WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement

Available online at www.rajournals.in RA JOURNAL OF APPLIED RESEARCH ISSN: 2394-6709 DOI:10.47191/rajar/v11i12.07 Volume: 11 Issue: 12 December 2025 International Open Access Impact Factor8.553 Page no.- 1136-1140 1136 Iffath Zeeshan1, RAJAR Volume 11 Issue 12 December 2025 WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement Iffath Zeeshan1, Haleema Azra2 1,2American College of Education, Department of Education, IN, USA ARTICLE INFO ABSTRACT Published Online: 16 December 2025 Corresponding Author: Iffath Zeeshan Optimizing WiFi router placement has become crucial for ensuring seamless network coverage with the increasing reliance on wireless internet connectivity in homes and schools. This research investigates the geometric patterns of WiFi signal strength distribution and develops mathematical models to predict dead zones and optimize router placement using smartphones as measurement devices. Through systematic data collection across various indoor environments, we analyzed signal strength patterns using inverse square law modifications, geometric modeling, and statistical regression analysis. Our findings demonstrate that WiFi signal propagation follows predictable mathematical patterns that can be modeled using modified exponential decay functions with obstacle interference coefficients. The developed models achieved 85% accuracy in predicting signal strength at untested locations and successfully identified optimal router placement positions that reduced dead zones by an average of 40%. This research provides practical tools for improving WiFi coverage in residential and educational settings using readily available smartphone technology. KEYWORDS: WiFi optimization, signal propagation, geometric modeling, smartphone sensing, network coverage INTRODUCTION 1.1 Background The proliferation of wireless devices and internetdependent applications has made reliable WiFi coverage essential in modern living spaces. Poor router placement often results in dead zones with insufficient signal strength for reliable internet connectivity. Traditional approaches to WiFi optimization rely on expensive professional equipment and complex software solutions that are inaccessible to most users (Cisco Systems, 2020). 1.2 Problem Statement Current methods for optimizing WiFi placement are either costly professional services or trial-and-error approaches that waste time and may not yield optimal results. There is a need for an accessible, mathematically based approach that can predict signal strength patterns and suggest optimal router placement using commonly available devices. 1.3 Research Objectives 1. To develop mathematical models that accurately represent WiFi signal strength distribution in indoor environments 2. To create a smartphone-based methodology for mapping WiFi signal strength 3. To identify geometric patterns in signal propagation and obstacle interference 4. To develop predictive models for identifying dead zones and optimal router placement 5. To validate the practical effectiveness of the proposed optimization methods 1.4 Significance This research bridges the gap between theoretical signal propagation models and practical WiFi optimization, making network optimization accessible to students, homeowners, and small businesses using smartphone technology (Mendoza-Silva et al., 2020). 2. LITERATURE REVIEW 2.1 WiFi Signal Propagation Theory WiFi signals operate in the 2.4 GHz and 5 GHz frequency bands and follow electromagnetic wave propagation principles. The inverse square law governs signal “WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement” 1137 Iffath Zeeshan1, RAJAR Volume 11 Issue 12 December 2025 attenuation, where intensity decreases proportionally to the square of the distance from the source (Rappaport, 2001; Goldsmith, 2005). Molisch (2011) expands on this by addressing indoor-specific factors such as multipath interference and material absorption. 2.2 Indoor Propagation Models Indoor environments introduce complex variables that affect signal strength. The IEEE 802.11 standard outlines the MAC and PHY specifications for wireless LANs (IEEE 802.11 Working Group, 2020). Cisco Systems (2020) emphasizes the role of walls, furniture, and layout in signal degradation. 2.3 Smartphone-Based Sensing Smartphones have become viable tools for RSSIbased signal mapping. Laoudias et al. (2021) evaluated RSSI accuracy across devices, noting hardware and orientation variability. MetaGeek (2024) explains RSSI interpretation and its limitations. Mendoza-Silva et al. (2020) provides a comprehensive overview of smartphone-based localization techniques. 2.4 Empirical Datasets The IEEE DataPort repository (2018) offers openaccess datasets of WiFi signal strength collected via smartphones, supporting reproducibility and benchmarking. 3. METHODOLOGY 3.1 Data Collection Setup Equipment Used: • Android smartphones with WiFi RSSI reporting capability • WiFi Signal Strength apps (WiFi Analyzer, NetSpot Mobile) • Measuring tape for distance measurements • Grid paper for location mapping Test Environments: • Residential home (1,200 sq ft) • School classroom (600 sq ft) • Library study area (800 sq ft) 3.2 Measurement Protocol 1. Grid Mapping: Each test area was divided into a 2m × 2m grid system 2. Signal Measurement: RSSI values were recorded at each grid intersection 3. Multiple Readings: Five measurements were taken at each point and averaged 4. Obstacle Documentation: Physical obstacles were mapped and categorized 5. Distance Recording: Direct distance from router to each measurement point was recorded 3.3 Mathematical Modeling Approach Basic Signal Strength Model: The signal strength model used is based on the logarithmic path loss formula (Rappaport, 2001): RSSI(d) = RSSI₀ - 10n × log₁₀(d/d₀) - ΣWL Where: • RSSI(d) = Signal strength at distance d • RSSI₀ = Signal strength at reference distance d₀ (1 meter) n = Path loss exponent • WL = Wall loss factors • d = Distance from router 3.4 Data Analysis Methods 1. Regression Analysis: Least squares fitting to determine path loss exponents 2. Geometric Modeling: Contour mapping of signal strength zones 3. Statistical Validation: Cross-validation using holdout test sets 4. Optimization Algorithms: Grid search for optimal router placement 4. RESULTS AND ANALYSIS 4.1 Signal Strength Mapping Measurements revealed distinct geometric patterns in WiFi signal distribution. Signal strength decreased predictably with distance but showed significant variations due to obstacles (Molisch, 2011; Mendoza-Silva et al., 2020). Table 1: Average Signal Strength by Distance Distance (m) Average RSSI (dBm) Standard Deviation Sample Size 1-2 -32.4 3.2 12 3-4 -45.8 5.7 16 5-6 -52.1 7.3 18 7-8 -58.7 9.1 14 9-10 -64.2 11.8 10 11-12 -69.8 14.2 8 “WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement” 1138 Iffath Zeeshan1, RAJAR Volume 11 Issue 12 December 2025 4.2 Obstacle Impact Analysis Table 2: Signal Loss by Obstacle Type Obstacle Type (dB) Average Loss Standard Deviation Frequency Drywall (1 layer) 3.2 1.1 24 Brick Wall 8.7 2.3 8 Metal Door 12.4 3.1 6 Wooden Furniture 2.1 0.8 18 Concrete Wall 15.6 4.2 4 Kitchen Appliances 6.8 2.9 12 4.3 Mathematical Model Development Through regression analysis, we developed an enhanced signal propagation model: RSSI(d,O) = -28.5 - 22.3 × log₁₀(d) - Σ(αᵢ × Oᵢ) + ε Where: • d = distance in meters • O = obstacle matrix • α = obstacle-specific attenuation coefficients • ε = environmental noise factor Model Performance: R² = 0.847 • RMSE = 4.2 dBm • Cross-validation accuracy = 85.3% 4.4 Dead Zone Prediction Table 3: Dead Zone Characteristics Environment Type Dead Zone Threshold Average Dead Zone Area Prediction Accuracy Residential -70 dBm 85 sq ft 88% Classroom -65 dBm 42 sq ft 82% Library -68 dBm 126 sq ft 91% 4.5 Router Placement Optimization Using our mathematical model, we identified optimal router placement positions that minimized dead zones and maximized overall coverage. Table 4: Optimization Results Test Environment Original Dead Zone Optimized Dead Zone Improvement Home Layout 142 sq ft 78 sq ft 45% Classroom 89 sq ft 34 sq ft 62% Library Area 203 sq ft 127 sq ft 37% 5. DISCUSSION 5.1 Model Effectiveness The mathematical model successfully captured the primary factors influencing WiFi signal propagation. The combination of distance-based attenuation and obstaclespecific loss factors provided accurate predictions (Goldsmith, 2005; IEEE 802.11 Working Group, 2020). 5.2 Practical Applications The smartphone-based measurement approach proved accessible and sufficiently accurate for practical optimization. Users can implement this methodology without specialized equipment (Laoudias et al., 2021; MetaGeek, 2024). 5.3 Geometric Insights Signal strength contours revealed interesting geometric patterns: • Circular propagation zones modified by rectangular obstacle shadows • Predictable "shadow zones" behind major obstacles • Optimal placement positions often offset from geometric centers 5.4 Limitations Several limitations were identified: • Model accuracy decreased in environments with complex multi-path interference • Smartphone RSSI measurements showed device-specific variations • Dynamic factors (moving people, changing device loads) were not accounted for 5.5 Future Improvements Potential enhancements to the methodology include: • Machine learning approaches for non-linear obstacle effects • Real-time optimization considering network traffic “WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement” 1139 Iffath Zeeshan1, RAJAR Volume 11 Issue 12 December 2025 Integration with building information modeling (BIM) systems 6. PRACTICAL IMPLEMENTATION 6.1 Step-by-Step Optimization Process Measurement Phase: Map signal strength across the target area using the grid method Model Application: Apply the mathematical model to predict signal strength at unmeasured locations Optimization Calculation: Use grid search algorithms to identify optimal router positions Validation Testing: Verify improvement through post-optimization measurements 6.2 Tools and Resources Students and practitioners can implement this methodology using: • Free smartphone apps for WiFi signal measurement • Spreadsheet software for data analysis and modeling • Online graphing tools for visualization • Basic mathematical concepts (logarithms, regression analysis) 7. CONCLUSION This research successfully demonstrates that smartphone-based WiFi signal mapping, combined with appropriate mathematical modeling, can effectively predict dead zones and optimize router placement. The developed methodology achieved significant improvements in network coverage while remaining accessible to users without specialized equipment or training. 7.1 Key Findings Mathematical Modeling: WiFi signal propagation follows predictable patterns that can be modeled using modified inverse square law relationships with obstacle-specific attenuation factors. Prediction Accuracy: Our model achieved 85% accuracy in predicting signal strength at untested locations, making it suitable for practical optimization applications. Optimization Effectiveness: Optimal router placement based on our model reduced dead zones by an average of 40% across different environment types. Smartphone Viability: Modern smartphones provide sufficiently accurate RSSI measurements for practical WiFi optimization purposes. 7.2 Practical Impact The research provides a cost-effective, mathematically grounded approach to WiFi optimization that can be implemented by students, homeowners, and small businesses. This democratizes network optimization technology and makes better internet connectivity more accessible. 7.3 Educational Value The methodology serves as an excellent example of applied mathematics, demonstrating how geometric concepts, statistical analysis, and optimization theory can solve real-world problems using commonly available technology. 7.4 Future Research Directions Future work should focus on: • Incorporating machine learning for improved obstacle modeling • Developing real-time optimization algorithms • Extending the model to outdoor environments • Creating automated smartphone applications for broader accessibility This research establishes a foundation for accessible, mathematically based WiFi optimization that bridges the gap between theoretical signal propagation models and practical network improvement solutions. Declarations Availability of data and materials The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request. Raw RSSI measurements, obstacle mapping data, and mathematical model parameters used in this study can be provided to researchers for validation and replication purposes. Competing interests The authors declare that they have no competing interests. REFERENCES 1. Cisco Systems. (2020). WiFi site survey and optimization guidelines. Technical Documentation. Cisco Systems Inc. 2. Goldsmith, A. (2005). Wireless communications. Cambridge University Press. 3. IEEE 802.11 Working Group. (2020). IEEE standard for information technology— telecommunications and information exchange between systems. IEEE Standards Association. 4. IEEE DataPort. (2018). Wi-Fi signal strength measurements from smartphone for various scenarios. Dataset Repository. https://ieeedataport.org/ 5. Laoudias, C., Constantinides, M., Nicolaou, S., Zeinalipour-Yazti, D., & Panayiotou, C. G. (2021). Evaluating smartphone accuracy for RSSI “WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement” 1140 Iffath Zeeshan1, RAJAR Volume 11 Issue 12 December 2025 measurements. Inria Research Report. https://inria.hal.science/hal-03063997 6. Mendoza-Silva, G. M., Torres-Sospedra, J., & Huerta, J. (2020). Fundamental concepts and evolution of Wi-Fi user localization: An overview based on different case studies. Sensors, 20(18), 5121. https://doi.org/10.3390/s20185121 7. MetaGeek. (2024). Understanding RSSI levels. Technical Documentation. https://www.metageek.com/training/resources/unde rstanding-rssi/ 8. Molisch, A. F. (2011). Wireless communications (2nd ed.). John Wiley & Sons. 9. Rappaport, T. S. (2001). Wireless communications: Principles and practice (2nd ed.). Prentice Hall.