^{1}

^{*}

^{2}

^{*}

Network planning, analysis and design are an iterative process aimed at ensuring that a new network service meets the needs of subscribers and operators. During the initial start-up phase, coverage is the big issue and coverage in telecommunications systems is related to the service area where a bare minimum access in the wireless network is possible. In order to guarantee visibility of at least one satellite above a certain satellite elevation, more satellites are required in the constellation to provide Global network services. Hence, the aim of this paper is to develop wide area network coverage for sparsely distributed earth stations in the world. A hybrid geometrical topology model using spherical coordinate framework was devised to provide wide area network coverage for sparsely distributed earth stations in the world. This topology model ensures Global satellite continuous network coverage for terrestrial networks. A computation of path lengths between any two satellites put in place to provide network services to selected cities in the world was carried out. A consideration of a suitable routing decision mechanism, routing protocols and algorithms were considered in the work while the shortest paths as well as the alternate paths between located nodes were computed. It was observed that a particular satellite with the central angle of 27° can provide services into the diameter of the instantaneous coverage distance of 4081.3 Km which is typical of wide area network coverage. This implies that link-state database routing scheme can be applied, continuous global geographical coverage with minimum span, minimum traffic pattern and latency are guaranteed. Traffic handover rerouting strategies need further research. Also, traffic engineering resources such as channel capacity and bandwidth utilization schemes need to be investigated. Satellite ATM network architecture will benefit and needs further study.

Network planning, Analysis and Design is an iterative process encompassing topological design, network syn- theses and network realization. It is aimed at ensuring that a new network or service meets the needs of sub- scribers and operators [

In this paper, therefore, we extend the idea of one satellite system to the idea of a constellation of satellites in two dimensions. Hence, we aim is to design and develop a geometrical topology model to determine to network coverage of an area. In Section 2, we develop a LEO satellite geometrical constellation network model. In Sec- tion 3, we present a global terrestrial coverage model. In Section 4, we present the implementation of the global network model internetworking LEO satellite network with the terrestrial networks. In Section 5, we conclude with recommendations for future work.

The integration of LEO satellites with the ground-based internet gateway and connection-oriented circuit-switch- ed telephony service also means that the end-to-end system connectivity will be provided transparently using the satellite infrastructures. LEO satellite networks are planned in large constellations to cover large portions of the earth, mainly targeted isolated mobile terminals where ground infrastructure is missing or temporarily unavaila- ble with different geometries [

Two main types of satellite constellations are stated in the literature: 1) walker delta (or Ballard Rosette) con- stellations and 2) Walker star constellations. The Rosette constellation covers a large band around the equator. A ground station is in the footprint of several satellites whose orbital planes overlap several times. The Earth sta- tion traces a sinusoidal shaped orbital track on the flattened surface of the Globe [

Irridium is a LEO satellite network, where connection oriented circuit-switched telephony service, and dial-up through satellite to ground Internet-gateway are offered on any spot on the earth. Irridium [

Two types of intersatellite links (ISLs) are often witnessed: Intra-plane ISLs, the ISLs between satellites on one orbital plane, and the interplane ISLs, the links between satellites on different planes. Both ISLs enable the communication between two users in different footprints with not more than two ground gateways being neces- sary. The interplane ISLs are permanently switched because of the fast change in relative positions of the satel- lite to each other. With the introduction of the advances in smart and adaptive radio [

It was noted in [

Four important factors that influence the design of any satellite communication system has also been identi- fied in [

Also, the design of a Non-Geosynchronous Satellite orbit system will be heavily influenced by the decision on whether or not to provide services directly to end-users (i.e. end-to-end system implementation). It will also be impacted by the decision on whether or not to include established telephone companies in the delivery of the service. By their very nature, mobile satellite systems have committed to serve the end user directly. However, dif- ferent approaches have been taken with regard to including established telephone companies. Two examples of organizations that took opposite decisions are the Global Star and Irridium. Global Star elected not to bypass the existing telephone companies while Irridium did. These decisions led to a very different architecture for the two systems.

In this sub-section, we consider the geometrical aspect of developing satellite constellation network model. First of all, we review the analysis of the motion of a satellite body of mass, m, which is at a height, h, above the earth and is revolving round the earth in a circle of radius, r_{s}, as given in [

Using the sine rule to triangle, SEC, we have that

which yields

where _{s} is the vector from the centre of the earth to the satellite, _{s} and r_{e}, the radius of the earth, is the angle between the earth station, E and the satel- lite, S; d is the vector from the earth station to the satellite.

But angle

where _{c} to d.

The diameter of the instantaneous coverage region is given by:

And the coverage angle at the centre of the earth is given by:

The angular displacement, _{s} by [

where l is the circumferential distance, a satellite body on the circle of rotation has moved (or would roll without slipping) if free to do so. This is Newton’s Law of circular motion.

We extend the above analysis to an idea of a LEO satellite constellation thus:

1) To establish whether a particular satellite location can provide service into a given region, a simple visibil- ity test can be carried out as shown in [

This means that the maximum central angular separation between the earth station and sub-satellite point is limited by this value. The central angle

2) The distance, d, will determine the free space path loss along the propagation path and will be a factor in the link budget design. This is given by:

where r_{s}, r_{e},

3) The elevation angle ^{0}.

4) The number of satellites required in one polar orbit. The decision on whether or not to use ISLs, whether to design to operate across the system if ISLs are used, is usually imparted by the number of satellites required to complete one plane with a suitable overlap. The satellites in a plane are separated from each other with an angu- lar distance given by:

5)

where N_{s} is the number of satellites required to complete one plane with a suitable overlap. Since the planes are circular, the radii of the satellites in the same plane are the same at all times and so are the distances from each other.

The length L_{v} of all intra-plane ISLs is fixed and is computed by [

where R is the radius of the plane.

6) Number of planes, M, for complete full global coverage. The Satellite Network is composed of M separate orbits (planes), each with N_{s} satellites at low distances from the earth. It has been observed that one plane of the satellites, if in the polar orbit, will have satellites on both hemispheres of the earth, some going Northwards (or Eastwards) and some going southwards (or Westwards). Hence, it will be technically necessary to have M planes equal to half of the number of the satellites per plane, N_{s} That is,

The planes are separated from each other with the angular distance given by:

The length L_{h} of the inter-plane ISLs is variable and is calculated by [

where

With lat as the latitude at which the iner-plane ISL resides (see

7) Total number of satellites for a global network coverage. Using the same logic as in (10) and (12) above, there will be N_{s} slots (or slices) around the equator made up of M_{p} planes of satellites. Therefore, the total mini- mum number of satellites needed for complete global network coverage is given by:

In this sub-section, we compute the values of the above parameters as follows:

1) Satellite visibility value: This is given in (8) by:

Given:

But we do know that

2) The central angle

We need to find out the central angle,

where

3) The diameter of the instantaneous coverage

The value ^{ }

We now have a situation set-up as shown in

4) The number of satellites required to complete one complete plane with suitable overlap is computed from (10) given by:

5) The number of planes for complete full global coverage is computed from (12) as shown below:

6) The total number, N_{T} of the satellites for the full continuous global satellite network is given by (15) above, i.e.,

The choice of the constellation model influences the other aspects of the network architecture such as the topol- ogy organization and routing scheme [

number of satellites in a constellation at any particular time is relaxed to 8 satellites in 4 planes which will in turn relax a total number of satellites to 32 satellites. This configuration can be arranged in 4 × 4 matrix struc- ture.

We propose a hybrid topology model in [

If we consider the hybrid topology model network shown in

All possible paths are shown in the hybrid mesh topology. And all of the paths using any one of the links with the specified directions are equal and are shortest paths. Also, all the paths using these directions are loop free. Thus, the routing problem for a satellite system becomes the “shortest paths” discovery problem. However, since the network is spherical and there exists many routing set between the source (S) and the destination (D) and most of them pass through the polar region on through the horizontal plane a virtual network has to be con- sidered while finding the right routing set [

The above analysis is fundamental to the determination of the Global Network that covers an earth geographi- cal Network service area if internetworked with the Space Network derived in Sub-Section 2.4 and 2.5 respec- tively.

In this section, we intend to develop a continuous global Earth Network Coverage area suitable for a Wide Area Network (WAN). Just as Local Area Network (LAN) provides internal connectivity to a small geographic area, and a Metropolitan Area Network (MAN) extends intermediate coverage to a wider area, wide area networks provide wider area coverage and they go beyond the boundaries of cities and extend globally. The extreme of the WAN is the Global Network. First of all, we model the positions of a location on the earth using the spheri- cal co-ordinates framework in 3.1. Next we compute the distances between the selected locations (cities) in the world.

We model the position of a satellite location on the earth using the spherical co-ordinate framework where the

position of a point is considered as being a point in a sphere as depicted in

The latitude of a place is measured in degrees North or South of the equator. The latitude of a place lies be- tween 90˚ North or 90˚ South of the equator.

Let G be a position on the earth’s surface as shown in

Let the line NGBS through G be the meridian.

EGHI = the parallel of latitude through G and H

In

Or

Similarly, the longitude of a place is measured in degrees East and West of the Greenwich meridian and it lies between East and West of the Greenwich meridian.

Let H be a position on the earth’s surface as shown in

Let the Greenwich meridian NGBS

Intersect the parallel of latitude EGHI at G. Let the meridian NHCS through H intersect the equator, ABCD at C and intersect the parallel of latitude EGHI at H.

The angle

Let H be the position on the earth’s surface of the equator as shown in

Let NHCS through H be the meridian;

Hence, by resolution of vectors, the total displacement between location H, G and B respectively is given by:

In general, therefore, the total distance along any parallel of latitude North or South of the equator and then meridian (or Greenwich meridian) East or West of the equator is given by the sum of the arc lengths travelled in x and y directions respectively. This implies two dimensional mobility model.

Suppose we plan to develop a Widea Area Network coverage area for a LEO satellite constellation network de- veloped in Section 2. We arbitrarily select eight satellite locations to represent points of Network access for the Widea Area Network (WAN). We select two satellite locations in each quadrant of the earth surface to cover the whole globe as shown in

Using Equations (17) to (20) derived in Sub-Section 3.1, we then can compute the total distances travelled between the selected cities in the world as shown in

For widely dispersed users, long paths exist that connect the various parts. Generally, a user at one location will send the desired message to a network entry point. We think of this wide area network as a cloud. That is, we do not know what is going on inside but we know that there are ways to get the messages from here to there either through 3 types of networking technologies [

Routing protocols could be divided into [

Quadrant | Countries (cities) | Locations (latitudes, longitudes) |
---|---|---|

First | Nigeria (Onitsha) | 06˚N, 07˚E |

Japan (Nagasaki) | 33˚N, 13˚E | |

Second | North America (Los Angeles) | 35˚N, 170˚E |

South America (Canada, Churchill) | 58˚N, 95˚E | |

Third | Stanley (Falkland) | 58˚S, 58˚W |

Ecuador (Marcus) | 03˚S, 78˚W | |

Fourth | South Africa (Port Elizabeth) | 44˚S, 24˚E |

New Zealand (Plymouth) | 39˚S, 174˚E |

Los Angeles | Churchill | Marcus | Falkland | Onitsha | Port Elizabeth | Nagasaki | New Plymouth | |
---|---|---|---|---|---|---|---|---|

Los Angeles | - | 1254 | 5087 | 2916 | 8470 | 8473 | 7352 | 6703 |

Churchill | 1254 | - | 6841 | 5812 | 4146 | 3360 | 7334 | 5812 |

Marcus | 5087 | 6841 | - | 7024 | 6326 | 4994 | 7640 | 5525 |

Falkland | 2916 | 5812 | 7024 | - | 3885 | 6259 | 8565 | 6649 |

Onitsha | 8470 | 4146 | 6326 | 3885 | - | 7852 | 5803 | 7684 |

Port Elizabeth | 8473 | 3360 | 4994 | 6254 | 7352 | - | 1923 | 8422 |

Nagasaki | 7352 | 7334 | 7640 | 8565 | 5802 | 1923 | - | 3575 |

New Plymouth | 6703 | 5812 | 5525 | 6649 | 7681 | 8422 | 3575 | - |

Also, the routing protocols are based on one of the following two algorithms namely: Distance vector and link state algorithms. The underlying concepts of distance vectors, link state routing, Dijkstra’s algorithm for the shortest path precede the discussion on any specific routing protocol. Hence, we first discuss the basics of link state routing in Sub-Section 4.1, then proceed to discuss the Dijkstra’s algorithm in 4.2 and finally, demonstrate the application of Dijkstra’s algorithm in the determination of the continuous global earth geographical network coverage area in 4.3.

Distance vector routing does not work well if there are changes in the internetwork. When two or more networks are interconnected, we refer to such extended network as interwork. The reasons why this routing algorithm does not work well are for the facts that the distance vectors sent to the neighbours do not contain enough in- formation about the topology of the internetwork. That is, every router tell its neighbours its distances to all the networks without knowing the Network topology. No wonder why it was stated in [

In a link state routing, every router maintains a database of Network topology. The database contains records of the links of the entire network. Each record consists of source router identification, its neighbouring router identifiers, and the costs associated with the link between them. Each record is called link state. The cost can be defined in terms of distance, hop, delay, inverse of bandwidth or any other parameters [

Identical database is available in all the routers. The database is refreshed at fixed intervals (30 minutes in open shortest path First). For refreshing the database, every router sends updates called link state advertisements [LSAs].

If there is a change in the neighbourhood (e.g. a link/router goes down or a new router is added), LSAs are sent immediately by the routers that detect the change. They do not wait for the regular schedule of advertise- ments for refreshing the records of the database. LSAs are sent using controlled flooding across the internet so that every router receives them.

Each router works out the shortest paths to every other router using the database and the Dijkstra’s algorithm, once the shortest paths are known, the forwarding table can be constructed readily.

An advantage of link-state routing is the availability of alternate paths. If a link goes down, a router can rea- dily work out alternative path from its topology database.

Dijkstra’s algorithm computes the shortest paths from a Node (called the root) to all other nodes from the link- state debatable. The root-node selects one of its neighbours having the least cost. The link costs of neighbours of these two nodes are examined. One of the neighbours having the least cost to the root is selected again. The pro- cess is repeated, and each time a neighbor with the least cost of the root is selected and added to the set of nodes whose link costs have been computed.

To understand the algorithm, let us consider a simple graph consisting of the nodes A, B, C…H that represents the eight cities and the link costs between any pair of interconnected nodes. See

We will first of all define the followings:

Root: The node from which the least cost paths are being determined.

Set (S): Set of those nodes whose least cost paths to the root have been determine.

Set (N): Set of neighbours of set S.

I : Node I has path cost “P” to the root via node J.

We note that since we are to determine the forwarding

Legend | Nodes | Cities | Nodes | Cities |
---|---|---|---|---|

A | Los Angeles | E | Onitsha | |

B | Churchill | F | Port Elizabeth | |

C | Falkland | G | Nagasaki | |

D | Marcus | H | Plymouth |

Steps | Set (S) | Set (N) |
---|---|---|

1 | A | B , D |

2 | A , B | C , D |

3 | A , B , C | D , D , D |

4 | A , B , C , 0 | D , D , E , E , E , E , E |

5 | A , B , C , E | F , F |

6 | A , B , C , F | G , G |

7 | A , B , C , D , E , F , G | H , H , H |

8 | A , B , C , D , E , F , G , H |

Dijkstra’s algorithm to determine the least paths from A to the rest of the nodes.

With Step 8, all the least cost paths to the root A have been determined.

It has been stated that an advantage of link state routing is the availability of alternate paths [

1) The route from Los Angeles (A) to Churchill (B) (i.e. A ® B) is 1254 km with two other alternate routes: A ® D ® B is 11,928; and A ® C ® D ® B is 16,779 km.

S/N | City to City Routes | Alternate Routes | Total Distances (Km) |
---|---|---|---|

1 | Los Angeles to Churchill | A ® D ® B; A ® C ® D ® B | 11,928 16,779 |

2 | Los Angeles to Marcus | A ® B ® D is A ® C ® D is | 7095 9,938 |

3 | Los Angeles to Falkland | A ® D ® C is A ® B ® D ® C is | 12,111 15,119 |

4 | Los Angeles to Onitsha | A ® C ® E is A ® D ® E is A ® B ® D ® E is A ® C ® D ® E is A ® C ® F ® E is | 6799 11,413 14,421 16,264 16,500 |

5 | Los Angeles to Port-Elizabeth | A ® B ® E ® F is A ® C ® E ® F is A ® D ® E ® F is A ® B ® D ® E ® F is A ® C ® D ® E ® F is | 12,772 14,131 18,745 20,753 23,596 |

6 | Los Angeles to Nagasaki | A ® B ® E ® G is A ® B ® E ® F ® G is A ® C ® E ® F ® G is A ® B ® D ® E ® F ® G is | 11,243 14,695 16,054 22,676 |

7 | Los Angeles to New Plymouth | A ® B ® E ® G ® H is A ® C ® F ® H is | 14,818 17,590 |

2) The route from Los Angeles (A) to Marcus D (i.e. A ® D) is 5095 km with two other alternate routes: A ® B ® D is 7095 km while route A ® C ® D is 9938 km.

3) The route from Los Angeles (A) to Falkland (C) is 2914 km with other two alternate routes: A ® D ® C is 12,111 km and A ® B ® D ® C is 15,119 km.

4) The route from Los Angeles (A) to Onitsha (E) (i.e. A ® B ® E is 5440 km with five other alternate routes: A ® C ® E is 6799 km, A ® D ® E is 11,413 km, A ® B ® D ® E is 14,421 km, A ® C ® D ® E is 16,264, while A ® C ® F ® E is 16,500 km.

5) The route from Los Angeles (A) to Port Elizabeth (F) (i.e. A ® C ® F is 9168 km with other five alternate routes: A ® B ® E ® F is 12,772 km, A ® C ® E ® F is14,131 Km; A ® D ® E ® F is 18,745 Km; A ® B ® D ® E ® F is 207,753 km while A ® C ® D ® E ® F is 23,596 Km.

6) The route from Los Angeles (A) to Nagasaki (G), A ® C ® F ® G, is 11,091 km with four other alternate routes: A ® B ® E ® G is 11,243 km, A ® B ® E ® F is 14,695 km, A ® C ® E ® F ® G is 16,054 km, A ® B ® D ® E ® F ® G is 22,676.

7) The route from Los Angeles, A to New Plymouth, H (i.e. A ® C ® H) is 9563 km with two other alternate routes: A ® B ® E ® G ® H is 14,818 km while A ® C ® F ® H is 17,590 km.

At times, we want to deviate from the shortest path strategy because the shortest path may not have enough capacity to carry the entire traffic due to its bandwidth limitations. Traffic engineering allows us to provision more traffic flows along the desired path which may not be the shortest path.

· Basic traffic engineering depends on coverage. When determining the coverage of a system both system ca- pacity for handling traffic and coverage must be considered. Hence, based on Equation (5) and (8) derived above, it has been shown that a particular satellite location provides service into a given instantaneous cov- erage region of 4081.3 km with a visibility angle of 37.32˚, and total instantaneous coverage angle of 2δ = 122.68˚ (i.e. 2 × 61.34˚). Hence, the concept of phased array antenna can be used on our satellite system to divide up among a set of receive antennas that provide 360˚ coverage, as in the sectored antenna approach of cellular systems [

· The implication of the instantaneous coverage distance range of 4081 km is that satellites must handover their connections to the earth stations at about this distance. The handover procedure requires a state transfer from one satellite to the next, and will result in a change in the delay characteristics of the connections at least for a short time interval. Considering that the orbital period of a satellite is 100.5 minutes [

· Also, two commonly used routing efficiency are channel traffic and communication latency. The channel traffic at any time instant (or during any time period) is indicated by the longest path transmission time in- volved. For instance, the route from Los Angeles (A) to New Plymouth (H) has an optimal route A ® C ® H that is 9563 km with two other alternate routes: A ® B ® E ® G ® H that is 14,818 km and A ® C ® F ® H that is 17,590 km. In traffic engineering, the shortest path may not have the required capacity to carry the entire traffic due to its bandwidth limitation; we therefore, choose the longest path transmission that has much more latency. An optimally routed network should achieve both minimum traffic and minimum latency for the communication pattern [

· The concept of virtual networks leads to the network partitions of a given physical network into logical sub- networks for multicast communication. Considering the results of the computed total distances travelled be- tween the selected cities in the world as tabulated in

But if we consider the orthogonal paths taken between the same source A and destination H, we would have a route from A (Los Angeles) vertically to C (Falkland) and horizontally to the destination H (New Plymouth) giving a total distance of 9563 km in 2 hops (links).

· Equally observable is the minimum span global geographical coverage area as shown in

An in-depth study for the development of the continuous global geographical coverage are for interworking LEO satellite network and terrestrial networks has been presented in this paper. First, a successful design of the LEO satellite geometric network connectivity is presented, and the analysis and computation of the LEO satel- lite system parameters were evaluated in terms of the satellite visibility, central angle, diameter of the instanta- neous coverage area, number of satellites required to complete plane with suitable overlap, number of planes for complete global coverage as well as the total number of satellites for the full continuous global satellite network through mathematical simulations. The values informed our choice of a hybrid mesh network model that has been configured to a 4 × 4 matrix structure and was implemented with a shortest path routing. Next, analytical equations were developed for computing point-to-point distances between nodes (cities) that were located under the satellite footprints. Eight cities, two in each quadrant were chosen to represent the point-to-pint network ac- cess points for the wide area network coverage of the satellite locations. A discussion of the Dijkstra’s algorithm and its application in the determination of the continuous global earth geographical network coverage area is presented through mathemtical simulation resulting in high but tolerable distance range of 4081 km as well as coverage time delays for a link state database routing scheme. We believe that this link state database routing scheme can smooth very effectively this result as well provide alternate paths with the longest paths that have required capacity and hence enough bandwidth to carry the traffic where traffic congestion (or router failures) exists.

In conclusion, therefore, we have developed an integrated terrestrial/space system that can be implemented with a link state database routing scheme. This scheme is capable of guaranteeing continuous global geographi- cal coverage area with minimum span whereby orthogonal set of paths taken from any source to destination will achieve both minimum traffic pattern and latency. Handover research and re-routing strategies should need fur- ther research. Traffic engineering resources such as channel capacity and bandwidth utilization schemes need to be investigated. Network architecture for implementing the interworking of LEO satellite ATM network and terrestrial networks also needs further research.