What's required for the ADS-B to function? A GPS or Mode S Transponder?
ADS-B, Automatic Dependent Surveillance - Broadcast, is a  broadcast of the aircraft's position and other information. 

The position is determined by a GPS receiver. It is possible to use another qualified position source, but today it is de facto GPS. Other GNSS (Galileo, GLONASS, Bei-Dou) are other likely candidates in the future, but as far as I know, none have been certified for ADS-B yet. 

The broadcast is usually by the Mode S transponder but can also be done by a dedicated transmitter / transceiver in the Mode S format and frequency (1090 MHz).

In the USA below 18 000 ft, in addition to the Mode S based ADS-B, a system based on Universal Access Transceiver  (UAT)  is used. This operates on 978 MHz

A third broadcast system was VDL mode 4, it was never rolled out on large scale.

So ADS-B uses GPS to determine the position and it operates either  on 1090 MHz (a frequency also used by Mode S)  or 978 MHz to broadcast information.