New Designed Model

Results from the proposed method to calculate the attenuation of radio signals transmitted through buildings, showed that an improvement on it is necessary in order to obtain a better agreement between the attenuation predicted for this model and the results obtained from measurements in [42].

108

Appendices

Appendix 1

• Definition of the angle a_i

Referring to this angle, if a local

obstructing building was present then a_i would be taken relative to the plane of wall 1.

Conversely, in the absence of an obstructing building a i would be the larger of the ai's for walls 1 and 2. By this definition a_i was always between

a

and 90⁰•

• Definition of the statistic C^p

W.lll

"uour'"•

buJldinr

Ob.tru~tml bluhhnl

The Cp statistic is a function of the error sums of squares for both the reduced and full models and allows a direct comparison of the reduction in variability of the response variable (in the paper's case mp) that can be attributed to the two models in a similar manner to the F statistic. Subset models for which Cp is small and

approximately equal top are said to be adequate reduced prediction models. There will generally be a number of equally valid subset models and it is then up to the research to select the most suitable of these models.

• Regression Analysis Technique

The multiple regression analysis requires a rigorous and careful estimation of its quality, which can be test using the F-test and the coefficient of detennination r²•

109

Appendixes: Appendix 1

Partial quality test of the individual variables should also be made using the t-test. In addition to these three essential quality tests, a close examination of the correlation between any two variables is also necessary. Even if all the statistical tests have shown that the assumed model was useful in predicting the dependent variables, it cannot be concluded that such a model is the best predictor model without further data analysis.Itis also necessary to consider that the calculated prediction equation, based on a set of independent variables, is appropriate only over the range of the sample values used in the analysis. Extrapolation beyond this range may lead to errors.

Simple regression analysis is used when the measured values are related to one variable, whereas for multiple variables, multiple regression analysis can be applied.

Suppose that n measurements of a certain quantity, say Y, have been

undertaken and thatm variables are thought to affect all the measured values ofY. A multiple regression model that relates an individual value of Yto the m variables can then be expressed by

m

Y; = b_o+IbjXij +c_i

j;\

for i= 1,2, ... ,n andXij is the ithvalue of thejth variable and c_ithe error or residual.

The parametersb^{I '} b^{2 , ••• ,} b^m are the regression coefficients corresponding to the m variables; bois a constant which can account for all the other unconsidered variables.

The predicted value of the independent variable Y_{i ,}can be expressed by

m

2; =

b_o+IbjXij

j;\

An important issue in regression analysis is assessing its overall quality. An analysis of residuals or errors is a useful way of evaluating how good the regression is. One possible statistical test dealing with residuals is theF-test, which for m independent variables (i.e., bl 'b2 , ••• , bm) andnobservations, is represented by

F

~ tit, ^-if 1

^m

~(Y; ^-2;) Iv

where

Y

is the mean value ofY. With the number of degrees of freedom m for the numerator and v=n-m-l for the denominator, the tabulated valueofFfor a given level of significance ais compared to the calculatedF. Ifthe computerF is greater than the tabulated value it can then be concluded that the regression results are significant, and the level of significance

a,

represents the probability that the wrong conclusion has been drawn. The overall quality of the regression analysis can be assessed using the

110

coefficient of detennination, which measures the degree of association between the dependent variable and all the independent variables taken together and is

t(f; -Y)

r² = ....:.i~....:.l _

t(r: - YY

i=!

The ratio r² must lie between zero and unity. When r²=1, all variation has been explained but ifit is equal to zero, the regression model does not explain

anything, that is Y is not a function of the variables Xi' X^{2 , •.• ,}X^m' After detennining r^2,the assumed model is useful in describing the dependent variable Y(i.e. the path loss between antennas), it is necessary to check the significance ofthe partial

coefficients b_j , which were considered to have practical importance. This is done by means of thet-test. The appropriate statistic of the test forthejth independent

variables, is

wherej=1,2, ... ,mand eijisthejth diagonal element of the matrix (X^T

xt,

^{with the}

first element e_oocorresponding to the constant tenn of the model being ignored. The quality,

is often referred to as the root mean square error (RMSE) value. As in theF-test, the computed t^j should be greater than the tabulated t^v;a%for a level of significance a.

One of the problems of multiple regression analysis is the possibility of selecting highly correlated independent variables, which indicates that the variables tend to change together. The correlation coefficient between any two variables, say

X_kand Xl' is

rx,X, = ----r.::===i~=l==========='"

[t(x;, -x.rt(x"- ^{X,)' ]}

111

Appendixes: Appendix 1

where X_ikand Xiiare the ith component ofX_kand XI' respectively. X_{k ,}XI'are the average values of two variables. A high correlation coefficient does not prevent finding an estimated regression equation; however, different sets of sample

observations could result in very different estimated regression coefficients, reflecting an inherent instability in the regression relationship. The elimination of one of the highly correlated variables from the regression breaks that pattern and yields different results for the interrelation among the remaining variables.

112

Appendix 2

• Definition of Parameter h

In theory, attenuation caused by sharp edge diffraction behaves according Huygen's principle and can be can be described using the Fresnel parameter 'D. For [41 the computation of'D for each location of interest is somewhat tedious. Instead, a 'geometric diffraction' parameterh,defined in Figure 1 for the case of a lateral corridor, or in Figure 2, for the case of a room adjacent to a main corridor where the signal source is located, has been used in this paper.

MAL""l CORRIDOR

LATERAL CORRIDOR

RX

Figure 1:GeQmetric DiffractiQn Parameter jQr Lateral CQrridQr Qpening Qn

Main CQrridQr.

113

MAIN CORRIDOR TX

Figure 2:GeQmetric DiffractiQn Parameter jQr RQQm Adjacent tQ CQrridQr.

Appendixes: Appendix 2

• Floor Attenuation Factor Path Loss Model

Values for the FAF in Table 10, Chapter 4, are an average (in decibels) of the difference between the path loss observed at multifloor locations and the mean path loss predicted by the simple dⁿ model using as n factor, the same floor exponent given in Table 11 in Chapter 4, for the particular building structure and d is the shortest distance measured in three dimensions, between the transmitter and the receIver.

114

Appendix 3

• Dependence of Parameters with the Mobile Receiver Position

From Figure 6 in Chapter 5 is clear that the angle of arrival can be defined as,

(1)

Taking this expression into account and knowing that is clear the following relation,

(2) the expression for the angle of arrival is,

(3)

Once the angle of arrival is known, the following expressions will relation the distances dr(r) , dIN (r), d R(r) with t9and, subsequently withr,

dr(r)

=

d¹ cos(t9(r»

d (r) w_ _

IN - cos(t9(r» dR(r)

=

d² (4) cos(t9(r»

As it was shown in Table 1 in Chapter 5, the frequencyused in the study is 2000 MHz; taking into account the relation between the frequency and the

wavelength,

115

Appendixes: Appendix 3

A

= - =

c 0.15 metres

f

⁽⁵⁾

and knowing the expression for the complex relative permittivity, c_r ^' is clear to deduce,

Cr

=

c-j~^{==c- j60crA}

=

c- j60 x 0.15 x 10-¹² (6)

mCa

As can be seen in equation (6), the second term of the expression will be very small, so it could be neglected. In this case, the simplest form for the complex relative permittivity would be,

(7)

• Matlab Functions

Data File

%Data File for the Program r=-80:0.1:80i %in metres

dl=50i %perpendicular distance between the transmitter and the building in metres

d2=20i %perpendicular distance between the receiver and the building in metres

w=15i %width of the building in metres f=2000i %frequency in MHz

c=300000i %ligth speed in kilometres per second n=4.0i %distance decay rate

epr=5i %dielectric constant sigma=10^A (-12) i %conductivity

Function angle

function ang=angle(r)

%Function which calculates the angle of arrival ang=asin(r./(sqrt(r.^A2+(dl+w+d2) ^{. A}2 ))) ⁱ

Function transmission

function coeff=transmission(theta) i

%Function which calculates the Fresnel transmission coefficient coeff= (2 *cos (theta) ) . / (cos (theta) + (sqrt (epr- ( (sin (theta) ) ) .^A2 ) ) )i

116

Function distance

function [dt,din,dr]=distance(theta)

%Function which calculates the distance between the transmitter and the building, the distance inside the building and the dictance between the building and the receiver

dt=dl./cos(theta) ; din=w./cos(theta) ; dr=d2./cos(theta) ;

Function Losses

function attdbr=losses;

%Function which calculates the path loss over the free-space losses for a given distance between the transmitter and the receiver

datos %data file

theta=angle(r) ;%angle of arrival

[dt,din,dr] =distance (theta) ; %distance from the transmitter to the building, distance inside the building and distance from the building to the receiver

coeff=transmission(theta) %Fresnel transmission coefficient att= (( ((4*pi *f) Ic) . A2 ) . * (dt. A2 ) . * (( (din+dt) . Idt) . An) . * (( (dr+dt+

din) .I (dt+din)) . A2 )) .1((coeff. A2 ). * (coeff. A2 )); %total losses between the transmitter and the receiver

free= (( (4*pi*f) Ic) . A2 ) . * ((dt+din+dr) . A2 ); %free-space losses freedb=lO*loglO(free); %free-space losses in decibels

attdb=lO*loglO(att); %total losses in decibels

attdbr=attdb-freedb; %difference between total and free-space losses

plot(r,attdbr)

title('Path loss variation with mobile receiver position including penetration losses');

xlabel('mobile receiver position (in metres) ');

ylabel ('path loss over free-space loss (in decibels) ');

117

PenetmtiO/l andTmn£mi~£iQna/UHFRadio Wave£ into/through Buildings-a Literature Review

Bibliography

[1] L.P. Rice, "Radio Transmission into buildings at 35 and 150 MHz", The Bell System Technical Journal,vol. 38, n° 1, pp. 197-210, 1959

[2] W. J. Tanis, II and G. J. Pilato, "Building penetration characteristics of 880 MHz and 1922 MHz radio waves", IEEE 43^rd Veh. Technol. Conf Person. Comm.-Freedom through wireless technology, pp. 206-209, 1993

[3] J. M. Durante, "Building penetration loss at 900 MHz ", IEEE Proc. Veh. Techno!.

Conf, pp. 1-7, 1973

[4] A. F. De Toledo andA. M. D. Turkmani, "Propagation into and within buildings at 900, 1800 and 2300 MHz", IEEE Veh. Technol. Conf Digest, pp.633-636, May 1992

[5] A. F. De Toledo andA. M. D. Turkmani, "Radio transmission at 1800 MHz into, and within, multistory buildings", lEE Proc. Part I, vol. 138, nO 6, pp. 577-584, Dec. 1991

[6] ^A.Davidson and C. Hill, "Measurement of building penetration into medium buildings at 900 and 1500 Mhz', IEEE Trans. Veh. Techno!., vol. 46, Iss: 1, pp.

161-8,1997

[7] P.1. Wells and P. V. Tryor, "The attenuation oflJHF radio signals by houses", IEEE Trans. Veh. Technol.,vol. 26, nO 4, pp. 358-362, 1977

[8] J. D. Parsons, "The mobile radio propagation channel", Pentech Press, pp.190-194, 1992

[9] J. D. Parsons and J. G. Gardiner, "Mobile communication systems", Blackie &-Sons,pp. 72-75,1989

[10] E. H. Walker, "Penetration of radio signals into buildings in the cellular

environment", The Bell System Technical Journal, vol. 62, nO 9, PartI,pp. 2719-2734, Nov. 1983

119

[11] D. C. Cox, R. R. Murray and A. W. Norris, "Measurement of 800-MHz radio transmission into building with metallic walls", The Bell System Technical Journal, vol. 62, pp. 2695-2717, 1983

[12] D. C. Cox, R. R. Murray and A. W. Norris, "800 MHz attenuation measured in and around suburban houses",AT&T Technical Journal, vol. 63, pp. 921-954, 1984

[13] J. Horikoshi,K. Tanaka and T. Morinaga, "1.2 GHz band wave propagation measurements in concrete building for indoor radio communications ", IEEE Trans. Veh. Techno!., vol. 35, n° 4, pp. 146-152, 1986

[14] A. F. De Toledo, A. M. D. Turkmani and 1. D. Parsons, "Estimating coverage of radio transmission into and within buildings at 900, 1800 and 2300 MHz",IEEE Pers. Comm., vol. 5, Iss: 2, pp. 40-47, April 1998

[15] D.M.J. Devasirvatham, "Time delay spread measurements of 850 MHz radio waves in building environments",IEEE Global Comm. ConI Rec.,

GLOBECOM'85, vol. 2, pp. 970-973, Dec. 1985

[16] A. M. D. Turkmani, J. D. Parsons and D. G. Lewis, "Radio propagation into buildings at 441,900 and 1400 MHz",Proc. 4^th Int. ConI Land Mobile Radio, Warwick, !ERE Conf. Publ., 1987

[17] A. M. D. Turkmani, 1. D. Parsons and D. G. Lewis, "Measurement of building penetration loss on radio signlas at 441,900 and 1400 MHz",IERE Journal, vol.

58,no6,pp. S169-S174, 1988

[18] H. H. Hoffman and D. C. Cox, "Attenuation of900 MHz radio waves

propagating into a metal building",IEEE Trans. Antennas Propagat., vol. 30, n°

4,pp. 808-811, 1982

[19] P. J. Barry and A. G. Williamson, "Statistical model for UHF radio-wave signals within externally illuminated multistorey buildings ", lEE Proc. Part I, vol. 138, n04,pp.307-318,Aug.1991

[20] A. M. D. Turkmani andA. F. De Toledo, "Modelling of radio transmissions into and within multistorey buildings at 900, 1800 and 2300 MHz",lEE Proc. Part I, vol. 140, n° 6, pp. 462-470, Dec. 1993

[21] C. J. Haslett and D. A. Jacklin, "Site shielding reduction due to transmission through buildings in a city centre environment",lEE ConI Antennas &

Propagat., pp. 37-41, April 1995

120

Penetration and TranvmivvionofUHF Radio Wavev into/through Buildillgv a Uterature Review

[22] C. J. Haslett, "The transmission of microwaves through buildings",Progress in Electromag. Res. Symp., The Netherlands 1994

[23] H. Hashemi, "The indoor radio propagation channel",IEEE Proc., vol. 81, nO 7, pp. 943-968, July 1993

[24] A. A. M. Saleh and R. A. Valenzuela, "A statistical model for indoor multipath propagation",IEEE Select. Areas Comm. Journal, vol. SAC-5, nO 2, pp. 128-137, Feb. 1987

[25] S. ^Y. Seidel and T. S. Rappaport, "914 MHz path loss prediction models for indoor wireless communications in multifloored buildings",IEEE Trans.

Antennas and Propagat., vol. 40, nO 2, pp. 207-217, Feb. 1992

[26] F. C. Owen andC. D. Pudney, "In-building propagation at 900 MHz and 1650 MHz for digital cordless telephones", 6^th Int. Con!Antennas & Propagat., ICAP'89, Part 2: Propagation, pp. 276-280,1989

[27] S.1. Patsiokas, B. K. Johnson and J. L. Dailing, "Propagation of radio signals inside buildings at 150,450 and 850 MHz", IEEE 36^th Veh. Technol. Conf, pp.

66-71, May 1986

[28] D.MJ. Devasirvatham, "A comparison of time delay spread and signal level measurements within two dissimilar office buildings",IEEE Trans. Antennas and Propagat., vol. 35, nO 3, pp. 319-324, 1987

[29] T. S. Rappaport, "Wireless communications. Principles and practice",Prentice Hall PTR, Upper Saddle River, New Yersey, pp. 123-133, 1996

[30] T. S. Rappaport, "The wireless revolution", IEEE Comm. Magazine, pp. 52-71, Nov. 1991

[31] H. W. Arnold, R. R. Murray and D. C. Cox, "815 MHz attenuation measured within two commercial buildings",IEEE Trans. Antennas and Propagat., vol.

37, nO 10, pp. 1335-1339, Oct. 1989

[32] D.MJ. Devasirvatham, M. J. Krain and D. A. Rappaport, "Radio propagation measurements at 850 MHz, 1.7 GHz and 4.0 GHz inside two dissimilar office buildings", Electr. Letters, vol. 26, nO 7, pp. 445-447, March 1990

[33] K. Pahlavan, R. Ganesh and T. Hotaling, "Multipath propagation measurements on manufacturing floors at 910 MHz",Electr. Letters, vol. 25, nO 3, pp. 225-227, Feb. 1989

121

[34] D.M.J. Devasirvatham, C. Banerjee,R. R. Murray and D. A. Rappaport, "Four-frequency radiowave propagation measurements on the indoor environment in a large metropolitan commercial building",IEEE Global Comm. Con! Rec., GLOBECOM'91, Phoenix, AZ, pp. 1282-1286, Dec. 1991

[35] S. E. Alexander, "Radio propagation within buildings at 900 MHz",Electr.

Letters,vol. 18, pp. 913-914, 1982

[36] 1. M. Keenan andA. J. Motley, "Radio coverage in buildings ", British Telecom.

Technol. Journal, vol. 8, nO 1, Jan. 1990

[37] 1. H. Tamg and D. W. Pemg, "Modelling and measurement of UHF radio propagating through floors in a mu1tifloored building", lEE Proc. Microw.

Antennas and Propagat.,vol. 144, nO 5, pp. 359-363, Oct. 1997

[38] S. Y. Seidel andT. S. Rappaport, "Site-specific propagation prediction for wireless in-building personal communication system design",IEEE Trans. Veh.

Technol., vol. 43, nO 4, pp. 879-891, Nov. 1994

[39] G. A. 1. van Dooren, "A deterministic approach to the modelling of electromagnetic wave propagation in urban environments", Ph. D. Thesis, Eindhoven University of Technology, The Netherlands, 1994

[40] P. Nobles and F. Ha1sall, "Delay spread and received power measurements within a building at 2 GHz, 5 GHz and 17 GHz",lEE

Id

^h Int. Con! Antennas &

Propagat., ConfPubl. 436, Part 2: Propagation, pp. 319-324, Apri11997 [41] 1.- F. Lafortune and M. Lecours, "Measurement and modelling of propagation

losses in a building at 900 MHz",IEEE Trans. Veh. Technol., vol. 39, nO 2, pp.

101-108, May 1990

[42] Y. L. C. de Jong, M. H. A. 1. Herben, 1.-F. Wagen and A. Mawira,

"Transmission of UHF radiowaves through buildings in urban cellular environments",Electr. Letters,vol. 35, nO 9, pp. 743-745, Apri11999

[43] Y. L. C. de Jong, "High-resolution time de1ay/ang1e-of-arriva1 measurements in microcellu1ar environments",Final Report Intership at Swisscom Corp.

Technol., June-Oct. 1998

[44] K. Rizk, J.-F. Wagen and F. Gardio1, "Two-dimensional ray tracing modelling for propagation prediction in microcellu1ar environments",IEEE Trans. Veh.

Technol., vol. 46, pp. 508-517

[45] K. Rizk, "Propagation in microcellu1ar and small cell urban environment",Ph. D.

Thesis, Ecole Po1ytechnique Federa1e de Lausanne, Lausanne, Switzerland, 1997

122

Penetration and Tran£mi££ion ofUHF Radio Waves into/through Buifdings-a Literature Review

In document Penetration and transmission of UHF radio waves into/through buildings a literature review (Page 97-111)