It is well-known that mm-wave (millimeter wave) communications have high potential for future wireless broadband systems. However, there are important challenges that need to be overcome when implementing those systems, both at the hardware level and due to the hostile propagation conditions. This is especially important for spectrally efficient communications based on large constellations, since the power requirements are higher, as well as the amplification difficulties, specially for large, dense constellations.In this paper we propose a multi-antenna transmitter combined with a frequency-domain receiver for broadband mm-wave systems based on large and dense constellations. Our transmitter is compatible with highly-efficient, low-cost, strongly nonlinear amplifiers, while allowing spacial multiplexing gains. 1