Satellite Communications Part 11 pot

Guidelines for Satellite Tracking 291   1 2 2 1 o o e    (13) o o a e      (14)         7 4 4 2 2 3 2 2 4 2 2 2 0 2 3 3 1 3 1 1 4 8 24 3 2 2 2 2 1 o o o o k C q s n a e e                                                (15) 1 2 *C B C  (16) * B is the SGP4 type drag coefficient   4 5 3,0 3 2 sin o o E o o q s A n a i C k e     (17) 3 3,0 3 E A J a  , (18) Whereas 3 J is the third gravitational zonal harmonic of the Earth.              7 4 4 2 2 3 2 2 4 2 2 2 3 2 2 3 1 1 2 2 1 2 1 2 2 1 3 1 3 3 1 3 1 2 1 2 cos2 2 2 4 o o o o o o o o o o o o k C n q s a e e a e e e e                                                                  (19) o  is the “mean” argument of perigee at epoch.       7 4 4 2 2 3 2 5 11 2 1 1 4 o o o o o C q s a e e                     (20) 2 2 1 4 o D a C    (21)   2 3 3 1 4 17 3 o o D a a s C      (22)   3 4 4 1 2 221 31 3 o o D a a s C      (23) The secular effects of atmospheric drag and gravitation are included through the equations       2 2 2 4 2 2 2 3 4 7 3 1 3 3 13 78 137 1 2 16 DF o o o o o o o k k M M n t t a a                            (24) Where o M is the “mean” mean anomaly at epoch and   o tt  is time since epoch         2 2 2 4 2 4 2 2 4 2 4 4 8 4 8 3 1 5 3 7 114 395 5 3 36 49 2 16 4 DF o o o o o o o o o k k k n t t a a a                                    (25) 4 4 4 3 8 E k J a  (26) According to previous cases, 4 J is the fourth gravitational zonal harmonic of the Earth       2 3 2 2 4 2 2 4 4 8 4 8 3 4 19 5 3 7 3 2 2 DF o o o o o o o o o k k k n t t a a a                                 (27) And o  is the “mean” longitude of ascending node at epoch.     3 * cos o o B C t t     (28)       4 3 3 4 2 * 1 cos 1 cos 3 E o DF o o a M q s B M M e                  (29) p DF M M M       (30) DF M        (31)   2 2 1 2 2 21 2 o DF o o o n k C t t a          (32)     4 5 * * sin sin o o p o e e B C t t B C M M     (33)         2 2 3 4 1 2 3 4 1 o o o o o a a C t t D t t D t t D t t                 (34)               2 3 4 2 3 1 2 1 3 1 2 1 5 2 2 4 4 1 3 2 1 2 1 3 1 2 3 12 10 2 4 1 3 12 6 30 15 5 p o o o o o IL M n C t t D C t t D C D C t t D C D D C D C t t                            (35)   2 1 e    (36) 3 2 e n k a (37) where   o tt  is time since epoch. Satellite Communications292 In cases where perigee height is less than 220 kilometers, the equations for a and IL should be truncated after the 1 C term, and all terms involving 5 C ,  , and M  should be dropped. Add the long-period periodic terms cos xN a e   (38)   3,0 2 2 sin 3 5 cos 1 8 o L A i IL e k a              (39) 3,0 2 2 sin 4 o yNL A i a k a   (40) T L IL IL IL  (41) sin y N yNL a e a    (42) Next step involves solving the Kepler’s equation for    E by defining T U IL  (43)       1i i i E E E           (44)             cos sin sin cos 1 yN xN i i i i yN xN i i U a E a E E E a E a E                     (45)   1 E U    (46) The following equations are used to calculate preliminary quantities needed for short-period periodics.     cos cos sin xN yN e E a E a E       (47)     sin sin cos xN yN e E a E a E       (48)   1 2 2 2 L xN yN e a a  (49)   2 1 L L p a e  (50)   1 cosr a e E  (51) sin e a r k e E r   (52) L e p rf k r   (53)     2 sin cos cos 1 1 yN xN L a e E a u E a r e                (54)     2 sin sin sin 1 1 xN yN L a e E a u E a r e                (55) 1 sin tan cos u u u         (56)   2 2 1 cos2 2 L k r u p     (57)   2 2 2 7 1 sin 2 4 L k u u p      (58) 2 2 3 sin 2 2 L k u p    (59) 2 2 3 sin cos 2 2 o L k i i u p    (60)   2 2 1 sin 2 L k n r u p       (61)     2 2 2 3 1 cos 2 1 3 2 L k n rf u p               (62) The osculating quantities are calculated with the addition of short-period periodics   2 2 2 2 1 3 1 3 1 2 L k L e r r k r p                (63) k u u u    (64) k      (65) k o i i i    (66) k r r r       (67) Guidelines for Satellite Tracking 293 In cases where perigee height is less than 220 kilometers, the equations for a and IL should be truncated after the 1 C term, and all terms involving 5 C ,  , and M  should be dropped. Add the long-period periodic terms cos xN a e   (38)   3,0 2 2 sin 3 5 cos 1 8 o L A i IL e k a              (39) 3,0 2 2 sin 4 o yNL A i a k a   (40) T L IL IL IL  (41) sin y N yNL a e a    (42) Next step involves solving the Kepler’s equation for     E by defining T U IL    (43)       1i i i E E E           (44)             cos sin sin cos 1 yN xN i i i i yN xN i i U a E a E E E a E a E                     (45)   1 E U    (46) The following equations are used to calculate preliminary quantities needed for short-period periodics.     cos cos sin xN yN e E a E a E       (47)     sin sin cos xN yN e E a E a E       (48)   1 2 2 2 L xN yN e a a  (49)   2 1 L L p a e  (50)   1 cosr a e E  (51) sin e a r k e E r   (52) L e p rf k r   (53)     2 sin cos cos 1 1 yN xN L a e E a u E a r e                (54)     2 sin sin sin 1 1 xN yN L a e E a u E a r e                (55) 1 sin tan cos u u u         (56)   2 2 1 cos2 2 L k r u p     (57)   2 2 2 7 1 sin 2 4 L k u u p      (58) 2 2 3 sin 2 2 L k u p    (59) 2 2 3 sin cos 2 2 o L k i i u p    (60)   2 2 1 sin 2 L k n r u p       (61)     2 2 2 3 1 cos 2 1 3 2 L k n rf u p               (62) The osculating quantities are calculated with the addition of short-period periodics   2 2 2 2 1 3 1 3 1 2 L k L e r r k r p                (63) k u u u   (64) k      (65) k o i i i   (66) k r r r      (67) Satellite Communications294 k rf rf rf       (68) Unit orientation vectors are calculated by sin cos k k u u U M N (69) cos sin k k u u V M N (70) where sin cos cos cos sin x k k y k k z k M i M i M i                  M (71) cos sin 0 x k y k z N N N                 N (72) Then, position and velocity are given by k rr U (73) and   k k r rf r U V    (74) 2.2 Propagation models modifications SGP propagation model was modified in time. Several minor points in the original SGP4 paper emerged where performance of SGP4 could be improved. To maximise the usefulness of all of these features, one should ideally use Two Line Elements formed with differential correction, using an identical model as well (Vallado, D. et al. 2006). Next chapter will shed some light on what Two Line Elements are. 3. Two Line Elements Orbit tracking programs require information about the shape and orientation of satellite orbits. That information was available from different websites. One of most common quoted sources is CelesTrak.com website, maintained by the group of satellite tracking enthusiasts. As a result of legislation passed by the US Congress and signed into law on 2003 November 24 (Public Law 108-136, Section 913), which was updated in 2006 (US National Archives, 2006.), Air Force Space Command (AFSPC) has embarked on a three-year pilot program to provide space surveillance data—including NORAD two-line element sets (TLEs)—to non- US government entities (NUGE). Since US Public Law prohibits the redistribution of the data obtained from this new NUGE service "without the express approval of the Secretary of Defence“a lot of other sources were immediately shut down. CelesTrak has received continuing authority to redistribute Space Track data from US government and that way become one of the most useful information sources for the community. TLE’s are redistributed in a form shown in Fig. 5. All relevant parameters are color-coded and explained in Table 1. ISS 1 25544U98067A10102.85853206 .0002565400000-017456-309629 2 25544 51.6472205.9374 0004892 166.2878 293.9622 15.74716373653188 Fig. 5. Two Line elements set Element Description ISS Satellite name 1 25544U 2 25544 Satellite number 98067A International designator 51.6472 Inclination 10102.85853206 Epoch Year & Day Fraction 205.9374 0004892 Right Ascension of the Ascending Node .00025654 First Derivative of Mean Motion 00000-0 Second Derivative of Mean Motion 166.2878 Eccentricity 293.9622 Argument of Perigee 15.747163736 Mean Anomaly 53188 Revolution Number at Epoch & Checksum 17456-3 Drag Term 0 Ephemeris Type 9629 Element number & Checksum Table 1. Two Line Elements Explained There are several things to consider. The accuracy of the original TLEs is not known. Some TLE data propagates into future quite well, while, the next set of elements can depart dramatically after only a day or less. Methods to overcome this problem are explained in (Vallado, D. et al. 2006). 4. Integrating Mathematical Models Our intention was to integrate all orbital propagation models into one C# program. Integral version of the program can be downloaded from http://medlab.elfak.ni.ac.rs/spacetrack/sgpsdp.rar. It is important to highlight main program methods used for satellite position calculations: publicvoidSGP(intIFLAG,doubleTSINCE) publicvoidSGP4(intIFLAG,doubleTSINCE) publicvoidSDP4(intIFLAG,doubleTSINCE) publicvoidSGP8(intIFLAG,doubleTSINCE) publicvoidSDP8(intIFLAG,doubleTSINCE) Guidelines for Satellite Tracking 295 k rf rf rf       (68) Unit orientation vectors are calculated by sin cos k k u u U M N (69) cos sin k k u u V M N (70) where sin cos cos cos sin x k k y k k z k M i M i M i                  M (71) cos sin 0 x k y k z N N N                 N (72) Then, position and velocity are given by k rr U (73) and   k k r rf r U V    (74) 2.2 Propagation models modifications SGP propagation model was modified in time. Several minor points in the original SGP4 paper emerged where performance of SGP4 could be improved. To maximise the usefulness of all of these features, one should ideally use Two Line Elements formed with differential correction, using an identical model as well (Vallado, D. et al. 2006). Next chapter will shed some light on what Two Line Elements are. 3. Two Line Elements Orbit tracking programs require information about the shape and orientation of satellite orbits. That information was available from different websites. One of most common quoted sources is CelesTrak.com website, maintained by the group of satellite tracking enthusiasts. As a result of legislation passed by the US Congress and signed into law on 2003 November 24 (Public Law 108-136, Section 913), which was updated in 2006 (US National Archives, 2006.), Air Force Space Command (AFSPC) has embarked on a three-year pilot program to provide space surveillance data—including NORAD two-line element sets (TLEs)—to non- US government entities (NUGE). Since US Public Law prohibits the redistribution of the data obtained from this new NUGE service "without the express approval of the Secretary of Defence“a lot of other sources were immediately shut down. CelesTrak has received continuing authority to redistribute Space Track data from US government and that way become one of the most useful information sources for the community. TLE’s are redistributed in a form shown in Fig. 5. All relevant parameters are color-coded and explained in Table 1. ISS 1 25544U98067A10102.85853206 .0002565400000-017456-309629 2 25544 51.6472205.9374 0004892 166.2878 293.9622 15.74716373653188 Fig. 5. Two Line elements set Element Description ISS Satellite name 1 25544U 2 25544 Satellite number 98067A International designator 51.6472 Inclination 10102.85853206 Epoch Year & Day Fraction 205.9374 0004892 Right Ascension of the Ascending Node .00025654 First Derivative of Mean Motion 00000-0 Second Derivative of Mean Motion 166.2878 Eccentricity 293.9622 Argument of Perigee 15.747163736 Mean Anomaly 53188 Revolution Number at Epoch & Checksum 17456-3 Drag Term 0 Ephemeris Type 9629 Element number & Checksum Table 1. Two Line Elements Explained There are several things to consider. The accuracy of the original TLEs is not known. Some TLE data propagates into future quite well, while, the next set of elements can depart dramatically after only a day or less. Methods to overcome this problem are explained in (Vallado, D. et al. 2006). 4. Integrating Mathematical Models Our intention was to integrate all orbital propagation models into one C# program. Integral version of the program can be downloaded from http://medlab.elfak.ni.ac.rs/spacetrack/sgpsdp.rar . It is important to highlight main program methods used for satellite position calculations: publicvoidSGP(intIFLAG,doubleTSINCE) publicvoidSGP4(intIFLAG,doubleTSINCE) publicvoidSDP4(intIFLAG,doubleTSINCE) publicvoidSGP8(intIFLAG,doubleTSINCE) publicvoidSDP8(intIFLAG,doubleTSINCE) Satellite Communications296 Previous FORTRAN IV code produced by T.S. Kelso in 1988 according to (Hoots, F. R et al. 1980) was not optimized and hard to execute on modern parallel (multi-core) architectures. The FORTRAN implementation of the SGP4 and SDP4 model in respective methods is rudimentary for the propagation process. It was necessary to produce functions which would help us calculate position ݎԦ and velocity ݎԦ of a satellite at any given time by using the TLE data. Models specified in (Hoots, F. R. and al., 1980) from the original FORTRAN IV code are ported to C# in respect to the corrections made during the years, especially in the SDP4 subroutine DEEP. C# code contains the same variable names and structures as in the original FORTRAN routines to ensure compatibility and expandability.  Additional encapsulation was done with the creation of ActiveX component ready to be integrated in any .NET project. 5. NAVSTAR Satellite Tracking Software NAVSTAR satellite tracking software presented in this paper is also based on the mathematical SGP4/SDP4 model. Program uses two line elements set as an input to calculate and visualize satellite’s position in Space. It can be used to navigate telescopes to space objects passing over certain point on Earth. The complete mathematical model is encapsulated in ActiveX control, so it acts like a black box. The data is provided from TLEs and on the other end viewport coordinates are calculated. NAVSTAR has three basic functions:  Graphical display of satellite positions in real-time, simulation, and manual modes;  Tabular display of satellite information in the same modes;  Generation of tables (ephemerides) of past or future satellite information for planning or analysis of satellite orbits. Fig. 6. Satellite selection dialog and Table Window The principal feature of NAVSTAR is a series of Map Windows, which display the current position of satellites and observers on a simple world map, together with information such as bearing (azimuth), distance, and elevation above the observer's horizon. The maps may be updated in real time, simulated time, or manually set to show the situation at any given moment of time, past or future. An additional Table Window displays much more-detailed information about one or more satellites in a tabular form. The tabulated items can be selected and rearranged to fit the screen. This information can be updated in real-time, manual, or simulation modes as illustrated in Fig. 6. Also, satellite 2D footprint (Fig.7) tracking is available, as well as a 3D view (Fig.8). Tracking algorithms SGP4 and SDP4 give considerable accuracy and opportunity of efficient computation of viewing opportunities. It’s also possible in 3D view to make a prediction on satellites position in the future, or to see its position in the past. All is based on the information gathered from TLE’s. The preciseness of visualization depends on accuracy and age of gathered TLE data. Fig. 7. 2D View Regarding the 3D View (Fig.8), options for variable view angle, zoom and time increment are implemented. This gives a user the opportunity to view satellite from all angles and possibility to see its path (orbit), area on the Earth covered by its signal (in a form of beam) and real-time movement, as well as possible faster movement caused by a time speed up. Fig. 8. 3D Satellite tracking View Guidelines for Satellite Tracking 297 Previous FORTRAN IV code produced by T.S. Kelso in 1988 according to (Hoots, F. R et al. 1980) was not optimized and hard to execute on modern parallel (multi-core) architectures. The FORTRAN implementation of the SGP4 and SDP4 model in respective methods is rudimentary for the propagation process. It was necessary to produce functions which would help us calculate position ݎԦ and velocity ݎԦ of a satellite at any given time by using the TLE data. Models specified in (Hoots, F. R. and al., 1980) from the original FORTRAN IV code are ported to C# in respect to the corrections made during the years, especially in the SDP4 subroutine DEEP. C# code contains the same variable names and structures as in the original FORTRAN routines to ensure compatibility and expandability.  Additional encapsulation was done with the creation of ActiveX component ready to be integrated in any .NET project. 5. NAVSTAR Satellite Tracking Software NAVSTAR satellite tracking software presented in this paper is also based on the mathematical SGP4/SDP4 model. Program uses two line elements set as an input to calculate and visualize satellite’s position in Space. It can be used to navigate telescopes to space objects passing over certain point on Earth. The complete mathematical model is encapsulated in ActiveX control, so it acts like a black box. The data is provided from TLEs and on the other end viewport coordinates are calculated. NAVSTAR has three basic functions:  Graphical display of satellite positions in real-time, simulation, and manual modes;  Tabular display of satellite information in the same modes;  Generation of tables (ephemerides) of past or future satellite information for planning or analysis of satellite orbits. Fig. 6. Satellite selection dialog and Table Window The principal feature of NAVSTAR is a series of Map Windows, which display the current position of satellites and observers on a simple world map, together with information such as bearing (azimuth), distance, and elevation above the observer's horizon. The maps may be updated in real time, simulated time, or manually set to show the situation at any given moment of time, past or future. An additional Table Window displays much more-detailed information about one or more satellites in a tabular form. The tabulated items can be selected and rearranged to fit the screen. This information can be updated in real-time, manual, or simulation modes as illustrated in Fig. 6. Also, satellite 2D footprint (Fig.7) tracking is available, as well as a 3D view (Fig.8). Tracking algorithms SGP4 and SDP4 give considerable accuracy and opportunity of efficient computation of viewing opportunities. It’s also possible in 3D view to make a prediction on satellites position in the future, or to see its position in the past. All is based on the information gathered from TLE’s. The preciseness of visualization depends on accuracy and age of gathered TLE data. Fig. 7. 2D View Regarding the 3D View (Fig.8), options for variable view angle, zoom and time increment are implemented. This gives a user the opportunity to view satellite from all angles and possibility to see its path (orbit), area on the Earth covered by its signal (in a form of beam) and real-time movement, as well as possible faster movement caused by a time speed up. Fig. 8. 3D Satellite tracking View Satellite Communications298 The part of Earth not covered with the Sun light is dimmed on the globe, so the user can predict when it will become possible to see the satellite by a naked eye. This software can be used to visualise the orbit trajectory of a satellite under different points of view. It gives the user the freedom of being able to study the satellite’s ground conjunctions by tracking the satellite over the ground, or, with another approach, by calculating the elevation and azimuth angle of the satellite from a static ground station position. Another very useful functionality, previously mentioned is satellite’s footprint visualisation. These functionalities can be used, from an engineering point of view, to adjust ground station dishes in order to establish reliable links to the satellite by calculating it’s precise position with the help of TLE data sets. 3D view can be used to simulate satellite’s orbit around the Earth. Time lapse function enables user to see the orbit in the future, and exact satellite’s position so we would be able to see which orbit parameters the satellite has to have in order to fulfil its task. 6. Conclusion It is assumed that “space age” started with the first artificial satellite in the orbit around the planet. Nowadays, satellites are used for various different purposes: telecommunications, broadcasting, observation, imaging and even espionage. What they all have in common is the fact that they all must obey the rules of celestial mechanics. To be able to visualise the motion, software presented in this chapter was created. For the satellite dynamics, the SGP4 and SDP4 models by NORAD were implemented. Both SGP4 and SDP4 are based on fundamental laws stated by Newton and Kepler. One of the biggest advantages of SGP4/SDP4 models is that they’ve been recognized and verified by NORAD thus providing a precise and manageable mathematical framework for the orbital calculations. But bear in mind that those are not perfect models. They work with mean values. NORAD has removed periodic variations in a particular way, and the models, in their present form do not contain numerical integration methods. Future investigations and updates will improve propagation making it more precise. This process will certainly increase the complexity, so the balance between complexity and preciseness must be kept. 7. References Binderink, A. L.; Radomski, M.S.; Samii M. V. (1989) Atmospheric drag model calibrations for spacecraft lifetime prediction; In NASA, Goddard Space Flight Center, Flight Mechanics/ Estimation Theory Symposium; 445-458 Bunnell, P. (1981) Tracking Satellites in Elliptical Orbits; Ham Radio Magazine; 46-50. Hoots, F. R.; Roehrich R. L. (1980) Models for propagation of NORAD element sets; Project Spacecraft Report No. 3; Aerospace Defence Command, United States Air Force, 3-6 King-Hele, D.G (1983), Observing Earth Satellites, Macmillan Montenbruck, O.; Gill, E (2000) Real-Time estimation of SGP4 Orbital Elements from GPS Navigation Data; International Symposium SpaceFlight Dynamics, MS00/28; 2-3 US National Archives and Records Administration.(2006) US Public Law, Section 109–364; Oct. 17, 2006, Stat. 2355. Vallado A. D.; Crawford P. (2006) SGP4 Orbit Determination; American Institute of Aeronautics and Astronautics publication; 19-21. Interference in Cellular Satellite Systems 299 Interference in Cellular Satellite Systems Ozlem Kilic and Amir I. Zaghloul X Interference in Cellular Satellite Systems Ozlem Kilic (1) and Amir I. Zaghloul (2,3) (1) The Catholic University of America, Washington, DC, U.S.A. (2) Virginia Polytechnic Institute and State University, VA, U.S.A (3) US Army Research Laboratory, MD, U.S.A. 1. Introduction In cellular satellite communications systems, a given coverage area is typically filled with a network of contiguous spot beams, which carry concentrated radiation along preferred directions. The coverage regions for such applications are typically large areas, such as continents and many beams need to be generated. Due to bandwidth limitations in cellular communications, the same bandwidth is allocated to beams which are isolated spatially. This is known as frequency reuse, and the beams operating at the same frequency are referred as co-channel beams. While this approach allows a large coverage area with limited bandwidth, the co-channel beams have the potential to interfere with each other. This is known as co-channel interference and its nature and how it could be reduced is the focus of this chapter. The interference in multiple beam satellite communications systems will be investigated under two different approaches. First approach, which is the conventional way of defining beam coverage on earth, is discussed in Section 2. This will be referred to as spot beam coverage as explained in further detail later. The interference will be investigated for two cases; first is the uplink where interference at the satellite antenna is the main concern, and the second is the downlink where interference at the user terminal is calculated. Section 3 discusses a new method of defining beam coverage on earth, referred to as sub-beam coverage. The motivation is to keep the coverage on earth identical but reduce the satellite antenna size as much as 50% (Kilic & Zaghloul, 2009). The advantages and overall performance of the sub-beam approach in terms of interference is the subject of Section 3. 1 2. Interference in Cellular Satellite Systems In multibeam satellite systems, the coverage area is divided into a number of beams often referred to as spot beams, which are much smaller in size and cover the area contiguously. 1 Copyright 2009 American Geophysical Union, This chapter has material substantially reproduced, with permission, from Radio Science, Volume 44, No. 1, January 2009, „Antenna Aperture Size Reduction Using Subbeam Concept in Multiple Spot Beam Cellular Satellite Systems,, O. Kilic and A.I. Zaghloul. 15 Satellite Communications300 Since satellite systems are bandwidth limited, the sub-division of beams into smaller portions allow for frequency reuse to increase capacity. The available bandwidth is shared among these beams as depicted in Figure 1 for reuse factor of n. Fig. 1. Frequency reuse in multi-beam satellite communications The size of the antenna that generates these beams on earth is related directly to the peak gain at the center of the spot beams and the smallest spot beam size. The spot beams are typically defined by the contours at 3 or 4 dB down from the peak power at the center of the beam. 2.1 Coverage on Earth Achieving a contiguous coverage is important so that there are no regions without service in the coverage area. Since the beams are defined by the projection of antenna patterns on earth at a certain contour value, they tend to be close to circular shape. These circles on earth need to be structured so that they overlap with each other to avoid any gaps in the coverage area. In order to have a systematic approach, these can be represented by various geometric lattices that tessellate. A few such possibilities are shown in Figure 2. It is often the hexagon that is used in the system design as it closely represents a circle, i.e. for the same distance from the center to the edge, the hexagon area is closest to that of the circle that circumscribes it. Therefore the hexagon represents the beam which circumscribes it as shown in Figure 3. This assures that there are no gaps between beams. Then the system is designed based on this artificial hexagonal geometry on earth as depicted in Figure 4. Fig. 2. Contiguous coverage on earth using tessalating shapes – hexagonal, square and triangular lattices Fig. 3. Hexagonal representation of a circular beam Fig. 4. Hexagonal Coverage on Earth 2.2 Frequency Reuse Since the satellite systems typically serve large ares such as countries or continents, a large number of beams need to share the available bandwidth. Therefore, the available bandwidth within a beam becomes a very limited resource, as is implied in Figure 1 earlier. To circumvent this, a frequency reuse scheme is often utilized. This is based on reusing the same frequencies in spatially isolated beams. Therefore, the available bandwidth is divided into a smaller number of beams than the total number of beams in the coverage area. The set of contiguous beams that share the total available bandwidth is known as a cluster. The clusters are then repeated in the coverage area relying on the fact that the beams operating at the same bandwidth will be separated from each other sufficiently so that they do not interfere with each other. [...]... spread farther apart 312 Satellite Communications Frequency Reuse=3 Total C/I =8.3953 Spot-center 110 90 C/I 70 50 30 10 -10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 #Tier Frequency Reuse=4 Total C/I =11. 3146 Spot-center 110 90 C/I 70 50 30 10 -10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #Tier Frequency Reuse=7 Total C/I =13.3563 Spot-center 110 90 C/I 70 50 30 10 -10 1 2 3 4 5 6 7 8 9 10 11 #Tier Fig... to the spot beam configuration First the definition of the spot beam concept is presented and the sources of interference in a multiple beam communication system are identified Then the sub-beam concept is introduced Finally, the performance of the conventional spot beam approach with the sub-beam partitioning technique is compared in terms of co-channel beam interference 3.1 Partitioning of spot beams... index (or spot beam cluster size) of seven is depicted in the figure The large circles encompassing sets of seven hexagons represent the spot-beam clusters based on this reuse factor The subbeams are shown for the center spot beam of each cluster A sub-beam cluster size of four is assumed in the demonstration Fig 18 Sub-beam partitioning for spot beams, reuse =7 Interference in Cellular Satellite Systems... assigned 316 Satellite Communications arbitrarily The choice will depend on the edge gain of the spot beam as well as the partition size, Ns Fig 19 Possible Sub-beam Partitions for Contiguous Coverage 3.4 Defining the Sub-beams to Achieve Desired Gain Reduction A contiguous coverage of the sub-beam clusters can be obtained by satisfying Equation 1, in which case the number of sub-beams that define a spot beam... dB) compared to the spot beam approach (36-40 dB) A group of these smaller sub-beams, i.e “sub-beam clusters,” represent each spot beam Fig 17 Sub-beam representation of a spot beam To satisfy the contiguity requirements of the coverage, the sub-beams intersect at the boundaries of the spot beam Figure 18 demonstrates the sub-beam concept, where the hexagons correspond to the spot beams in the coverage... at the center of the spot beam and the smallest spot beam size The spot beams are typically defined by the contours at 3 or 4 dB down from the peak gain at the center of the beam While it is the edge gain requirement which needs to satisfy the communication link, the satellite antennas have to be sized for the maximum gain to achieve the 3-4 dB drops around the perimeter of the spot beam Therefore it... 500 The spot beams generated by the 40x40 element phased array antenna for frequency reuse of three are shown in Figure 15 The radii of all spot beams are assumed equal to that of the center spot beam, and are computed using the beam width at -4dB relative to the peak gain and the altitude as follows: Radius  H (altitude)* tan( 4 dB _ down ) (8) Interference in Cellular Satellite Systems 311 For the... occurs in the software-driven processor on board the satellite, with minimal addition to the hardware 3.5 Interference in Sub-beam Partitioned Coverage The same LEO system as in section 2.5 is considered for the interference analysis of the subbeam partitioned coverage A comparison of beam coverage on earth for spot beam and subbeam configuration with partition size of 3 is shown in Figure 23 The beams... Coverage on Earth – Spot beam pattern (left) versus Sub-beam pattern (right) Sub-beam partition sizes of four and seven will be considered for the interference analysis Figure 24 shows a zoomed in depiction of which one of the sub-beams that replace a spot beam are used for interference calculations The spot beam to be replaced is the blue circle, while the red circles are the sub-beams for a partition size... edge gain requirements In order to do this, each spot beam in the coverage area is divided into a number of smaller beams defined by contour levels less than the typical 3 or 4 dB, as depicted in Figure 17, where four sub-beams are used to replace a spot beam For an edge gain requirement of 36 dB, it is observed that the sub-beam approach 314 Satellite Communications provides a more uniform gain distribution . Reduction Using Subbeam Concept in Multiple Spot Beam Cellular Satellite Systems,, O. Kilic and A.I. Zaghloul. 15 Satellite Communications3 00 Since satellite systems are bandwidth limited, the. as possible faster movement caused by a time speed up. Fig. 8. 3D Satellite tracking View Satellite Communications2 98 The part of Earth not covered with the Sun light is dimmed on the globe,. multi-beam satellite communications The size of the antenna that generates these beams on earth is related directly to the peak gain at the center of the spot beams and the smallest spot beam