Embodiments of a system and method for providing fundamental group modulation are generally described herein. In some embodiments, a trajectory mapper is arranged to receive a modulation symbol sequence. A signal trajectory sample memory is arranged to store a representation of signal trajectories for a topological space having a set of predetermined removed regions therein. The trajectory mapper accesses the signal trajectory sample memory to select a signal trajectory relative to the set of predetermined removed regions in the topological space based on the received modulation symbol sequence and produces a sequence of in-phase (I) and quadrature (Q) sample values at a specified sample rate in response to the selected signal trajectory, the I and Q sample values serving as a basis for an amplified radio frequency signal.