Tvt JAcuna 2015329 Proof

8/3/2019 Tvt JAcuna 2015329 Proof

1/18

IEEE

Proo

f

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1

Propagation Model for Small Urban Macro Cells1Juan M. Casaravilla, Gabriel A. Dutra, Natalia Pignataro, and Jos E. Acua2

AbstractThis paper presents the MOPEM1

propagation3 model for dense urban areas in the frequency band from 8504to 900 MHz. This work is based on the COST 231-WI model,5but the hypothesis of infinite screen blocks is replaced by finite6screens, taking into account the street crossings, predicting the7signal attenuation along the block. The dependence of the prop-8agation loss with the terrain height is reviewed and optimized by9considering an absolute reference, whereas the dependence on the10angle between the street and the wave propagation is modified to11obtain a continuously differentiable loss function. The standard12deviation obtained with this model is 5.1 dB, and the mean er-13ror is 0 dB versus 6.6 and 6.2 dB, respectively, for the COST14231-WI model, with validation measurements from two areas in15Montevideo, Uruguay.16

Index TermsElectromagnetic propagation.17

I. INTRODUCTION18

N EW services being launched in mobile networks, such19 as multimedia transmissions, produce a traffic increase20that, together with constant service price reduction, demands21

more accurate cell planning from the operator and his suppliers.22

Progressive cell size reduction requires greater accuracy of23

system coverage estimations. This requires an accurate cover-24age prediction methodology with an easy implementation. The25

current models consider neither the height difference between26

the floor levels at the mobile station (MS) location and the base27

station (BS) nor the signal strength variation along the block28and do not have a differentiable orientation angle-dependent29

loss function.30

The aim of this paper is to find a model for the radio channel31

loss in the frequency range from 850 to 900 MHz. This model32

has been developed for urban areas with small macro cells2 in33Montevideo, Uruguay, with no line of sight (NLOS) between34

the transmitter and the receiver. The model gives a propaga-35

tion loss function LMOPEM with the following parameters:36

Manuscript received May 11, 2006; revised March 7, 2007, July 24, 2007,February 1, 2008, May 5, 2008, September 22, 2008, and November 27, 2008.

The review of this paper was coordinated by Dr. D. W. Matolak.J. M. Casaravilla is with Alcatel-Lucent, 11300 Montevideo, Uruguay

(e-mail: [email protected]).G. A. Dutra is with Nokia Siemens, Uruguay.N. Pignataro is with ANTEL, 11800 Montevideo, Uruguay (e-mail:

[email protected]).J. E. Acua is with the Universidad de la Repblica Oriental del Uruguay,

11100 Montevideo, Uruguay, and also with the University of Vigo, 36310 Vigo,Spain (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2009.2015329

1The Spanish acronym for Propagation Model for Small Urban Macro Cells.2According to [1], a small macro cell is an outdoor cell that is placed higher

than the average building height, but some buildings could be higher than theantennas. Its typical coverage radius is less than 3 km.

Fig. 1. Two rays at the MS considered by models in [1] and [2].

Fig. 2. Definition ofb, w, and as the angle between the axis of the street

and the direction of the propagation.

frequency f, base station height hbase, MS height hm, distance 37between the MS and the BS d, street width w, angle between 38the street and the propagation direction , building height hroof, 39building separation b, and terrain height. 40

This paper is organized into seven sections. The theoretical 41

backgrounds, the base models, and the proposed modifications 42

are presented in Section II. The proposed model is described in 43Section III. Section IV describes the urban areas and the mea- 44

surement methodology, whereas Section V shows the results 45

and compares the MOPEM with the COST 231-WI model. A 46

series of applications is presented in Section VI. We conclude 47

this paper in Section VII. 48

II. THEORETICAL ANALYSIS 49

The MOPEM model bases its initial analysis on the semi- 50

empirical propagation models proposed by COST 231-WI [1], 51

Ikegami and Yoshida [2], and Walfisch and Bertoni [3]. All 52of them consider multiple rays between the BS and the MS. 53

The model presented in [2] considers two rays, as illustrated in 54

Fig. 1: Ray A has experienced one diffraction, whereas ray B 55

has experienced one diffraction and one reflection. 56

The most restrictive hypothesis of model [2] is to consider 57

the line of sight (LOS) and, hence, the free-space propagation 58between the BS and the diffracting building. 59

It also shows a lower dependence on the distance than what 60

is verified with measurements, but it takes into account the 61parameters of the mobile environment, such as hroof and w. 62It also introduces a factor that accounts for the dependence 63

with the angle shown in Fig. 2, which is the most innovative 64contribution. 65

Reference [3] eliminates the LOS hypothesis to the last 66

diffracting building, studying the multiple screen diffraction 67

and proposing a simple solution to the electromagnetic problem 68

under the additional hypothesis of uniformity ofhroof, which is 69modeled as absorbent screens. It considers h

basegreater than 70

0018-9545/$25.00 2009 IEEE


2/18

IEEE

Proo

f

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

hroof. This model takes into account the street width w and the71building separation b, but it does not consider the angle .72

The COST 231-WI model proposed in [1] considers the loss,73

which is composed of the free-space loss Lo, the multidiffrac-74tion loss Lmsd, and the roof-to-street diffraction loss Lrts, as75can be observed in the following equations:76

LCOST 231-WI = Lo + Lrts + Lmsd (1)

L0 = 32.4 + 20 log d + 20 log f (2)

Lrts =16.9 10log w + 10 log f+ 20 log(hroof hm) + Lori (3)

Lmsd = Lbsh + ka+ kdlog d + kflog f 9log b (4)

where77

[d] = km, [f] = MHz, [w] = m, [hroof] = m

[hm] = m, [] =, [b] = m

kd = 18, kf = 4.06, ka = 54

Lbsh = 18 log(1 + hbase hroof).The COST 231-WI model includes the contributions from78

[2] and [3], with the terms Lrts and Lmsd. The estimated mean79error (e) is from 3 to 3 dB, and the standard deviation is80between 4 and 8 dB.81

The reason to choose COST 231-WI as the base model for82this paper is that it was fitted using measurements in European83

cities, and Montevideo is very similar to these cities. The84

MOPEM model was improved by fitting the loss function,85

adding the terrain height, considering finite screens, and modi-86fying the orientation loss function.87

The MOPEM model is obtained from (1)(4) by modifying88

the underlined terms and adding a new term called Lesq.89

A. Influence of the Terrain Height Variation90

The loss dependence on hm has extensively been ana-91lyzed in previous works, but its influence is different in each92

model. The empirical models are fitted with measurements such93

as the Ibrahim and Parsons method [4], which obtained an94

8log10(hm) law. In the semiempirical models, such as COST95231, the attenuation produced between the diffracting edge and96

the MS depends on the distance between the MS hm and the97building roofs (hroof), with the term 20log10(hroof hm).98

The parametershroof

andhm

are measured with respect to99the floor level at the site.100

The MOPEM model considers the dependence with the101

height using a fitted khm instead of 20, with the term102khm log10(hAroof hAm). The heights hAroof and hAm are103measured with respect to a common reference level (e.g., the104sea level) to account for terrain height variations (see Fig. 3).105

B. Building, Mobile, and Terrain Heights106

It is necessary to define a criterion to estimate hroof and hm.107Usually, hm is taken as 1.5 m above the ground, because it is108the mean value between the head and the waist of a person.109

The MOPEM model adds the terrain height to this value when110measuring from a common reference level.111

Fig. 3. Model considering heights from a common reference level instead ofthe local floor level.

Two methods to estimate the parameter hroof have been 112reported in the literature. The first method is to take hroof as 113the last building height (as shown in building #2 in Fig. 1). 114Nevertheless, it is inaccurate in environments with great differ- 115

ent building heights, because in several cases, a higher building 116located between the BS and the last building produces the last 117

diffraction. Another method is to use a local height average, but 118the choice of the area size is arbitrary and not well justified. The 119

MOPEM model proposes the evaluation ofhAroof as an average 120height, as proposed by Sakagami and Kuboi [5], considering the 121

highest buildings of each block in the studied area but measured 122from a common reference level. This criterion was based on ur- 123

ban considerations, since the most significant screens between 124

the BS and the MS are the prominent buildings. 125

See Fig. 3 to understand the influence of variable terrain 126

heights when using an averaged building height. 127Mobiles in low areas (m1) have a lower signal than mobiles 128

in higher areas (m2), because they are far from the average 129building height and have a larger diffraction angle (1), which 130reduces the received signal. 131

The MOPEM model considers the variation of the terrain 132

height by using a common reference level for the heights hAroof 133and hAm. The dependence is adjusted through. 134

C. Finite Multiscreen Effect 135

The effect of the multiscreen diffraction is based on the 136

analysis presented in [3], when the BS antenna is placed above 137

hroof (a requirement that is fulfilled in this paper). The buildings 138are considered to be absorbent half-screens of the same height, 139

infinite width, and infinitesimal thickness. Such screens are 140

located in the center of the buildings and perpendicularly to the 141

propagation direction. 142This geometrical assumption simplifies the electromagnetic 143

problem that was previously mentioned, but it does not con- 144

sider the existence of the corners where the building line is 145

interrupted by the streets. As shown in Fig. 4, additional rays 146reach the MS by diffraction and reflection on the buildings of 147

the crossing street located near the corner, causing higher levels 148

of the signal than in the middle of the block. The MOPEM 149

model adds a loss term (Lesq) with a logarithmic dependence 150with the distances from each street intersection, i.e., desq1 and 151

desq2 in Fig. 4, which has empirically been adjusted based on 152field measurements. 153


3/18

IEEE

Proo

f

CASARAVILLA et al.: PROPAGATION MODEL FOR SMALL URBAN MACRO CELLS 3

Fig. 4. Rays to be considered in the case of finite screens reaching the MScoming from the corners.

D. Dependence on the Angle Between the Propagation154

Direction and the Street Centerline155

The loss dependence on the angle (see Fig. 2) is a phe-156nomenon that has already been studied in [1] and [2]. The157

model proposed by Ikegami and Yoshida [2] considers the158angle , where it calculates the electric field E at the MS159based on the Fresnel equation of diffraction that depends on the160

distance between the MS and the diffracting point on the last161

diffracting building edge. This distance was calculated in [2] as162the projection of the MS perpendicular distance to the building,163

i.e., w

, over the ray with the direction . This calculation leads164to (5), which shows the relation between the diffracted electrical165

field E and the incident electrical field E0 at the diffracting166point in terms of . K is a constant, which is independent of167 and E0, as shown in the following equation:168

E = K E0

w/ sin . (5)

This approach does not address two important issues. First,169

for small angles, the signal levels incorrectly go to infinity170

prediction when the street is parallel to the direction of propa-171gation, but in this case, there is no diffraction. Second, it is cal-172

culated using the hypothesis of infinite screens and, therefore,173

underestimates the E level at the corners. The crossing streets174with the angle (usually 90) have similar urban variables175at the corners, but one with the angle and the other with176 . Therefore, the model incoherently predicts different177signal levels at the corner, depending on which street is used178

for estimation, because the function is not symmetric around179

/2(45). The new orientation angle function Lori-MOPEM180must have a continuous signal transition from one street to181

another in the intersection.182

The Lori function (see Fig. 5) was empirically adjusted, but183it is defined by intervals and is not continuously differentiable;184

this is in disagreement with Maxwell equations. Furthermore,185

the bounds of the intervals at 35 and 55 do not have a186theoretical justification.187

Fig. 5. COST 231 loss function Lori with respect to the street orientationangle , which is not continuously differentiable at arbitrary values .

Fig. 6. Definition of the urban parameters of the MOPEM model.

The previous discussion justifies the search for a continu- 188

ously differentiable function, without arbitrary intervals bounds 189

in the Lori function and near symmetric around 45. 190

III. MOPEM MODEL 191

The MOPEM model describes the loss as the sum of four 192independent terms: 1) Lo in (2) is the loss due to the free-space 193propagation; 2) Lrts-MOPEM is the loss of the diffraction from 194the last building to the MS; 3) Lmsd-MOPEM is the loss caused 195by the multiscreen diffraction; and 4) Lesq accounts for the 196finite multiscreen assumption. The following equation shows 197

the base attenuation model, whose terms are described by (2) 198

and (7)(10), which are shown later: 199

LMOPEM = Lo + Lrts-MOPEM + Lmsd-MOPEM + Lesq. (6)

The terms Lrts-MOPEM, Lmsd-MOPEM, and Lesq are new 200contributions. 201

The following parameters that describe the urban environ- 202ment are defined in Figs. 2 and 6: 203

1) building height hAroof: average of the heights of the 204highest building of each block (in meters); A205

2) street width w: the average width of all streets (in meters); 2063) building separation b: estimated as half of the block207

average (in meters); 208

4) orientation angle : bounded by the street centerline 209

and the propagation direction, as shown in Fig. 2 210(in degrees). 211


4/18

IEEE

Proo

f


Fig. 7. Circle, whereLesq is equal to the value on the boundary.

The average of the parameters is estimated in the coverage212

area.213

The Lrts-MOPEM term (7), shown below, adds two new214improvements to the Lrts term (3): the terrain height included215in hAm and hAroof and the Lori-MOPEM function. Thus216

Lrts-MOPEM = 1.87 10log10(w) + 10 log10(f)+ 10.4log10(hAroof hAm) + Lori-MOPEM

(7)Lori-MOPEM = 2.8

45

4+ 13.2

45

329.5

45

2+ 30.3

45

3.5. (8)

The Lmsd-MOPEM term models the loss due to the multi-217screen diffraction, as proposed in [1] and [3]. This term is based218

on (4) and has empirically been fitted in this paper with d to219achieve more accuracy, i.e.,220

Lmsd-MOPEM = +54 18log10(1 + hAbase hAroof)+ kf log10(f) + 27.7log10(d)

9log10(b) (9)

with kf = [4 + 0.7(f /925 1)] from [1].221hAroof and hAbase are measured from a common reference222

level.223

The Lesq term models the signal variation along the block.224The expression was empirically fitted, as shown in the follow-225ing equation:226

Lesq = 11.32 + 3.3[log10(desq1) + log10(desq2)] . (10)

The parameters in (10), namely, desq1 and desq2 (in meters),227are the distances from the MS to each center of the streets228intersection, as defined in Fig. 4.229

The signal values taken to derive this dependence were230

obtained by averaging the measurements in 40 (in this case,23114-m intervals), according to ITU-R P.1406 recommendation232

[6], to eliminate fast fading.233Thus, the expression is strictly valid outside a 7-m circle from234

the center of the street intersection, as shown in Fig. 7. Inside235

the 7-m circle, we recommend maintaining the boundary value.236

IV. ENVIRONMENT AND MEASUREMENTS237

A brief description of the environment and an explanation238

of the parameters used in the proposed model are presented in239

the following discussion. A complete area description and the240survey methods used can be found in [7].241

Fig. 8. Map of the studied area showing the Pocitos and Punta Carretasneighborhoods of Montevideo.

A. Area Description 242

Fig. 8 shows the studied area, which is located in two 243

neighborhoods of Montevideo, called Pocitos and Punta 244

Carretas. Pocitos has an hroof of approximately 24 m and a b 245of 50 m. In the center of the blocks, there is an area free of 246buildings. Pocitos includes two different areas: 1) Pocitos Viejo, 247

with one-family houses (hroof approximately 9 m), and 2) the 248area near the coastline, with high-rise buildings (hroof approxi- 249mately 30 m). 250

Punta Carretas has an hroof of five floors. It has a high 251occupation of the land but with some parks. Further information 252

about these areas can be found in [7]. 253

B. Attenuation Measurement 254

The measured cellular system was the Advanced Mobile 255

Phone System (AMPS)/Digital AMPS system in the 850-MHz 256

frequency band. Three different macro cell sectors of two BSs 257

were chosen: two of them covering the same area of Pocitos 258

from different angles and another covering Punta Carretas area. 259

The sites are located at 345451.27" S, 560905" W and 260345427.76" S, 560911.7" W, as shown in Fig. 8. 261

The analog and digital control channels of each sector were 262

used to measure the attenuation, and it is calculated as follows: 263

L = EIRP RSSI (11)

where L is the signal loss between the BS and the MS (ex- 264

pressed in decibels). Effective isotropic radiated power (EIRP)265

is the power radiated from the BS antenna (measured in decibel 266

meters), whereas received signal strength indication (RSSI) 267indicates the received power (in decibel meters) measured 268

with a TEMS Agilent E7474A TDMA drive test system. A 269

total of 90 000 significant measurements of RSSI were taken 270

in two different campaigns to overcome temporal effects that 271could produce distortion in the measurements. According to 272

[6], it is convenient to divide spatial variability into fast fading 273

and slow fading. When analyzing measurements, fast fading 274

can be eliminated by taking a median signal level from 36 275measurements in a distance of about 40 (14 m), obtaining 276accuracy within 1 dB with a 90% probability. Experience has 277

shown that the distribution of these median values will be 278lognormal, and therefore, their distribution can be characterized 279


5/18

IEEE

Proo

f


by their mean or median and their standard deviation. This leads280

to an averaging of the measurements in 14-m intervals, thus281obtaining a set of 2500 representative values of RSSI. This set282

was subdivided into two sets: One was used for model tuning283

(T set), and the other was used for model validation (V set).284

V. RESULTS285

A. Model Adjustment286

Two indicators were used to quantify the model performance:287the mean error e and the standard deviation . Model tuning288was made by minimizing the mean square error using the T set289

of measurements. The model uncertainty was estimated, con-290

sidering of the prediction error (4.4 dB) and the uncertainties291in the measured values (RSSI and urban parameters, 2.6 dB).292

B. Model Validation293

To validate the model, hypothesis testing of model e and 294based on the V set of measurements was carried out, with the295following definitions and values:296

e =

ni=1

yi yip

n = 0.003 dB (12)

=

ni=1

(yi yip)2

(n 1) = 4.4 dB. (13)

For the model mean error, the null hypothesis Ho is de-297fined as298

Ho : = o (14)

and the confidence interval according to [8]299

I = [o t(/2, n 1) n, o + t(/2, n 1)

n

= [0.269, 0.269] (15)

where is the mean error of the model, and o is the proposed300mean error of the model, which is 0 in this test. The significance301level is taken as 95% in this test for a confidence level of 95%.302

Parameter t(/2, n 1) is the inverse Student distribution303

function with (n 1) degrees of freedom for /2. Parameter n304is the number of samples (measurements), yi is the ith sample305of the V set of measurements, and yip is the model predicted306value for yi. As e is inside the 95% confidence interval I, the3070 mean error hypothesis was not rejected. To validate the model308

uncertainty, a one-tailed null hypothesis Ho is defined as309

Ho : MOPEM (16)

and the confidence interval as310

I = 0, 2(1 , n 1) 2o/(n 1)

= [0, 5.3] (17)

where 2 is the chi-square distribution, and was taken as 5%311for a 95% confidence level in this test. The proposed uncertainty312

TABLE IMEA N ERROR AND UNCERTAINTY PROPOSED FOR THE MOPEM MODELCOMPARED WITH THE COST 231 MODEL AND THE VALUES OBTAINED

WITH THE MOPEM MODEL WITH THE V SET OF MEASUREMENTS

of the MOPEM model o = MOPEM is 5.1 dB according to 313the following equation, where a = , and b is the uncertainty 314of the measurements: 315

MOPEM = 2a +

2b = (4.4)

2 + (2.6)2 = 5.1 dB. (18)

This is in the range expected by Siwiak [9] from 5 to 12 dB 316and better than the expected variability distribution of [6], 317

which is given by 318

L = 5.25 + 0.42 log10(f /100) + 1.01 (log10(f /100))2

= 6.5 dB at 870 MHz. (19)

The model uncertainty hypothesis was not rejected because 319

the uncertainty estimator S is inside the 95% confidence 320interval I. 321

C. Comparison With the COST 231-WI Model 322

To evaluate the performance of the MOPEM model against 323

the COST 231-WI model, two precision estimators were used 324

for comparison: e and . These estimators were calculated 325using the V set, with the results shown in Table I. 326

It can be seen in Table I that the error and the uncertainty 327

of the MOPEM model are smaller than those achieved by the 328

COST 231-WI model. We have to point out that COST 231 is 329a more general model; thus, this could be one reason to have 330

larger e and . 331Fig. 9 shows the measurements in one street of the studied 332

area as an example, as well as the predictions of both models. 333

The MOPEM model achieves greater precision following the 334pattern of the signal levels along the block and with less error. 335

D. Distance Dependence Adjustment 336

A precise dependence of the loss function with d significantly 337improves the accuracy of a model. The models presented in [1] 338

and [3] have coefficients of 38 dB/dec for the distance term 339

log(d); however, the coefficient of the MOPEM model, adding 340the distance terms in (2) and (9), is 20 + 27.7 = 47.7 dB/dec. 341This difference is caused by the higher density of tall buildings 342

than that found in the environments where the COST 231 [1] 343

model measurements were done. The theoretical value pro- 344posed in [1] and [3] can be rejected with a confidence level 345


6/18

IEEE

Proo

f


Fig. 9. Signal measurements in four blocks in one street and the correspond-ing estimations of the COST 231 and MOPEM models.

TABLE IIMEA N ERROR FOR DIFFERENT RANGES OF THE TERRAIN HEIGHT

MEASURED FROM A COMMON REFERENCE LEVEL

of 95% after the uncertainty analysis of this coefficient and the346

corresponding hypothesis testing (see [8] and [10]).347This result is in accordance with [11], which presents coef-348

ficients from 30 to 48 dB/dec, and with [12], which achieves349

43.4 dB/dec (lateral route) to 55 dB/dec (transverse route) in350

high-rise building environments.351

E. Influence of the Terrain Height Variation352

If the terrain variation is not considered in the model, a353

correlation between it and the error can be observed. This can354be verified in Table II, where the measurements were fitted355

without taking heights from a common reference.356

It can be seen that for ranges of terrain heights below 14 m357

over sea level, the attenuation is underestimated, whereas it is358overestimated in ranges over 14 m.359

Previous models average this effect, appearing as a model360

uncertainty. Taking into account the terrain height variation, the361

uncertainty is reduced to 1.1 dB, as modeled by (7) and (9).362

F. Finite Multiscreen Effect363

The traditional model prediction uses an approach for the364

signal behavior, which globally predicts along several blocks365but averages the signal behavior within the block. In contrast,366

the MOPEM model considers the variations within a block367

through a variable attenuation Lesq, which depends on the368distance from the center of the street intersection.369

Fig. 10. Gain produced by finite screens (Lesq) in a 100-m block proposedin the MOPEM model. Rays diffracted in the corner edges increase the signalnear them.

On the other hand, the MOPEM model predicts the signal 370increase behavior in the corners, which is confirmed by the 371

measurements. A comparison between the COST 231-WI and 372

the MOPEM model predictions along a block can be observed 373

in Fig. 9, whereas the term calculated as a gain in the signal 374

(Lesq) can be seen in Fig. 10. 375The term was tested to be statistically significant in the 376

adjustment of the constants in the term with a confidence 377

level of 95%. The uncertainty is reduced by 0.1 dB with this 378

contribution and is important in the signal description along 379the block, showing lower values than the average along it and 380

revealing possible coverage holes. 381

G. Street Orientation Dependence 382

The measurements are consistent with the theoretical analy- 383sis of the attenuation signal dependence on the orientation 384

angle (see Fig. 2) and show that the minimum attenuation 385is observed on angles near 0 and 90. A graphical criterion, 386which is suggested by [8] and [10], is to plot in the y-axis the 387prediction error without against in the x-axis. 388

If errors are distributed around zero, there is no dependence. 389

Fig. 11 shows the error distribution of the validation set of 390

measurements against the model predicted values, which are 391

not uniformly distributed around zero, displaying an angle 392dependence pattern. 393

This analysis supports the adjustment of the Lori-MOPEM 394function, as shown in Fig. 12. 395

The prediction difference at the corner between both streets, 396i.e., , is reduced to the street orientation term difference be- 397cause almost all variables are very similar near the intersection 398

of the streets (building height, elevation, street width, etc.). 399

Thus 400

= Lori() Lori(90 ). (20)

Fig. 13 shows the values for different street orientations 401

and for three models. Previous models predict different levels 402of signal in two streets with and 90 angles. 403


7/18

IEEE

Proo

f


Fig. 11. Example of the error distribution between the predictions withoutand the measurements.

Fig. 12. Attenuation function Lori-MOPEM of the MOPEM model versusstreet orientation angle.

Fig. 13. Prediction differences at the corners of the MOPEM, COST 231, andIkegami models.

The MOPEM model difference is below the model uncer-404

tainty, which is coherent at both values.405

Lori-MOPEM() and Lori-MOPEM(90 ) are in the 95%406trust interval of the other. Therefore, the hypothesis about407

Fig. 14. Influence of the street grid in the coverage area produced by theorientation angle dependence.

the behavior in the corners is verified, showing a decrease 408of 0.4 dB. 409

VI. APPLICATIONS 410

The most remarkable applications of the proposed model are 411

described in the following sections. 412

A. Coverage Area Depending on the Transmitter Orientation 413

The Lori-MOPEM function has its minima at = 0 and 414 = 90 and a maximum at = 45. Therefore, in a cell with 415the direction of maximum propagation parallel to the streets, the 416

MOPEM model estimates a longer and narrow coverage area, 417

as shown in Fig. 14 for Tx1. On the other hand, a transmitter 418

with an antenna with its maximum propagation direction at 45 419with respect to the streets has a broader and shorter coverage 420

area, as shown in Fig. 14 for Tx2. 421

B. Estimation of the Coverage Area Depending on 422

the Terrain Height 423

In the MOPEM model prediction, the coverage footprint 424

becomes considerably misshapen when the terrain height varies 425

around 20 m, with a lower signal in low areas and an increased 426signal in high areas. Therefore, the MOPEM model allows 427

calculation of the signal with more accuracy and revealing 428

coverage holes in low areas and interfered points in high areas. 429

C. Prediction Improvements Along the Block 430

The Lesq term accounts for the variation of the signal along 431the block; for example, it has 2 dB in 100-m blocks. The 432

improved prediction obtained allows plans based on the worst 433case, using central points of each block for coverage area analy- 434

sis and values close to the corners for interference analysis. 435

VII. CONCLUSIONS 436

A semiempirical propagation model for the frequency band 437

from 850 to 900 MHz has been proposed. This model is in 438the accuracy limit for a statistical model, as given in [9], and 439


8/18

IEEE

Proo

f


is better than expected, as given in [6]. Significant modifica-440

tions have been proposed with regard to the reference model441COST 231-WI [1]. These variations are based on theoretical442

justifications, which were previously analyzed and empirically443

confirmed through a wide set of measurements.444

The first modification involved the attenuation loss caused445

by the street orientation, leading to a continuous behavior at the446street crossings.447

The second modification was based on the modeling of the448

finite screen effect through Lesq, which considers additional449rays in the signal level near the corners.450

Finally, the dependence on the terrain height variation has451

been included in the loss function LMOPEM to adapt the model452to coverage areas with important terrain height differences453

compared with the building height. These three modifications454achieve a better performance, obtaining a model of easy appli-455

cation, which incorporates new concepts for cell planning.456

REFERENCES457

[1] Digital mobile radio towards future generations systems, in Cost 231458Final Rep., ch. 4, pp. 134140.459

[2] F. Ikegami and S. Yoshida, Analysis of multipath propagation structure460in urban mobile radio environments, IEEE Trans. Antennas Propag.,461vol. AP-28, no. 4, pp. 531537, Jul. 1980.462

[3] J. Walfisch and H. Bertoni, A theoretical model of UHF propagation463in urban environments, IEEE Trans. Antennas Propag., vol. 36, no. 12,464pp. 17881796, Dec. 1988.465

[4] J. D. Parsons, The Mobile Radio Propagation Channel. New York:466Wiley, 1992.467

[5] S. Sakagami and K. Kuboi, Mobile propagation loss prediction for468arbitrary urban environments, IEICE Trans. Commun. (Japan), vol. J74-469B-111, no. 10, pp. 1725, Oct. 1991.470

[6] Propagation Effects Relating to Terrestrial Land Mobile Service in the471VHF And UHF Bands. ITU-R P.1406 Recommendation.472

[7] J. Casaravilla, G. Dutra, and N. Pignataro, Modelo de propagacin473para entornos urbanos de pequeas macroceldas, in (Propagation Model474

for Urban Areas of Small Macrocells in Urban Areas). Montevideo,475Uruguay: Faculty Eng., Univ. de la Repblica, 2002. Academic studies476final project.477

[8] S. Chatterjee and A. S. Hadi, Sensitivity Analysis in Linear Regression.478New York: Wiley, 1988.479

[9] K. Siwiak, Radiowave Propagation and Antennas for Personal Commu-480nications, 2nd ed. Boston, MA: Artech House, 1998.481

[10] N. R. Draper and H. Smith, Applied Regression Analysis. Toronto, ON,482Canada: Wiley, 1980.483

[11] H. H. Xia, A simplified analytical model for predicting path loss in urban484and suburban environments, IEEE Trans. Veh. Technol., vol. 46, no. 4,485pp. 10401046, Nov. 1997.486

[12] D. Har and H. H. Xia, Path-loss prediction model for microcells, IEEE487Trans. Veh. Technol., vol. 48, no. 5, pp. 14531462, Sep. 1999.488

Juan M. Casaravilla received the B.S. degree 489in electrical engineering from the Universidad 490de la Repblica Oriental del Uruguay (UdelaR), 491Montevideo, Uruguay, in 2002. 492

He was an Teaching Assistant with the Insti- 493tute of Electrical Engineering (IIE), UdelaR, during 49420002001. He is currently a Technical Manager 495for UMTS/3G project implementation with Alcatel- 496

Lucent, Montevideo. 497

Gabriel A. Dutra received the B.S. degree in 498electrical engineering from the Universidad de 499la Repblica Oriental del Uruguay (UdelaR), 500Montevideo, Uruguay, in 2002. 501

In 1999, he was an Assistant Professor with the 502Institute of Mathematics and Statistics (IMERL), 503UdelaR, and since 2001, he has been an Assistant 504Professor with the Institute of Electrical Engineer- 505ing (IIE), UdelaR. He currently works as technical 506support for Nokia SIEMENS Telecomunicaciones 507S.A. and 3W S.A. on telephone exchanges and wired 508

networks management systems. 509

Natalia Pignataro received the B.S. degree in 510electrical engineering from the Universidad de 511la Repblica Oriental del Uruguay (UdelaR), 512Montevideo, Uruguay, in 2002. 513

Since 2000, she has been with the National Tele- 514communications Office, ANTEL, Montevideo, per- 515forming technical support functions with the Mobile 516Network Planning and Optimization Department. 517

Jos E. Acua received the B.S. degree in electrical 518engineering from the Universidad de la Repblica 519Oriental del Uruguay (UdelaR), Montevideo, 520Uruguay, in 1994. He is currently working toward 521the Ph.D. degree with the University of Vigo, Vigo, 522Spain. 523

Since 1992, he has been with the Electrical Engi- 524neering Institute (IIE), UdelaR, where he is currently 525an Assistant Professor with the Telecommunications 526Department. He has been engaged in research on 527radio channel modulation, electromagnetic compat- 528

ibility, radio frequency and its environmental impact, and modeling of sub- 529scriber lines based on xDSL and broadband wireless technologies (HSPA and 530WIMAX). 531


9/18

IEEE

Proo

f

AUTHOR QUERIES

AUTHOR PLEASE ANSWER ALL QUERIES

AQ1 = Please provide the city and postal address for Nokia-Siemens, Uruguay.AQ2 = The University of Vigo was captured as another affiliation of author Acua to match the data in the

vitae. Is this appropriate? If not, please make the necessary corrections.AQ3 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ4 = Please check if the changes made here are appropriate. If not, please make the necessary corrections.AQ5 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ6 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ7 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ8 = The authors affiliation in the first footnote does not match the information given in the vitae. Please

provide the complete affiliation data for author Dutra.AQ9 = What does ANTEL stand for?

END OF ALL QUERIES


10/18

IEEE

Proo

f

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1

Propagation Model for Small Urban Macro Cells1Juan M. Casaravilla, Gabriel A. Dutra, Natalia Pignataro, and Jos E. Acua2

AbstractThis paper presents the MOPEM1

propagation3 model for dense urban areas in the frequency band from 8504to 900 MHz. This work is based on the COST 231-WI model,5but the hypothesis of infinite screen blocks is replaced by finite6screens, taking into account the street crossings, predicting the7signal attenuation along the block. The dependence of the prop-8agation loss with the terrain height is reviewed and optimized by9considering an absolute reference, whereas the dependence on the10angle between the street and the wave propagation is modified to11obtain a continuously differentiable loss function. The standard12deviation obtained with this model is 5.1 dB, and the mean er-13ror is 0 dB versus 6.6 and 6.2 dB, respectively, for the COST14231-WI model, with validation measurements from two areas in15Montevideo, Uruguay.16

Index TermsElectromagnetic propagation.17

I. INTRODUCTION18

N EW services being launched in mobile networks, such19 as multimedia transmissions, produce a traffic increase20that, together with constant service price reduction, demands21

more accurate cell planning from the operator and his suppliers.22

Progressive cell size reduction requires greater accuracy of23

system coverage estimations. This requires an accurate cover-24age prediction methodology with an easy implementation. The25

current models consider neither the height difference between26

the floor levels at the mobile station (MS) location and the base27

station (BS) nor the signal strength variation along the block28and do not have a differentiable orientation angle-dependent29

loss function.30

The aim of this paper is to find a model for the radio channel31

loss in the frequency range from 850 to 900 MHz. This model32

has been developed for urban areas with small macro cells2 in33Montevideo, Uruguay, with no line of sight (NLOS) between34

the transmitter and the receiver. The model gives a propaga-35

tion loss function LMOPEM with the following parameters:36

Manuscript received May 11, 2006; revised March 7, 2007, July 24, 2007,February 1, 2008, May 5, 2008, September 22, 2008, and November 27, 2008.

The review of this paper was coordinated by Dr. D. W. Matolak.J. M. Casaravilla is with Alcatel-Lucent, 11300 Montevideo, Uruguay

(e-mail: [email protected]).G. A. Dutra is with Nokia Siemens, Uruguay.N. Pignataro is with ANTEL, 11800 Montevideo, Uruguay (e-mail:

[email protected]).J. E. Acua is with the Universidad de la Repblica Oriental del Uruguay,

11100 Montevideo, Uruguay, and also with the University of Vigo, 36310 Vigo,Spain (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2009.2015329

1The Spanish acronym for Propagation Model for Small Urban Macro Cells.2According to [1], a small macro cell is an outdoor cell that is placed higher

than the average building height, but some buildings could be higher than theantennas. Its typical coverage radius is less than 3 km.

Fig. 1. Two rays at the MS considered by models in [1] and [2].

Fig. 2. Definition ofb, w, and as the angle between the axis of the street

and the direction of the propagation.

frequency f, base station height hbase, MS height hm, distance 37between the MS and the BS d, street width w, angle between 38the street and the propagation direction , building height hroof, 39building separation b, and terrain height. 40

This paper is organized into seven sections. The theoretical 41

backgrounds, the base models, and the proposed modifications 42

are presented in Section II. The proposed model is described in 43Section III. Section IV describes the urban areas and the mea- 44

surement methodology, whereas Section V shows the results 45

and compares the MOPEM with the COST 231-WI model. A 46

series of applications is presented in Section VI. We conclude 47

this paper in Section VII. 48

II. THEORETICAL ANALYSIS 49

The MOPEM model bases its initial analysis on the semi- 50

empirical propagation models proposed by COST 231-WI [1], 51

Ikegami and Yoshida [2], and Walfisch and Bertoni [3]. All 52of them consider multiple rays between the BS and the MS. 53

The model presented in [2] considers two rays, as illustrated in 54

Fig. 1: Ray A has experienced one diffraction, whereas ray B 55

has experienced one diffraction and one reflection. 56

The most restrictive hypothesis of model [2] is to consider 57

the line of sight (LOS) and, hence, the free-space propagation 58between the BS and the diffracting building. 59

It also shows a lower dependence on the distance than what 60

is verified with measurements, but it takes into account the 61parameters of the mobile environment, such as hroof and w. 62It also introduces a factor that accounts for the dependence 63

with the angle shown in Fig. 2, which is the most innovative 64contribution. 65

Reference [3] eliminates the LOS hypothesis to the last 66

diffracting building, studying the multiple screen diffraction 67

and proposing a simple solution to the electromagnetic problem 68

under the additional hypothesis of uniformity ofhroof, which is 69modeled as absorbent screens. It considers hbase greater than 70

0018-9545/$25.00 2009 IEEE


11/18

IEEE

Proo

f


hroof. This model takes into account the street width w and the71building separation b, but it does not consider the angle .72

The COST 231-WI model proposed in [1] considers the loss,73

which is composed of the free-space loss Lo, the multidiffrac-74tion loss Lmsd, and the roof-to-street diffraction loss Lrts, as75can be observed in the following equations:76

LCOST 231-WI = Lo + Lrts + Lmsd (1)

L0 = 32.4 + 20 log d + 20 log f (2)

Lrts =16.9 10log w + 10 log f+ 20 log(hroof hm) + Lori (3)

Lmsd = Lbsh + ka+ kdlog d + kflog f 9log b (4)

where77

[d] = km, [f] = MHz, [w] = m, [hroof] = m

[hm] = m, [] =, [b] = m

kd = 18, kf = 4.06, ka = 54

Lbsh = 18 log(1 + hbase hroof).The COST 231-WI model includes the contributions from78

[2] and [3], with the terms Lrts and Lmsd. The estimated mean79error (e) is from 3 to 3 dB, and the standard deviation is80between 4 and 8 dB.81

The reason to choose COST 231-WI as the base model for82this paper is that it was fitted using measurements in European83

cities, and Montevideo is very similar to these cities. The84

MOPEM model was improved by fitting the loss function,85

adding the terrain height, considering finite screens, and modi-86fying the orientation loss function.87

The MOPEM model is obtained from (1)(4) by modifying88

the underlined terms and adding a new term called Lesq.89

A. Influence of the Terrain Height Variation90

The loss dependence on hm has extensively been ana-91lyzed in previous works, but its influence is different in each92

model. The empirical models are fitted with measurements such93

as the Ibrahim and Parsons method [4], which obtained an94

8log10(hm) law. In the semiempirical models, such as COST95231, the attenuation produced between the diffracting edge and96

the MS depends on the distance between the MS hm and the97building roofs (hroof), with the term 20log10(hroof hm).98

The parametershroof

andhm

are measured with respect to99the floor level at the site.100

The MOPEM model considers the dependence with the101

height using a fitted khm instead of 20, with the term102khm log10(hAroof hAm). The heights hAroof and hAm are103measured with respect to a common reference level (e.g., the104sea level) to account for terrain height variations (see Fig. 3).105

B. Building, Mobile, and Terrain Heights106

It is necessary to define a criterion to estimate hroof and hm.107Usually, hm is taken as 1.5 m above the ground, because it is108the mean value between the head and the waist of a person.109

The MOPEM model adds the terrain height to this value when110measuring from a common reference level.111

Fig. 3. Model considering heights from a common reference level instead ofthe local floor level.

Two methods to estimate the parameter hroof have been 112reported in the literature. The first method is to take hroof as 113the last building height (as shown in building #2 in Fig. 1). 114Nevertheless, it is inaccurate in environments with great differ- 115

ent building heights, because in several cases, a higher building 116located between the BS and the last building produces the last 117

diffraction. Another method is to use a local height average, but 118the choice of the area size is arbitrary and not well justified. The 119

MOPEM model proposes the evaluation ofhAroof as an average 120height, as proposed by Sakagami and Kuboi [5], considering the 121

highest buildings of each block in the studied area but measured 122from a common reference level. This criterion was based on ur- 123

ban considerations, since the most significant screens between 124

the BS and the MS are the prominent buildings. 125

See Fig. 3 to understand the influence of variable terrain 126

heights when using an averaged building height. 127Mobiles in low areas (m1) have a lower signal than mobiles 128

in higher areas (m2), because they are far from the average 129building height and have a larger diffraction angle (1), which 130reduces the received signal. 131

The MOPEM model considers the variation of the terrain 132

height by using a common reference level for the heights hAroof 133and hAm. The dependence is adjusted through. 134

C. Finite Multiscreen Effect 135

The effect of the multiscreen diffraction is based on the 136

analysis presented in [3], when the BS antenna is placed above 137

hroof (a requirement that is fulfilled in this paper). The buildings 138are considered to be absorbent half-screens of the same height, 139

infinite width, and infinitesimal thickness. Such screens are 140

located in the center of the buildings and perpendicularly to the 141

propagation direction. 142This geometrical assumption simplifies the electromagnetic 143

problem that was previously mentioned, but it does not con- 144

sider the existence of the corners where the building line is 145

interrupted by the streets. As shown in Fig. 4, additional rays 146reach the MS by diffraction and reflection on the buildings of 147

the crossing street located near the corner, causing higher levels 148

of the signal than in the middle of the block. The MOPEM 149

model adds a loss term (Lesq) with a logarithmic dependence 150with the distances from each street intersection, i.e., desq1 and 151

desq2 in Fig. 4, which has empirically been adjusted based on 152field measurements. 153


12/18

IEEE

Proo

f


Fig. 4. Rays to be considered in the case of finite screens reaching the MScoming from the corners.

D. Dependence on the Angle Between the Propagation154

Direction and the Street Centerline155

The loss dependence on the angle (see Fig. 2) is a phe-156nomenon that has already been studied in [1] and [2]. The157

model proposed by Ikegami and Yoshida [2] considers the158angle , where it calculates the electric field E at the MS159based on the Fresnel equation of diffraction that depends on the160

distance between the MS and the diffracting point on the last161

diffracting building edge. This distance was calculated in [2] as162the projection of the MS perpendicular distance to the building,163

i.e., w

, over the ray with the direction . This calculation leads164to (5), which shows the relation between the diffracted electrical165

field E and the incident electrical field E0 at the diffracting166point in terms of . K is a constant, which is independent of167 and E0, as shown in the following equation:168

E = K E0

w/ sin . (5)

This approach does not address two important issues. First,169

for small angles, the signal levels incorrectly go to infinity170

prediction when the street is parallel to the direction of propa-171gation, but in this case, there is no diffraction. Second, it is cal-172

culated using the hypothesis of infinite screens and, therefore,173

underestimates the E level at the corners. The crossing streets174with the angle (usually 90) have similar urban variables175at the corners, but one with the angle and the other with176 . Therefore, the model incoherently predicts different177signal levels at the corner, depending on which street is used178

for estimation, because the function is not symmetric around179

/2(45). The new orientation angle function Lori-MOPEM180must have a continuous signal transition from one street to181

another in the intersection.182

The Lori function (see Fig. 5) was empirically adjusted, but183it is defined by intervals and is not continuously differentiable;184

this is in disagreement with Maxwell equations. Furthermore,185

the bounds of the intervals at 35 and 55 do not have a186theoretical justification.187

Fig. 5. COST 231 loss function Lori with respect to the street orientationangle , which is not continuously differentiable at arbitrary values .

Fig. 6. Definition of the urban parameters of the MOPEM model.

The previous discussion justifies the search for a continu- 188

ously differentiable function, without arbitrary intervals bounds 189

in the Lori function and near symmetric around 45. 190

III. MOPEM MODEL 191

The MOPEM model describes the loss as the sum of four 192independent terms: 1) Lo in (2) is the loss due to the free-space 193propagation; 2) Lrts-MOPEM is the loss of the diffraction from 194the last building to the MS; 3) Lmsd-MOPEM is the loss caused 195by the multiscreen diffraction; and 4) Lesq accounts for the 196finite multiscreen assumption. The following equation shows 197

the base attenuation model, whose terms are described by (2) 198

and (7)(10), which are shown later: 199

LMOPEM = Lo + Lrts-MOPEM + Lmsd-MOPEM + Lesq. (6)

The terms Lrts-MOPEM, Lmsd-MOPEM, and Lesq are new 200contributions. 201

The following parameters that describe the urban environ- 202ment are defined in Figs. 2 and 6: 203

1) building height hAroof: average of the heights of the 204highest building of each block (in meters); A205

2) street width w: the average width of all streets (in meters); 2063) building separation b: estimated as half of the block207

average (in meters); 208

4) orientation angle : bounded by the street centerline 209

and the propagation direction, as shown in Fig. 2 210(in degrees). 211


13/18

IEEE

Proo

f


Fig. 7. Circle, whereLesq is equal to the value on the boundary.

The average of the parameters is estimated in the coverage212

area.213

The Lrts-MOPEM term (7), shown below, adds two new214improvements to the Lrts term (3): the terrain height included215in hAm and hAroof and the Lori-MOPEM function. Thus216

Lrts-MOPEM = 1.87 10log10(w) + 10 log10(f)+ 10.4log10(hAroof hAm) + Lori-MOPEM

(7)Lori-MOPEM = 2.8

45

4+ 13.2

45

329.5

45

2+ 30.3

45

3.5. (8)

The Lmsd-MOPEM term models the loss due to the multi-217screen diffraction, as proposed in [1] and [3]. This term is based218

on (4) and has empirically been fitted in this paper with d to219achieve more accuracy, i.e.,220

Lmsd-MOPEM = +54 18log10(1 + hAbase hAroof)+ kf log10(f) + 27.7log10(d)

9log10(b) (9)

with kf = [4 + 0.7(f /925 1)] from [1].221hAroof and hAbase are measured from a common reference222

level.223

The Lesq term models the signal variation along the block.224The expression was empirically fitted, as shown in the follow-225ing equation:226

Lesq = 11.32 + 3.3[log10(desq1) + log10(desq2)] . (10)

The parameters in (10), namely, desq1 and desq2 (in meters),227are the distances from the MS to each center of the streets228intersection, as defined in Fig. 4.229

The signal values taken to derive this dependence were230

obtained by averaging the measurements in 40 (in this case,23114-m intervals), according to ITU-R P.1406 recommendation232

[6], to eliminate fast fading.233Thus, the expression is strictly valid outside a 7-m circle from234

the center of the street intersection, as shown in Fig. 7. Inside235

the 7-m circle, we recommend maintaining the boundary value.236

IV. ENVIRONMENT AND MEASUREMENTS237

A brief description of the environment and an explanation238

of the parameters used in the proposed model are presented in239

the following discussion. A complete area description and the240survey methods used can be found in [7].241

Fig. 8. Map of the studied area showing the Pocitos and Punta Carretasneighborhoods of Montevideo.

A. Area Description 242

Fig. 8 shows the studied area, which is located in two 243

neighborhoods of Montevideo, called Pocitos and Punta 244

Carretas. Pocitos has an hroof of approximately 24 m and a b 245of 50 m. In the center of the blocks, there is an area free of 246buildings. Pocitos includes two different areas: 1) Pocitos Viejo, 247

with one-family houses (hroof approximately 9 m), and 2) the 248area near the coastline, with high-rise buildings (hroof approxi- 249mately 30 m). 250

Punta Carretas has an hroof of five floors. It has a high 251occupation of the land but with some parks. Further information 252

about these areas can be found in [7]. 253

B. Attenuation Measurement 254

The measured cellular system was the Advanced Mobile 255

Phone System (AMPS)/Digital AMPS system in the 850-MHz 256

frequency band. Three different macro cell sectors of two BSs 257

were chosen: two of them covering the same area of Pocitos 258

from different angles and another covering Punta Carretas area. 259

The sites are located at 345451.27" S, 560905" W and 260345427.76" S, 560911.7" W, as shown in Fig. 8. 261

The analog and digital control channels of each sector were 262

used to measure the attenuation, and it is calculated as follows: 263

L = EIRP RSSI (11)

where L is the signal loss between the BS and the MS (ex- 264

pressed in decibels). Effective isotropic radiated power (EIRP)265

is the power radiated from the BS antenna (measured in decibel 266

meters), whereas received signal strength indication (RSSI) 267indicates the received power (in decibel meters) measured 268

with a TEMS Agilent E7474A TDMA drive test system. A 269

total of 90 000 significant measurements of RSSI were taken 270

in two different campaigns to overcome temporal effects that 271could produce distortion in the measurements. According to 272

[6], it is convenient to divide spatial variability into fast fading 273

and slow fading. When analyzing measurements, fast fading 274

can be eliminated by taking a median signal level from 36 275measurements in a distance of about 40 (14 m), obtaining 276accuracy within 1 dB with a 90% probability. Experience has 277

shown that the distribution of these median values will be 278lognormal, and therefore, their distribution can be characterized 279


14/18

IEEE

Proo

f


by their mean or median and their standard deviation. This leads280

to an averaging of the measurements in 14-m intervals, thus281obtaining a set of 2500 representative values of RSSI. This set282

was subdivided into two sets: One was used for model tuning283

(T set), and the other was used for model validation (V set).284

V. RESULTS285

A. Model Adjustment286

Two indicators were used to quantify the model performance:287the mean error e and the standard deviation . Model tuning288was made by minimizing the mean square error using the T set289

of measurements. The model uncertainty was estimated, con-290

sidering of the prediction error (4.4 dB) and the uncertainties291in the measured values (RSSI and urban parameters, 2.6 dB).292

B. Model Validation293

To validate the model, hypothesis testing of model e and 294based on the V set of measurements was carried out, with the295following definitions and values:296

e =

ni=1

yi yip

n = 0.003 dB (12)

=

ni=1

(yi yip)2

(n 1) = 4.4 dB. (13)

For the model mean error, the null hypothesis Ho is de-297fined as298

Ho : = o (14)

and the confidence interval according to [8]299

I = [o t(/2, n 1) n, o + t(/2, n 1)

n

= [0.269, 0.269] (15)

where is the mean error of the model, and o is the proposed300mean error of the model, which is 0 in this test. The significance301level is taken as 95% in this test for a confidence level of 95%.302

Parameter t(/2, n 1) is the inverse Student distribution303

function with (n 1) degrees of freedom for /2. Parameter n304is the number of samples (measurements), yi is the ith sample305of the V set of measurements, and yip is the model predicted306value for yi. As e is inside the 95% confidence interval I, the3070 mean error hypothesis was not rejected. To validate the model308

uncertainty, a one-tailed null hypothesis Ho is defined as309

Ho : MOPEM (16)

and the confidence interval as310

I = 0, 2(1 , n 1) 2o/(n 1)

= [0, 5.3] (17)

where 2 is the chi-square distribution, and was taken as 5%311for a 95% confidence level in this test. The proposed uncertainty312

TABLE IMEA N ERROR AND UNCERTAINTY PROPOSED FOR THE MOPEM MODELCOMPARED WITH THE COST 231 MODEL AND THE VALUES OBTAINED

WITH THE MOPEM MODEL WITH THE V SET OF MEASUREMENTS

of the MOPEM model o = MOPEM is 5.1 dB according to 313the following equation, where a = , and b is the uncertainty 314of the measurements: 315

MOPEM = 2a +

2b = (4.4)

2 + (2.6)2 = 5.1 dB. (18)

This is in the range expected by Siwiak [9] from 5 to 12 dB 316and better than the expected variability distribution of [6], 317

which is given by 318

L = 5.25 + 0.42 log10(f /100) + 1.01 (log10(f /100))2

= 6.5 dB at 870 MHz. (19)

The model uncertainty hypothesis was not rejected because 319

the uncertainty estimator S is inside the 95% confidence 320interval I. 321

C. Comparison With the COST 231-WI Model 322

To evaluate the performance of the MOPEM model against 323

the COST 231-WI model, two precision estimators were used 324

for comparison: e and . These estimators were calculated 325using the V set, with the results shown in Table I. 326

It can be seen in Table I that the error and the uncertainty 327

of the MOPEM model are smaller than those achieved by the 328

COST 231-WI model. We have to point out that COST 231 is 329a more general model; thus, this could be one reason to have 330

larger e and . 331Fig. 9 shows the measurements in one street of the studied 332

area as an example, as well as the predictions of both models. 333

The MOPEM model achieves greater precision following the 334pattern of the signal levels along the block and with less error. 335

D. Distance Dependence Adjustment 336

A precise dependence of the loss function with d significantly 337improves the accuracy of a model. The models presented in [1] 338

and [3] have coefficients of 38 dB/dec for the distance term 339

log(d); however, the coefficient of the MOPEM model, adding 340the distance terms in (2) and (9), is 20 + 27.7 = 47.7 dB/dec. 341This difference is caused by the higher density of tall buildings 342

than that found in the environments where the COST 231 [1] 343

model measurements were done. The theoretical value pro- 344posed in [1] and [3] can be rejected with a confidence level 345


15/18

IEEE

Proo

f


Fig. 9. Signal measurements in four blocks in one street and the correspond-ing estimations of the COST 231 and MOPEM models.

TABLE IIMEA N ERROR FOR DIFFERENT RANGES OF THE TERRAIN HEIGHT

MEASURED FROM A COMMON REFERENCE LEVEL

of 95% after the uncertainty analysis of this coefficient and the346

corresponding hypothesis testing (see [8] and [10]).347This result is in accordance with [11], which presents coef-348

ficients from 30 to 48 dB/dec, and with [12], which achieves349

43.4 dB/dec (lateral route) to 55 dB/dec (transverse route) in350

high-rise building environments.351

E. Influence of the Terrain Height Variation352

If the terrain variation is not considered in the model, a353

correlation between it and the error can be observed. This can354be verified in Table II, where the measurements were fitted355

without taking heights from a common reference.356

It can be seen that for ranges of terrain heights below 14 m357

over sea level, the attenuation is underestimated, whereas it is358overestimated in ranges over 14 m.359

Previous models average this effect, appearing as a model360

uncertainty. Taking into account the terrain height variation, the361

uncertainty is reduced to 1.1 dB, as modeled by (7) and (9).362

F. Finite Multiscreen Effect363

The traditional model prediction uses an approach for the364

signal behavior, which globally predicts along several blocks365but averages the signal behavior within the block. In contrast,366

the MOPEM model considers the variations within a block367

through a variable attenuation Lesq, which depends on the368distance from the center of the street intersection.369

Fig. 10. Gain produced by finite screens (Lesq) in a 100-m block proposedin the MOPEM model. Rays diffracted in the corner edges increase the signalnear them.

On the other hand, the MOPEM model predicts the signal 370increase behavior in the corners, which is confirmed by the 371

measurements. A comparison between the COST 231-WI and 372

the MOPEM model predictions along a block can be observed 373

in Fig. 9, whereas the term calculated as a gain in the signal 374

(Lesq) can be seen in Fig. 10. 375The term was tested to be statistically significant in the 376

adjustment of the constants in the term with a confidence 377

level of 95%. The uncertainty is reduced by 0.1 dB with this 378

contribution and is important in the signal description along 379the block, showing lower values than the average along it and 380

revealing possible coverage holes. 381

G. Street Orientation Dependence 382

The measurements are consistent with the theoretical analy- 383sis of the attenuation signal dependence on the orientation 384

angle (see Fig. 2) and show that the minimum attenuation 385is observed on angles near 0 and 90. A graphical criterion, 386which is suggested by [8] and [10], is to plot in the y-axis the 387prediction error without against in the x-axis. 388

If errors are distributed around zero, there is no dependence. 389

Fig. 11 shows the error distribution of the validation set of 390

measurements against the model predicted values, which are 391

not uniformly distributed around zero, displaying an angle 392dependence pattern. 393

This analysis supports the adjustment of the Lori-MOPEM 394function, as shown in Fig. 12. 395

The prediction difference at the corner between both streets, 396i.e., , is reduced to the street orientation term difference be- 397cause almost all variables are very similar near the intersection 398

of the streets (building height, elevation, street width, etc.). 399

Thus 400

= Lori() Lori(90 ). (20)

Fig. 13 shows the values for different street orientations 401

and for three models. Previous models predict different levels 402of signal in two streets with and 90 angles. 403


16/18

IEEE

Proo

f


Fig. 11. Example of the error distribution between the predictions withoutand the measurements.

Fig. 12. Attenuation function Lori-MOPEM of the MOPEM model versusstreet orientation angle.

Fig. 13. Prediction differences at the corners of the MOPEM, COST 231, andIkegami models.

The MOPEM model difference is below the model uncer-404

tainty, which is coherent at both values.405

Lori-MOPEM() and Lori-MOPEM(90 ) are in the 95%406trust interval of the other. Therefore, the hypothesis about407

Fig. 14. Influence of the street grid in the coverage area produced by theorientation angle dependence.

the behavior in the corners is verified, showing a decrease 408of 0.4 dB. 409

VI. APPLICATIONS 410

The most remarkable applications of the proposed model are 411

described in the following sections. 412

A. Coverage Area Depending on the Transmitter Orientation 413

The Lori-MOPEM function has its minima at = 0 and 414 = 90 and a maximum at = 45. Therefore, in a cell with 415the direction of maximum propagation parallel to the streets, the 416

MOPEM model estimates a longer and narrow coverage area, 417

as shown in Fig. 14 for Tx1. On the other hand, a transmitter 418

with an antenna with its maximum propagation direction at 45 419with respect to the streets has a broader and shorter coverage 420

area, as shown in Fig. 14 for Tx2. 421

B. Estimation of the Coverage Area Depending on 422

the Terrain Height 423

In the MOPEM model prediction, the coverage footprint 424

becomes considerably misshapen when the terrain height varies 425

around 20 m, with a lower signal in low areas and an increased 426signal in high areas. Therefore, the MOPEM model allows 427

calculation of the signal with more accuracy and revealing 428

coverage holes in low areas and interfered points in high areas. 429

C. Prediction Improvements Along the Block 430

The Lesq term accounts for the variation of the signal along 431the block; for example, it has 2 dB in 100-m blocks. The 432

improved prediction obtained allows plans based on the worst 433case, using central points of each block for coverage area analy- 434

sis and values close to the corners for interference analysis. 435

VII. CONCLUSIONS 436

A semiempirical propagation model for the frequency band 437

from 850 to 900 MHz has been proposed. This model is in 438the accuracy limit for a statistical model, as given in [9], and 439


17/18

IEEE

Proo

f


is better than expected, as given in [6]. Significant modifica-440

tions have been proposed with regard to the reference model441COST 231-WI [1]. These variations are based on theoretical442

justifications, which were previously analyzed and empirically443

confirmed through a wide set of measurements.444

The first modification involved the attenuation loss caused445

by the street orientation, leading to a continuous behavior at the446street crossings.447

The second modification was based on the modeling of the448

finite screen effect through Lesq, which considers additional449rays in the signal level near the corners.450

Finally, the dependence on the terrain height variation has451

been included in the loss function LMOPEM to adapt the model452to coverage areas with important terrain height differences453

compared with the building height. These three modifications454achieve a better performance, obtaining a model of easy appli-455

cation, which incorporates new concepts for cell planning.456

REFERENCES457

[1] Digital mobile radio towards future generations systems, in Cost 231458Final Rep., ch. 4, pp. 134140.459

[2] F. Ikegami and S. Yoshida, Analysis of multipath propagation structure460in urban mobile radio environments, IEEE Trans. Antennas Propag.,461vol. AP-28, no. 4, pp. 531537, Jul. 1980.462

[3] J. Walfisch and H. Bertoni, A theoretical model of UHF propagation463in urban environments, IEEE Trans. Antennas Propag., vol. 36, no. 12,464pp. 17881796, Dec. 1988.465

[4] J. D. Parsons, The Mobile Radio Propagation Channel. New York:466Wiley, 1992.467

[5] S. Sakagami and K. Kuboi, Mobile propagation loss prediction for468arbitrary urban environments, IEICE Trans. Commun. (Japan), vol. J74-469B-111, no. 10, pp. 1725, Oct. 1991.470

[6] Propagation Effects Relating to Terrestrial Land Mobile Service in the471VHF And UHF Bands. ITU-R P.1406 Recommendation.472

[7] J. Casaravilla, G. Dutra, and N. Pignataro, Modelo de propagacin473para entornos urbanos de pequeas macroceldas, in (Propagation Model474

for Urban Areas of Small Macrocells in Urban Areas). Montevideo,475Uruguay: Faculty Eng., Univ. de la Repblica, 2002. Academic studies476final project.477

[8] S. Chatterjee and A. S. Hadi, Sensitivity Analysis in Linear Regression.478New York: Wiley, 1988.479

[9] K. Siwiak, Radiowave Propagation and Antennas for Personal Commu-480nications, 2nd ed. Boston, MA: Artech House, 1998.481

[10] N. R. Draper and H. Smith, Applied Regression Analysis. Toronto, ON,482Canada: Wiley, 1980.483

[11] H. H. Xia, A simplified analytical model for predicting path loss in urban484and suburban environments, IEEE Trans. Veh. Technol., vol. 46, no. 4,485pp. 10401046, Nov. 1997.486

[12] D. Har and H. H. Xia, Path-loss prediction model for microcells, IEEE487Trans. Veh. Technol., vol. 48, no. 5, pp. 14531462, Sep. 1999.488

Juan M. Casaravilla received the B.S. degree 489in electrical engineering from the Universidad 490de la Repblica Oriental del Uruguay (UdelaR), 491Montevideo, Uruguay, in 2002. 492

He was an Teaching Assistant with the Insti- 493tute of Electrical Engineering (IIE), UdelaR, during 49420002001. He is currently a Technical Manager 495for UMTS/3G project implementation with Alcatel- 496

Lucent, Montevideo. 497

Gabriel A. Dutra received the B.S. degree in 498electrical engineering from the Universidad de 499la Repblica Oriental del Uruguay (UdelaR), 500Montevideo, Uruguay, in 2002. 501

In 1999, he was an Assistant Professor with the 502Institute of Mathematics and Statistics (IMERL), 503UdelaR, and since 2001, he has been an Assistant 504Professor with the Institute of Electrical Engineer- 505ing (IIE), UdelaR. He currently works as technical 506support for Nokia SIEMENS Telecomunicaciones 507S.A. and 3W S.A. on telephone exchanges and wired 508

networks management systems. 509

Natalia Pignataro received the B.S. degree in 510electrical engineering from the Universidad de 511la Repblica Oriental del Uruguay (UdelaR), 512Montevideo, Uruguay, in 2002. 513

Since 2000, she has been with the National Tele- 514communications Office, ANTEL, Montevideo, per- 515forming technical support functions with the Mobile 516Network Planning and Optimization Department. 517

Jos E. Acua received the B.S. degree in electrical 518engineering from the Universidad de la Repblica 519Oriental del Uruguay (UdelaR), Montevideo, 520Uruguay, in 1994. He is currently working toward 521the Ph.D. degree with the University of Vigo, Vigo, 522Spain. 523

Since 1992, he has been with the Electrical Engi- 524neering Institute (IIE), UdelaR, where he is currently 525an Assistant Professor with the Telecommunications 526Department. He has been engaged in research on 527radio channel modulation, electromagnetic compat- 528

ibility, radio frequency and its environmental impact, and modeling of sub- 529scriber lines based on xDSL and broadband wireless technologies (HSPA and 530WIMAX). 531


18/18

IEEE

Proo

f

AUTHOR QUERIES

AUTHOR PLEASE ANSWER ALL QUERIES

AQ1 = Please provide the city and postal address for Nokia-Siemens, Uruguay.AQ2 = The University of Vigo was captured as another affiliation of author Acua to match the data in the

vitae. Is this appropriate? If not, please make the necessary corrections.AQ3 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ4 = Please check if the changes made here are appropriate. If not, please make the necessary corrections.AQ5 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ6 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ7 = Kindly check if the intended thought of this rephrased sentence is achieved.AQ8 = The authors affiliation in the first footnote does not match the information given in the vitae. Please

provide the complete affiliation data for author Dutra.AQ9 = What does ANTEL stand for?

END OF ALL QUERIES

Documents

Tvt JAcuna 2015329 Proof