Rain attenuation problems affecting the performance microwave communication systems

pp. 437-451 4 3 7

John D. KANELLOPOULOS * Stelios G. KOUKOULAS * Nicolaos J. KOLLIOPOULOS * Christos N. CAPSALIS * Spyros G. VENTOURAS *

of

Rain attenuation problems affecting the performance

microwave communication systems

Abstract

Rain attenuation is considered to be a dominant factor affecting the reliability of both terrestrial and earth- to-satellite paths operating at frequencies above 10 GHz. The subject of the present paper is the development of some efficient models for the prediction of the operational characteristics (such as the path enlargement factor, accumulation thermal noise, site diversity improvement) of microwave systems operating at these frequencies. The numerical results taken from the present models have been compared with available experimental data from operated links in USA, Europe, Japan and the agreement has been found to be quite encouraging.

Key words : Radiocommunication, Microwave, Radio relay link, Space diversity, Rain, Earth satellite propagation.

Etats-Unis d'Am~rique, en Europe et au Japon montre une assez bonne concordance.

Mots el~s : Radiocommunication, Hyperfr~quence, Faisceau hert- zien, Diversit6 spatiale, Pluie, Propagation Terre satellite.

Contents

I. Introduction. II. Study of the performance

of the microwave multirelay systems. III. Study of the performance of a microwave satellite

system. IV. Conclusion. References (25 ref.).

PROBLI~MES LI~S AUX AFFAIBLISSEMENTS DUS A, LA PLUIE

AFFECTANT LES PERFORMANCES DES SYSTI~MES DE RADIOCOMMUNICATION

EN HYPERFRI~QUENCES

R~sum~

L'affaiblissement da dt la pluie est consid~r~ comme un facteur d~terminant de la jiabiliM des liaisons radio- ~lectriques terrestres et par satellite pour des frdquences sup~rieures ~ 10 GHz. Cet article traite des moddles efficaces dans la pr~vision des caracMristiques de fonc- tionnement des systdmes de radiocommunication hyperfr~quences. La comparaison des r~sultats th~oriques obtenus gz partir de ces moddles avec les donn~es exp~ri- mentales obtenues ~ partir des liaisons fonctionnant aux

I. INTRODUCTION

Rain attenuation is a major factor limiting the reliability of both terrestrial and earth-to-satellite paths operating at frequencies above 10 GHz. Some problems dealing with the study of the performance of microwave systems working at these frequencies are treated here.

First, the performance of the terrestrial digital radio- relay systems is analysed. In this vein, the route diversity technique has been considered as one of the available means for reducing the rain outage time and constructing an economical circuit. Some models dealing with the prediction of the outage performance of a route diversity system have been proposed [1, 2]. Most recently, a general predictive analysis for the same matter, valid for any location and frequency, has also been presented [3]. The whole analysis has exclusively been based on the

* Department of Electrical Engineering, National Technical University of Athens, 42 Patission Street, Athens, GR-10682 Greece.

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438 J. D. KANELLOPOULOS. - RAIN ATTENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS

convective raincell model for the spatial structure of the rainfall medium. An alternative approach is presented here. According to the present methodology, the idea of a global spatial rainrate profile adopted for the evaluation of the single hop attenuation [4] is combined with the calculation of path correlation coefficient, based either on the convective raincell model [5] or on possible experimental data in the specific region [2]. Numerical results using the present analysis are compared with experimental data of this kind taken from an operated multi-relay system located, in Tokyo, Japan.

The second part of the paper is dealing with the analysis of the performance of a multi-relay communication system including unregenerating type repeaters such as an analog or a hybrid transmission system using analog and digital signals. A theoretical model for the prediction of the noise distribution has recently been proposed [6], using appropriate data for the rainfall statistics together with the geometrical and electrical characteristics of the system. An extension of the previous predictive analysis is presented here, employing correlated variables for the modelling of the single hop attenuations.

In the next section of the paper, analysis of the microwave satellite communication systems is presented. The first task in this area is concerned with the consideration of an effective method for the prediction of the rain attenuation in satellite radio links, satisfying the features established in 1982 by the ccm [7]. The proposed method is an extension of that suggested most recently for terrestrial links [8], and it is tested over 62 satellite links placed in Europe, the USA and Japan. Comparisons with the ccm method are also given [9].

The subject of the last part of the paper is referring to the application of the simple site diversity technique to reduce the outage time due to rain attenuation for a satellite system. The latter technique is well known and involves the deployment of two spatially separated, but interconnected, earth terminals to provide alternate propagation paths, with the capability of switching to the least impaired path as required. The attention in the present work will be focused in the analysis of the prediction of the improvement in using dual-site diversity techniques. A general model dealing with the diversity effect in satellite communication systems was first proposed by Morita and Higuti [10]. An improvement of the Morita and Higuti method is proposed here.

Numerical results using the present predictive analysis are compared with experimental data taken from operated site diversity links. The agreement has been found to be quite encouraging.

II. STUDY OF THE PERFORMANCE OF THE MICROWAVE

MULTIRELAY SYSTEMS

The configuration of the line-of-sight microwave systems considered here is the same as that shown in

0.1

0.01%

joint probability of attenuation (%)

(5) I..d=22,9 km " - ~ ~

o experiment (!.-u=4 km) x experiment (Ld=9.1 kin)

path separation (km) 20

5

-2 1

l~c. 1. - - Joint attenuation probability versus separation for various hop lengths, using single hop probability as parameter (location Japan,

f : 20 GHz).

Probabilitd d'affaiblissement conjointe en fonction de la sdpara- tion des itin~raires pour diffdrentes longueurs des bonds, en utili- sant comme paramdtre la probabiliM de bond unique (localisation :

Japon ; f : 20 GHz).

Figure 1 in [3]. More complicated route diversity systems require the knowledge of joint attenuation probabilities of higher complexity, and this kind of information is not presently available. For the proceeding analysis some assumptions should be taken into account.

(a) All the repeaters are assumed to be equal and equally spaced.

(b) The climatological properties of rain are assumed to be uniform over the region crossed by the multirelay system.

(c) The specific rain attenuation (in dB/km) is considered to be given by the following expression :

(1) Ao(dB/km) = aRb(mm/h), where R is the rainrate (mm/h) and the constants a and b depend upon frequency, incident polarization and temperature. Their values can be taken from the recent revised report of ccm [11].

(d) The unconditional lognormal form for the repre- sentation of the long-term point rainfall rate R and path attenuation distribution A and in extension, the bi-variate unconditional log-normal distribution for rain attenuation in two paths are adopted, for a certain range of values of R and A. The above assumption for the distribution of R and A has first been employed by Lin [5] but for the conditional case. A motivation for using

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J. D. KANELLOPOULOS. - RAIN ATrENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS 439

the unconditional forms is given in [3]. Further, the log- normal form has been selected due to its very wide use to represent the rainfall rate and attenuation cumulative distributions throughout the world. In addition, the mul- tivariate analysis for the log-normal form is well established and can easily be applied to the particular problems treated here.

The analysis of the performance of microwave multirelay systems can further be divided into two parts. The first part is concerned with the digital systems whereas the other part is associated with multirelay systems using unregenerating type repeaters.

II.1. Outage performance of a digital multirelay system.

In this case, the overall outage probability for a single tandem system due to rain attenuation can be expressed as [12] :

M

(2) MPT = E ( - 1 ) i+1 MPi(x), i = 1

where MPi(x) is the sum of probabilities that rain attenuation simultaneously exceeds x dB on each of links, which contain the all possible combinations of i links from the M relay links. Sasaki et aL [12] using experimental data from tandem links located in Japan, have proposed the following approximate expression :

(3) MPT = MPx(x) - (M - 1)P2(x),

where Pl(x) is the probability that rain attenuation exceeds x dB on a single link and P2(x) represents the joint exceedance attenuation probability on two adjacent links of the system. For frequencies not much exceeding l0 GHz, Drufuca and Torlaschi [1] have indicated that' P2(x) << Pl(x) and so expression (3) gives :

(4) MPT = M P i ( x ) .

The simplified proportional value of MPT(X) gives an overestimation of outage probability which can approximately be used for this frequency range.

Further, the overall outage probability for a twin route diversity system can approximately be given by [3] :

M

(5) 2NPd = E Pi,, = MP1,2. i = 1

Where P1,2 is the joint exceedance probability for a pair of opposite hops of the route diversity system. As has been pointed out by Drufuca and Torlaschi [1] and recently by Sasald and Nagamune [2], expression (5) is an upperbound of the overall outage probability for the diversity system.

In this section of the paper the main topic of the analysis is concerned with the evaluation of the joint probability P1,2 in terms of the parameters of the rainfall distribution along the propagation path and the main characteristics of the spatial structure of the rainfall medium. An analysis of the probability/91,2 based entirely

on the convective raincell model has been published in [3]. A more flexible approach is treated here.

II.1.1. Evaluation of the joint probability P1 ,2 .

According to the present methodology, the idea of a global spatial rainrate profile adopted for the evaluation of the single hop attenuation [4] is combined with the calculation of path correlation coefficient p, based either on the convective raincell model [5] or on possible experimental data in the specific region [2]. Following the spatial rainrate profile, the single hop attenuation, can be evaluated as :

(6) A = a R b L , for R o < 1 0 m m / h ,

1 - exp ( - T b l n ( 1 ~ ) L ) = aR b

7bln ( 1 ~ )

for Ro > 10 mm/h,

where L is the hop length, R0 is the rainfall rate referred to the z = 0 end of the path and 7 is a parameter controlling the rate of the decay of the profile [4].

As a direct result of expression (6), the single hop attenuation probability can be calculated as :

(7)

PI(X) = P ( A > x) = P(Ro _> rz) = ~ erfc

where : In rx - in Rm

( 8 ) = , s r

Rm, Sr are the statistical parameters of the unconditional log-normal distribution of R and rx can be derived by means of the transcendental equation :

(9) x = a r ~ L , for x < X 0 ,

a - e x p ( - T b l n ( r x ) ) x = ar b -~ L ,

7bln (~0 )

for x > Xo,

and

(10) Xo = alObL.

In the same way, the joint probability P1,2 can be given by :

(11) P1,2(x) = P(A1 >_ x, A2 >_ x)

= P(R1 >_ rx, R2 >_ rz)

= f/zlR2 (rl, r2) drldr2, x x

where A1, A2 are the corresponding attenuations in two opposite hops of the diversity system, x is the exceeded value of attenuation and R1, R2 are the rainfall rates referred to the z = 0 ends of the two paths. Further, according to assumption (d), fR1 R2 (rl, r2) is considered

3/15 ANN. "I~.~COMMUN., 45, n ~ 7-8, 1990


to be the joint log-normal density function of R~, R2 given by :

1 (12) fRIR2(TI,T2):

- p 0T r2

exp - 2 ( 1 - p2o)" S~ +

lnr2 - In Rm 2 57 ) - 2pno( lnr l - lnRm)( lnr2-1nRm)]}

S ~ "

In the previous expression Pn0 is the correlation coefficient between the normal variables In R1 and In R2. Following now a straight forward statistical analysis, we can obtain. (For more details, one is referred to [3].)

1 f ~ 1 (13) P1,2(x)= ~ o v f ~

e -~'~/2 erfc uo - pnoul dul. - On0)

The next step is the evaluation of the correlation coefficient Pno in terms of the path correlation coefficient p between attenuations A1 and A2.

As mentioned before, several considerations have been proposed so far, dealing with the calculation of the path correlation coefficient p.

Adopting the convective raincell model, p can be formulated as :

(14) p = H2/H1,

where the H1, /-/2 are given by (see also ref. [3]).

/?/? (15) n l = px(dn,) dlldl~,

/?/? (16) H2 = pl(d12) dlldl2,

and

(21)

and

(22)

with

(23)

and Higuti [13] have proposed the following negative exponential semi-empirical expression for pl :

(20) Pl = exp(-av/-d),

where a is a constant ranging from 0.2 to 0.3 km -1/2. Taking into account expressions (19), (20) the analy-

tical forms for H1 and//2 have been evaluated and they are presented in [3] where the same problem has been treated, based entirely on the convective raincell model.

In an alternative way, the correlation coefficient p has experimentally been determined in the specific area of Tokyo [2]. The following semi-empirical expression for p has been proposed,

p = exp[-0.09L~ for0 < S < $1,

p = 0.38L ~ forS > $1,

$1 = v/L--S(0"967 - 0.168 lnLd)

0.09

Coming back to the calculation of the correlation coefficient Pno in expression (12), the following integral equation can be derived, as a direct consequence of the definition of p :

(24) E[A1A2] - pvar[A1] - (E[A1]) 2 = 0,

where :

( 2 5 )

E[AIA2] = A1A2fRI R~ (rl , r2, P,~O) drldr2,

and :

f0 ~ (26) E[A1] = AlfR1 (rl) dr1,

/J (27) E[A 21 -- A~fRI (rl) dr1.

(17) dll, --- Ill - l~l,

(18) d12 ~- (S 2 5w (/1 - 12)2) 1/2.

As it is obvious the H1, H2 are functions of path separation S, hop length of the diversity system Ld and depend also on the spatial rainfall inhomogeneity. The latter is characterized by the spatial correlation coefficient Pl of attenuation gradient A0 between two points of the rain medium. More particularly, for locations in Europe and North America the coefficient Pl can be considered to be given by the following semi-empirical expression [5] :

G (19) pl [A0(z), A0(z')] - (G 2 + d2)1/2,

where d = [z - z'[ is the distance between the two particular points, z, z' and G is a characteristic distance in kilometers ranging from 0.75 to 3 km.

On the other hand, for locations in Japan, Morita

In the above expressions fRl(rl) is the log-normal density function [14] for the point rainfall rate and the single hop attenuations A1, A2 are given by expression (6).

The final step of the predictive procedure is the calculation of the integral in expression (13), which can be carried out by using efficient numerical techniques such as Gaussian quadratures. As a consequence of the above analysis, a compact algorithm for the evaluation of the operational characteristics of the route diversity system such as the path enlargement factor, can be developed.

II.1.2. Prediction of the path enlargement factor.

The path enlargement effect can be defined as the fact that the hop length of a diversity system can be increased compared to the corresponding one of a tandem system operating at the same outage performance conditions. This leads to a more economical design of the diversity

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J. D. KANELLOPOULOS. - RAIN ATTENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS 441

system by using a smaller number of repeaters, or by preserving the hop length, using the same number but lower quality repeaters [2].

Strictly speaking, the hop enlargement factor Fd can be defined as :

Ld (28) Fd = ~w > 1,

where LT and La are the lengths of the tandem and diversity hops respectively.

Following the same steps as in the corresponding case of the predictive model based on the convective raincells [3], a compact algorithm for the calculation of the enlargement factor Fd Can be constructed.

More particularly, the rain outage probability P1 for the single hop of the tandem system can be obtained as :

(29) P1 = p0LT,

where Po is some imposed value for the outage probability per unit length for the tandem or diversity system and LT is a logical value for the tandem hop length.

Considering now the unconditional log-normal form for the attenuation probability distribution of the single hop :

1 (U0T ~ (30) P1 = ~ erfc k ~ ) '

the outage level u0w can be obtained. Combining now expressions (8) and (9), the corresponding attenuation level XT is derived. Further, using the definition of the margin Ms of both (tandem and diversity systems) which is a measure of repeater quality [15], we have :

(31) Ms = X T -~- 201og10 LT = Xd "1- 20log10 Ld,

and as result, the attenuation level Xd exceeded in the single hop of the diversity system can be found, as :

(32) X d • X T - 20 loglo Fd,

multirelay system located in Japan. More particularly, the experimental data has been taken by Sasaki and Nagamune [2] and refers to a set of 13 tandem links between the Musashino electrical communication labo- ratory (Musashino, ECL) and the Yokosnka ECL located near Tokyo, using vertically polarised, 19.9 GHz waves. As has been pointed out by Sasaki and Nagamune [2] only data corresponding to about two and a half years from May 1975 to September 1977 has been presented.

The first step for the development of the present algorithm is the appropriate estimation of the parameters Rm, Sr of the point rainfall distribution. This pair of parameters can be evaluated by using the experimental rainfall rate distribution in the Tokyo bay area [16]. The parameters a and b encountered in the previous expressions can be estimated by using the recent revised report of ccm [11], Further, the numerical value ~/ = 1/14 has been taken, as suggested by Stutzman and Dishman [4].

In Figure 1, the joint probability P12(x) of rain attenuation in a pair of opposite hops has been drawn for various values of path separation S and hop length Ld, using the single-hop attenuation probability as a parameter.

The predictive results for the PI,Z based entirely on the convective raincell model, have been published elsewhere [3]. In the present work, the semi-empirical model for p based on experimental data in Tokyo bay area (expressions (21)-(23)) has been employed. The comparison between numerical and experimental results is quite good although at the lower single hop attenuation probabilities some significant discrepancies exist. A reasonable explanation may be due to the very limited period of the existing experimental data and this leads, for such small probabilities, to unreliable conclusions.

for each value of the factor Fd. Next, the joint exceedance probability P1,2 of attenua-

tion on a pair of opposite hops of the diversity system, is given by :

I f oo 1 (33) P1,2=FdP1 = ~ Od Y ~

e -u~/2 erfc U0d _- p~oul ] dul, /2(1 - p .o) J

and : In rxd - In Rm

(34) U0d = Sr

Where rzd is the solution of the transcendental equation (9) setting Xd in the place of X. Expression (33) is an integral equation used for the numerical evaluation of the correlation coefficient P,~0. Using further equation (24), one is able to obtain the corresponding path correlation coefficient p, or equivalently the path separation distance S.

Numerical results using the predictive procedure are given in comparison with data taken from an operated

11.2. Accumulation of thermal noise in a multirelay system using unregenerating type repeaters.

The analysis pertaining to the prediction of the accumulated thermal noise NM refers to the line-of-sight microwave system consisting of M repeaters connected in tandem. The definition of all the parameters appearing in this section can be found in [6], where NM was analyzed under the assumption of statistical independence among the single hop attenuation variables. In this work, the basic assumption that the attenuations of the different hops are correlated, is employed. Following the assumptions, explained analytically in [6], the propagation losses Xi(i = 1, 2 , . . . , M) will be considered to have a truncated log/log-normal distribution form taking values in the closed region [1,Xh]. In the same vein, the nor- malized propagation loss gl defined as the arithmetical mean of Xi, will also have a similar truncation distribution form. The corresponding truncated variables will be denoted as Xt~(i = 1, 2 , . . . , M) and gJt.

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442 J. D. KANELLOPOULOS. - RAIN ATFENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS

11.2.1. Evaluation of the moments of t i t .

The first step of the proposed algorithm requires the evaluation of the central moments of tit- The following relations hold [14] :

(35) /3 u = < t i 2 > - < t i t >2

7u = < ti3 > - 3 < tit 2 > < tit > +2 < t i t > 3

(Sy = < ti4 > - 4 < tit 3 > < tit > +4 < ti2 >

< t i t >2 - 3 < ~ t >4

where flu, 7u, 6u "- are the second, third, fourth etc central moments of the variable tit , while < tit >, < tit 2 >, < tit 3 > ... are the initial moments of the same variable.

Since the individual propagation losses Xt~(i = 1, 2 , . . . , M) have the same statistical distribution, and in conjunction with the definition of tit, the analytical expressions for the above moments up to the third one are presented next.

< tilt > = < Xt >, 1

< tit 2 > = M---- 5

M < X~ > + E ( M + 1 - i ) < X t ~ , X t ~ > , i=2

1 (36) < ti~ > = M------ 5

M < Xt a > + 6 E ( M + 1 - i ) < Xt2~,Xt, > + i=2

/*

6 E [ M - 2 ( i - 1)] < X t , , X t , , X t , > + i=2

/.d M }

12 E E ( M + I - i ) < X t l , X t ~ , X t , > , j = 2 i=23

where v = 2 i - 1 , and # = #~ = M/2 i f M is an even number and # = (M + 1)/2, #' = (M - 1)/2 if M is an odd number. Due to the complexity in the formulation and computation of the higher moments of tit, the proposed algorithm has been developed in such a way, that initial moments of the variable tit up to the third order, are only required.

Using now the Jacobian transformations and the multidimensional normal distributions, the joint density functions Px, x~ (xi, xj) and Px, x~x~ (x~, xj , Xk), which are required for the calculation of the moments of q t , can be obtained. The above density functions are expressed in terms of the statistical parameters m, a and pnij(i , j = 1, 2 , . . . , M, i ~ j). More particularly, m is the mean value and a the standard deviation of the variable In Ai(i = 1, 2 , . . . , M), where Ai is the attenuation of the i th hop. Additionally, pnij (i # j ) denotes the correlation coefficient between a pair of normal variables lnA~, l n A j ( i , j = 1 , 2 , . . . , M , i # j).

All these parameters depend upon the characteristics of the rainfall medium. As far as the description of the spatial rainfall structure is concerned, the model of convective raincells is adopted. Consideration of

the same problem by using a global spatial rainrate profile for the calculation of the single hop attenuation combined with possible experimental data for the path correlation coefficient, will be examined in a future work.

An expression is now established relating the Pnij in terms of pij, where Pij is the path correlation coefficient between any two log-normal attenuation variables Ai and Aj. This expression has been given by Morita and Higuti [10] as an intermediate step for the analysis of the prediction of the site diversity improvement for an earth-space system. According to this formulation, we have :

1 ln[1 +p~j(e ~ (37) Pni3 = a-- 5 - 1)].

The coefficient Pij is given by the following equation :

(38) PiJ" = H1

where H1 is formulated by using expression (15) and Hij can be expressed in integral form as (see Fig. 1 in [6]) :

(39) Hij = [Jo pl(dij) d/ld/2,

where :

(40) dij -- S~ + Ilu - ll h

Sij zx li _ j] L is the distance between the mid-points of the arbitrary hops i and j of the multi-relay system. Taking into account the semi-empirical form (19), an analytical expression for Hi is given in [5], whereas Hij can be obtained as :

(41) Hij = G2[(L/G)t s inh - l (L t /G)+

(L/G)( t - 2) sinh - l [ ( L / c ) ( t - 2)I-

2 ( L / G ) ( t - 1) s i n h - l [ ( L / G ) ( t - 1)]-

v/(L/G):t 2 + 1-

x/(L/G)2(t - 2) 2 + 1 + 2v/(L/G)2(t - 1) 2 + 11,

where the index t is defined by :

(42) t ~ li - J] + 1.

In the same way, analytical expressions for the parameters ra and a based on the formulation (19) for Pl and appropriate data for the point rainfall rate distribution, are presented in [6].

On the other hand, for regions in Japan (formulation (20) for Pl), the integrals H1 and H~j can be derived as �9

4 (43) Hi =

[ 2L - + 2(3 + 3 ,/Z + 2L)

H# = 4{r - L) ] -

202(cz2S,#) + r + L)]},

ANN. ~ O M M O N . , 45, n ~ 7-8, 1990 6/15

J. D. KANELLOPOULOS. - RAIN ATTENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS 443

where :

(44) #~2(x) = (x + 3x /x+ 3 ) e x p ( - v ~ ) ,

and the single hop parameters m, a are evaluated in this case, by substituting//1 from the first of (43) into equations (6), (7) in [6].

The evaluation of the central moments of the variable ~t given in expression (35) can now be proceed by substituting the appropriate density functions Px (x), Px, x~ (xi, xj), Px, x~xk (xi, xj, xk), expressed in terms of m, a and Pnij, into (36). In tum, the integrals encountered there, are computed by using efficient numerical techniques such as Gauss-Legendre quadratures.

II.2.2. Calculation of the exceedance probability of the thermal noise power.

A logical assumption is made concerning the particular type of the statistical distribution of the variable ~t . As a result of a computer simulation program and using appropriate statistical tests the distribution of ~t has also been approximated by a truncated log log-normal form. The next step is the effective estimation of the statistical parameters of �9 in terms of the central moments of the truncated variable ~t which have been computed in the previous section. For this reason, an effective algorithm has been developed and presented elsewhere [6]. The algorithm is also applicable here. The above parameters then are used to evaluate the statistical distribution of and in turn that of NM [6].

The results obtained by this procedure are compared with those obtained under the assumption of statistical independence among the attenuation variables as well as the available experimental data [6], for various exceedance probabilities (Fig. 2 and 3).

24_accumulated thermal noise (dB)

experimental . . . . . . . . distribution sum

u ncorrelated 20 correlated (Lin)

correlated (Morita-Higuti)

16

- . . / .>-/. , 7 , . # / / /

12- / , / . , , - " ~

,~./>/. . . . .- .,~/~ . . ."

,"7_.-"" / , , " 1 % exceedance

/ , " probability level o

i ~ i i ' l

2 ;* ; ; ' lo 1'2 number of links

FIG. 2. - - Accumulated thermal noise (in dB) versus the number of links, at the 1% exceedance probability level.

Bruit thermique accumuM (en dB) en fonction du nombre de liaisons, au niveau de probabilitd de ddpassement de 1%,

accumulated thermal noise (dB) '61 p /

44 / "/~,.

42 ] / / ~ ~

4ol ,,,.~" S~.~ ~ J I / . . y X / / ';"// I , / ' / . / /

30-~ ' / . . . . . . . . distribution sum r / . . . . . . . unco!rela!ed , 28_1 / . . . . . correlated (Lin) r . . . . . . . . correlated (Morita-Higuti)

2 4 6 8 10 12 number of links

FIG. 3. - - Accumulated thermal noise (in dB) versus the number of links, at the 0.01% exceedance probability level.

Bruit thermique accumuld (en dB) en fonction du hombre de liaisons, au niveau de probabilitd de d~passement de 0,01%.

As a general conclusion, the numerical results derived by using the present theory are generally closer to the experimental data than the predicted ones corresponding to the model of uncorrelated attenuation variables. This kind of agreement occurs with the results derived by using the Morita-Higuti [13] model for the rainfall spatial structure for at least up the probability level 10-2%. Due to the lack of data, no comparison can be made for levels beyond 10-2%, although some discrepancy can exist because rainfall rate in Japan follows a log-normal behaviour for low and mean rainrate and gamma behaviour for higher values.

The same kind of agreement does not occur however with the results corresponding to the model suggested by expression (19) for the rainfall spatial correlation. This is quite expectable because the latter model has mainly been based on measurements taken from a Florida net- work. As a matter of fact, it is not appropriate to describe the rainfall spatial structure in the whole Japan area.

III. STUDY O F THE PERFORMANCE

OF A MICROWAVE SATELLITE SYSTEM

The configuration of a satellite communication system using one or two earth stations is shown in Figures 4a and 4b respectively. In this latter configuration known as site diversity technique, $12 is the separation of the two earth stations, D is their horizontal separation whereas for both cases Oi(i = 1, 2) is the corresponding elevation angle. Generally, D < $12 except when the

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A A A J, D. KANELLOPOULOS. - RAIN ATTENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS

Ls ,' TH / ~tation~ )0 i __~ _

I S

to satellite

/ a )

to satellite

(b)

/', / $12 / I D / I/I / d , 2 1

(c)

FIG. 4.

(a) Configuration of an earth space system. (b) Diversity configuration between earth stations (1) and (2). (e) Definition of the variables 11, /2, $12, D, K12 appearing in

expressions (67)-(69).

(a) Configuration d'un systdme Terre-espace. (b) Configuration en diversitd entre les stations terriennes (I) et

(2). (c) D~finition des variables 11, 12, $12, D, K12 apparaissant dans

les expressions (67)-(69).

baseline is perpendicular to the satellite azimuth. For the further analysis, some considerations should be taken into account.

(a) The climatological properties of rain are assumed to be uniform over the region crossed by the earth-space paths.

(b) Let H be the long-term average height of the freezing level in the atmosphere, measured in relation to sea level. The effective average length of the earth- satellite path concerning the stations 1 and 2 affected by ~ain is given by [17] :

H - H0~ (45) L s , - - s i n 0 ~ ' i = l ' 2 ' 0~_>10 ~

where Hoi(i = 1, 2) is the corresponding ground elevation measured from the sea level.

Since $12 and D are negligible compared to the earth's radius and to the distance between the stations and the satellite, 01 and 02 are considered to have a common value 0. The 0~ isotherm height varies with latitude and season of the year. According to

the ccm recommendations [17], the height H can be approximated as :

H = 4, 0 < IAI < 36 ~ (46)

= 4 - 0.075(IAI - 36~ IAI > 36 ~

where A is the latitude of the specific location in degrees.

(c) As a result of the previous considerations, attenuation distributions for the two slant paths are taken to be identical.

(d) To clarify the terms involved, the cumulative single-site exceedance probabilities/91, P2 are given by :

(47) P , = P ( A s , _ > x s ) , i = 1 , 2 ,

whereas the joint exceedance attenuation probability for the two slant paths is defined as :

(48) /91,2 = P (A s l >_ xs, As2 >_ xs),

where As, (i = 1, 2) are the rain induced attenuations of the two earth-space paths, and x, is the corresponding outage level (in dB).

In the proceeding analysis, we shall use Crane's simplified considerations [18] for the vertical variation of the rainfall structure. In this way, one is able to obtain tl~e single and joint exceedance probabilities for the above slant paths as :

(49) Pi = P(A~, >_ xs) = P ( A i >_ XD), i = 1,2;

(50) P1,2 = P (As l >_ x~,As2 >_ xs)

= P(A1 >_ XD, A2 >__ XD),

with :

(51) X D --~ X s COS 0 ,

Ai( i = 1,2) is the surface-projected attenuation as calculated for an hypothetical terrestrial link with path length LD ---- Ls cos0 and XD is the corresponding outage level as given by expression (51).

(e) The specific rain attenuation A0 (in dB/krn) is given by the expression (1) as used in the case of the terrestrial microwave systems.

(f) As far as the horizontal variation of the rainfall structure is concerned, the convective raincell model [5, 13] is also adopted in this section (expressions (19) and (2O)).

(g) A simple mathematical model which provides a good description of the global cumulative rainfall rate distribution [19] will be employed for the prediction of the single site attenuation probability. The proposed method can be considered to be an extension of that suggested most recently for the prediction of the single hop attenuation for terrestrial links [8]. On the other hand, the site diversity prediction problem treated in the section III.2. requires the elaboration of bi-variate forms. In this case, the log-normal form is most suitable and has been selected there.

ANN. T~L~COM~., 45, n ~ 7-8, 1990 8/15

J. D. KANELLOPOULOS. - RAIN A'ITENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS 445

III.1. Consideration of the single-site attenuation prediction problem.

According to the above considerations the predictive analysis is concentrated in the calculation of the exceedance probability P(A > XD) referring to the case of an hypothetical terrestrial link. The global method recently suggested for the prediction of the rain attenuation for a single hop of a terrestrial multirelay system can now be used [8]. The main points of this analysis are briefly presented here.

(a) The method is based on the following empirical rainfall-rate distribution model [19] describing the whole cumulative rainfall intensity distribution, as

e -~r r (52) P ( R >_ r) = a~ rb----:--- for r >_ e~(mm/h),

where a~, b~, ur are parameters depending on the in- tegration time of the used raingauge as well as on the geographical characteristics of the location concerned. At it is suggested by Moupfouma [19] the evaluation of the above parameters in a world-wide basis can be obtained by means of the tabulated values R0.01 (mm/h) for the rainfall-rate observed during 0.01 time percentage. Moreover, the parameters at , b~, ur and er should satisfy the relationship :

(53) ar e U~, b,

as a result of the obvious probability law P ( R >_ c,) = 1.

(b) The exceedance attenuation probability is expressed in a manner similar to that used in expression (52) for the point rainrate, as :

e--UAXD (54) P(A >_ XD) = aA X-----~ for XD > CA.

Using the probability law P(A >_ CA) = 1, we also have :

(55) aA = e uAeA ~bA,

(c) Further, the parameters aA, UA and bA are evaluated in terms of the corresponding at, ur, br and the other (geometrical and electrical) characteristics of the link. Using a straightforward statistical analysis, the following transcendental equation for the parameter bA can be obtained :

(56) E(A) -- Ca = e (CbA+D) E bA (C bA § D ) bA-1

F(1 - bA, (CbA § D)CA),

where :

C = 2(CA -- E(A)) var(A) + 2(E(A) - CA)CA § (E(A) - CA) 2 '

and :

In addition :

(58 ) UA = Cba § D.

The lower limit of attenuation CA in expression (54) can be evaluated by means of the relation :

(59) C A = aebr LD,

in terms of the constants a and b given by ccm [l l] and the path length LD of the hypothetical terrestrial link. The parameters E(A) and var(A) encountered in the expressions (57) have the following form :

E(A) = (ba,ub'-baF(b - b,, Urn,) § cb a)LD,

and :

(60) var(A) = (-b2a~u~(b'-b)a2r2(b- b , ,u ,~ , )+ 2bara2 u b`- 2b.

r(2b - b,, u ~ , ) - - b~--b b 2ba~% e~ar (b - b~,c~Ur))L2Dgl.

In the above expressions F(a, x) is the incomplete gamma function. An approximate formula for its numerical evaluation is given in [20]. Further, the factor H1 takes into account the spatial inhomogeneity of the rainfall medium in the horizontal structure. Details for its evaluation have been presented previously.

The prediction model presented in this section has been tested using the method recently suggested by ccm [17]. The testing of the predictive procedure is based on a data bank containing attenuation measurements for each of 62 satellite links located in Japan, USA and Europe. For each percentage of time (from 0.001 to 1.0 percent of the year) for which data is available, the percentage error e~ given by :

Ap - Am (61) ei - Am x 100%,

has been calculated for each of 62 satellite links (with i -- 1 , 2 , . . . , 6 2 ) located in Europe, USA and Japan. Further, the mean (#e), standard deviation (ar and the rms value of the ei values (rms = V/-~e § a 2) have been calculated for each percentage of the time. In the comparison of prediction methods, the best prediction produces the smallest rms value [17]. Some comments concerning the application of the present method are given here.

First, tabulated data for the R0.m values is available for only 31 locations of the whole data bank [19]. In the remaining cases, the R0.01 values have been estimated by using corresponding diagrams [18].

Second, the appropriate lower limit CA, for satellite links with elevation angle less than about 20 ~ (0 < 20 ~ has been taken to be :

(62) CA = avbr LD/500.

(57) D = 2(E(A) - CA) § 2~A

var(A) + 2(E(A) - CA)C A § (E(A) - CA) 2

The present predictive procedure has been compared with the prediction method adopted by CCIR [9]. In Table I, /ze, ere and rms values calculated by using

9/15 ANN. Tt~LI~COMMUN., 45, n ~ 7-8, 1990


TABLE I. - - Mean, standard deviation and rms value for the ccm and the method proposed here as a function of time percentage.

Moyenne, ~cart-type et valeur quadratique moyenne, pour la mdthode du CCIR et la m(thode propos~e duns cet article, en fonction du pourcentage de temps.

Percentage of time (%)

10-3 3.10 -3 10 -2 3.10-2 10-1

/z, 19.43 12.52 9.99 2.83 - 5.28

ae 35.45 27.12 22.17 26.72 34.67

De 40.43 23.87 24.32 26.87 35.07

1 0 - 3 3 .10 - 3 10-2 3.10-2 10-1

/ze 5.23 - 5.05 2.89 4.11 17.82

ae 40.48 27.76 28.06 26.01 37.81

De 40.82 28.22 28.21 26.33 41.8

3.10 -1 1.0

- 24.73 - 25.15

37.19 55.11

44.66 6o.58

3.10 -1 1.0

33.35 63.98

54.58 92.63

63.96 112.25

the present prediction method are compared to those obtained by employing the ccm technique, for various percentages of time.

In Figure 5, the average relative errors for the proposed and the CCIR method have been plotted.

40

0 �84

�9 o %

-4C

1 Present method / / " 2 CCIR method / /

p%

10-3 I0-2 ' 18~ '

FIG. 5. - - Average relative errors in percent against probability level, obtained testing 62 satellite links placed in Europe, Japan and the

USA.

Erreurs relatives moyennes en pourcent en fonction du niveau de probabiliM, obtenues en testant 62 liaisons par satellite en Europe,

au Japon et aux Etats-Unis.

A general inspection of Table I and Figure 5 shows that the present method underestimates the real situation for higher percentages of time whereas for lower percentages an overestimation occurs. The opposite is quite obvious as concerned with the performance of the ccm method. Further, the present technique gives a somewhat uniform error performance for all the probability levels for which data is available.

In addition, taking as a criterion the rms value the present method has more advantages as compared to the ccm procedure, for probability levels greater than 0.1%. On the other hand, the two methods give about the same results for lower percentages of time.

The present predictive procedure and the ccm method have also been tested, by using the limited data bank

for the 31 locations where tabulated Ro.01 values are available.

In Table II, the corresponding #e, ae and rms values for various percentages times are presented. In Figure 6 the rms relative errors are drawn. As it can be seen, the present method gives improved results, particularly for the higher percentages of time. On the other hand, it should be noted that the lower time percentages are the more essential due to high rainrates.

111.2. Cons iderat ion o f the site diversity performance predict ion problem.

Two standard expressions exist for characterizing site diversity performance : diversity improvement fac tor is defined as the ratio of the single-site time percentage to diversity time percentage at the same attenuation level. Diversity gain is the difference (in dB) between the single-site and diversity attenuation values for the same time percentage.

In the present work, the joint exceedance attenuation probability will be predicted in terms of the single- site probability for the location under consideration, at the same outage level. To calculate P1,2 we use the expressions (48) and (50) and consequently, we have :

(63) P1,2(xs) = P(A81 >_ x s , A s 2 >_ xs )

= P ( A 1 >_ XD, A2 >_- x o )

CC = (xl, x2) dzldx2, D D

where fAiA2(Xl ,2g2) is the joint probability density function of the variables A1 and A2.

According now to consideration (g), the variables A1 and A2 will have a joint unconditional log-normal distri-

ANN. TI~LI~COMMUN., 45, n ~ 7-8, 1990 10/15

J. D. KANELLOPOULOS. - RAIN ATI'ENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS

TABLE II. - - Mean, standard deviation and rms value for the CCIR and the present method as a function of time percentage (only 31 locations where tabulated values of R0.01 are available).

Moyenne, ~cart-type et valeur quadratique moyenne, pour la m~thode du CCIR (pour les seuls 31 emplacements off des valeurs tabul~es de R0,01 ~taient disponibles)

et la m~thode propos~e dans cet article, en fonction du pourcentage de temps.

Percentage of time

10-3 3.10-3 10-2 3.10-2 10-x

/~e 11.42 7.73 11.52 8.47 - 1.32

ae 24.61 19.04 24.79 30.24 43.85

De 27.13 20.55 27.34 31.4 43.87

10-3 3.10-3 10-2 3.10-2 10-1

/~e 1.63 - 6.75 2.65 1.35 20.66

ae 35.65 23.7 30.97 23,14 42.36

De 35.69 24.64 31.08 23.18 47.13

3.10 - i 1.0

- 19.59 - 32.39

44.36 41.08

48.49 52.31

3.10 - i 1.0

34.54 42.54

58.81 70.62

68,2 82.44

447

D, %

80 1 Present method ~ ~ / ~ 2 CCIR method ~2(~/..'//

/ f f

40 " ~

p*/o

0 1 0 _ 3 : 1~}_ 2 i ' r I0-~

FIG. 6. - - Rms relative errors in percent against probability level, obtained testing 31 satellite links placed in Europe, Japan and the

USA (R0.01 tabulated values are available).

Erreurs quadratiques moyennes relatives en pourcent en fonction du niveau de probabilitY, obtenues en testant 31 liaisons par satellite en Europe, au Japon et aux Etats-Unis (les valeurs R0.01

sont disponibles).

bution. Following a straightforward statistical analysis, one gets [3] :

1 f ~ 1 (64) P i , 2 = ~ o v / ~

exp ( - - ~ ) e r f c U0 -- p n s U l

and :

(65) Uo = ~ e r f c - l (2Po) .

The above results give the joint probability/~ as a function of the single site probability Po, taken as the average of P1, P2 and Pns which is the correlation coefficient between the normal variables In A: and In A~.

The next step is the evaluation of the correlation coefficient Pns as a function of the path correlation coefficient Ps between attenuations A1 and As. For

11/15

this reason, application of the expression (37) is made. Further, the path correlation coefficient Ps is given by :

H2s (66) Ps = H i '

where the factor H 2 s is formulated in integral form as (see Fig. 4c) :

fo LD /0 LD (67) H 2 s = P2 d/ld/2.

For locations in Europe and North America where the expression (19) for the spatial correlation coefficient Pl holds, P2 can be expressed as :

G

(68) P2 ---- jG02 q- iK12 d- ll - / 2 ) 2 '

where (see also Fig. 4c) :

(69) Go = v / ~ + D 2,

K12 = ~/$22 - D 2 .

Using a straightforward analysis, one is able to obtain :

(70) g 2 s = G G o ( H a - g / 3 ) ,

where :

(71) H , ~ - - r \ Go ] +

ffPl (K12 - LD ( K 1 2 ~ Co ) - \-5 o /

= \ Go ] +

Go

ANN. TI~LI~2OMMUN,, 45, n ~ 7-8, 1990

448

and the functions ##l(z), &b2(z) are defined by :

(72) ff l(z) = z s inh- l (z) ,

r = + 1.

For locations in Japan and regions with similar clima- tic conditions where the expression (20) for Pl is valid H2s can be expressed as [3] :

(73) H2s = H i - H~ ,

where :

(74) H ~ = (K12 + L D ) ~ ' t ( K 1 2 + L D ) +

(Kt~ - LD)CP'1(K12 - L D ) - 2K12~(K12) , i ' g

H'~ = ~'2(K12 + L D ) + ~ ( K 1 2 - L D ) - 2(I)2(12)

and the functions (I)~(z), (I)~(z) are defined by :

I" (7s) e l (z ) exp(- {/D2 + dx,

/0" e;(z) xexp(- b dx.

It should be noted that the present modelling for the correlation coefficient ps is based on the assumption of the isotropy of the spatial rainfall auto-correlation. How- ever, ttogg and Chu [21] have pointed out an ellipticity in the shape of rainfalls at some geographic locations due to the predominant orientation of weather fronts in the specific region with major axis parallel to the front [22]. This means that the spatial correlation coefficient Pl may depend not only on the spacing but also on the orientation. In this way, Zawadzki [23] has also pointed out that the spatial auto-correlation of R may be not isotropic since frontal lines are frequently oriented. On the other hand, the presently available information is not sufficient for a quantitative description of the anisotropy. It is believed that some of the discrepancies between calculated and measured diversity distributions may be caused by neglecting the anisotropy of the spatial correlation function.

Further, the influence of the parameter a, encountered in expression (37) relating p,~, to p~, is examined in detail. In their work, Morita and Higuti [10] have taken a = 1.5 for all the cases. In Figure 7 the function P1,2 = f ( P o ) for an arbitrary diversity system has been plotted, using Ps = 0.2 and a as a parameter. It is obvious that the dependence of /912 on a is quite significant and consequently the numerical value of a should be estimated precisely for each case. From equation (6) in [6], it can be shown that o- depends on the parameter S~ of the point rainrate distribution in the specific region. As a matter of fact estimation of the parameter Sr by means of the available point rainfall distribution is very critical for the diversity calculations.

The present predictive analysis has been applied to several situations where site diversity systems have been operated. More particularly, the majority of the cases in- cluded in [24] has been analyzed. The appropriate data for the communication systems operated by BTL (Bell Telephone Laboratories) is referred to three different regions in USA (Georgia, New Jersey and Colorado). Fur-

ANN. 'r~..I~COMMUN.. 45, n ~ 7-8, 1990

J. D. KANELLOPOULOS. - RAIN ATTENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS

el' twin site exceedance probability %

0.1

.01

1.10-

(1) r (2) r (3) r (4) r (5) r

single site exceedance probability %

FIG. 7. - - Twin site exceedance probability versus single site exceedance probability using a as a parameter.

Probabilit~ de d~passement d' un affaiblissement donn~ pour une diversit( ~ deux emplacements en fonction de ta probabilit~ de d~passement

du re#me affaiblissement sans diversitY, avec ~r comme paramdtre.

ther, comparison has been made with data taken from diversity links operated in Tampa, Florida [25]. The geometrical and electrical characteristics of the communication systems mentioned above, such as frequency, elevation angle, latitude of the location, ground height of the location, site separation and horizontal path separation have been tabulated and shown in Table III.

Some points concerning the proper implementation of the predictive procedure are reported here. First, the appropriate rainfall data for Georgia, New Jersey, Flo- rida has been taken from Lin [5]. The rainfall data for Colorado has been taken from Bodtmann and Ruthroff [15]. Second, the diversity experimental results which are presented here are referred to USA locations where the model suggested by expression (19) for the rainfall spatial correlation is valid. As a matter of fact expressions (68)-(72) are applicable and they are used in the present calculations. Numerical values for the characteristic parameter G as well as S~ and a for all the cases have also been tabulated and shown in Table III.

In Figure 8, the results of the predictive procedure together with experimental data are given for the radiome- ter site-diversity experiments in Georgia sites (Palmetto, Temple and Major). In Figure 9 the results for the New Jersey sites, in Figure 10 for the Florida sites, and fi- nally in Figure 11 for the Colorado sites, are presented. It should be noted that the diversity measurements cot-

12/15

J. D. KANELLOPOULOS. - RAIN ATTENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS

Region

Georgia

New Jersey

Colorado

Florida

T A B L E III . - - Parameters of the site diversity experiments.

Paramdtres des experiences en diversit~ d' emplacement.

Sites A Ho f O S12 D S r cr G

(deg) (kin) (GHz) (deg) (kin) (km) (kin)

P-M 34 0.29 17.8 38.2 16 16 1.848 1.975 1.75

P-T . . . . . . . . 31 31 . . . . . .

T-M . . . . . . 47 47 . . . . . .

C-S 40 0.15 15.5 32 11 11 2.0 2.189 1.5

C-A . . . . . . 19 19 . . . . . .

S-A . . . . . . 30 30 . . . . . .

L-G 40 1.5 17.8 42.6 33.3 30.6 2.243 2.46 1.5

L-U 28 0.01 19 55 11 6 2.45 2.35 0.75

U-S . . . . . . . . 16 13.5 . . . . . .

L-S . . . . . . 20 19.5 . . . . . .

449

A : latitude, H 0 : height of the location, f : frequency, 0 : elevation, $12 : site separation, D : horizontal path separation, Sr : unconditional standard deviation of lnR. ~r : unconditional standard deviation of lnA. G : characteristic distance.

10 3

10 2

10

exceedance time (min/year)

~ single site ~ 10 3 -

--.......

%

~ "~',~ P-M

I m e l ~ 10 1 P : Palmetlo ~ ~ - " ~ ~ T : Temple M : Majot

t heoretical . . . . . . experimental

attenuation (dB) ii I I I i

, ; s g

FIG. 8. - - E x c e e d a n c e a t t e n u a t i o n p r o b a b i l i t y with and without site diversity for Georgia sites.

Probabilit~ de ddpassement d' un affaiblissement donnd avec et sans diversitd d'emplacement

pour des emplacements en G~orgie (Etats-Unis).

exceedance time (min/year)

~ ~ ---., ~ / - single site

S : Savreville C : Crawford Hill A : Asbury Park

theoretical . . . . . . experimental

attenuation (dB) D

PIG. 9. - - Exceedance attenuation probability with and without site diversity for New Jersey sites.

Probabilit~ de d(passement d'un affaiblissement donn~ avec et sans diversitd d' emplacement

pour des emplacements dans le New-Jersey (Etats-Unis)~

responding to the triangle (Perrineville, Asbury Park and Crawford Hill) in New Jersey have been excluded from our comparisons due to the strong anisotropic behaviour of spatial rainfall autocorrelation in this region.

As it is pointed out by Hogg and Chu [21], this anisotropic behaviour of rain can be explained by the fact that the direction of persistent weather fronts at the particular location would result in an ellipticity in the shape of cells, with major axis parallel to the front.

The main conclusions which can be drawn from the above comparisons (Figs. 8-11) are the following :

a) For all the cases, the agreement between theoretical predictions and experimental data is quite good except at the lower region of attenuation where the theoretical results underestimate the real situation. This is quite expectable, because the convective raincell model [5] does not take into account the homogeneous stratiform rain which is valid for low rainrates (< 10 mm/h).

13/15 ANN. TP_.L~COMMUN., 45, n ~ 7-8, 1990


excaedance t ime (min/year)

~ ~ ~ " . . . . 2: single site

10 3" . . . . . . . . . ~ _ ~ .

10 2 - L : Lutz U : University $ - U & L - S S : Sweetwater

theoretical . . . . . experimental

attenuation (dB)

FIG. 10. - - Exceedance attenuation probability with and without site diversity for Florida sites.

Probabilit# de d~passement d' un affaiblissement donn~ avec et sans diversit# d'emplacement

pour des emplacements en Floride (Etats-Unis).

exceedance time (rain/year)

t 0 h3-

"~\\ single site

10 2. ~-. .

L : Longmont xxx',. G : Greeley

10- \ ~ " L-G theoretical . . . . experimental

1 2 3 4 5 6 7 attenuation (dB)

FIG. 11. - - Exceedance attenuation probability with and without site diversity for Colorado sites.

Probabilit~ de d#passement d' un affaiblissement donn~ avec et sans diversitd d'emplacement

pour des emplacements dans le Colorado (Etats-Unis).

b) The slight discrepancy between theoretical and experimental results can also be explained by the fact that the data is referred to a limited period of measurements (for the majority of cases is about two years). As it has been pointed out by Lin et al. [24] the measured diversity improvement factor varies considerably from year to year. The reason for this instability is the small number of extreme rain storms per year which cause simultaneous deep fades on the diversity sites. Consequently, many years of continuous measurements are required to experience sufficient number of extreme rain storms for stable, representative statistics of simultaneous fades on multiple sites.

IV. CONCLUSION

The reliability of both terrestrial and earth-to-satellite paths operating at frequencies above 10 GHz is seriously affected by the rain attenuation. A number of problems dealing with the analysis of the performance of the above systems has been presented here.

More particularly, models for the prediction of the operational characteristics of a multirelay terrestrial system using digital or analog signals have been developed. Further, methods for the prediction of the operational characteristics of a microwave satellite system have also been considered. Numerical results taken from the above models have been compared with available experimental data from operated links in USA, Europe, Japan and the agreement has been found to be quite encouraging.

Manuscrit refu le 16 juin 1989, accept~ le 14 mai 1990.

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[15] BODTMA~ (W. E), Rtrrrmo~ (C. L.). Rain attenuation on short radio paths : Theory, experiment and design. Bell. Syst. Tech. J., USA (1974), 55, n ~ 7, pp. 1329-1349.

[16] MoRrrA (K.). Study on rain rate distribution. Rev. of the Elec. Commun. Labs., Japan (1978), 26, n ~ 1-2, pp. 268-277.

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ANN. TI~LI~COMMUN., 45, n ~ 7-8, 1990 14/15

J. D. KANELLOPOULOS. - RAIN ATI'ENUATION AFFECTING MICROWAVE COMMUNICATION SYSTEMS 451

[19] MOtYeFOtrMA (F.). Model of rainfall-rate distribution for radio system design, lEE Proc. Pt. H, GB (1982), 132, n ~ 1, pp. 39-43.

[20] A~t~,Mowrrz (M.), ST~GUN (I.). Handbook of mathematical functions. Dover Publ., New York (1965).

[21] Hoo3 (D. C.), CHU (T. S.). The role of rain in satellite communi- cations. Proc. of the 1EEE, USA (1975), 63, n ~ 9, pp. 1308-1331.

[22] ALL~aYr (J. E.), HALL (M.). Site-diversity advantage for satellite communication at 11.6 GHz. Electron. Lee., GB (1974), 10, pp. 527-528.

[23] ZAWADZ_Xl (I. I.). Statistical properties of precipitation patterns. J. Appl. Meteor., USA (1973), 12, p. 459.

[24] Ln~ (S. H.), BERGMAN (H. J.), PURSLEY (M. V.). Rain attenuation on earth-satellite paths : Summary of 10-year's experiments and studies. Bell. Syst. Tech. J., USA (1980), 59, n ~ 2, pp. 182-228.

[25] TANG (D. D.), DAVlDSON (D.), BLOCH (S. C.). Diversity reception of Comstar satellite 19/29 GHz beacons with the Tampa Triad 1978-1981. Radio Sci., USA (1982), 17, pp. 1477-1488.

BIOGRAPHY

John D. KANELLOPOULOS, Was born in Athens, Greece on December 12, 1948. He received the diploma of mechanical and electrical engineering and the Dr. Eng. degree from the National technical

university of Athens (NASA) in 1971 and 1979, respectively. He has also received the DIC and Ph.D. degree from Imperial College of science and technology, University of London, in 1979. He is now a Professor at the National technical University of Athens.

Nicolaos J. KOLLIOPOULOS, was born in Kouvelia, Tripoli, Greece in 1943. He studied in the USA and received his BSEE, MSEE and MBA degrees from the University of Illinois (1965), Univ. of Missouri (1966) and Loyola Univ. (1971), respectively. He received his Ph.D. (1987) from the National technical university of Athens (NTUA) in Greece. He is now a Professor at the Tech. Educ. Inst. of Athens, Greece.

Stelios G. KOUKOULAS, was born in Athens on October 9, 1940. He received the diploma of mechanical and electrical engineering in Jtlne 1965 and the Dr. Eng. degree from National technical university of Athens (NTUA) in November 1987. He is now a Professor at the Tech. Educ. Inst. of Athens, Greece.

Christos N. CAPSAL~S was born in Athens on October, 1956. He received the diploma of mechanical and electrical engineering in June 1979, and the Dr. Eng. degree from National technical university of Athens (m'UA) in May 1985. He is now an Assistant Professor at the National technical university of Athens.

Spyros G. VENTOURAS, was born in Greece in 1960. He graduated in electrical engineering from the National technical University of Athens in 1984. Currently, he is a Ph.D. candidate in the department of electrical engineering at the National technical university of Athens.

[5/15 ANN. ~t~OMMUN.. 45, n ~ 7-8, 1990

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Rain attenuation problems affecting the performance microwave communication systems