As millimeter waves will be widely used in the Internet of Things (IoT) and Telematics to provide high bandwidth communication and mass connectivity, the coverage optimization of base stations can effectively improve the quality of communication services. How to optimize the convergence speed of the base station coverage solution is crucial for IoT service providers. This paper proposes the Muti-Fusion Sparrow Search Algorithm (MFSSA) optimize the situation to address the problem of discrete coverage maximization and rapid convergence. Firstly, the initial swarm diversity is enriched using a sine chaotic map, and dynamic adaptive weighting is added to the discoverer location update strategy to improve the global search capability. Diverse swarms have a more remarkable ability to forage for food and avoid predation and are less likely to fall into a “precocious” state. Such a swarm is very suitable for solving NP-hard problems. Secondly, an elite opposition-based learning strategy is added to expand the search range of the algorithm, and a t-distribution-based one-fifth rule is introduced to reduce the probability of falling into a local optimum. This fusion mutation strategy can significantly optimize the adaptability and searchability of the algorithm. Finally, the experimental results show that the MFSSA algorithm can effectively improve the coverage of the deployment scheme in the base station coverage optimization problem, and the convergence speed is better than other algorithms. MFSSA is improved by more than 10% compared to the original algorithm.
The fifth generation of mobile communication technology (5G) has gained significant attention in academia and industry due to its high bandwidth, low latency, and low power consumption [
Micro-base stations are gaining attention from both academia and industry due to their flexibility and mobility, as well as their resistance to terrain interference [
Although mobile communication networks face many privacy protection and data security issues, their mobile and flexible advantages have conquered the majority of communication service providers [
This paper is structured as follows: Chapter 2 introduces the signal coverage model and the probabilistic optimization objective. Chapter 3 describes the specific design mechanism of the MFSSA. In Chapter 4, the efficiency and accuracy of the MFSSA are demonstrated by comparing the final coverage and convergence speed of the MFSSA with other algorithms in different scenarios. Chapter 5 gives a detailed list of recent research work. Chapter 6 provides an overall summary of the article.
The base station coverage problem requires a reasonable model simplification based on the wireless communication channel modeling theory to construct a characteristic spatial model of the signal coverage. A precise mathematical description of the base stations, users, and coverage requirements is necessary for wireless communications. Firstly, a detailed analysis of the existing beam assignment is conducted to build a plane model of the signal coverage of the base station. Secondly, a joint probabilistic perception model is constructed to consider the realistic signal interference situation and determine the problem’s final optimization objective. Finally, the problem is transformed to facilitate subsequent solutions.
Let
In wireless communication systems, directional enhancement of signal coverage is required due to the limited capacity of omnidirectional antennas and the radiation of electromagnetic waves across space. Beamforming is the design solution to enhance the signal in the horizontal direction. It involves transmitting the signal using two or more antennas with controlled delay or phase shift to create a directional constructive interference pattern. This simplifies the spatial model of signal coverage of the base station. In practical scenarios, micro base stations can move horizontally and vertically, leading to changes in their coverage radius. Assuming a micro-base station has a vertical range of movement, the signal coverage radius
If the distance between
This paper adopts a probabilistic sensing model, denoted by
The coverage of the base station cluster in region
As SSA is more effective in solving the minimum value problem, this paper converts the maximum coverage problem into a minimum value problem. The objective function for solving the algorithm presented in this paper is obtained.
SSA offers numerous advantages, such as higher search accuracy, faster convergence, stability, and robustness. Specifically, in the scenario of base station coverage, this algorithm effectively compresses the problem’s solution space, resulting in improved convergence speed. To enhance the algorithm’s global search performance, this paper introduces dynamic adaptive weighting, such as improving the convergence ability using adaptive weighting through the chaotic map. Additionally, this paper enhances the algorithm’s strong global search ability by integrating the opposition-based learning strategy and the t-distribution-based one-fifth rule.
SSA simulates various threads or functions as a group of simple agents based on the laws of nature, using specific mechanisms to achieve emergent collective intelligence. The simple swarm can be represented as follows:
Let
In SSA, individuals with higher fitness find food earlier and act as discoverers who provide foraging directions for followers with lower or equal fitness values. Thus, the discoverer has a larger foraging range than the follower and its position according to the following strategy.
Let
The followers update their positions according to the following strategy:
A group of vigilantes was selected to signal other individuals to avoid predation of the sparrow swarm during foraging. The percentage of individuals chosen as vigilantes ranged between 10% and 20%.
The vigilante location update strategy is as follows:
The equation describes how the sparrow swarm adjusts its foraging position during a search. The variable
Uneven distribution in the randomly generated swarm can limit the search space and reduce the algorithm’s accuracy. The chaotic map can be utilized to address this issue, given its advantages of ergodicity, randomness, and regularity. It can be seen from
As the algorithm iterates, the discoverers and followers approach the optimal global solution, causing the search range of the swarm to decrease gradually. This, in turn, weakens the global search ability of the swarm and can lead to the algorithm getting stuck in local extrema, limiting its search accuracy. This paper introduces a dynamic adaptive weighting, denoted by the symbol
The opposition-based learning strategy enhances sparrow swarm diversity and somewhat improves the algorithm’s performance [
A mutation strategy is introduced to address the swarm being too homogeneous and susceptible to local optima. After an individual updates its state, mutation is performed to enhance the diversity of the sparrow swarm and allow it to jump out of local optima. Using a dimension-by-dimension variation approach can prevent mutual interference between dimensions, improving the quality of individuals post-variation [
The discoverer’s movement direction significantly affects the foraging direction of the sparrow swarm. The one-fifth rule for all individuals in the swarm is too burdensome, which can reduce the algorithm’s search efficiency. Thus, only some of the optimal individuals from the discoverer are selected for the t-distribution-based one-fifth rule to avoid the reduction in search efficiency.
The variable denotes the result
The simulated coverage optimization problem is tackled by using sparrow foraging to search for the optimal location of the micro-base station. Each iteration involves updating the micro-base station’s position by updating the sparrow’s part. The fitness value of the sparrow at the current location is calculated to determine the optimal solution and motivate the sparrow to update its site. The implementation of MFSSA is shown in
This paper selects several commonly used swarm intelligence algorithms to compare with the proposed multi-fusion swarm intelligence algorithm and verify its algorithmic model properties. Different algorithms generate and solve a set of coverage target points separately. The coverage and convergence metrics of each algorithm are calculated. This paper conducts 100 experimental simulations under the same environmental conditions to ensure accuracy. The resulting practical data sets are sorted, and each group’s top and bottom 5% are excluded.
This paper compares the multi-fusion swarm intelligence optimization algorithm proposed in this study with three other algorithms: the basic SSA algorithm, ISSA [
Parameter symbol | Parameter | Value |
---|---|---|
L | Target area side length (m) | |
S | Target area (m^{2}) | |
N | The number of UAV micro base stations | 40 |
M | Number of targets covered | 150 |
R_{s} | UAV micro base station coverage radius (m) | |
Max_{iter} | The maximum number of iterations | 150 |
pop | Sparrow swarm | 30 |
Times | Number of repetitions for each experiment | 100 |
Based on the experimental simulation results, this paper analyzes the coverage optimization effects of different algorithms in two dimensions: the target area’s size and the signal coverage radius, as the perceived radius of the base stations is not uniform across the target area.
To visualize the performance of the MFSSA for base station coverage optimization, base station signal coverage radiuses of 10.0, 17.5, 27.5, and 32.5 m are selected for a coverage area with a side length of 400 m. The deployment effects of the five algorithms are visualized in the four cases mentioned above. The coverage targets’ distribution locations in
From
The MFSSA’s iterative curve remains consistent as the target site and signal coverage radius conditions become stricter. Furthermore, its convergence is more stable than that of other algorithms. However, the algorithm’s growth trend will gradually decrease for sites with an edge length of1100 m and a base station coverage radius of 10.0 m. Although the curve gradually levels off at the early iteration stage, its optimization-seeking accuracy is still superior to other algorithms. In contrast, the convergence stability of the MSSA, SSA, and ISSA is inferior to that of MFSSA. Additionally, these algorithms are more susceptible to location and target conditions, resulting in poorer stability.
The MFSSA’s superior searchability and pioneering ability are attributed to its dynamic adaptive weighting and elite opposition-based learning strategy. While the other algorithms struggle with more demanding conditions, resulting in low coverage and a smooth iteration curve, the MFSSA’ tendency to fall into a local optimum is mitigated by its t-distribution-based one-fifth rule. This feature enables the MFSSA algorithm to jump out of the local optimum effectively, and its better compression ability for the solution space makes it stand out from other algorithms.
Combined with
Length(m): | 400 | 400 | 400 | 700 | 700 | 700 | 1100 | 1100 | 1100 |
---|---|---|---|---|---|---|---|---|---|
Radius(m): | 17.5 | 27.5 | 32.5 | 17.5 | 27.5 | 32.5 | 17.5 | 27.5 | 32.5 |
SSA | 0.34 | 0.58 | 0.70 | 0.16 | 0.29 | 0.36 | 0.09 | 0.16 | 0.19 |
MFSSA | 0.67 | 0.89 | 0.96 | 0.45 | 0.62 | 0.70 | 0.33 | 0.44 | 0.50 |
MSSA | 0.64 | 0.85 | 0.92 | 0.41 | 0.58 | 0.66 | 0.30 | 0.40 | 0.46 |
RWSSA | 0.33 | 0.57 | 0.69 | 0.16 | 0.28 | 0.35 | 0.09 | 0.15 | 0.20 |
ISSA | 0.32 | 0.55 | 0.67 | 0.15 | 0.27 | 0.34 | 0.08 | 0.15 | 0.18 |
Many vital advances have emerged from high-level academic papers in the field of web services problems in IoT and research on swarm intelligence algorithms. These works are of great significance in guiding and helping multi-convergence swarm intelligence algorithms. Therefore, this paper has compiled some representative results.
The IoT connects people, machines, and things profoundly and extensively. With the integration of new-generation information technology and the traditional manufacturing industry, IoT has widespread use in industrial manufacturing, energy interconnection, and intelligent medical applications [
Swarm intelligence optimization algorithms are well-suited for addressing the problem of base station coverage and sensor node deployment in the IoT due to their fast convergence and strong adaptability. However, the direct application of the genetic algorithm to sensor node coverage scenarios may not produce ideal optimization results, as the initial swarm’s parameters and quality heavily influence its effectiveness. Hanh et al. [
This paper proposes the MFSSA to maximize the coverage of discrete coverage targets and achieve rapid convergence of base stations. The algorithm is based on the SSA and incorporates several improvements to enhance its performance. Specifically, the sine chaotic map enriches the initial swarm diversity. Dynamic adaptive weighting is added to the discoverer position update strategy to improve the global search capability and accelerate the convergence speed. The elite opposition-based learning strategy is introduced to expand the search range of the algorithm and prevent it from getting trapped in a “premature” state. Finally, the optimal global solution of the current iteration is subjected to a t-distribution-based one-fifth rule to improve the pioneering ability of the algorithm and reduce the probability of falling into a local optimum. Simulation experimental results demonstrate that the MFSSA outperforms other algorithms regarding strong search capability, fast convergence, and good stability. It can effectively optimize the rapid deployment of base stations and reduce the redundant coverage problem. Future work will consider specific physical scenarios, optimal coverage paths, and the algorithm’s solving capability in complex systems.
The authors wish to express their gratitude to the School of Petroleum at China University of Petroleum-Beijing in Karamay for their generous support in conducting this research.
The authors received no specific funding for this study.
The authors declare that they have no conflicts of interest to report regarding the present study.