How small can a radio transmitter be?
Smallest transmitter:

(http://www.extremetech.com/extreme/171309-the-worlds-most-smallest-fm-radio-transmitter-made-from-graphene)

I quote "Columbia University have just revealed to us the world’s smallest FM transmitter, which they managed to build around a nanoscale graphene oscillator. Details of their device have just appeared in the current online issue of Nature Nanotechnology."

(also see http://www.nature.com/nnano/journal/v8/n12/full/nnano.2013.232.html)

Smallest receiver.

According to the Guinness World record (http://www.guinnessworldrecords.com/records-10000/smallest-radio/) and I quote "the smallest radio has been built using a single carbon nanotube by scientists at the University of California, Berkeley, USA, the world’s smallest radio receiver measures only 10 micrometres diameter by 100 micrometres long. The carbon tube is electrically charged and can vibrate in harmony with incoming radio waves in the 40 to 400 Megahertz range.

The precise tuning is achieved by changing the voltage applied to the tube to isolate individual radio frequencies. Connecting this receiver to a small loudspeaker, the inventor’s laboratory rang to the sound of Derek and The Dominos' "Layla" when first switched on."