Extensions to the field strength prediction technique based on dominant paths between transmitter and receiver in indoor wireless communications G. W¨olfle1 , F. M. Landstorfer1 , R. Gahleitner2 , E. Bonek3 1
Institut f¨ur Hochfrequenztechnik, University of Stuttgart, Germany e-mail:
[email protected] WWW: http://www.ihf.uni-stuttgart.de 2 Scientific Consulting, Cologne, Germany, formerly with 3 3 Institut f¨ur Nachrichtentechnik und Hochfrequenztechnik, Technical University of Vienna, Austria
Abstract |
A new model for the field strength prediction for mobile communication networks inside buildings is presented in this paper. The model is based on the determination of the dominant paths between the transmitter and the receiver. The field strength is predicted with artificial neural networks, trained with measurements. In contrast to other neural prediction models a good generalization is achieved, so the prediction results are also very accurate in buildings not used for the training of the neural network. Two algorithms for the selection of the training patterns for the neural networks are also presented and compared with each other. I. I NTRODUCTION
The planning of indoor wireless communication networks depends on an accurate prediction of the electric field strength received from a potential base station. Until now, there are two different approaches to the prediction of the electric field strength inside buildings, both of which have their individual disadvantages. The first group comprises empirical models, based on the regression of data gained in measurement campaigns like the Motley–Keenan–Model for indoor environments [1]. While these models are very fast in computing the field strength, they are not able to consider waveguiding in corridors. The second group contains ray–optical or deterministic methods mostly based on ray tracing or ray launching techniques [2]. While in principle it is possible to determine all relevant rays between transmitter and receiver with such deterministic models on the basis of very accurate data bases, the main disadvantage of the ray–optical models is their high dependency on the accuracy of the data base and their very long computation time. Prediction models based on artificial neural networks [3], [4] are an alternative to the methods mentioned above. In these models, the neural networks are trained with measured data and adapt their parameters in such a way that they optimally approximate the measured field strengths for the input data provided [5],[6].
However, some of these neural prediction models are developed for a single room or a special situation only, others are applied to the interpolation between measured field strength values [7]. While very accurate predictions are possible in nearly similar environments, all these models are not suited for planning purposes where the field strength in different buildings, not previously used in the training process, has to be predicted. Over the last years two new prediction models have been developed which can be applied to very general environmental situations [8], [9]. One is an extension of the empirical models, because it is based on the direct ray between the transmitter and the receiver [8]. For improving the prediction accuracy, additional parameters are determined and included in the calculations. These parameters are waveguiding [9], local arrangements of walls [8], visibility (line of sight, obstructed line of sight, non line of sight), and the shape of the rooms. These new parameters improve the prediction, especially in buildings not previously used for the training of the neural network. The second model is based on dominant paths between a transmitter and a receiver. A prediction of the field strength along these paths is obtained with neural networks [9]. This model has been developed for buildings with very long corridors, as often found in office buildings. New parameters for this model improve the prediction results and are described in this paper. Because of the efficient algorithms for the determination of the dominant paths (see section IV), this model is very fast in computing the field strength. The computation time is nearly similar to the computation time of empirical models. A special method in selecting the training patterns for the neural network leads to a very good generalization capability (see section IV). So the prediction model and the neural network can be used in different buildings and environments not included in the training process of the neural network. This is shown in the prediction results obtained for a building of the Technical University of Vienna (see section V). The measurement data of Vienna used for comparison were not utilised in the training process of the neural network, but the predictions in Vienna are very accurate.
II. M ULTIPATH PROPAGATION IN INDOOR
III. P RINCIPLE OF THE DOMINANT PATHS
ENVIRONMENTS
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If the rays in the right part of figure 1 are analyzed, it seems to be obvious that most of them are nearly similar to one another. So R the rays can be subdivided into different groups, each group defined by the following criteria:
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Fig. 1: Map of a building and multipath propagation
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In indoor scenarios there are many possible rays between a transmitter and a receiver, as shown in figure 1. OnR the one side the computation of all of these rays is very time conT suming [2], on the other, these rays are not time-invariant and depend on Rthe accuracy of the data base. Both probR figure lems are shown in figure 2. In the left part of the the influence of a door is presented. If the door is open, T E determined rays (for the situationTwith closed door) are the E no longer valid and so the predicted field strength is wrong. R Also people and moved furniture are time–variant obstacles and can not be included into the data base of the building.
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Fig. 2: Accuracy of the data base and time–variant effects R inside a building 2
The second problem is shown in the right part of figure T F and G are not known ex2. If the positions of the walls actly (they may vary in the grey shadowed area) some of the determined rays do not reach the receiver R 1 . In most data bases the positions of the walls are not known as precisely as they should be for a ray tracing algorithm [10]. So a new approach for the prediction of the field strength should not rely on the knowledge of all possible rays between a transmitter and a receiver. Only the representative paths should be determined and they should be independent of the accuracy of the data base and of the time–variant effects. Actually these effects influence wave propagation, but there are many rays passing the same rooms between the transmiter and the receiver with different reflection and diffraction points, so changes in these points of interaction do not influence the received power. It is only necessary to know which rooms are passed by the rays and which walls are penetrated. The waveguiding by mutiple reflections must not be determined by the computation of all possible reflection and diffraction points. It should be determined independently of the different points of interaction. All these aspects are included in the approach with domiR nant paths which is described in the following section. R
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This effect is pointed out with the example given in figure 3. All rays reaching receiver R 2 in the left part of figure 3 can be described by their corresponding dominant path in the right part of the figure. Three dominant paths are necessary to describe the possible rays between the transmitter and the receiver R 1 , the first transmitting wall F , the sec6 and the third transmitting wall E . For ond passing room T example, both rays passing room 6 on their way to the receiver R1 can be described by the corresponding dominant R G and L (Number of walls and path, also passing wall rooms as mentioned in the left part of figure 1). As these dominant paths have no reflection or diffraction points but only points of changing directions, it is impossible to compute the field strength at their ends by using GTD/UTD [11]. One possibility for computing the field strength is some kind of empirical models, based on the regression of measurements. Another approach is artificial neural networks [9]. In this paper the neural network approach is presented and described in section V.B. One of the basic ideas of the new prediction model is the fast determination of the dominant paths. While in principle T it is possible to determine all rays with a ray tracing algorithm and then combining the different groups of rays to R and very fast algorithm is presented dominant paths, a new for the determination of the dominant paths. This algorithm is described in section IV and is nearly as fast as the predicT tion with empirical models. The algorithm is explained in 2 D while in principle it also works in 3 D, but it is more R complicated to describe. R
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IV. D ETERMINATION OF THE DOMINANT PATHS A. Sequence of rooms and walls passed E
1 In a first step, the sequence of the transmitted walls and E2 rooms passed must be determined. Therefore an analysis R2 R of2 the data base is mandatory. In the data base only information on walls and the material of the walls is given, no information about rooms is available. So rooms must be determined in a first step.T After this initial step, a tree of the room–structure is computed as shown in figure 4.
The coordinates of the path are always computed with the R1 same algorithm, independent of the number of transmitted walls and passed rooms. This is only possible by combining all passed rooms to one room for the determination of the path. This is shown in figure 5 for a given dominant path. E (Names of Rooms 1 and 5 are combined, erasing wall the walls and rooms are given in figure 1). Now the situation is similar to the situation where the receiver and the transmitter are located in the same room. The solution for the determination of the path inside a single room is now described in the following section. R2
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Fig. 4: Tree of the room–structure of the building presented in figure 1
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The root of the tree corresponds to the room in which the transmitter is placed. The first layer contains all neighbouring rooms. If there are different walls between the transmitter room and the neighbouring rooms (e.g. wall E and F between room 1 and 5 ), the neighbouring room is placed 1 inRthis layer of the tree as many times as there are coupling walls between the rooms. After this first layer of the tree, the second layer is determined in a similar way, i.e. all neighbouring rooms (and coupling walls) are branches of the corresponding rooms of the first layer. The tree contains as many layers as necessary for completeness, i.e. each room of the building must occur in the tree at least once. After the determination of the tree, the dominant paths between the transmitter and the receiver can be computed very easily, because if the receiver is located in room i , the tree must only be examined for room i . If room i is found in the tree, the corresponding dominant path can be determined by following all branches back to the root of the tree. For example the path to room 5 through wall E is highlighted in figure 4 to show the determination of the paths.
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Fig. 6: Convex and concave corners of the room The concave corners are not used for determining the path and so the path between the two points must pass different convex corners (at least one convex corner). For the corners of the room two trees are generated, as shown in figure 7.
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There are two different cases Tfor the determination of the R R dominant path between a transmitter and a receiver located in the sameRroom: Line of sight and obstructed line of sight R R 1 of the (No line of sight is not possible because the rooms transmitter and the receiver are combined to a single room as described in section IV.A). In the first case (Line of sight) the determination of the dominant path is very easy because it corresponds to the direct ray between the two points. The second case (Obstructed line of sight) is a bit more complicated. In a first step, all the corners of the room get a number and are arranged in two lists, one containing all convex corners and the second one all concave corners (see figure 6).
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Fig. 5: Combination of the rooms
Fig. 7: Determination of paths in the corner–tree
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Two trees are necessary, one for the transmitter and one for the receiver. If there is line of sight between the transmitter (receiver) and a convex corner, this corner is put in the first layer of the tree. The second layer consists of all convex corners which are visible (by line of sight) from the corners in the first layer and so on. The determination of the path is very easy now, because it is only necessary to compare the trees for the transmitter R and the receiver. If there is the same corner number on the first layer in both trees, the path leads via this corner (For 10 in figures 6 andR 7). If there are different example corner R numbers, the second layer in both trees must be compared to the first layer in the other tree and if there occurs the same number, the path leads via this corner and the corresponding corner in the first layer. If no path is found at this stage, the corners in the second layers of both trees are compared. This is done till the same number in both trees is found. In the last step the dominant path must be modified to be independent of the exact location of the corners, as mentioned in section III. Therefore the path is moved inside the room, depending on the angle of the corner and the distance to the next wall (see figure 8). 1
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Interaction loss LI Changes in the direction of the path represent an additional loss. An analysis of the walls around the points of changing directions leads to the empirical coefficient LIi for each interaction. The computation of the L Ii is similar to the determination of the local transmitter environment, described in [8]. The total interaction loss L I is computed by accumulating the L Ii .
If different paths are determined for a receiver point, the path with smallest total attenuation L is chosen. By adjusting the three weighting factors w F S , wT and wI it is possible to determine different types of dominant paths. But only some of these possible paths are necessary for the determination of the field strength. Three different sets of parameters lead to the best predictions:
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Transmission loss LT 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 LT is computed from n LT = Li (3) i=1
Path A: wF S wT ; wI A very short path compared to other alternatives. Path B: wT wF S ; wI A path with a very small transmission loss. Path C: wI wF S ; wT A path with a small number of changes in direction and small accumulated transition angles i (see figure 9).
These three dominant paths are now determined for each prediction point and are used for the computation of the field strength. An example for these three paths in a typical scenario is given in figure 9.
Fig. 8: Post processing for the dominant paths
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C. Selection of the dominant path The algorithm for the determination of the dominant paths leads to different solutions. But not all of them are necessary for the prediction. So the important ones must be chosen and this is done by the user-definable criterion given in the following equation:
L = wF S LF S + wT LT + wI LI
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L represents the total attenuation along the path consisting
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Free space attenuation L F S The free space loss LF S is computed with the path length l and the transmitting frequency f :
f + 20 log l LF S /dB = ;27:56 dB + 20 log MHz m
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Fig. 9: Three dominant paths As a prediction of the electric field strength along the dominant paths with the UTD is not possible, because they do not correspond to optical rays and no reflection or diffraction points have been determined [2], artificial neural networks, trained with representative measurements, are used for this purpose [5].
V. P REDICTION OF THE FIELD STRENGTH
Prediction area
A. Parameters of the dominant path As described in section III, the dominant paths represent a group of nearly similar rays between the transmitter and the receiver. The paths must now be described in such a way that all relevant parameters governing propagation are covered. Best results have been obtained with the following parameters: 1 General parameters a) Free space attenuation along the path As described in equation (2), includes distance and frequency. b) Visibility (LOS, OLOS, NLOS) Line of Sight (LOS), Obstructed Line of Sight (OLOS – Transmitter and receiver are in the same room, but there is no line of sight) and Non line of sight (NLOS – Transmitter and receiver are in different rooms). c) Accumulated transition–angles i For details concerning the transition angle i see figure 9. 2 Influence of walls along the path a) Transmission loss along the path Computation with equation (3). b) Waveguiding along the path This parameter describes the waveguiding effect due to walls oriented more or less parallel to the path and is presented in [9]. 3 Local arrangement of the walls at the transmitter site a) Local reflectors Local directivity due to the arrangement of walls as described in [8]. b) Local shielding effects Local shielding influenced by walls [8]. 4 Influence of the receiver site a) Local reflectors The same definition as at the transmitter site b) Local shielding effects The same definition as at the transmitter site c) Shape of the room containing the receiver Circumference U vs. area A of the room, computed with following equation:
p
S = 4UA
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d) Size of the room containing the receiver All these parameters are gained from a vector oriented data base for each of the three dominant paths for each prediction point. Now they can be combined with an empirical equation gained by measurements or with a neural network trained with measurements. In this paper we present the prediction with a neural network, as shown in figure 10. The three prediction results for the paths are combined with an additional neural network to provide the field strength at the prediction point.
Building data base
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Fig. 10: Neural network for the field strength prediction B. Prediction with the neural network In this section the artificial neural network, used for the combination of the parameters of the dominant paths is described. It is a multi–layered feed–forward perceptron, trained with the backpropagation algorithm. Free Space
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Fig. 11: Topology of the neural network for the field strength prediction The 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. All these patterns are now used for the calibration of the neural network. To avoid an overadaption to the special situation at the University of Stuttgart, only some of them are used for the training (see next section), all others are used for the validation, i.e. the error of these validation patterns is also computed after several training epochs. In the first phase of the training process, the error of the validation pattern decreases while in the second phase the error increases due to overadaption of the neural network to the training patterns. Before the overadaption of the network is reached, the training process must be stopped. At this stage the neural network has a very good capability of generalization.
C. Influence of the training patterns Many thousands of points of measurements have been considered (more than 5000 measurement points are available at the University of Stuttgart), but only some of them are necessary for the training of the neural network. On the one side some transmitter locations are not included in the training and are only used for validation (see section V.B), to get more realistic results in the validation process. If different transmitter locations are used in the validation pattern for the deciding of the end of the training process, better generalization of the neural network is achieved. On the other side, many patterns contain nearly the same information for the network. If all of them are used for the training, the network is overadapted to these patterns. Therefore an algorithm was developed to select only the important patterns and to delete all redundant ones.
by the quantized values of the input neurons. Each supporting vector represents exactly one possible training pattern. Supporting vectors and patterns are shown for the two– dimensional case in figure 12. Two approaches are possible for selecting the training patterns from N available patterns using supporting vectors ~sj :
Smallest distance dkj between pattern p~k and supporting vector ~sj . The pattern p~k is selected, if dkj dij for i = 1 : : : N (6) All patterns p~k with dkj smaller than a threshold to be defined are taken to form a single vector with averaged components. Neuron 2
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VI. S ELECTION OF TRAINING PATTERNS FOR THE -1
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The statistical distribution of each input parameter contained in the data sets used for the training of the neural network should be homogeneous. But it is also important that the combination of the different input parameters should be evenly distributed. Otherwise particular situations are overadapted and other situations are never trained. To avoid this, an algorithm for the selection of representative training patterns has been developed and is presented in the following. Each training pattern with n input parameters can be considered a vector p~ in n–dimensional space. If the distance between pattern p~i = (pi1 ; : : : ; pin ) and pattern ~ pj is very small, both contain nearly the same information and only one of the two should be considered for the training. The distance dij between pattern p~i and p~j is computed according to equation (5):
dij = jp~i ; p~j j =
vuuX t p n
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Fig. 13: Selection of patterns The first approach (see left part of figure 13) selects only one pattern for a supporting vector. If there is an error in the measured field strength value of this selected pattern, the neural network will give a wrong prediction value. To reduce the influence of a single pattern and its measured field strength value, the second approach for the selection of patterns is implemented. In this approach, the mean value of different patterns is computed and the influence of one faulty value is therefore rather small (see figure 13). The number of training patterns can be reduced by the selection algorithms mentioned above e.g. from 5000 to 300 while the prediction results will remain the same for the training patterns and will even improve, if predictions are made for scenarios not included in the training phase, as overadaption is avoided. A smaller number of training patterns also reduces the time necessary to train the network. VII. P REDICTION RESULTS
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Fig. 12: Training patterns and supporting vectors The selection of the patterns can be improved if supporting vectors ~sj are defined. The components s j 1 ; : : : ; sjn of these supporting vectors in n–dimensional space are given
The neural network was trained with measurements obtained at the University of Stuttgart. A new office building in the style of the 1970s, mainly constructed of concrete and glass was chosen. Its ground plan is given in figure 14. Different positions of the transmitting antenna were used for deriving the training patterns. The results presented in this paper were gained with a neural network, trained with measurements of five transmitter locations (T 1 . . . T5 in figure 14). T1 and T2 are representing transmitter locations in a corridor while T 3 , T4 , and T5 are inside different rooms.
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Fig. 14: Transmitter locations included in training patterns (IHF, University of Stuttgart) For each transmitter location many measurements in different rooms are taken, as shown in figure 15 for the transmitter location T1 . Many of these measurements contain the same information for the neural network, so the representative situations have to be determined with the algorithms presented in section VI.
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Fig. 17: Prediction and measurement in corridor 1 of the IHF office building
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After the training of the neural network, the new model was used for the prediction of different transmitter locations not included in the training process. For these transmitter locations also a high accuracy was obtained, as shown in figure 16. The difference between the measurement and the prediction for the transmitter location in figure 16 is very small (Mean error of the magnitude smaller than 3.3 dB). In contrast to the empirical or deterministic prediction models, which have very big errors in shadowed NLOSregions, the dominant path model is very accurate in these situations, as shown in the comparison of measurement and prediction in corridor 1 of the IHF-building (see figures 16 and 17).
The performance and generalization capability of the network is verified by using it for the field strength prediction within a building of the Technical University of Vienna [12], dating back to the turn of the last century (see figures 18 and 19). In spite of the significantly different environment, the values predicted by the neural network method and those measured compare favourably (Mean error smaller than 8 dB for the prediction in figure 18). Even in shadowed corridors far away from the transmitter the prediction is very accurate (see corridor 2 in figures 18 and 19). Fieldstrength [dB µV/m]
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[4] B. E. Gschwendtner and F. M. Landstorfer, “Adaptive propagation modelling based on neural network techniques,” in IEEE 46th Vehicular Technology Conference (VTC) 1996, Atlanta, pp. 623 – 626, Apr. 1996.
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urban environments using neural nets,” in IEEE 6th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 1995, Toronto, pp. 120 – 124, Sept. 1995.
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Fig. 19: Prediction and measurement in corridor 2 (University of Vienna) VIII. C ONCLUSIONS In this paper a new model for the prediction of the field strength inside buildings is presented. It is based on the determination of the newly defined dominant paths between the transmitter and the receiver. The parameters of these paths are then used as input values for a neural network, which is trained with measurements. Good prediction results and very high accuracy can be achieved not only in buildings used in the training process of the network, but also in buildings of significantly different structure and architecture. This is achieved by a proper selection of the training patterns of the neural network and by a validation of the training progress. The computation time of the new prediction model is also very small, nearly similar to the empirical models. Predictions of the delay spread or the fast fading are not possible with the presented prediction model till now, but the structure of the model and the determination of the paths are very flexible and so an extension for the prediction of the delay spread and the fast fading will be implemented in the near future. IX. ACKNOWLEDGEMENTS The authors thank Post and Telekom Austria AG for the permission to publish propagation data and the Deutsche Forschungsgemeinschaft (DFG) for supporting their work. X. R EFERENCES [1] J. M. Keenan and A. J. Motley, “Radio coverage in buildings,” In: BTSJ, vol. 8, pp. 19 – 24, Jan. 1990. [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), pp. 486 – 490, Sept. 1994. [3] T. Balandier, A. Caminada, V. Lemoine, and F. Alexandre, “170 MHz field strength prediction in
[5] G. W¨olfle and F. M. Landstorfer, “Field strength prediction in indoor environments using neural networks,” in Progress in Electromagnetics Research Symposium (PIERS) 1996, Innsbruck, Austria, p. 517, Jul. 1996. [6] G. W¨olfle and F. M. Landstorfer, “A recursive model for the field strength prediction with neural networks,” in IEE 10th Conference on Antennas and Propagation (ICAP), Edinburgh, pp. 2.174 – 2.177, Apr. 1997. [7] M. R. Pakravan, “Estimation of indoor infrared channel parameters using neural networks,” in IEEE 6th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 1995, Toronto, pp. 311 – 315, Sept. 1995. [8] G. W¨olfle and F. M. Landstorfer, “Field strength prediction in indoor environments with neural networks,” in IEEE 47th Vehicular Technology Conference (VTC) 1997, Phoenix, pp. 82 – 86, May 1997. [9] G. W¨olfle and F. M. Landstorfer, “Field strength prediction with dominant paths and neural networks,” in MIOP 1997, Sindelfingen, Germany, pp. 216 – 220, Apr. 1997. [10] P. Danielle, V. Degli-Esposti, F. Falciasecca, M. Frullone, and G. J. Riva, “Evaluation of the reliability of a ray tracing microcellular field prediction model,” in Progress in Electromagnetics Research Symposium (PIERS) 1996, Innsbruck, Austria, p. 513, Jul. 1996. [11] R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” in Proceedings of the IEEE, vol. 62, pp. 1448 – 1461, Nov. 1974. [12] R. Gahleitner, Radio Wave Propagation in and into Urban Buildings. PhD thesis, Technical University of Vienna, 1994.
