A complete static and low frequency noise characterization of ultra-thin body InAs MOSFETs is presented. Characterization techniques, such as the well-known Y-function method established for Si MOSFETs, are applied in order to extract the electrical parameters and study the behavior of these research grade devices. Additionally, the Lambert-W function parameter extraction methodology valid from weak to strong inversion is also used in order to verify its applicability in these experimental level devices. Moreover, a low-frequency noise characterization of the UTB InAs MOSFETs is presented, revealing carrier trapping/detrapping in slow oxide traps and remote Coulomb scattering as origin of 1/f noise, which allowed for the extraction of the oxide trap areal density. Finally, Lorentzian-like noise is also observed in the sub-micron area devices and attributed to both Random Telegraph Noise from oxide individual traps and g-r noise from the semiconductor interface.