EFFECT OF THE OSCILLATORY SHAPE OF THE EARTH STATION ANTENNA RADIATION PATTERN IN THE AGGREGATE INTERFERENCE GENERATED BY NON-GSO SATELLITE SYSTEMS

This paper focuses on interference aspects related to non-GSa satellite systems and presents results reflecting the effect of the oscillatory shape of the earth station antenna sidelobe gain pattern in the statistical behaviour of the aggre­ gate interference produced by an interfering non-GSa sys­ tem into the satellites of an interfered-with system. A Bessel function type of radiation pattern was adopted as a more re­ alistic model for the antenna sidelobe gain since it reflects the oscillatory behaviour encountered in measured radiation patterns. This sidelobe gain oscillatory behaviour plays an important role when addressing interference calculations in­ volving non-GSa systems, since due to the non-GSa system satellites dynamics not all entries in the aggregate interfer­ ence are associated with the maximum sidelobe earth station antenna gain. Results indicate that. although often used in GSa satellite systems. this type of worst case interference calculation tends to be overly pessimistic if applied to the non-GSa satellite environment.


INTRODUCTION
Interference calculations involving GSa satellite systems are usually based on the assumption that the earth station sidelobe antenna gain is equal to an envelope of the form x -25 log e.However, the oscillatory behaviour encountered in measured radiation patterns plays an important role when addressing interference calculations involving non-GSa sys tems, since due to the non-GSa system satellites dynamics not all entries in the aggregate interference are associated with the maximum sidelobe earth station antenna gain rep resented by its envelope.This paper considers two non-GSa satellite systems, here referred to as LEa I and LEa 2, and addresses the more critical case of up-link interference, in which the number of earth stations and their geographical distribution play an important role.The effect of the oscil latory shape of the earth station antenna sidelobe gain in the cumulative distribution functions of the carrier to aggregate interference ratio is evaluated considering the up-link inter ference from LEa I earth stations into a LEa 2 satellite.To obtain accurate interference statistics, full constellation of the interfering system is considered.Furthermore, multiple earth station locations (up to 120 earth stations for LEa I l, with multiple earth station antenna beams (up to 4) are assumed.The results were obtained through the analytical/numerical method described in [I, 2].As pointed out in [2], if com pared to computer simulation the results generated by this analytical method correspond to an infinite number of simu lated days, and therefore the method does not suffer from the need for long running times as may be required in computer simulation methods to assure statistically significant results.
The methodology and the interference model used in the interference computations are described in Section 2, where a Bessel function type of radiation pattern is adopted as a more realistic model for the antenna sidelobe gain since it reflects the oscillatory behaviour encountered in measured radiation patterns.This section also contains a brief description of the algorithm developed to determine the worst location for an interfered-with satellite in the victim non-GSa system.Numerical results are presented in Section 3.These results illustrate the effects of the earth station antenna sidelobe gains and of the number of interfering earth stations in the up-link C / I cumulative distribution function.This type of result is important for the establishment of design objectives for the antennae of earth stations operating with non-GSa satellites.Finally.main conclusions are highlighted in Section 4.

METHODOLOGY
As mentioned before the computation of the probabil ity distribution of the carrier to aggregate interference ratio was based on the analytical/numerical method described in [I, 2].The situation involving up-link interference from LEO I earth stations into LEO 2 satellites is illustrated in Figure I.In this figure, each earth station is assumed to have four an tennae (beams), pointed to the LEO I satellites corresponding to the four highest elevation angles that satisfy the minimum elevation angle constraint.Considering that all feeder link earth stations transmit the same power, the aggregate up-link interference power reaching a LEO 2 satellite (say, satellite i), located at a given point, is proportional to the quantity ) !Jijk (I) j=O k=O IJ where G s.i (au) is the receiving antenna gain of satellite i in a direction aij degrees off the main beam axis, G e .j ((3ijd is the earth station transmitting antenna gain in a direction (3ijk degrees off the main beam axis and d ij is the range between satellite i and the earth station j.Note that the random vari able Zi is a function of the given location of the considered LEO 2 interfered-with satellite and the random location of the LEO I reference satellite (see [I, 2]).The integers N e and N a represent, respectively, the number of earth stations and the number of antennae (per earth station) tracking a LEO I satellite with an elevation angle higher than the prescribed minimum value.The following assumptions were made in the interference computations:

SYSTEMS PARAMETERS
The LEO I and LEO 2 system characteristics used here were assumed to be respectively equal to those for LEO D and LEO F in Recommendation ITU-R S.1328-2 (year :WOO version) [3], except for the following parameters: • the minimum operating elevation angle for the LEO I earth stations was assumed to be 5 degrees (instead of the 10 degrees in Recommendation ITU-R S.1328-2); • the LEO 2 satellite antenna radiation pattern was as sumed to be the one in Annex I to Appendix 30B of the Radio Regulations [4], with maximum gain set to 13 dB for transmission and 12 dB for reception.In both cases the half-power beamwidth was 26 degrees; • the LEO I transmitting and receiving satellite antenna radiation patterns were both given by the curve in Figure 2; \ .
-30 Concerning the earth station switching strategies, it was as sumed that each LEO I gateway contains four ES antennae that track LEO I satellites with elevation angles higher than the prescribed minimum value.

INTERFERED-WITH SATELLITE LOCA TION (WORST CASE)
For the purpose of interference calculations, the location of the interfered-with satellite (LEO 2) was determined based on a worst case criterion.An algorithm was developed to determine the distribution, over the whole spherical surface containing the satellites of the interfered-with system (sys tem "shell"), of the "in-line" interference levels produced by all earth stations tracking visible satellites in the inter fering system, averaged with respect to the random location of the interfering system reference satellite [I, 2].Next, the interfered-with system "shell" is partitioned into square re gions (I by I degree) centered at {Cij = (ePi ej)T; i = -180, ... ,180,j = -e max ,"" em ax }, and the average "in line" interference level distribution is then used to determine the total "in-line" interference I IL (Cij) level contained inside each square region.To take into account the uncertainty in the location of the interfered-with satellite, the worst location is defined as the point cj'j corresponding to the maximum value of Iw(ci j ) = IIL(cT J ) p(ci j ), where p(cj'j) is the probabil ity of finding a satellite of the interfered-with system inside the square region centered at ci j .This probability was ob tained from the satellite location probability density function in [I. 2].
Figure 3 present the results obtained with this procedure in a particular situation where 120 LEO I earth stations pro duce up-link interference into LEO :2 satellites and illustrate the location of the 120 LEO I earth stations.Figure 3 also il lustrates the contour curves of the function.The black cross indicates the worst location for the LEO 2 satellite.Figure 4 illustrates an earth view from a LEO 2 satellite placed at this worst location.

CARRIER-TO-INTERFERENCE RATIO (C/ I) EXPRESSIONS
The C / I cumulative probability distribution (CDF) cor responding to a interfered-with satellite at the worst loca tion was obtained by first determining, using the analytical method in [I, 2], the CDF of the random variable ZdB = 10 log z, with Z in the form of (l).The COF of the carrier to interference ratio C / I (in dB) was then obtained using the following relations: • Interference into a LEO 2 satellite (C/ I within the re ceiver bandwidth): ( with . G 82 (n)

EARTH STATION ANTENNA SIDELOBE RADIATION PATTERNS
Two alternatives were considered for the antenna radiation patterns used in interference calculations.The first alterna tive refers to earth station antenna radiation patterns with the usual sidelobe gain of the form x -2.5 log e, and is generally and where D represents the earth station antenna diameter and ,\ the wavelength corresponding to the carrier frequency, both in the same unit.Figure 5 illustrates earth station radia tion patterns with usual [5, 6, 7] sidelobe gains of the form .1' -25 log (I different values of ;£.The second alternative corresponds to a Bessel function radiation pattern having a side lobe gain that shows an oscillatory behaviour similar to that encountered in measured radiation patterns.By using this radiation pattern it is possible to get closer to the actual situation in which not all entries in the aggregate interference are associated with the maximum sidelobe earth station an tenna gain.The Bessel function type of antenna radiation pattern used here is a version of that presented in [8], mod ified to better fit an envelope 32 -2510g 8 which could be used as a design objective for the radiation patterns of earth stations operating with non-GSa satellites.This antenna ra diation pattern is given by with 11(8) = 7fD T sin( 8) and (15) X 48 The values of the parameters a and a 2 are adjusted to fit the 32 -25 log 8 envelope and depend on the value of G max' This Bessel function radiation pattern is illustrated in Figure 6 for a 6 meter antenna operating in a 5.175 GHz with G max = 47.5.In this particular case a = 0.5 and a = 16.This figure also shows the 32 -25 log 8 sidelobe gain radiation pattern.As described in Section 2.3, the C / I cumulative proba bility distribution (CDF) corresponding to a interfered-with satellite at a given location was obtained by first determining, using the analytical method in [1, 2], the CDF of the random variable ZdB = 10 log z, with Z in the form of (1).The CDF of the carrier to interference ratio C / I (in dB) was then ob tained considering the relations in ( 2) and (3).It was assumed that the interfered-with satellite was at the worst location (see Section 2.2).Furthermore, the earth station transmitting the desired carrier was assumed to be located in such way that its transmitting antenna operates with the minimum permissible elevation angle (smallest desired carrier power C).
Performance results were obtained for a total of n = 30, n = 60, n = 90 and n = 120 LEO 1 earth stations.Starting with a given set of 120 locations smaller sets were obtained by eliminating station locations in such way that the relative geographical distribution was maintained.The resulting sets of earth station locations corresponding to n = 60 and n = 120 are respectively illustrated in figures 7 and 8 together with the corresponding worst location for the interfered-with LEO 2 satellite.The CDFs of the aggregate C / I ratio as sociated with the sets of locations in figures 7 and 8 are re spectively displayed, in both linear and logarithm scales, in figures 9 to 12.
Worst sotelli:e position: longitude 335: 'atitude 445  The following observations can be made based on the re sults in figures 9 to 12: • A comparison of the curves associated to the x -25 log e type of sidelobe gain with those corresponding to the Bessel function radiation pattern with an envelope of the form 32 -25 log eshows that the worst-case type of in terference calculation that considers that all entries in the aggregate interference are associated with the maxi mum sidelobe antenna gain leads to results that are pes simistic even for values of x as low as 25.
• If the earth station antennae satisfy the current design objective of 29 -25 log e [6] and the usual worst-case type of interference calculation indicates that the inter ference criteria are met, then these same interference cri teria are also met by earth station antennae that have a less stringent design objective (as for example the 32 -25 log e objective) when the oscillatory shape of the radiation pattern is taken into account.This indicates that antennae of earth stations operating with non-GSa satellites could have a design objective substantially less stringent than that of earth stations operating with GSa satellites..The impact of increasing number of LEO I earth stations in a LEO 2 satellite aggregate interference is illustrated by figures 13 to 16 respectively for the Bessel function type of earth station antenna radiation pattern and the more pes simistic 32 -25 log etype of antenna sidelobe gain.
The results in figures 13 to 16 indicate that an increase in the number of interfering LEO I earth stations impacts more the lower aggregate interference levels since, in general, higher levels of interference correspond to "in-line" interfer ence which are mainly dominated by interference from a few earth stations (one in most cases).

CONCLUSION
The effect of the oscillatory behaviour of the earth station antenna sidelobe gain in the cumulative distribution functions for the carrier to aggregate interference ratio was evaluated for a situation involving up-link interference from LEO I earth stations into a LEO 2 satellite.The C / I CDFs were obtained through the analytical method described in [I. 2].A Bessel function type of radiation pattern was adopted as a more realistic model for the antenna sidelobe gain since it reflects the oscillatory behaviour encountered in measured radiation patterns.
Using the Bessel function pattern as a reference, and con sidering the interference situation examined, results have shown that the worst-case type of interference calculation that considers that all entries in the aggregate interference are as sociated with the maximum sidelobe antenna gain leads to results that are overly pessimistic when applied to the non GSa satellite environment.Results have shown that if the earth station antennae satisfy the current design objective of 29 -25 log e [6] and the usual worst-case type of interfer ence calculation indicates that the interference criteria are met, then these same interference criteria are also met by earth station antennae that have a less stringent design objec tive (as for example the 32 -25 log eobjective) when the os cillatory shape of the radiation pattern is taken into account.This indicates that antennae of earth stations operating with non-GSa satellites could have a design objective substan tially less stringent than that of earth stations operating with GSa satellites.

Figure 2 .
Figure 2. LEO I satellite antenna radiation pattern (transmit ting and receiving)

Figure 3 .Figure 4 .
Figure 3. Contour curves of the function I wand worst loca tion for the LEO 2 satellite (black cross).

Figure 6 .
Figure S. Earth station antenna sidelobe patterns.

Figure 7 .
Figure 7. LEO 1 Earth station distribution and worst location for the LEO 2 satellite (n = 60).

Figure 8 .
Figure 8. LEO I Earth station distribution and worst location for the LEO 2 satellite (n = 120).

Figure 9 .Figure 11 .
Figure 9. Aggregate C / I ratio CDF corresponding to up link interference into a LEO 2 satellite at the worst location (60 LEO I earth stations worldwide).

Figure 12 .Figure 13 .
Figure 12.Expanded view of the aggregate C / I ratio CDF corresponding to up-link interference into a LEO 2 satellite at the worst location ( 120 LEO I earth stations worldwide).

XFigure 14 .
Figure 14.Expanded view of the aggregate C / I ratio CDF corresponding to up-link interference into a LEO 2 satellite at the worst location for different number of LEO I earth sta tions(Bessel function radiation pattern).

: 2 ~Figure 15 .Figure 16 .
Figure 15.Aggregate C / I ratio CDF corresponding to up link interference into a LEO 2 satellite at the worst location for different number of LEO I earth stations(:32 -25 log () antenna sidelobe gain).
Raimundo Sampaio-Neto received both the E.E. and the M.E.E.degrees from Universidade Cat6lica do Rio de Janeiro (PUC-Rio) in 1975 and 1978, respectively, and the PhD.degree from Univer sity of Southern California (USC) in 1983.He was associated with the Communication Science Institute of the Department of Electri cal Engineering at USC as a Post-Doctoral fellow from November 1983 to June 1984 with an appointment as a member of the techni cal staff of Axiomatic Corporation, Los Angeles.He is now a Re searcher at CETUC and Associate Professor of the Department of Electrical at PUC-Rio, where he has been since July 1994.During 1991 he was Visiting Professor in the Department of Electrical En gineering at USc. Prof. Sampaio has participated in various projects and has consulted for several private companies and government agencies.He was co-organizer of the Session on Recent Results for the IEEE Workshop on Information Theory, 1992, Salvador.He has also served as Technical Program co-Chairman for IEEE Global Telecommunications Conference (Globecom'99) which took place at Rio de Janeiro in December 1999 and as a member of the technical committees of several national (SBT) and intenational (ITS) sym posia of the Brazilian Telecommunications Society.He has been in office for two consecutive terms on the Board of Directors of the Brazilian Telecommunications Society as First Secretary (2000 LEO Iwhere a is the LEO 2 satellite antenna main beam off-set angle in the direction of the LEO 2 earth station trans mitting the desired carrier, d the is distance between this earth station and the LEO 2 satellite, BLEO I and B LEO 2 denote, respectively, the LEO I and LEO 2 re ceiver noise bandwidth and the equil'Glent isotropically radiated power (e.i.r.p.) values refer to e.i.r.p. per car rier.Note that the ratio BB I F{) 2 < 1 corresponds to an LL'O 1 interference reduction factor due to the difference, in bandwidth, of the interfering and interfered-with carri ers.
Jose Mauro P. Fortes received the E.E.(Telecommunications) de gree in 1973 and the M.Sc.E.E. in 1976, both from Pontiffcia Uni versidade Cat6lica do Rio de Janeiro (PUC-Rio).He received later the M.Sc.and Ph.D. degrees from Stanford University, CA, USA in 1978 and 1980, respectively, returning to PUC-Rio in June 1980.There he is Associate Professor with an appointment at Centro de Estudos em Telecomunica~6es da Pontiffcia Universidade Cat61ica (CETUC).He took a sabbatical leave during 1992 at the General Electric Research and Development Center in Schenectady, NY, USA, where he was a researcher with the Ultrasound Group.Prof. Fortes has published various papers in national and international journals and conferences.He has also participated in several re search projects and consulted for private companies and government agencies.He was Vice-President for Study Group 4 of the Ra diocommunication Sector, Intenational Telecommunication Union (lTU) in Geneva.He was also president of the Brazilian Telecom munications Society from March 1996 through February 2000.His research interests include sattelite transmission, communication the ory, estimation theory, and digital transmission.