Space missions often carry antenna instruments that are sensitive to dust impacts, however, the understanding of signal generation mechanisms remained incomplete. A signal generation model in an analytical form is presented that provides a good agreement with laboratory measurements. The model is based on the direct and induced charging of the spacecraft from the collected and escaping fraction of free charges from the impact generated plasma cloud. A set of laboratory experiments is performed using a 20:1 scaled down model of the Cassini spacecraft in a dust accelerator facility. The results show that impact plasmas can be modeled as a plume of ions streaming away from the impact location and a cloud of isotropically expanding electrons. The fitting of the model to the collected antenna waveforms provide some of the key parameters of the impact plasma. The model also shows that the amplitudes of the impact signals can be significantly reduced in typical space environments due the discharging effects in the ambient plasma.