Broadcast on air, with the somewhat dodgy character? (8)

I believe the answer is:
antihero
'somewhat dodgy character?' is the definition.
'antihero' can be an answer for 'character?' (antihero is a kind of character). I'm not sure about the 'somewhat dodgy' bit.
'broadcast on air with the' is the wordplay.
'broadcast' is an anagram indicator (letters scattered or cast around).
'with' is a charade indicator (letters next to each other).
'on'+'air'='onair'
'onair' put after 'the' is 'theonair'.
'theonair' with letters rearranged gives 'ANTIHERO'.
Can you help me to learn more?
(Other definitions for antihero that I've seen before include "baddie" , "ignoble character" , "Principal character without virtue" , "Winston Smith in Orwell's 1984, for example" , "Less than admirable character" .)
