Aggravation of radio interference effects on a dual polarized Earth-space link by two adjacent interfering satellites under rain fades

Transcription

1 RADIO SCIENCE, VOL. 40,, doi:10.109/004rs003137, 005 Aggravation of radio interference effects on a dual polarized Earth-space link by two adjacent interfering satellites under rain fades A. D. Panagopoulos, T. D. Kritikos, and J. D. Kanellopoulos Wireless and Satellite Communications Group, Division of Information Transmission Systems and Materials Technology, School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece Received 9 July 004; revised 9 March 005; accepted June 005; published 1 September 005. [1] Interference phenomena affecting the performance and availability of an Earth-space system are of utmost importance for the reliable design of a satellite communication network. Commercial satellite networks operate or will operate at Ku, Ka, and V frequency bands, in which rain is the dominant fading mechanism. Nominal interference induced on an Earth-space link by an adjacent satellite network operating at the same frequency is further aggravated because of the potential existing differential rain attenuation, as well as the rain and ice crystals depolarization valid for a frequency reuse system. In the present paper, an existing model, predicting the degradation of the total carrier-to-interference ratio under rain fade conditions, is properly modified considering interference effects by two adjacent satellites. The method is based on a convective rain cell model and the lognormal assumption for the point rain rate statistics. The obtained numerical results indicate the significant impact of the second interfering satellite on the aggravation of radio interference effects. Also presented are some simple mathematical formulas for the prediction of the carrier-to-interference ratio, based on the above theoretical results, appropriate for use by the system designer for back of the envelope computations. Citation: Panagopoulos, A. D., T. D. Kritikos, and J. D. Kanellopoulos (005), Aggravation of radio interference effects on a dual polarized Earth-space link by two adjacent interfering satellites under rain fades, Radio Sci., 40,, doi:10.109/004rs Introduction [] Satellite communication networks play an important role on the increasing demand of broadband communication services. The number of satellites on geostationary orbit has been increased dramatically during the last years, creating congestion of the geostationary satellite orbit spectrum. Adjacent satellite networks operating at the same frequency band might cause nonpermissible mutual radio interference levels due to their close spacing to one another in the geostationary satellite orbit [International Telecommunication Union (ITU), 1994a, 00]. Commercial satellite communication networks operate or will operate at Ku (14/1 GHz), Ka (30/0 GHz) and V (50/40 GHz) bands. In these frequency bands, the performance of the operating satellite Copyright 005 by the American Geophysical Union /05/004RS communication networks is mainly aggravated because of the induced severe rain attenuation and rain and ice crystals depolarization on the propagation slant path [Crane, 003]. The depolarization phenomena affect, of course, dual polarized channels, which are usually employed to double the transmitted capacity. [3] Examining now the ground terminal antennas and other hardware sizes, we observe that they have been reduced and can now be installed in customers premises (direct-to-home-services (DTH)). On the other hand, they do not have too directive antennas (very small aperture terminal (VSAT)); thus they are vulnerable to harmful downlink interference by adjacent satellite networks. The problem becomes more serious nowadays with the employment of downlink fade compensation techniques from all the satellite networks, such as the adaptive downlink power control [Castanet et al., 003]. [4] As is obvious from the above, the dominant sources of interference encountered in these frequency bands are interference because of the signal leakage from neighbor- 1of14

2 Figure 1. Configuration of the problem. ing satellites operating at the same frequency and cross talk between orthogonally polarized signals. The whole interference condition is generally aggravated under rain fading conditions, due to the potentially existing differential rain attenuation and the depolarization due to both rain and ice crystals existing above the melting layer [Matricciani and Mauri, 1996; Matricciani, 1997; Kanellopoulos et al., 1993; Kanellopoulos and Panagopoulos, 001]. [5] All the above-described interference effects are included in the calculation of the degradation of the carrier-to-interference ratio (CIR) for a frequency reuse system interfered by a neighboring satellite under the condition that the rain attenuation of the wanted signal is less than a maximum rain fade level. This matter has been treated and published elsewhere [Kanellopoulos and Panagopoulos, 001]. [6] The subject of this paper is the extension of the previous work to include the interference effects considering also a second interfering neighboring satellite. This is, of course, not an unusual case by taking into account all the previous discussion. The degradation of CIR of a dual polarized satellite link interfered by two neighboring satellites, under rain fades, is thus calculated. The method is based on a model of convective rain cells [Lin, 1975] and the lognormal distribution assumption for both point rain rate and attenuation statistics. The necessary inputs of the proposed model are consistent with the recently released ITU-R recommendations [ITU, 003a, 003c] concerning reliable worldwide rain rate and rain height statistics, respectively. [7] In section 3, the sensitivity of various parameters affecting the level of CIR under rain fades is investigated. The obtained numerical results show that neglecting the interference effects from a second satellite with nominal interfering power comparable to the one from the first satellite leads to much different prediction results. [8] Furthermore, because of the complexity of the expressions derived here, some simplified formulas based on an appropriate regression fitting analysis are also suggested, appropriate for use by the system designer for back of the envelope computations or educational purposes.. Interference Analysis [9] The configuration of the problem under consideration is demonstrated in Figure 1, where an Earth station E is in communication with a satellite S. Two neighboring satellites S 1 and S, operating at the same frequency band with S, are in close orbit subtending an angle q 01 and q 0 with the satellite S, respectively, as seen from Earth station E. The elevation angles of the constituted slant paths are j 0 (ES), j 1 (ES 1 )andj (ES ). The following random variables are necessary for the proceeding analysis: the rain attenuation A C of the wanted signal and the rain attenuations A I1, A I of the potential interfering signals concerning the slant paths (ES 1 ) and (ES ), respectively. [10] Our objective is the calculation of the additive contribution of interference on the total outage time which is taken into consideration by means of the following probability: the fraction of the time when the system suffers from interference, as part of the time when the event A C M is not valid but the system is under rain fade conditions. It is obvious that a noise dominant system is examined and M is the prescribed rain fade margin. In mathematical terms, this conditional probability can be expressed as P C I rjr M A C M ¼ P C I r; r M Ac M Pr ½ M A C MŠ ¼ P 1 : ð1þ P of14

3 In the above expression, (C/I) (db) is the carrier-tointerference ratio level, at the input of the receiver. Moreover, r is the nonexceeded carrier-to-interference ratio level, while r M depends on the sensitivity of the attenuation measurements. For numerical calculation, the 0.5 db value is adopted here [Rogers et al., 198]. [11] The main sources of interference considered here are the signal leakage from the two adjacent satellites S 1 and S operating at the same frequency with S and the cross polarization from the orthogonal channel. The total interference level is further aggravated under rain fade conditions, due to potential differential rain attenuation as well as rain and ice crystals depolarization effects. The carrier-to-interference ratio can be expressed as C I ¼ A I1 þ A I A C db 10 log A I CIR 1;nomo 10 þ 10 A I CIR 1 ;nomo 10 þ 10 A I þa 1 I A C XPD A C 10 ¼ CA ð C ; A I1 ; A I Þ: ðþ Details for the derivation of expression () can be found in Appendix A. In the above expression, CIR 1,nomo and CIR,nomo are the carrier-to-interference ratios in db, under clear sky conditions, supposing that there is only one interfering satellite at a time, S 1 and S respectively, with respect to a single polarized wanted signal. The total carrier-to-interference ratio under clear-sky conditions CIR nomo, for the single polarization case, taking into account both the interfering signals from the two satellites S 1 and S, is given as ð Þ CIRnomo 10 ¼ 10 CIR 1nomo 10 þ 10 CIR nomo 10 : ð3þ The carrier-to-interference ratio concerning a double polarized wanted signal in db, is given by 10 CIRnom 10 ¼ 10 CIRnomo 10 þ 10 XPDnom 10 : ð4þ During rain fade, XPD (db) is deteriorated because of the depolarization effects by raindrops and ice crystals. The relation between XPD and A C, taking into account all the potential cases of depolarization can be found elsewhere [Kanellopoulos and Panagopoulos, 001]. In expression (4), XPD nom is the cross-polarization discrimination during nominal conditions, mainly depending on receiver antenna characteristics. [1] For the calculation of the conditional probability (1), all the fundamental assumptions taken into account by Kanellopoulos and Panagopoulos [001] are also considered here. The evaluation of the conditional probability is straightforward and the main steps of the analysis are presented here. First, the numerator of the conditional probability in expression (1) can be expressed as P 1 ¼ P 8 A 0 I 1 þ A0 I A0 C cos j 1 cos j cos j 0 A 0 A I 0 I cos j CIR 1 1;nomo 10 log þ 10 >< 3 >: ¼ MZcos j 0 x S þ10 dx A 0 A I 0 1 I A 0 cos j þ 1 cos j C cos j XPD 0 10 A 0 C cos j 0 r M cos j 0 A 0 C M cos j 0 Z R 1 0 dy Z R 0 cos j CIR 1 ;nomo r; 9 >= >; dz f A 0 C A 0 A I 0 ðx; y; zþ; 1 I ð5þ where f A 0 C A 0 I A 0 (x, y, z) is the joint density function of the 1 I lognormal distributed random variables AC, 0 AI 0 1, AI 0, which are the attenuations calculated for hypothetical terrestrial links with path lengths L Dj = L j cos j j (j =0, 1, ), after employing the Crane s simplified considerations for the description of the vertical variation of the rainfall structure [Crane, 1996]. Moreover, L j is the effective length of the jth slant path with respect to (ES), (ES 1 ), and (ES ), respectively, given by [Crane, 1996] L j ¼ H H 0 ; ðj ¼ 0; 1; Þ; ð6þ sin j j where H is the average rain height at the receiving location [ITU, 003c], and H 0 is the height of the Earth station above sea level. [13] The limits x S, R 1, R encountered in the triple integral can be defined as (see also Figure ) 8 M cos j 0 ; x 0 > M cos j 0 >< x s ¼ x 0 ; 0:5 cos j 0 x 0 M cos j 0 ð7þ >: 0:5 cos j 0 ; x 0 < 0:5 cos j 0 ; where x 0 is the root of the transcendental equation x C ; 0; 0 r ¼ 0; cos j 0 R 1 is the root of the transcendental equation x R 1 C ; ; 0 r ¼ 0; x S x M cos j cos j 0 cos j 0 ; 1 ð8þ ð9þ 3of14

4 u M ¼ ln ð M cos j 0Þ lnða m0 Þ u R1 ¼ ln ð R 1 S a0 Þ lnða m1 Þ S a1 ð14þ ð15þ Figure. Surface A 0 C, A 0 I 1, A 0 I. and R is the root of the transcendental equation x y R C ; ; r ¼ 0; cos j 0 cos j 1 cos j x S x M cos j 0 ; 0 y R 1 : ð10þ u R ¼ ln ð R Þ lnða m Þ : ð16þ S a The expressions for m, s and the two-dimensional normal distribution f U0 U 1 (u 0, u 1 ) can be found in work by Panagopoulos and Kanellopoulos [00]. [14] Furthermore, the denominator of the conditional probability (1) is obtained via straightforward algebra: P ¼ 1 erfc u p 00 ffiffi erfc p um ffiffi ; ð17þ where u 00 ¼ ln ð 0:5 cos j 0Þ lnða m0 Þ : ð18þ S a0 Using the transformations u 0 ¼ ln x ln A m 0 S a0 u 1 ¼ ln y ln A m 1 S a1 u ¼ ln z ln A m S a 9 >= ; ð11þ where A mj, S aj (j = 0, 1, ) are the lognormal statistical parameters of the rain-induced attenuations A 0 C, A 0 I 1, A 0 I, respectively, the probability presented in (5) can be expressed as P 1 ¼ Z u M u xs du 0 Z u M Z u R 1 1 Z u R 1 du 1 Z ur 1 >; du f U0 U 1 U ðu 0 ; u 1 ; u Þ ¼ du 0 du 1 (f U0 U 1 ðu 0 ; u 1 Þ u xs erfc u ) R m pffiffiffi ; ð1þ s where u xs ¼ ln ð x s Þ lnða m0 Þ S a0 ð13þ Table 1. Parameters of the Case Study in Tokyo, Japan Parameter Value R m S r H, km 4.1 H 0,km 0. G 1.5 j 0, deg 46 j 1, deg 45 j, deg 47 q 01, deg.3 q 0, deg 4.5 XPD nom,db 30 Outage time, min/yr 300 a, f = 1 GHz Horizontal Circular a, f = 0 GHz Horizontal Circular b, f = 1 GHz Horizontal Circular b, f = 0 GHz Horizontal Circular M, db, f = 1 GHz Horizontal 3.0 Circular.887 M, db, f = 0 GHz Horizontal Circular of14

5 Figure 3. Numerical evaluations of conditional probability for a single and dual polarized Earthspace system located in Tokyo, for three pairs of adjacent satellite nominal carrier-to-interference ratios (f = 0 GHz, t =45 ): curve A, single polarization, CIR 1,nomo = 5 db, CIR,nomo = 50 db; curve B, double polarization, CIR 1,nomo = 5 db, CIR,nomo = 50 db; curve C, single polarization, CIR 1,nomo = 5 db, CIR,nomo = 30 db; curve D, double polarization, CIR 1,nomo = 5 db, CIR,nomo = 30 db; curve E, single polarization, CIR 1,nomo = 5 db, CIR,nomo = 5 db; and curve F, double polarization, CIR 1,nomo = 5 db, CIR,nomo = 5 db. The rest of the parameters of the system under consideration are given in Table 1. [15] Finally, A mj, S aj (j = 0, 1, ) can be calculated using the following relationships: ( ) S aj ¼ ln 1 þ H 1j L exp b Sr 1 ð19þ Dj A mj ¼ ar b m L Dj exp b Sr! S a j ; ð0þ where R m, S r are the lognormal statistical parameters of the rainfall rate different for every location and obtained through appropriate regression fitting analysis on the corresponding rainmaps [ITU, 003a]. In addition, a and b are the constants of the specific attenuation [ITU, 003b] and H 1j ¼ L Dj G sinh 1 L Dj þ G 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G 1 L 1 þ1a; ð1þ G where G is a characteristic parameter describing the inhomogeneity of the rainfall medium [Kanellopoulos and Panagopoulos, 001]. 3. Numerical Results and Discussion 3.1. Numerical Evaluation [16] In this section, we apply the proposed model for the prediction of the interference statistics induced by two adjacent slant paths on an Earth-space system using frequency re-use technique. According to the authors knowledge, there are not available experimental data of this kind in the literature; thus we apply the proposed procedure to hypothetical links suffering from interference. On the other hand, the present methodology could be regarded as an extension of the experimentally validated propagation model proposed by Kanellopoulos et al. [000], where only one interfering satellite has been considered. In addition, as pointed out previously, the inputs of the proposed model concerning rain rate and 5of14

6 Figure 4. Numerical evaluations of conditional probability for a single and dual polarized Earthspace system located in Athens, for three pairs of adjacent satellite nominal carrier-to-interference ratios (f = 0 GHz, t =45 ). Curves A F are the same as in Figure 3. The rest of the parameters of the system under consideration are given in Table. rain height statistics are consistent with ITU-R recommendations [ITU, 003a, 003c]. [17] Moreover, the presenting numerical results investigate the impact of two interfering satellites on the prediction of the degradation of the total carrier-tointerference ratio concerning a dual polarized Earthspace system. For this reason, we consider a case study, where an Earth terminal located in Tokyo (35.40 N, E) is in communication with satellite JCSAT (154 E), while two adjacent satellites, OPTUS B3 (156 E) and JCSAT 1B (150 E) operating at the same frequency, induce interference on the wanted signal. The system under consideration is supposed to operate either at 1 GHz or at 0 GHz downlink. In Table 1, the values of the parameters used for the development of the procedure concerning the above communication system are tabulated, and most of them are common for all the extracted figures. [18] In Figure 3, the conditional probability that the carrier-to-interference ratio of the examined satellite system never exceeds a specified level r (db), for various levels of r, and for different values of CIR 1,nomo and CIR,nomo (see section ), is shown. Both the cases of single and double polarization for the wanted signal have been considered. The Earth-space system has been assumed that uses circular polarization (equivalent to polarization tilt angle t = 45 under raining conditions), and operates at Ka band. We have considered the following cases: (1) CIR 1,nomo = CIR,nomo,()CIR 1,nomo < CIR,nomo and (3) CIR 1,nomo CIR,nomo. It should be noted that the corresponding curves for single polarization arise from the proposed model, by taking in formula (), XPD!1. As can be seen, a significant degradation of the CIR level at a certain conditional probability is obvious, when the second source of interference is taken into consideration, especially for cases 1 and. Case 3 is practically equivalent to the subject of having only one interfering satellite, and the numerical results presented here coincide with the ones taken from the Kanellopoulos and Panagopoulos [001] model. One can also observe the substantial degradation of CIR level, moving from the single polarization to the dual polarized mode, particularly for case 3, where only one interfering satellite is involved. On the other hand, for cases 1 and, the impact of signal depolarization on the degradation of the total carrier-to-interference ratio is not so significant. This is a useful conclusion because the dual polarization technique, as it is obvious, is recommended for a system suffering already from interference from two adjacent satellites operating at the same frequency. 6of14

7 Table. Parameters of the Case Study in Athens, Greece Parameter Value R m S r H, km 4.1 H 0,km 0. G 1.5 j 0, deg 43.4 j 1, deg 44.5 j, deg 4.3 q 01, deg 3.37 q 0, deg 3.36 XPD nom,db 30 Outage time, min/yr 300 a, f = 1 GHz Horizontal Circular a, f = 0 GHz Horizontal Circular b, f = 1 GHz Horizontal Circular b, f = 0 GHz Horizontal Circular M, db, f = 1 GHz Horizontal Circular M, db, f = 0 GHz Horizontal Circular [19] Another case study of an interfered Earth-space system located in Athens, Greece (37.58 N, 3.43 E) communicating with Hellas Sat (39 E) is considered in Figure 4. The two adjacent interfering satellites are Eutelsat Sesat (36 E) and Eurasiasat 1 (4 E). The same interfering situations as in Figure 3 have been examined and similar conclusions are drawn. The necessary input parameters for the numerical calculation of the model are given in Table. As can be seen, the degradation of the CIR is greater in Tokyo than in Athens, since Athens is less rainy than Tokyo. [0] Another set of useful diagrams is the following (see Figures 5 and 6), where the variation of the nonexceeded CIR level versus the angular separation q 01 between the wanted satellite S and the interfering satellite S 1 is shown. The second interfering satellite S is considered to be at a fixed angular distance from S in the geostationary orbit. In this case, the q 0 =4.5 value has been taken into account. In Figure 5, the presented curves concern a dual polarized Earth-space system, located in Tokyo as previously, considering two different levels for CIR,nomo = 5, 50 db. The other operational parameters are: f = 1 GHz, t =0, outage time = 300 min/yr while two levels of conditional probability (p%) = 1% and 0.001% are examined. The corresponding carrier-tointerference ratio for a single polarized Earth-space sys- Figure 5. Carrier-to-interference ratio (CIR) numerical evaluations versus the angular separation (q 01 ) from the one satellite for two values of CIR,nomo = 5 db, CIR,nomo = 50 db and conditional probabilities 0.001% and 1% (f = 1 GHz, t =0 ) for the same Earth-space system as in Figure 3, operating in double polarization mode: curve A, CIR,nomo = 50 db, conditional probability 1%; curve B, CIR,nomo = 50 db, conditional probability 0.001%; curve C, CIR,nomo = 5 db, conditional probability 1%; and curve D, CIR,nomo = 5 db, conditional probability 0.001%. 7of14

8 Figure 6. CIR nonexceeded levels versus the angular separation (q 01 ) from the one satellite system with parameters f = 0 GHz and t =45 for three different values of CIR* 1,nomo = 10 db, CIR* 1,nomo = 15 db, and CIR* 1,nomo = 0 db. CIR,nomo = 3 db is considered constant. The other operational parameters are the same as in Figure 3: curve A, single polarization, CIR* 1,nomo = 0 db; curve B, single polarization, CIR* 1,nomo = 15 db; curve C, single polarization, CIR* 1,nomo = 10 db; curve D, double polarization, CIR* 1,nomo = 0 db; curve E, double polarization, CIR* 1,nomo = 15 db; and curve F, double polarization, CIR* 1,nomo = 10 db. tem, taking only into account the induced adjacent interference from S 1, is given by CIR 1;nomo ¼ CIR 1;nomo * þ 5 logðq 01 Þ; ðþ where CIR* 1,nomo represents the CIR 1,nomo for q 01 =1. The last term of the above expression comes from the recommended sidelobe envelope level relative to the normalized peak gain [ITU, 1994b]. In the present example, the value of CIR* 1,nomo = 15 db has been selected. Considering the variation of the angular separation q 01, there are obviously different nominal interference conditions for the wanted Earth-space link. In the case of strong nominal interference from S (CIR,nomo = 5 db) the total CIR level remains low and almost independent of the angular separation angle q 01, particularly for angular separations greater than about 3. Consequently, the CIR level after this threshold becomes also independent to the increase of CIR 1,nomo and is mainly limited by the CIR,nomo value. The alternative case examines the interference effects from S, when CIR,nomo = 50 db, and as a result the CIR level follows CIR 1,nomo improvement for all the range of q 01 values. [1] In Figure 6, the impact of the CIR* 1,nomo on the CIR variation of a dual polarized Earth-space system (f = 0 GHz, t =45 ) is investigated, with the same characteristics as described before. Three different values of CIR* 1,nomo (10, 15 and 0 db) have been selected simulating strong, moderate and weak satellite interference conditions from the first satellite. The CIR,nomo has been chosen as 3 db. As can be seen, the variations of CIR* 1,nomo value have a noticeable effect on the degradation of the total CIR level for small angular separations q 01. Moving to greater 8of14

9 Figure 7. Three-dimensional diagram showing the joint variation of CIR (db) versus the angular separations q 01 and q 0. The parameters of the communication systems are the same as in Figure 3. values of angular separations, which means weaker levels of nominal interference from S 1, the total CIR level seems to be independent of CIR* 1,nomo, converging to a level mainly dependent on the constant CIR,nomo. In the present example, because of the t = 45 selected value, the rain and ice crystals depolarization effects are also a considerable limiting factor of the performance of the system [Kanellopoulos and Panagopoulos, 001]. [] Finally in Figure 7, a three-dimensional presentation of CIR variation versus both the angular separations q 01 and q 0, with respect to the same Earth-space path as above with outage time 300 min/yr and conditional probability 0.001%, is shown. The CIR* i,nomo (i =1,) values have been chosen as 10 and 0 db, respectively, by considering an analogue formula as () for CIR,nomo expressed in terms of q 0. A two-dimensional section of this diagram (see Figure 8) is much more useful to the system designer, illustrating nonexceeded levels of CIR ratio versus the two angular separations. In particular, from this diagram, one can extract the combinations of angular separations under which a nonexceeded level of CIR can be achieved for a given conditional probability and outage time. 9of14 Figure 8. Sections of three-dimensional diagram (Figure 6) for various CIR levels.

10 Table 3. Arithmetic Values of the Parameters in Equations (4) and (5) for Two Frequencies and Three Climatic Zones Climatic Zone M Climatic Zone K Climatic Zone P Single Polarization Double Polarization Single Polarization Double Polarization Single Polarization Double Polarization A 1f(GHz) = ,106 15,987 17,863 f(ghz) = ,387 11,67 1,147 A CIR*,nomo CIR*,nomo B K B 1f(GHz) = f(ghz) = B c c c c c c c c c c c c 1a c 1b c c c c [3] Additionally, these curves can be used for the choice of the satellite transponder to communicate with, to have the fewest interference effects for a specific location. Diagrams of this kind are also very useful for the satellite communications organizations, in order to make the optimum utilization of the geostationary orbit. Observing further Figure 8, we can see that the CIR threshold of 1 db can never be achieved at angular distances q 01 <3 wherever the second satellite is laid in the geostationary orbit. On the other hand, the corresponding value for q 0 is only 1.5. This is because of the fact that the normalized nominal adjacent satellite interference from the first considered satellite has been taken much greater than the second one (CIR* 1,nomo < CIR*,nomo ). Similar conclusions can also be deduced for the other nonexceeded levels of CIR. 3.. Practical System Design Approximation [4] The implementation of the proposed model for the prediction of a nonexceeded CIR for a given conditional probability is rather a complicated procedure. For this reason, taking into account the proposed model results and appropriate regression fitting analysis, after employing the Levenberg-Marquadt algorithm for nonlinear least squares fitting [Jacobs, 1977], simple expressions estimating the CIR are suggested. The obtained formulas are very useful to the system designer and concern the calculation of the nonexceeded CIR levels in terms of the nonexceedance conditional percentage probability (p%), the outage time (min), the angular separations q 01, q 0 (degrees), the elevation angles j (under the assumption that j j 1 j ) (degrees), the operating frequency f (GHz), the polarization tilt angle t (degrees) and the normalized nominal carrier-to-interference ratios CIR* i,nomo (i = 1, ), which are used in the following expressions: CIR i;nomo ¼ CIR i; * nomo þ 5 log q 0j ; ðj ¼ 1; Þ: ð3þ More particularly, for a noise dominant interfered satellite system, the level of signal-to-interference ratio under rain fade conditions can be calculated by CIR ¼ A ½1 expð B 1 q 01 ÞŠ½1 expð B q 0 ÞŠ F 1 ðoutageþf ðp% ÞF 3 ðjþf 4 ðtþ k ð4þ 10 of 14

11 Figure 9. CIR nonexceeded levels versus the outage time for four case studies in different climatic conditions (climatic zones K, M, and P and the Tokyo area), with identical geometrical and electrical parameters (f = 1 GHz, t =0, p% = 0.01%; j = j 1 = j =35, q 01 =, q 0 =3 ) and with CIR* 1,nomo = 18 db and CIR*,nomo = 0 db. Application is of the simple expressions (4) and (5). A ¼ a 1* G CIR ;nomo * a B 1 ¼ b 1* q b 0 G 1 CIR* 1;nomo G CIR* ;nomo F4 ðtþ G 1 CIR* 1;nomo ¼ c1 CIR 1;nomo * þ c CIR 1;nomo * G CIR ;nomo * ¼ c3 þ c 4 CIR ;nomo * þ c 5 CIR ;nomo * þ c 6 CIR ;nomo * 3 F 1 ðoutage Þ ¼ c 7 expð c 8 * outageþ F ðp% Þ ¼ c 9 þ c 10 * p% þ c 11 ðp% Þ þ c 1a ðp% F 3 ðjþ ¼ 1 expð c 13 jþ F 4 ðtþ ¼ c 14 þ c 15 * t þ c 16 * t Þ c 1b 9 >= ; >; ð5þ 11 of 14 where the values of the parameters a 1, a, k, B, b 1, b and c 1 to c 16 can be found for every location of the world using the rainmaps [ITU, 003a] or local rain rate statistics. (The general C code concerning the derivation of the appropriate values applicable to any frequency, geographical latitude, elevation angles, nominal carrierto-interference ratios, nominal cross-polarization discrimination, outage time, and conditional probability can be obtained by sending a request to thpanag@cc.ece. ntua.gr). Here we present the regression fitting numerical results for three climatic zones, M, K and P, and two downlink frequencies, 1 and 0 GHz (see Table 3). We have chosen to show arithmetic values for the constants of expressions (4) and (5), for two frequencies (Ku and Ka band downlink frequencies) and three representative climatic regions (K, Mediterranean region; M, subtropical; and P, tropical region). The proposed relationships with specified arithmetic constants can be obtained for every downlink frequency and specific location climatic conditions using ITU-R rainmaps [ITU, 003a]. It also should be noted that expressions (4) and (5) are only valid under the condition that the used parameters take values in the following restricted ranges: 0 j :5 q 01 ; q 0 10 >= 30 min =yr outage time 300 min=yr ; ð6þ 0:001% p% 0:1% 7dB CIR i;nomo * 30 db ði ¼ 1; Þ >;

12 which are usual in commercial satellite networks design. The regression-fitting model reproduces the results taken from the physical model with RMS error being less than 0.7 db in all the tested cases. [5] Finally, in order to show the application of the easy-to-use equations (4) and (5), we have considered four interfered Earth terminals located in different climatic regions, such as K, M and P climatic zones, and the Tokyo area, with identical geometrical and operational parameters. In Figure 9, the nonexceeded level of CIR for a given conditional probability level versus the outage time is plotted. The corresponding predicted values of CIR for a 10 min/yr outage time are 3.6 db if the Earth terminal is located in K climatic zone and 19. db in P zone. The influence of the rain alone on the deterioration of the CIR level is thus demonstrated. 4. Conclusions [6] The congestion of the communication satellites in geostationary orbit, the necessary employment of downlink power control as fade mitigation technique in VSAT networks along with the close existence of Earth terminals in urban areas have increased the interference environment of an Earth space station. For this reason, the design of satellite systems suffering from interference induced by two adjacent satellites operating at the same frequency may be a problem of current interest. In the present paper, an analytical model for the prediction of CIR statistics concerning a dual polarized Earth-space link suffering by interference from two adjacent satellites under rain fade conditions has been proposed. An important conclusion that has become evident from the numerical results analysis is that the frequency reuse technique is recommended for Earth-space systems suffering from interference from two adjacent satellites, because the total CIR is slightly further degraded. Various parameters affecting the CIR statistics have also been thoroughly examined. To sum up, experimental verification of the proposed procedure is still needed, but we believe that expressions (4) and (5) may be proved very useful either for back of the envelope computations or educational purposes. Appendix A: Carrier-to-Interference Ratio Under Rain Fading [7] According to the configuration of the problem, as shown in Figure 1, the amplitudes of the signals received in the Earth station E are defined as follows: C wanted signal from satellite S under clear-sky conditions; C 0 I 1 wanted signal from satellite S under rain fading; interfering signal from adjacent satellite S 1 under clear-sky conditions; I 0 1 I I 0 D D 0 interfering signal from adjacent satellite S 1 under rain fading; interfering signal from adjacent satellite S under clear-sky conditions; interfering signal from adjacent satellite S under rain fading; interfering signal induced by cross talk on the wanted signal during clear-sky conditions; interfering signal induced by cross talk on the wanted signal during rain fading. Using the above definitions the rain attenuations A C, A I1, A I of the wanted and interfering signals can be expressed as A C ¼ 10 log C C 0 A I1 ¼ 10 log I 1 I1 0 ða1þ ðaþ A I ¼ 10 log I I 0 : ða3þ The following carrier-to-interference ratios under clearsky conditions are also defined as C CIR nom ¼ 10 log I1 þ I þ D ða4þ C CIR i;nom ¼ 10 log Ii ði ¼ 1; Þ ða5þ þ D CIR i;nomo ¼ 10 log C Ii ði ¼ 1; Þ: ða6þ In addition, the cross-polarization discrimination ratio under clear-sky conditions is defined as XPD nom ¼ 10 log C D : ða7þ We also define the cross-polarization discrimination under rain fading XPDðA C Þ ¼ 10 log C0 D 0 : ða8þ 1 of 14

13 Finally, using a straightforward algebra the carrier-tointerference ratio under rain fade conditions can be expressed as C I db C 0 ¼ 10 log I1 0 þ I 0 þ D0 ¼ 10 log 10 A C A I CIR 1;nomo 10 þ 10 A I CIR ;nomo 10 þ 10 A C XPD A C 10 ¼ A I1 þ A I A C 10 log 10 A I CIR 1;nomo 10 þ 10 A I CIR 1 ;nomo 10 þ 10 A I þa 1 I A C XPDðA C 10 ð Þ! Þ ða9þ in terms of the above variables, which is expression () of the main text. Notation j i elevation angle of the slant paths pointing toward satellite S i (i =0,1,); q 0j differential angle between satellites S and S j (j =1,); A C rain attenuations of the wanted signal referring to Earth-space path ES 0 ; A Ii rain attenuations of the interfering signals referring to Earth-space paths ES i (i = 1, ); M rain fade margin for the system under consideration; (C/I) carrier-to-interference ratio at the Earth station E receiver; CIR 1,nomo nominal (under clear-sky conditions) CIR of the system, operating under the single polarization mode, considering only the existence of satellite S 1 ; CIR,nomo nominal (under clear-sky conditions) CIR of the system, operating under the single polarization mode, considering only the existence of satellite S ; CIR* 1,nomo nominal CIR of the system for q 01 =1, considering only the existence of satellite S 1 ; CIR*,nomo nominal CIR of the system for q 0 =1, considering only the existence of satellite S ; XPD(A C ) cross-polarization discrimination due to rain attenuation concerning ES satellite path; a, b constants of the specific rain attenuation; t polarization tilt angle; AC 0 rain attenuation calculated for the projection of the slant path ES; 13 of 14 AI 0 i rain attenuations calculated for the projections of the slant paths ES i (i = 1, ); A m0, S a0 lognormal statistical parameters of the distribution concerning AC; 0 A mi, S ai lognormal statistical parameters of the distributions concerning AI 0 i (i =1,); r nonexceedance level of the (C/I) ratio (db); T out outage time (min/yr); f U0 U 1 two-dimensional normal joint density function; m, s statistical parameters expressed in terms of system and rainfall medium parameters. [8] Acknowledgment. This work was cofunded by the European Social Fund (75%) and National Resources (5%) Operational Program for Educational and Vocational Training II (EPEAEK II) and particularly the program PYTHAGORAS 68/816. References Castanet, L., A. Bolea-Alamañac, and M. Bousquet (003), Interference and fade mitigation techniques for Ka and Q/V band satellite communication systems, paper presented at International Workshop on Satellite Communications From Fade Mitigation to Service Provision, Comm. on Sci. and Technol., Noordwijk, Netherlands, May. Crane, R. K. (1996), Electromagnetic Wave Propagation Through Rain, John Wiley, Hoboken, N. J. Crane, R. K. (003), Propagation Handbook for Wireless Communication System Design, CRC Press, Boca Raton, Fla. International Telecommunication Union (1994a), Recommendation ITU-R S.741., Carrier-to-interference calculations between networks in the fixed-satellite service, S Series, Geneva, Switzerland. International Telecommunication Union (1994b), Recommendation ITU-R S.465-5, Reference Earth-station radiation pattern for use in coordination and interference assessment in the frequency range from to about 30 GHz, S Series, Geneva, Switzerland. International Telecommunication Union (00), Recommendation ITU-R S.133-, Maximum permissible levels of interference in a satellite network (GSO/FSS; non-gso/fss; non-gso/mss feeder links) in the fixed-satellite service caused by other codirectional FSS networks below 30 GHz, S Series, Geneva, Switzerland. International Telecommunication Union (003a), Recommendation ITU-R P.837-4, Characteristics of precipitation for propagation modeling, P Series, Geneva, Switzerland. International Telecommunication Union (003b), Recommendation ITU-R P.838-, Specific attenuation model for rain for use in prediction methods, P Series, Geneva, Switzerland. International Telecommunication Union (003c), Recommendation ITU-R P.839-3, Rain height model for prediction methods, P Series, Geneva, Switzerland.

14 Jacobs, D. A. H. (1977), The State of the Art in Numerical Analysis, Elsevier, New York. Kanellopoulos, J. D., and A. D. Panagopoulos (001), Ice crystals and raindrop canting angle affecting the performance of a satellite system suffering from differential rain attenuation and cross-polarization, Radio Sci., 36(5), Kanellopoulos, J. D., S. Ventouras, and C. N. Vazouras (1993), A revised model for the prediction of differential rain attenuation on adjacent Earth-space propagation paths, Radio Sci., 8(6), Kanellopoulos, J. D., A. D. Panagopoulos, and S. N. Livieratos (000), A comparison of copolar and cochannel satellite interference prediction models with experimental results at 11.6 and 0 GHz, Int. J. Sat. Commun., 18, Lin, S. H. (1975), A method for calculating rain attenuation distribution on microwave paths, Bell Syst. Tech. J., 54(6), Matricciani, E. (1997), Copolar and cochannel interference during rain at 11.6 GHz estimated from radar measurements, Int. J. Sat. Commun., 15, Matricciani, E., and M. Mauri (1996), Cochannel interference in satellite communication systems derived from rain attenuation measurements at 0 GHz, Int. J. Sat. Commun., 14, Panagopoulos, A. D., and J. D. Kanellopoulos (00), Prediction of triple-orbital diversity performance in Earth-space communication, Int. J. Sat. Commun., 0, Rogers, R. R., R. L. Olsen, J. L. Strickland, and G. M. Coulson (198), Statistics of differential rain attenuation on adjacent Earth-space propagation paths, Ann. Telecommun., 37, J. D. Kanellopoulos, T. D. Kritikos, and A. D. Panagopoulos, Wireless and Satellite Communications Group, Division of Information Transmission Systems and Materials Technology, School of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Politechniou Street, Zografou GR-15780, Athens, Greece. (ikanell@cc.ece.ntua.gr; thkri@cc.ece.ntua.gr; thpanag@cc.ece.ntua.gr) 14 of 14