are you saying from the moment he goes out he barks until hecomes back in? obviously he isn't barking when you take him to the park or when you are out running together. I have two things I am thinking.
One is that he is barking because he hears something you don't hear. My brothers dog (not a boxer, but a malamute) Will let out unrelenting noise when he is out side. It is either because he sees someone and is "inviting" them over to play, or he hears a train - way, way out in the distance. Golly is he ever annoying.
My other idea is that one day he started barking at soemthing legitimate and one of the neighbors (how close are they?) either yelled at him or squirted him and he is trying to warn you that the bad person still lives there. Or maybe he hears someones TV on and people are arguing on TV.
When my girl is out and she starts barking, I always go see what the matter is. Usually it is a neighbor walking down the street or a utility person, and I will pet her and tell her - okay I see them thanks. But if I go inside and she starts barking at the same thing - then I go out and scold her. I don't want her to bark everytime she sees the neighbor. I can't think of a time that she has barked while she was inside the house though. Guess she figures we have it covered in here, but when she is outside alone, she is in charge of guarding the yard and alerting us to every little thing.
I don't know if that helped or not. hope so