Your only chance will be to perform an investigation and get information about your ancestor's origin from Spain (if they were from there!), after that you might be able to find military records from Spain to see if any of those ancestors were part of the army (if registers exist). Actually being a 16th to 18th generations, you might be talking about XV century kind of far from Armada.
I would say that the best chance is that your spanish ancestors were descendant from lower nobility that might as well descend from nobility which married with spanish nobility. That might be easy to evidence based on baptism records and nobility information. That's more likely than invaders getting married in the failled invasion.