Mixed-integer linear programming for multibeam satellite systems design: Application to the beam layout optimization

Abstract

International audienceIn a society where the demand for multimedia applications and data exchange is experiencing an unstoppable growth, multibeam systems have proven to be one of the most relevant solutions for satellite-based communication systems. Though already well represented among the geostationary satellites today, there are still several unresolved design optimization challenges for these complex systems that could lead to improved performances and to better system costs. The satellite platform, the repeater, and the antennas are examples of subsystems that should be designed jointly in order to reach an optimized technical solution that fulfills the service requirements. Traditionally, such complex tasks are addressed through a decomposition of the overall system design into a sequence of smaller decision problems. In this article, we propose to rely on operations research techniques to, on the one hand, take into account explicitly the in-terdependencies of these decomposed problems, and on the other hand, to handle the own constraints of each subsystem and their interactions. In this paper, the focus is laid on the optimization of the beam layouts of the multibeam satellites. Indeed, in addition to being a perfect example of the aforementioned importance of dealing with subsystem constraints, this problem appears early in the chain of design of a multibeam satellite system and is therefore critical for the quality of the telecommunication system: the weaknesses of a beam layout cannot be made up for later on in the system design. For this crucial optimization phase, the strength of the methodology we propose in this paper is to use mixed-integer linear programming to incorporate explicitly technological feasibility constraints of the subsystems involved, while preparing at best the subsequent design problems. Most importantly, our approach allows to overcome several resisting flaws of the already existing algorithms

Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design

“…where the direction i min ∈ U is defined as the closest direction to u − v in terms of angular separation. Therefore, since ||U i min || = 1 and since θ max ∈ [0, π 3 ]: (6) and since i min ∈ U and therefore verifies the equation 4:…”

“…Another example in the satellite industry is the problem of optimizing the beam layouts of a multibeam telecommunication satellite system (see [5], [6] and [14] for instance). It consists of defining the positions in the Euclidean plane of a certain number of disks, each one representing the spatial extent of a radiofrequency beam that carries telecommunication signals for various applications: television, telephone, radio or internet by satellite for instance.…”

Static beam placement and frequency plan algorithms for LEO constellations

“…For the beam placement, Camino et al 11,12 approached the problem with mixed-integer linear and linearization techniques and provided solutions for up to 300 user terminals. Although optimal, finding a solution for larger scenarios is computationally infeasible.…”

MILP formulation improvement with k-means clustering for the beam layout optimization in multibeam satellite systems

“…However, papers dealing with beam layout algorithms are not frequently published. In this paper we consider the NP-hard integrated beam layout and reflector allocation optimization problem previously considered in [4,5]. Each user station in the service area is defined by its (x, y) coordinates in a projected 2D space and a traffic demand.…”

“…Figure 1: Forward link of a multibeam satellite system Another example displayed in Fig. 2 and taken from [4] illustrates the interest of continuous positioning of the beams and diameter selection. On the left side with subfigures (a), (c) and (e), three different beam layouts and antenna reflector assignments represented by the different colors are used to cover the same service area.…”