Orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-output (MIMO) are wireless radio technologies adopted by the new Fifth Generation (5G) of mobile communications. A very large number of antennas (massive MIMO) is used to perform the beam-forming of the transmitted signal, either to reduce the multi-user interference (MUI), when spatially multiplexing several users, or to compensate the path-loss when higher frequencies than microwave are used, such as the millimeter-waves (mm-Waves). Usually, a coherent demodulation scheme (CDS) is used in order to exploit MIMO-OFDM, where the channel estimation and the pre/post-equalization processes are complex and time consuming operations, which require a considerable pilot overhead and also increase the latency of the system. As an alternative, non-coherent techniques based on a differential modulation scheme have been proposed for the up-link (UL). However, it is not straightforward to extend these proposals to the down-link (DL) due to the (usually) reduced number of antennas at the receiver side. In this paper we overcome this problem, and assuming that each user equipment (UE) is only equipped with one single antenna, we propose the combination of beam-forming with a differential modulation scheme for the DL, enhanced by the frequency diversity. The new transmission and reception schemes are described, and the signal-to-interference-plus-noise ratio (SINR) and the complexity are analysed. The numerical results verify the accuracy of the analysis and show that our proposal outperforms the existing CDS with a significant lower complexity.