DOMINANT PATHS FOR THE FIELD STRENGTH PREDICTION

Transcription

1 DOMINANT PATHS FOR THE FIELD STRENGTH PREDICTION G. Wölfle and F. M. Landstorfer Institut für Hochfrequenztechnik, University of Stuttgart, Pfaffenwaldring 47, D-755 Stuttgart, Germany WWW: Abstract An algorithm for the determination of the dominant paths for indoor wave propagation is presented. The algorithm computes a tree of the relations between the rooms inside the building and the branches of the tree are used for the determination of the dominant paths. Based on these dominant paths, three different prediction models are presented and compared with one another and with measurements. Two of the three models are based on neural networks, trained with measurements and the third model is an empirical model. With the neural prediction models a good generalization is achieved and they are very accurate in buildings not used for the training of the neural network. I. INTRODUCTION There are basically two different approaches to the prediction of the electric field strength inside buildings, both of which have their individual disadvantages. Empirical models, based on the regression of data gained in measurement campaigns, are very fast but not very accurate [1]. Deterministic models (ray optical models) depend heavily on the accuracy of the data base [3] and are very time consuming [2]. A new approach is given by prediction models based on artificial neural networks. In these models, the neural networks are trained with measured data and adapt their parameters to approximate the measured field strength [4]. Especially for indoor environments some successful improvements of empirical models were developed [5], but they are based on the direct ray and do not consider multipath propagation. II. ANALYSIS OF MULTIPATH PROPAGATION Fig. 1: Multipath propagation: Possible rays If multipath propagation with indoor scenarios is analyzed, two different effects must be considered. As shown in figure 1, different rays may reach the receiver passing the same sequence of rooms and penetrating the same walls. The contributions of those rays which offer the same number of interactions to the over all field strength are very similar and if other rays show more interactions, they can generally be neglected because of their higher attenuation. The new approach presented in this paper introduces dominant paths to describe all rays passing the same rooms and walls. The dominant paths for the scenarios in figure 1 are given in figure 2. Fig. 2: Multipath propagation: Representation of multipaths by a single dominant path The second effect of multipath propagation is shown in figure 3. There are different dominant paths, passing different rooms and penetrating different walls. These paths do not contribute equally to the total field strength and cannot be represented by a single path. Fig. 3: Multipath propagation: Different dominant paths The difference of the path losses between two dominant paths for the same receiver point is often greater than 6 db. These paths with higher attenuation can be neglected for the computation of the over all field strength, because their contribution is very small as compared to the main path. In most cases it is only necessary to determine the main dominant path to get an accurate prediction. More than one or two dominant paths are necessary in very particular situations, but the error by neglecting the third or fourth path is generally very small. A further improvement of the approach with dominant paths as compared to deterministic models consists in the fact that small tolerances in the locations of the walls have only a limited influence on the paths, because in contrast to the ray optics no exact location of the reflection and diffraction points is necessary for the determination of the path.

2 III. DETERMINATION OF THE DOMINANT PATHS A. Location of rooms The data base of a building generally contains only information about the location and the material of the walls but no information about rooms. For determining the dominant paths, a detailed information about the location of the rooms is mandatory, however. A new algorithm for the computation of the location of rooms was implemented in 2D and 3D. While the faster 2D algorithm can be used in cases where only a single floor in considered, the 3D algorithm is necessary for multi floor buildings. In a first step the intersections of lines symbolizing the walls are computed. Thus the corners of rooms are found (2D). In 3D the intersecting lines define wedges. The second step combines walls (or wedges) to rooms. The determination of the rooms includes an analysis of the neighboring rooms. For each room all neighboring rooms and walls coupling to these rooms are determined. The space around the building is also considered as a room. B. Tree for the room relationship The information about the neighboring rooms is used to compute a tree of the room structure of the building. For the building presented in figure 4 the tree of the room structure is shown in figure 5. ing rooms lead to a new branch in the tree, except if the wall is already used in this path in a layer above. After the determination of the tree, the dominant paths between the transmitter and the receiver can easily be computed, because the tree represents in its branches all possible dominant paths and the sequence of rooms passed. If the receiver is located in room i, the tree must only be examined for room i. The corresponding dominant path can be determined by following all branches from room i back to the root of the tree. Further information about the tree and the determination of the paths is given in [6]. C. Combination of rooms For determining dominant paths the same algorithm should be applicable to situations where a path passes through a sequence of rooms or where transmitter and receiver are located in the same room. If a path passes through a sequence of rooms, all rooms considered are combined to form a new single room by erasing all coupling walls in the branch representing the dominant path in the room tree (see figure 5). This combination of different rooms to a new room is shown in figure 6 for the two examples given in figure 1. Now the path inside the new room can be computed by using the algorithm described in the following section. D. Determination of the path inside a room If transmitter and receiver are located in the same room, the dominant paths inside this room are determined with the information about the convex corners as shown in figure 6. Fig. 4: Room numbers (left) and coupling walls (right) Fig. 6: Convex corners (or wedges) of a room and their influence on the determination of the paths Fig. 5: Tree of the room structure presented in figure 4 The root of the tree corresponds to the room in which the transmitter is located. The first layer contains all neighboring rooms and if there is more than one coupling wall between the room of the transmitter and the neighboring rooms, the neighboring room is placed in the first layer as many times as there are coupling walls between the two rooms. All further layers are determined in a similar way. All coupling walls to the neighbor- Each room is described by its surrounding walls. For the sake of simplicity the following explanations refer to the 2D case. In the 2D case all convex corners of the room get a different number. There are two different scenarios for the determination of the path between the transmitter and the receiver: Line of sight and obstructed line of sight. The first case is very easy because the dominant path is the direct ray between transmitter and receiver. In obstructed line of sight the dominant path must lead via convex corners to the receiver. For the determination of the path a tree with the convex corners is computed. All corners visible from the examined corner are new branches in the tree. As shown in figure 7, the corner tree starts with the corners visible

3 from the transmitter. The receiver is also included in the tree. Each time the receiver is found in the tree, the corners along the path can be determined by following the branches back to the transmitter. Fig. 7: Relations between the convex corners of the room E. Selection of the minimum loss dominant path (MLDP) The algorithm for the determination of the dominant paths leads to more than one solution [6]. But in most cases only one solution with the smallest path loss is necessary for an accurate prediction. This most important path is called minimum loss dominant path (MLDP). The MLDP is chosen by utilizing the user-definable criterion L: L = w FS L FS + w T L T + w I L I (1) L represents the empirical determination of the total attenuation along the path and consists of three different parts: Free space attenuation L FS The free space loss L FS depends on path length l and frequency f: L FS /db = ;27:56 db +log f MHz +log l m Transmission loss L T The accumulated transmission loss of all walls passed is represented by L T. If the path intersects n walls with their individual transmission losses L i, the total transmission loss L T is computed from L T = XNT (2) L i (3) i=1 Interaction loss L I Changes in the direction of the path as given by angle i at point i represent an additional loss. All angles i are accumulated and normalized with a factor L to give the interaction loss L I. X L I = 1 NI L i (4) i=1 Best results are gained with L = 5 :::8. If some walls are supporting the changes in the direction (waveguiding) at a specific point, the contribution at this point to the path loss is reduced, depending on the support of the walls as described in [5] for the transmitter environment. Different paths are determined for each receiver point and the path with the smallest total attenuation L is chosen and called minimum loss dominant path (MLDP). It is possible to determine different types of dominant paths by adjusting the three weighting factors w FS, w T and w I. In contrast to the model described in [6], only one criterion (w FS = w T = w I =1)is chosen for the models presented in this paper. Two of the three prediction models presented in this paper need only the minimum loss dominant path (MLDP) for the prediction of the field strength. Alternative paths with higher attenuation values are only considered in the third model, if the difference between their attenuation L and the attenuation L MLDP of the MLDP is smaller than a definable threshold. IV. PREDICTION OF THE FIELD STRENGTH Three different prediction models are presented in this paper and described in the following sections. The first two models are based on the minimum loss dominant path (MLDP), the last one needs further information about alternative paths (ADP model). A. Empirical prediction of the field strength with MLDP The computation of the path loss of the empirical MLDP model is given in equation (5). L E = L FS + L T + L (5) The offset L can be used for the calibration of the model. This model is nearly similar to that of Motley and Keenan [1], but in contrast to the latter this model is based on dominant paths and not on direct rays. The improvement gained with using dominant paths can be seen by comparing with results obtained with the model of Motley Keenan, as shown in figure 12. B. Parameters of the dominant path for the neural networks For the computation of the field strength with neural networks, the parameters of the minimum loss dominant path must be determined. Because the dominant paths represent a group of nearly similar rays between transmitter and receiver (see section II), all relevant parameters of these rays governing propagation should be considered in the description of the dominant path. Very good results have been obtained with the following parameters: Free space attenuation L FS along the path As described in equation (2). Transmission loss L T The transmission loss is computed with equation (3). Interaction loss L I The accumulated angles i of changes in direction are normalized with equation (4). Waveguiding along the path Each dominant path represents different rays. All of them are guided by reflections at the walls or by diffractions at the

4 corners of wedges in the same direction (see section II). To include all these rays in the prediction, they are described by the new parameter waveguiding. The waveguiding of the walls depends on their material (reflection loss), their orientation (reflection angle) and the distance between the walls and the path [4]. These three parameters are combined to give the parameter waveguiding, as described in [4]. Local reflectors and shielding effects at the transmitter site The computation of these local effects is described in [5]. Local reflectors and shielding effects at the receiver site For each dominant path all mentioned parameters are gained from a vector oriented data base and are normalized for the input of the neural network. The prediction of the field strength is based only on these parameters. C. Neural network prediction of the field strength with MLDP In this model an artificial neural network is used for the computation of the field strength. The parameters of the dominant path (see section IV.B) are combined with a multi layered feed forward perceptron. The backpropagation algorithm was used to train the network with measurements. Figure 8 shows the structure of the neural network. input neurons represent the normalized difference of the parameters (path length, transmission loss, interaction loss and waveguiding) between the alternative and the minimum loss dominant path (MLDP). In contrast to the model described in [6], the relative and not the absolute parameters of the alternative paths are used. A relative description is much better because the neural network must be trained with measurements and if the alternative path is described with absolute values, more combinations of input values (measurements) for the neural network are necessary to achieve a good generalization. The advantage of this model is obvious, if the results in figure 11 are compared with the results in figure. In shadowed regions often two paths have nearly the same contribution to the field strength, but the first and the second model use only the MLDP for the prediction. This model considers also the alternative path and the prediction is more accurate. But the computation time for the ADP model increases because all alternatives and their relative description to the MLDP wmust be computed. E. Training patterns for the neural networks The neural network models were trained with measurements obtained at the University of Stuttgart. The field strength of more than 5 receiver points and 15 transmitter positions in different environments was measured to get enough data for the training and the validation of the neural networks. To improve the generalization capability, not all possible patterns were used. If each pattern is interpreted as a vector in vector space, the Euclidian distance between the patterns can be computed. As patterns with very small distances contain nearly the same information only one of them is necessary for the training. The details of the algorithms for the selection of the patterns are described in [5] and [6]. V. PREDICTION RESULTS Fig. 8: Topology of the neural network for the prediction All training patterns of the network are gained from measurements at the University of Stuttgart. For each measured point inside the building all parameters of the dominant paths (input values of the neural network) are determined and stored in the training pattern together with the measured field strength. The improvement of the neural networks compared to the empirical model are obvious from figure 12, especially in shadowed regions and in long corridors with waveguiding effects. D. Neural network prediction of the field strength with ADP In this model again a neural network is used for the prediction of the field strength, but the prediction is based not only on the MLDP. Alternative dominant paths (ADP) are also considered in the prediction model. The neural network is similar to the network described in figure 8, the only difference is the four additional input neurons for the description of the alternative path. These additional A comparison between the new dominant path models and measurements is shown in figures 9 to 11. In addition to presenting the accuracy of the three models, these figures also show the dominant paths for different scenarios. Compared to standard empirical models [1], the new models are more accurate and compared to deterministic models [2] they are very fast because the computation time for whole buildings ( pixels) is smaller than minutes on a workstation. A comparison between the measurements and the new MLDP empirical prediction model is given in figure 9 (Mean error = 5.8 db, standard deviation = 9.9 db). In contrast to the standard empirical prediction models (Motley Keenan model: mean error = 24 db, std-dev = 26 db), the dominant path model is more accurate in nearly every situation. The prediction of the neural MLDP model (section IV.C) leads to a mean error of -.4 db and to a standard deviation of 3.3 db for the scenario given in figure. The performance of the alternative path model (ADP model, see section IV.D) is presented in figure 11 (mean error =.2 db, std-dev = 3.6 db).

5 4 3 - > 2. >. > -2. > -4. > -6. > -8. > Field strength db[µv/m] Measurement Motley Keenan Empirical model Neural network Alternative paths Fig. 9: between measurement and prediction with the new empirical model AK A A corridor > 2. >. > -2. > -4. > -6. > -8. > Fig. : between measurement and prediction with the neural network model > 2. >. > -2. > -4. > -6. > -8. > Fig. 11: between measurement and prediction with the alternative path model A comparison between the three different models and the Motley Keenan model is given in figure 12. For this analysis the scenario of figure was used and the three predictions for corridor 1 are compared with one another. Figure 12 also shows the improvement gained by the use of the neural networks for the dominant path models. The dominant path models were also used for the prediction in different buildings not used for the training of the neural network and the models turned out to be very accurate even in these buildings [6] Distance [m] Fig. 12: Prediction and measurement in corridor 1 of the IHF office building VI. CONCLUSIONS Three different prediction models for the prediction of the electric field strength inside buildings were presented in this paper and compared with measurements. All of them are based on dominant paths, a new and very fast approach to the determination of multipath indoor propagation. The results are highly accurate, even in buildings not previously used for the training. ACKNOWLEDGMENTS The authors want to thank Deutsche Forschungsgemeinschaft (DFG) for supporting their work. REFERENCES [1] J. M. Keenan and A. J. Motley, Radio coverage in buildings, In: BTSJ, vol. 8, pp , Jan [2] T. Huschka, Ray tracing models for indoor environments and their computational complexity, in IEEE 5th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 1994, pp , [3] V. Degli Esposti, C. Caciofi, M. Frullone. G. Riva Sensitivity of ray tracing indoor field prediction to environment modeling, in Internat. Conference on Electromagnetics in Advanced Applications (IECAA), Turin, Italy, Sept [4] G. Wölfle and F. M. Landstorfer, Field strength prediction with dominant paths and neural networks, in MIOP 1997, Sindelfingen, Germany, pp , Apr [5] G. Wölfle and F. M. Landstorfer, Field strength prediction in indoor environments with neural networks, in IEEE 47th Vehicular Technology Conference (VTC) 1997, Phoenix, AZ, pp , May [6] G. Wölfle, F. M. Landstorfer, R. Gahleitner, E. Bonek Extensions to the field strength prediction technique based on dominant paths between transmitter and receiver in indoor wireless communications, in 2nd European Personal and Mobile Communications Conference 1997, Bonn, Germany, pp. 18, Sept