Field strength prediction by ray-tracing for adaptive ...

University of Wurzburg Institute of Computer Science Research Report Series

Field strength prediction by ray-tracing for adaptive base station positioning in mobile communication networks Th. Fritsch



Report No. 122

K. Tutschku



K. Leibnitz



August 1995



Institute of Computer Science, University of Wurzburg Am Hubland, 97074 Wurzburg, Germany Tel.: +49-931-8885513, Fax: +49-931-8884601 e-mail: ffritsch,tutschku,[email protected] Abstract: The Adaptive Base Station Positioning Algorithm (ABPA) is presented, which is based on a neural net approximation of the trac density in the coverage area of a cellular mobile communication system. ABPA employs simulated annealing, thereby achieving quasi-optimal base station locations depending on the topography of the investigated area. Furthermore, ABPA considers the radio wave propagation within this area for the base station positions. Therefore, a three dimensional digital surface model is used to approximate the topography and two eld strength prediction methods, a line-of-sight (LOS) approach and a ray-tracing technique, are investigated within the context of adaptive positioning. In particular, the results obtained by the ray-tracing technique are encouraging, showing supplying areas, which seem to be similar to those, stemming from real measurements. However, as simulations show, the more realistic eld strength prediction by ray-tracing has a strong in uence on the performance of ABPA, resulting in dierent base station locations. As an outlook, the combination of eld strength prediction using ray-tracing with adaptive trac prediction on a road graph by neural nets is proposed for further investigation. Keywords: mobile communication, planning tools, base station location, eld strength prediction, ray-tracing submitted to the 2nd ITG Conference on Mobile Communication '95, Sep. 26.-28.

1995, Neu Ulm, Germany.

1 Introduction The growth of the mobile cellular market imposes a dicult task to the designers of mobile communication systems. The determination of the base station locations depends mainly on two factors: a) the inhomogeneously distributed user density in the coverage area of the base stations, e.g. a location area in the GSM system, and b) the varying radio signal strength. When a mobile unit is moving through the supplying area of a base station, it receives a time-varying radio signal due to re ections, shadowing on obstacles and diusion by scattering. In the planning process, the disturbances of the radio signal caused by these physical phenomena are usually considered by rough estimations of the eld strength models using statistical assumptions [7]. Another method is the approximation of the eld strength level with models developed in the context of geometrical optics [9]. However, the latter models require an extremely high computing eort. Moreover, since the mobile subscribers move through the cellular network along trac highways, the resulting mobile teletrac density depends both on geographical location and on time. Consequently, the mobile teletrac distribution can be decomposed in two parts, the one concerning the average local distribution of mobile user density in a coverage area, the other representing the time-varying component due to trac mobility caused by working hours, car trac behavior, etc. The planning of adequate base station positions has to consider the rst part, whereas the second can be tackled by dynamic frequency assignment or network restructuring methods. In this paper we focus on the problem of nding optimal positions of base stations, whose supplying areas are covering the regions where the teletrac takes place. An adaptive base station positioning algorithm (ABPA), using a set of formal neurons, distributed according to the estimated local user density, was presented in [6]. In Section 2 we present a short outline of ABPA. This algorithm is already able to provide a meaningful solution of the base station positioning problem, but the eld strength prediction method used by ABPA can essentially be improved, since its approximation quality was kept low to avoid extensive computations. In Section 3 of this paper, free space propagation of radio waves is shortly reviewed and the Line-of-Sight (LOS) approach used so far in ABPA is described. Furthermore, the concept of eld strength approximation using ray-tracing techniques in combination with ABPA is discussed. In Section 4 we present rst results of ABPA using this modi cation. The improvement of ABPA will facilitate solutions of the base station positioning problem, which take realistic topographical scenarios into account. As a future task, the combination of ray-tracing based eld strength prediction methods with a modi cation of selforganizing feature maps, the Neural Gas algorithm, is proposed in Section 5. This combination is supposed to tackle more accurately the problem of adapting the local average trac density in the context of ABPA.

2 Outline of ABPA Using Selforganizing Feature Maps

The Adaptive Base Station Positioning Algorithm, presented in [5, 6], is based on the idea that competing base stations try to maximize their supplying areas by covering 2

(a) Digital Terrain Model

(b) Selforganizing feature map

Figure 1: Neural approximation of the digital terrain model

a maximum number of sensory objects, called sensory neurons. These neurons are distributed in the terrain, to be supplied with radio frequencies, according to a given density, which stems from the learning process of a selforganizing neural net. This density is assumed to be an estimation of the local teletrac density, since it is more likely that car trac and thereby mobile telephony takes place at data points of low terrain than at data points of high terrain. A selforganizing feature map was used to adapt the low terrain data of the digital terrain model of the topography, depicted in Figure 1(a). In Figure 1(b) the result of the adaptation process is illustrated. The geographical topography, which was investigated, represents the area north-west of Wurzburg. Selforganizing feature maps (SOM) are preserving the topology of the input vector space by adapting their weight structure accordingly. The reader is referred to [8] for a detailed description of SOMs. The usage of neurons by ABPA in the prestructuring step provides a set of sensory elements for the eld strength level. In the algorithm, the supplying areas of the base stations, described by their location, transmitting power and a positioning error, are determined. Hereby the comparison of the received eld strength level with a given threshold at the neuron positions is taken as the criterion, whether a neuron belongs to a base station supplying area or not. Each new arrangement of base stations is denoted as an adaptation step of the algorithm. Each base station can change its position or its transmitting power, thereby achieving dierent supplying areas. The positioning error of the base stations is a measure for a reasonable choice of their current locations, before the actual adaptation of these locations takes place. In this step, the base station with the worst positioning error is moved into the direction where clusters of attracting sensory neurons are located or into the direction which is resulting from the repellation of other base stations located in the immediate surrounding of the base station considered. The determination of supplying areas afterwards implies the eld strength prediction for all neurons in the coverage area according to the methods described in detail in Section 3. In the course of ABPA, each complete adaptation step is followed by a system state 3

evaluation, which is embedded in a simulated annealing process [1]. A system state Z at time step t is characterized by the assignment of all sensory neurons Si depending on the current distribution of the transmitting stations Tj and their corresponding supplying areas V (Tj ) to one of the following sets: 1. free sensory neurons Sf := fSijSi 62 Vg 2. multiply assigned sensory neurons Sm := fSijSi 2 Sl;j fV (Tj ) \ V (Tl)gg; 8l; 8j; l 6= j

3. de nitely assigned sensory neurons (Sf [ Sm) A system state is associated with a system energy, which is proportional to the magnitude of (Sf [ Sm). A minimization of the system energy corresponds to the maximization of the de nitely assigned neurons. Thus, an optimal coverage of the terrain can be obtained. However, such a result can only be achieved if the simulated annealing procedure [1] is used to govern the system state transitions. Hereby each state transition takes place with probability:

P fZ (new) = Z (cur)g = e?
E : (1) This implies, that the current system state Z (cur) is accepted as a new system state Z (new) according to the expression on the right hand side of eqn. (1). The decreasing temperature  plays the role of a cooling parameter of the system and is introduced to prevent the system of getting stuck in local minima of the energy function landscape. A nal stationary state, representing the suboptimal locations of base stations, is reached, if  declines to zero. The accuracy of ABPA depends on the determination of the eld strength level at the neuron positions, as well as on an appropriate distribution of the neurons itself. An improvement of ABPA concerns the restriction of the neuron positions to road and highway locations in the coverage area and is proposed in Section 5.

3 Field Strength Approximation in the Supplying Area A key issue in mobile system planning as well as in ABPA is the prediction of eld strength in the investigated supplying area. The received signal depends mainly on two environmental factors: a) the topographical structure and b) the morphographical properties of the area. These factors determine the in uence of three basic radio propagation phenomena: diraction, re ection and scattering. Diraction is mainly governed by the topographical structure and occurs, when the direct radio path between transmitter and receiver is obstructed by natural (e.g. hills) or human-made objects (e.g. buildings). Based on Huygen's principle, secondary waves are formed behind the object, even if there is no line of sight between transmitter and receiver. Thus a radio signal can be received in the \shadow" of an object. Re ections are observed, when a radio wave strikes an object which is very large, comparing to the wave length. The re ection coecients 4

vary for dierent surfaces of objects. Scattering occurs when the radio path contains objects with dimensions that are in the order of the wave length (e.g. leafs of trees). Since scattering is based on the same mechanism as re ection, it causes the energy of the radio beam to be reradiated diusely. The strength of re ection and scattering is substantially in uenced by morphographical properties. In the literature, a lot of models for radio wave propagation are proposed [2, 7, 9]. Complex proposals provide a good approximation of the path loss, but require high computational eort. Simple models require less computational power, but estimate the eld strength only roughly. Within ABPA, the eld strength prediction takes place in each adaptation step. Therefore, the applied eld strength prediction method has to show a good trade-o between computation requirements and approximation accuracy. After a short outline of path loss within free space propagation, the line-of-sight (LOS) approach used by ABPA is described in subsection 3.2.

3.1 Characterization of Path Loss within Free Space Propagation

A detailed description of the free space propagation model can be found in [3, 7]. For this model, it is assumed that no obstruction disturbs the propagation of the radio wave. The signal strength in the supplying area is characterized by the electromagnetic eld strength of the received wave. Since in free space waves are propagating equally in each direction, the wavefront has the form of a a sphere. Therefore the power density Sr at the receiver in distance d is: Sr = PtGt =Asphere = Pt Gt=(4d2): (2) Hereby Pt denotes the transmitting power and Gt the antenna gain. The product Pt
Gt is called equivalent isotropically radiated power (EIRP) considering the fact, that only antennas, emitting waves of equal strength in each direction, are taken into account. The eld strength Er at the receiver is: q q (3) Er = Sr Z0 = 30Gt(Pt=W )=(d=m)V=m; where Z0 = 120 denotes the wave resistance for vacuum. The eld strength level er at the receiver is de ned as: er =(db(V=m)) = 20 lg(Er =(V=m)) = 74; 8 + 10 lg(Pt=W ) + 10 lg(Gt) ? 20 lg(d=km): (4) In general, the signal loss is equivalent to the ratio between the transmitted and the received power, which is calculated in logarithmic scale. Regarding Ae as the eective absorption cross section of an antenna and Gr as the antenna gain, the received power Pr results to: Pr = Sr Ae = Sr Gr 2 =4 = Er2 2Gr =(4Z0) with Ae = Gr 2 =4: (5) Thus, regarding the path loss level LP, the following applies: 2 LP(db) = 10 lg(Pt=Pr ) = 10 lg Pt ? 20 lg Er ? 10 lg 4 + 10 lg Z0: (6) 5

transmitter

diffraction at the hill top

mobile station obstructed distance

Figure 2: Modeling the shadowing eect

From eqn. (6) follows that the path loss only depends on the transmitting power and the eld strength. In case of free space propagation, eqn. (6) can be simpli ed to: L0 = 32:5 + 20 lg(d=km) + 20 lg(f=MHz) ? gt=dBi ? gr =dBi ; (7) where f is the frequency of the radio signal and gr and gt denote the logarithmic measure of the antenna gain. Eqn. (7) provides a simple formula to compute the free space path loss, which only considers the distance between receiver and transmitter. Hata [7], extended the free space propagation model regarding morphographical properties. More generally, an additional parameter n is used, describing the relationship between distance and received power: L(d) = L(d0) + 10 n lg(d=d0) + X ; (8) where X is a zero-mean Gaussian random variable, that represents the variation in average received power, and d0 denotes a reference distance. The parameter n varies for dierent signal environments [2]. In eqn. (5) the value of n is 2, denoting the exponent of Er .

3.2 Line-of-Sight (LOS) Approach

In ABPA, the eld strength level is calculated according to eqn. (4), which was modi ed to take the path loss, caused by diraction, into account. In Figure 2 a typical scenario is depicted. A mountain is obstructing the direct propagation of the radio wave from the transmitter to the mobile station. Due to diraction, occurring at the top of the hill, the radio signal can also be received in the shadow of the mountain. In the LOS approach the actual distance as well as the amount of the obstructed radio path is considered. The eld strength level at the mobile station is approximated by: e0r = (db(V=m)) = er ? S
dobstruct = (db(V=m)) ; (9) where S is a proportional factor. The obstructed distance dobstruct can eectively be computed using Bresenham's line algorithm [4]. For rural environment, the heuristic assumption made above is quite useful since the diraction eects are not very strong in this case. In urban regions the distances from transmitters to the obstructing objects are usually smaller and thus diraction has higher impact. As a consequence, the LOS approach fails for urban environment. 6

ideal wavefront diffraction Tx

r reflection

d Ω

transmission

Tx

Figure 3: Ideal wavefront represented by each source ray

Figure 4: Diracted and re ected rays from transmitter Tx

3.3 Field Strength Approximation Using Ray-Tracing

Originally, ray-tracing techniques have been introduced in computer graphics applications to create photorealistic pictures of 3D sceneries [12]. Ray-tracing algorithms are able to visualize accurately optical eects like shadowing, transparency, etc. This capability makes the method attractive for eld strength predictions [11]. Ray-tracing is based on the light house idea. Radio beams are emitted from a transmitter Tx in distinct directions. The beams \illuminate" the scenery, i.e. the supplying area. In the algorithm, the beams are modeled as ray tubes with the xed solid angle d and of identical shape and size in distance r from the transmitter, cf. Figure 3. The path of an individual beam is traced recursively until it strikes an object, cf. Figure 4. If a ray strikes an edge or the surface of the digital terrain model, diraction or re ection of the ray takes place. Re ection can be modelled very easily using the Fresnel equations [13]. For diraction, Huygen's principle in conjunction with the Kircho laws has to be used to compute the decline in energy of the ray. Since ray-tracing tracks each beam individually, the behavior of the ray can be traced in detail at the cost of increased computing eort. A remaining problem, using ray-tracing, is the determination of the correct beam width d , i.e. the number of emitted rays, to achieve a certain approximation accuracy.

3.4 Supplying Areas

Using the two eld strength approximation methods described above, simulations with a single transmitter for a real supplying area have been carried out. The investigated terrain is again the 10km  10km area in the north-west of the city of Wurzburg, cf. Figure 5(a). The city center is located in the lower part of the picture and on the left side the river Main is visible. The hilly topography of this area can be considered typical for central Europe. The 3D model of this area consists of altitude values, sampled every 100 meters, and the surface is interpolated by triangles using the altitude points as vertices. The sensory neurons are distributed according to the prestructuring step of ABPA, cp. Section 2. The transmitter Tx in Figure 5(b) and Figure 5(c) is located in the center of each picture and the neurons, receiving a eld strength level above a certain threshold, are marked by bold print. These neurons form the \supplying area" of the transmitter. The approximation of this area using the LOS approach is depicted 7

(a)

(a)

(b)

(b)

(c)

(c)

Tx

Tx

Figure 5: The 3D terrain model (a) and the supplying areas for (b) LOS and (c) ray-tracing

Figure 6: Initial con guration (a) of ABPA and the base station locations obtained by (b) LOS and (c) ray-tracing

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in Figure 5(b). Here, eqn. (4) and eqn. (9) have been applied to compute the eld strength level. The connectivity of the supplying area is very high, whereas for the raytracing approach, cf. Figure 5(c), the \lacunarity" of this area is high. In the latter case, re ection were followed until depth one, using a re ection coecient of 1.0. The signal level was obtained by eqn. (4) with the total traversed path length as the distance d. The large \holes" in the supplying area indicate that the path loss is greater, than predicted by the LOS approach. As shown in Section 4, this will eect the ABPA substantially.

4 Finding Optimal Base Station Locations To prove the capability of ABPA and the two eld strength prediction techniques discussed in this paper, ABPA was tested on the topography north-west of Wurzburg. The algorithm was used to nd the best locations of six transmitters in this terrain. The initial con guration of the transmitter and the sensory neurons is depicted in Figure 6(a). Figures 6(b) and (c) show the base station locations, obtained by using the LOS approximation and the ray-tracing prediction, respectively. The transmitters are marked by ã and the dierent supplying areas for the individual transmitters are tagged by various symbols. The ABPA using LOS (cf. Figure 6(b)) achieved a very good coverage of the supplying area: 77% of the sensory neurons are de nitely assigned, 19% of the neurons are not assigned (marked by a
) and 4% are supplied by at least two base stations (marked by ¢). The locations of the base stations are fairly regularly distributed over the terrain. The result of ABPA in conjunction with ray-tracing is depicted in Figure 6(c). In this case the algorithm achieved only a poor coverage: 29% of the sensory neurons are de nitely assigned, 68% of the neurons are not assigned and 3% are multiply supplied. Two transmitters are placed on dominant positions in the central part of the picture. The others are placed at the margins of the investigated area. Since the supplying areas of the individual transmitters don't overlap very much, the transmitters located in the center increase their sphere of in uence and force the other base stations to cover only the marginal areas.

5 Outlook A possible extension of the ABPA to increase the accuracy of the algorithm consists of using a dierent distribution of the sensory neurons. Instead of approximating low terrain data by a selforganizing feature map, as described in Section 2, the neurons can be distributed on a road graph of the coverage area using a variant of the original SOM algorithm, the so-called Neural Gas [10]. The neurons behave analogously to particles of a gas and can therefore adapt readily any probability distribution. A special feature of this algorithm is its ability to approximate subspaces of varying dimensions and preserving its topologies. If measurements of mobile car trac are available, this data can be used to estimate the local average teletrac density along the road graph. As a result of the Neural Gas learning process, the neurons will distribute themselves inhomogeneously

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Figure 7: Neural approximation of the road graph in coverage area

on the road graph according to the measured vehicle trac density. The approximation of the road graph using the Neural Gas algorithm is depicted in Figure 7. Hereby the adaptation of the trac density has not yet been implemented and therefore the neurons are spaced equally on the road graph. Due to the dierent distribution of the neurons ABPA is expected to locate the base stations in accordance to the actual teletrac.

6 Conclusions We presented a neural net approach for the adaptive positioning of base stations (ABPA) in a cellular mobile communication system using an LOS and a ray-tracing technique for eld strength approximation. The obtained results are encouraging, since ABPA can also be used, when the radio wave propagation is modelled by ray-tracing in a more realistic way. Although ABPA using ray-tracing does not achieve the same high coverage as with LOS, the algorithm has the ability to nd suboptimal base station locations. Some extensions to avoid the driving out of some base station to the margins should be implemented. We expect that the approach presented in this paper will provide a powerful tool for planning cellular mobile communication networks.

Acknowledgement: The authors would like to thank Prof. Dr. P. Tran-Gia for giving commentary remarks on ABPA and its improvements. We would also like to give an appreciation to M. Becker, M. Dummler and M. Muller for their programming eorts.

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