Generalized Regression Neural Network Prediction Model for Indoor Environment

Transcription

1 Generalized Regression Neural Networ Prediction Model for Indoor Environment Ileana Popescu, Philip Constantinou Mobile Radiocommunications Laborator, National Technical Universit of Athens, Greece Miranda Nafornita, Ioan Nafornita Department of Telecommunications, Politehnica Universit of Timisoara, Romania Abstract This paper presents the results of our studies regarding the applications of the neural networs to the propagation path loss prediction in indoor environment. The proposed model consists of a Generalized Regression Neural Networ trained with measurements. The results of the prediction made b the proposed model showed a good agreement with the measurements. I. Introduction The basis for a propagation model ma be either theoretical or empirical, or a combination of these two. Theoretical propagation models allow recognition of the fundamental relationships that appl over a broad range of circumstances. The also allow definition of relationships that eist among an 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 the can be separatel recognized and theoreticall studied. Empirical models offer the opportunit to provide probabilistic descriptions of the propagation phenomena. The validit of empirical models is limited onl b the accurac with which individual measurements are made and b the etent to which the environment of the measurements adequatel represents the phsical environment in which the model is to be applied [1]. Indoor radio propagation is a ver comple and difficult radio propagation environment because the shortest direct path between transmit and receive locations is usuall bloced b walls, ceilings or other 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, bric, metal, glass, etc.), tpes of interiors (rooms with or without windows, hallwas with or without door, etc.), locations within a building (ground floor, n th 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 b prediction models based on artificial neural networs [2] - [5]. The problem of field strength prediction is viewed as a function approimation 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 stud develops a Generalized Regression Neural Networs model trained on etended data set of propagation path loss measurements taen in an indoor environment. The performance of the neural networ model is evaluated b maing a comparison between predicted and measured values based on the absolute mean error, standard deviation and root mean square error. 2. Neural Networ Architecture The Generalized Regression Neural Networ is a neural networ architecture that can solve an function approimation 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

2 use of this multidimensional surface to interpolate the test data. 1 2 m M 1 () 1 () K K () Input laer Hidden laer Output laer Figure 1. General Regression Neural Networ architecture As it can be seen from Figure 1, the Generalized Regression Networ consists of three laers of nodes with entirel different roles: The input laer, where the inputs are applied, The hidden laer, 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 dimensionalit. The linear output laer, where the outputs are produced. The most popular choice for the function ϕ is a multivariate Gaussian function with an appropriate mean and autocovariance matri. The outputs of the hidden laer units are of the form ϕ [] ( ) ( ) ( ) T 2 = ep v v σ (1) 2 when v are the corresponding clusters for the inputs and v are the corresponding clusters for the outputs obtained b appling a clustering technique of the input/output data that produces K cluster centers [6]. v is defined as v = ( p) (2) ( p) cluster N is the number of input data in the cluster center, and T d, v = v v (3) ( ) ( ) ( ) with ( p) v = (4) ( p) cluster The outputs of the hidden laer nodes are multiplied with appropriate interconnection weights to produce w 1 w w K i the output of the networ. The weight for the hidden node (i.e., w ) is equal to v w = (5) K 2 d(, v ) = N ep σ The selection of an adequate set of training eamples is ver 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 networs and it is used to evaluate the performances of the models [7] - [8]. 3. The Measurements The measurements used to build the neural networ based model were performed in the 1890 MHz frequenc 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 bac corridors. The offices are flaned on both sides of the main corridor and of the two short bac corridors, as shown in Figure 2 [9]. Offices are in consecutive order and are separated b soft partitions. Measurements were done along the corridors and inside the offices, in all three branches. In ever position of the receiver inside the offices about samples of the received power were recorded while the receiving antenna was rotating. The transmitting antenna was located alwas 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 tpes of transmitting antenna: OMNI and directional. The receiving antenna was alwas an OMNI antenna [9]. The presented stud includes the single floor scenario and the procedure used to select the measurement data is described below. In order to train the neural networ the measurements collected from two branches have been used: one branch where the transmitter was alwas located and onl one of the branches adjacent to it. The fast fading was eliminated, in the case of longitudinal measurements (along the corridors), b averaging the measured received power using a 2 windowing

3 technique [10]. In the case of static measurements, the average values of the recorded samples in ever 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, respectivel) were obtained for different combination of the position, height and gain of the transmitter antenna. Figure 2. The building topolog 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 networ model is evaluated b maing 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: measured predicted Ei = PLi PL (6) i where i represents the number of the measured sample. The absolute mean error is computed b: 1 N µ = E i (7) 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: 1 N σ = 2 2 E µ i N (8) N 1 i= 1 The RMS error is given b: 2 RMS = µ + 2 σ (9) 4. Results In our stud we consider the Generalized Regression Neural Networs, which are a ind of Radial Basis Networ, often used for function approimation [7]. As described in Section 2, the Generalized Regression Neural Networ consists of two laers of nodes (ecluding the input laer where the input data are applied): a hidden radial basis laer and an output linear laer. The outputs of the hidden laer units are of the form given b equation (1) and the weights for the hidden laer nodes are shown in equation (5). In the MATLAB implementation of this ind of neural networs, the centers of the Gaussian are chosen equal to the training input patterns, that is to sa that the first laer has as man neurons as the number of input patterns. Each hidden node has an associate bias that plas the role of the variance of the Gaussian. The bias is set to a column vector of /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 laer of the Generalized Regression Networ is responding with a nonzero output. On the other hand, SPREAD should not be large enough so that ever node in the hidden laer is efficientl responding in the same, large area of the input space [6]. After the outputs of the hidden laers are determined, the weights from the hidden laer to the output laer are chosen to be equal to the desired (target) vectors. In order to build the database necessar to train and test the neural networ, 34 files containing measurement data (covering all five scenarios) from corridors were used, together with 41 measurement points corresponding to offices. All measurement points taen into account correspond to the non-line-ofsight (NLOS) case. The inputs of the neural networ are as follows: 1. Influence of the transmitter site Position of the transmitter (the transmitter antenna was located alwas in the same sector, in two different positions), Gain of the transmitter antenna Height of the base station antenna 2. Receiver site

4 The sector where the receiver antenna is located Tpe of interior (corridor, room) where the receiver is located 3. Distances Distance between transmitter and starting point of measurements Distance covered b the mobile unit; 4. Penetration parameters Number of walls penetrated b the direct ra between transmitter and receiver Number of windows penetrated b the direct ra between transmitter and receiver Accumulated losses of walls and windows penetrated b the direct ra. The input parameters that describe the transmitter and receiver site are quantized so the effect of each parameter is more obvious for the neural networ. For eample, in order to describe the tpe of interior where the receiver is located, parameters lie 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 tpes of walls intervening between transmitter and receiver, as well as the loss for glasses were used as reported in [11] for this particular tpe of building. All parameters are normalized to the range [-1, +1]. The output laer of the Generalized Regression Networ 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, respectivel b the proposed Generalized Regression Neural Networ. Table 1. Result of prediction Training patterns Test patterns µ [db] [db] RMS [db] 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: Received power [dbm] Covered distance [m] Measurements NN Figure 3. Prediction and measurements (received power) L = L ( d ) Kw w 0 10n log L where: L = the path loss in db, L 0 = the path loss at 1 meter distance from the transmitter, n = the path loss depending on the environment outside the wall, K w = number of penetrated walls L w = the penetration loss due to the wall The parameter L w depends on the tpe 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 eists between the transmitter and the receiver, a detailed analsis is required to calculate the total loss ( L w ). Path loss [db] Covered distance [m] Measurements RBF-NN Empirical Model Figure 4. Predicted and measured values Appling the above-mentioned model to the particular route under investigation, as it can be seen from Figure 4, the prediction made b the neural networ model is more accurate, the improvement obtained on the RMS value being 4.37 db. In [12], a Multilaer Perceptron trained with the Resilient Bacpropagation algorithm was used to predict the field strength in the same indoor environment. B maing a comparison between the two tpes of neural networs, it is noticed a slight improvement obtained b the Generalized Regression

5 Networ over the Multilaer Perceptron model, about 0.15 db in the RMS sense. 5. Conclusions In this paper, the performances of the Generalized Regression Neural Networs 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-nown empirical models, high accurac can be obtained, because the Neural Networ is trained with measurements inside building and thus include realistic propagation effects and also consider parameters, which are difficult to include in analtic equations. The implementation of the proposed neural networ model requires a database eas to obtain. The proposed model showed ver good accurac. Acnowledgement We would lie to than to all the team that has conducted the measurements and delivered us the measured data in order to investigate the neural networs applicabilit to the environment under discussion. [8] S. Hain, Neural Networs: A Comprehensive Foundation, IEEE Press, McMillan College Publishing Co., [9] N. Papadais, A. G. Kanatas, E. Angelou, N. Moraitis, and P. Constantinou, Indoor Mobile Radio Channel Measurements and Characterization for DECT Picocells, Third IEEE Smposium on Computers and Communications, Athens, Greece, 30 June-2 Jul, ISCC 98. [10] W. Honchareno, 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 Technolog, 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 Buildings, European Transactions on Telecommunications, Vol. 14, pp , 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 References [1] P. Constantinou, Properties of wireless channels, Wireless LAN sstems, Addison Wesle, [2] G. Wolfle, and F. M. Landstorfer, A recursive model for the field strength prediction with neural networs, IEE 10 th Conference on Antennas and Propagation (ICAP) 1997, Edingburgh. [3] G. Wolfle, F. M. Landstorfer, R. Gahleitner, and E. Bone, Etensions 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 ra-optical models, COST 259, [5] A. Nesovic, N. Nesovic, D. Paunovic, Indoor electric field level prediction model based on the artificial neural networs, IEEE Communications Letters, vol. 4, no. 6, June 2000, pp [6] C. Christodoulou, and M. Georgiopoulos, Applications of Neural Networs in Electromagnetics, Artech House, 2001 [7] H. Demuth, and M. Beale, Neural Networ Toolbo For Use with MATLAB. User s Guide, Version 3.0