Models of the radio channel power delay profile are proposed for low-complexity 60 GHz communications systems that employ beam tracking capability in realistic indoor non-line-of-sight scenarios. A single-carrier transmission system that does not employ equalization, but only uses forward error correction is considered. The channel models were obtained from measurements done in a novel way in a conference room in which non-line-of-sight scenarios are created through a human-sized blocking object, and in which beamforming is applied at the receiver to track and obtain reflected paths. By deploying beamforming antennas and then switching to the best path when the LoS path is cut, it was found through measurements and models that very low delay spreads could be achieved. As a result, not only the new channel models are verified, but the proposed model could replicate the measured channel with narrow antenna beamwidth together with beam tracking and switching. The low delay spread performance could lead to low-power consuming devices and multi-gigabits-per-second transmission by a single carrier with simple FEC.