1、 Rec. ITU-R BO.1212 1 RECOMMENDATION ITU-R BO.1212 CALCULATION OF TOTAL INTERFERENCE BETWEEN GEOSTATIONARY-SATELLITE NETWORKS IN THE BROADCASTING-SATELLITE SERVICE (Questions ITU-R 83/11 and ITU-R 85/11) (1995) Rec. ITU-R BO.1212 The ITU Radiocommunication Assembly, considering a) that successful im
2、plementation of satellite systems in the World Administrative Radio Conference for the Planning of the Broadcasting-Satellite Service (Geneva, 1977) (WARC BS-77) and the First Session of the World Administrative Radio Conference on the Use of the Geostationary-Satellite Orbit and the Planning of the
3、 Space Services Utilizing It (WARC ORB-85) broadcasting-satellite service (BSS) plans is dependent upon accurate calculation of mutual interference between satellite networks; b) that geostationary-satellite networks in the BSS operate in the same frequency bands; c) that interference between networ
4、ks in the BSS contributes to noise in the network; d) that it is necessary to protect a network in the BSS from interference by other source networks; e) that, due to increased orbit occupancy, the detailed estimation of mutual interference between satellite networks, requires more accurate values o
5、f polarization discrimination in order to take account of the use of different or identical polarizations by wanted and interfering systems, recommends 1 that to calculate the total interference between two satellite networks considered, the method described in Annex 1 should be used. ANNEX 1 Calcul
6、ation of total interference When evaluating the power produced at a given point by a single satellite (downlink) or at a given satellite location by an earth-station transmitter (up link) the concept of an equivalent gain for each partial link may be employed. There are two antennas involved in each
7、 partial link, and these have both co-polar and cross-polar transmission and reception characteristics. In addition, atmospheric propagation effects, represented principally by co-polar attenuation and cross-polar discrimination, influence the net signal level. 2 Rec. ITU-R BO.1212The equivalent gai
8、n (as a power ratio) for one partial link can be represented by the following approximation:G = G1cos2 + G2sin2G1= GtpGrpA + GtcGrcA + GtpGrcA X + GtcGrpA XG2= GtpGrcA + GtcGrpA2+ GtpGrpA X + GtcGrcA X(1)where: for linear polarization, is the relative alignment angle between the received signal pola
9、rization plane and theplane of polarization of the receive antenna;for circular polarization, = 0 is assumed to correspond to co-polar transmission and reception and = 90is assumed to correspond to mutually cross-polarized transmission and reception;for cases of differing polarizations (e.g. linearl
10、y polarized wanted receive antenna and circularly polarizedinterfering transmissions, or vice versa), = 45Gtp : co-polar gain characteristic of the transmit antenna expressed as a power ratio (Recommend-ation ITU-R BO.652)Gtc : cross-polar gain characteristic of the transmit antenna expressed as a p
11、ower ratioGrp : co-polar gain characteristic of the receive antenna expressed as a power ratio (Recommend-ation ITU-R BO.652)Grc : cross-polar gain characteristic of the receive antenna expressed as a power ratioA : co-polar attenuation on the interfering partial link (as a power ratio 1)X : cross-p
12、olar discrimination on the interfering partial link (as a power ratio 1)X = 10 0.130 log f 40 log (cos s ) 20 log ( 10 log A)for 5 s 60where:f : frequency (GHz)s : satellite elevation angle as seen from the earth station (degrees).For s 60, use s= 60 in calculating the value of X.(See Appendix 1 for
13、 derivation of the relative alignment angle, .)In the expression for G1, power summation of the terms is assumed throughout. Near the main axis of the wantedtransmission, a voltage addition of the first two terms may be more appropriate due to phase alignment while away fromthis axis random effects
14、dictate power addition. However, since the second term is insignificant near this axis theassumption of power addition does not compromise the approximation. Atmospheric depolarization is a random effectthus the last two terms are power summed.In the expression for G2, voltage addition of the first
15、two terms is assumed since, near axis, either term could bedominant and phase alignment of these terms would dictate voltage addition. Away from this main axis the third andfourth terms become the dominant contribution; thus, although a power addition of the first two terms is warranted, inthis regi
16、on as for the G1discussion, the validity of the assumed model is not unduly compromised by maintainingvoltage addition in all regions. Since the transition from voltage addition near axis to power addition off-axis isnebulous, the above expressions, in view of the arguments presented, would appear t
17、o be a reasonable compromisebetween accuracy and simplicity.Rec. ITU-R BO.1212 3Using the equivalent gain concept, the wanted carrier power, C, or the single-entry interfering power, I, on each partiallink is simply given by:C (or I ) = PT LFS LCA+ G dBW (2)where:PT : wanted (interfering) transmitti
18、ng antenna power (dBW)LFS : free-space loss on the wanted (interfering) link (dB)LCA : clear-air absorption on the wanted (interfering) link (dB)G : equivalent gain on the wanted (interfering) link (dB).The aggregate interference power is obtained by adding the powers so calculated for all interfere
19、rs. The ratio of thedesired signal power to the aggregate interference power is the downlink aggregate carrier-to-interference ratio, C/I. Theup-link aggregate interference power and C/I are obtained in a similar way, and the two aggregate values of C/I are thencombined to obtain the total aggregate
20、 C/I.If the ratio of the wanted carrier power to the power of an interfering signal, where both powers are calculated usingequation (2), is to be evaluated for the worst case, such parameters as satellite station-keeping tolerances, satelliteantenna pointing errors, and propagation conditions must b
21、e taken into account. The station-keeping and satellitetransmit-antenna beam errors which should be included are those which result in the lowest receive level of the wantedsignal and the highest receive level of the interfering satellite signal. When the interfering satellite is at a lower elevatio
22、nangle than the wanted satellite, worst-case interference conditions usually occur during clear-sky operation. Conversely,if the interfering satellite is at a higher elevation angle, worst-case interference usually occurs during heavy rainconditions.APPENDIX 1TO ANNEX 1Derivation of the relative ali
23、gnment angle for linear polarizationThis Appendix defines the polarization angle of a linearly polarized radiowave and outlines the method for calculatingpolarization angles and relative alignment angles for both the downlink and feeder link interference cases. Calculation ofrelative alignment angle
24、s are necessary for determining the equivalent gain as defined by equation (1).1 Definition of principle and cross-polarized components of a linearly polarizedradiowaveIn general, the polarization of a radiated electromagnetic wave in a given direction is defined to be the curve traced bythe instant
25、aneous electric field vector, at a fixed location and at a given frequency, in a plane perpendicular to thedirection of propagation as observed along the direction of propagation. When the direction is not stated, the polarizationis taken to be the polarization in the direction of maximum gain. In p
26、ractice, polarization of the radiated energy varieswith the direction from the centre of the antenna, so that different parts of the pattern may have different polarizations.Polarization may be classified as linear, circular or elliptical. If the vector that describes the electric field at a point i
27、nspace as a function of time is always directed along a line, the field is said to be linearly polarized. In the most generalcase, the figure that the electric field traces is an ellipse, and the field is said to be elliptically polarized. Linear andcircular polarizations are special cases of ellipt
28、ical when the ellipse becomes a straight line or a circle, respectively. Forthe interference calculations, we are interested in the far-field polarization of the antenna where the E-field component inthe direction of propagation is negligible so that the net electric field vector can be resolved int
29、o two (time-varying)orthogonal components that lie in a plane normal to the outward radial direction of propagation. In the case of linearpolarization, the reference directions of these orthogonal components must first be defined before one can define apolarization angle. One of these reference dire
30、ctions is designated as the principle or main polarization componentdirection while the orthogonal reference direction is designated as the cross-polarization component direction.4 Rec. ITU-R BO.1212Surprisingly, there is no universally accepted definition for these reference directions. Some altern
31、ative definitions ofprinciple and cross-polarization component directions are discussed in Arthur C. Ludwigs paper, “The Definition ofCross Polarization”, in the IEEE Transactions on Antennas and Propagation, January 1973. In his paper, Ludwig derivesexpressions for the unit vectors for three differ
32、ent cross-polarization definitions in terms of a spherical antenna patterncoordinate system, which is the coordinate system usually adopted for antenna measurements. We briefly describe thesethree definitions below. In this Appendix the unit vector uprepresents the reference direction for the princi
33、plepolarization component of the electric field vector while ucrepresents the direction of the cross-polarized component. Itis helpful to first review the transformation of vectors among rectangular, cylindrical and spherical coordinate systems.1.1 Vector transformation among rectangular, cylindrica
34、l and spherical coordinate systemsFigure 1 shows the three coordinate systems and their associated unit vectors. The transformation matrix fortransforming a vector A in rectangular components (Ax,Ay,Az) to cylindrical components (Ap,A,Az) is:Mrc= cos sin 0 sin cos 0001(3)The transformation matrix fo
35、r transforming a vector A in cylindrical components (Ap,A,Az) to spherical components(Ar,A,A) is given by:Mcs= sin 0 cos cos 0 sin 01 0(4)The transformation matrix for transforming a vector A in rectangular components (Ax,Ay,Az) to spherical components(Ar,A,A) is then:Mrs= McsMrc= sin cos sin sin co
36、s cos cos cos sin sin sin cos 0(5)so that, in terms of components:ArAA= sin cos sin sin cos cos cos cos sin sin sin cos 0AxAyAz(6)Because the matrix is orthogonal, the transformation matrix for transforming from spherical (Ar, A, A) to rectangular(Ax, Ay, Az) components is simply the transposed matr
37、ix:Msr= sin cos cos cos sin sin sin cos sin cos cos sin 0(7)so that:AxAyAz= sin cos cos cos sin sin sin cos sin cos cos sin 0ArAA(8)Rec. ITU-R BO.1212 5The unit vectors ur, u, and uof the spherical coordinate system are in spherical coordinatesur= 100u= 010u= 001(9)ur= sin cos sin sin cos u= cos cos
38、 cos sin sin u= sin cos 0(10)in rectangular coordinates.1.2 Alternative definitions of principal polarization and cross-polarization reference directionsLudwig describes three definitions for the cross polarization by deriving unit vector irefand icross(which we haverenamed upand uc) such that the d
39、ot product of the electric field vector E (t, , ) along some direction (, ) in thefar-field antenna pattern with these unit vectors defines the principal and cross-polarization components, respectively. Inthe direction specified by the spherical coordinate angles (, ), the principal and cross-polari
40、zation components of theelectric field vector are therefore given by:Ep(. ) = E upEc(. ) = E uc(11)(Note that, in general, E, upand ucwill themselves vary with and .)Figure 2 illustrates the polarization patterns corresponding to the three definitions for the case in which the antenna istransmitting
41、 horizontal polarization along its main beam axis.In the first definition, the reference unit vector upis simply taken to be one of the rectangular basis vectors of theantenna pattern coordinate system while ucis another one of the basis unit vectors. For example, we can define:up= yauc= xa(12)where
42、 yaand xaare unit vectors in the positive y and x directions.From the transformation matrices above the spherical coordinate components of these vectors are given by:up= ya= sin sin ur+ cos sin u+ cos u(13)uc= xa= sin cos ur+ cos cos u sin u(14)Ludwig notes that this definition leads to inaccuracies
43、, since in practice, the polarization of the radiated field does varywith direction from the centre of the antenna and that the far-field of the antenna is not planar, but tangent to a sphericalsurface. Ludwigs second and third definitions of polarization therefore involve unit vectors which are tan
44、gent to asphere. In his second definition, the principle polarization direction is chosen to be one of the spherical coordinate unitvectors while the cross-polarization direction is chosen to be one of the other spherical unit vectors. For example, we canchoose:up= uuc= u(15)In Ludwigs third definit
45、ion, the principal and cross-polarization component directions are defined according to how oneusually measures the polarization pattern of an antenna. The standard measurement method is described in Fig. 3. The6 Rec. ITU-R BO.1212probe polarization angle (angle between uand up) is measured from uto
46、wards u. In the case where the transmittedfield is linear horizontal polarization (i.e. in the +y direction) along the boresight ( = 0), turns out to be equal to .Therefore the principal and cross-polarization components in the direction (,) are given by:Ep(t) = E(t) upEc(t) = E(t) uc(16)so that the
47、 electric field E(t ), in that direction can be expressed as:E(t) = Ep(t) up+ Ec(t) uc= Epm cos( t) up+ Ecm cos( t + ) uc(17)This is the general expression for an elliptically polarized wave. Note that in order for E(t ) to be linearly polarized thetime phase between the two orthogonal linear compon
48、ents must be zero (or an integer multiple of pi). The amplitudesof the components Epmand Ecmhowever, need not be equal.The principal and cross-polarization unit vectors, upand uccan be expressed in terms of the spherical coordinate unitvectors, uand u, and the angle = (when the transmitted field is polarized in the +y direction at = 0) by:up= sin u+ cos u(18)uc= cos u sin u(19)Finally, by expressing uand uin rectangular coordinate
