Neural Model for Path Loss Prediction in Suburban Environment

Transcription

1 Neural Model for Path Loss Prediction in Suburban Environment Ileana Popescu, Ioan Nafornita, Philip Constantinou 3, Athanasios Kanatas 3, Netarios Moraitis 3 University of Oradea, 5 Armatei Romane Str., Oradea, Romania Visitor Researcher at the Mobile Radiocommunications Laboratory, National Technical University of Athens, Greece Tel: , Fax: ipopes@cc.ece.ntua.gr Technical University of Timisoara, Vasile Parvan Str., Timisoara, Romania ioan-naf@hermes.ee.utt.ro 3 Mobile Radiocommunications Laboratory, National Technical University of Athens, 9 Heroon Polytechniou Str. GR-57 73, Zografou, Athens, Greece fonst@mobile.ntua.gr, anatas@mobile.ntua.gr, morai@mobile.ntua.gr Abstract This paper presents neural networ based model for the prediction of propagation path loss in suburban environment. The performance of the neural model is compared to the measured path loss values from the measurements conducted in Oia village on Santorini Island, Greece, based on the absolute mean error, standard deviation and the root mean squared error between predicted and measured values. Keywords: channel measurements and characterization, neural networs, propagation loss model.. Introduction The prediction of propagation path loss is an important step in planning a mobile radio system and accurate prediction methods are needed in order to determine the parameters of a radio system that will provide efficient and reliable coverage of a specified area. Prediction models can be divided in the following three categories: - empirical models [5] consisting of diagrams or equations for path loss calculation, which are obtained from statistical analysis of a large number of measurements,

2 - deterministic models [3] - [4], based on an abstract environment, retaining some basic features of it in order to mae a theoretical treatment possible, - semi-empirical models [6] resulting from an empirical modification of the deterministic models in order to improve the agreement with measurements. The neural networs represent an alternative approach to the propagation prediction models. The advantages of this approach are given by their flexibility to adapt to different environments, the high speed processing and their ability to process a high amount of data.. The Measurements Field strength measurements used to design and test the models were performed in the 890 MHz band in Oia village on Santorini Island (Greece). The village of Oia is built on a high peninsula on the island of Santorini. The area cannot be easily characterized as suburban because of the unique Cycladic environment, which is characteristic in Gree islands. Oia is a tourist area with narrow waling paths, except of three main streets. The buildings are mostly stony and two-floors. Many of them are embedded into the roc, being carved out of the stones with non-canonical shape. The tree density was negligible on the island. The street and the village plan are also non-uniform. The transmitter hardware consists of a signal generator supplying a CW tone at 890 MHz. The output power level was +33 dbm. The transmitting antenna was an omnidirectional antenna with a gain of.5 dbi. Typical system and cable losses were.5 db. The transmitting unit, the mast and the antenna were placed on a specially designed car-trailer that could be easily transported. The height of the base station antenna was always 4 m above the ground level. The receiver hardware consists of an omnidirectional antenna with.5 db gain, a low noise amplifier, a receiver, a sampling card and a personal computer to record the data. The

3 receiver (including the low noise amplifier) has a 0dBm noise floor while the system and cable losses were.5 db. Thus the maximum path loss that could be measured by the system was 53 db. The receiving antenna was always.8 m above the ground level. The fast fluctuations effects were eliminated by averaging the measured received power over a distance of 6 m, that corresponds to approximately 40λ sliding window. After converting the values from received power to path loss versus distance, we compare the measured path loss with the predicted values of path loss by the neural networ model, based on the absolute mean error, standard deviation and root mean square error. In addition, the measured values were compared with the results obtained by Walfisch-Bertoni model (WB) [3], COST3-Walfisch-Iegami model (CWI) [7] and simple regression model (SRM) [0]. The absolute error between the measured and predicted path loss is computed with: Ei measured predicted PLi PLi = () where i represents the number of the measured sample. The absolute mean error is computed by: N μ = E i N i= () where N is the total number of measured samples. The standard deviation is determined from the absolute error () and the mean absolute error (): σ = N E μ i N N i= (3) The RMS error is given by: RMS = μ + σ (4) The designed neural models and the examined empirical models require parameters that describe the propagation environment such as the street width, the roof top height and the building bloc spacing. Average values were used since these variables change continuously

4 along one route. For the determination of these geometric parameters a map with building database was used. In Oia village the roof top height ranges from 5m to 5m, the street width ranges from 5m to 30m and the building bloc spacing ranges from 0m to 50m. 3. Neural Networ Configuration In our study we have used multilayer feedforward networs, commonly referred to as multilayer perceptrons (MLPs). The basic component of a neural networ is the neuron. Figure shows the configuration of a multilayer perceptron with one hidden layers and an output layer. The networ shown here is fully interconnected, that is each neuron of a layer is connected to each neuron of the next layer so that only forward transmission through the networ is possible, from the input layer to the output layer through the hidden layers. w ji w oj x 0 x y x n- Input Layer Hidden Layer Output Layer Figure : The configuration of the Multilayer Perceptron The output of the neural networ is described by the following equation: M N y = F 0 woj Fh w ji xi j= 0 i= 0 (5) where: -w oj represents the synaptic weights from neuron j in the hidden layer to the single output neuron, -x i represents the i th element of the input vector,

5 -F h and F 0 are the activation function of the neurons from the hidden layer and output layer, respectively, -w ji are the connection weights between the neurons of the hidden layer and the inputs. The learning phase of the networ proceeds by adaptively adjusting the free parameters of the system based on the mean squared error E, described by equation (6), between predicted and measured path loss for a set of appropriately selected training examples: E = m i= ( y ) i di (6) where y i is the output value calculated by the networ and d i represents the expected output. When the error between networ output and the desired output is minimized, the learning process is terminated and the networ can be used in the testing phase with test vectors. The goal of the prediction is not only to produce small errors for the set of training examples but also to be able to perform well with examples not used in the training process. This generalization property is very important in practical prediction situation where the intention is to use the propagation prediction model to determine the coverage area of potential transmitter locations for which no or limited measured data are available. Bacpropagation learning algorithm was created by generalizing the Widrow-Hoff learning rule to multiple layer networs and nonlinear differentiable transfer functions. There are many variations of the bacpropagation algorithm. The simplest implementation of it updates the networ weights and biases in the direction in which the performance function decreases most rapidly the negative of the gradient. One iteration of this algorithm can be written: x + = x a g (7)

6 where x is a current vector of weights and biases, g is the current gradient and a is the learning rate. In the conjugate gradient algorithms a search is performed along conjugate directions. All of the conjugate gradient algorithms start by searching in the steepest descent direction (negative of the gradient) on the first iteration: p0 = g0 (8) A line search is then performed to determine the optimal distance to move along the search direction: x + = x + a p (9) Then the next search direction is determined so that it is conjugate to previous search directions. The general procedure for determining the new search direction is to combine the new steepest descent direction with the previous search direction: p + = g + b p (0) For all conjugate gradient algorithms, the search direction will be periodically reset to the negative of the gradient. The standard reset point occurs when the number of iterations is equal to the number of networ parameters (weights and biases) but there are another reset methods that can improve the efficiency of training. In our application the neural networs is trained with the Powell-Beale version of the conjugate gradient algorithm. This method was proposed by Powell [8], based on the earlier version proposed by Beale [9]. For this technique the restart taes place if there is very little orthogonality left between the current gradient and the previous gradient. This is tested with the following inequality: g T g 0. g () If this condition is satisfied, the search direction is reset to the negative of the gradient.

7 4. Results The neural networ model is trained with physical data that includes distance between transmitter and receiver, the width of the streets, the height of the buildings, the building separation and the street orientation. Since our purpose is to train the neural networ to perform well for all the routes, we should build the training set including points from the entire set of measurements data. We have train the networ with 333 measurement points (from the total of 665 points). The rest of available measurements have been used for testing purpose. The neural model has a single output which represents the normalized propagation path loss. Two hidden layers with neurons each were used in the configuration of the neural networs. The transfer function used for the hidden layer is the sigmoidal tangent and for the output layer is the linear function. The results obtained over the entire test set have been compared with the results obtained by using the Walfisch-Bertoni model (WB) [3], the COST3-Walfisch-Iegami model (CWI) [7] and the simple regression model (SRM) [0]. The performances achieved by the above-mentioned models for the entire test data are represented in Table. Table. Comparison between the NN approach and the other empirical models [db] NN SRM WB CWI Mean Error Std Dev RMS Error If in the neural networ input data we also include the multi-screen diffraction loss and the roof-to-screen diffraction computed by COST3-Walfisch-Iegami algorithm, the root mean square error reduced by 0.54 db. Figure represents the measured and predicted propagation path loss by the Multilayer Perceptron models and CWI model in case of one particular route.

8 Path Loss [db] Distance [m] Measurements NN Model CWI Model Figure. Comparison between the measured and the predicted propagation path loss by the neural model and the CWI model for one particular route. 5. Conclusions In this paper we have studied an application of the neural networ model for the prediction of propagation path loss and we have compared it with measurements and with the prediction made by different empirical models. The results of the neural networ application are more accurate than the other empirical models. References [] T. Balandier, A. Caminada. V. Lemoine, F. Alexandre, 70 MHz Field Strength Prediction in Urban Environments Using Neural Nets, Proc. IEEE Inter. Symp. Personal, Indoor and Mobile Radio Comm., vol., pp. 0-4, Sept. 995

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