I29

Letters to the Editor

Prediction of the Outage Performance of an Orbital Diversity Earth-Space System

John D. Kanellopoulos, Adrianos Reppas Department of Electrical Engineering National Technical University of Athens Athens42 Patission Street, 10682 Greece

Abstract. Diversity systems are forseen for earth to satellite links operating at frequencies above 10 GHz in localities with high rain-induced attenuation. The paper discusses orbital diversity, which uses two satellites and an earth receiving site. A recently suggested model for the predic- tion of site diversity performance is properly modified by considering the particular geometry of the present problem. Both types of rain (stratified and convective raincells) are also examined. Numerical results are compared with experimental data taken from a simulated earth-space system located in Italy. The agreement was found to be quite encouraging.

1. INTRODUCTION

Frequencies above 10 GHz will be of high importance in future satellite systems, as they will allow high com- munication capacities and less interference problems with terrestrial radio relay systems. When the 10 GHt threshold is passed, rain attenuation may become the limiting factor for high system availability. Different solutions have been proposed to overcome outage due to rain attenuation. One is the brute-force method of increasing the power as far as needed, but this must be abandoned and more intelligent methods (adaptive methods) must be introduced. Among the latter the site- diversity (SD) is well known which consists of two re- ceiver and/or transmitter terminal sites spaced far enough apart to be jointly capable of reducing system attenuation. It is a simple technique but has the draw- back of requiring two installations and a terrestrial link between them. Some other more intelligent methods such as burst-length control (BCL) and frequency- diversity (FDV), have recently been developed [l], avoi- ding such inconvenience, but their implementation re- quires a large amount of data concerning the joint pro- bability of attenuation in pairs of distant sites. Ano- ther diversity scheme, avoiding also the previous incon- venience, is one that employs two geostationary satel- lites angularly spaced [2, 3, 4) which is called orbital diversity (OD). The reduction in link power margins of the earth terminals is achieved by selecting the least- attenuated radio path between two converging to the earth terminal, from the two satellites. Of the two, one is regularly used (normal mode of operation) and the

other one is used only when needed (spare channel or system resource) [S]. In r e n t years, attention has been paid to the pre-

dictive analysis of the outage performance of an earth- space system using the above diversity techniques. More particularly, a general model dealing with the site di- versity problem has first been proposed by Morita and Higuti [a]. Capsoni and Matricciani (71 have modified this latter formulation using information on the struc- ture of rain in a slant path obtained by means of a me- teorological radar located at Spino d’Adda near Mila- no. Most recently, another improved version of the Mo- rita and Higuti work based on both stratified rain and convective raincell models of the spatial structure of the rainfall has been proposed [8, 91. On the other hand, few investigations exist on orbi-

tal diversity and a very limited set of available experi- mental data [3, 10, 111. Matricciani (41 has developed a theoretical model for the prediction of the outage per- formance of orbital diversity systems, which is an ex- tension of the technique proposed by Capsoni and Ma- tricciani for the site diversity problem [7].

The subject of the present paper is an approach to extend the improved version of Morita and Higuti work [8, 91 in order to include the orbital diversity case. Both types of rain structure, convective raincells and strati- fied rain, valid for higher and lower rainfall rates, re- spectively, are also examined. It should be emphasi- zed that the above modeling for the rainfall structure is important for the design of the near future 20/30 GHz earth-space paths. In this band of frequencies the lower rainrates may contribute significantly to the ou-

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130 John I). Kadlapoulos, Adrianor Heppw - Prcdiclinn of lhe OiilaRe Perfarmanre of an Orbital OivmiCy CjlrIhSparr System

tage performance of the system. Finally, numerical results are compared with expe-

rimental data taken from a simulated orbital diversity earth-space system located in Italy.

2. THE ANALYSIS

An orbital diversity configuration-between two geo- stationary satellites is shown in Fig. la). The effective average length of the path 1 or 2 affected by rain is given by

H - Ho L, = 9 sin L cos - 2,

where H i s the annual average rain height measured in relation to sea level [12], HO the station altitude above sea level and L is the common elevation angle concer- ning the corresponding site diversity system as shown in Fig. 1. Further 8 is the orbital diversity aperture an- gle. It should be noted that the above configuration cor- responds to a symmetrical orbital diversity. The pre- diction model proposed here, particularly the part con- cerning the evaluation of the correlation coefficient. is appropriate for this case. The more complicated but

practical case of asymmetric orbital diversity will be examined in a future work.

For the proceeding analysis the following basic as- sumptions, similar to those employed for the correspon- ding site diversity problem (8) are taken into account and are briefly presented here. a) The unconditional log-normal probability distribu-

tion for modelling the long-term point rainfall rate R, for a certain range of values of R, is adopted.

b) The available single attenuation distribution is mo- delled by using two different log-normal distribu- tions valid for the lower and higher values of atte- nuation, respectively. Stratified rain, which is do- minant for the lower values of rainfall, requires a different model than convective rain. It should be emphasized here that the assumption of lognorma- lity For the distributions of R and single attenuation have first been employed by Lin [13] but for the conditional time, i.e. when it rains. Using the un- conditional forms, we avoid uncertainties in choo- sing the correct expressions of rainfall probabilities Po(O), Po(L) for single-variate distributions [ 131 and mainly P0(0,0), Po(L, L ) for the bivariate ones. Coming now to the analysis, the parameter charac- terizing the outage performance of an orbital diver- sity system is the joint exceedance attenuation pro-

---

rata l l i to te

lite

(bJ

Fig. la) Configuration of the orbital divcrsiry sysnm. b) Horizontal projections of the slanr parhs.

730

John D. Kanellopoulos, Adrhnos Reppu - PrrdMlon of tk Outage Performance of an w t d -(Y Earth-Space I 3 1

bability P1.2. This will be predicted in terms of the single site probability Po for the location under con- sideration, at the same outage level, as foIIows.

The cumulative single-site exceedance probability PO is given by

Po=P(ASi2xs) (i= 1,2) (2)

Whereas the joint exceedance probability PI,^ for the

(3)

Ari (i = 1.2) are the rain induced attenuations and xr is the corresponding outage level (in dB).

Assuming now that the joint denpity function bet- ween the attenuations on the two links is a two- dimensional lognormal, the standard equations used for this case [8], give the joint probability PI,Z as a func- tion of the single probability PO and Q. which is the correlation coefficient between the variables lnA1 and lnA2. A and A2 are the surface-projcctcd attenuations as calculated for hypothetical terrestrial links with path length

two converging slant paths is defined as

PI,Z = P(Asl 2 XI, Ar2 2 XI)

LD = L,COSC~ (4)

where (p is the common elevation angle for the two con- verging slant paths under consideration. If no availa- ble data exist for the single attenuation distribution, then its lognormal statistical parameters A,,, and S, (me- dian value and standard deviation of the logarithm va- riable), can be obtained by means of the known para- meters of the rainfall medium. Furthermore, the cor- relation coefficient Q,, is expressed in terms of the path correlation coefficient Q between attenuations A I and A2 by 161.

1 S: - S:

en = -In[(e 1) Q + I] ( 5 )

where the path correlation coefficient Q is given by

and

(7)

dil is the distance between two points in the same hop and d;2 is expressed as (Fig. lb)

In the above expressions, A s is the projected azimu- thal differential angle and QO (R?; Rf; di1) is the auto- correlation coefficient of specific attenuation between two points in the same hop. In the same way, Q O ( R ~ ; Rf ; d12) is the correlation coefficient between two points each belonging to a different hop.

The expressions for the HI and S, are the same as the corresponding ones for the site diversity problem

Sr is the standard deviation of lnR and the constant b is found in the specific attenuation formula aRb (dB/km). Tabulated values for the constants o and b are given elsewhere [14].

Using now a straightforward algebra the parame- ter HZ is given by

H2 = 1 [(P-A~)ZI + AsZ2-2Z3-2Z41 sin (A*)

for A*<<' (12)

for A9>90°

where

I2 4 f eo (Rf, R f . u) udu LO

A

and

k 9 f i L ~ d l - cos (As) (18)

The evaluation of the parameters H I , H2 and S,, can further proceed by using two independent models for the rain structure referring to stratified and convecti- ve rain, respectively. This is a simplification of the rea- listic problem, but on the other hand, consideration of the same matter by means of a more complex model combined the convective raincells with the stratified ty- pe of rain, is a very difficult task. More particularly, an attenuation threshold A, can be adopted given by

Ac = aR,b Ls (19)

and the R, value varies from 10 to 20 mm/hr depen- ding on the specific location [IS]. Considering now the two cases (stratified and convective rain) separately, we will have

a) x r c A r

In this case, the stratified rain is dominant and the parameters HI, Hz, S, can be obtained by using the

73 I VOL. 2 - N. 6 N0V.-DEC. 1991

I32 John D. Knncllnpoulns. Adrianos Reppas - Pndiclion of the Outage Performanrt of an OrbiIal Diversity EPrch-Space System

Latitude of the location, A (deg) Station altitude above sea level. Ho (km: Elevation angle, c (deg) Frequency, f (GHz) Characteristic distance, G (km) Parameter C (km) Median value Rm Standard deviation S,

set of expressions (7)-( 18), after substituting Qo therein, by the following expression [8]

where Po(O), P(1,2) are the rain probability and the probability that rain will occur simultaneously at the points 1.2 respectively. For the latter probability, a little information can be found in the literature. Using a li- mited sd of experimental data given by Freeny and Gab- be (16) for locations in U.S.A., together with extrapo- lation and regression fitting techniques, the following expression can be obtained

(21)

which is a decreasing function of the distance d bet- ween the points 1 and 2. In the above expression, C is a parameter (in km) depending on the structure of the rainfall medium in the specific region, ranging from 4 to 6 km. For further details one is referred elsewhere 181 *

Proceeding further, we substitute P (1.2) from ex- pression (21) into (20). and the correlation coefficient QO can now be given by

P( 1,2) = (PO (0) - pZ0 (0)) e--Jd'c + pZ0 (0)

eo (R?, Rf, d) = SI exp( - d d x ) + SZ (22)

with

P 0 (0) exp (b2 $1 - 1 s2 =

exp (6' Sf) - 1

At this point we should notice that the introduction of rainfall probability Po(0) is inevitable here, but the uncertainty in estimating its exact value can be shown to have a slight influence on the final result.

Finally, the evaluation of the HI and HZ in (10) and (12)-(18) requires the calculation of some simple inde- finite integrals given in the Appendix.

b) xs>Ac

In this case, the convective raincells are dominant and the parameters H I , Ht S,, can be obtained by using theset of expressions (7)-(18) after substituting QO the- rein, by the following expression [ 13)

where G is a characteristic distance ranging from 0.75 to 3 km.

The evaluation of the HI and HZ factors in (10) and (12148) requires the calculation of some other indefi- nite integrals which are also given the Appendix.

Summarizing now the whole procedure, the calcu- lation of the joint exceedance attenuation probability Pt.2 can generally proceed as follows: a) For values of x, (outage level in dB) less than A, the

standard equations of two-dimensional lognorma- lity along with expressions (1)-( 18) are combined with (20)-(23) and (A-l)-(A-3).

b) On the other hand, for values of x, greater than A, the expressions (1)-(18) together with the standard equations mentioned above are combined with (24) and (A-4)-(A-6).

3. NUMERICAL RESULTS AND DISCUSSION

The analysis has been applied to and compared with several OD communication systems simulated at the ex- perimental station in Spino d'Adda of the Centro per le Telecomunicazioni Spaziali (CSTS) of the Italian Na- tional Research Council (CNR) [lo], during the sum- mers of 1981 and 1982. On the other hand, the experi- mental data relative to the asymmetric orbital diversi- ty configuration at Fucino between the satellites SIR10 and OTS in the 12 GHz band [ l 1) are not considered here. As mentioned previously, an extension of the pre- sent modelling to include the asymmetric OD systems is needed and it will be examined in a future work.

The geometrical and electrical characteristics of the communication system located in Spino d'Adda are ta- bulated in Table 1. The data for the point rainfall di- stribution for the location of interest has been taken by Fedi (17) while the pair G = 2.5 km and C = 5 km has been chosen to give a best fit to the data. The nu- merical values for Rm, S, (unconditional lognormal pa- rameters), and G, C are also given in Table l . The aperture angles considered in the particular experiment ranged from 16" to 95" in about 1s" steps. The maxi- mum aperture angle corresponds to an elevation of about 2 1 " . TABLE 1 - Parameters of the orbital divemity experiments

in Spino d'Adda

Region I Milano I 45.4O

32" 11.6 2.5 5 0.0618 1.832

0.084

The performance of OD may be assessed either by the diversity gain G or by the improvement I. Both the gain and the improvement describe OD completely [ 1 11. Fig. 2 shows results of the predictive procedure toge- ther with experimental data in the form of the gain ver- sus the aperture angle for selected single link attenua- tions. Due to the fact that the frequency of the experi- ment is relatively low (1 1.6 GHz), the attenuation thre- shold Ac given by expression (19) is less than about 2 dB and hence the predictive results relative to the convective raincells are only presented there.

The effect of the spatial structure of the rain medium is analyzed separately in Figs. 3-4, where the commu- nication system located in Spino d'Adda is examined again but considering higher frequencies, such asf = 20

732 E n

John 0. Kandlapoulos. Adrianm Reppas - Prediction af the OUIaRe Pcrformancv of an orbitrl U i v m i t y Fhlh-Spar- System I33

7 .

6 .

5 - - 0 'II

0 1. -

3 .

2 -

1 -

-------- FADAR

----------

I I 1 1 I I I *

100 110 120 1 0 20 30 40 5 0 6 0 7 0 80 90

e ( - 1

Fig. 2 - Comparison between radarderived and model-predicted orbital diversity gain, for several single link attenuations.

ATTENUATION

Fig. 3 - Irnprovmeat I of a 20 GHr orbital diversity system as a function of the attenuation exceeded on the single paths. ( I ) Predictive ruulu wing the stratified rain (8 = 15"). (2) Predictive results using the convective raincells (8 = 15'). (9 Predictive results udng the stratified rain (8 = 95.). (4) Predictive results using the convective raincells (8 = 9s').

VOL. 2 - N. 6 NOV.-DEC. 1991 733

I34 John D. Kamllopoulos. Adrianos Reppns - Prediction of lhe Outage Performance of an Orbital Diversity Earth-Span System

1 6

15

14

1 3

1 2 - 11 - 1 0 - 9 -

r 8 . 6 g 7. $ 2 6 - U

5 -

4 -

*9S0

1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 15 16 1 7 18

*9S0

1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 15 16 1 7 18

0'

/'

ATTFNUATSON

Flg. 4 - Improvement 1 of a 30 GHz orbital diversity system as a function of the attenuation exceeded on the single paths. (1) Predictive results using the stratified rain (0 = 15"). (2) Predictive results using the convective raincells (0 = :So). (3) Predictive results using the stratified rain (0 = 95"). (4) Predictive results using the convective raincells (8 = 95").

and 30 GHz. In this case, no available experimental sin- gle link attenuation data exist. Moreover, we have se- lected the improvement I for presentation of the pre- dictive results, because using this technical term the ran- ge of validity of both considerations (stratified rain or convective raincells) can be clearly shown. The predic- tive results are also presented for two characteristic va- lues of aperture angle (8 = 15" and 95"). For both frequencies the attenuation thresholds Aci (i = 1.2) cor- responding to 8 = 15" and 95" have been marked. The approximate range of validity of both considerations is noted by the solid curve.

The main conclusions which can be drawn from the above comparisons (Figs. 2-4) are the following: a) The agreement between theoretical predictions and the experimental data (Fig. 2) is generally encoura- ging. More specifically, for all the single attenuation levels there is a tendency of overestimation, which is quite obvious at the 4 and 10 dB levels. On the other hand, the agreement is very good at the lower and higher attenuations (2 dB and 14, 16 dB respectively).

We can also see that the OD gain is not at all signifi- cant: it represents a sizable fraction of the single link attenuation, though its maximum value is lower than the one achievable in the corresponding site diversity system (101. This can be explained by the fact that the distance between the two terminal sites can be theore- tically increased up to statistical independence or mo- re realistically to a distance greater than the extent of intense rain. OD aperture angle has a limit angle equal

to 180", although an upper operational aperture angle is around 90°, and the gain cannot reach that corre- sponding to statistical independence. However, if we consider that in OD there is no need for any terrestrial connection, and the second satellite should be consi- dered already in orbit for other services, then this di- versity scheme should be of practical interest. b) Considering now the Figs. 3-4, we can note that the difference between the theoretical predictions derived by using the stratified type of rain and the correspon- ding ones derived by using the convective raincells, for low aperture angles, is quite small. This is obvious for 8 = IS", where the two predictive curves almost coincide. As a final remark, the influence of the rainfall spa-

tial structure on the outage performance of the orbital diversity system is less pronounced as compared to the corresponding site diversity system.

4. CONCLUSIONS

A statistical model for evaluating diversity perfor- mance of earth to space radio links using orbital di- versity (OD) technique has been discussed.

The results are compared with a set of available ex- perimental data taken from a simulated earth-space sy- stem located in Italy. The agreement between theore- tical predictions and the experimental data concerning the gain versus the aperture angle, has been shown to

ETT 734

John D. Knncllopoulos. Adrianor Roppas - Predictinn of the OulnRe Performance of an Orbital Diversity Ear!h-Spnce System 135

be quite encouraging, especially at the higher attenua- tion levels.

Furthermore, the influence of the rainfall spatial structure on the outage performance of the orbital di- versity system has been examined, and it has been found to be less pronounced as compared to the cor- responding site diversity system.

where 7 - L i d (A*) (A-6) b(u) =

Manuscript received on January 2. 1991

APPENDIX

Evaluation of the indefinite integrals

The following indefinite integrals are needed for the evaluation of HI and Hz, considering the stratiform ty- pe of rain

gl(u) = j e x p ( - m a u d u = - 2 e e x p ( - m Q -

. ( d 2 2 + 3 A + 6 tConst (A-1) c

\ u l

The last integral is evaluated numerically by using the well-known Gauss quadratures [MI.

In this vein, the evaluation of HI and HZ conside- ring the convective raincells requires the calculation of the following indefinite integrals

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