This paper provides a high level comparison of several multi-carrier and single-carrier waveforms based on the evaluations performed in mmMAGIC project. The waveforms are assessed for the performance indicators that are relevant to mobile radio communication above 6 GHz, especially the millimeter wave frequencies. The evaluations are performed in mmMAGIC waveform simulators under common assumptions on carrier frequencies, waveform parameters, channel and impairment models. The evaluation results reveal that OFDM is suitable for above 6 GHz communication. For above ?30 GHz communication, OFDM with PAPR reduction and DFTS-OFDM are both promising options. Moreover, some potential enhancements to OFDM (use of window/pulse shape, subband filters, unique word, zero tailing), parametrization of FBMC, and constrained envelop continuous phase modulation for above 6 GHz communication have been discussed. © 2016 IEEE.