The results of Monte Carlo simulation of GaAs MOSFETs under impact ionization conditions in the conduction channel are presented. The main attention is paid to the transistor operation at a positive gate bias when the electron concentration in the channel under the gate considerably exceeds the channel doping level. The stationary characteristics including current voltage relation and velocity, energy and field profiles in the channel are calculated. Also, the drain current noise spectra at various drain biases are presented. The Gunn-effect dynamics in excess of electrons in the channel is investigated. The optimization of transistor geometrical, doping, and biasing parameters for high frequency generation is performed. It is shown that GaAs MOSFET can generate at 325 GHz frequency.