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The impact of gateway distribution on the system capacity of CDMA mobile satellite systems Liang, Hongyi 1999

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The Impact of Gateway Distribution on the System Capacity of CDMA Mobile Satellite Systems B y H o n g y i L i a n g B . Eng.(EE), Harbin Institute of Technology, 1992 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1999 © Hongyi Liang, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date A ^ ) r i g , <4<?7 DE-6 (2/88) Abstract Recent research indicates that satellite diversity is a practical means of mitigating the effects of satellite fading for Mobi le Satellite Systems (MSS) employing C D M A . However, the underlying assumption of such research is that satellite diversity is available all the time, which is not true in reality. We wi l l investigate the impact of improper gateway distribution on the system capacity of M S S . We investigate the principle of distributing the gateways to ensure single and. dou-ble satellite service and present some strategies of searching for the optimal gateway distribution for single and double satellite service. To analyze the impact of gateway distributions on the system capacity of M S S , we classify the general mobile terminal environments into five states. B y computing the required power margin of each state to reach the same average Bit-Error Rate (BER) and taking the occurrence probability of each state into account, the capacity of a Mobi le Satellite System, expressed as the average number of mobile terminals per satellite over the area ranging from South 80° to North 80°, is analytically derived and thoroughly validated by means of computer simulations. After comparing the system capacity of a M S S with improper gateway distributions to that with the optimal gateway distribution, we show that the capacity of a M S S is decreased considerably due to improper gateway distributions. Moreover, the quantitative results indicate that a M S S in a propagation environment of light shadowing suffers more capacity loss due to improper gateway distribution than a M S S in an environment of heavy shadowing. Contents Abstract ii List of Tables vi List of Figures vii Acknowledgment x Chapter 1 Introduction 1 1.1 Motivation and Objectives 1 1.2 Thesis Outline 5 Chapter 2 Multiple Satellite Service Availability Analysis 7 2.1 Terminology .".' . 7 2.2 Multiple Satellite Coverage Analysis 9 2.2.1 J. G. Walker Constellation and Sub-satellite Equations . . 9 2.2.2 Coverage Analysis 10 2.3 Multiple Satellite Service Availability 14 2.4 Optimal Gateway Distribution 19 2.4.1 Optimal Gateway Distribution for Single Satellite Service . 19 2.4.1.1 Problem Statement 19 2.4.1.2 : Sufficient Condition of Gateway Distribution Ensuring Single Satellite Service 20 2.4.1.3 Refined Sufficient Condition Ensuring the Single Satellite Service . 21 2.4.1.4 Gateway Distribution Employing General Solution Algorithm 22 iii 2.4.1.5 Gateway Distribution Employing Local Solution Algorithm . 24 2.4.2 Optimal Gateway Distribution for Double Satellite Service . 25 Chapter 3 Impact of Gateway Distribution to Mobile Satellite System Capacity 30 3.1 Definitions and System Outline 31 3.1.1 System Capacity 31 3.1.2 System Outline 32 3.1.3 Channel Model 35 3.2 Analysis of Average Probability of Error 37 3.3 Power Margins for Each Scenarios 41 3.3.1 SS/C: Single Satellite Service/LOS Path 41 3.3.2 SS/S: Single Satellite Service/Shadowing Path 42 3.3.3 DS/CC: Double Service/Both Paths are LOS . . . 43 3.3.4 DS/SS: Double Service/Both Paths are Shadowed .... 45 3.3.5 DS/CS: Double Service/One Path is LOS, Another Path is Shadowed 47 3.4 The Average Interference for Each Scenario 49 3.4.1 Fraction of Double Satellite Service Links 49 3.4.2 Terminology 54 3.4.3 Effect of gateway distribution on PSS distribution 57 3.4.4 Interference Calculations . 61 iv 3.5 Capacity Calculation . 6 3 3.6 Numerical and Simulation Results . . 1 65 3.6.1 Numerical Results 66 3.6.2 Simulation Results . . 6 9 3.6.2.1 Simulation Algorithm . 6 9 3.6.2.2 Simulation Results .71 Chapter 4 Conclusion and Discussion 74 Bibliography 76 Appendix A List of Abbreviations and Acronyms 80 Appendix B Supporting Calculations 81 B.1 DS/SS Calculation .81 B.2 DS/CS Calculation 81 Appendix C Supporting Figures 83 Appendix D Simulation Programs in Matlab 84 V List of Tables Table 1 Recently proposed LEO/MEO satellite systems 2 Table 2 Power margins for different scenarios 48 Table 3 The average number of pairs of links providing double satellite service and the average pds for the Globalstar System 53 Table 4 The average pds for different GW distributions . 54 Table 5 Path States 55 Table 6 Summary of States 56 Table 7 Double satellite service transition matrix 60 Table 8 The system capacity comparison for GW distribution 4 and GW distribution 5 under different channel conditions . . . 69 Table 9 The simulation results for system capacity on channel condition (B=0.3, c=10) 72 vi List of Figures Figure 1 Satellite diversity 3 Figure 2 Gateway distribution and satellite diversity 4 Figure 3 Satellite diversity 8 Figure 4 Globalstar satellite constellation 10 Figure 5 Half-Central angle 11 Figure 6 Satellite coverage analysis model . . . 12 Figure 7 Satellite coverage analysis for NYC 13 Figure 8 Average fraction of time when multi-satellite coverage is available at different latitudes 14 Figure 9 Overlapping coverage circles centered at MT and GW . . 15 Figure 10 Satellite service analysis model . 17 Figure 11 Satellite Service analysis for New York city 18 Figure 12 Gateway distribution 2 21 Figure 13 Optimal gateway distribution for single satellite service . . 22 Figure 14 Gateway distribution 3: GW distribution without considering satellite orbits 23 Figure 15 The optimal gateway distribution for single satellite service , 24 Figure 16 Gateway distribution 4 employing local solution 25 Figure 17 Gateway distribution for double satellite service model . .26 Figure 18 The Max—Min satellite distance 28 vii Figure 19 Gateway Distribution 5 ensuring double satellite service between North (South) 25° and 45° in the Globalstar system 29 Figure 20 The isoflux antenna of Globalstar 31 Figure 21 System model 33 Figure 22 Two-Arm Rake receiver. . . 34 Figure 23 Channel model 37 Figure 24 Uplink of reverse link scenarios 41 Figure 25 SS/C: Single satellite service/LOS channel 41 Figure 26 SS/S: Single satellite service/Shadowing path 42 Figure 27 DS/CC: Double satellite service/Both paths LOS 44 Figure 28 DS/SS: Double service/Both paths are shadowed 45 Figure 29 DS/CS: Double service/One path is LOS, another path is shadowed 47 Figure 30 The required power margins for different scenarios . . . . 49 Figure 31 Interference calculation 50 Figure 32 One pair of satellite links capable of providing double satellite service 52 Figure 33 Path and satellite service analysis . 58 Figure 34 The tree diagram of PS—>PSS 59 Figure 35 Distributions of PSS states of Globalstar system 62 Figure 36 Multiple access interference in the Globalstar system . . . 64 Figure 37 BER Vs. pds (Varied system capacity J) 66 Figure 38 BER Vs. pds (varied B) 67 Figure 39 Capacity Vs. pds 68 viii Figure 40 3912 MTs equally distributed on the Earth .70 Figure 41 The simulation diagram 71 Figure 42 The theoretical and simulation results (B=0.3,c=10) . . . . 72 Figure 43 Flowchart for calculating satellite service 83 ix Acknowledgment I would like to express my gratitude to my research supervisor, Prof. Victor C. M . Leung, for his direction, guidance and support throughout my studies at University of British Columbia. His helpful comments and critical questions made research interesting for me. This work is funded by the Canadian Institute for Telecommunications Research (CITR) through a Research Assistantship provided by Prof. Leung. Also , I would like to thank my friend M r . Wee Liat Er for his kind help to review this thesis. Further, special thanks to my colleagues and staff in the department for their help. Finally, I would like to thank my family for their encouragement and consistent support for me to pursue my personal goal. Without them nothing would have been possible. Chapter 1 Introduction 1.1 Motivation and Objectives The concept of the Mobile Satellite Systems (MSS) [1], providing Personal Mobi le Satellite Communication System (PMSCS) , holds the promise of truly global ubiquitous hand-held low-delay real time communications for mobile telephony and data transmis-sions, without the need for complex ground-based infrastructures required by existing land-based cellular systems. P M S C S wi l l complement terrestrial cellular systems by of-fering service in regions where the cellular systems cannot economically be deployed. A number of M S S s based on low or medium earth orbiting ( L E O , M E O ) satellites, as shown in Table 1 [2][3], have been proposed. Currently, some of these systems are under development and some of them are already in service. These systems employ two distinct architectures for which the Iridium [4] and Global-star [5] systems are archetypal. In the Iridium system, satellites with onboard-switching and onboard-processing capabilities are networked together through intersatellite links and interconnected to the terrestrial public switched telephone network (PSTN) via a small number of gateways (GWs) (11 G W s are planned [2]). In the Globalstar system, communications employ Code Division Multiple Access ( C D M A ) [6] [7] over mobile satellites bent-pipe transponders which work like frequency-translating repeaters [8], and all. the necessary data switching and processing are com-pleted in the GWs, which interconnect the M S S to the P S T N . The Globalstar system generally requires a larger number of G W s (200 G W s are required [2]), as a mobile terminal (MT) and at least one G W must be simultaneously illuminated by the same satellite in order to communicate with each other over this satellite. 1 Chapter 1. Introduction Description ARIES CALLING ELLIPSO GLOBALSTAR IRIDIUM Service Cellular-like Cellular-like Cellular-like Cellular-like Cellular-like voice, voice, voice, voice, voice, Positioning- Positioning- Positioning- Positioning- Positioning-RDSS, RDSS, RDSS, RDSS, RDSS, Paging, Paging, Paging, Paging, Paging, Messaging Messaging Messaging Messaging Messaging, Data Transfer Coverage CONUS Global CONUS CONUS Global offshore US offshore US Total Active 46 840 17 48 66 Satellites Orbit Planes 7 circlular 21 circular 2 elliptical 6 circular 6 circular inclined, 1 polar inclind inclined (52°) polar(86.5°) circular (116.6°), 1 equatorial circular equatorial Satellite Per 5 in each 40 5 in each 8 11 Orbital Plane inclined orbit, inclind orbit, 7 11 in equatorial in equatorial orbit orbit Switching and ground-based onboard cellular ground-based ground-based onboard Processing switching switching, switching switching cellular inter-satellite switching, link inter-satellite link Multiplexing CDMA TDMA/FDMA FDMA/CDMA CDMA FDMA/TDMA Modulation PN/QPSK DQPSK Capacity 2,400 1,100 Table 1 Recently proposed L E O / M E O satellite systems The main advantages of the Globalstar system over the Iridium system are lower system complexity and cost, tighter integration with terrestrial networks, and most importantly, the capability of employing satellite diversity, a key feature of M S S s employing C D M A . 2 Chapter 1. Introduction Figure 1 Satellite diversity In essence, satellite diversity as shown in Fig . 1 allows signals transponded over multiple satellites to be coherently combined at the Rake receivers in the G W s and M T s . It has been shown [9][10] that satellite diversity is an effective method to combat blocking and shadowing effects and thus considerably improves the link quality through a noticeable reduction of Signal-to-Noise Ratio (SNR) variations. This immediately leads to a reduction of outage probability, i.e., the probability that S N R falls below a specified minimum value dictated by the kind of application. Propagation measurements performed with several aircrafts simulating satellites indicate that the required link margin can be reduced by up to 70% [11] when two or three simultaneous paths are available. A modified Rake receiver suitable for the small delay between two satellite paths has also been developed [12]. Note that performance improvements due to satellite diversity depend heavily on the spatial distribution of GWs, as diversity reception is possible only via those satellites which simultaneously illuminate the M T and the G W connecting it to the P S T N . Consider the two cases shown in Fig . 2 where a M T is illuminated by two satellites. With a proper G W distribution as in case (a), there exists at least one G W illuminated by the same 3 • . Chapter I. Introduction two satellites. Transmissions from the M T are received by each of the two satellites and re-transmitted to the G W ; diversity reception is performed at the G W and the reception performance at the G W is improved due to satellite diversity. However, i f the G W serving the M T is only illuminated by one of the two satellites, which path to the M T is shadowed as in case (b), not only would diversity reception at the G W be impossible, but the M T would also have to increase its transmit power to maintain the desired performance. A s a result, the M T generates additional interference to the other satellite. Since the number of M T s lacking satellite diversity to a G W at any specific time period may be large, the cumulative impact on system capacity could be significant. SAT1 SAT2 Figure 2 Gateway distribution and satellite diversity So far, a host of papers evaluating the system capacity and the link performance of L E O M S S systems have been published. Especially, an elaborated analysis for reverse (mobile-to-satellite) link performance of multi-beam multi-satellite C D M A is found in [13] and a detailed performance analysis of the forward (gateway-satellite-mobile) link performance is reported in [14]. A l l the papers have assumed that satellite diversity is 4 Chapter 1. Introduction always available. This assumption might not be realized for reasons of geographical limitations (e.g. sea, desert), economical, or political considerations. U p to date, analysis of satellite service availability and the effects of G W distribution on M S S capacity, have not yet been found in the literature. A detailed examination of the relationship between satellite system capacity and G W distribution is necessary. In this thesis, we mainly address the following problems: 1. For a given satellite constellation, analyze the effects of G W distribution on satellite service availability and present some strategies to find the optimal gateway distri-bution. 2. For a given G W distribution, analyze its effects on the system capacity, based on the reverse link performance of a M S S . 1 .2 Thesis Outline In chapter two, we analyze the percentage of time satellite coverage and satellite service are available to a specific location under a given G . J Walker L E O satellite con-stellation. To ensure satellite service availability, we present the optimal G W distribution including a general solution and a local solution for single satellite service, and some strategies to find the optimal G W distribution for double satellite service. The results in this chapter wi l l be applied in the capacity evaluations by analytical and simulation methods. In chapter three, we classify the general M T environment into five distinct scenarios. B y computing the required power margins for each scenario to achieve the same prob-ability of Bit-Error Rate (BER) and taking the occurrence probability of each scenario into account, the reverse link capacity is analytically derived and thoroughly validated 5 Chapter 1. Introduction by means of computer simulations. The summaries of this thesis are presented in chapter four. 6 Chapter 2 Multiple Satellite Service Availability Analysis 2.1 Terminology The capacity of a CDMA-based M S S is largely constrained by the required S N R at the M T and G W receiver. The G W distribution has a significant effects on S N R calculations as it determines whether satellite diversity can be exploited. Therefore, a complete and detailed analysis of satellite coverage and service for a given G W distribution is necessary. In this chapter, we wi l l analyze satellite coverage and satellite service for a M T under a given satellite constellation. Furthermore, we wi l l try to search for the optimal G W distribution for single and double satellite service, or, a G W distribution providing single or double satellite service when the optimal distribution is very difficult to pursue. Based on these results, we wi l l be able to investigate the relationship between system capacity and system coverage and services in the next chapter. To facilitate further discussions, a consistent terminology is necessary. We distinguish the concepts of satellite coverage and satellite service as follows, • Satellite Coverage — A G W or M T is covered by a mobile satellite i f the satellite's elevation angle is higher than a specified minimum value (assumed to be 10° in this thesis). • Satellite Service — A M T may receive service from a satellite enabling it to communicate with some G W if the satellite covers both the M T and G W . We can further extend these definitions as follows: • Single Satellite Service — the M T and at least one G W are covered by the same satellite(s); it is the minimal condition for a M T to receive service; 7 Chapter 2. Multiple Satellite Service Availability Analysis E E B Q E E B L E G E N D GATEWAY MOBILE TERMINAL c SATELLITE Figure 3 Satellite diversity • Double Satellite Service — the MT and at least one GW are under double satellite coverage of the same set of satellites; it is a precondition for satellite diversity to be enabled. In the snap shot shown in Fig. 3, the ellipses represent the 10 degrees elevation contours of mobile satellites SAT 1 and SAT 2. GW a and MT A receive double satellite coverage from both satellites while GW b and MT B receive single satellite coverage from SAT 2 only. Thus MT A may receive single satellite service from SAT 2 via GW b, or double satellite service from both SAT 1 and SAT 2 via GW a, in which case satellite diversity is enabled. However, MT B may only receive single, satellite service from SAT 2 via GW a or b, without the availability of satellite diversity. Note that the coverage and service each MT receives may change over time due to satellite movements. For any given MSS constellation, we address the following problems in this chapter. 1. Given the GW distribution, to determine the fraction of time a MT at any given location receives single satellite service while it has single coverage, single satellite service while it has double coverage, and double satellite service while it has double coverage. 8 Chapter 2. Multiple Satellite Service Availability Analysis 2. To find the optimal G W distributions guaranteeing single satellite service for M T locations receiving single satellite coverage. Since all the computation is based on spherical geometry, all distances are angular measured (in degree) with respect to the Earth's surface in the following discussions. 2 . 2 Multiple Satellite Coverage Analysis 2.2.1 J. G. Walker Constellation and Sub-satellite Equations A number of constellation schemes have been proposed [15][16][17] for M S S . However, the J . G . Walker Constellation [18] by J . G Walker has been proved the optimal satellite constellation, which requires a minimum number of satellites for global or zone coverage of the earth, for inclined circular orbits. The J . G . Walker constellation is specified by a reference code T/P/F, where there are a total number of T satellites in P orbital planes having the same inclination angle rj, with a F x 360°IT phase increment. The phase increment is defined as the angle between a satellite and its ascending node when its easterly neighbor satellite is crossing the equator (ascending node is the intersection of the orbit with the plane of the equator, the satellite crossing this plane from south to north). Globalstar employs the J . G.Walker 48/8/1 constellation. There are a total of 48 satellites in. 8 planes with 45° separation between ascending nodes of adjacent planes, and 7.5° delay between 2 correspondent satellites between two adjacent satellite orbital planes. The satellite constellation of the Globalstar system is illustrated in F ig . 4. For a given constellation, the orbital period To is given by (2.1) 9 Chapter 2. Multiple Satellite Service Availability Analysis Figure 4 Globalstar satellite constellation where H is the satellite altitude. In Globalstar, H is 1389 Km and To is 113 minutes. For a given T7F7F J. G. Walker constellation, in the following sections, we assume that the right ascension angle of first orbit plane is —180°. Therefore, the sub-satellite position of the jth satellite of the zth orbital plan at time t is given by . . 2TXF . 2TXP 2itt ° =1 * ~Y~ +) * ~Y~ + ~r~ la = s i n - 1 (sin (5) * sin (r/)) 2TT lo = —7r + i * — + t a n - 1 (tan (6) * cos (n)) (2.2) where la and lo are the latitude and longitude of the sub-satellite position (the satellite's projection posistion on the Earth) respectively. 2.2.2 Coverage Analysis For a given minimum elevation angle, the half-central angle r (i.e., the radius of the satellite coverage area, or, footprint) is given by, r = cos - l COS (j) where 4> is minimum elevation angle. COs(l + egyg ) 10 (2.3) Chapter 2. Multiple Satellite Service Availability Analysis Minimal Elevation Angle Satellite Altitude Half-central Angle center of Earth Figure 5 Half-Central angle In the Globalstar system, we assume the minimum elevation angle is 10°. Therefore, the radius of satellite coverage is 26°, which equals to 1842 K m . In contrast to geosynchronous earth orbiting (GEO) satellites, L E O satellites are continuously moving relative to the Earth. A s such, satellite coverage for a given M T is a time-dependent variable. To analyze satellite coverage for a given M T , an algorithm is developed. There are three procedures. 1. Determine which orbital planes are visible to the M T . 2. Determine the connection time, the period of time the M T is illuminated by some satellites of a visible orbital plane. 3. Combine all the connection time periods from all visible orbital planes. Step 1 is accomplished by computing the displacements between orbital planes and the M T . A l l the orbital planes whose displacements from the M T are less than the radius of satellite coverage are visible to the M T . A s illustrated in F ig . 6, the displacement from 11 Chapter 2. Multiple Satellite Service Availability Analysis a given M T to the ith orbital plane is given by rf = s i n - ^ s i n ( c ) . s i „ ^ n - ' ( ^ j - , j j (2.4) where n is the orbit's inclination angle, la and lo are the M T ' s latitude and longitude, respectively, and c is the great circle distance between the right ascending node of ith orbital plane and the M T , calculated as: c = cos - 1 (cos (la) * cos (lo — i * — ^ ^ (2.5) Figure 6 Satellite coverage analysis model Step 2 is achieved by computing the satellite crossing points ( X I and X 2 in F ig . 6). Since we know the satellite speed with knowledge of the satellite constellation, we wi l l be able to derive satellite connection time based on the distance between 2 crossing points. Referring to F ig . 6, the distance from X I and X 2 to the ascending node is given by: • - l ( c o s ( r ) \ x = sin I — — J \^sin2(c) * cos2((f) + cos2(c) J i / cos(c) \ -tan-1! K ' \sin{c) * cos(ip) j where c is given by Eqn. (2.5). Step 3 find the overlapping period from different orbital planes. 12 Chapter 2. Multiple Satellite Service Availability Analysis A s an example, the latitude and longitude of New York is North 40.7517° and West 73.9942°, respectively. Assuming the Globalstar constellation and the right ascension of the first orbital plane is West 180°. The satellite coverage for each orbital plane and the overall satellite coverage for New York City ( N Y C ) are calculated and illustrated in F ig . 7 Coverage Analysis for NYC by orbit 5 4.5 <u 1 4 V) o 3.5 » 3 o> o> 5) 8 2 1.5 1 0.5 0 Overall Coverage Analysis for NYC 10 12 Time (Minute) 14 16 . 18 Figure 7 Satellite coverage analysis for N Y C A C program is written to analyze satellite coverage for a total of 360 * 180 sample points on the Earth in an increment of 30 seconds to show the percentile of one satellite period, averaged over all longitudes, during which a given latitude receives the indicated satellite coverage. Note that, since the satellite pattern repeats itself when a satellite 13 Chapter 2. Multiple Satellite Service Availability Analysis moves to the precedent satellite's position, it is only necessary to analyze 113*60/6=1130 seconds for the Globalstar system. The overall satellite coverage for the whole system is illustrated in Fig . 8 100r 90 -80 -70 -O 0 Q. 60 -~m 50 -15 o 40 -o 30 -20 -10 -0 -I I I I \ I \ I 7 double/ coverage 3 or more satellites •. V ^^jxJnore_sa tellites single coverage -90-80 -60 -40 LEGEND: - single coverage - - double coverage 20 0 20 40 60 80 90 L a t i t u d e 3 or more satellites 4 or more satellites Figure 8 Average fraction of time when multi-satellite coverage is available at different latitudes From Fig . 8, we can see that single satellite coverage is guaranteed in the areas with latitudes between North and South 70° latitude, and double satellite coverage or even higher satellite coverage is guaranteed in the areas with latitudes of South 25° to 45° and North 25° to 45° . 2.3 Multiple Satellite Service Availability To determine the satellite service available at a M T location, a graphical analysis, as shown in F ig . 9, which consists of two overlapping circles having the same radius as the satellite coverage pattern, is performed. The MT circle is centered at the M T location 14 Chapter 2. Multiple Satellite Service Availability Analysis for which service is being evaluated, and the GW circle is centered at a GW which may provide service to the MT. The GW circles of more than one GWs may overlap the MT circle, but we only show one GW circle in the figure for clarity. The following scenarios exist for satellite service availability at the MT location: 1. No GW exists which GW circle overlaps the MT circle. It is not possible for any satellite to simultaneously cover the MT and any GW. Therefore, no satellite service is available at the MT location. 2. No satellite orbital plane goes through the overlapping area between the MT circle and any GW circle (e.g., SAT2 does not go through the overlapping area in Fig. 9). Again, no satellite simultaneously covers the MT and any GW, so that no satellite service is available at the MT location. SAT3 4 \ mt l e n d SAT2 SAT ,1 t start srv LEGEND: r G A T E W A Y S A T E L L I T E MOBILE T E R M I N A L ORBITAL P L A N E Figure 9 Overlapping coverage circles centered at MT and GW 15 Chapter 2. Multiple Satellite Service Availability Analysis 3. There exists one satellite orbital plane (e.g., SAT1 in F ig . 9) intersecting the overlap-ping area between the M T circle and a G W circle. Single satellite service is available from time t%lrt to ts™d over a satellite in this orbital plane via the respective G W . 4. If at least two satellite orbital planes intersect the overlapping area between the M T circle and the respective G W circle, double satellite service is available via the G W during the times when the satellites on at least two of these orbital planes are located simultaneously within the overlapping area. A t other times only single satellite service is available. Based on the above considerations, a satellite service algorithm, similar to previous section but more complicated, is presented to evaluate the satellite service availability at a specific M T location. The algorithm consists three steps as follows: 1. Determine which G W s ' circles overlap the M T circle; 2. For each G W , find the orbital planes going through the overlapping area of the M T and G W circle; 3. Determine the satellite service time. Step 1 is accomplished by computing the distances between the M T and nearby G W s . A l l the G W s at a distance less than the diameter of the satellite coverage pattern from the M T are selected. Step 2 is accomplished by calculating the displacements from the G W s or the M T to each orbital plane. With the aid of F ig . 10, the displacement d between an orbit plane specified by the inclination angle rj and the longitude of the ascending node and a specific M T (or G W ) location is given by, d = sin~l(sin(l) * sin(9)) (2.7) 0 = tan~1(tan(la)/sin(lo)) — n 16 Chapter 2. Multiple Satellite Service Availability Analysis where lo and la are the differences in1 longitudes and latitudes between center O of the MT/GW circle and the ascending node E of the orbit, and / is the distance between E and O. If the displacements of the M T and GW to an orbit and the distance between the GW and M T are less than the radius of the satellite coverage pattern, the orbit goes through the overlapping area of the M T and GW circles Satellite Orbit Ascending Node L Equator F i g u r e 10 Satell ite service analysis m o d e l Step 3 is accomplished by computing the crossing points XI and X2 of the orbital plane and the MT/GW circle and calculating overlapping satellite service time. The distance x between the ascending node and the crossing point XI or X2 of the orbital plane and the MT/GW circle is determined by - l / . c o s ( r ) y/sin2(l) * cos2 (9) + cos2 (I) J (2 8) -tan-l( C ° S { 1 ) ^ \sin(l) * cos(0) J where r is the radius of the satellite coverage pattern. The satellite coverage time t1^ for the MT, which is the time period that the M T is illuminated by the satellite, is 17 Chapter 2. Multiple Satellite Service Availability Analysis determined by, ±mt t mt start X2 — I * OJ V xi — i * OJ (2.9) v 4 j.mt j.mt tX = te„A ~ tc "end start where X2 and x\ are the distances between X I , X 2 and the ascending node given by Eqn. (2.9), and t™art, t™^ , as shown in Fig. 9, are the start and end time of the satellite trajectory crossing the M T circle, i is the satellite orbit number, OJ is the phase increment of ith orbital plane, and v is the satellite angular velocity. The satellite crossing time for a G W circle can be derived by similar method. Thus, the single satellite service time, which is the intersection of the satellite crossing time intervals of the M T and G W , can be obtained. 3r 2.5-o a) co 0.5 10 12 Time (min.) 14 16 18 Figure 11 Satellite Service analysis for New York city The flowchart for calculating satellite service is shown in Fig. 43 in Appendix C . With a G W distribution as described later in Fig. 12 ensuring single satellite service, the overall satellite service for New York City is illustrated in Fig. 11. From the figure above, we conclude that the G W distribution shown in Fig. 12 does not guarantee double satellite service for N Y C , and more GWs are needed. Chapter 2. Multiple Satellite Service Availability Analysis 2.4 Optimal Gateway Distribution The optimal Gateway distribution is defined as a minimum number of G W s guaran-teeing satellite service when the satellite coverage is available. When a single G W is dropped, the same level of satellite service can not be maintained everywhere. Although in reality it is impossible to employ an optimal G W distribution obtained by mathematical calculation, because of geography limitation or economic or even political considerations, . the intention to pursue an optimal G W distribution is to present a best scenario. This information is very useful for M S S system design. 2.4.1 Optimal Gateway Distribution for Single Satellite Service 2.4.1.1 Problem Statement Let MT be a set of K MTs on the Earth mt\, mi'i mt}., ST a set of M sub-satellite points sti(t),st2(t), stM(t) of the corresponding satellites 1 to M respectively. The positions of the members of S T are time-variant and are governed by Eqn. (2.2), and GT the set of TV G W s gt\,gt2, gt^ on the Earth. The computation of the minimum G W distribution for single satellite service can be restated mathematically as follows: min(N) (2.10) under the constraint that, for any given mt^ £ MT, there exist gtn £ GT, stk £ ST such that the following two conditions are satisfied: \mtk- stm(t)\ <r Vt (2.11) \stm(t) - gtn\ <r where r is the radius of satellite coverage. Before we go into further analysis of optimal G W distribution for single satellite service, we wi l l first derive the sufficient condition of G W distribution ensuring single satellite service. 19 Chapter 2. Multiple Satellite Service Availability Analysis 2.4.1.2 : Sufficient Condition of Gateway Distribution Ensuring Single Satellite Service Proposition: For a given J. G . Walker Constellation, or any other constellations, where single satellite coverage is available, i.e., there exist st^ £ S T such that \mtk — stm(t)\ < r V i at any mt^ G M T , the sufficient condition on the G W dis-tribution providing single satellite service is that \stm(t) — gtn\ < r Vt, Explanation: A s illustrated in Fig 8, the inherent design of the J. G . Walker Constellation already ensures that most areas receive single satellite coverage, and the mid-latitudes receive double satellite coverage most of the time. Consider a M T location where \mtk — stm(t)\ < r, Vt is satisfied. If each satellite in the constellation is able to communicate with at least one G W at any time, then condition \stm — gtn\ < r, Vt is met for the M T . B y the definition, single satellite service is guaranteed. We wi l l now propose two G W distributions in order to a) investigate the basic characteristics of G W distribution patterns satisfying Proposition / to refine the sufficient condition of optimal G W distribution, and b) provide some useful G W distribution configurations in the future capacity analysis and simulations. Gateway Distribution 1: Uniformly distribute the G W s along the satellite orbital planes at an interval equal to the diameter of the satellite coverage pattern. 40 G W s are required to ensure single satellite service. Gateway Distribution 2: Distribute the G W s between adjacent orbital planes at the intersections of coverage patterns of satellites orbiting these planes, which is shown in F ig . 12. 32 G W s are required to ensure single satellite service. Applying the similar terminology in the previous section, the circles in G W distri-bution 2 are called the G W service circles. The center of a G W service circle is located at G W gtn, and its radius is r. 20 Chapter 2. Multiple Satellite Service Availability Analysis - -150 -100 - 5 0 .0 50 100 150 longitude Figure 12 Gateway distribution 2 After studying G W distributions 1 and 2, we notice that i f the satellite tracks (satellites' trajectory on the Earth) are completed covered by the service circles of the G W s , Proposition I is satisfied. Therefore, a refined sufficient condition of G W distribution ensuring single satellite service is derived. 2.4.1.3 Refined Sufficient Condition Ensuring the Single Satellite Service Proposition II: Let SK be the set of M satellite tracks (satellite's trajectory on the Earth) on the Earth ski,sk-2,.:....skM, resulting from a given constellation of M Satellites. If all members of SK are completely covered by G W service circles, single satellite service is ensured. Explanation: Because ski is the trajectory on the Earth of the ith satellite, therefore, ski = sti(t) Vt. If SK is completely covered by GT, at any time t, there exists gt _ G T such that |s i i(i) — gtf \ < r V i . Therefore, Proposition I is satisfied. . 21 Chapter 2. Multiple Satellite Service Availability Analysis Based on Proposition II, the problem to search for an optimal G W distribution ensuring single satellite service becomes a problem of searching for a G W distribution covering all the satellite tracks with a minimum number of G W s . To cover an object using a number of other kinds of objects is called a Packing and Covering Problem [19] [20]. Covering a square by circles is one of the well-known Packing and Covering Problem [21]. U p to date, there are a few proven optimal solutions to the packing problem and covering. For majority of cases, especially problems involving a large number of circles, searching for an optimal solution is extremely difficult. In the optimal theory, there are two algorithms which can be applied to search for the optimal G W distribution [22], namely, General Solution algorithm and Local Solution algorithm-The General Solution can be applied to a diverse set of problems. But, it does not necessarily yield the optimal solution for each specific case. The local solution, although it produces a better solution, is usually only applicable to one specific situation. 2.4.1.4 Gateway Distribution Employing General Solution Algorithm The general solution algorithm is obtained by constructing a G W distribution without considering the satellite orbits. If a G W distribution completely covers the areas under EQUATOR GATEWAY Figure 13 Optimal gateway distribution for single satellite service 22 Chapter 2. Multiple Satellite Service Availability Analysis Figure 14 Gateway distribution 3: G W distribution without considering satellite orbits the satellite orbits which lie from South 52° to North 52° in the Globalstar system, all the satellite tracks are covered by G W . service circles. In plane geometry, the hexagon has been proved to be the optimal covering solution in the plane [23]. The equivalent solution in spherical theory is to place circles in such a pattern that the centers of any 3 closest circles form an equilateral triangle and these circles intersect of only one common point. The pattern in F ig . 13 results in the minimum number of G W s to completely cover the satellite tracks. From Fig . 13, the distance between two G W gtA and gtg is given by: dAB = cos-1 (cos2(R) — sin2(R) * COS(OAOB)) (2.12) where R is the radius of satellite coverage, and OAOB is 120°. In the Globalstar system, dAB is 44° . 23 Chapter 2. Multiple Satellite Service Availability Analysis If the areas with latitude from South 52° to North 52° are covered, then the boundary of these area must be covered as well. On the latitude side, ^ = 2.36, therefore, three layers-are required to cover the boundary. On the longitude side, since maximal distance between 2 points in the same latitude occurs in the equator, ^ = 8.18, 9 G W s per layer are required. The lower bound of the number of G W is given by N > 27. Fig . 14 illustrates the location of G W s for G W distribution 3 in the Globalstar system employing the general solution. The scheme requires 27 G W s in total to ensure that MTs between South 70° and North 70° receive single satellite service. 2.4.1.5 Gateway Distribution Employing Local Solution Algorithm General Solution Local Solution Orbit- satellite track SKI Gateway Service Circle —satellite track S k 5 Figure 15 The optimal gateway distribution for single satellite service B y investigating in more detail the G W distribution derived from the general solution in F ig . 15, we find that as long as the service circle gw\ covers A, the intersection point between gw2 and sk^, and B, the intersection point between gwz and ski, satellite tracks ski and sk^ are still completely covered by G W s service circles. Thus, the G W service circle Cl may be centered at a higher latitude and the total number of G W s may be reduced. Based on the local solution algorithm, G W distribution 4, a distribution of 21 G W s for the Globalstar system is illustrated in F ig . 16. 24 Chapter 2. Multiple Satellite Service Availability Analysis Figure 16 Gateway distribution 4 employing local solution In F ig . 16, 7 G W s are placed along the equator in the first layer and 7 G W s are in the layers on North and, South 32.3°. The areas shown between the two horizontal lines on South 52° and North 52° denote the satellite orbital areas. Note that i f the radius of G W service is changed, G W distribution 4 may no longer be valid. 2.4.2 Optimal Gateway Distribution for Double Satellite Service Since the derivation of the optimal G W distribution for double satellite service is far more complicated and difficult than that for single satellite service, and for the reason that our main goal is to present a G W reference system for further capacity analysis, we wi l l attempt to develop an algorithm for constructing a G W distribution to provide double satellite service, rather than pursuing an optimal distribution as we did for single satellite service. 25 Chapter 2. Multiple Satellite Service Availability Analysis In order to construct a G W distribution GT to provide double satellite service, we equally distribute G W s in a hexagonal pattern pn the spherical surface, as shown in the right picture of Fig . 17. If the separation distance d between 2 closest G W s is sufficiently small, GT w i l l ensure that at least one G W is available within any double satellite coverage areas. A s a result, double satellite service is available to the M T s in those areas. The minimum number min(N) of G W s is obtained when d is maximum. LEGEND \ ~ . GATEWAY | MOBILE TERMINAL ™*WM SATELLITE Figure 17 Gateway distribution for double satellite service model To maximize the value of d, let us consider a case illustrated in F ig . 17. A t any given time t, a M T mt^ £ MT illuminated by m(t) > 2 satellites in {sti,st2 stm} satisfies the following condition: \stm(t) - mtk\ < r (2.13) For clarity, only sti • £ ST and st2 £ ST are shown in the figure. Let Cstm denote satellite coverage area of stm. Based on double satellite service analysis in the previous section, in order to ensure that mt^ receives double satellite service from sti and st2, there must exist at least one G W gtn, in the junction or overlapped area of the satellite 26 Chapter 2. Multiple Satellite Service Availability Analysis coverage of st\ and sti, i-e. f]Cst2- To simplify the analysis, we assume that the satellite coverage patterns of st\ and stq, are fixed, and Cg^ f] Cst2 is free to be oriented in any direction. The distance d of GT guaranteeing that there is always a G W located in Cstl H Cst2 is given by al = c o s - 1 (cos2l + sin2l * cos ( — j j V V 3 / / (2.14) , dst\—st2 where dst\-st2 is the width of P | C a i 2 . dsh-st2, which is closely related to the distance between st\ and st2, is calculated as: dst\-st2 = 2 * r - dtiStust2 (2.15) where r is the radius of satellite coverage area and dt stltSt2 is the distance between 5^1 and 5^2 at time t. Clearly, the closer the satellite distance is, the larger the G W separation distance is. , Since there are m(t) satellites visible to the typical M T mtk and only one pair of them is needed to provide double satellite service, the G W separation distance can be /m(t)\ maximized by choosing dmtk t, i.e. the minimum distance of I J possible distances between m(t) satellites for mtk at time t. The G W distribution GT derived from the above algorithm wi l l ensure that at least one G W is located within one double satellite coverage area. Subsequently, for all the MTs or sample points, the G W separation distance d ensuring all MTs receiving double satellite service is d = m&x(dmtk) (2.16) The M a x - M i n distance dmt for the Globalstar system in the areas with latitude from North 25° to North 45° , (i.e. areas which receive 100% double satellite coverage as shown in F ig . 8), is illustrated in Fig . 18. The figure shows that the satellite separation 27 Chapter 2. Multiple Satellite Service Availability Analysis distance dmt is larger in the mid latitude than high latitude. This result can be justified since the orbit separation at lower latitude is larger than higher latitude. Figure 18 The M a x — M i n satellite distance The M a x - M i n distance of the Globalstar system in the areas with latitude from North 25° to North 45° is 39.4°. Accordingly, the G W separation distance d equals to 10.38°. Providing double satellite service to these areas requires their boundaries being covered. On the latitude side, ss 2 layers are required to cover the boundary. On the longitude side, since the rhumb distance at the latitude of North 25° is 326°, ~ 32 G W s per layer are required. Therefore, the lower bound of number of G W s is given by N > 6 4 . Based on the above analysis, G W distribution 5, a distribution of 200 G W s for the Globalstar system is illustrated in Fig . 19. 28 Chapter 2. Multiple Satellite Service Availability Analysis 80 60 40 20 ^ I! • • •! I ^"" | ^ I! • • * I " " |" ^ !' • '5(" * *" | * C 5 • • •! * * |" | ) ' I • • • ^fr* *^ f^  ^i^* 4^ (^^ * ^fr* *^ )^  ¥fc ^ « ^ ^ ^ ^ ^ m^f* ^ ^ ^ f r . ^ ^ ^ ^ ^ • ^ * ^ ^ ^ * ^ . ^ 0) 3 0*--20 -40^ -60 -80 gateway * »^ «^  * * ^ » »^  * " jj^  ^ «^  *^  ^ * «^ * . '. ::«••:: i '. ::••>::)... ;:: i \ \ . . . ' , ; : i • • : : ; ; : : • • « : : ; . . . ' . : : i •»:: *. I I.. satellite orbit -150 -100 -50 0 longitude 50 100 150 Figure 19 Gateway Distribution 5 ensuring double satellite service between North (South) 25° and 45° in the Globalstar system In F ig . 19, 32 G W s are placed in each of the layers of North and South 25°, 33.4° and 41.8° and 8 G W s are placed along the Equator. MTs in the areas with latitude between North 25° to 45° and South 25° to 45°, which are guaranteed to receive double satellite coverage as shown in F ig . 8, are ensured to properly receive double satellite service all the time. MTs in the areas with latitude from South 25° to North 25° are also guaranteed for single satellite service all the time. 29 Chapter 3 Impact of Gateway Distribution to Mobile Satellite System Capacity Diversity techniques in conjunction with D S - C D M A have been very effective for terrestrial cellular systems [24], where line-of-sight (LOS) signals are usually absent and Rayleigh fading is experienced. Furthermore, the terrestrial system capacity is generally interference limited. On the contrary, satellite system are typically power limited and are forced to exploit the L O S signal. The intention of this chapter is to offer some insight on the relationship between.the system capacity and G W distribution. The focus is on the reverse link (mobile-satellite-gateway). Because both mobile terminals and mobile satellites have limited transmit power due to government communication and health regulations, and battery constraint in mobile terminals, the reverse link results in the system capacity bottleneck. The analytical model presented hereafter is of general applicability, whereas numerical results are specific to the Globalstar system. Although coding and interleaving are essential to maximize the system capacity, they have been excluded from the analysis to make our results independent from specific system design parameters such as bit rate and frame length. A s discussed in the previous chapter, satellite service is closely related to G W distribution. The analytical model, drawing on established theory, wi l l be verified with the use of simulation. 30 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity 3.1 Definitions and System Outline 3.1.1 System Capacity To maximize frequency utilization efficiency and increase system capacity, all modern mobile satellites employ multiple spot beam antennas. A s we know, in terrestrial cellular systems, the near-far problem is a big concern for system design. However, in mobile satellite systems, because a M T is almost stationary compared to a high speed mobile satellite, a proper antenna design can alleviate the effects of near-far problem. 3 direction of flight path Figure 20 The isoflux antenna of Globalstar The radiation pattern of an isoflux antenna of the Globalstar system [25] is shown in F ig . 20. The circle in the figure shows satellite coverage area. The coverage area is divided by 6 elliptical beams with their major axes aligned parallel to the satellite flight path. Due to the path difference between satellites and MTs, the path loss between a M T located at the sub-satellite point and a M T located at the edge of the coverage with 10 degree of minimum elevation angle is as high as 8dB [25]. To ensure that the C D M A system functions properly, the antenna gains on the Earth's surface should be maintained as uniform as possible. This is accomplished by shaping the radiation patterns of each 31 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity coverage beam in a way that antenna directivity increases proportionally to the path loss. In the following sections, we assume that all MTs in the spot beam of the satellite in interest are illuminated equally with one unit of gain. Since all MTs are illuminated by equal gain and reuse of the entire frequency band for each beam is assumed, we may analyze the MSS capacity per satellite rather than per satellite beam. In this case, the satellite coverage and service analysis in the previous chapters for single spot beam satellite system are still valid for multiple spot beam systems. System capacity is defined as the average number of simultaneously active users per satellite with a given average probability of error. Suppose there are totally S mobile satellites, nSit MTs the 5th satellite is able to accommodate at time t, and T samples per satellite over the time, the system capacity is given by: ST 3.1.2 System Outline The mobile satellite system to be analyzed is depicted in Fig. 21. It consists of three parts: MTs, mobile satellites (SATs) and GWs. The link from a GW to a MT via a SAT is called the forward link or feeder link; and the link from a MT to a GW via a SAT is called the reverse link or user link. On the forward link, a pilot channel, which is transmitted by each GW to each satellite beam, is used for CDMA synchronization and GW identification. On the reverse link, the signal of a MT is uplinked to a SAT using an omnidirectional antenna, and then transparently resent to a GW by the satellite's pent-pipe transponders. In the GW, the satellite signal is despreaded and decoded accordingly. For analytical convenience and in order to determine the basic performance of a MSS, we assume that the baseband signal of a MT is encoded by BPSK modulation 32 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity r Information BPSK Handset Modulator! User Link Gateway |nforrrjatiqD BPSK A PN Sequence PN Sequence LEGEND Omindirection Antenna High Gain Tracking Antenna Figure 21 System model and decoded by coherent detection. While traditional frequency or time division multiple access is widely used in terrestrial mobile communication, C D M A [26] [27] is frequently selected as the access scheme because of its noteworthy low-power flux density emission, time-domain signal discrimination, and interference resilience. Please note that different types of C D M A technologies are adopted for the forward and the reverse link. Typi-cally, synchronous C D M A ( S - C D M A ) [28] is adopted for the forward link to avoid the intrabeam self-noise effect since all the signals are transmitted together and they could be coordinated by the satellites. However, because signal synchronization can not be reason-ably achieved on the reverse link, asynchronous C D M A ( A - C D M A ) is employed. Each M T is assigned with a different random-like pseudo-random noise (PN) to distinguish signals from different other MTs . Performance of CDMA-based mobile satellite systems can be improved by employing satellite diversity with the use of Rake receivers [29]. B y using the autocorrelation characteristics of a C D M A signal, correlators or arms of a Rake receiver synchronize the 33 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity signals of a particular M T ' s P N code and separate the incoming signal into multiple path signals. A n d then each of these signals is fed to a diversity combiner and thus signal level attenuation due to fading is reduced. The best diversity combining techniques is maximal ratio combining [30]. X, PNi Estimated • Signal T PN 2 2 Two Arm RAKE Receiver Figure 22 Two-Arm Rake receiver The advantages introduced by satellite diversity generally increase as the number of diversity branches increases, but the complexity also increases. A s indicated in [11][14], a two-arm Rake receiver yields sufficient performance to exploit diversity advantages in most situations. Therefore, we assumed that G W s employ a modified version of the two-arm Rake receiver as shown in Fig . 22. Two arms of the Rake receiver despread their received signals by correlating them with locally generated replicas of the assigned P N code. The signals from the two arms are combined to decode the transmitted information while the third arm listens to and searches for pilot signals from other satellites and compares the SNRs to the active arms. When the listening arm finds a signal with a 34 Received Signal Rake, Finger 1 Active Rake, Finger 3 Listening Rake, Finger 2 Active CD c £ o O Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity better S N R , the Rake receiver wi l l switch one of the active arms and the listening arm according to the preset rules. To achieve the same average probability of error or B E R at the G W for MTs in the different satellite services (i.e. single satellite service or double satellite service) with different channel conditions (i.e. L O S or shadowed channel), we assume that a simplified closed-loop power control is used. When a M T is illuminated by two satellites, the M T detects the pilot channels of both satellites and reports the signal strengths to the G W . Based on satellite and G W identification information and by comparing S N R of the received signal to a threshold, the G W is able to determine the satellite service and channel condition of the M T . Accordingly, the G W then sends out a command to have the M T increase or decrease its transmit power margin to a preset value. The power marg in is defined as the increase in transmit power needed to achieve a specific average B E R , compared to the transmit power of a non-shadowed and non-fading M T . Since the large round trip time delay is in the order of 10 to 20 ms even for a L E O system [13], closed loop power control is not very effective, and rapid fades such as those experienced in the vehicular mobile environment cannot be mitigated. 3.1.3 Channel M o d e l The propagation between a satellite and a mobile terminal is classified as either unshadowed or L O S when the mobile receiver has unobstructed L O S path to the satellite, or shadowed when the L O S path is obstructed by either terrain, vegetation, or man-made structures. The overall multipath-fading propagation is related to many factors, such as the elevation angle, the particular type of environment, the aerial directional characteristics, 35 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity the relative mobile-satellite speed, etc. A mobile terminal located in open areas (rural or suburban environment) receives a LOS link from satellites most of the time, apart from temporary shadowing. However, a mobile terminal in urban areas lacks LOS link and experiences shadowing. The measurement results in [31] indicate that the fraction of shadowed users is in the range of 0.2-24% on highways, corresponding to satellite elevations from 43° to 13°. In urban areas, the fraction of shadowed users is much higher from 55% to 90% for the same range of elevation angle above. In our simulation, we will verify the effect of GW distribution on system capacity based on different levels of shadowing. For ease of analysis, we take the channel model from [32]. It is assumed that a certain fraction, B, of the MTs experience shadowing. For simplicity, we neglect fading for non-shadowed MTs. For shadowed MTs, the probability density function of the received amplitude given by the Rayleigh distribution [13] [32]: fR(R) = ^e~^ (3.2) or /7(7) = -e? (3.3) 7 .. • where 2a 2 is the average received power of a shadowed user experiencing Rayleigh fading and T is the average signal-to-noise-plus-interference ratio given by: 7 _ R/(N + l). T 2o2/(N + l) K ' J The overall PDF of the received amplitude is given by a combined density function in Eqn. (3.5) and is illustrated in Fig. 23, 36 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity 1-B Line-of-Sight B Rayleigh Fading Figure 23 Channel model Conforming to the notation introduced in [31], we define the direct-to-multipath signal power ratio c as: 1 2a' (3.6) Then, -cR2 fR(R) = 1- B + 2.*B*ce' 3.2 Analysis of Average Probability of Error (3.7) For S N R calculations, it is assumed that only one M S S is available, and there is no other interference from other M S S or terrestrial communications systems. Furthermore, it is assumed that the downlink (SAT to G W ) of the reverse link does not introduce further interference and the noise can be neglected. This is a reasonable consideration because the tracking antenna of the G W must have a high directivity and a high figure of merit G/T. Therefore, the signal-to-noise-plus-interference-ratio of reverse link can be calculated as [33]: 'I + N \ fl + N S S + s MT-SAT S SAT-GW J + N J Reverse V + # ) MT-SAT where / is the multiple access interference (MAI) from other active users. (3.8) (3.9) 37 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity It is assumed that a mobile satellite can communicate with a total of J users under the satellite coverage of the M T . The transmitted signal of ith M T is given by In Eqn. (3.10), s,-(i) is the overall B P S K signal, di(t) is the ith user's data sequence, which is a sequence of unit amplitude, positive and negative, rectangular pulses of duration T and is assigned a P N waveform PNi(t), which consists of a periodic sequence of unit amplitude, positive and negative, rectangular pulses of duration of Tc and At is the equal transmitted power for all MTs . Pi represents the power margin of M T i relative to a non-shadowed and non-fading The transmission from a M T is received by a SAT and re-transmitted to a G W , where demodulation is actually performed. The total received signal at a G W from one mobile satellite is j Si(t) = AtPi'UiWPNiWcosiuct) (3.10) M T . r(t) = ^2At* G3at * y/pl'* Ri *di(t- Ti) * PNi(t -Ti)* COs(uct + Oi) (3.11) i=i +nw(t) where R= the independent flat fading the independent deplay satellite antenna gain the phase of the carrier additive white Gaussian noise with the two-sided power spectral desity No/2 T = Mobile terminals are assumed to have omnidirectional antennae. At * Gsat is the amplitude of received signal in the non-fading and non-shadowing environment. With 38 Chapter 3. ' Impact of Gateway Distribution to Mobile Satellite System Capacity isoflux antenna design, we assume that At * Gsat is a constant and it equals to A. Therefore, by assuming an ideal correlation receiver, the received signal is calculated as: ./ r(t) = A VFi * Ri * di(t - Ti) * PNi(t - n) * cos{uct + 0t) i=i ( ' +nw(t) The test statistics for the user of interest, or the reference user r, is given by, J Dr(T) = Ajv~r *Rr*T*dr + Aj2^/P~i*Ri* h{T) (3.13) i=i +N(T) where Ii(T) = J di(t - Ti) * PNi(t - Ti) * PNr{t - Tr)cos(et)dt . (3.14) o The computation of M A I h{T) is the subject of a host of papers. The standard assumption [34] [35] to perform a reasonably accurate yet simple analysis is to model interference coming from other J-1 users as an additional zero-mean Gaussian random variable or Gaussian noise. This assumption turns out to be particularly well founded when the number of interfering users is not small (not less than 5 users) or/and processing gain Gp is large [27]. A n improved and more accurate Gaussian approximation is presented in [36]. How-ever, for ease of analysis, the standard Gaussian approximation [34][35] is used. The variance of M A I contributed from one M T is given by: VMAI = var{Ii{T)) = (3.15) Because Ri and Ii are independent random processes, therefore, the interference from other MTs is A2 ^ erf = — * 22 Pi * v a r i R i ) ( 3 -16 ) 39 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity The average signal-to-noise-plus-interference-ratio for a particular M T and the av-erage total interference including white Gaussian noise and the interference from other MTs are given as follows: SNRr = (3.17) N 1 J _ 1 Gr i=l Before further calculation of the variance of noise plus interference a2ot, we notice that there are five distinct scenarios which can arise as depicted in F ig . 24. M T s can be distinguished as follows: • satellite service: single satellite service (SS) and double satellite service (DS) for a two-arms Rake receiver • channel condition: unshadowed or clear of any obstruction (C) in the line-of-sight path or shadowed (S) path In F ig . 24, the two MTs in the left communicate with satellite #1 without satellite diversity. M T #1 experiences a L O S channel, and M T #2 experiences a shadowed channel. The three MTs in the right communicate with two satellites using satellite diversity: M T #4 experiences two L O S channels, M T #4 experiences one shadowed channel and one L O S channel, and M T #5 experiences two shadowed channels. Realizing the fact that the power margin for each scenario wi l l be different (a M T , receiving double satellite service is augmented by less power margin than a M T receiving single satellite service, and a M T experiencing a L O S channel requires less power margin than a M T experiencing shadowing), to compute of, and have to a. quantify the power margin, pi, for each scenario; b. calculate the average variance of interference, var(R?), for each scenario. 40. Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity SAT1 SAT2 Single Satellite Service | Double Satellite Service Figure 24 Uplink of reverse link scenarios We wi l l address this topics in the following two sections. 3.3 Power Margins for Each Scenarios 3.3.1 SS/C: Single Satellite Service/LOS Path In this scenario, the uplink channel is a L O S channel. This scenario occurs when: • A M T is illuminated by only one satellite and experiences a L O S channel; • A M T is illuminated by two or more satellites. However, due to lack of proper G W distribution, the M T is not able to reach the same G W via two different satellites and one of the channels is a L O S channel. S A T 1 L E G E N D MOBILE TERMINAL SATELLITE Figure 25 SS/C: Single satellite service/LOS channel 41 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Since the M T experiences a non-faded and non-shadowed L O S channel, by definition, the power margin of M T in SS/C is Pss/c = 1-Suppose the variance of white Gaussian noise plus interference from other M T s is cr£t, the B E R of B P S K [30] is given by *=Mv*y- <3-i9) 3.3.2 SS/S: Single Satellite Service/Shadowing Path In this scenario, a M T communicates only one satellite and experiences a shadowed channel. This scenario occurs when: • A M T is illuminated by only one satellite and experiences a shadowed channel; • A M T is illuminated by two or more satellites. However, due to lack of proper G W distribution, satellite diversity is not enabled and the channel experiencing shadowing is the only channel to reach the G W . SAT1 E E Q Q E f f l L E G E N D ^ B lockage , t MOBILE TERMINAL m^m SATELLITE Figure 26 SS/S: Single satellite service/Shadowing path Based on Eqn. (3.17), for a given fixed Rr, the B E R for M T in SS/S scenario is given by 1 / Pssls * Rr \ P(e\Rr) = -erfcU " / ^ [ (3.20) 42 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Since Rr is Rayleigh-distributed, R2 has a chi-square probability distribution with 2 degree of freedom. The P D F of R2r is given by [30]: x = Rt i 2a 2 ce~cx -x/2a2 Therefore, the average B E R is given by, Pe / I N f 1 / Pss/s * x J-2erfc{\l-^ri Ice cxdx Let 7fc and 7(, = M^-, therefore, ''"tot Latot OO f 1 1 2k Pe= / 7 7 e r / c ( v / 7 i ) = e 7 6 c ? 7 6 J 2 7 i After integration, 1 - lb Finally, the average B E R is given by 1 + -1/2-p, ss/s For a given required B E R Pe, the power margin is given by _ API- 4pe + 1 76 = -1 ss/s 4p2 —4pe ^ L ( 4 P e - 4 p e + l ) 2 P e - 2p^  3.3.3 DS/CC: Double Service/Both Paths are LOS (3.21) (3.22) (3.23) (3.24) (3.25) (3.26) In this scenario, a M T employs satellite diversity. The M T is illuminated by two satellites, and the transmission from the M T is received by two different mobile satellites 43 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity SAT1 SAT2 LEGEND MOBILE TERMINAL Blockage SATELLITE Figure 27 D S / C C : Double satellite service/Both paths L O S and re-transmitted to the same G W on the ground. Diversity reception is then performed in the G W . The channels between the two satellites and the M T are L O S channels. This scenario happens when a M T is illuminated by 2 or more satellites and at least 2 channels to the satellites are L O S channels. Using the same notation as in Eqn. (3.13), with maximal ratio combining technique [29], the test statistic for Rake receiver is given by: +-Rri * +Rr2 *N2 where RT\ and RT2 are the effects of fading via SAT1 and SAT2 respectively. The desired signal power m and variance cr2 of interference are given by Dr{T) =A^fv-r *R2rl*T* dr + ARrl J2V&*Ri* *i(T) »=i J (3.27) + A^p-T * R2r2 * T* dr + ARr2 ^r^/pl*Ri* Ii(T) S = m 2 rn = E(Dr(T)) (3.28) = Ay/pi * R?rl * T * dr + Ay/p'r * R2r2*T *dr A(R2rl + R2r2)Tdr 44 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity cry —var(DT(T)) J =A2R2Tlc-MAI Pi2 * Ril i=l J + A2R2r2o2MAIYJPi2*Rl (3-29) 2=1 + R2rlN0T + R2r2NQT ••(R2i + R22) I A2a2MAI \ i=l For fixed Rr\ and Rr2, the BER is given by P(e | RrlRr2) = lerfc I J | (3.30) 'tot Because RTi = 1 and Rr2 = 1, therefore, j where a20t = 3 ^ - ]T Pi^f + JJF' which is same as Eqn. (3.18). P i=l 3.3.4 DS/SS: Double Service/Both Paths are Shadowed In this scenario, a M T employs satellite diversity. The M T experiences shadowed on both channels to the two satellites. This scenario arises when a M T is illuminated by 2 or more satellites and no channel is a LOS channel. SAT1 SAT2 jr LEGEND [ ^ I MOBILE TERMINAL } • SATELLITE Figure 28 DS/SS: Double service/Both paths are shadowed 45 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Similar to D S / C C scenario, for a fixed set of Rri and Rr2, the B E R is given by:, 1 , / IPds/ss(R2rl + R22) 2 6 r f C V ~2cT2 where o2ot = ^ E P 4 + 'tot \ J 1 = 1 N0 27? Since i ? n and R\2 are Rayleigh distributed, i ? 2 ^ and R22 are Chi-square distributed with 2 degrees of freedom. Therefore, R\x + i?f 2 is a chi-squared variable with four degrees of freedom. Accordingly, the P D F of R\x + R22 [30] is given by = 4 / ( x ) = * / , xnl2-le-x'2(T2 (3.33) 1 -xe-^2 T*222' = c2xe-cx o oo = ^ / e- i 2 (-2e*l«lPto,aat2-e-^*lP«>" - e ~ ^ ^ » + l ) o For the details of derivation of Eqn. (3.34), please refer to Appendix B . Let 76 = 0 Pi° , after integration, where u, by definition, is given by: For a required B E R , the power margin is derived as p ^cr20iu2 ^ds/ss x_u2 U = 2 4 6 (3.34) Pe = (3.35) 1 + 7i I((6i/3 + r1/3) + zV3(V/3 - 6 - 1 / 3 ) ) (3-37) b = 2Pe - 1 + 2^/pj-pe Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity 3.3.5 DS/CS: Double Service/One Path is L O S , Another Path is Shadowed In this scenario, a M T employs satellite diversity. The M T experiences a shadowed channel and a L O S channel from the satellites. This scenario occurs when a M T and a G W are illuminated by 2 or more satellites, and only one channel is L O S while others are shadowed. SAT1 SAT2 LEGEND Blockage M O B I L E T E R M I N A L • S A T E L L I T E Figure 29 DS/CS: Double service/One path is L O S , another path is shadowed Similar to DS/SS scenario, for a fixed set of Rr\ and Rr2, the B E R is given by, , , x 1 / Pds/cs(R2n +Rr2) P(e | Rn,Rr2) = g e r / c j \ / \*2 •pi I p \ 1 t I Pds/cs(± + i f f 2 ) (3.38) The detailed derivation of Eqn. (3.38) can be found in Appendix B . Therefore, the P D F of R?r2 is a chi-squared variable with two degrees of freedom. The average B E R is given by x = /r r / c(/ Pds/csO- + x) 2 * L ce "dx = —er fc 2 J 1 cs + 1 --erfci A c + P, dsjcs (3.39) 47 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity For a given B E R , there is no closed-form solution for P ^s /c s -With the same noise-plus-interference from other MTs , to ensure the same B E R P e at the G W , the power margins for each scenario are listed in Table 2. senario power margin SS/C . Pss/c = 1 (3.40) SS/S c c r L (4p? - 4pe + 1) Pss/s = i o t \ e 0 2 1 (3.41) 2pe - Ipl DS/CC Pos/cc = 1/2 (3.42) DS/SS PDS/SS- X _ Y 2 u = -I((ti/3 + + i > / 3 ( 6 1 / 3 - 6 - 1 / 3 ) ) (3.43) 6 = 2pe - l + 2\/p2 _ p e DS/CS No closed-form solution. A computer program is written to solve for Pd,/cs Table 2 Power margins for different scenarios Suppose that the carrier-to-multipath ratio is c = 10, the required power margins for different scenarios to meet the same required B E R from 1 0 - 3 to 10~ 2 are shown in F ig . 30. For MTs experiencing shadowed channels, it can be seen from Fig . 30 that satellite diversity dramatically reduces the required power margins to maintain the same B E R at the G W . However, satellite diversity, is less effective when one satellite is seen with a L O S channel. For example, when we choose BER = 1 0 - 3 as our goal, M T s employing satellite diversity (DS/SS) require 12.87 dB less power margin than MTs without satellite diversity (SS/S) to meet the same B E R . When at least one L O S channel can be exploited, the difference in power margin between SS/C and D S / C C scenario is merely 3.01 dB. 48 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity 30 SS/C DS /CS DS/CC 5 6 Bit Error Rate 9 10 x10"3 Figure 30 The required power margins for different scenarios 3.4 The Average Interference for Each Scenario 3.4.1 Fraction of Double Satellite Service Links To reveal the relationship between G W distribution and system capacity of a M S S and provide some meaningful results in this thesis, our first challenge is how to assess a G W distribution. The natural and straightforward assessment method is to use the probability of double satellite service, which is defined as the average fraction of time of MTs receiving double satellite service while they have double satellite coverage. However, the use of the probability of double satellite service to assess the quality of a G W distribution has some shortcomings. Let us quantify the interference results in F ig . 2 in Chapter 1 to show the reasons. 49 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity S A T 1 S A T 2 S A T 1 S A T 2 c) S i n g l e Satel l i te S e r v i c e L E G E N D ^~ GATEWAY | MOBILE TERMINAL EBQ-gffl SATELLITE ^ B l o c k a g e Figure 31 Interference calculation For ease of comparison, F ig . 2 is re-drawn in F ig . 31 and a M T in SS/S scenario is added in the figure. In Fig . 2 a), MT A is illuminated by two satellites and experiences one shadowed channel and one L O S channel. Ideally, MT A would employ satellite diversity and thus reduce its transmit power. However, due to an improper G W distribution, MT A may not be able to take advantage of satellite diversity and is forced to transmit more power to maintain the same performance. In a pessimistic scenario, MT A communicates 50 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity with SAT 1 via the shadowed channel and generates severe interference to SAT 2 as shown in Fig. 31b). We assume that both MT A and MT B are interfering MTs, the average interference contributed by MT A in a) and b) and the interference contributed by MT B in c) are given by: respectively, and c denotes the direct-to-multipath signal power ratio. For c=10 and B=0:3, the average interference for a), b) and c) are P,-)a = -2.59 dB, P;^ = 24.69 dB and PitC = 17.29 dB respectively. As indicated in our power margin analysis, usually, Pss/s ^> PDS/CS- s i n c e c > 1, therefore, Phb > Pj j C > P;, a. From the. above analysis, it shows that. 1. although both MT A in b) and MT B in c) receive single satellite service, the average interference contributed by MT A in case b) is much higher than MT B in case c); 2. the average interference is determined by not only the satellite service a M T receives, but also its satellite coverage. Apparently, the probability of satellite service is not good enough to compute the average interference contributed by a M T and it is necessary to find an "indicator" reflecting MT's satellite service and satellite coverage to compute the average interference contributed by a MT. The fraction of double satellite service links is introduced. The computation of the average pds does not include MTs with single satellite coverage. c (3.44) where PDS/CS a n d Pss/s denote the power margins for MTs in DS/CS and SS/S 51 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Definition: fraction of double satellite service links, pds is calculated by counting the average number of satellite-link pairs which provide double satellite service to a M T as a fraction of the possible combinations of satellite-link pairs accessible by the M T . The concept fraction of double satellite service links only applies to MTs receiving double or higher satellite coverage. Example: For a M T in New York City as shown in Fig . 32, its connection status generated by a simulation is shown as follows TIME MT ID SAT ID GW ID E l e v a t i o n 2 120 52 2 22 2 120 52 8 22 2 120 0 2 13 2 120 43 15 12 L E G E N D [j"" G A T E W A Y | M O B I L E T E R M I N A L S A T E L L I T E Figure 32 One pair of satellite links capable of providing double satellite service Since there are three satellites visible to the M T , the total number of combinations of satellite-link pairs are C(3,2) = 3. Because only one pair of satellite links (MT-Sat #0-GW # 2 and M T - S A T # 5 2 - G W #2) is able to provide double satellite service to the 52 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity M T , Pds = I- Therefore, for any pair of satellite links for this particular M T , the chance to. provide double satellite service to the M T is For a M T receiving m-fold satellite coverage, suppose there are pairs of satellite links which are able to provide double satellite service to the M T , pds is given by Pds = nds (3.45) C(m,2) A pair of satellite links providing double satellite service is considered to be indepen-dent from each other because each M T has its own SAT links and G W links. Therefore, pds has a consistent value for MTs in different satellite coverage. Our simulation results support our observation. For the Globalstar system with the G W distribution shown in Fig . 16, the average number of pairs of satellite links capable of providing double satellite service and average pds for MTs receiving single, double, triple and four-fold satellite coverage are shown in Table 3 respectively. The average pds is obtained by computing the average value of all the sample M T s ' pds ° v e r the time. Single Satellite Coverage Double Satellite Coverage Triple Satellite Coverage four-fold satellite coverage Percentage of Total Time 12% 40.3% 37.9% 10% Average # of Satellite-Link Pairs providing double satellite service 0 0.524 1.5337 3.1639 Total Possible Combinations of Satellite-link Pairs 0- 0-Average pds 0 0.5241 0.5100 0.5267 Table 3 The average number of pairs of links providing double satellite service and the average pds for the Globalstar System The average pds for G W distribution 1 on p. 20, G W distribution 2 in F ig . 12, G W distribution 3 in Fig . 14, G W distribution 4 in F ig . 16 and G W distribution 5 in F ig . 19 are 53 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity shown in Table 4. Based on the results of confidence interval calculations, we conclude that fraction of double satellite service links is a inherent and consistent indicator for the performance of G W distributions. # of G W s (pds) (means) 99% Confidence Interval Variation in terms of pencentage of mean G W 1 40 0.6557 [0.6377,0.6736] 2.73% G W 2 32 0.6456 [0.6330,0.6581] 1.94% G W 3 27 0.6196 [0.6299,0.6637] 2.61% G W 4 21 0.5190 [0.5014,0.5365] 3.37% G W 5 200 0.8923 [0.8803,0.9034] 1.34% Table 4 The average pds for different G W distributions Pds has a close relationship with probability of double satellite service. B y definition, for MTs receiving double satellite coverage, pds equals the fraction of double .satellite service. For MTs receive m-fold (m>2) satellite coverage, the probability of the MTs receiving single satellite service is the probability that all pairs of satellite links of the M T fail to provide double satellite service to the M T . Therefore, the probability of double satellite service is given by: Pr(double satellite service) = 1 — (1 — pds)C(jn'2^ (3.46) Based on the above analysis, we conclude that pds is a good indicator to assess a G W distribution. A higher value of pds results in a higher probability of double satellite service. The contrary is also true that a higher probability of double satellite service yields a higher value of pds-3.4.2 Terminology To facilitate further analysis, a consistent terminology is necessary. 54 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Definition: Path State (PS) is defined as the state of channel condition of a M T . PS is introduced to characterize a particular propagation environment of a M T . A s described before in the channel model, a M T experiences a shadowed channel (S) for B fraction of the time and a clear of path ( Q channel for 1-B fraction of the time. The PS sample space consists of two discrete states PS € {C, S} Let Pr(PS = (k,m — k)) denote the probability of a M T experiencing k L O S channels and m-k shadowed channels and let Pr(CG = m) denote the probability of a M T receiving m-fold satellite coverage. Suppose that a M T receives m—fold satellite coverage, the conditional probability of a particular PS for the M T is given by: Pr(PS = (k,m-k)\CG = m) = C(m,k)(l - B)kBm-k (3.47) Because satellite coverage is an independent event from satellite channel propagation, the probability in a particular PS is given as follows: , pr(PS = (fc, m - Jfej, CG = m) = C(m, k)(l - B)kBm-kPr(CG = m) (3.48) For the Globalstar system, which has up to four-fold satellite coverage as shown in Fig . 8, all 14 possible propagation or PSs are given in Table 5. Single Double Triple 4-fold Satellite Satellite Satellite Satellite Coverage Coverage Coverage Coverage C C C ccc cccc S'. ' CS C C S C C C S ss CSS cess 1 csss. ssss Table 5 Path States For example, for a M T receiving triple satellite coverage, the probability of a M T in the CSS PS is given by 3 £ 2 ( 1 - B)Pr(CG = 3). 55 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity DehnitiomSatellite Service State (SSS) is denned as the state of satellite service of a M T . SSS is introduced to characterize a particular satellite service a M T receives. For a G W distribution guaranteeing single satellite service, a M T receives either single satellite service (SS) or double satellite service (DS). The SSS sample space consists of two discrete states SSS e {SS,DS}. A s mentioned in Eqn. (3.46), for a given pds, the probability of the a M T receiving single and double satellite service given m-fold satellite coverage are given by: Pr(SSS = SS\CG = m) = (1 -pdsf{m'2) (3.49) Pr(SSS = DS\CG = m) = 1 - (1 - Pdsf{m'2) Definition '.Path and Satellite Service State (PSS) is defined as a combination of PS and SSS state of a M T . A s discussed in the previous section, an in-service M T with a two-armed Rake receiver wi l l be in one of five scenarios, i.e., SS/C, SS/S, D S / C C , D S / C S and DS/SS. Since each scenario is unique, we can classify the general M T environments into five PSS states. The PSS sample space consists of five discrete states PSS € {SS/C, SS/S, D S / C C , D S / C S , DS/SS}, which can be ranked in order of decreasing link performance as D S / C C , D S / C S , SS/C, DS/SS, SS/SS based on the required power margin. Each PSS state has a certain occurrence probability 7, which is a function of the channel propagation and satellite service availability. If a G W distribution ensuring single satellite service is assumed, the sum of all the probabilities is unity. For the Globalstar system, the state diagram describing all 5 PSS states and 14 possible path states is illustrated in F ig . 33. The summary of the above three states is shown iri Table 6. Name Symble Sample Space Path State PS C, S Satellite Service State SSS SS, DS Path and Satellite Service State PSS D S / C C , D S / C S , DS/SS, SS/C, SS/S Table 6 Summary of States 56 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity 3.4.3 Effect of gateway distribution on PSS distribution If a G W distribution guaranteeing double satellite service is assumed, a M T wi l l ideally employ a PSS state with less required power margin (the solid line in F ig . 33 corresponds the preferred PSS). For example, a M T in the (PS=(0,2)) PS wi l l employ PSS state DS/SS. However, under an improper G W distribution, the M T may not be able to employ the preferred PSS state and may be forced to employ a less performing PSS state (the dashed line in Fig . 33). A s a result, the M T needs to transmit at a higher power level and generates more interference to the M T s ' connections. For example, a M T in the (PS=(0,2) PS employs PSS state SS/S. B y definition, the probability of a PSS state is a function of satellite service and channel propagation. Since satellite service, which depends on the satellite constellation and G W distribution, and channel propagation, which depends on the environment of MTs , are independent events, the probabilities of PSSs can be rewritten as: n i Pr(PSS) = E Pr(pSS\CG = i, PS = (j, i - j)) »=i j=o *Pr(CG = i,PS = (j,i-j)) ( 3 5 Q ) = E E Pr{PSS\CG = i, PS = (j, i - j)) *Pr(CG = i,PS = (j,i-j)) where n is the maximal satellite coverage a M T can receive and Pr(PSS\CG = i,PS=(j,i — j)) denotes the transition probability from a par-ticular PS state to a desired PSS state. A convenient way of describing and computing Eqn. (3.50) is by using a tree diagram (CG=3 as a example) as illustrated in F ig . 34. 57 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Single Satellite Coverage P1 Double Satellite Coverage Triple Satelite Coverage LOS transition probability / [DS/CS, , (1-Ft|S)/2. / V O D ' - M * ^ Shadowed Four-fold Coverage cccs cess V^6(1-EJBV Prefered PSS state Less Performing PSS state Legend: Path and Satellite Service State Probability of PS SS S S S S f — P a t n s t a t e probabilty of path state Figure 33 Path and satellite service analysis 58 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Path State Path and Satellite Service State Pr(CG= Single P_| Satellite ' Service Pr(SICG=i,PS=0,i-j)) f 3 Double 1 " Satellite Service Pr(PS=(j, i-j)) Pr(PSICG=i, PS=(j,i-j)) Figure 3 4 The tree diagram of PS—>PSS Therefore, Eqn. (3.50) can be further derived as follows: n i Pr(PSS) = ]T Pr(PS\CG = i,PS = (j, i - j))Pr(CG = i) i=l j=o • * Pr(SSS\CG = 'i, PS = (j, i - j))Pr(PS = (j, i - j)) = ^Pr(CG = i)Pr{SSS\CG = i) i = l i * £ Pr(PS\CG = i, PS = (j, i - j))Pr(PS = (j, i - j)) (3.51.) i=o =Pr(PS) Pr{CG = i)Pr(SSS\CG = i) i = l Based on the above equations, the overall probabilities of single and double satellite service under different satellite coverage situations are given by m Pr(SSS = SS) = (1 - pds)C(l'2)Pr{CG = i) i=l m (3.52) Pr(SSS = DS) = J2(±- {l-Pds)C{l'2))Pr{CG = i) i=l 59 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity The probabilities of SS/C and SS/S PSS states are given by: m l t l h = {l-B)^{l-Pi.)c^Pr{CG = i) m i = 1 (3-53) l s s / s = B J2 (1 - pdsf^2)Pr(CG = i) and the probabilities of D S / C C , DS/CS and DS/SS PSS states are given, by: m 7<W« = (1 - 5 ) 2 ^  ( l - (1 - W 3 ) C ( i ' 2 ) ) Pr(CG = 0 t = l m T d s / c s = (1 - B)B ( l - (1 - Pdsfli,2)) Pr(CG = i) (3.54) 1 = 1 m Single Satellite Coverage Pi = Pr(CG=l) Double Satellite Coverage P2 = Pr{CG = 2) Triple Satellite Coverage P3 = Pr(CG = 3) Four-fold Satellite Coverage Pr(CG = 4) SS/C (1 - B) 1 \~Pda (1 -Pdsf (1 - P d s ) 6 SS/S B 1 1-Pds (1 - Pdsf D S / C C 0 Pds HI-Pds)3 l - ( l - P d s ) 6 DS/CS 2B(l-B) 0 Pds l - ( l - W s ) 3 H^-Pdsf DS/SS £ 2 0 Pds Hi-Pds)3 Hi-Pds)6 Table 7 Double satellite service transition matrix The probability for each PSS state is listed in Table 7. The probability of a particular PSS state is the product of the probability of satellite coverage, the probability of single (double) satellite service and the probability of PS. For example, the probability of D S / C S 6 0 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity is given by: Iss/s = s(pi + (1 - Pds)P2 + (1 - Pdsf Pi + (1 - Pdsf Pi) pi = Pr(CG = 1) p2 = Pr(CG = 2) (3.55) p 3 = Pr(CG = 3) p 4 = Pr(CG = 4) For Globalstar system with the G W distribution in Fig . 16, the distributions of M T s in a particular PSS under the condition where B=0.3 and the heavy shadowed channel condition where B=0.9 are shown in Fig . 35. Note that pds = 100% corresponds to an ideal situation where all the satellite pairs capable of providing double satellite service. This may not be realized because an enormous number of G W s are required. Fig . 35 a) and c) show the PSS state probabilities for MTs under normal (B=0.3) and heavy shadowed (B=0.9) channel conditions with an improper G W distribution. F ig . 35 b) and d) show the PSS state for the same channel condition with a proper G W distribution. It can be seen from figure that an improper G W distribution prevents a significant portion (close to 1/3) of MTs receiving double satellite coverage from acquiring double satellite service. The G W distribution has less impact on MTs receiving triple or higher satellite coverage than MTs receiving double satellite service. 3.4.4 Interference Calculations Suppose that a M T is illuminated by m satellites and experiences k L O S channel and m-k shadowed channel, and the transmit power is P, the average interference generated by the M T is given by p(k + m-k) E(Pi) = -± c—!- (3.56) m 61 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity PSS distribution.B=0.3.pds=0.52 b) PSS distfibution,B=0.3,pds= 4-fold CVG Triple CVG Double CVG Single CVG Satellite Coverage PSS distribution,B=0.9.pds=0.S DS/CC DS/CS DS/SS 4-lold CVG Triple CVG Double CVG Single CVG 4-fold CVG Triple CVG Double CVG Satellite Coverage rj\ PSS distribution, B=0.9,pds=1 Satellite Coverage DS/CC DS/SS 4-fold CVG Triple CVG Double CVG Single CVG Satellite Coverage Figure 35 Distributions of PSS states of Globalstar system where c denotes the direct-to-multipath ratio. Accordingly, based on Eqn. (3.50), the expected interference given by a specific PSS state is as follows: n i E(Pi\PSS) = J 2 H Pr{PS\CG = i, PS = (j, i - j))Pr(CG = i) i=l j=0 * Pr(SSS\CG = i, PS = ( j , i - j))Pr(PS = {j, i - j)) (3-57) . ( ' • + * ) * : i Suppose a M T is in PS = (k.m — k), the probability that the first channel selected in PSS state is a L O S channel is ^ . If the first channel is L O S , then the probability that 62 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity the second is a L O S channel is ^Mj- . Thus, the probability that all channel in the PSS state are L O S channels is given by Pr(PS = CC\PS = (k,m-k),CG = m m ) . = — * ^ ~ X \ (3.58) m ( m — 1) Similarly, the probabilities for other PSS states are given by: Pr(PS = C\PS = (k,m- k), CG = m) = — m fY) h Pr(PS=S\PS=(k,m-k),CG = m) = »"(».-*)' < 3 5 9 ) Pr(PS = CS\PS = (fc, m - k), CG = m) = — * ± m (m — 1) Pr(PS = SS\PS = (Jb, m - k), CG = m) = ( m ~ ^ * ^"['t^y ' 3.5 Capacity Calculation Based on the previous results, we wi l l now derive the system capacity of a mobile satellite system. Eqn. (3.18) can be further derived as follows: 2 -^ 0 1 / r>2\ °tot = ^42 + 3^" l u Pt * V a r y R i ) " 1 = 1 (3.60) rh + E E(P1\PSS)PV(PSS) 2A2 3 G p Vpss where E(Pi\PSS) is the expected interference for a specific PSS state given in Eqn. (3.57) Applying the same parameters in the analysis in F ig . 35 and based on the power margin analysis in Section 3.3, the multiple access interference is shown in F ig . 36. It can been seen from Fig . 36 a) and c) that due to improper G W distribution, the MTs receiving double and triple satellite coverage are forced to be in the SS/S PSS state and thus they contribute the most interference to other MTs . When a proper G W distribution 63 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity a) 4-lold C\ Triple CVG Double CVG Single CVG satellite coverage c) 4-fold CV Triple CVG Double CVG Single CVG satellite coverage b) -Mold CVG Triple CVG Double CVG singi.cvG satellite coverage d) 4-fold CVG Triple CVG Double CVG Single CVG satellite coverage Figure 36 Mul t ip le access interference in the Globalstar system is available, the interference generated by MTs receiving double satellite coverage is fairly low, as shown in Fig. 36 b) and d). When the system capacity J in Eqn. (3.60) is sufficiently large, we assume that the multiple access interference from all MTs other than the M T of interest contribute an equal amount of interference to the M T of interest. Therefore, the noise-plus-interference a2ot of the M T of interest is given by: atot = 1 erfcinv(pe) (3.61) 64 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity where erfcinv(pe) is, the inverse complimentary error function for a given BER. Therefore, the system capacity is given by: . j = 3 G p ( a l t - J & ) , l ( 3 6 2 ) E{Pi\PSS)Pr(PSS) K } V P S S There is no closed-form solution to solve the system capacity / . We develope an algorithm to compute the system capacity and a computer program based on this algorithm is written. 3.6 Numerical and Simulation Results In this section, we will first present numerical results of the system capacity of a CDMA-based mobile satellite system with different values of pds based on Eqn. (3.62). Then, we will verify the theoretical computations with simulations. We will demonstrate how important it is for a proper GW distribution to be employed. In this sub-section, we will use fraction of double satellite service links pds to assess a GW distribution. As we discussed in sub-section 3.4.1, a higher value of pds corresponds to a higher probability of double satellite service. Hence, a higher value of pds indicates a better GW distribution. Note that achieving pds = 100% is economically prohibitive in reality because it requires an enormouse number of GWs. Also, pds = 0% implies that double satellite service link pairs are not available. Therefore, the numerical results for pds = 100% and pds = 0 should be considered as the upper and lower bounds of the system capacity of a MSS. 65 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity 3.6.1 Numerical Results The numerical results shown in Fig . 37, F ig . 38 and F ig . 39 are based on Eqn. (3.62) and computed for code length Gp = 1024 and = 30dB. We assume c = lOdB as a typical value in a L E O channel [31]. BER Vs. Pds . _ 0 1 0 p 1 1 1 1 1 1 1 1 r 10"' 1 i i i i i i . J = 1 2 0 B=0 .3 J=100 \ \ \ " c=10 J = 8 o \ \ \ ; -3 \ : BER=10 \-i i i i i i i t i 0 10 20 30 40 50 60 70 80 90 100 fraction of double satellite service links pds (%) Figure 37 BER Vs. pds (Varied system capacity J) In F ig . 37, we show the bit error probability vs. the fraction of double satellite service links for a given fixed number of MTs per satellite. We choose B = 0.3, a value as a compromise between a large value, representing an urban area, and a smaller value, representing a suburban or rural environment. It can be seen from the figure that the average B E R of MTs are dramatically decreased when the pds is increased. A proper 6 6 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity GW distribution, ensuring that most MTs receive double satellite service while receiving double satellite coverage, is critical to the performance of a MSS. In Fig. 37, when the pds value for J = 80 and J = 100 are less than 94% and 97% respectively, the average BER of MTs cannot achieve the desired BER level of 10-3. As shown in Table. 4, even GW distribution 5 with 200 GWs can only achieve Pds = 89%. A GW distribution with an enormous number of GWs is required to reach. Pds = 97%. We conclude that the MSS referred in Fig. 37 is under-designed for the assumed fading channel. BER Vs. Pds (varied B) 1 i i 1 I I 1 1 1 : ' B=O.5 X / V v : B=0.1^ ^ ^ ^ ^ >\ • > / i • B=U7 \ / \ -\ . B=0.9\ 1 G=1024 J=80 c=10 i i i i i i 0 10 20 . 30 40 50 60 70 80 90 100 fraction of double satellite service links pds (%) Figure 38 BER Vs. pds (varied B) In Fig. 38, we show the average BER of the MTs vs. pds under different channel conditions for a fixed number of MTs per satellite (J=80). It is shown that the performance of MTs is more sensitive to an improper GW distribution under a lightly shadowed channel condition than under a heavily shadowed channel condition. The results are justified 67 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity because the interference is usually dominated by MTs receiving double or higher satellite coverage but working in the SS/S PSS state as shown in Fig . 36,. Now, let us examine the relationship between system capacity and G W distribution. We choose B E R of 1 0 - 3 as our goal. The Capacity Vs. Gateway Distribution 300 -B=0.1 fraction of double satellite service links pds(%) Figure 39 Capacity Vs. pds It can be shown from Fig . 39 that a G W distribution imposes a tremendous effect on the system capacity of a CDMA-based M S S satellite system. Under a normal channel condition where B=0.3, deploying G W distribution 5 in F ig . 19 improves the system capacity from 13 MTs with G W distribution 4 in Fig . 16 to 60 MTs . The numerical results of the system capacity of a M S S deploying the G W distribution 5 in F ig . 19 and G W distribution 4 in Fig . 16 are listed in Table 8 under different channel conditions. 68 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity channel condition G W 4, Pds=0.52 G W 5, Pds=0.S9 B=0.1 40 141 B=0.3 13 60 B=0.5 12 41 B=0.7 11 33 B=0.9 10 31 Table 8 The system capacity comparison for G W distribution 4 and G W distribution 5 under different channel conditions Table 8 and F ig . 39 also show that a M S S in a lightly shadowed propagation environment suffers more capacity loss due to improper G W distribution. 3.6.2 Simulation Results In this subsection, the main objectives of simulations are twofold: 1) to provide the statistics of satellite coverage, satellite service and fraction of double satellite service links Pds of the Globalstar system; and 2) to verify the numerical results based on Eqn. (3.62) with the simulations. G W distribution 1 on p. 20, G W distribution 2 in F ig . 12, G W distribution 3 in Fig . 14, G W distribution 4 in Fig . 16 and G W distribution 5 in F ig . 19 are used in our simulations. Each simulation runs for 113 minutes, which is the orbital period of the Globalstar system. The system capacity of the M S S is obtained by calculating the average value of the capacities of .48 mobile satellites over 113 minutes. 3.6.2.1 Simulation Algorithm A simulator consisting of two sub-simulators: the Orbital information sub-simulator and the Interference information sub-simulator are used throughout all the simulations. 69 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity Satellite orbital information sub-simulator provides the sub-satellite position (the satellite's projection on Earth) of mobile satellites and the distances between the satellites and the MT-of-interest, and it produces the statistics of satellite coverage, satellite service, and pds of a particular M S S . The specifications of the Globalstar system are employed by the sub-simulator as typical system parameters. Equally Distributed M T s on the Earth sen 60 - / 40 <: 20 cu I 0 ra -20 -40 -60 -80 -150 -100 -50 0 longitude 50 100 150 Figure 40 3912 M T s equally distributed on the E a r t h B y using the hexagon M T distribution pattern as shown in Fig . 13, a total of 3912 sample M T s are equally distributed in the areas between latitudes South 80° and North 80° as shown in F ig . 40. The distance between any two neighboring MTs is the same. Note that more MTs are distributed in the lower latitudes than higher latitude because the orbital separation at a lower latitude is higher than that at a higher latitude. The Interference information sub-simulator is employed in the calculation of the total received interference power and the sigal-to-noise-plus-interference-ratio. It is assumed that each M T has a 10-stage P N linear shift register and is assigned a 2 1 0 bits P N sequence. Fig . 41 illustrates the simulation flow diagram. A M T , which is randomly chosen by the simulator to avoid the correlation between MTs, sends a channel request to a G W via 70 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity MT randomly chosen by simulator Time increment Orbital Information Sub-simulator N Check the satellite service and channel condition Gatway, Satellite Position Send Channel request to all visiable satellites If All satellites are in full capacities Interference Information Sub-simulator GW compare the total received interference to maxium tolerable interfrence reject Grant the request Transmite the power margin based its path and satellite service RECORD the inference, # of MTs served Figure 41 The simulation diagram a mobile satellite. If the B E R of the requested satellite is not higher than the required B E R , the G W wi l l grant the request and the M T is able to transmit its signal based on its PSS state. However, i f the B E R of the requested satellite is higher than the required B E R , the satellite has already reached its capacity limit and wi l l reject the channel request of the MT-of-interest accordingly. A computer program based on F ig . 41 are enclosed in Appendix. D . 3.6.2.2 Simulation Results The simulation results for the system capacity of a M S S under a normal channel condition where B=0.3 and c=10 are listed in Table 9. 71 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity G W distri-bution # of G W s (Pds) (means) Theoriticalsystem capacity (No of MTs) Simulation system capacity (No of MTs) G W 1 40 0.6557 24 35 G W 2 32 0.6456 23 37 G W 3 27 0.6196 22 35 G W 4 21 0.5190 17 25 G W 5 200 0.8923 57 81 Table 9 The simulation results for system capacity on channel condition (B=0.3, c=10) In Table 9, it shows that the simulation results are higher than the theoretical results. It could be attributed to the fact that the theoretical results do not consider any resource managements of a M S S . Using the channel management as described in F ig . 41, MTs with larger power margin would be more likely denied access by the M S S than M T s with smaller power margin. Therefore, a .MSS is able to accommodate more M T s . simulation results 0 10 20 30 40 50 60 70 80 90 100 Fraction of Double Satellite Service Links Figure 42 The theoretical and simulation results (B=0.3,c=10) 72 Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity J Nevertheless, our simulation results confirm our previous finding that a G W distribu-tion is very important for the system capacity of a M S S . A s shown in F ig . 42, deploying a G W with a higher value of pds results in a higher system capacity. 73 Chapter 4 Conclusion and Discussion In this thesis, we have investigated the principle of gateway distribution to ensure single and double satellite service and presented an analysis of the effects of gateway distribution on a CDMA-based L E O M S S . A well-designed gateway distribution is critical for mobile satellite system design. Accordingly, we have proposed some strategies to derive the optimal or sub-optimal gateway distributions for single satellite and double satellite service. To ensure single satellite service for Globalstar system, 27 gateways are required by the general solution algorithm and 21 gateways are required by the local solution algorithm. To ensure double satellite service, at least 64 G W s are required by employing the M a x - M i n satellite distance algorithm to ensure MTs in the areas with latitude between North 25° and 45° . A 200 G W s distribution is proposed to ensure double satellite service in the areas with latitude between North and South 25° and 45° and single satellite service from South 80° to North 80°. To analyze the impact of gateway distributions on the system capacity of a C D M A -based L E O mobile satellite system, we classified the general mobile terminal environ-ments into five states. B y computing the required power margin of each state in order to reach the same average probability of error and taking the occurrence probability of each state into account, the capacity of the mobile satellite system, expressed as the average number of MTs per satellite, was analytically derived and validated by means of computer simulations. We have shown that an improper gateway distribution have a detrimental effect on the system capacity of the mobile satellite system. For example, under a condition where 30% of the time a M T experiences a shadowed channel, our numerical results indicate 74 . Chapter 4. Conclusion and Discussion that a M S S is able to accommodate 60 MTs with G W distribution 5 in F ig . 19, but only 13 MTs with G W distribution 2 in Fig . 12. Our simulation results confirm this finding. Also , the system capacity of a M S S under a lightly shadowed channel is more sensitive to the gateway distribution mismatch than that under a heavily shadowed channel. A s a final observation, we would like to point out that the C D M A performance results presented in this thesis, which we take the channel model from [32], are optimistic because we assumed that non-shadowed MTs experienced no fading at all , although in practice they experience a Rician fading channel. A more accurate channel model like Loo ' s model [37] and Rayleigh/lognormal model [38] should be used to quantify the degradation due to an improper gateway distribution. In addition, in order to get specific results, we assumed that the system capacity is sufficiently large and thus the interference to all MTs are the same. More research remains to be done to investigate the effect of the gateway distribution on the system capacity when the total number of users is small. 75 B i b l i o g r a p h y [1] J. Lodge, "Mobile satellite communications systems: Toward global personal com-munications," IEEE Comm. Mag., , no. 436-440, Nov. 1991. [2] J. Evans, "Satellite systems for personal communications," Proceedings of the IEEE, vol. 86, pp. 1325-1341, July 1998. [3] G . Maral , "The ways to personal communications via satellite," International Journal of Satellite Communications, pp. 3-12, 1994. [4] P. Brunt, "Iridium—overview and status," Space Communications, vol . 14, pp. 6 1 -68, 1996. [5] F . Dietrich, P. Metzen and P. Monte, "The Globalstar cellular satellite system," IEEE Trans, on Antennas and Propagation, pp. 935-942, June 1998. [6] M . Simon, J. Omura, R. Scholtz and B . Levitt, Spread Spectrum Communications, Rockville, M D : Comput. Sci. Press, 1985. [7] A . Salmasi and K . Gilhousen, "On the system design aspects of code division multiple access ( C D M A ) applied digital cellular and personal communications networks," Vechicular Technology Conference, pp. 19-22, May 1991. [8] E . Hirschfeld, "The Gloabalstar: Breaktroughs in efficiency in microwave and signal processing technology," Space Communications, vol . 11, pp. 69-82, 1996. [9] R. Gaudenzi and F. Giannetti, " D S - C D M A satellite diversity reception for personal satellite communication: Downlink performance analysis," IEEE Transactions on Vehicular Technology, vol. 47, pp. 658-672, May 1998. [10]R. Akturan and W . Vogel, "Path diversity for L E O Satellite-PCS in the urban environment," IEEE Trans, on Antennas and Propagation, vol . 45, pp. 1107-1116, July 1997. 76 [11]N. Hart, T. Goerke and A . Jahn,. " A discussion on mobile satellite system and the myths of C D M A and diversity revealed," Proc. 4th IMSC, Ottawa, Canada, pp. 469-475, June 1995. [12]P. Taagehol, A . Sammut, R. Tafazoli and B . G . Evans, "Satellite diversity and its implication on the R A K E receiver for C D M A - B a s e d S-PCNs," Proc. Int. Mobile Sate. Conf. ' IMSC 95, pp. 457-462, 1995. [13]B. Vojcuc, R. Pickholtz and L . Milstein, "Performance of D S - C D M A with imperfect power control operating over low earth orbiting satellite link," IEEE Journal on Selected Areas in Communication, pp. 560-567, May 1994. [14]R. Gaudenzi and F. Giannett, " D S - C D M A satellite diversity reception for personal satellite communication: Downlink performance analysis," Proc. Int. Mobile Sate. Conf. ' IMSC 95, pp. 463-468, 1995. [15]A. Ballard, "Rosette constellations of earth satellites," IEEE Trans, on Aerospace and Electronic System, vol . AES-16 , pp. 656-673, Sept. 1980. [16]H. Emara and C. Leodnes, "Minimum number of satellites for three-dimentional continuous worldwide coverage," IEEE Transaction on Aerospace and Electronics, pp. 108-111, Mar. 1977. [17]D. Beste, "Design of satellite constellations for optimal continuous coverage," IEEE Transaction on Aerospace and Electronic Systems, pp. 466-473, May 1977. [18]J. Walker, "Circular orbit patterns providing continuous whole earth coverage," Royal Aircraft Establishment Technical Report 70211, Nov. 1970. [19]C. Rogers, Packing and Covering, Cambridge University Press, 1964. [20]P. Hilton, Advanced Topology, An introduction course, Courant Institute of Mathe-matical Sciences, 1969. 77 [21]S. Verblunsky, "On the least number of unit circles which can cover a square," J. London Math. Soc, vol. 24, pp. 164-170, 1949. [22]D. Pierre, Optimization theory with applications, Dover Publications, 1986. [23]J. Conway, Sphere Packings, Lattices, and Groups, Springer-Verlag, 1993. [24]K. Gilhousen, I. Jacobs, R. Padovani and A . Viterbi, "On the capacity of a cellular C D M A systems," IEEE Trans. Veh. Tech., vol. 40, pp. 303-312, Feb. 1991. [25]C. Tsao, P. Jung and G . Raguenet, " A n isoflux antenna for a low earth orbit satellite mobile communication system," Proc. of American Institute of Aeronautics and Astronautics, pp. 639-641, May 1992. [26]K. Gilhousen, I. Jacobs and R. Padovani, "Increased capacity using C D M A for mobile satellite communication," IEEE JSAC, vol. 8, pp. 503-513, M a y 1990. [27]R. Gaudenzi, F . Gianetti and M . Luise, "Advances in satellite C D M A transmission for mobile and personal communications," Proceedings of IEEE, pp. 18-39, Jan. 1996. [28]P. Monte and S. Carter, "The Globalstar air interface," Proc. AIAA 1994 Satellite Communication Conf, pp. 1614-1621, Mar. 1994. [29]R. Price and P. Green, " A communication technique for multipath channels," Proc. IRE, pp. 555-570, Mar. 1958. [30]J. Proakis, Digital Communications, McGraw-Hi l l Book Company, 1989. [31]E Lutz, "The land mobile satellite channel — recording, statistics and channel model," IEEE Trans, on Vechicular Technolgy VT 40, vol. 40, pp. 375 — 386, M a y 1991. [32]B. Vojcic, L . Milsteintard and R. Pickholtz, "Power control versus capacity of a C D M A system operating over a low earth orbiting satellite l ink," GLOBECOM' 93: IEEE Global Telecommunications Conference, pp. 40—44, 1993. 78 [33]G. Maral and M . Bousquet, Satellite Communication Systems, John Wiley & Sons Ltd. , 1993. [34]M. Pursley, "Performance evaluation for phase-coded spread-spectrum mutiple-access communication-part I: System analysis," IEEE Transactions on Communications, pp. 795-799, Aug . 1977. [35]E. Geraniotis and M . Pursley, "Error probability for direct-sequence spread-spectrum multiple-access communications-part II: Approximations," IEEE Transactions on Communications, pp. 985-995, May 1982. [36]J. Holtzman, " A simple, accurate method to calculate spread-spectrum Multiple-Access Error Probabilities," IEEE Trans, on Communications., pp. 461^164, Mar. 1992. [37]C. Loo, " A statistical model for a land mobile satellite l ink," IEEE Trans. Veh. Technol., vol . 34, pp., 122-127, Aug . 1985. [38]G. Corazza and F. Vatalaro, " A statistical model for land mobile satellite channels and its application to non-geostationary orbits," IEEE Trans. Veh. Technol, pp. 738-742, A u g . 1994. 79 Appendix A List of Abbreviations and Acronyms A - C D M A Asynchronouse C D M A B E R Bit Error Rate C D M A Code Division Multiple Access C G Satellite Coverage C O N U S ContientUS D S Double Satellite Service D S / C C Double Satellite Serivice/Two L O S Channels D S / C S Double Satellite Service/One L O S , One Shadowed Channel DS/SS Double Satellite Service/Two Shadowed Channel G W Gateway L E O L o w Earth Orbiting Satellite System L O S Line-of-Sight M A I Multiple Access Interference M E O Medium Earth Orbiting Satellite System M S S Mobile Satellite System M T Mobile Terminal P M S C S Personal Mobi le Satellite Communication System P N Pseudonoise Code PS Path State PSS Path and Satellite Service State P S T N Public Switched Telephone Network SAT Mobile Satellite S - C D M A Synchronouse C D M A S N R Signal-to-Noise Ratio SS Singal Satellite Service SS/C Single Satellite Service/LOS Channel SS/S Single Satellite Service/Shadowed Channel 80 Appendix B Supporting Calculations B . l DS/SS Calculation oo o i o t oo oo : = -)=/ J e-t2dtc2xe-™dx = ^/=J ^ J c2xe-cxdxdt 0 0 oo = ~Je-t2(-cxe-™ - e-')\la'"t/p*-'"dt 0 oo (B.l) B.2 DS/CS Calculation Let Pio = Pr f s / c s 81 82 Appendix C Supporting Figures Check whether MT and GW have common oevrlapped Area Compare the distance bwteen MT and GW to radius of satellite coverage Distance is less than radius Check which Orbital Plane go through MT and GW circle Compare the distance from MT or GW to Orbital Plane to radius of satellite coverage Distance is less than radius Check whether the Orbital Plane go through overlapped area Caculate the starting and ending time of crossing GW and MT circle The starting time of crossing GW(MT) is in the period of crossing GT(MT) Check wether the double satellite service is applicable Compare starting and ending time of all crossing orbital planes to find the MT can be illuminated by two satellites Figure 43 Flowchart for calculating satellite service 83 Appendix D Simulation Programs in Matlab % The Scenario Simulator % Usage: [SATCAP,S,SENREC,SATCVG]=simulation(BER,c,SHADOW,L) % S : percentage of Single S a t e l l i t e Service % B: Percentage of Shadow % C : Multipath Ratio % L: length of PN Code function [SATCAP,S,SENREC,CVGREC]=simulation(BER,c,B,L) % function [SATCAP,CAPFLAG,SO,SI,Sll,S1000,S10] %=simulation(BER,c,B,L) t i c constant; QMAX=qmax (1, BER, 1, c).; % Assign PN code for each MT load data/pncode; load data/mtdata; [MTN,tmp]=size(MT); [sm,sn]=size(PN); i f sm ~= MTN | .sn ~= L PN=mt_pncode(MTN,L); end NOISE=0; PNref=pngen(L); % The reference MT load data/mtdata; Sl=[]; • S10=[]; S l l = [ ] ; S1000=[]; , . , S0=[] ; R= [ ] ; SATCAP= [•] ; CAPFLAG=[ ] ; CVGREC=[ ] ; SENREC=[]; for time=l:1 % I n i t i a l i z a t i o n CAPFLAG=zeros (PERIOD, 48) ;• % The s a t e l l i t e capacity Flag Matrix'; 1: reach the capacity S1=[S1; zeros(1,48)] ; S0=[S0; zeros(1,48)] ; S11=[S11; zeros(1,48)]; S10=[S10; zeros(1,48)] ; S1000=[S1000; zeros(1,48)]; R=[R; ones(1,48).*NOISE]; % Receive Power White Noise SATCAP=[SATCAP; zeros(1,48)]; %' # of users CVGREC=[CVGREC; ones(1,MTN)*(-1)]; SENREC=[SENREC; ones(1,MTN)*(-!)]; 84 M=MTN; TMP=[] ; MTTMP=MT; % Determine the capacity for each s a t e l l i t e at given time for counter=l:MTN % Random Access MTS. row=ceil(M*rand); mtn=MTTMP(row,1); [TMP,MTTMP]=movedata(TMP,MTTMP,row); [M,tmp]=size(MTTMP); % Connection Analysis CONN=connection(MT(mtn,:),time); i f isempty(CONN)== 1 CVGREC(time,mtn)=0; else % Check the s a t e l l i t e coverage i s a v a i l a b l e or not SAT=unique(CONN(:,3)); % v i s i b l e s a t e l l i t e s [SATN,tmp]=size(SAT); %"# of v i s i a b l e s a t e l l i t e s SEN=senario(CONN); % record the senario for a MT CVGNO=satcvg(CONN); % S a t e l l i t e Coverage SENREC(time,mtn)=SEN; % record the senario for a MT CVGREC(t ime,mtn)=CVGNO; % record the s a t e l l i t e coverage for a MT % checkcap=capcheck(SAT,CAPFLAG,QMAX); % Check the v i s i b l e s a t e l l i t e checkcap=l; % disable capcheck' function i f checkcap== 1 %%% S a t e l l i t e Coverage & Service Information %%% Interference Caculation P=pmargin(SEN,BER,QMAX,c); 1= (pnpn(PNref,PN(mtn,:),delay(L)))"2; %%% Connection Request % c a l c u l a t e the MAI between 2 MTs % MT Request the connection to the v i s i b l e s a t e l l i t e s % I f one s a t e l l i t e has reached the capacity , % which means the interference % i s higher than the allowed l e v e l , and thus declines % the connection, the % MT w i l l not be able to connect to other % s a t e l l i t e s , even the connection % i s avaiable flag=[]; Pnew=[]; % The update Received Power Jnew=[]; %.Capacity % the connection f l a g . flag=l, which means % s a t e l l i t e allowes the new conection 85 for satn=l:SATN . SATID=satconv(SAT(satn,1)); % convert s a t e l l i t e . Only use for variables % Calculate the interference LOS=CONN(find(CONN(:,3)==SAT(satn,1)),4); los=LOS(1,1); Prev=I*(channel(los,P,c))"2; % The received power Pnew(SATID)=R(time,SATID)+Prev; Jnew(SATID)=SATCAP(time,SATID)+1; i f Pnew(SATID) <= QMAX flag=[flag; 1] ; else flag=[flag; 0]; CAPFLAG(time,SATID)=1; % reach the capacity end end % MT Request Processing CHECK=find(flag==0) ; i f isempty(CHECK) ==1 % MT's request i s granted, since a l l the % s a t e l l i e s have not reached % the t o t a l l allowed interference % R=Ptotal, add 1 users to s a t e l l i t e record for satn=l:SATN SATID=satconv(SAT(satn,1)); R(time,SATID)=Pnew(SATID); SATCAP(time,SATID)=Jnew(SATID); % Record Single S a t e l l i t e Service . % & Double S a t e l l i t e Service % S1/S2 > S a t e l l i t e and SENREC > MTs i f SEN ==1 SI(time,SATID) = SI(time,SATID)+1; e l s e i f SEN == 0 SO(time,SATID)=S0(time,SATID)+1; e l s e i f SEN == 10 S10(time,. SATID)=S10(time,SATID)+1; e l s e i f SEN == 1000 S1000(time,SATID)=S1000(time,SATID)+1; e l s e i f SEN ==11 S11(time,SATID)=S11(time,SATID)+1; end end end end % checkcap > end % CONN? empty end % counter end % time % S=S1./(S1+S2); 86 save r e s u l t SATCAP CAPFLAG SENREC CVGREC Si S10 S l l S1000 SO %S SENREC CVGREC toe % Check the v i s i b l e s a t e l l i t e s have yet reached the capacity % 1: capacity i s s t i l l avaible function [TEST]=capcheck(SAT,CAPFLAG,QMAX). Il = [ ] ; I 2= [ ] ; [m,n]=size(SAT); for counter=l:m 11=[II; satconv(SAT(counter,1) ) ] ; end I2=find(CAPFLAG==l); M=intersect(II,12) ; TEST=isempty(M); % 1: No i n t e r s e c t i o n . % No s a t e l l i t e reach the capacity 87 

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