Measurements of 60GHz proximity channels are performed in desktop environments with a digital camera, a laptop PC, a tablet, a smartphone, and a DVD player. The results are characterized by a statistical channel model. All measured channels are found to be similar to conventional exponential decay profiles that have a relatively large first path due to line-of-sight components. We also show that the power difference between the first path and the delay paths is related to randomization of radio wave polarization by internal reflections in the devices, whereas this is conventionally dependent on only a Rice factor. To express this effect, the conventional model is modified by adding one parameter. Computer simulations confirm that RMS delay spreads of the modeled channels are a good fit to measured channels under most conditions.