Generalized Regression Neural Network Prediction Model for Indoor

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Generalized Regression Neural Network Prediction Model for Indoor Environment. Ileana Popescu, Philip Constantinou. Mobile Radiocommunications ...
Generalized Regression Neural Network Prediction Model for Indoor Environment Ileana Popescu, Philip Constantinou Mobile Radiocommunications Laboratory, National Technical University of Athens, Greece [email protected]

Miranda Nafornita, Ioan Nafornita Department of Telecommunications, “Politehnica” University of Timisoara, Romania

Abstract objects. Signals propagate along the corridors and other open areas, depending on the structure of the building. In modeling indoor propagation the following parameters must be considered: construction materials (reinforced concrete, brick, metal, glass, etc.), types of interiors (rooms with or without windows, hallways with or without door, etc.), locations within a building (ground floor, nth floor, basement, etc.) and the location of transmitter and receiver antennas (on the same floor, on different floors, etc.) [1]. An alternative approach to the field strength prediction in indoor environment is given by prediction models based on artificial neural networks [2] - [5]. The problem of field strength prediction is viewed as a function approximation problem consisting of a nonlinear mapping from a set of input variables containing information about the potential receiver onto a single output variable representing the predicted field strength. The presented study develops a Generalized Regression Neural Networks model trained on extended data set of propagation path loss measurements taken in an indoor environment. The performance of the neural network model is evaluated by making a comparison between predicted and measured values based on the absolute mean error, standard deviation and root mean square error.

This paper presents the results of our studies regarding the applications of the neural networks to the propagation path loss prediction in indoor environment. The proposed model consists of a Generalized Regression Neural Network trained with measurements. The results of the prediction made by the proposed model showed a good agreement with the measurements.

I. Introduction The basis for a propagation model may be either theoretical or empirical, or a combination of these two. Theoretical propagation models allow recognition of the fundamental relationships that apply over a broad range of circumstances. They also allow definition of relationships that exist among any combination of input parameters. Empirical models models are derived from measurements and observations and offer a major advantage in that all environmental influences are implicit in the result regardless of whether or not they can be separately recognized and theoretically studied. Empirical models offer the opportunity to provide probabilistic descriptions of the propagation phenomena. The validity of empirical models is limited only by the accuracy with which individual measurements are made and by the extent to which the environment of the measurements adequately represents the physical environment in which the model is to be applied [1]. Indoor radio propagation is a very complex and difficult radio propagation environment because the shortest direct path between transmit and receive locations is usually blocked by walls, ceilings or other

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2. Neural Network Architecture The Generalized Regression Neural Network is a neural network architecture that can solve any function approximation problem. The learning process is equivalent to finding a surface in a multidimensional space that provides a best fit to the training data, with the criterion for the “best fit” being measured in some statistical sense. The generalization is equivalent to the

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the output of the network. The weight for the hidden node k (i.e., wk) is equal to v ky wk = (5)  d x, v x 2  K k  ∑ N k exp−  2 σ2  k =1   The selection of an adequate set of training examples is very important in order to achieve good generalization properties. The set of all available data is separated in two disjoint sets: training set and test set. The test set is not involved in the learning phase of the networks and it is used to evaluate the performances of the models [7] - [8].

use of this multidimensional surface to interpolate the test data.

(

ij 1 (x) x1

1 w1

x2

ij k (x)

wk

k

y i

wK

xm ij K (x) xM

K

Hidden layer

Input layer

Output layer

Figure 1. General Regression Neural Network architecture

3. The Measurements

As it can be seen from Figure 1, the Generalized Regression Network consists of three layers of nodes with entirely different roles:  The input layer, where the inputs are applied,  The hidden layer, where a nonlinear transformation is applied on the data from the input space to the hidden space; in most applications the hidden space is of high dimensionality.  The linear output layer, where the outputs are produced. The most popular choice for the function ϕ is a multivariate Gaussian function with an appropriate mean and autocovariance matrix. The outputs of the hidden layer units are of the form

(

ϕ k [x] = exp − x − v kx 

) (x − v ) (2 σ ) T

x k

2

The measurements used to build the neural network based model were performed in the 1890 MHz frequency band, at the Hellenic Telecommunication Organization premises following different scenarios. A detailed description of the measurement procedure can be found in [9]. Each floor of the building consists of a circular sector of 60 m in circumference located at the center of each floor and 3 branches departing from the circular sector, where at each branch there are one main long corridor, two short front corridors departing from the circular sector and another two short back corridors. The offices are flanked on both sides of the main corridor and of the two short back corridors, as shown in Figure 2 [9]. Offices are in consecutive order and are separated by soft partitions. Measurements were done along the corridors and inside the offices, in all three branches. In every position of the receiver inside the offices about 10000 samples of the received power were recorded while the receiving antenna was rotating. The transmitting antenna was located always in the same sector of the eleventh floor in two different sites (position: 1 or 2 in Figure 2). The base station antenna heights used were 2.2m, 2.6m and 2.7m. The measurements were performed using two different types of transmitting antenna: OMNI and directional. The receiving antenna was always an OMNI antenna [9]. The presented study includes the single floor scenario and the procedure used to select the measurement data is described below. In order to train the neural network the measurements collected from two branches have been used: one branch where the transmitter was always located and only one of the branches adjacent to it. The fast fading was eliminated, in the case of longitudinal measurements (along the corridors), by averaging the measured received power using a 2Ȝ windowing

(1)

when v kx are the corresponding clusters for the inputs and v ky are the corresponding clusters for the outputs obtained by applying a clustering technique of the input/output data that produces K cluster centers [6]. v ky is defined as

v ky =



y(p )

(2)

y (p )∈cluster k

Nk is the number of input data in the cluster center k, and d x, v kx = x − v kx T x − v kx (3)

(

with v xk =

) (

)(

∑ x(p )

x (p )∈ cluster k

)

)

(4)

The outputs of the hidden layer nodes are multiplied with appropriate interconnection weights to produce

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technique [10]. In the case of static measurements, the average values of the recorded samples in every position of the receiver inside the offices were computed. Two values for the received power in each office (with closed doors and with open doors, respectively) were obtained for different combination of the position, height and gain of the transmitter antenna.

σ=

(8)

The RMS error is given by:

RMS = µ 2 + σ 2

(9)

4. Results In our study we consider the Generalized Regression Neural Networks, which are a kind of Radial Basis Network, often used for function approximation [7]. As described in Section 2, the Generalized Regression Neural Network consists of two layers of nodes (excluding the input layer where the input data are applied): a hidden radial basis layer and an output linear layer. The outputs of the hidden layer units are of the form given by equation (1) and the weights for the hidden layer nodes are shown in equation (5). In the MATLAB implementation of this kind of neural networks, the centers of the Gaussian are chosen equal to the training input patterns, that is to say that the first layer has as many neurons as the number of input patterns. Each hidden node has an associate bias that plays the role of the variance of the Gaussian. The bias is set to a column vector of 0.8326/SPREAD, where SPREAD determines the distance of an input vector to a neuron’s weight vector at which the Radial Basis Function will respond with an output of 0.5 [7]. In practice, SPREAD should be large enough so that more than one node in the hidden layer of the Generalized Regression Network is responding with a nonzero output. On the other hand, SPREAD should not be large enough so that every node in the hidden layer is efficiently responding in the same, large area of the input space [6]. After the outputs of the hidden layers are determined, the weights from the hidden layer to the output layer are chosen to be equal to the desired (target) vectors. In order to build the database necessary to train and test the neural network, 34 files containing measurement data (covering all five scenarios) from corridors were used, together with 41 measurement points corresponding to offices. All measurement points taken into account correspond to the non-line-ofsight (NLOS) case. The inputs of the neural network are as follows: 1. Influence of the transmitter site  Position of the transmitter (the transmitter antenna was located always in the same sector, in two different positions),  Gain of the transmitter antenna  Height of the base station antenna 2. Receiver site

Figure 2. The building topology and the transmitter positions Following the filtering process of the measured data, more than 1400 measurement locations corresponding to the non-line-of-sight (NLOS) case were obtained. The performance of the neural network model is evaluated by making a comparison between predicted and measured values based on the absolute mean error, standard deviation and root mean square error. The absolute error between the measured and predicted path loss is computed with: (6) E i = PL measured − PL predicted i

 1 N 2  ∑ Ei − N ⋅ µ 2  N − 1  i =1 

i

where i represents the number of the measured sample. The absolute mean error is computed by: 1 N (7) µ = ∑ Ei N i =1 where N is the total number of measured samples. The standard deviation is determined from the absolute error and the absolute mean error:

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The sector where the receiver antenna is located  Type of interior (corridor, room) where the receiver is located 3. Distances  Distance between transmitter and starting point of measurements  Distance covered by the mobile unit; 4. Penetration parameters  Number of walls penetrated by the direct ray between transmitter and receiver  Number of windows penetrated by the direct ray between transmitter and receiver  Accumulated losses of walls and windows penetrated by the direct ray. The input parameters that describe the transmitter and receiver site are quantized so the effect of each parameter is more obvious for the neural network. For example, in order to describe the type of interior where the receiver is located, parameters like size of the corridors are quantized as follows: 1 for the large corridor and 0.3 for the medium corridor. The attenuation factors for different types of walls intervening between transmitter and receiver, as well as the loss for glasses were used as reported in [11] for this particular type of building. All parameters are normalized to the range [-1, +1]. The output layer of the Generalized Regression Network consists of one neuron that provides the received power. A data set of 289 patterns, that represents 20% from all available patterns, was used for training purpose. A set of 1155 patterns was used to test the model. In Table 1 are represented the absolute mean error, the standard deviation and the root mean square error obtained for training and test set, respectively by the proposed Generalized Regression Neural Network.

-85

Received power [dBm]

-90 -95

-100 -105 -110 -115 -120 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 Covered distance [m]

Measurements

NN

Figure 3. Prediction and measurements (received power)

L = − L0 − 10 n log(d ) − ∑ K wL w where: L = the path loss in dB, L0 = the path loss at 1 meter distance from the transmitter, n = the path loss depending on the environment outside the wall, Kw = number of penetrated walls Lw = the penetration loss due to the wall The parameter Lw depends on the type of the wall construction between the transmitter and the receiver and the angle of incidence of the transmitted wave. In the case where more than one wall exists between the transmitter and the receiver, a detailed analysis is required to calculate the total loss (ȈLw).

Path loss [dB]

-50 -60 -70 -80 -90 -100

Table 1. Result of prediction µ [dB] ı [dB] RMS [dB]

Training patterns 1.49 1.71 2.27

-110 0

Test patterns 3.09 2.88 4.23

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Covered distance [m]

Measurements

RBF-NN

Empirical Model

Figure 4. Predicted and measured values Applying the above-mentioned model to the particular route under investigation, as it can be seen from Figure 4, the prediction made by the neural network model is more accurate, the improvement obtained on the RMS value being 4.37 dB. In [12], a Multilayer Perceptron trained with the Resilient Backpropagation algorithm was used to predict the field strength in the same indoor environment. By making a comparison between the two types of neural networks, it is noticed a slight improvement obtained by the Generalized Regression

In Figure 3, is shown a comparison between predicted and measured values of the received power, in case of a particular route: the receiver being located in a different sector (from the transmitter), along the main corridor. An empirical model corresponding to the NLOS situation, when the transmitter and the receiver antenna are on the same floor, is:

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Network over the Multilayer Perceptron model, about 0.15 dB in the RMS sense.

[8] S. Haykin, Neural Networks: A Comprehensive Foundation, IEEE Press, McMillan College Publishing Co., 1994. [9] N. Papadakis, A. G. Kanatas, E. Angelou, N. Moraitis, and P. Constantinou, “Indoor Mobile Radio Channel Measurements and Characterization for DECT Picocells”, Third IEEE Symposium on Computers and Communications, Athens, Greece, 30 June-2 July, ISCC ’98. [10] W. Honcharenko, H. L. Bertoni, J. L. Dailing, J. Qian, and H. D. Yee, “Mechanisms Governing UHF Propagation on Single Floors in Modern Office Buildings”, IEEE Trans. on Vehicular Technology, vol. 43, No. 4, November 1992 [11] A. Kanatas, N. Moraitis, E. Angelou, and P. Constantinou, “Measurements and Channel Characterization at 1.89 GHz in Modern Office European Transactions on Buildings”, Telecommunications, Vol. 14, pp. 177-192, 2003 [12] I. Popescu, I. Nafornita, Gh. Gavriloaia, P. Constantinou, C. Gordan, “Field Strength Prediction in Indoor Environment with a Neural Model”, FACTA UNIVERSITATIS, Electronics and Energetics series, vol. 14, no. 3, December 2001, pp. 329-336

5. Conclusions In this paper, the performances of the Generalized Regression Neural Networks used to predict the propagation path loss in indoor environment are investigated. The designed model was trained on data measurements collected in the 1890 MHz band. In contrast to well-known empirical models, high accuracy can be obtained, because the Neural Network is trained with measurements inside building and thus include realistic propagation effects and also consider parameters, which are difficult to include in analytic equations. The implementation of the proposed neural network model requires a database easy to obtain. The proposed model showed very good accuracy. Acknowledgement We would like to thank to all the team that has conducted the measurements and delivered us the measured data in order to investigate the neural networks applicability to the environment under discussion. References [1] P. Constantinou, Properties of wireless channels, Wireless LAN systems, Addison Wesley, 1986. [2] G. Wolfle, and F. M. Landstorfer, “A recursive model for the field strength prediction with neural networks”, IEE 10th Conference on Antennas and Propagation (ICAP) 1997, Edingburgh. [3] G. Wolfle, F. M. Landstorfer, R. Gahleitner, and E. Bonek, “Extensions to the field strength prediction technique based on dominant paths between transmitter and recveiver in indoor wireless communications”, EPMCC, September 1997 [4] G. Wolfle, and F. M. Landstorfer, “Prediction of the field strength inside buildings with empirical, neural and ray-optical models”, COST 259, 1999. [5] A. Neskovic, N. Neskovic, D. Paunovic, “Indoor electric field level prediction model based on the artificial neural networks”, IEEE Communications Letters, vol. 4, no. 6, June 2000, pp. 190-192 [6] C. Christodoulou, and M. Georgiopoulos, Applications of Neural Networks in Electromagnetics, Artech House, 2001 [7] H. Demuth, and M. Beale, Neural Network Toolbox For Use with MATLAB. User’s Guide, Version 3.0

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