# Programming an Artificial Neural Network Tool for Spatial Interpolation in GIS - A Case Study for Indoor Radio Wave Propagation of WLAN

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Wireless local area networks

- 2.4 GHz IEEE 802.11g Radio Standard
- Configurable output power up to 100 mW
- 10.4 cm wide; 20.5 cm high; 3.8 cm deep physical dimensions
- Integrated 2.2 dBi dipole antennas
- Up to 54 Mbps date rate for range of 27 m

#### 2.2. Kriging interpolation

#### 2.3. Artificial neural networks in GIS

_{kj}and ${C}_{k}^{j}$ are matrixes of weights and outputs respectively.

## 3. Methodology

#### 3.1. The measurements

#### 3.2. Data preparation and use of geographic information systems

_{0}is the wavelength, c = 3.10

^{8}m / s is the velocity of light and f

_{0}= 2.4GHz is the operating frequency of the wireless transmitter. In this calculation receiver antenna gain is assumed as unity.

#### 3.3. Application of Kriging interpolation

#### 3.4. Programming a neural networks tool in GIS for spatial interpolation

#### 3.4.1. The topology of multilayer feed-forward back-propagation artificial neural network

#### 3.4.2. Programming the application with Visual Basic in GIS; the ANN interface

- The files about 672 training points, 413 test points and observed electromagnetic field values are added from the computer.
- After training, 413 input points are tested by the updated network with optimized weight matrixes and the average error and accuracy of the neural network is calculated by equation (4) (network performance).
- “Result” button executes another interface as shown in Figure 10b. It is used for comparing between ANN outputs and observed (expected) values of electromagnetic field in test data.
- Coordinates of the points are added from the map screen mentioned before and it can be rearranged in XYZ boxes.
- The electromagnetic field (V/m) and power (dB) values are predicted.

#### 3.4.3. ANN interpolation pattern

## 4. Results and Discussions

#### 4.1. Coverage results

#### 4.2. Comparison between ANN prediction and Kriging interpolation method

## 5. Conclusions

## Acknowledgments

## References and Notes

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**Figure 1.**A WLAN Architecture using BSS infrastructure. Adapted from Nichols and Lekkas [13].

**Figure 2.**(a) Processing unit or neuron. (b) Architecture of a multi-layer feed-forward network with 3 units in the input layer, 3 units in the hidden layer and 1 unit in the output layer (3-3-1) and threshold units. Adapted from Rigol et al. [6].

**Figure 3.**Attribute table of the points at 100 cm high from the floor; electromagnetic field values (V/m) are in the column “EM_Field” and power values (dB) are in the column “Power_dB”.

**Figure 4.**T-Block entrance floor map, access point (AP), observation points and electromagnetic field values (V/m) at 100 cm from the floor.

**Figure 5.**(a) T-Block building. (b) T-Block entrance floor. (c) Observation points along the corridor at 5 different height levels.

**Figure 6.**Kriging interpolation pattern of the electromagnetic power values (dB) at 100 cm from the floor.

**Figure 8.**The topology of artificial neural networks for spatial interpolation of electromagnetic field values; x-y-z are the input coordinates, T1 and T2 are threshold matrixes, V/M is electromagnetic field value and 15 neurons in the hidden layer.

**Figure 10.**(a) Artificial neural network tool for spatial interpolation of electromagnetic field values. (b) The performance assessment of test results with error values.

**Table 1.**The comparison of ANN models for spatial interpolation of observed points at 100 cm from the floor. MAE, mean after all errors made positive and RMSE, square root of mean squared predicted electromagnetic power minus observed electromagnetic power.

Neural nets | Learning rate | Momentum rate | Iterations | RMSE (dB) | MAE (dB) |
---|---|---|---|---|---|

3-15-1 | 0.2 | 0.4 | 200 | 1.51 | 1.16 |

3-15-1 | 0.6 | 0.7 | 50 | 2.82 | 2.40 |

3-6-1 | 0.2 | 0.4 | 200 | 1.83 | 1.47 |

3-10-1 | 0.2 | 0.4 | 100 | 3.21 | 2.80 |

**Table 2.**Performance of the selected 3-15-1 network and Kriging interpolation of observed points at 50 cm, 100 cm, 140 cm, 215 cm and 290 cm from the floor. MAE, mean after all errors made positive and RMSE, square root of mean squared predicted electromagnetic power minus observed electromagnetic power.

Data set | Interpolation method | RMSE (dB) | MAE (dB) |
---|---|---|---|

50 cm height | ANN | 1.48 | 1.13 |

Kriging | 1.02 | 0.78 | |

100 cm height | ANN | 1.51 | 1.16 |

Kriging | 1.04 | 0.80 | |

140 cm height | ANN | 1.52 | 1.17 |

Kriging | 1.05 | 0.81 | |

215 cm height | ANN | 1.55 | 1.22 |

Kriging | 1.07 | 0.85 | |

290 cm height | ANN | 1.56 | 1.24 |

Kriging | 1.08 | 0.87 |

© 2008 by the authors; license Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Sen, A.; Gümüsay, M.U.; Kavas, A.; Bulucu, U.
Programming an Artificial Neural Network Tool for Spatial Interpolation in GIS - A Case Study for Indoor Radio Wave Propagation of WLAN. *Sensors* **2008**, *8*, 5996-6014.
https://doi.org/10.3390/s8095996

**AMA Style**

Sen A, Gümüsay MU, Kavas A, Bulucu U.
Programming an Artificial Neural Network Tool for Spatial Interpolation in GIS - A Case Study for Indoor Radio Wave Propagation of WLAN. *Sensors*. 2008; 8(9):5996-6014.
https://doi.org/10.3390/s8095996

**Chicago/Turabian Style**

Sen, Alper, M. Umit Gümüsay, Aktül Kavas, and Umut Bulucu.
2008. "Programming an Artificial Neural Network Tool for Spatial Interpolation in GIS - A Case Study for Indoor Radio Wave Propagation of WLAN" *Sensors* 8, no. 9: 5996-6014.
https://doi.org/10.3390/s8095996