We observed the presence of both a symmetric spectral broadening of the pump wave and a noise with frequencies close to the growth rate of a parametric instability in a magnetic mirror trapped plasma heated by microwaves. The microwave frequency agreed on certain surfaces in the trap with the local electron cyclotron resonance (ECR) frequency. Parametric instabilities introduce a system of interacting oscillators, namely plasma waves, providing a mechanism of phase randomization, different from the phase randomization due to single-particle motion considered so far for ECR heating in quasilinear theory. Including the effect of the observed potential noise we obtain a modified model for ECR heating exhibiting a shorter randomization time.