Inspired by this answer, and to avoid lengthy back and forth comments, I decided to make this a question in itself.
You can put on your helmet for +1 AC and disadvantage on Perception checks. In combat, this'll likely mean -5 to your passive Perception.
I believe that this is a pretty amazing trade. You are becoming a lot more difficult to hit because of bounded accuracy, and trading this for a minuscule chance that some enemy will be able to hide better from you to gain advantage.
Note that this is not, mathematically, the same as trading +1 AC for giving enemies advantage. As they will have to first take the Hide action to even be hidden to get that advantage, they're essentially sacrificing attacking twice to gain advantage (unless they're a rogue of sorts).
Is gaining +1 AC in combat by gaining disadvantage on Perception checks a balanced trade?
Note: I am working under the assumption that you will simply take your helmet off again after the fight, so you are not walking into traps or ambushes with disadvantage. You are putting on your helmet as your free object interaction in the first turn. The penalty only comes into effect during combat, as does the +1 AC.