CHAPTER 7: CONCLUSION AND FUTURE WORK
7.1. Conclusion
The aim of this research work is to analyse and identify the limitations of traditional propagation Path Loss (PL) models as well as different Artificial Neural Network (ANN) models and proffer an improve hybrid adaptive ANN models that will cater for the limitations of (i) traditional PL models and (ii) conventional ANN models in modelling a micro-cellular outdoor environment using real world data from Long Term Evolution (LTE) cellular networks. The research objectives have been set to reflect the aim and to guarantee achieved set goals. As a result, this research work considered traditional propagation PL modelling techniques: the empirical and the deterministic models, prediction of PL with different traditional models and conventional ANN models: Multi-Layer Perceptron (MLP) neural network, Radial Basis Function (RBF) neural network, Generalized Regression Neural Network (GRNN) and Adaptive Linear Element (ADALINE) neural network. Different ANN training algorithms and training techniques have been analysed to ascertain their performances during the network training.
A hybrid adaptive neural network model that combines ADALINE model and MLP ANN has been developed to cater for the stochastic signal attenuation phenomenon and the heterogeneity of the spatial propagation channels in various LTE environments. Furthermore, another improved PL prediction model that combines vector order statistics based smoothing technique and a MLP ANN has been developed. These works have been successfully executed in different submitted, accepted journal and conference papers presented in this thesis.
Chapter 2 of this thesis deals with a detailed review of baseline knowledge on traditional propagation modelling techniques in wireless cellular networks. It considered and studied key empirical and deterministic models. The analysed models have their own distinctiveness and limitations. They are affected by factors such as reflection, refraction,
145 diffraction and multi-path phenomenon. Also, terrain profile, Base Station (BS) operating frequency, transmitter antenna height, and receiver antenna height all affects the performances of these models. Furthermore, review of some of the conventional ANN such as MLP ANN, RBF ANN, GRNN, ADALINE network has been done considering their peculiarities, characteristics and limitations. Finally, literature review of some past works on the modelling of propagation PL using different traditional empirical and deterministic models as well as conventional ANN models has been done.
Simulation and analysis of propagation PL using traditional models were carried out in chapter 3 with real world data from LTE cellular network to ascertain the effects of propagation parameters on PL. Each of the considered models has been studied and compared under the variation of different parameters such as transmitter-receiver distance, base and mobile station antenna heights and different transmitting frequencies. The simulation results validate increase in PL as the link distance between transmitter and receiver increases because of spreading and attenuation of electromagnetic energy by various propagation mechanisms.
There is also increase in PL as the operating frequency increases as a result of decrease in both antenna aperture and wavelength of the radio signal. However, at the increase of both the transmitting and the receiving antenna heights, there was a drastic reduction in PL as the losses due to building roof tops to street diffraction are reduced. The research work in this chapter concludes with the need for an improved PL model that will be adaptive to any environment while combining the benefits of both the empirical and the deterministic models.
The predictions of propagation PL in different areas has been analysed in Chapter 4 using conventional ANN model: the MLP ANN. The focus was on the prediction performance of different ANN training algorithms during the network training using real world data from LTE cellular network. First order statistical performance indices: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Standard Deviation (SD) and Correlation Coefficient (r) has been used for error measurement during network training.
Comparisons of the training results show an outstanding performance with Bayesian Regularization (BR) algorithm with the least measurement errors and the highest correlation coefficients, thus the best in terms of accuracy, but require longer training time. Lavenberg- Marquardt (LM) algorithm performs best in terms of training speed. However, the error margins between Bayesian regularization algorithm and Lavenberg-Marquardt algorithm is
146 very minimal. Also, Bayesian regularization algorithm is an improvement on Lavenberg- Marquardt to address poor network generalization by addition of a small overhead to the Hessian approximation already in existence in Lavenberg-Marquardt algorithm.
In part I of chapter 5, different ANN training techniques to overcome the tendencies of over-fitting thereby avoiding poor network generalization during network training has been investigated and the results compared using two neural network models: the RBF ANN and the MLP ANN. These techniques include neuron variation in the hidden layer of neural network architecture, Bayesian regularization approach and early stopping approach. For MLP ANN, the network demonstrates an excellent capability of modelling a moderate size network with 40 neurons in hidden layer. Subsequent increase in neuron results to over-fitting showing the need for intermediary layers to improve network generalization. However, with RBF ANN, network generalization ability increases with increase in the number of neurons in the hidden layer. This is because of its fixed three-layer architecture, hence there is no poor network generalization resulting from architectural intricacy. Training the RBF ANN using early stopping approach shows a better PL prediction with lesser measurement errors using first order statistical performance indices in comparison to MLP ANN. Finally, training the RBF ANN shows no changes during the network training using Bayesian regularization approach. This is because of it fixed three-layer structure, hence, there is no poor generalization as a result of architectural complexity which Bayesian regularization approach addresses.
Part II of chapter 5 presented an evaluation of the effect of learning rate on two ANN models: the GRNN model and the MLP ANN model while also analysing the effect of spread factor in GRNN and the effect of different combination of non-linear and linear transfer functions in hidden layer of MLP ANN. Small spread factor leads to good network generalization in GRNN while hyperbolic tangent and logistic transfer function in hidden and output layer of MLP ANN out-performed other combination of transfer functions. Also, small spread factor in GRNN requires small learning rate for an excellent prediction with minimal errors while MLP ANN requires higher learning rate.
In part III of chapter 5, the prediction effectiveness of ADALINE and MLP ANN have been analysed using data from two base stations. Data from BS 1 is used to analyse the effect
147 of learning rate on the two different ANN models while data from BS 2 is used to validate the results of analysis from base station 1. The gradient and the momentum parameter of the two ANN models have been analysed at different variation of learning rates. Adaptive linear element neural network shows good prediction capability using small learning rate but at higher learning rate, the gradient is approximately zero which approximate to the local minima. The reverse was the case for MLP ANN model. However, there is need for an adequate learning rate to be selected to ensure increase convergence but not too high learning rate that will lead to over-fitting during network training. Hyperbolic tangent and logistic sigmoid perform excellently in hidden and output layers of MLP ANN while purelin transfer function performs well with ADALINE neural network.
A hybrid adaptive neural network predictor that combines ADALINE neural network and MLP ANN has been developed and presents in part I of chapter 6. The prediction accuracy of the developed model has been tested and analysed using real world data from LTE cellular network environment with varied residential, commercial and clustered buildings. Comparison of the prediction accuracy of the hybrid adaptive neural model using first order statistical performance evaluation indicators give better PL prediction accuracy than the analysed conventional ANNs. The superior performance of the hybrid adaptive neural network is a result of its adaptive response and ability to predict the fluctuating patterns of the cited propagation loss data in course of network training. Furthermore, in part II of chapter 6, a second model has been developed where a vector order filters based pre- processing method built on MLP ANN is used to enhance adaptive prediction trend of the stochastic noisy data. The developed model shows that pre-processing of signals enhances the training and prediction accuracy.