreases exponentially as the difference between the first hop link signal-to-noise ratio and the preset first hop minimum signal-to-noise ratio threshold increases.

[0008] In some embodiments of the present invention, the important node deployment guarantee index is obtained by weighted comprehensive calculation based on the direct connection gap of each weak direct connection node, the first hop link quality penalty value, and the node importance weight; the direct connection gap is the positive part of the difference between the preset received signal-to-noise ratio threshold and the direct connection reference signal-to-noise ratio of the weak direct connection node; the larger the first hop link quality penalty value of the weak direct connection node, the greater the important node deployment guarantee index tends to be; the node importance weight is used to reflect the priority of each weak direct connection node in communication guarantee.

[0009] In some embodiments of the present invention, the load balancing metric is calculated in the following manner: Obtain the transmission demand weight of each weakly directly connected node; the transmission demand weight is configured according to the service type of the weakly directly connected node, the transmission demand weight of high data volume node is greater than the transmission demand weight of latency-sensitive node, and the transmission demand weight of latency-sensitive node is greater than the transmission demand weight of low data volume node. The transmission demand weights of all weakly directly connected nodes within each service cluster are summed to form the cluster load of each RIS. Calculate the average cluster load for all RIS; Calculate the squared deviation of the cluster load of each RIS from the average value, then average the squared deviations of all RIS, and use the average value as the load balancing index.

[0010] In some embodiments of the present invention, the reallocation and location update operations are repeatedly performed until convergence to obtain the optimal deployment location and optimal service relationship for the number of RIS currently being deployed, including: Given the current number of RIS to be deployed, perform multiple random initializations. After each random initialization, independently perform the reallocation and position update operations until convergence, and obtain the local optimum solution corresponding to that random initialization. Compare the inner cost function values ​​corresponding to the local optima obtained from each random initialization, and select the local optima with the smallest inner cost function value as the optimal deployment location and optimal service relationship for the current number of RIS to be deployed.

[0011] In some embodiments of the present invention, the second hop link attenuation constraint is: The second-hop link attenuation value between each RIS and the central data access point does not exceed the difference between the preset first-hop minimum signal-to-noise ratio threshold and the preset received signal-to-noise ratio threshold.

[0012] In some embodiments of the present invention, the method further includes: When assigning each weakly directly connected node to one of the RIS to form a corresponding number of service clusters, the spatial distance between any two weakly directly connected nodes within the same service cluster is limited to not exceeding a preset pairwise distance threshold.

[0013] In some embodiments of the present invention, a set of feasible candidate deployment points is generated, consisting of multiple candidate locations with line-of-sight links to the central data access point, including: The installation-available areas in the underground space are sampled in a gridded manner to obtain initial sampling points; Remove sampling points from the initial sampling points that overlap with existing node positions; From the remaining sampling points, select those sampling points that have a line-of-sight link with the central data access point as candidate locations in the set of feasible candidate deployment points.

[0014] In some embodiments of the present invention, the deployment quantity penalty metric is the square of the ratio of the number of RIS currently attempted to be deployed to the preset maximum number of RIS deployments.

[0015] On the other hand, the present invention also provides a multi-RIS collaborative deployment system for underground space based on improved weighted k-medoids, including a processor, a memory, and a computer program or instructions stored in the memory, wherein the processor is used to execute the computer program or instructions, and when the computer program or instructions are executed, the system implements the steps of any of the methods mentioned above.

[0016] This invention replaces the traditional Euclidean distance with the first-hop link quality penalty value as the basis for node allocation, enabling the partitioning of RIS service clusters to directly address the actual communication link quality rather than spatial distance. This overcomes the traditional cognitive bias that proximity equates to quality in complex underground environments. It can accurately target the reflection gain of the RIS to the weakest directly connected nodes with the largest direct connection gaps, significantly improving the link guarantee ratio of non-directly connected nodes. Simulation results show that the guarantee rate of this invention for weakly directly connected nodes can reach 62.96%, which is more than 10 percentage points higher than random deployment and uniform deployment schemes.

[0017] Furthermore, this invention introduces a load balancing metric into the inner cost function, using the node service type weights to measure the actual service pressure of each RIS and suppress load deviation. This effectively avoids the imbalance where some RISs are overloaded due to carrying too many high-demand nodes, while other RISs are relatively idle. Simulation results show that the load range between RISs is only 0.45, far better than the range of 3.80 in the no-load-balancing scheme, creating fair load conditions for subsequent resource scheduling and interference coordination among multiple RISs.

[0018] Furthermore, this invention introduces a deployment quantity penalty index that increases quadratically with the number of RIS in the outer layer optimization, enabling the optimization process to achieve an adaptive balance between link quality gain and deployment cost. This avoids insufficient link assurance due to an insufficient number of RIS, and also suppresses the increase in equipment overhead and scheduling complexity caused by blindly adding RIS.

[0019] Furthermore, this invention employs a two-layer solution framework: an outer layer that traverses the number of RIS (Relationships in Calculation) and an inner layer that alternately optimizes the position-allocation. This decomposes the mixed integer optimization problem into efficiently iterative subproblems, ensuring solution quality while maintaining good computational scalability, and adapting to the deployment needs of underground spaces of different scales.

[0020] In summary, this invention provides a complete and highly systematic technical solution for the collaborative deployment of multiple RIS in complex underground environments.

[0021] Additional advantages, objects, and features of the invention will be set forth in part in the description which follows, and will also become apparent in part to those skilled in the art upon studying the description, or may be learned by practice of the invention. The objects and other advantages of the invention can be realized and obtained by means of the structures specifically pointed out in the description and drawings.

[0022] Those skilled in the art will understand that the objectives and advantages achievable with the present invention are not limited to those specifically described above, and that the above and other objectives achievable with the present invention will become clearer from the following detailed description. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, are not intended to limit the scope of the invention. In the drawings: Figure 1 This is a flowchart illustrating the main steps of a multi-RIS collaborative deployment method for underground space based on improved weighted k-medoids in one embodiment of the present invention.

[0024] Figure 2 This is a scenario diagram of a multi-RIS deployment algorithm in underground space according to an embodiment of the present invention.

[0025] Figure 3 This is a two-layer framework flowchart of a multi-RIS collaborative deployment method for underground space based on improved weighted k-medoids in one embodiment of the present invention.

[0026] Figure 4 This is a comparison chart of the proportion of weakly directly connected nodes that meet the first hop threshold requirement under different deployment methods in one embodiment of the present invention.

[0027] Figure 5 This is a comparison diagram of the type weight load distribution within each RIS cluster under different methods in one embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0029] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the structures and / or processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted.

[0030] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, element, step, or component, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0031] It should also be noted that, unless otherwise specified, the term "connection" in this article can refer not only to a direct connection, but also to an indirect connection involving an intermediary.

[0032] In the following description, embodiments of the invention will be illustrated with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar parts, or the same or similar steps.

[0033] It should be emphasized here that the step markers mentioned below are not a limitation on the order of the steps, but should be understood as meaning that the steps can be executed in the order mentioned in the embodiments, or in a different order than in the embodiments, or several steps can be executed simultaneously.

[0034] To address the shortcomings of existing technologies, such as the lack of rational basis for RIS deployment location selection under complex constraints in underground spaces, severe uneven service load among multiple RISs, and high computational complexity in solving mixed-integer optimization problems while struggling to balance link assurance and deployment cost control, this invention provides a collaborative deployment method for multiple RISs in underground spaces based on improved weighted k-medoids. Figure 1As shown, the method includes the following steps S101~S104: Step S101: Obtain the direct connection reference signal-to-noise ratio between each node and the central data access point in the underground space communication scenario, classify the nodes whose direct connection reference signal-to-noise ratio is not greater than the preset weak threshold as weak direct connection nodes, and generate a set of feasible candidate deployment points consisting of multiple candidate locations that have line-of-sight links with the central data access point.

[0035] Step S102: Given the number of RISs currently being attempted to be deployed, select candidate locations from the set of feasible candidate deployment points that satisfy the second-hop link attenuation constraint and whose number is equal to the number of current attempts to be deployed as the current RIS deployment locations. Assign each weakly directly connected node to one of the RISs to form a corresponding number of service clusters, and determine the first-hop link quality penalty value of each weakly directly connected node within its assigned service cluster.

[0036] Step S103: Using the first-hop link quality penalty value instead of Euclidean distance as the allocation basis, reallocate each weakly directly connected node to the RIS that minimizes the penalty value and update each service cluster; and construct an inner cost function based on the important node deployment guarantee index and load balancing index, and update the deployment position of each RIS one by one by traversing the candidate positions in the feasible candidate deployment point set with the goal of minimizing the inner cost function; repeat the reallocation and position update operations until convergence, and obtain the optimal deployment position and optimal service relationship under the current number of RISs to be deployed. Among them, the important node deployment guarantee index is calculated based on the direct connection gap and the first-hop link quality penalty value of each weakly directly connected node, and the load balancing index is calculated based on the sum of the transmission demand weights of the weakly directly connected nodes in each service cluster.

[0037] Step S104: Within the preset range of RIS quantity values, iterate through each possible value, obtain the optimal deployment location and optimal service relationship for each possible value, and calculate the overall optimization objective function value for each possible value based on the deployment quantity penalty index. Select the possible value that minimizes the overall optimization objective function value and its corresponding deployment location and service relationship as the final output optimal RIS deployment scheme. The deployment quantity penalty index increases as the possible values ​​increase.

[0038] In step S101, the underground space communication scenario is first preprocessed. The purpose is to identify weakly directly connected nodes requiring RIS (Remote Information Service) assistance and generate a set of candidate locations for RIS deployment, laying the data foundation for subsequent optimized deployment. This step mainly includes two sub-tasks: weakly directly connected node identification and the generation of a set of feasible candidate deployment points.

[0039] In some embodiments, the direct reference signal-to-noise ratio between each node and the central data access point in the underground space communication scenario is first obtained. Specifically, the underground space communication scenario includes one central data access point (CDAP) and M sensing nodes. The CDAP is located at one end of the underground space as the origin of the coordinate system, and the position coordinates of each node can be denoted as follows: The system obtains the direct reference signal-to-noise ratio (SNR) between each node and CDAP through measurement or link budgeting. The direct reference SNR can be denoted as... .

[0040] It should be noted that the nodes mentioned in this invention, also known as sensing nodes, sensor nodes, or user nodes, refer to various terminal devices that need to communicate with CDAP in underground space communication scenarios, including but not limited to environmental monitoring sensors, facility status monitoring devices, and safety early warning terminals.

[0041] Due to the enclosed nature, complex structure, and dense obstructions of underground spaces, some nodes suffer from poor quality direct links with CDAP due to obstructions such as building walls, large equipment, and pipelines, making reliable communication impossible. Therefore, it is necessary to select nodes with weak direct links from all nodes to serve as RIS auxiliary services.

[0042] Specifically, the preset weakness threshold is denoted as... For any node If its direct-connected reference signal-to-noise ratio is not greater than the preset weak threshold, i.e. If the direct link between the node and CDAP is weak and cannot independently guarantee communication reliability, it is classified into the weak direct link node set; otherwise, if its direct link reference signal-to-noise ratio is greater than the preset weak link threshold, i.e. If the quality of the direct link of this node meets the basic communication requirements, no RIS assistance is needed, and it is included in the set of direct links. The above division rule can be expressed by formula (1): ; (1) in, This represents the set of weakly directly connected nodes.

[0043] After identifying the weakly directly connected nodes, it is necessary to further generate a set of candidate locations that can be used to deploy the RIS. It should be noted that, in the technical solution of this invention, in addition to obtaining the node direct connection reference signal-to-noise ratio in step S101, it is also necessary to obtain the location coordinates of each node. The node's location coordinates are used in subsequent steps to calculate the link signal-to-noise ratio between the node and the RIS, the spatial distance between nodes, and the pairwise distance constraints within the cluster.

[0044] In some embodiments, the set of feasible candidate deployment points is generated in the following ways: First, the installable areas in the underground space are discretized and gridded. Specifically, based on the actual physical layout of the underground space, the area where RIS can be installed is delineated, and then uniform sampling is performed on this area according to a preset grid spacing to obtain a series of initial sampling points. These initial sampling points constitute a set. .

[0045] Next, occupied locations are removed from the initial sampling points. Specifically, the location coordinates of the central data access point and all sensing nodes are obtained, and the locations occupied by these existing devices (including CDAP and all sensing nodes) are denoted as a set. From the set Elimination and Set Overlapping sampling points ensure that the deployment location of the RIS will not conflict with existing equipment.

[0046] Finally, line-of-sight filtering is performed on the remaining sampling points. For each remaining sampling point... It determines whether there is an unobstructed line-of-sight (LoS) propagation path between it and CDAP.

[0047] In some embodiments, a line-of-sight indication function is defined. When position With position When there are no obstructions and a direct line of sight exists, this function takes a value of 1; otherwise, it takes a value of 0. In practice, this line-of-sight determination can be based on ray tracing calculations using a 3D Building Information Model (BIM) of the underground space, or it can be based on actual channel measurement results. Only when the following conditions are met... Only sampling points that have a line-of-sight link with CDAP are retained as feasible candidate deployment points.

[0048] The above screening process can be represented by formula (2): ; (2) in, This results in the final set of feasible candidate deployment points. Each candidate location in this set has a line-of-sight link with CDAP, ensuring the basic feasibility of the RIS backhaul link. It's important to note that a line-of-sight link is a prerequisite for the RIS to function properly, as the RIS needs to interact with CDAP for control signaling and reflect received node signals back to CDAP. If the RIS and CDAP are completely blocked by an obstacle, the entire RIS auxiliary link cannot be established. Therefore, the line-of-sight selection in this step is a crucial prerequisite for ensuring the physical feasibility of subsequent deployment plans.

[0049] like Figure 2 The figure shows a scenario diagram of a multi-RIS deployment algorithm in underground space provided by an embodiment of the present invention. In the figure, the underground space communication scenario includes a central data access point, multiple sensing nodes distributed in the environment, some of which are in a non-directly connected state due to obstacles, and multiple candidate RIS deployment locations are distributed within the installable area.

[0050] In some embodiments of the present invention, if the number of candidate locations in the feasible candidate deployment point set after the above screening is less than the preset minimum deployment number requirement, the sampling density can be increased by reducing the spacing of the gridded sampling, thereby expanding the number of candidate locations to ensure that the optimization algorithm has enough deployment locations to choose from.

[0051] In step S102, an initial deployment scheme is constructed based on the number of RISs currently being attempted to be deployed. Its core objective is to select RIS deployment locations that meet the backhaul link quality requirements, initially allocate weakly directly connected nodes to each RIS to form service clusters, and establish a first-hop link quality evaluation benchmark for each weakly directly connected node under its associated RIS, providing an initial feasible solution and penalty value basis for iterative optimization in subsequent steps.

[0052] In this invention, it is necessary to pre-define the range of values ​​for the number of RIS. Let the preset maximum number of RIS deployments be... The number of RIS systems currently being attempted to deploy. It can be from 1 to The value is taken from between. In step S102, for a specific one currently being attempted to be deployed... The value needs to be selected from the set of feasible candidate deployment points. The candidate locations are selected as the current RIS deployment locations.

[0053] When selecting the RIS deployment location, in addition to the line-of-sight link condition guaranteed in step S101, the signal attenuation constraint of the second-hop link also needs to be considered. In this invention, the second-hop link refers to the backhaul link from the RIS to the CDAP. The working principle of the RIS dictates that the link quality between it and the CDAP must be good enough; otherwise, even if the RIS can receive the node signal well, it cannot effectively forward the signal back to the CDAP.

[0054] In some embodiments, let the first The second-hop link attenuation value between RIS and CDAP is This value can be calculated using a link budget model based on factors such as the spatial distance between the RIS deployment location and the CDAP location, the path loss index of underground space, and obstacle penetration loss. The second-hop link attenuation constraint requirement is shown in formula (3): ; (3) in, This indicates the minimum signal-to-noise ratio threshold for the first hop; This represents the received signal-to-noise ratio (SNR) threshold. The physical meaning of this constraint is that only when the backhaul link attenuation between the RIS and CDAP is sufficiently small, not exceeding the difference between the minimum SNR threshold of the first hop and the received SNR threshold, can the signal forwarded by the RIS still meet the demodulated SNR requirement at the CDAP end. This constraint is a concrete manifestation of the hierarchical modeling concept of the second hop being a hard constraint and the first hop being an optimization objective in this invention. Only candidate locations that satisfy the above constraints are allowed as the actual deployment locations of the RIS.

[0055] In some embodiments of the present invention, if a candidate location selected from the set of feasible candidate deployment points does not meet the second-hop link attenuation constraint, the candidate location is filtered out and not considered. This filtering operation can be performed in real-time during step S102, or it can be completed as an independent preprocessing step after step S101 generates the set of feasible candidate deployment points and before step S102. That is, candidate locations that do not meet the second-hop link attenuation constraint are pre-removed from the set of feasible candidate deployment points, and the remaining locations constitute a set of usable deployment locations that meet both line-of-sight and second-hop attenuation requirements. Both methods fall within the protection scope of the present invention.

[0056] In some embodiments, the number selected is equal to the current number of deployment attempts (i.e. (Number) candidate locations are selected as the current RIS deployment location. The deployment locations constitute the set of actual RIS deployment locations.

[0057] Having determined the current situation After the deployment location of each RIS is determined, each weakly directly connected node is assigned to one of the RISes, so that each weakly directly connected node has a specific associated RIS, which provides signal reflection services for it.

[0058] In some embodiments, the initial allocation can employ various strategies, such as random allocation or allocation based on the nearest spatial distance. Let... Represents a node The associated RIS index, i.e., the node Assigned to the The RIS. For the first RIS. Each RIS (Relationship Provider Association) consists of a service cluster comprised of all its weakly directly connected nodes. , defined as formula (4): ; (4) The meaning of this definition is: the first Each RIS service cluster contains all associated indexes equal to Weakly directly connected nodes.

[0059] After the initial allocation was completed, the following was formed Each weakly directly connected node is assigned to one of the service clusters, and only to one service cluster, satisfying the requirements of completeness and uniqueness of the allocation.

[0060] After the initial node allocation is completed, it is necessary to determine the first-hop link quality penalty value for each weakly directly connected node within its assigned service cluster. In this invention, the first-hop link refers to the communication link from the weakly directly connected node to its associated RIS, i.e., the node→RIS link.

[0061] Specifically, first obtain the weakly directly connected nodes. With the RIS (i.e., the first) assigned to it The signal-to-noise ratio of the first-hop link between RIS) can be denoted as: ,in The signal-to-noise ratio can be calculated based on factors such as the spatial distance between the node location and the RIS deployment location, transmit power, and path loss model.

[0062] Then, based on the relationship between the first-hop link signal-to-noise ratio and the preset first-hop minimum signal-to-noise ratio threshold, the first-hop link quality penalty value is calculated.

[0063] In some embodiments, the present invention designs a piecewise penalty function, the calculation rule of which is as follows: When the signal-to-noise ratio of the first hop link is less than the preset minimum signal-to-noise ratio threshold for the first hop, i.e. This indicates that the link quality between the node and its associated RIS does not meet the minimum requirements. In this case, the penalty value increases linearly with the increase of the signal-to-noise ratio gap. As shown in formula (5): ; (5) in, This represents the quality penalty value of the first-hop link; This is a preset scaling parameter used to control the rate at which the penalty value changes as the signal-to-noise ratio gap increases. The specific value of this scaling parameter can be configured according to the dynamic range of the signal-to-noise ratio in the actual underground space communication environment.

[0064] When the signal-to-noise ratio of the first hop link is not less than the preset minimum signal-to-noise ratio threshold for the first hop, that is... This indicates that the link quality between the node and its associated RIS has met the minimum requirements, and the penalty value decreases exponentially with further improvement in the signal-to-noise ratio. As shown in formula (6): ; (6) The physical meaning of formula (6) is that for nodes whose first-hop signal-to-noise ratio has not reached the threshold, the penalty value increases linearly for each point of deterioration in link quality, guiding the optimization algorithm to prioritize the allocation of such nodes to RIS that can provide better first-hop quality; for nodes whose first-hop signal-to-noise ratio has reached the threshold, the marginal benefit of continuing to improve the signal-to-noise ratio decreases, the penalty value decays exponentially, and the algorithm avoids excessively pursuing additional improvement in signal-to-noise ratio at the expense of other optimization objectives.

[0065] In summary, the above penalty value calculation rules can be uniformly expressed by formula (7): ; (7) in, .

[0066] In step S103, iterative optimization is performed. Its core objective is to fix the number of RIS systems currently being attempted for deployment. Below, by alternately optimizing node associations and RIS deployment locations, the inner cost function is minimized, thereby obtaining the desired result. The optimal deployment scheme under the given value. This step reflects two key improvements of the present invention to the traditional k-medoids algorithm: first, replacing Euclidean distance with the first-hop link quality penalty value as the basis for node allocation; and second, using an inner cost function that includes important node deployment guarantee indicators and load balancing indicators to guide position updates.

[0067] In the traditional k-medoids clustering algorithm, the assignment of a node (data point) is determined based on its Euclidean distance to each cluster center; that is, the node is assigned to the nearest cluster center. However, in the underground space RIS deployment scenario of this invention, a close spatial distance between a node and the RIS does not necessarily mean good communication link quality. Underground spaces have complex obstacle distributions, and even if two locations are not far apart, severe signal attenuation may occur due to obstructions from walls, pipes, and other obstacles. Therefore, simply assigning nodes based on spatial distance cannot effectively guarantee the actual quality of the communication link.

[0068] To address this issue, this invention uses the first-hop link quality penalty value instead of Euclidean distance as the basis for node allocation. Specifically, in the current... Under the condition that the deployment location of each RIS is fixed, for each weakly directly connected node, the first-hop link quality penalty value to each RIS is calculated, and the calculation method is the same as the penalty value calculation rule in step S102. Then, the node is assigned to the RIS that minimizes the first-hop link quality penalty value, as shown in formula (8): ; (8) in, Represents a node To the The first-hop link quality penalty value for each RIS.

[0069] The above allocation rule means that each weakly directly connected node selects the RIS that can provide it with the best first-hop link quality, even if the first-hop link quality penalty value is the smallest, as the associated object.

[0070] This improvement replaces the spatial nearest allocation criterion in traditional k-medoids with the communication link quality best allocation criterion, making the clustering direction directly aligned with the communication quality optimization objective, rather than merely pursuing spatial compactness. Since the first-hop link quality penalty value has already comprehensively considered whether the signal-to-noise ratio reaches the threshold, the gap size when it does not reach it, and the marginal benefit after reaching the threshold through the piecewise function in step S102, the allocation based on this penalty value can more realistically reflect the actual communication quality between the node and the RIS.

[0071] After the above reallocation is completed, each service cluster will be updated accordingly: The service cluster contains all those reassigned to the [number]th service cluster. A weakly directly connected node of a RIS.

[0072] After completing the node redistribution, it is necessary to evaluate the merits of the current deployment scheme. To this end, this invention constructs an inner cost function, which consists of two evaluation metrics: a critical node deployment guarantee metric and a load balancing metric.

[0073] The critical node deployment assurance index is used to quantify the quality assurance level of the first-hop link for nodes with weak direct connections. Its calculation involves three elements: direct connection gap, first-hop link quality penalty value, and node importance weight. These will be explained in detail below.

[0074] The direct link gap is used to measure the degree of inadequacy of the direct link of a weakly connected node relative to a preset received signal-to-noise ratio threshold. It is defined by formula (9): ; (9) in, Represents a node Direct connection gap; This is a preset receive signal-to-noise ratio (SNR) threshold, representing the minimum SNR required for CDAP to correctly demodulate the received signal. A larger direct link gap indicates a poorer quality direct link for that node, making the need for RIS (Remote Information Retrieval System) assistance more urgent.

[0075] First hop link quality penalty As detailed in step S102, it will not be repeated here. The larger the penalty value, the worse the quality of the first-hop link of the node under its associated RIS.

[0076] In underground space communication networks, the importance of services and the value of data carried by different nodes vary significantly. Some nodes undertake tasks such as critical area perception, reporting of key facility status, or monitoring of abnormal events; a decline in the link quality of these nodes will have a more significant impact on the overall monitoring capability of the system. Therefore, this invention introduces node importance weights to reflect the priority of each weakly directly connected node in communication assurance. The importance weight can be quantified based on the criticality of the area where the node is located, the importance level of the monitored equipment, or the value of the reported data. The higher the importance weight, the more important the node is, and the higher its priority level should be assigned in optimization.

[0077] Based on the above three factors, the key node deployment guarantee indicator is defined by formula (10): ; (10) in, This indicates the deployment and protection indicators for key nodes; Indicates the importance weight of nodes; Use extremely small positive numbers to avoid having a denominator of zero.

[0078] Based on formula (10), it can be seen that nodes with large direct connection gaps and high importance weights have a higher influence ratio in the indicator; if the first-hop link quality penalty value of a node is large, that is, the link quality is poor, the indicator tends to increase. Therefore, the smaller the deployment guarantee indicator of important nodes, the better the first-hop link quality obtained by weak direct connection nodes, especially nodes with large direct connection gaps and high importance.

[0079] Load balancing metrics are used to quantify the degree of service load balance among different RIS (Resource Identifiers). In the collaborative deployment of multiple RIS in underground spaces, nodes with different service types consume RIS resources differently. For example, high data volume (HDV) nodes continuously generate a large amount of monitoring data, requiring the RIS to allocate more reflection beam resources and transmission time slots; latency-sensitive (LS) nodes, although their data volume may not be large, require the RIS to provide higher service priority and lower scheduling latency; low data volume (LDV) nodes require only a small amount of transmission resources, consuming the least amount of RIS resources.

[0080] To reflect this difference, the present invention configures different transmission demand weights for different types of nodes.

[0081] In some embodiments, the transmission demand weights are configured according to the rule of formula (11): ; (11) in, Represents a node The transmission demand weights; Represents a node Business types; , , These are the transmission demand weights for high data volume, latency-sensitive, and low data volume nodes, respectively. The transmission demand weight for high data volume nodes is greater than that for latency-sensitive nodes, and the transmission demand weight for latency-sensitive nodes is greater than that for low data volume nodes. Each weight can be quantified and configured according to the service characteristics in the actual underground space communication scenario.

[0082] Based on transmission demand weights, the first The service cluster load of a RIS is defined as the sum of the transmission demand weights of all weakly directly connected nodes served by that RIS, as shown in formula (12): ;(12) The average load of all RIS clusters in the entire network is shown in formula (13): ; (13) The load balancing metric is measured by the mean of the squared deviations of the load of each RIS cluster from the average load, as shown in formula (14): ;(14) in, Indicates the first The load of a RIS service cluster; This represents the average load across all RIS clusters in the entire network. This represents a load balancing metric. The smaller the value of this metric, the more balanced the weighted service load is among the RIS, which is beneficial to the fairness of subsequent resource scheduling and avoids the imbalance where some RIS are overloaded while others are idle.

[0083] Fixed number of RIS currently being attempted to be deployed. Below, the inner optimization objective is to minimize the weighted sum of the deployment guarantee index and the load balancing index of important nodes, as shown in formula (15): ; (15) in, This is a preset regularization weighting factor used to adjust the weighting of load balancing metrics in the total cost. This weighting factor can be configured according to the business requirements of actual underground space communication scenarios.

[0084] After completing the node redistribution, it is necessary to further optimize the deployment location of each RIS. For each RIS, while keeping the deployment locations of other RIS unchanged, traverse all candidate locations in the set of feasible candidate deployment points, calculate the inner cost function value after moving the RIS to each candidate location, and select the candidate location that minimizes the inner cost function value as the new deployment location of the RIS.

[0085] In some embodiments, the reallocation and position update operations are repeated until convergence. The convergence condition can be set as follows: the change in the inner cost function value between two consecutive iterations is less than a preset convergence threshold, or a preset maximum number of iterations is reached. When the convergence condition is met, the current iteration is considered complete. The optimization under the given value has reached a stable state. The current RIS deployment location and node service relationship will be used as the number of RIS to be deployed in the current attempt. Output the optimal deployment location and optimal service relationship.

[0086] It should be noted that the iterative optimization in step S103 is a local search method, and its convergence result may depend on the quality of the initial solution, making it prone to getting trapped in local optima. To overcome this problem, this invention also introduces a multi-round random restart mechanism. Specifically, for the number of RIS currently being deployed... Instead of performing a single iteration optimization, multiple independent random initializations are executed. After each random initialization, starting from a different initial RIS deployment location and initial node allocation, a complete reallocation and position update iteration process is independently executed until convergence, obtaining the local optimum corresponding to that random initialization. Then, the inner cost function values ​​corresponding to the local optima obtained from each random initialization are compared, and the local optimum with the smallest inner cost function value is selected as the current local optimum. Output the optimal deployment location and optimal service relationship under the given value.

[0087] The multi-round random restart mechanism significantly increases the probability of finding the global optimum or a high-quality suboptimal solution by starting the search from multiple different starting points, thus enhancing the robustness of the algorithm.

[0088] Figure 3 A flowchart of a multi-RIS deployment algorithm based on improved weighted k-medoids provided for embodiments of the present invention. Figure 3 As shown, the algorithm uses the outer layer A two-layer framework combining scanning and inner position-allocation iteration: outer traversal arrive For each Value calls the inner algorithm; the inner algorithm is fixed. The following joint determination The deployment location and node service relationship of each RIS, each The system performs multiple rounds of random restarts to overcome local optima.

[0089] In step S104, the final optimal RIS deployment scheme is output. The core objective of this step is to complete the single step in step S103. Based on value optimization, we iterate through all possible RIS deployment numbers, introduce a deployment number penalty index, and select the comprehensive optimal deployment scheme from different number schemes, thereby achieving joint optimization of RIS number, deployment location, and node service relationship.

[0090] As mentioned earlier, deploying RIS in underground spaces is not a case of the more the better. On the one hand, increasing the number of RIS increases the costs of equipment procurement, installation, construction, and maintenance. On the other hand, in situations with complex obstacle distribution and limited available deployment locations, blindly increasing the number of RIS may lead to poor deployment locations for the new RIS, resulting in a sharp decrease in their marginal gain, and even reduced overall efficiency due to overlapping and mutual interference among the coverage areas of the RIS. Therefore, in this invention, a penalty mechanism for the number of RIS is also introduced into the optimization objective.

[0091] In some embodiments, the deployment quantity penalty metric is defined as shown in formula (16): ; (16) in, This indicates a penalty metric based on the number of deployments. This represents the number of RIS systems currently being attempted to deploy; Set the maximum number of RIS deployments to preset.

[0092] The design intent of formula (16) is: when When the value is small, the penalty value increases relatively slowly, allowing the algorithm to enjoy a low penalty cost when deployed in small numbers, encouraging active deployment when the number of RIS is small; when Approaching At this time, the penalty value increases rapidly, exerting significant punitive pressure on over-deployment behavior, thereby inhibiting the blind increase of the number of RIS.

[0093] Combining the important node deployment guarantee indicators, load balancing indicators, and deployment quantity penalty indicators introduced in step S103, a complete overall optimization objective function is constructed, as shown in formula (17): ; (17) in, Denotes the overall optimization objective function; , These are regularization weighting factors, used to adjust the weighting of load balancing metrics and deployment quantity penalty metrics in the overall objective. The larger the value, the heavier the penalty for increasing the number of RIS, and the more likely the algorithm will choose to deploy fewer RIS. The smaller the value, the more the algorithm focuses on ensuring link quality, and may select more RIS (Reference Orders). The values ​​of these two weighting factors can be configured according to the cost budget and performance requirements in actual engineering projects.

[0094] Therefore, the problem solved by this invention can be formally expressed as: under preset constraints, minimizing the overall optimization objective function by optimizing the number of RIS deployments, the set of deployment locations, and the set of node-related variables, as shown in formula (18): ; (18) in, Number of RIS deployments; For the set of deployment locations; This is the set of variables associated with the node.

[0095] To obtain the globally optimal solution, this invention employs an outer-layer traversal strategy: within a preset range of RIS values ​​from 1 to... Inside, iterate through each possible value (i.e., each integer). For each The value is obtained by calling the inner layer optimization method described in step S103. Optimal deployment location under the given value and optimal service relationship and the corresponding inner cost function value .

[0096] Then, for each The value, will Substituting the value into the calculation formula for the deployment quantity penalty index, we get... Then calculate the total objective function value under this value, as shown in formula (19): ; (19) After traversing all, compare all value corresponding Select the one that minimizes the overall objective function value. Value, denoted as the optimal number of RIS deployments. . The corresponding optimal deployment location and optimal service relationship This is the optimal RIS deployment scheme for the final output.

[0097] In some embodiments, the final output of the optimal RIS deployment scheme automatically satisfies the following constraints: (1) The actual deployment location of each RIS is selected from the set of feasible candidate deployment points. (1) The weak direct connection node is uniquely associated with a RIS; (2) All weak direct connection nodes are assigned to a certain service cluster without omission; (3) The spatial distance between any two weak direct connection nodes in the same service cluster does not exceed the preset pairing distance threshold. Among them, constraint (4) is to avoid the spatial span of a single service cluster being too large. If the nodes served by a RIS are too scattered, it will cause the reflected beam of the RIS to be difficult to cover all service nodes at the same time, and the actual beamforming gain will be significantly reduced. Therefore, it is necessary to limit the maximum pairing distance of nodes in the cluster when the cluster is formed.

[0098] Regarding the intra-cluster pairwise distance constraint, its specific meaning is: for any serving cluster Any two weakly directly connected nodes and The position coordinates are respectively and If the square of the spatial distance between the two does not exceed the preset pairwise distance threshold, as shown in formula (20): ; (20) in, This indicates a preset pairwise distance threshold.

[0099] After optimization through the above steps, the method of the present invention can automatically determine the optimal number of RIS deployments, the optimal address of each RIS, and the optimal service relationship from weakly directly connected nodes to each RIS under the complex constraints of underground space. At the same time, it comprehensively ensures the link quality of important non-directly connected nodes, balances the weighted load of each RIS, and controls the deployment scale. Figure 4 and Figure 5The effects of the present invention are demonstrated from two dimensions: weak direct connection node guarantee rate and type weight load balancing. Figure 4 This chart compares the proportion of weakly directly connected nodes that meet the first-hop threshold requirement under different deployment methods. Figure 4 As shown, the weak direct connection node guarantee rate of the method of the present invention reaches 62.96%, which is significantly improved compared with random deployment (44.44%), uniform deployment (48.15%), distance clustering deployment (51.85%) and no load balancing deployment (48.15%), and is 11.11 percentage points higher than the best comparison scheme. Figure 5 This is a comparison chart showing the type weight load distribution within each RIS cluster under different methods. (Example:) Figure 5 As shown, the load distribution of each RIS type weight is balanced under the method of this invention, with load values ​​concentrated between 2.55 and 3.00, and a range of only 0.45; while the no-load-balancing scheme and the distance clustering scheme have load ranges of 3.80 and 3.05 respectively, with some RISs being severely overloaded. This indicates that the load balancing term in this invention can effectively suppress the uneven load among RISs.

[0100] Compared with existing technologies such as random deployment, uniform deployment, distance clustering deployment, and no load balancing deployment, this invention has significant advantages in terms of weak direct connection node guarantee rate and load balancing: the weak direct connection node guarantee rate can reach 62.96%, which is 11.11 percentage points higher than the best comparison scheme; the type weight load range between each RIS is only 0.45, which is far lower than the maximum load range of 3.80 in the comparison scheme, effectively avoiding the imbalance of some RIS being overloaded while other RIS are idle.

[0101] In some embodiments, from a computational complexity perspective, the time complexity of the algorithm of the present invention is: ,in, The maximum number of RIS deployments is preset; This represents the number of random restarts within the inner layer. The total number of nodes; This represents the number of candidate locations in the set of feasible candidate deployment points. Because... and Typically much smaller than the number of nodes. The algorithm exhibits good computational scalability as the node size increases, enabling it to adapt to the deployment needs of underground spaces of varying sizes.

[0102] Corresponding to the above method, the present invention also provides a multi-RIS collaborative deployment system for underground space based on improved weighted k-medoids, including a processor, a memory, and a computer program or instructions stored in the memory. The processor is used to execute the computer program or instructions, and when the computer program or instructions are executed, the system implements the steps of the method described above.

[0103] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the aforementioned method. The computer-readable storage medium may be a tangible storage medium, such as random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, register, floppy disk, hard disk, removable storage disk, CD-ROM, or any other form of storage medium known in the art.

[0104] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention. When implemented in hardware, it can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this invention are programs or code segments used to perform the desired tasks. The programs or code segments can be stored in a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried in a carrier wave.

[0105] It should be clarified that the present invention is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of the present invention.

[0106] In this invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or in place of features of other embodiments.

[0107] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations of the embodiments of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids, characterized in that, The method includes: The direct connection reference signal-to-noise ratio between each node and the central data access point in the underground space communication scenario is obtained. Nodes with a direct connection reference signal-to-noise ratio not greater than a preset weak threshold are classified as weak direct connection nodes. A set of feasible candidate deployment points is generated, consisting of multiple candidate locations that have line-of-sight links with the central data access point. Given the current number of RISs to be deployed, select candidate locations from the set of feasible candidate deployment points that satisfy the second-hop link attenuation constraint and whose number is equal to the current number of deployment attempts as the current RIS deployment locations. Assign each weakly directly connected node to one of the RISs to form a corresponding number of service clusters, and determine the first-hop link quality penalty value of each weakly directly connected node in its assigned service cluster. Using the first-hop link quality penalty value instead of Euclidean distance as the allocation basis, each weakly directly connected node is reallocated to the RIS that minimizes the penalty value, and each service cluster is updated; and, an inner cost function is constructed using the important node deployment guarantee index and the load balancing index, and with the goal of minimizing the inner cost function, the deployment position of each RIS is updated one by one by traversing the candidate positions in the feasible candidate deployment point set; the reallocation and position update operations are repeated until convergence, and the optimal deployment position and optimal service relationship under the current number of RISs to be deployed are obtained; wherein, the important node deployment guarantee index is calculated based on the direct connection gap of each weakly directly connected node and the first-hop link quality penalty value, and the load balancing index is calculated based on the sum of the transmission demand weights of the weakly directly connected nodes in each service cluster; Within the preset range of RIS quantity values, each possible value is traversed to obtain the optimal deployment location and optimal service relationship corresponding to each possible value. The total optimization objective function value under each possible value is calculated in combination with the deployment quantity penalty index. The possible value that minimizes the total optimization objective function value and its corresponding deployment location and service relationship are selected as the final output optimal RIS deployment scheme. The deployment quantity penalty index increases as the possible value increases.

2. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, Determine the first-hop link quality penalty value for each weakly directly connected node within its assigned service cluster, including: Obtain the signal-to-noise ratio of the first-hop link between the weakly directly connected node and its assigned RIS; When the signal-to-noise ratio of the first hop link is less than the preset first hop minimum signal-to-noise ratio threshold, the quality penalty value of the first hop link increases linearly as the difference between the first hop link signal-to-noise ratio and the preset first hop minimum signal-to-noise ratio threshold increases. When the signal-to-noise ratio of the first hop link is not less than the preset first hop minimum signal-to-noise ratio threshold, the quality penalty value of the first hop link decreases exponentially as the difference between the first hop link signal-to-noise ratio and the preset first hop minimum signal-to-noise ratio threshold increases.

3. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, The critical node deployment guarantee index is calculated by weighting the direct connection gap of each weak direct connection node, the first-hop link quality penalty value, and the node importance weight. The direct connection gap is the positive part of the difference between the preset received signal-to-noise ratio threshold and the direct connection reference signal-to-noise ratio of the weak direct connection node. The larger the first-hop link quality penalty value of a weak direct connection node, the greater the critical node deployment guarantee index tends to be. The node importance weight is used to reflect the priority of each weak direct connection node in communication guarantee.

4. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, The load balancing metrics are calculated in the following way: Obtain the transmission demand weight of each weakly directly connected node; the transmission demand weight is configured according to the service type of the weakly directly connected node, the transmission demand weight of high data volume node is greater than the transmission demand weight of latency-sensitive node, and the transmission demand weight of latency-sensitive node is greater than the transmission demand weight of low data volume node. The transmission demand weights of all weakly directly connected nodes within each service cluster are summed to form the cluster load of each RIS. Calculate the average cluster load for all RIS; Calculate the squared deviation of the cluster load of each RIS from the average value, then average the squared deviations of all RIS, and use the average value as the load balancing index.

5. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, Repeat the reallocation and location update operations until convergence, obtaining the optimal deployment location and optimal service relationship for the current number of RIS to be deployed, including: Given the current number of RIS to be deployed, perform multiple random initializations. After each random initialization, independently perform the reallocation and position update operations until convergence, and obtain the local optimum solution corresponding to that random initialization. Compare the inner cost function values ​​corresponding to the local optima obtained from each random initialization, and select the local optima with the smallest inner cost function value as the optimal deployment location and optimal service relationship for the current number of RIS to be deployed.

6. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, The second hop link attenuation constraint is: The second-hop link attenuation value between each RIS and the central data access point does not exceed the difference between the preset first-hop minimum signal-to-noise ratio threshold and the preset received signal-to-noise ratio threshold.

7. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, The method further includes: When assigning each weakly directly connected node to one of the RIS to form a corresponding number of service clusters, the spatial distance between any two weakly directly connected nodes within the same service cluster is limited to not exceeding a preset pairwise distance threshold.

8. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, Generate a set of feasible candidate deployment points consisting of multiple candidate locations with line-of-sight links to the central data access point, including: The installation-available areas in the underground space are sampled in a gridded manner to obtain initial sampling points; Remove sampling points from the initial sampling points that overlap with existing node positions; From the remaining sampling points, select those sampling points that have a line-of-sight link with the central data access point as candidate locations in the set of feasible candidate deployment points.

9. The method for collaborative deployment of multiple RIS in underground space based on improved weighted k-medoids according to claim 1, characterized in that, The deployment quantity penalty metric is the square of the ratio of the number of RIS currently attempted to be deployed to the preset maximum number of RIS deployments.

10. A multi-RIS collaborative deployment system for underground space based on improved weighted k-medoids, comprising a processor, a memory, and computer programs or instructions stored in the memory, characterized in that, The processor is configured to execute the computer program or instructions, and when the computer program or instructions are executed, the system implements the steps of the method as described in any one of claims 1 to 9.

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