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Two-Dimensional Ray-Tracing Modeling for Propagation Prediction in Microcellular Environments Karim Rizk, Student Member, IEEE, Jean-Fr´ed´eric Wagen, Member, IEEE, and Fred Gardiol, Fellow, IEEE
Abstract—The application of diffraction theory and geometrical optics for modeling the propagation in microcellular urban environments is investigated. The model simplifies the reality by considering only a two-dimensional (2-D) geometry, where the building walls are modeled by segments and the buildings are considered infinitely high. The model can handle arbitrary layouts of buildings according to an efficient algorithm briefly described in this paper. Comparisons between several predictions and measurements in two different cities in Switzerland are presented. A detailed investigation of the two main parameters considered in the predictions, i.e., the reflection and diffraction coefficients, is also provided. The study shows that the ray tracing model is appropriate for path-loss coverage prediction even in complex environments. Index Terms—Cellular, diffraction, microcell, propagation, radio, reflection, wireless.
I. INTRODUCTION
T
HE PERFORMANCE of a mobile radio communication system depends on the radio propagation environment. The propagation phenomena are quite involved, and the prediction of their effects in a theoretical way is very difficult. Even if rigorous computations are performed, the accuracy of the predictions will depend on the chosen assumptions necessary to solve the wave-propagation problem. Of course, the prediction accuracy will also depend on how the environment is modeled so that the complex problem of wave propagation in a mobile radio environment can be reduced to a manageable level. Thus, empirical and semi-empirical wave-propagation models [1], [2] are usually used to produce the predictions required to plan cellular radio communication networks. Recently, the drive to increase the capacity of the cellular communication systems has led to the introduction of the microcell concept. In a microcell, the height of the base-station antenna is lower than the average height of the buildings to confine the radio coverage within a small area of less than 300 m in radius, for example. In microcell environments, propagation models Manuscript received July 26, 1995; revised March 20, 1996. K. Rizk is with Ecole Polytechnique F´ed´erale de Lausanne, ELB-Ecublens, Lausanne, Switzerland (e-mail:
[email protected]). J.-F. Wagen is with Mobile Communications, FE421, Radio Network Planning Group, Swiss Telecom PTT R&D, CH-3000 Bern, Switzerland (e-mail: wagen
[email protected]). F. Gardiol is with Ecole Polytechnique F´ed´erale de Lausanne, ELBEcublens, Lausanne, Switzerland (e-mail:
[email protected] and http://lemawwww.epfl.ch/members/gardiol.html). Publisher Item Identifier S 0018-9545(97)03119-8.
used for the conventional larger cells may lead to poor results since they are based on computations over radials from the base station [3] and, thus, do not take into account the radio energy that propagates around the buildings. Efforts toward more accurate models appear to be promising [4]–[8]. These models are also more deterministic and use the layout of the buildings. These models are mostly based on ray tracing according to geometrical optics and using specular reflection and diffraction theory. This paper presents a deterministic model based on reflection and diffraction theory. The model uses an efficient implementation of the image theory to handle arbitrary layout of buildings. The goal of this paper is to determine the effect of various assumptions, related reflections, and diffractions effects used in a two-dimensional (2-D) ray tracing scheme. 2-D ray tracing approaches were presented by several authors [4]–[8]. However, we provide here a detailed investigation of the various parameters considered in the predictions. This paper separately analyzes the influence of specular reflections, single diffraction, and double diffraction. Furthermore, the effect of varying the reflection coefficient and the influence of various diffraction coefficients are discussed. Several predictions are compared to measurements in two cities showing that even a rather simple model provides useful information to system designers and network planners. The ray-tracing-based model is described in Section II and the measurements in Section III. The effects of specular reflections and the Fresnel reflection coefficient are investigated in Section IV. Section V analyzes the influence of single and double diffraction by building corners. Finally, Section VI concludes that the ray tracing model is appropriate for short propagation prediction, even in complex environments. II. MODEL DESCRIPTION The model developed to predict the propagation in an urban environment is based on image theory and ray tracing. The inputs are the: 1) 2-D geometry described by means of vectors specifying the location of building walls; 2) estimated electrical characteristics of the building walls (permittivity and conductivity or constant scalar reflection coefficient); 3) base-station location; 4) antenna pattern; and 5) frequency. The computations presented here account only for reflection by building walls and diffraction by building corners. Ground reflections and rays over rooftops are neglected. The
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Fig. 1. The reflection by an obstacle is modeled by an image source associated with a lit region. The vector represents one building wall.
software computes all reflected and diffracted rays up to some predetermined order. This is performed according to a careful implementation of image theory, where vectors or part of vectors not in line-of-sight (LOS) of a given source do not produce image sources. Thus, the computation time is kept reasonable since the exponential complexity of a bruteforce image method is drastically reduced at the expense of only minor additional processing linked to the lit region of every source. The algorithm used to determine the image sources is illustrated in Figs. 1 and 2. In our algorithm, we associate a so-called lit region to each image source generated (Fig. 1). Higher order image sources are generated with respect to vectors (building walls), entirely or partly included, in the visibility region of the image source considered (Fig. 2). Vectors outside the visibility region, do not generate any higher order image sources. Therefore, only the illuminated part of a vector will yield a new reflection. To take into account the diffraction effects, virtual sources are placed on every illuminated building corner. The virtual sources of diffraction are then used to generate higher order image sources. All possible combinations of reflected and diffracted rays reaching a mobile are determined after all image and virtual sources have been created by checking for every source if the mobile belongs to its visibility region. Then, all rays can be traced and their associated wave field-computed. Note that starting from the original source at the base-station antenna location, the image and virtual sources depend only on the building layout (i.e., on the vectors). Therefore, the generation of the image and virtual sources does not depend on the mobile (observation point) location. Furthermore, our algorithm can handle arbitrary layout of buildings without any restriction on building shape as long as it can be described by vectors. The reflected wave fields are computed using either the well-known formula for the Fresnel reflection coefficient or a scalar constant reflection coefficient. Since this investigation is relevant to mobile communications, where the base-station antennas usually radiate the vertically polarized wave, the electric field is assumed to be parallel to the building walls (vertical polarization). The diffracted wave fields can be computed using a diffraction coefficient valid for either: 1) perfectly absorbing wedges (PAW’s); 2) perfectly conducting wedges; or 3) wedges with impedance faces, as described in Section V.
Fig. 2. An image source creates itself other image sources with respect to vectors entirely or partly included in its relevant lit region.
Different buildings may have different materials, but for the results presented here, all buildings are assumed to have the same value for the permittivity and conductivity. The values of these electrical characteristics are determined by preliminary comparisons with measurements. Unless otherwise noted, the electrical characteristics of the building walls have been chosen equal to for the electric relative permittivity and [S/m] for the conductivity. Unless mentioned otherwise, the following phenomena are taken into account in the model: the direct LOS ray when it exists, up to nine reflections, or up to eight reflections and a single diffraction per path. The number of reflections (reflection order) is closely related to the electrical parameters of building walls and should be chosen to ensure that taking a larger reflection order will not significantly change the computation results. This condition was found to be fulfilled with an order equal to nine when using the electrical parameters mentioned above. The path loss is computed by summing the power of every ray. This procedure is used to smooth the results without losing the necessary information and thus clarifies the figures. In order to make a comparison with measurements, the electrical field is computed every 1 or 2 m along a line located in the street, where measurements have been taken.
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Fig. 3. Map of Bern as considered in the prediction. The crosses indicate the position of the sources (transmitters) and the segments in thin line indicate the receiver locations. The arrows on the observation segments indicate the measurement route direction.
III. MEASUREMENT DESCRIPTION The two sets of measurements considered here below were undertaken in Bern and Fribourg in Switzerland. Both cities are typically European, characterized by an irregular layout of buildings, although measurements were performed in areas that have almost perpendicular street crossings in an attempt to simplify the investigation of the propagation mechanisms. Measurements have been carried out at 1890 MHz, with a commercial stacked dipole array placed at about 6 m above ground and with a car mounted quarter-wave monopole (height: 1.5 m). The sounding signal is a burst BPSK modulated to a 1890-MHz carrier [9]. The modulation signal is a special binary sequence of 103 b generated at 10 Mb/s. Measurement samples were recorded every 1.75 m for the transmitter source (SRC) 2 in Bern (Fig. 3) and every 0.9 m in Fribourg. For the transmitter SRC 3 in Bern (Fig. 3), a time trigger was used instead of a distance trigger to record the measurements. Therefore, a possible shift between measurements and predictions could appear, although care was taken to drive at a speed as constant as possible. Our measurement equipment measures the amplitude of the channel-impulse response. The power sum used to compute the total received power filters to some extend the fast fading. Furthermore, in the results presented in this paper, a moving average over three sequential measurements in Bern (five in Fribourg) is computed to further remove the fast-fading effects. The resulting processed measurement still exhibits the slow variations due to buildings and obstacles since the moving average corresponds to a moving spatial average of about 5 m. A. Bern The area considered for the results presented here has the most regular layout that could be found in Bern. The map of the area considered in our predictions is shown in
Fig. 3. The crosses indicate the considered positions of the sources (transmitters). The segments in thin lines indicate the measurement path. The area considered is characterized by a somewhat irregular layout of three–four-story concrete buildings, narrow streets ( 10–15 m), some trees, and almost no traffic (residential area). Rodtmatt Street, however, is a two-lane street with some traffic. B. Fribourg The map of the area considered in our prediction is shown in Fig. 4. The four crosses indicate the position of the sources (transmitters), and the segments in thin lines indicate the measurement routes. The measurements were limited to Perolles Street to investigate the difference between the propagation in a so-called four-corner intersection (observation segment labeled Route 1) and the so-called two-corner intersection (observation segment labeled Route 2). The area considered is characterized by an irregular layout of three–four-story concrete buildings and some traffic on Perolles Street (a commercial street). C. Measurement Repeatability In order to better interpret the divergence that could appear between measurements and predictions, it is important to determine the reliability and repeatability of the measurements. In fact, due to the: 1) nonstationarity of the environment, mainly because of traffic, and 2) difficulty to record the measurement twice exactly at the same observation location, it is expected that two measurements on the same observation route and for the same transmitter location could be different, even if the measurements are repeated within a short period of time. Fig. 5 shows the repeatability of the measurement on Wiesen Street for the transmitter location SRC 2 in Bern.
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Fig. 4. Map of Fribourg as considered in the prediction. The crosses indicate the position of the sources (transmitters), and the two segments in thin line indicate the measurement routes. The arrows on the two observation segments indicate the direction driven.
Fig. 5. Measurement repeatability on Wiesen Street in Bern: transmitter at SRC 2.
It is pointed out that a divergence of about 5 dB appears in some locations between the repeated measurements over distances shorter than 50 m. However, the overall shape does repeat very well. Contrary to what was expected, the traffic did not cause any influence on the measurement repeatability. In fact, although not shown here, the measurements repeat in a similar manner in both Wiesen Street in Bern and Perolles Street in Fribourg in spite of the fact that the traffic in Wiesen Street is very low compared to the one on Perolles Street. Furthermore, the traffic did not cause noticeable influence on the measurement repeatability in Rodtmatt Street (Bern), which is characterized by a traffic of middle density. A statistical analysis of the difference between two repeated measurements for the transmitter labeled SRC 2 in Bern was performed to evaluate the error that is significant when one
compares predictions to measurements. The study included 1500 points spread in the area of Bern, shown in Fig. 3. The resulting mean error and the standard deviation are 0.5 and 3 dB, respectively. The measurements were averaged over three samples, which correspond to a distance of 5 m. Averaging over five samples (8.75 m) decreases the standard deviation to 2.6 dB, whereas the mean error remains unchanged. It is concluded from this investigation of the repeatability that a divergence of up to 5 dB over a distance shorter than 50 m between measurement and prediction can be considered to be negligible. Also, a standard deviation of 3 dB between predictions and measurements is not significant. The comparison should rather emphasize on the measurement and prediction global shape. IV. SPECULAR REFLECTIONS AND REFLECTION COEFFICIENTS This section investigates the effects of specular reflections and of the reflection coefficient attributed to the building walls. To study the validity of a model based only on specular reflections, predictions are compared to measurements on: 1) a perpendicular street: Stauffacher Street in Bern for the source labeled SRC 2 and 2) a parallel street: Rodtmatt Street in Bern for the source labeled SRC 3 (Fig. 3). These two streets were chosen as they emphasize different propagation mechanisms. Figs. 6 and 7 show the comparisons on Stauffacher and Rodtmatt streets, respectively. The predictions were computed using three different sets of electrical parameters attributed to the building walls: and , and , and and . It is pointed out that
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Fig. 6. Comparison on a perpendicular street: Stauffacher Street in Bern. Transmitter at SRC 2: measurements in thick gray line. The predictions account only for specular reflections. Three different electrical parameters: ("r = 5; = 1004 ), ("r = 10; = 1004 ), and ("r = 5; = 2) are considered.
Fig. 8. The magnitude of the vertical polarization Fresnel reflection coefficient versus the incidence angle using four different electrical parameters: ("r = 5; = 1004 ), ("r = 10; = 1004 ), ("r = 15; = 7), and ("r = 5; = 2). The frequency is 1890 MHz as in the measurements presented in this paper.
where
Fig. 7. Comparison as in Fig. 6, but on a parallel street: Rodtmatt Street in Bern. Transmitter at SRC 3: measurements in thick gray line. The predictions account only for specular reflections. Three different electrical parameters: ("r = 5; = 1004 ), ("r = 10; = 1004 ), and ("r = 5; = 2) are considered.
whatever electrical parameters are taken, it is impossible to fit the measurements. This demonstrates the limitation of a model based only on reflections. Specular reflections could explain the propagation in areas near the transmitter, but other phenomena have to be considered to account for the propagation in areas far from the transmitter. In the results shown in Figs. 6 and 7, predictions using the two sets of electrical parameters, and and and , consider up to 19 reflections. Indeed, since these two sets of electrical parameters lead to relatively large reflection coefficients, rays reflected more than nine times, as usually considered in this paper, are not always weak enough to be neglected. The comparison between the different predictions in Figs. 6 and 7 also shows that the value of the reflection coefficient attributed to the building walls is critical for the model. The sensitivity of the prediction to the electrical parameters attributed to the building walls is due to the sensitivity of the Fresnel reflection coefficient to these parameters. Assuming vertical polarization as usual for mobile communications, the Fresnel reflection coefficient is given by
is the incidence angle and
In Fig. 8, the magnitude of the Fresnel reflection coefficient versus the incidence angle using four different electrical parameters is presented. The chosen frequency is the same as for the measurement, i.e., 1890 MHz. It is pointed out that the variation of the loss due to one reflection could vary by up to 6 dB, depending on the electrical parameters used. Due to the complexity of the urban environment, it is difficult to determine the electrical parameters from the physical environment. It is proposed instead that, before undertaking complete predictions, a few preliminary comparisons with measurements are performed in order to select the parameters that give the closest match between predictions and measurements. Further investigation should indicate whether the electrical parameters are city-, area-, or even street-dependent. In this paper, a relative permittivity of and a conductivity of were used in both cities of Bern and Fribourg. Part D of the next section discusses in more details the influence of the reflection coefficient on the predictions when the diffraction effects are also taken into account. V. DIFFRACTION
BY
BUILDING CORNERS
To overcome the limitation of a model based only on specular reflections by building walls, the diffraction by building corners is considered. In previous published works about propagation in urban environments, various diffraction coefficients were introduced to account for the diffraction by building corners. The PAW coefficient was used in [4] and [10], whereas the uniform theory of diffraction (UTD) for a perfectly conducting wedge and its heuristic extension for a wedge with impedance faces was used in [5]–[7]. In this section, a theoretical comparison between the PAW, UTD, and heuristic extension of the UTD is presented. Then, predictions using the three diffraction coefficients are compared to measurements in Bern and Fribourg. The effect of double diffraction is also analyzed. Lastly, the influence of the chosen value of the reflection coefficient is further investigated.
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A. Theoretical Comparison Between PAW and UTD The diffracted field at the receiving antenna be calculated using the following expression:
(Fig. 9) can
(1) where is the diffraction coefficient, is the free-space wave is the free-space field strength, and and are number, defined in Fig. 9. The PAW diffraction can be calculated using [11]
sgn where
(2)
is given by Fig. 9. Geometry and notation for an intersection and a wedge.
where
is the transition function (3)
and
The heuristic extension of the UTD for a wedge with impedance faces can be calculated using (assuming vertical polarization) [12]
(4) where
is the transition function (3) and
angle , respectively, is the exterior wedge angle. If and are replaced by 1, the UTD formulation for the diffraction by a perfectly conducting wedge is recovered [13]. Fig. 10 illustrates the diffraction by Corner 1 in Fig. 9 for different incidence angles ( ) using the PAW, UTD, and its heuristic extension for a dielectric constant and a conductivity . Due to the complexity of the PAW and UTD expressions, no simple rule could indicate in terms of and which diffraction coefficient predicts a higher or lower loss. However, path-loss prediction using the three different diffraction coefficients in one scenario that could occur very often in urban microcellular environments, i.e., the four-corner intersection (Fig. 9), leads to similar results with all the expressions, as it is shown in Fig. 11(a), whereas in the two-corner intersection (Corners 1 and 4 in Fig. 9), since no backscattering toward the receiver exits, the PAW predicts more diffraction, i.e., less path loss than the UTD, as it is shown in Fig. 11(b). From the theoretical comparisons presented in this section, it is difficult to predict which diffraction coefficient will give the highest or lowest path loss when applying the model to a real environment. This will depend on the dominant rays reaching the receiver location. In a real environment, rays hit building corners and bounce from them at all angles, therefore, it is expected that the three diffraction coefficients give similar results. B. Comparison with Measurements
where and the equations
are the integers that most nearly satisfy
and are the reflection coefficients for the zero face for an incidence angle , and for the face for a reflection
To illustrate the influence of the diffraction by building corners, predictions using the PAW and UTD are compared to measurements on: 1) Stauffacher Street for the transmitter SRC 2 (Bern) in Fig. 12; 2) Rodtmatt Street for the transmitter SRC 3 (Bern) in Fig. 13; 3) Route 2 for the transmitter SRC G30 (Fribourg) in Fig. 14;
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Fig. 10. Diffraction by Corner 1 on Route 1 (see Fig. 9). Results for an absorbing wedge are compared to UTD results for a perfectly and partially conducting wedge with "r = 5 and = 1004 : (a) 0 = 45 , (b) 0 = 5 , (c) 0 = 135 , and (d) 0 = 90 . 0 = 100 m. The considered geometries are given in each figure.
Fig. 11. Path-loss prediction using one reflection and one diffraction on Route 1 (Fig. 9): (a) four-corner intersection and (b) two-corner intersection (Corners 1 and 4 in Fig. 9). Predictions using the PAW and UTD for a perfectly and partially conducting wedge, with "r = 5 and = 1004 . 0 = 5 . 0 = 110 m.
4) Route 1 for the transmitter SRC I30 (Fribourg) in Fig. 15. Comparisons between predictions on Stauffacher and Rodtmatt Streets, first based only on reflection (Figs. 6 and 7) and then considering the diffraction phenomena (Figs. 12 and 13), show the dramatic improvement obtained by taking into account the diffraction. Depending on the diffraction coefficient considered, predictions could vary by up to 5 dB in some locations. The highest path loss is either given by the PAW or UTD. However, the global shape of the predictions is not influenced by the type of diffraction considered. Table I shows the average error and the standard deviation obtained from comparisons between predictions and measurement on 860 points located on Stauffacher, Park, Rutli, Tell, and Wiesen Streets for the transmitter location labeled SRC 2 in Bern. It is pointed out that the errors given by the three diffraction coefficients are comparable. However, further investigation is needed
TABLE I THE AVERAGE ERROR AND THE STANDARD DEVIATION OBTAINED FROM COMPARISONS BETWEEN MEASUREMENTS AND PREDICTIONS CONSIDERING REFLECTIONS AND SINGLE DIFFRACTION PER PATH ON 860 POINTS LOCATED ON STAUFFACHER, PARK, RUTLI, TELL, AND WIESEN STREETS FOR THE TRANSMITTER SRC 21 IN BERN
to characterize in detail the statistical distribution of the prediction error so that the mean error and standard deviation can be better interpreted. In spite of the complexity of the microcellular environment and the somewhat very simple phenomena considered by the model, the divergence between predictions and measurements is reasonable, especially since a standard deviation of 3 dB exits between two repeated measurements.
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Fig. 12. Comparison on a perpendicular street: Stauffacher Street in Bern. Transmitter at SRC 2: measurements in thick gray line. The predictions account for up to nine specular reflections and a single diffraction per path: "r = 5 and = 1004 .
Fig. 15. Comparison as in Fig. 14, but on a four-corner intersection: Route 1 in Fribourg. Transmitter at SRC I30: measurements in thick gray line. The predictions account for up to nine specular reflections and a single diffraction per path: "r = 5 and = 1004 .
Fig. 13. Comparison as in Fig. 12, but on a parallel street: Rodtmatt Street in Bern. Transmitter at SRC 3: measurements in thick gray line. The predictions account for up to nine specular reflections and a single diffraction per path: "r = 5 and = 1004 .
Fig. 16. Comparison on route 1 in Bern. Transmitter at SRC 2: measurements in thick gray line. The predictions account for up to nine specular reflections and either a single or double diffraction per path: "r = 5 and = 1004 .
the measurement, probably because trees in the upper side of Route 2 have weakened the rays reflected by the building on this same side. C. Double Diffraction
Fig. 14. Comparison on a two-corner intersection: Route 2 in Fribourg. Transmitter at SRC G30: measurements in thick gray line. The predictions account for up to nine specular reflections and a single diffraction per path: "r = 5 and = 1004 .
Figs. 14 and 15 show comparison between predictions and measurement on Routes 2 and 1 for the two transmitter locations SRC G30 and SRC I30 in Fribourg, respectively. The two locations were chosen to investigate the influence of the missing buildings in the upper side of Route 2. The difference between the measured results (thick line) on Routes 1 and 2 is much smaller than expected from the prediction, m). This shows the especially at the loss of the LOS (at influence on the propagation of features other than buildings, m such as a lamp post, fences, etc. The peak at on Route 2 in the prediction (Fig. 14) does not appear in
The results presented so far consider one diffraction per path. The number of diffractions that have to be considered should be fixed to ensure that a larger number will not change the results. Thus, predictions using double diffraction are compared to measurement on our 860 test points (located on: Stauffacher, Park, Rutli, Tell, and Wiesen Streets for the transmitter location labeled SRC 2 in Bern). The resulting average error and the standard deviation are shown in Table II. Again, the errors given by the three diffraction coefficients are comparable. Comparison between the errors obtained, considering one diffraction (Table I) and double diffraction (Table II), shows that the double diffraction has little influence on the predictions. This is due to the fact that the areas considered in the comparison, shown in Table II, can be reached by rays that have undergone multiple reflections, one diffraction, and then multiple reflections. However, there are areas that are not illuminated without taking into account the double diffraction. An example is the driven Route 1 in Bern (Fig. 3). In such areas far from the transmitter, the effect of double diffraction cannot be neglected, as shown in Fig. 16, where predictions, considering either single or double diffraction, are presented. In spite of the improvement due
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TABLE II THE AVERAGE ERROR AND THE STANDARD DEVIATION OBTAINED FROM COMPARISONS BETWEEN MEASUREMENTS AND PREDICTIONS CONSIDERING REFLECTIONS AND UP TO TWO DIFFRACTIONS PER PATH ON 860 POINTS LOCATED ON STAUFFACHER, PARK, RUTLI, TELL, AND WIESEN STREETS FOR THE TRANSMITTER SRC 2 IN BERN
TABLE III THE AVERAGE ERROR AND THE STANDARD DEVIATION RESULTING FROM THE COMPARISON BETWEEN MEASUREMENTS AND PREDICTIONS CONSIDERING REFLECTIONS AND SINGLE DIFFRACTION PER PATH ON 860 POINTS LOCATED ON STAUFFACHER, PARK, RUTLI, TELL, AND WIESEN STREETS FOR THE TRANSMITTER SRC 2 IN BERN. NINE REFLECTION COEFFICIENTS ARE CONSIDERED
to the double diffraction, up to 20-dB divergence remains between measurement and predictions. This shows the effect of phenomena, such as scattering and over-rooftop propagation, which are not yet considered by the model. D. Reflection Coefficient In Section III, it was shown that the values of the electrical parameters attributed to the building walls are critical for the ray tracing model presented in this paper. The difficulty in estimating these parameters for a given building was also mentioned. It was suggested that few preliminary comparisons with measurements should be performed before undertaking complete predictions in order to select the reflection coefficients that give the closest match between predictions and measurements. This process was applied in Bern. The electrical parameters and were selected to give the best fit between predictions and measurements on two streets (Breitfeld and Rodtmatt) for the SRC 1. In order to validate this method of selecting the reflection coefficient and to investigate how the predictions are influenced by the reflection coefficient, predictions using the nine following different characteristics are compared: 1) and ; 2) and ; 3) and ;
4) and ; and ; 5) and ; 6) 7) 10.45-dB loss per reflection; 8) 6-dB loss per reflection; 9) 3-dB loss per reflection. Predictions for these nine different cases are computed on our 860 test points (located on Stauffacher, Park, Rutli, Tell, and Wiesen Streets for the transmitter location labeled SRC 2 in Bern). The last three reflection coefficients that are independent from the incidence angle were considered because they lead to faster computations. Table III shows the mean and standard deviation of the error resulting from the difference between the predictions and measurements (error prediction measurement). It is concluded that the reflection coefficient selected from preliminary comparisons with the measurement is suitable for the whole area under investigation. Variations of three units of the permittivity could lead to completely erroneous predictions, as it can be seen by comparing cases 1) and 3) above. The predictions are more sensitive when the permittivity is low. The use of constant loss per reflection leads to less satisfactory predictions, especially in terms of the standard deviation of the error, than the computations using the Fresnel reflection coefficient. Thus, the use of a reflection
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coefficient that depends on the incidence angle provides better results.
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when applying this process in Bern was shown to be suitable for the whole area. REFERENCES
VI. CONCLUSIONS A versatile software has been developed to simulate the radio-wave propagation in microcellular environments, taking into account multiple specular reflections by building walls and single- or double-corner diffraction. This software can be used to investigate arbitrary building layouts. The algorithm is based on an image method that takes advantage of nontransmitting walls to avoid the usual exponential complexity and, thus, dramatically reduces the computation time. For instance, one prediction presented in Table III takes less than one half hour on the HP series 735 workstation. Several predictions were performed and compared to measurements in two different cities in Switzerland. A study of repeated measurements showed a good repeatability, with little influence of the traffic. Up to 3-dB standard deviation was observed between two repeated measurements. Comparisons between predictions and measurements indicate that: 1) Multiple specular reflection by building walls are not sufficient to explain the behavior of radio-wave propagation in microcellular environments. 2) Accounting for a single diffraction per path leads to a reasonable agreement between our computations and measurements. The predictions obtained with three different diffraction coefficients valid for: 1) PAW’s; 2) perfectly conducting wedges; or 3) wedges with impedance faces were found to be similar. The UTD for perfectly conducting wedges showed the lower standard deviation, but a higher mean error between predictions and measurements. The PAW, which has a simpler expression, is suitable for propagation prediction. 3) Comparisons between the so-called two-corner and fourcorner intersections in Fribourg show the effects of nonsmooth building walls, trees, lamp posts, parked cars, etc. 4) The double diffraction cannot be neglected in areas, where multiple reflected, diffracted-once, and then multiple reflected rays do not exist, for example, in parallel streets far from the source. However, in such areas, predictions still underestimate the measurements. This hints to the effects of phenomena neglected in the model, such as scattering and propagation over the rooftop, which may become important far from the base-station antenna. 5) The value of the reflection coefficient attributed to the building walls is critical. Because of the difficulty in estimating the reflection parameters, it is suggested that, first, a few preliminary comparisons with measurements are performed in order to determine the suitable electrical parameters that give the closest match between predictions and measurements. Predictions can then be undertaken over other areas in the same region or for other configurations. The reflection coefficient found
[1] M. Hata, “Empirical formula for propagation loss in land mobile radio services,” IEEE Trans. Veh. Technol., vol. VT-29, pp. 317–325, 1980. [2] S. Sakagami and K. Kuboi, “Mobile propagation loss prediction for arbitrary urban environments,” Trans. Inst. Electromag. Info. Comm. Engrs. (Japan), vol. J74-b-II, pp. 17–25, 1991. [3] K. Loew, “Comparison of urban propagation models with CWmeasurements,” in Proc. Veh. Technol. Conf., Denver, CO, 1992, pp. 936–942. [4] N. Feng and H. Bertoni, “Path loss and cell coverage of urban microcells in high-rise building environments,” in Proc. GLOBECOM ’93, Phoenix, AZ, 1993, pp. 266–270. [5] S. Y. D. Tan and H. S. Tan, “UTD propagation model in urban street scene for microcellular communications,” IEEE Trans. Electromag. Compat., vol. 35, no. 4, pp. 423–428, 1993. [6] C. Bergljung and L. G. Olsson, “Rigorous diffraction theory applied to street microcell propagation,” in Proc. GLOBECOM ’91, Phoenix, AZ, 1991, pp. 1292–1296. [7] V. Erceg, A. J. Rustako, and R. S. Roman, “Diffraction around corners and its effects on the microcell coverage area in urban and suburban environments at 900 MHz, 2 GHz, and 6 GHz,” IEEE Trans. Veh. Technol., vol. 43, no. 3, pp. 762–766, 1994. [8] K. R. Schaubach, N. J. Davis, and T. S. Rappaport, “A ray tracing method for predicting path loss and delay spread in microcellular environments,” in Proc. Veh. Technol. Conf., Denver, CO, 1992, pp. 932–935. [9] J.-P. de Weck, J. Ruprecht, B. Nemsic, and H. Buhler, “Sounding radio channel for 1.8 GHz personal communications systems,” in Proc. Veh. Technol. Conf., Denver, CO, 1992, pp. 490–493. [10] J.-F. Wagen and K. Rizk, “Simulation of radio wave propagation in urban microcellular environments,” in Proc. IEEE Int. Conf. Universal Personal Comm. ICUPC ’93, Ottawa, Canada, 1993, pp. 595–599. [11] L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves. Englewood Cliffs, NJ: Prentice-Hall, 1973, Sec. 6.4. [12] R. J. Luebbers, “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE Trans. Antennas Propagat., vol. 32, no. 1, pp. 70–76, 1984. [13] R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE, vol. 62, pp. 1448–1468, Nov. 1974.
Karim Rizk (S’95) earned the Diplˆome d’Ing´enieur Electricien degree from the Swiss Federal Institute of Technology of Lausanne (EPFL), Lausanne, Switzerland, in 1992. He is currently working towards the Ph.D. degree in the same institution. From August 1992 to December 1992, he was with the Mobile Communications Section of Swiss Telecom, where he developed a ray tracing prediction tool. In March 1993, he joined the Laboratory of Electromagnetism of the EPFL in a position funded by the Swiss Telecom. From August to November 1995, he was with PTT Research in the Netherlands working on the validation of the 2-D/3-D ray tracing technique for the prediction of microcellular propagation. His research aim is the investigation of the physical phenomena involved in the propagation in microcellular environments.
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Jean-Fr´ed´eric Wagen (S’82–M’87) received the Ph.D. E.E. degree from the University of Illinois at Urbana-Champaign in 1988, the M.S.E.E. degree from Lehigh University, Bethlehem, PA, in 1984, and the Diplˆome d’Ing´enieur Electricien degree from the Swiss Federal Institute of Technology of Lausanne, Lausanne, Switzerland, in 1982. Following graduation, he joined GTE Laboratories, Waltham, MA, working on various aspects of air-to-ground and mobile communications systems and focusing especially on the areas related to radio propagation and modeling. In May 1991, he joined the Swiss Telecom PTT in Bern, Switzerland, where he is currently leading a group in the Mobile Communications Section of the R&D department. Besides developing, with his collaborators and universities, several coverage prediction models, his tasks include managing several projects in the areas of radio network planning and radio-wave propagation for wireless communication systems. He has also given seminars on mobile communications fundamentals, systems, and radio planning. Dr. Wagen currently acts as the Secretary and Delegate for the Commission F-Propagation for the Swiss Committee of URSI. From 1992 to 1996, he was also the Swiss Delegate and an active member of the European research project COST 231.
Fred Gardiol (S’68–M’69–SM’74–F’87) was born in Switzerland in 1935. He received the diploma of physicist engineer degree in engineering physics at Ecole Polytechnique de l’Universit´e de Lausanne, Lausanne, Switzerland, in 1960, the M.S.E.E. degree in electrical engineering from the Massachusetts Institutute of Technology (MIT), Cambridge, MA, in l965, and the Ph.D. degree in applied science from Louvain University, Louven, Belgium, in 1969. He developed high-power microwave ferrite devices (Raytheon SMDO, from 1961 to 1966) and then joined Louvain University, becoming Assistant Professor in 1969. Since 1970, he has been a Professor at the Ecole Polytechnique F´ed´erale de Lausanne and Director of the Laboratory of Electromagnetism and Acoustics (LEMA). He was a Visiting Professor in Canada, Algeria, Brazil, India, Japan, France, and Italy. He authored three books in French [Electromagnetisme (two versions) and Hyperfrequences] and four in English (Introduction to Microwaves, Lossy Transmission Lines, Microstrip Circuits, and, with J.-F. Z¨urcher, Broadband Patch Antennas). He contributed more than 250 technical publications on microwaves, waveguides, microstrip circuits and antennas, and electromagnetic field analysis. Dr. Gardiol chaired the Commission B of the International RadioScientific Union (URSI, Field and Waves, from 1990 to 1993) and the Swiss National Committee of URSI. He was Chairman of the IEEE Switzerland Section from 1975 to 1976, Founder and First Chairman of the IEEE Swiss Joint MTT/AP Chapter, and Member of the IEEE-MTT Speaker’s Bureau (from 1988 to 1989) and APSEAdCom (from 1988 to 1990). He organized the Fourth European Microwave Conference in Montreux in 1974. He is a Member of the Swiss Electrotechnical Association, Swiss Federal Commission for Space Affairs, Swiss Astronautics Association, and Swiss Alpine Club.
