Avalanche photodiodes (APDs) are essential components in quantum key distribution systems and active imaging systems requiring both ultrafast response time to measure photon time of flight and high gain to detect low photon flux. The internal gain of an APD can improve system signal-to-noise ratio (SNR). Excess noise is typically kept low through the selection of material with intrinsically low excess noise, using separate-absorption-multiplication (SAM) heterostructures, or taking advantage of the dead-space effect using thin multiplication regions. In this work we demonstrate the first measurement of excess noise and gain-bandwidth product in III-V nanopillars exhibiting substantially lower excess noise factors compared to bulk and gain-bandwidth products greater than 200 GHz. The nanopillar optical antenna avalanche detector (NOAAD) architecture is utilized for spatially separating the absorption region from the avalanche region via the NOA resulting in single carrier injection without the use of a traditional SAM heterostructure.