Infrared emissions from a Dyson sphere are not "broadcasts", per se, but they ARE inevitable. Maybe we are as far off base as early telescopic explorers of Mars were, looking for gaslights and vast diagrams of the Pythagorean theorem laid out in cultivated Martian fields. If the aliens have any brains at all they will be laying low and keeping a lookout, too.
Wow, you are aiming high ! Do you have any comprehension what amount of resources would be required to construct a Dyson sphere ? Such a civilization would have to be
much older and
much more advanced than ourselves. It stands to reason how likely the existence of such a construct actually is.
And even just briefly thinking about this, there would be engineering challenges of almost incomprehensible magnitude involved in actually pulling this off. I think the more logic alternative would be something more along the lines of the ringworld in Halo. Much easier to construct and hold together
