A Rapid Algorithm for Beam Illumination Patterns and Hopping Time Plan

Beam hopping (BH) is a satellite communications technique in which sets of beams are sequentially illuminated over a defined time interval. Geographically varying the duty cycle of satellite transmission allows for reduced resource wastage as satellite capacity is matched to non-uniform user demands. Total feasible active beam combinations is given by $2^n$ for $n$ beams. With in service satellite systems operating in excess of 100 beams, complete enumeration of optimum illumination patterns is not tractable. Developing efficient optimization methods which minimize resource wastage is essential to realising the benefits of modern BH systems. We present a computationally efficient pattern generation method which uses the binary logarithm to decompose beam demands into common powers of two. This method is shown to produce feasible patterns within 0.047 and 0.31 seconds for systems using 49 and 132 beams respectively and within 19.109 seconds for a 1085 beam system. When averaged across all testing configurations, this method reduced capacity error by 94% compared to a conventional even data distribution. To facilitate algorithm comparison, two integer linear programming formulations are developed. Even though they can only solve problems of modest sizes to proven optimality, they provide valuable insights in the optimality gap for our proposed heuristic approach.