  The use of regional coverage satellite constellations is on the rise, urging
the need for an optimal constellation design method for complex regional
coverage. Traditional constellations are often designed for continuous global
coverage, and the few existing regional constellation design methods lead to
suboptimal solutions for periodically time-varying or spatially-varying
regional coverage requirements. This paper introduces a new general approach to
design an optimal constellation pattern that satisfies such complex regional
coverage requirements. To this end, the circular convolution nature of the
repeating ground track orbit and common ground track constellation is
formalized. This formulation enables a scalable constellation pattern analysis
for multiple target areas and with multiple sub-constellations. The formalized
circular convolution relationship is first used to derive a baseline
constellation pattern design method with the conventional assumption of
symmetry. Next, a novel method based on binary integer linear programming is
developed, which aims to optimally design a constellation pattern with the
minimum number of satellites. This binary integer linear programming method is
shown to achieve optimal constellation patterns for general problem settings
that the baseline method cannot achieve. Five illustrative examples are
analyzed to demonstrate the value of the proposed new approach.
