A greedy approach combined with graph coloring for non-uniform beam layouts under antenna constraints in multibeam satellite systems

Abstract

Because of the ever-increasing traffic and quality demands for both internet and television, satellite systems must aim at designs that use the satellite resources in the most efficient way possible. In the case of multibeam satellite systems, this is achieved by making optimal use of the plurality of beams in terms of frequency reuse, power allocation, and quality of the layout. That last point is the one addressed in this paper, the optimisation of the beam layout being a complex but crucial task for the resulting telecommunication system since it directly affects its performances and cost. In the case of broadband systems, the key data is the repartition of the traffic demand over the zone to be covered which is never rigorously uniform. Though, it is common for satellite system design tools to rely on this fairly unrealistic assumption to provide regular coverage which is therefore often suboptimal : inappropriate beamwidths, overprovisioned or unsatisfied user stations, unprofitable beams. Nonetheless, one strong advantage of the regular scheme is that it is known to be compatible with the single feed per beam antenna constraint of minimum angular distance for all the couples of beams coming from the same reflector. The aim of this paper is to present a randomized multi-start heuristic to build a non-uniform layout, driven by the different telecommunication mission criteria and by the aforementioned antenna constraint that is dealt with by a graph recoloring procedure via local search and simulated annealing.

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

“…On larger instances, the results are more mitigated since there are cases were the solution reached is relatively far from the estimated best possible solution. Yet, the good results on small instances have motivated a comparison with the greedy heuristic solution of [3]. This comparison is natural since it is the only other known algorithm that considers the SFPB antenna separation constraints and that handles the beam centers actively.…”

“…But the major drawback of treating the placement of the beams and their allocation to the antenna reflectors sequentially is that one is very likely to discover that, with a layout built regardless of the antenna constraint, even the optimal mapping of the beams to the reflectors can turn out to be technologically infeasible for the Single Feed Per Beam antennas. Guided by a combinatorial model of the problem, [3] proposes a heuristic procedure combining a randomized multi-start greedy approach and graph coloring to find jointly interesting positions for the beams and an acceptable beam mapping to the reflectors, with an upper-bounded number of beams and a pre-processing of the beamwidths to use.…”

Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design

“…In the context of radiotherapy equipment configuration, the authors of [16] propose to linearize the quadratic terms of the convex proximity constraints with extra variables and a notion of approximation points, but without really discussing the error made in the end on the approximated Euclidean distances. Another way of linearizing the Euclidean distances is to discretize the possible positions of the originally continuous variables allowing then to pre-compute all the possible pointto-point distances, as done both in [16] and [5]. Although, our ambition in this work was to preserve this continuity of the position variables so this type of discretization has been discarded.…”

“…For antenna feasibility reasons detailed in [5], two beams associated to the same reflector must have sufficiently separated beam centers, which makes the link with our work on Euclidean separation constraints in section 2 . The rule adopted in this study is that this separation distance is proportional to the mean of two beam diameters, according to a proportionality coefficient κ ∈ R + (physically realistic values varying in [ 3 2 , √ 3]).…”

“…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.…”