Due to the nature of SSB, in order to properly recover the fidelity of the original audio, a pilot carrier was distributed to all locations (from a single very stable frequency source), such that, the phase relationship of the demodulated (product detection) audio to the original modulated audio was maintained. 
 

Also, SSB was used by the U.S. Air force's Strategic Air Command (SAC) to insure reliable communications between their nuclear bombers and NORAD. In fact, before satellite communications SSB was the only reliable form of communications with the bombers. 

The main reason SSB is superior to AM, and most other forms of modulation is due to the following: 

   SSB ver AM
(1) Since the carrier is not transmitted, there is a reduction by 50% 
      of the transmitted power (-3dBm). 
(2) Because only one sideband is transmitted, there is a further reduction 
      by 50% in transmitted power (-6dBm). 
(3) Finally, because only one sideband is received, the receiver's needed 
      bandwidth is reduced by one half--thus effectively reducing the 
      required power by the transmitter another 50% (-9dBm). 

Example: A HAM running 2000 Watts AM, would sound no better than another 
                 HAM running 250 Watts PEP (Peak Envelop Power) on SSB.