Outdoor Path Loss Predictions Based on Extreme Learning Machine

Abstract

In a typical outdoor environment, the propagation of radio waves is usually random in nature, to the extent that the characterization of the wireless channel often becomes very difficult. Several models have been developed to predict the average Received Signal Strength (RSS) for specified distance ranges. However, the use of deterministic models requires high computational efficiency while the prediction results of empirical models may not be as accurate as required. On machine learning approach, the performances of multi-layered feed-forward network models are limited by slow convergence and local minimum, such that a global optimal solution is not guaranteed. In this paper, Extreme Learning Machine (ELM) algorithm is considered in the development of an optimal path loss prediction model for outdoor propagation scenario. Single Hidden Layer Feed-forward Neural Networks (SHLFNNs) are trained and tested with the path loss data that were computed based on the RSS data of a commercial 1800 MHz base station located along Lagos-Badagry highway in Nigeria. The training speed, learning effectiveness, and the generalization ability of Artificial Neural Network Back-Propagation (ANN-BP) and ELM algorithms are analysed. Experimental results show that ELM models are 140 times faster to train than the ANN-BP models. On prediction accuracy, the outputs of ELM, ANN-BP, Okumura-Hata, and COST-231 models have Root Mean Squared Error (RMSE) values of 2.896, 2.449, 7.456, and 6.116 dB respectively; and regression coefficient (R) values of 0.959, 0.973, 0.935, and 0.935 respectively, when compared to the target variable of the training dataset. When the models were tested with new input data that were excluded from the training process, RMSE values of 4.250, 6.622, 8.732, and 7.087 respectively; and R values of 0.893, 0.876, 0.904, and 0.904 respectively are obtained. In conclusion, the findings of this study confirm that ELM algorithm guarantees an optimal path loss model with fast training convergence, high prediction accuracy, and good generalization ability for radio network planning and optimization in outdoor environments.