Prediction of cellular characteristics for various urban environments

Christos Chrlstodoulou Naflali (Tuli) Herscovici Splke Technologies Inc Computer Englneerlng 1 Chestnut St Noshua N H 03060 USA + I (603) 594-8856 +1 (603) 577-9647 (Fax) naftallHerscovlclQieeeorg (e-mall)

Department of Electrlcal and

Unlverslty of New Mexico Albuquer ue N M 87131-1356 USA + I (505) 277-6580 +1 (505) 277-1439 (Fax) chrlstosQeeceunmedu (e-mall)

Prediction of Cellular Characteristics for Various Urban Environments

N Bluunstein Department of Electrical and Computer Engineering Ben Gurion University of the Negev PO Box 653 Beer Sheva 84105 Israel Tel (972-7) 6461-589 E-mail blauueesrveebguacil

Keywords Land mobile radio cellular systems electromagnetic propagation urban areas UHF propagation microwave propagation co-chaunel interference

1 Abstract

The propagation charnel for UHFiX-band waves in the city is modeled for two typical cases in the urban scene (a) by regularly distributed rows of buildings placed on flat terrain (b) by an array of randomly distributed buildings placed on rough terrain The law of distribution of buildings in both cases is assumed to be Poisson The loss characteristics in such urban propagation channels as well as the co-channel interference parameter the carrier- to-interference ratio (CII) are investigated In case (a) the three- dimensional multi-slit waveguide model is used for LOS conditions and the two-dimensional multi-diffraction model is used for NLOS conditions In case ) the statistical parametric model of wave propagation is used including single and multiple scattering effects diffraction from buildings roofs the actual built-up relief and various positions of receiver and transmitter antennas on rough terrain The full algorithm for predicting propagation and cellular characteristics to increase the accuracy of radio and cellular maps is presented

tion phenomena in urban cellular channels as well as the frequency planning concept based on existing propagation models can be effectively used to predict propagation and cellular characteristics in various built-up areas at the earlier stages of cellular- network planning To develop such wireless systems successfully it is very important to investigate the loss characteristics in urban radio channels to estimate the cell radius for cellular maps for various built-up areas and to predict the co-channel interference between different cellular radio links

As is well known [I-201 modem cities are complicated areas in which radio-propagation phenomena differ dramatically from those in other media Therefore the analytical description of this process camot he presented without some simplifications for the concrete radio-link situation

For UHFiX-band radio waves most buildings are practically non-transparent and their dimensions are larger than the wavelength A In such situations a wide spectrum of shadow zones is observed inside the street level and very sharp boundaries between light and shadow zones are created [1-14] Moreover in cases where buildings are randomly distributed on a rough ground sur- facace-which is considered to be non-smooth-all specific properties of city topography affect the specific conditions of wave propagation at the street level [16-19]

2 Introduction In such a situation we propose more-realistic deterministic models which use a statistical description of the real building pattern inside the city to determine the field-strength variations To

map we need detailed information about the spatial distribution of

135

t the present time a detailed strategy for cellular-network

wireless-access systems [1-14] An actual description of propaga-

IEEEAntennas and Propagation Magazine Vol 41 No 6 December 1999

A planning and design is very useful both for mobile and fixed obtain a statistical description of the city based on its topographic

city buildings and natural obstacles the sizes and ranges of reflected and diffracted surface sections of the ground relief and the spatial distribution of the scattering points of each building placed in areas surrounding the receiver and transmitter antennas

Below in Section 3 following the approach presented in [7- 91 we describe the contribution to the path loss along the street in LOS (line-of-sight) conditions for buildings placed on the flat terrain An important parameter of microcells at the street level the ldquobreak pointrdquo range which can define the lower limit of the effi- cient radius of a microcell in LOS conditions between the receiver and transmitter at the stage of cellular-map construction is exam- ined

Then in Section 4 using the modified two-dimensional model of multi-diffraction [4-6]-because it more correctly predicts the experimental data for the obstructed radio paths than other empirical and deterministic models (see the bibliography in [14])- we present theoretical aspects of radio coverage and a cellrsquos effective-radius prediction in NLOS (non-line-of-sight) conditions In Section 5 we introduce lhe statistical-parametric model for rough built-up terrain according to [11-13] We then examine the average intensity of the total field in the layer of city buildings with randomly distributed obstacles placed on the rough terrain including single and multiple scattering and the diffraction from rooftops In Section 6 we present the full algorithm for predicting propagation and cellular characteristics for various built-up environments

3 Prediction of cellular characteristics in LOS conditions

The ldquotwo-rayrdquo model consisting of the direct and the ieflected rays [ I 21 and the two-dimensional propagation model consisting of multiple reflections from the walls [3] are usually used for the conditions when both antennas are placed at the street level below the rooftop level in LOS condilions Instead a multi- slit-waveguide model was proposed in [7-91 for describing wave propagation in urban areas with straight streets and with randomly distributed building walls (screens) and gaps between them (slits) (see Figure I) Let us present the propagation and cellular characteristics in LOS conditions according to [7-91 taking into account

Moving radio porl

I

Figure 1 An urban area with a crossing-street-grid plan

136 euroeuroeuroAntennas and Propagation Magazine Vol 41 No 6 December 1999

Rays ^

i i i

Figure 2 A schematic diagram of a three-dimensional model of a street multi-slit waveguide

= t

lsquo I Y

1+---

Figure 3 A two-dimensional diagram of crossing-street waveguides in the zy plane The coordinates of the source are y = 0 and z = h a and b are the widths of the crossing streets

the real dielectric properties of building walls the actual dishibu- tion of street widths and the reflection from the road (see Figure 2)

31 Contribution to path loss

Let us consider that the buildings on the streets are replaced by randomly distributed non-transparent screens with scales Y rdquo the electrical properties of which are defined by surface imped- ances u=O (see the definition in [7-91) The distances between the building slits we define as S nm =123 (see Figure 3 the radial waveguide ldquoIrdquo and crossing waveguide ldquo11rdquo) The laws of their differential distribution are postulated as independent and exponential with mean values ( L ) and ( I ) respectively The probability density functions are given by [7-91

(L)-rsquoexP-~rdquo(~)]

(vexP-L (9 ]~

nm = 123 (1)

One radial street waveguide plane is placed at the waveguide side z = 0 and the second one is at z = a (a is the street width see Figure 3 the radial waveguide ldquoIrdquo) One crossing (side) street waveguide plane is placed at the waveguide side y = d and the second one is at y = d + b (b is the side-street width see Figure 3) We also assume that a vertical electric dipole as a real transmitter is placed in the xz plane with coordinates x = hT y = 0 z = h where 0 lt h lt a on the z axis 0 lt hT lt hb on the x axis hT is the transmitter height and hb is the average building height (see Fig- ures 2 and 3) Taking into account that all dimensions are much greater than the radiation wavelength A we use the approximation of the GTD according to [7-91 and present the full field as a superposition of a direct wave field from the source fields reflected from the road and then from the walls and fields diffracted from the building edges Alternatively the resulting field can be considered as the sum of the fields arriving at the receiver kom the image sources as schematically presented in Figures 2 and 3 According to the approach proposed in [7-91 we also introduce here the ldquotelegraph signalrdquo functions L k ( y ) and amp(y)

i k = 12 Segments with frk ( y ) = 1 represent screens including their edges hut segments with frk ( y ) = 0 represent slits (Figure 3) In order to calculate the full field from the source we substitute for each reflection from the walls an image sowce Il (for the first reflection from the left-hand walls of the radial street waveguide) and Il (for the first reflection from the right-hand walls) where n is the number of reflections (sec Figure 3) n = 123 To calculate the path loss along the street waveguide according to [7-91 we take into account the exponential distributions of the screens and slits Equation (l) the transmitter antenna as a vertical electric dipole and the simple evaluations from the GTD In these the formulations of diffracted waves are similar to those obtained for reflected waves and the reflection coefficient r of each wave reflected from the screen (wall) is simply replaced by a diffraction coefficient D for each ray diffracted from the walllsquos edge [7-91 We use the method of averaging the arbitrary-order moments of the ldquotelegraph-signalrdquo functions h2 ( y ) presented in [7-91 and we combine the reflected and diffracted waves with the direct wave (LOS component) from the soune according to the procedure proposed in [7-91 We then finally obtain the approximate expression for the path loss at a large range from the source ( r gtgt a )

L = 32i-401og~~~r~-2oiog~~[i-(~~r~)2][i+(~~r~)2]

+178Ioglo r - 2Olog10 +Dmnl) (2)

+86llnMlrnlj[(nn - a)a]rdorsquoa)

where 1rl and qn are the absolute value and the phase of the coefficient of reflection r from the building impedance walls This can be described by

(4) 21mKkZzM I qn =tali- (ReK)rsquo+(ImK)Z-(kZM)rsquo rsquo

Here K =(m+i l lnMl ) a =Reamp +ImK is the wave number of each normal mode ( n =012) inside the broken impedance multi-slit waveguide M = (L ) ( (L )+( l ) ) is the parameter of ldquobrokennessrdquo We do not present here the expression for the reflection coefficient Tg because it is sufficiently and fully described in the literature (see Cor example [12 141) As was shown in [7-91 Equation (2) can he used for the prediction of the path-loss distribution in LOS conditions in the straight-street scene Simultaneously Equation (2) can be used to estimate the lower limit of the cell radius along the streets in LOS conditions for various distributions of buildings and geometry along the street

32 Cell radius in LOS conditions along straight streets

As was shown in [7-91 the approximate waveguide model of Equation (2) can he successfully used instead of the strict waveguide model to describe the field path loss along the street in LOS conditions Using this fact and the derivations presented in [7-91 one can present the ldquobreak-pointrdquo range as a cell radius (see Figure 4)

Let us now examine the expressions of Equations (2) and ( 5 ) for various actual experimental situations in the urban street scene

321 Wide avenues Let us consider that the street width is larger than the average building height and both antenna heights that is a gt h hT hR In this case at distances less than the ldquobreak pointrdquo in the approximate formula of Equation (2) the second term which describes the direct wave and the waves reflected from the ground and which attenuates as a spherical wave - r- is larger than the first term which describes the attenuation of the normal reflecting modes along the multi-slit street waveguide Beyond the ldquobreak pointrdquo conversely the first term in Equation (2) is larger and the field intensity attenuates exponentially This law of attenuation is close to that obtained experimentally in most measurements where the attenuation mode of field intensity beyond the ldquobreak pointrdquo was - F q y = 5 - 7 (see Figure 4a) This law cannot be explained using the ldquotwo-rayrdquo model [l 2 141 This effect can be clearly understood using the waveguide street model and from it follows the exponential attenuation of field intensity (which is close to mode - - - q y = 5 - 7 ) at distances beyond the ldquobreak pointrdquo At the same time for the case of wide streefs ie for a gt hb and arsquo gt hThR the ldquobreak-pointrdquo range

IEEE Antennas and Propagation Magazine Vol 41 No 6 December 1999 137

L t

built-up area built-up area

c = l O l o g I [ -(3N)TRy A y ] (dB) (8)

the observed wavelength hand 1 = 001 - 03 m with decreasing street width or with increasing building height Hence the waveguide multi-slit model more generally than the ldquotwo-rayrdquo model predicts the propagation characteristics in LOS conditions along straight streets

We will examine this equation for various situations in the urban scene with regularly or irregularly planned rows of buildings

33 Co-channel interference-parameter prediction

U built-up area I built-up area

U 0

According to the propagation situation in the urban scene the service and co-channel sites (cells) can lie both inside and outside the break-point range ru (Figure 4) which was postulated as the lower level of the cellrsquos radius for cellular networks [I-IO] Ifboth of the investigated cell sites are located beyond the break-point range according to [I21 the equation can he given as

presented in Figure 4

4 Prediction of propagation characteristics in NLOS conditions

Ilsquo =r r

Figure 4a The attenuation of the field intensity beyond the

B (7)

ldquoGeak pointrdquo of a building This ldquobreak pointrdquo is used as part of the definition of the cell radius see Figure 4b where y is the field attenuation or the so-called slope parameter

y = 2 + A y Ay Z 1 and D is the reuse frequency distance [12] If

- _ see Figure 5a) the radiating field propagates over the rooftops by a process of buildings are non-transparent with dimensions larger than the

332 Narrow streets In the inverse case of urban areas with narrow Streets ( a lt h b ) as fOl~OWS from Equation ( 5 ) for ltlt hb

diffraction past rows of As

and arsquo lt hThR the range of the ldquobreak pointrdquo tends to infinity for

138

wavelength 1 ie hd gtgt 1 the majority of the propagation

iEEE Antennas and Propagation Magazine Vol 41 No 6 December 1999

Figure Sa A schematic diagram of a two-dimensional model of the urban region with regularly distributed rows of buildings for the case where the transmitter antenna is higher than the first building in the vicinity of its position ie If gt h

If lt I

I J

Figure Sb A schematic diagram of a two-dimensional model of the urban region with regularly distributed rows of buildings for the case where the transmitter antenna is lower than the first building in the vicinity of its position ie I lt h

path cannot be through the buildings Moreover when there is propagation between buildings the rays reflected from the ground after a second diffraction from the roofs (path 3 in Figure 5a) are attenuated very quickly (according to [4-61)

42 Contributions to path loss and the slope parameter

Let us now present the equations above in the form of an equation of a straight line as was done in [ I 21 For this case we will simplify the problem and consider that the rows of buildings are regularly distributed on flat terrain with uniform building height h as a median value for roofrops and with uniform gaps between buildings y = dN - w as a median value of this parameter In the general case using the above formulas one can easily obtain the same equation of a straight line Treating the base station as a transmitter and assuming that the receiver is at street level we can obtain the path loss in dB as the sum of the free- space path loss

amp=324+20logfo+201ogR (9)

and the excess loss La This last quantity can he presented as the sum of two parts [4-61

1 The excess due to the propagation over the rows of buildings

L = 689 - 9 log(d N - W ) - 9 logfo + I8 log R - 18 iog(U - h)

(10)

IEEEAntennas andPropagafion Magazine Vol 41 No 6 December 1999 139

2 The excess due to rootlop-to-street diffraction

Le = -1 17 t IOlogr + lOlogf0 + 20log (11)

where ON = t a f 1 [ 2 ( h N - h r ) x ] is thc angle presented in Fig-

ure 5b (for a uniform distribution of building heights ON = and

r = ( h hr)2 +[(d-w)Z] according to [4-61) Here x is

the distance between the receivcr and the last building which is close to the receiver and 11 is the receiver-antenna height

I12 1 -

If this is so one can present the formulas above in the straight-line form

where the intercept is

Lq = -896- 2110g fo t 9lOgx - IOlogr t 1 Llog(t1- I) - 2OlogS (13)

and the attenuation slope [I 21 is

So as in [ I 21 according lo [4-61 and using Equations (9)-(13) one can obtain the result that the signal decay due to rooftop multi- diffraction varies as - R- as a function of the range between both antennas transmitter and receiver for equal conditions in the urban scene under consideration (whcn L =constant see Fig- ure4a) ie A y = 18 the same result that was obtained for rural and residential areas by use of empirical approaches 112 141 Hence in NLOS conditions the cell radius Q can be obtained from Equation (12) as the range at which the law of field-intensity attenuation changes from y = 2 to y t 4

S Prediction of cellular characteristics in an urban area with irregularly distributed huildings placed on rough terrain

91 Statistical description of city relief

In [10-13] an array of randomly dislributcd buildings and obstacles placed on a rough ground surface was considered The heights of the terrain relief were described in the coordinate system (x y 2) placcd on the plane z = 0 or thc ground surface by the generalized function Z ( x y ) accordiiig to Shwartz [15] This function describes the irregular non-smooth ground-surface relief z = Z (x y ) as prescnled in Figure 6

511 Spatial distribution of city buildings Following [I 1- 131 let us consider the characteristic function lt ( r ) = ( ( x y z ) as the relicf of some boundav surface between two half spaces ( ( r )=O for z gt Z ( x y ) and ( ( r ) = I for z lt Z ( x y ) For the case z gt 0 we can present this fuuction as

points rI and rz within the layer of buildings For the statistical quasi-homogeneous building area this probability can he presented as [11-13]

Serinin pfilc Building profile

Figure 6a The non-regular built-up terrain profile z = Z ( x y )

This formula was obtained for the case of zz gt zI and for an arhi- t r ay spatial orientation of the unit vector q 191 = 1 I = lr2 -rll rz - rl = ql r and qI1 are the projection of corresponding vec-

tors at the plane z = 0 qz = 1 - 4 and yo is the density of huildings in the plane of qL = (qxqy)

From Equation (18) one can obtain the average distance of the direct visibility plz from point rl to point rz which is given by

Figure 6b The built-up terrain profile of Figure 6a shown as a superposition of a flat perfectly reflecting surface SI and a random built-up relief Sz

were N is the number of buildings randomly distributed at the surface plane z = 0 function lt (x y) = 1 if the projection of the point (x y z) at the plane z = 0 hits inside or at the boundary of a building contour and lt ( x y ) = 0 in the opposite case b = h is

the height of the building with number n lt (z) is the characteristic function that is equal to 1 inside the range a lt z lt b (parameter a can he equal to zero) and is equal to 0 outside this interval

After some straightforward calculations according to [ I 1- 131 one can present the average value of lt(r) for the ensemble of its possible realizations in the following form

Here w(h) is the density of the building-height distribution and determines the probability of the event z lt h The multiplier X in Equation (16) determines the probability of the event that the projection of the point r at the plane z = 0 hits inside any building

The statistical functions constmcted above allow us to calculate the probability of direct visibility between two observed

140 euroeuroeuroAntennas andPropagafion Magazine Vol 41 No 6 December 1999

where

These foimulas allow us to obtain the probability of direct visibility between arbitrary observers inside the layer of city buildings If ( L ) is the average length of screens (buildings) surrounding the

points A(r) and B(r2) (see Figure 7) then the probability of the intersection of the line AB with the building screens is equal to

from which we can easily define the parameter yo

ltLgt = L

b

Figure 7 The distribution of screens between the transmitter and the receiver

I where q2=[(x2-xI) 2 +(y2-y l ) The function Ph(z ) was

introduced earlier as the probability of the event where point z is located below the level of the building roofs (ie within thc layer of hl lt z lt h 2 h lt h 2 ) According to Equation (17) this function is related to the density of the building height distribution w(h) Now we assume according to [11-13] that the height profile of buildings inside the city layer is in the following form

ph (2) = N (hi -2) + I f ( Z - h l ) [ ( h 2 - Z ) ( h 2 -hl)]n (27) n gt O O c z lt h 2

The height distribution oCEquation (27) dcscribes a wide spectrum of city building profiles from a one-level height close to h (for n gtgt 1) or to h (for n ltlt 1 ) up to various levels of building heights h i including a quasi-Iiomogeneous distribution of hi with equal probability from hl to h2 when n = 1

52 Field intensity attenuation in the city with randomly distributed buildings

Let us consider the city building layer described by the random surface S which was introduced earlier as a superposition of a flat perfectly reflecting surface SI and of a random built-up relief S2 (see Figure 6)

Figure 8 The observation of a scatterer with a horizontal length I and a width I from point r

y o = 2 ( L ) v n (22)

Here v is the density of buildings in the investigated area of 1 h 2 The parameter yo determines the average horizontal distance of line-of-sight ( p ) and

( P ) = Yo (23)

512 The distribution of reflected sections for each scatterer Let us consider the case when direct visibility exists between two points rl and r2 The point r belongs to the vertical screen (see Figure 8) If a horizontal segment with length 1 can be seen from the point r I a vertical segment with width I can he seen from this point as well Let us now determine the probability that the horizontal segment which includes the point B(r2) can he

observed from the point A(r) The vertical screen forms an angle I with the segment AB (see Figure 8) Following [11-13] we can obtain the probability of the direct visibility of segment cd with length I from point A at range q2

e d =exp(-yoym -~~12 l j~ l s in p ) (24)

E =( -ZJl jEj(z)(z-zI)(z2 -zJ dz 22

2

zgtziz2 (25)

521 Single scattering and diffraction As was shown in [11-13] the role of single scattering is very important when one of the antennas (generally the base-station antenna) is above the roof level but another is below the buildings roofs This case is presented in Figure 9 where the reflecting point C is inside the building contour with average height h The building orientation is determined by the angle I$ to the vector (rs -rl) The receiver (or transmitter) is placed at the point B (r2) and the transmitter (or

receiver) is placed at the point A(r I ) Taking into account the approach presented in [16-19] we can present the field over rough terrain by using Greens theorem in its integral form

513 Influence of city building profile Taking into account that real areas of the urban environment are distributed inhomoge- neously we must present a probability of direct visibility between two points rl and r2 according to Equation (26)

Bigure 9 The three-dimensional geometry of single scattering from any screen at the point C

141

1 1 1

22

P(qra)=exp -yoq2(22-21)- Iph(z)dz (26)

lEEEAntennas and Propagation Magazine Vol 41 No 6 December 1999

where U(rz) is the incidcnt wave ficld G(r2r) is the Greens function of the half space

and ns is the vector normal to the terrain surface S a t the scattered point I ~ Here r is the point symmetrical to rl relative to the earth surface SI k = 2n2 where 1 is the wavelength We consider in the intcgral of Equation (28) the random surface S (the relief of the ground surface with buildings) to he the superposition of the ground surface SI and the built-up surface S that is created by the tops of the buildings (Figure 6) We conslfuct the Greens function in such a form in Equation (29) so as to satisfy the electrodynamic approach eg to describe both vertical (sign + in Equation (29)) and horizontal (sign - in Equation (29)) polarization and corresponding boundary conditions In fact by introducing the Greens function of Equation (29) with + in the integral equation of Equation (29) we satisfy the Dirichlet boundary conditions on the non-disturbed terrain SI ( z = 0) for which

dU G= = 2 and - = 0 if with - we satisfy the Neumann

811s

boundary conditions at the plane z = 0 for which Gz=o = 0 and u = o

If the sonrce is described by Equation (29) assuming the SUI- face SI to he perfectly reflecting one can exclude the integration over a non-disturbed surface SI ie one can use the integration only over the disturbed surface S according to the well-known approach presented in [ I l 16-19] Using now this fact and the well-known Kirchhoff approximation [ 16-19] let us determine the field Uamp) scattered from the building layer as a superposition of an incident wave Ui(r2) the reflection coefficient r(ylsrs)

with correlation scale I and the shadow function Z(rlr2)

Z(rlr2) equals one if the scattered point rs inside the city layer can he observed from both points q and r2 of the transmitter and receiver locations (see Figure 9) and equals zero in all other cases (see in more detail [ I I 121) Let it be assumed that L ltltltp gt hzlz2 ltltrz -r I where lt p gt is determined by Equation (23) and zI z2 are the height of the source and receiver respectively and h is the height of a local obstacle placed on the ground surface Then taking into account the above the last Equation (28) can he rewrten in the case of single scattering as

rs -rI where sinyls = nS - (see Figure 9) I r ~ - rl I

The average intensity of the scattered field at the observed point rz can he obtained by taking into account expressions in

142 Eeuroeuro Antennas and Propagation Magazine Vol 41 No 6 December 1999

Equations (18) and (30) and also the effect of diffraction from the rooftops of the buildings according to the approach presented in [12] To account for this effect we use the Huygens-Kirchhoff approximation for the integral equation Equation (30) and the following expression for the average intensity of the received field

(I(r2)) = (U(r2) U(r2)) We average Equation (30) over the non-transparent screens spatial distribution over their number and over the reflection properties of screens [ I I 121 After some straightforward derivations taking into account the build-up profile distribution of Equation (26) and the single diffraction from the building layer we finally obtain the following formulas for the incoherent part of the average intensity for the single-scattered field

112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~

As follows from Equation (31) for the case where the base-station antenna as a receiver is higher than the average building height-

that is ( I d 4 n 3 ) lt lt ( r - h ) -Equation (31) is limited to the incoherent spectrum without taking into account the effect of diffraction [ I l l Moreover as zz increases the process of diffraction becomes more important and for z2 = h the single-scattered-wave

average intensity ( I ~ ~ ) - ( a d 4 n 3 ) ie is not equal to zero In

2

112

both cases the distance dependence is only the same - d - 3 when

(Ad 4 z 3 ) ltlt (zZ - h) In the inverse case when

( L d 4 z 3 ) gtgt (q - A ) this dependence is - d- Hence in the

case of single scattering the slope parameter y = 25 - 3 ie Ay = 05-1

53 Multiple scattering and diffraction

The same analysis can he carried Out for multiple scattering from the buildings (see Figure IO) Here the angle a is an angle between vectors (ritl -ri) and (r -ri-l) for all i=l2 n rurlrz r are the radius vectors of points A ClC2 C B respectively The same procedure of averaging taking into account the built-up area profile of Equation (26) allows us to obtain the incoherent part of the average intensity for multiply scattered waves with diffraction [12]

f ( q ) = H(h l -zl)(h -z l )+H(z l -h)(hz -q)n+l(n +l)(hz -h)

f ( z 2 ) = H(hl - z2) (h - z2 )+ H(z2 - h ) ( b -q)nl(n +l)(h2 - kl) (33)

h = k2 -n(h2 - h l ) ( n + I ) (34)

where h is an average height of the buildings The built-up profile distribution of Equation (34) is more general than that obtained in

R B 61 Initial data

The initial data which are the input parameters of cellular- map construction are as follows

A A J

4 hl

Figure 10 The geometry of multiple scattering from n randomly distributed screens

[ I l l and as was shown in [12] strictly describes actual city relief As follows from Equation (32) in the case of multiple scattering the slope parameter y = 3 ie A y = 1

The coherent spectrum ( I co ) of the total field intensity can

be presented by taking into account the distribution function I j ( 2 )

ofEquation (26) [ I I 121

The total wave-field intensity from the transmitter is a superposition of a scattered (incoherent) spectrum (I) described by Equation (31) or (32) and a coherent spectrum (Ico) of the total field energy described by Equation (35) ie

To summarize the principal results described in this work we present here a general technique for radio-coverage prediction and for construction of the related radio map as well as for cellular- map construction for the concrete urban environment considered

6 Algorithm for propagation and prediction of cellular characteristics

We will present our prediction concept in the form of a prediction algorithm

Terrain elevation data that is the digital terrain map consisting of ground heights as grid points h ( x y )

A clutter map that is the ground cover of artificial and natural obstructions as a distribution of grid points h o ( x y ) the average length of the obslructions ( L ) the average height of obstructions in the test area h the obstruction density per km2 v

The effective antenna height that is the antenna height plus a ground or obstruction height if the antenna is assembled on a concrete obstruction z and z2 for the transmitter and receiver respectively

The antenna pattern or directivity and its effective radiated power (ERP) the operating frequency f

62 Steps of the predictinn algorithm

621 Pirst step of the algorithm The first step is to introduce the built-up terrain elevation data for three-dimensional radio- path profile construction As a result there is a digital map (coverage) with actual heights of obstructions present in the computer memory

622 Second step of the algorithm Using all parameters of the built-up terrain and of both antennas transmitter and receiver (according to above initial data) the three-dimensional digital map is analyzed to theoretically predict the clearance conditions between the antennas and the localization of the obstructions as reflectors surrounding both antennas In this case where the test area is built as asfreet grid eg blocks the additional parameters presented in Sections 3 and 4 are needed

For LOS conditions along the street the average street width a the average length of buildings and gaps between them ( L ) and ( l ) respectively the average height of the buildings lining the street h the type of building material dominant in the test area (brick wood concrete etc) All these parameters allow us to obtain the parameter of ldquobrokennessrdquo A4 = (L)((L)+(i)) which indicates the density of buildings lining the street in the block the characteristic impedance ZBM of the building materials the normal wave-propagation constant K and finally the modulus I R 1 and the phase pn of the reflection coefficient R of the normal modes that propagate along the street waveguide (according to Equations (3) and (4)) and the modulus lDl of the diffraction coefficient (according to [12]) All these parameters allow us to obtain the break range according to Equation ( 5 ) as a distance of clearance between two subscribers that is the lower limit of the cell radius

In the case of rough terrain with randomly distributed buildings in NLOS conditions between both antennas the following


Figure 11 An example of radio coverage The circled values are the theoretical prediction the curves are the measurements

parameters in addition to those presented above mnst be used the typical correlation scales of the obstructions e and e (see Section 5 ) and the type of building material dominant in the test area Finally all these parameters allow us to obtain the density of building contours at the plane z = 0 (the ground level) yo =2(L)vn and then the clearance conditions between the receiver and transmitter eg the average horizontal distance of the line-of-sight ( p ) as a minimum limit of

the cell radius ( p ) = yorsquo

623 Third step of the algorithm The various factors obtained earlier then must he used for the computer program based on the three-dimensional multi-slit waveguide model in LOS conditions and the two-dimensional multi-diffraction model in NLOS conditions for urban areas with regularly distributed rectangular crossing streets and based on the three-dimensional parametric model for irregular built-up terrain In the first case Equation (2) is used to describe the radio coverage along the straight streets in LOS conditions and Equations (12) and (13) are used to describe the situation in an urban scene with rectangular crossing streets in NLOS conditions In the second case of an irregular built-up terrain Equations (31)-(36) are used As a result the signal-power distribution over the terrain can be obtained for cases both of iso- tropic and directive (by introducing their EPR) antennas These data must he constructed as a two-dimensional radio map which describes the ground coverage of the radio signal for the built-up area being tested an example of which is presented in Figure 11

624 Fourth step of the algorithm At this last step we can split the coverage map into a set of cells to obtain the cellular map of the urban area being tested and to estimate the co-charnel interference parameter CII Because the radius of the cell and the slope parameter y both depend on the propagation phenomena we rec- ommend the use of the technique described above using Equations (5 ) (19)-(23) and (7)-(8) respectively for the concrete situation in the urban scene

7 References

I L B Milstein D L Schilling R L Pickholtz et al ldquoOn the Feasibility of a CDMA Overlay for Personal Communications Networksrdquo IEEE Selected Areas in Communications 10 4 1992 pp 665-668

2 A I Rustako Jr N Amitay M J Owens and R S Roman ldquoRadio Propagation at Microwave Frequencies for Line-of-Sight Microcellular Mobile and Personal Communicationsrdquo 1EEE Transactions on Vehicular Technology VT-40 2 1991 pp 203- 210

3 S Y Tan and H S Tan ldquoA Theory of Propagation Path Loss Characteristics in a City Street-Grid Scenerdquo IEEE Transactions on Electromagnetic Compatibility EMC-37 2 1995 pp 333-342

144 IEEE Antennas and Propagation Magazine Vol 41 No 6 December 1999

4 H L Bertoni W Honcharenko L R Maciel and H H Xia ldquoUHF Propagation Prediction for Wireless Personal Communica- tionsrdquo Proceedings of the IEEE 8291994 pp 1333-1359

5 H H Xia H L Bertoni L R Maciel et al ldquoRadio Propaga- tion Characteristics for Line-of-Sight Microcellular and Personal Communicationsrdquo IEEE Transactions on Antennas and Propaga- tion AP-41 IO 1993 pp 1439-1447

6 L R Maciel H L Bertoni and H H Xia ldquoUnified Approach to Prediction of Propagation Over Buildings for All Ranges of Base Station Antenna Heightrdquo IEEE Transactions on Vehicular Technology VT-42 1 1993 pp 41-45

7 N Blannstein and M Levin ldquoVHFNHF Wave Attenuation in a City with Regularly Distributed Buildingsrdquo Radio Science 31 1996pp 313-323

8 N Blannstein R Giladi and M Levin ldquoLOS Characteristicsrsquo Prediction in Urban and Suburban Environmentsrdquo IEEE Transac- tions on Vehicular Technology VT-47 I 1997 pp 11-21

9 N Blannstein ldquoAverage Field Attenuation in the Nonregnlar Impedance Street Waveguiderdquo IEEE Transactions on Antennas andPropagation AP-46121998 pp 1782-1789

IO N Blaunstein M Levin I Matateyahu and M Shalukhin ldquoPrediction of Loss Characteristics in Urban Environments with Non-Regularly Distributed Buildings Placed at the Rough Ter- rainrdquo Proceedings of International URWIEEE Conference Athene GreeceMay 14-18 1998pp121-124

11 G A Ponomarev A N Knlikov and E D Telpnkhovsky Propagation of Ultra-Short Waves in Urban Environments Tomsk USSR Rasko 1991

12 N Blaunstein Radio Propagation in Cellular Network Bos- ton-London 1999

13 N Blaunstein and M Levin ldquoParametric Model of UHFL- Wave Propagation in City with Randomly Distributed Buildingsrdquo IEEE International Symposium on Antennas and Propagation Digest Volume 3 Atlanta Georgia June 21-26 1998 pp 1684- 1687

14 I D Parsons The Mobile Radio Propagation Channel New York Halsted Press 1992

Fred Gardiol Lab of Electromagnetlcs and AcOUStkS Ecole Polytechnlque FBdBrale de Lausanne ELB Ecublens CH-1015 Lausanne Switzerland (41121-6932670

16 F G Bass and I M Fuks Wave Scuttering from Statistically Rough Surfaces Oxford Pergamon Press 1979

17 M I Chamotskii and V I Tatarskii ldquoTilt-Invariant Theory of Rough-Surface Scattering Irdquo Waves in Random Media 5 4 1995 pp 361-380

18 V 1 Tatarskii and M I Chamotskii ldquoOn the Universal Behaviour of Scattering from a Rough Surface from Small Grazing Anglesrdquo IEEE Trunsuctions on Antennas and Propagution AP- 46 I 1995 pp 61-12

19 A G Voronovich Wave Scutteringfrom Rough Surfaces Ber- lin Germany Springer-Verlag 19948

Antenna Design Engineer

RSI designs manufactures markets and installs satellite earth station antenna systems for common carriers broadcasting services and commercial and government agencies worldwide

Requirements are MSEE with emphasis in electromagneticsantennas and at least two years experience Will design and modify feed assemblies to include new feed development and cost reduction research Analytical and hands-on skills antenna testing experience and some domestic and international travel also required May be subject to security investigation

RSI 4825 River Green Parkway

Duluth Georgia 30096 Fax 770 497 1009

E-ma e i r rue ers corn c o r

i 4 i j 11-693-2673 (FOX) FredGardiolepflch (emall) h t tp l l l emowep f l ch

ross out in the grid all the words that appear in the list below C They may appear horizontally vertically or diagonally Six letters should then remain indicating a way to get from one place to another

Alert Aperture Awry Beep Bolus Branch Chiral Client Coating Decay Denoting Extra Finite Fractal Global Glossy Horror Idler Integral Jest Jitter Jogger Keen Lapel Leaky Limitation Lull Matrix Next Objective Optimal Orhiter Overlay Pilot Planet Plasma Poster Pound Principle Printed Process Quay Reply Ring Root Side Sling Slot Slumber Spot Starry Stray Sweep Tetrahedral Trend Wheel Window Wipe Wireless

S L U M B E R L J Y E Y O O N S A M S A L P D I B V N L O l Y K A E L A M I T P O S T E R


city buildings and natural obstacles the sizes and ranges of reflected and diffracted surface sections of the ground relief and the spatial distribution of the scattering points of each building placed in areas surrounding the receiver and transmitter antennas

Below in Section 3 following the approach presented in [7- 91 we describe the contribution to the path loss along the street in LOS (line-of-sight) conditions for buildings placed on the flat terrain An important parameter of microcells at the street level the ldquobreak pointrdquo range which can define the lower limit of the effi- cient radius of a microcell in LOS conditions between the receiver and transmitter at the stage of cellular-map construction is exam- ined

Then in Section 4 using the modified two-dimensional model of multi-diffraction [4-6]-because it more correctly predicts the experimental data for the obstructed radio paths than other empirical and deterministic models (see the bibliography in [14])- we present theoretical aspects of radio coverage and a cellrsquos effective-radius prediction in NLOS (non-line-of-sight) conditions In Section 5 we introduce lhe statistical-parametric model for rough built-up terrain according to [11-13] We then examine the average intensity of the total field in the layer of city buildings with randomly distributed obstacles placed on the rough terrain including single and multiple scattering and the diffraction from rooftops In Section 6 we present the full algorithm for predicting propagation and cellular characteristics for various built-up environments

3 Prediction of cellular characteristics in LOS conditions

The ldquotwo-rayrdquo model consisting of the direct and the ieflected rays [ I 21 and the two-dimensional propagation model consisting of multiple reflections from the walls [3] are usually used for the conditions when both antennas are placed at the street level below the rooftop level in LOS condilions Instead a multi- slit-waveguide model was proposed in [7-91 for describing wave propagation in urban areas with straight streets and with randomly distributed building walls (screens) and gaps between them (slits) (see Figure I) Let us present the propagation and cellular characteristics in LOS conditions according to [7-91 taking into account

Moving radio porl

I

Figure 1 An urban area with a crossing-street-grid plan

136 euroeuroeuroAntennas and Propagation Magazine Vol 41 No 6 December 1999

Rays ^

i i i

Figure 2 A schematic diagram of a three-dimensional model of a street multi-slit waveguide

= t

lsquo I Y

1+---

Figure 3 A two-dimensional diagram of crossing-street waveguides in the zy plane The coordinates of the source are y = 0 and z = h a and b are the widths of the crossing streets

the real dielectric properties of building walls the actual dishibu- tion of street widths and the reflection from the road (see Figure 2)

31 Contribution to path loss

Let us consider that the buildings on the streets are replaced by randomly distributed non-transparent screens with scales Y rdquo the electrical properties of which are defined by surface imped- ances u=O (see the definition in [7-91) The distances between the building slits we define as S nm =123 (see Figure 3 the radial waveguide ldquoIrdquo and crossing waveguide ldquo11rdquo) The laws of their differential distribution are postulated as independent and exponential with mean values ( L ) and ( I ) respectively The probability density functions are given by [7-91


(vexP-L (9 ]~

nm = 123 (1)



L = 32i-401og~~~r~-2oiog~~[i-(~~r~)2][i+(~~r~)2]











L t







U 0




Ilsquo =r r


B (7)







138




If lt I

I J









(10)








I12 1 -























where




ltLgt = L

b









y o = 2 ( L ) v n (22)


( P ) = Yo (23)





2

zgtziz2 (25)





141

1 1 1

22






811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References

































(vexP-L (9 ]~

nm = 123 (1)



L = 32i-401og~~~r~-2oiog~~[i-(~~r~)2][i+(~~r~)2]











L t







U 0




Ilsquo =r r


B (7)







138




If lt I

I J









(10)








I12 1 -























where




ltLgt = L

b









y o = 2 ( L ) v n (22)


( P ) = Yo (23)





2

zgtziz2 (25)





141

1 1 1

22






811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References
































L t







U 0




Ilsquo =r r


B (7)







138




If lt I

I J









(10)








I12 1 -























where




ltLgt = L

b









y o = 2 ( L ) v n (22)


( P ) = Yo (23)





2

zgtziz2 (25)





141

1 1 1

22






811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References

































If lt I

I J









(10)








I12 1 -























where




ltLgt = L

b









y o = 2 ( L ) v n (22)


( P ) = Yo (23)





2

zgtziz2 (25)





141

1 1 1

22






811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References













































where




ltLgt = L

b









y o = 2 ( L ) v n (22)


( P ) = Yo (23)





2

zgtziz2 (25)





141

1 1 1

22






811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References







































y o = 2 ( L ) v n (22)


( P ) = Yo (23)





2

zgtziz2 (25)





141

1 1 1

22






811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References



































811s










112 rajv [ ( M 4 n 3 ) + ( z 2 - h ) ]

(I(r2)) = 8n(12 + [ 2 n C ~ ~ f ( z ~ ) ] ~ d ~




2

112









h = k2 -n(h2 - h l ) ( n + I ) (34)


R B 61 Initial data


A A J

4 hl

























7 References
































R B 61 Initial data


A A J

4 hl

























7 References





































7 References
















































Documents

Prediction of cellular characteristics for various urban environments