In many quantum gravitational models of the universe, spacetime is quantized. However, to ultimately prove that this is actually the case, we need to observe its consequences experimentally. In this work I present a model of nonperturbatively quantized gravitational waves, i.e., spacetime perturbation, inspired by loop quantum gravity, which is a nonperturbative theory of quantum spacetime. I then show how one can attempt at detecting signatures of discreteness of spacetime through the study of these gravitational waves, particularly their waveform and speed of propagation.