According to an article in The Daily Mail, Philadelphia experimenter W W McFarlane invented a mobile telephone in 1920 that required three pieces of stove pipe stuck to a board as an aerial. It reportedly worked over a range of up to 500 yards.
I find it interesting that the person talking on the “telephone” in the above picture was not driving. I wish people today would not drive and talk on the phone simultaneously.
You can read more about the first mobile telephone in The Daily Mail at http://goo.gl/BxIC5J. You can also watch a Pathé video about a similar, although apparently different, invention from 1922 at https://www.youtube.com/watch?v=ILiLaRXHUr0 or in the video player below: