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Air Traffic Control System Based on Low Elevation Orbit (LEO) Satellite Constellation
Air navigation currently is insured by the Secondary Surveillance Radar SSR located on the ground. Satellite systems are a valid alternative system to cover wide areas on the earth and to provide broadband communications to mobile and fixed users. In this paper, a low-Earth orbit satellite constellation is presented. A novel
hierarchical and distributed QoS routing protocol (HDRP) is investigatedThis paper investigates the problem of management in Low Earth Orbit (LEO) satellite systems is addressed in this paper. Particularly, an analytical study of a newly proposed architecture for a constellation. In order to perform the Air Traffic Control over the entire Earth, a new architecture is designed and evaluated. It suplies the surveillance and data link capabilities of radar SSR Mode S by means of a constellation of Low Earth Orbit (LEO) satellite systems
The current tendencies are toward satellite systems  that provide permanent relays between ground stations and aircraft through the entire globe. The systems currently used are the GPS and GNSS that provide position data standard for embedded systems to provide navigation position around the world. To ensure efficient air traffic control over the oceans and deserts, the controller should view its traffic on a screen like the SSR radar , for that some basic data are needed such as altitude, the position of each plane provided by three satellites, the direction provided by two successive positions, and the ground speed calculated with the distance traveled during a definite time. The same technique is used by SSRs and we use this technique to perform our system and the pair of frequencies  is kept. Mode S transponders  send the aircraft identification, its altitude and geographic coordinates. To achieve this we will design a system based on a constellation of satellites low altitude  and many ground centers.
This global approach has sparked the development of several new communication satellite systems, which abandon the traditional use of geostationary earth orbit (GEO) in favor of medium earth orbit (MEO) and low earth orbit (LEO) satellite systems. LEO and MEO satellite networks increase the service regions of their designers, providing services to regions of the world where there is little or no telecommunication infrastructure, such as Asia, Africa, Eastern Europe, South America, and the polar regions. These LEO and MEO satellite networks provide global coverage to their users, which a typical GEO satellite system cannot provide. One such LEO satellite system, Motorola’s IRIDIUM system, was completely deployed in May 1998.
The satellite constellation is designed to provide links to important data. The overall architecture is studied, taking into account the requirement to use the standard SSR transponders mode S and it necessitates the use of low earth orbit (LEO Low Elevation Orbit)  with a height of 1500 km; we use a constellation based on the low polar orbits. We use four low polar orbits, the angle between two successive orbits is 450 and each orbit contains ten satellites. We use also five satellites distributed on the low equatorial orbit ELEO (Equatorial low Earth orbit), the length of each orbit is about 49455 km, and so 45 satellites are used in our constellation.
The geographical coordinates are traditionally expressed in the sexagesimal system (Degrees (°) minutes (‘) Seconds (“)). The basic unit is the degree of angle (one full turn = 360 °), then the minute of angle (1 ° = 60 ‘), then the second angle (1’ = 60 “). Measures less than one second are noted with the decimal system. Our model is to express the coordinates in decimal degrees with 7 decimal to have an accuracy of less than ± 1 m as follows:
Latitude: 47.6193757 – Longitude: 006.1529374
Each point contains 19 digits coded on 76 bits transmitted in binary code that pulse has a duration of 23.75 µs 76 bits, it is modulated by differential phase  DPSK (Differential Phase Shift Keying). The terminal calculates the elapsed time between transmission and receipt of the request sent to the antenna, it can then calculate its distance from the latter.
A. The basic system geometry
The system geometry is shown in Figure 1. Each satellite can cover a circular area of diameter D depending on the minimum grazing angle Ψmin which should not be less than 3° , to avoid the occurrence of adverse propagation effects.
From Figure 1 we can have the following relations:
Where R is the mean radius of the Earth: R = 6371 km and the range of the satellite Rmax is given by:
B. Expected advantages
1. The implementation of this principle eliminates all Garbling which is a fundamental problem in the design of the classical SSR system and the situation is made worse by increased traffic; asynchronous response phenomenon; the phenomenon of multipath  and response on side lobes which requires interrogator side lobe suppression system .
2. It is possible to envisage an extension of the transactions between the satellites and the transponders, this will introduce real functions “data link”.
3. The identification will be directly and unambiguously with the ability to display live information on the controller screen: call sign of plane or flight number.
4. Moreover, the standard information (altitude and distance) can be done on a single exchange which leads to a strong reduction in bulk electromagnetic. And this process gives the information of instantaneous position of each aircraft.
5. The satellite constellation provides a global coverage for ATC and economical solutions for air companies rather than using SSRs
We assume that the altitude of the satellite is H = 1500 km, therefore:
From (5) we have according to calculation of the great circle :
Where Rz is the radius of the area covered by a satellite and it is an arc of a great circle Orthodromy . Knowing that β is expressed in minutes and Rz in nautical mile (1 NM = 1.852 km).
Using expression (6) we obtain area surface Sz:
But the real surface is a part of a sphere (spherical cap of radius R and height h), and not a circle and given by:
Using some trigonometric relations we find:
C. Satellite design requirements
The main features of the satellite are given regarding to the altitude and coverage and they are quasi similar to Global star and Iridium satellites:
– The satellite must be equipped with a large L-band active phased array with a surface of about 70 m2.
– The use of turning antenna is not necessary because the azimuth is determined by geographical coordinates of two points.
– The position of satellite must not be based on GPS aiming to provide an independent surveillance realized by ICAO.
– The satellite must be equipped with a UHF communication tools for links with the ATC centers.
II. RESULTS DISCUSSION
For the satellite with elevation is 1500 km, and Ψmin = 3º we have Rmax = 4640 km (Rmin =1500 km) represents a valid distance for transmitting data on the frequencies 1030 MHz and 1090 MHz through very short time (62 ms ), so we will have about 16 interrogations and answers in a second. The data will be transmitted alternately as: AC P AC P AC P AC P (AC = identification and altitude, P = geographical position: latitude and longitude).
A satellite, at 1500 km, can cover an area of 5,107 .107 km2. To get the exact geographical coordinates at least three satellites are needed and the usage of the fourth satellite enables to ensure the relief in case of failure and in addition four satellites give the altitude of an aircraft, this parameter shouldn’t be transmitted but it should be compared to the security minimal altitude of given area and in case of danger, the crew must be alerted.
The number of satellite available in equatorial areas are three and it increases when the latitude increases to the North or South Pole and figure 2 shows this variation. The procedure for handover (HO)  will be managed between satellites when the transponder of an aircraft flying in an area covered by a satellite S1 and receiving the signal from another satellite adjacent S2.