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In the EHF (extremely high frequency) domain, W-band (75-110 GHz) offers promising perspectives for future satellite communications, mainly in terms of large bandwidth availability for high-bit-rate transmission. In this work an innovative physical (PHY) layer design for broadband satellite connections operating in W-band is proposed, which is based on the prolate spheroidal wave functions (PSWFs). PSWF waveforms (originally proposed in short-range indoor ultra-wideband communications) are aimed at optimizing the tradeoff between the concentration of pulse energy in a finite time interval and in a limited bandwidth. In our paper, PSWF-based 4-ary pulse shape modulation (PSM), characterized by a nearly optimal compromise between spectral and envelope compactness, has been tested for the radio interface of a W-band geostationary (GEO) downlink connection. The effect of nonlinear distortions, introduced by power-efficient saturating amplifiers, can be drastically reduced without any power back-off and will maintain a very good spectral efficiency. Experimental results obtained by means of realistic simulations fully demonstrate the potential advantages taken by PSWF in terms of increased spectral efficiency, link availability, and net payload rate with respect to state-of-the-art pulse-shaped modulations, raised-cosine filtered quadrature amplitude modulation (QAM), and Gaussian minimum shift keying (GMSK) commonly employed in satellite communications.