Improvement of the computation efficiency for a ray launching model

Improvement of the computation efficiency for a ray- launching model

K. R. C hang H.T. Kim

Indexing terms: Ray launching, Mobile communications

Abstract: An enhanced ray-launching model is proposed to improve the efficiency and the speed of computation of propagation characteristics. To obtain the improvements, two methods are used: the effective-propagation-area method and the dominant-corner extraction method. The effective-propagation-area method is a method which restricts the propagation region to be considered when the wave propagation characteristics are predicted. The dominant corner-extraction method is used to diminish the amount of the diffraction ray computation by considering only the particular building corners which have a significant influence on the received power. The received power and the RMS delay spread are predicted for microcellular environments using the proposed model and compared with the results of the general ray- launching model. It is observed from the prediction results that the proposed model shows the considerable improvement in computation speed, and good agreement with the general ray- launching model.

1 Introduction

The enormous expansion in the demand for mobile- communication services requires systematic planning of wireless-communication cells. As a method to meet the demand for the mobile-communication services and to increase the capacity of the mobile system, cell splitting is carried out in the urban area. Cell splitting has accel- erated the evolution into the microcell/picocell and sequentially, gives rise to the development of a propagation prediction model available for the small-sized interference-limited cells. In urban microcellular environments, an individual building located near or between the base station and the mobile has a significant effect on the propagation characteristics [l, 21. In addition, when a wideband signal as in a CDMA system is transmitted, it is necessary to analyse the wide-

0 IEE, 1998 IEE Proceedings online no. 19981882 Paper first received 26th August 1997 and in revised form 5th January 1998 The authors are with the Department of Electronic and Electrical Engi- neering, POSTECH PIRL 421, San31 Hyojadong, Nam-Gu, Pohang, Kyungbuk, 790-784, Korea

band channel characteristics by predicting two parameters: average time delay and RMS delay spread. To satisfy these requirements in designing the cell-coverage area, it is essential to develop a site-specific ray- tracing model which is capable of taking account of the buildings located near the base station and the mobile and also calculating the propagation characteristics by tracking the propagation paths of the rays scattered from every building. For this purpose, a number of rigorous ray-tracing models for a microcellular environments have been developed [l-51. The rigorous ray- tracing model can be divided into two classes in accordance with its ray-tracing technique - the multiple image method and the ray-launching method.

In the ray-launching model, the fundamental operation is simply the intersection of a ray with a building, and it can be performed regardless of the shape, the orientation, or the location of the building. Therefore, it is highly suitable for applying to real urban microcel- Mar environments and very flexible in coping with various propagation environments. However, since the ray-tracing process of the ray-launching method is accomplished by an exhaustive search of a ray which arrives at the receiver, the prediction process is exceed- ingly inefficient and considerably time consuming. The objective of this paper is to enhance its practical utility by reducing the large amount of computation and the corresponding excessive prediction time without loss of the advantages of the existing ray-launching model, such as simplicity and flexibility.

2 Theory

In the ray-launching model, a test ray which scans from 0" to 360" with angular separation a is launched, and the ray which arrives at the mobile with a significant level of power is identified [4]. To determine if a transmitted ray reaches a mobile, it is necessary to construct a reception circle about the mobile [5]. In the proposed model, the test ray is launched in the two- dimensional path and then, the three-dimensional propagation path is determined from the two- dimensional path by considering the height of the base station and the mobile. The antennas of the base station and the mobile are assumed to be omnidirectional and spherical-wave propagation is therefore assumed. The received power of the multiple- reflection rays is expressed as follows:

IEE Proc-Microw. Antennas Propag., Vol. 145, No. 4, August 1998 303

' " n=l

(1) where P, is the transmitted power, N is the maximum number of reflections including the ground reflection to be considered. r, is the total propagation distance of a ray which experiences n reflections, and r, is the multiplication of the n reflection coefficients. rk is the total propagation distance when a ground reflection is added to n reflections on building walls. ri is the multiplication of the n reflection coefficients and a ground reflection coefficient.

The received power of the diffracted rays arrived at the mobile is computed using UTD [6]. The received power of the rays which experience single diffraction and multiple reflections can be expressed by eqn. 2 [7]:

l 2

r , o r , ; j q n d

(2) where r'; is the multiplication of the m reflection coefficients including the ground reflection and D denotes diffraction coefficient. A d is the spreading factor where p is the principal radius of curvature of the reflected wavefront and s is the unfolded distance from diffraction point to the mobile.

The average delay time zd and the RMS delay spread A are given by eqns. 3 and 4 [SI:

(3) r,P,

C L P% r d =

112

- .d'/ (4) I EL P% E2 1 7," Pb A =

where z, and P, denote the delay time and the received power of ith ray, respectively, and n is the number of rays which have received power above a specified threshold. In this paper, the threshold is chosen to be -150 dBW when P, is 1 W.

The fundamental operation of the general ray- launching method is the intersection of a ray with a building. However, since all the building corners act as new transmitters and receivers for diffraction, the computation time taken in the prediction of propagation characteristics is so excessive that the ray-tracing model needs modification for the practical application.

In this paper, two methods - the effective-propagation-area method, and the dominant-corner-extraction method - are suggested to diminish the excessive computation time in the rigorous ray-launching model. To improve the computation speed, the proposed ray- launching model does not consider all the buildings contained in a geographical database but only the particular buildings which have a significant influence on the propagation characteristics. The effective-propagation-area method considers only the buildings included in the effective propagation area, which is defined as the region where the buildings which have dominant effects on the propagation characteristics are distributed. In the suggested model, the boundary of the effective propagation area (EPA) is defined in terms of the average delay time and the RMS delay spread of the received signal.

304

When an impulse is transmitted, the number of delayed impulses which arrive at the mobile is uncount- able, but it can be assumed that there exist n pulses which satisfy a specified threshold of received power. If the distribution of delayed pulses is Gaussian with a mean zd and a standard deviation A, 84.1% of delayed pulses will arrive at the mobile within (zd + A). There- fore, if those pulses are taken into consideration, the accuracy of the prediction has an 84.1% confidence level compared with the case where n pulses are considered. However, since the practical distribution of the arriving rays does not show a Gaussian distribution and the number of arriving rays decreases rapidly after zd, the confidence level is higher than 84.1%. In (zd + A), the propagation distance of a ray is c x (zd + A), where c is the propagation velocity. The region within the propagation distance of a launched ray c(zd + A) is an ellipse whose foci are the locations of the base station and the mobile. Since the rays which propagate through the outer region of the ellipse contribute insignificant power to the total received power, they can be ignored in the calculation of propagation characteristics. The length of the major axis vv' of EPA is c(zd + A). The average delay time and the RMS delay spread should be given for the calculation of the length of the major axis of EPA. In this paper, the average delay time and RMS delay spread in the street-grid environment shown in Fig. 1 are used to calculate the EPA. The area of each building shown in Fig. 1 is assumed to be lOOm x 100m. In Figs. 2 and 3, the ratio of the length of the major axis of EPA to the distance from the base station to the mobile are plotted when the width of streets is 30m and loom, respectively.

Fig. 1 Street-grid-shaped urban microcellular environment

Since the ratio of vv' to the distance between the base station and the mobile varies greatly in accordance with the location of the mobile, it is meaningless to fit the ratio curve to a straight line However, if the ratio of vv' to the distance between the base station and the mobile is set to 1.3 - 1.5, a major portion of the distances plotted in Figs. 2 and 3 are included. To enhance the confidence level, the arrival time of rays to be considered can be extended to (zd + 2A), (zd + 3A) etc. but, in these cases, the area of EPA increases to incur the excessive prediction time. The area of EPA varies in accordance with the orientation of buildings and the distribution density of buildings, i.e. the ratio of the area occupied by buildings to street and empty space. However, since the distribution of buildings in

IEE Proc -Microw Antennas Propag , Vol 145, No 4, August 1998

an urban area is generally similar to the street-grid shape and the widths of streets are between 10 and loom, it is appropriate to choose vv’ to be 1.3 - 1.5 times of the distance from the base station to the mobile.

0 50 100 150 200 distance, m

Ratio of vv’ to the distance from transmitter to receiver when the Fi .2 wi%h of the street is 30m ~ ratio of EPA diameter _ _ _ _ 1.3 EPA diameter . . . . . . . . . . . 1.5 EPA diameter

1.8r

0.21 , , , , , , , 0 100 200 300 LOO 500 600 700

distance, m Ratio of vv’ to the distancefrom transmitter to receiver when the Fi .3

wi%h of the street is I00 m __ ratio of EPA diameter _ _ _ _ 1.3 EPA diameter . . . . . . . . . . . 1.5 EPA diameter

On this basis, it can be said that the buildings which are distributed near the base station and the mobile have a significant effect on the overall propagation characteristics in urban microcellular environments. Therefore, by considering only these buildings, one can obtain the accurate predictions with high computation efficiency. However, if the mobile is located far away from the base station, most of the buildings in the geographical database are included in the EPA and, as a result, the improvement of computation speed cannot be expected. To remove the dependence of EPA on the distance between the base station and the mobile, the dominant-corner-extraction method is added.

The dominant-corner-extraction method considers only the particular building corners which have dominant influences on the propagation characteristics of the diffracted rays. In the ray-tracing process of the ray-launching model, each building corner operates as a diffraction wedge and the corresponding diffracted ray paths are obtained by applying the ray-launching method in which the corners are regarded repeatedly as new transmitters and receivers. As a result, the actual

IEE Proc.-Microw Antennas Propag.. Vol. 145. No. 4, August 1998

number of base stations to be considered increases with the number of the building corners. If the number of corners to be considered is reduced, the prediction time of the ray-launching model can be reduced greatly.

In the street-grid environment shown in Fig. 1, there exist many ray paths and propagation modes such as reflections, diffractions, reflections-single diffraction etc.. Analysing the field strength of the various combi- nations of reflected-diffracted rays, one realises that every ray does not contribute equally on the total received power. In other words, there exist dominant rays which provide most of the power and have a significant influence on the delay spread. In the dominant- corner-extraction method, the corners on which the dominant rays are diffracted are picked out and taken into calculation.

In street-grid environments, two typical propagation paths are path U where a launched ray propagates around the group of buildings and path V where a launched ray propagates through the stairway shape or zig-zag path as shown in Fig. 1. When the mobile turns around a building corner, a path loss of about 30dB is incurred [9]. Therefore, even if the propagation lengths of path U and V are the same, the path loss occurred in path V is generally severer than the path loss in path U. However, this tendency can be changed in accordance with the variations of the width of streets.

I

150 200 250 0 50 100 100 150 200 250 0 50 distance, m

Fig.4 Width of street 20m

Comparison of the receivedpower of the dflracted rays

U > .- : L

path Ao

1 path Ab - 80

0 100 200 300 LOO 500 600 distance,m

Fig.5 Width of street lOOm

Comparison of the receivedpower of the dflracted rays

Figs. 4 and 5 show the received power profiles of the diffracted rays when the width of street is 20m and loom, respectively. When the width of streets is 20m,

305

the diffracted rays which propagate through path V experience greater path losses than those which propagate through path U. The propagation paths which belong to path U in Fig. 4 are path Aa, Bb, Cc and Dd. The diffracted rays which propagate through path Aa dominate over or have comparable power level with the other diffracted rays regardless of the location of the mobile. Moreover, the dominant paths which have comparable received power to path Aa are paths Bb, Cc and Dd, which also belong to path U. Therefore, it can be said that path U dominates over path V abso- lutely in this case. The diffracted rays which propagate through path V suffer from the severe path loss incurred from frequent turns in propagation and therefore, do not provide significant received power. Fig. 4 shows that the diffracted rays which propagate through path V provide insignificant power or cannot even reach the mobile.

However, when the ratio of the area of the streets and empty space to that of the building and scattering objects becomes large, the diffracted rays, even through path V, can propagate without the sharp turns which cause severe path loss. It is observed in Fig. 5 that the diffracted rays which propagate through path V provide considerable received power. The propagation paths which belong to path U in Fig. 5 are paths Aa and Dd. Paths Ab and Cd belong to path V. The received power of path Aa shows significant power level regardless of the location of the mobile; similarly to Fig. 4. However, path Aa does not have enough received power level to dominate over the other paths. In particular, the received power of path Ab, which does not show a significant power level in Fig. 4, becomes comparable with that of path Aa. Also, path Cd a significant contribution in total received power. It means that there is a little opportunity to occur the severe path losses caused by reflection or diffraction on building walls when the width of the street becomes greater. However, note from Fig. 5 that, in spite of wide streets, path V does not have enough received power to dominate over path U, but just shows a power level compared with that of path U. This prop- erty of path V has to be considered when the dominant corners are chosen from paths U and V. The occupying density of buildings is 15% for Fig. 5.

Judging from Figs. 4 and 5, it can be said that the paths of the dominant diffracted rays do not deviate widely from the shape of path U or path V as shown in Fig. 1. Therefore, for path V, the dominant diffraction corners are likely to be chosen from the building corners located near the imaginary straight line connecting the base station and the mobile. For path U, the dominant diffraction corners are selected from the building corners located near the edge region of path U. The corners which satisfy the following equations are selected as the dominant corners:

min [J { (Xiorne, - X R ~ ) ~ (x:oTn,T )yczorlleT)

+(Korner - Y T ~ ) ~ } ] for path U (5)

min (XL, e T YL., e r 1

subyRx'l IYsubXkner + XsubY,rner -YsubXR,-X

d cx,",b + y,",b)

for path V (7) i

where i z j z k. Xsub and Ysub are substituted by (ITx - X,) and (YRx ~ YTJ, respectively. (XTx, YTx) and (IRx, Yh) denote the locations of Tx and Rx, respectively. (ATE,,,,,, , YE,,,,,,) denotes the location of ith corner among the all corners within EPA. The selection of (X;&,r , Y;&v ) proceeds until the predetermined number of dominant corners is satisfied. The reason why there are two equations for selecting dominant corners from path U or corner regions is that two corner regions exist, as shown in Fig. 6.

-egion) ~

Fig. 6 Distribution ofdominant ._ corners in stueet-grid environment -

It is important to determine the ratio of the number of dominant corners selected in path U to those in path V. When the street becomes narrow or wide, it is not reasonable to choose the dominant corners from path U or path V and exclude the other one because PIIP2 varies within the finite bound when PI and P, denote the average received power of the diffracted rays which propagate through path U and path V, respectively. In this paper, when the occupying density of buildings becomes large, the ratio of the number of dominant corners to be chosen from paths U and V is set to be 2:l and when the occupying density becomes small, the ratio of the number of dominant corners is set to be 1:l.

transmitter 0

U n 0

"- El E3 Fig. 7 Propagation environment 1

3 Simulations

To estimate the accuracy and computation efficiency of the proposed model using two methods - the effective- propagation-area method and the dominant-corner-

IEE Proc.-Microw. Antennas Propag., Vol. 145, No. 4, August 1998 306

extraction method - the predictions of received power and RMS delay spread are compared with the simula- tion results of the general ray-launching model. Figs. 7 and 8 show propagation environments l(PE1) and 2(PE2), respectively to which the proposed model is applied. The antenna heights of the base station and the mobile are assumed to be 6m and 1.5m, respectively. The widths of streets are given as 30m and 20m for PE1 and PE2, respectively.

I I tmnsmitter Postech HQ RIST

Fig. 8 Propagation environment 2

The general ray-launching model is firstly applied to PE1 and PE2. Single diffraction is assumed and the propagations over rooftops are ignored because the antennas are located much lower than the surrounding buildings. The building wall is characterised by average relative permittivity E, and conductivity 0. cr and 0 are assumed to be 7 and 0.001 for the ground and building wall, respectively.

I I I I I

0 50 100 150 200 250 300 distonce. m

Comparison of the received power between the proposed model Fi .9 an% the general ray-launching model for propagation environment I ______ proposed model _ _ - - rigorous ray launching

I I J

0 50 100 150 200 250 300 distonce,m

Fig. 10 model and the general ray-lauching model for propagation environment I __ proposed model _ _ - - rigorous ray launching

IEE Proc-Microw. Antennas Propag., Vol. 145, No. 4, August 1998

Comparison of the @4S delay spread between the proposed

Figs. 9-12 show the comparisons between the predictions of the suggested model and those of the general ray-launching model for the given propagation environments. The threshold is assumed to be -150dBW when PT = 1W. In PE1, the street is wider and the ratio of empty space to buildings is higher than that in PE2. The buildings in PE2, however, distribute in street-grid shape with high density. In PE1, it is reasonable to choose the dominant corners mainly from the diagonal region, while in PE2, the dominant corners are mainly selected from the corner region. Six corners in the corner region and another six corners in the diagonal region are selected as dominant corners in PE1. In PE2, eight corners in the corner region and four corners in the diagonal region are chosen as dominant corners. As mentioned in Section 2, vv' of the effective propagation area is fixed at 1.3 times of the distance from the base station to the mobile, regardless of the width of streets.

-1OOr

-150 250 300 35 0 400

distonce,m Comparison of the received power between the proposed model Fi . I1

an9 the general ray-launching model for propagation environment 2 - proposed model - _ - - rigorous ray launching

I

250 300 350 LOO distance, m

Fig. 12 model and the general ray-launching mode6or propagation environment 2 __ proposed model

Comparison of the RMS &la spread between the proposed

rigorous ray launching _ _ _ _

From the predictions of received power as shown in Figs. 9 and 11, it is observed that the suggested model shows good agreement with the general ray-launching model with 3.73 dB and 4.65dB divergencies, respectively. When the distance that the mobile has travelled is less than 150m, the predictions of the average received power and the RMS delay spread are consist- ent with those of the general ray-launching model. However, at distances over 200m, small discrepancies are observed between the two models, for the following reasons. When the mobile is not far away from the base station, the influence of the dominant-corner-

307

extraction method is not significant because the reflected rays which can arrive at the mobile in the short distance without severe path loss dominate over the diffracted rays and, as a result, the received power of the diffracted rays is swamped by that of the reflected rays. However, when the mobile travels far from the base station, the diffracted rays are comparable with or dominant over the reflected rays. In the dominant-corner-extraction method, only selected corners which have a significant influence on the received power are considered. Therefore, the small discrepancies in prediction are caused by the effect of the diffracted rays excluded by the dominant-corner- extraction method. Since the main focus of this paper is how to improve the computation speed of the existing ray-launching model, which has already been widely used in the cell design of mobile-communication systems, the numerical results of the proposed model are compared not with those of experimental measurements but with those of the existing model. The valid- ity of the existing ray-tracing model is given in [l-51.

It is observed from Table 1 that the prediction speed of the proposed model is faster than that of the general ray-launching model by ten times. The gain in computation speed can increase when a propagation environment has more building corners than those in PE1 and PE2. In the prediction of received power and RMS delay spread using a computer code, the small discrepancies in the numerical results of two models, as shown in Figs. 9-12, are insignificant.

Table 1: Computation speed of the proposed model compared with the general ray-launching model

Speed of Discrepancy Discrepancy in proposed in received RMS delay model power, dB spread

Propagation environment

1 10.4 times 3.73 1.77 x IO4 2 11.0 4.65 2.63 x IO4

4 Conclusions

In this paper, two methods - the effective-propagation-area method and the dominant-corner-extraction method - are suggested to improve the computation

efficiency of the ray-launching model. The effective- propagation-area method provides a useful criterion to define a propagation region to be considered in the actual calculation of propagation characteristics when the locations of the base station and the mobile are given. It is shown that a comparison of the predictions of the proposed model with those of the general ray- launching model shows good agreement. The dominant-corner-extraction method is another method of efficiency improvement by considering only those building corners which distribute in the corner region or in the diagonal region. Application of this method reduces remarkably the number of diffracted rays to be considered. The proposed model has an advantage in computation speed of ten times without significant loss of accuracy.

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Improvement of the computation efficiency for a ray launching model

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