Crossword Genius

Radios lost first sign-off (5)

Ross

I believe the answer is:

adios

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'radios lost first sign-off' is the definition.
I can't tell whether this definition defines the answer.

'radios lost first sign-off' is the wordplay.
'radios' becomes 'adi' (I can't justify this - if you can you should believe this answer much more).
'lost' indicates anagramming the letters.
'first' suggests taking the first letters.
The first letters of 'sign off' is 'so'.
'so' is an anagram of 'os'.
'adi'+'os'='ADIOS'

Can you help me to learn more?

(Other definitions for adios that I've seen before include "See you in Ibiza" , "Spanish farewell" , "Goodbye to Spain" , "Goodbye (Spanish)" , "Adieu, arrivederci" .)

I've seen this clue in The Mirror.
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