Basic Ultralights are generally only authorized to fly in Class G & E airspace (with a few exceptions mentioned in the previous question). Radios are not required to fly in Class G (uncontrolled airspace) or Class E (controlled airspace). Therefore Basic ultralights almost never require a radio, however having a radio can improve pilot awareness and coordination with other aircraft.

Radios are required to fly in Class A, B, C & D (controlled airspace)
Advanced Ultralights may fly in Class C & D airspace if the aeroplane is equipped in accordance with CARs 605.14 (which includes a radio). Class A airspace starts at an elevation of 18,000ft ASL and VFR flight is not allowed. Class B airspace starts at an elevation of 12,500ft ASL or above. Most Ultralight pilots fly well below Class A & B airspace!