Enabling ultra fast systems has been widely investigated during recent decades. Although polarization has been deployed from the beginning in satellite communications, nowadays it is being exploited to increase the throughput of satellite links. More precisely, the application of diversity techniques to the polarization domain may provide reliable, robust, and fast satellite communications. Better and more flexible spectrum use is also possible if transmission and reception can take place simultaneously in close or even overlapping frequency bands. In this paper we investigate novel signal processing techniques to increase the throughput of satellite communications in fixed and mobile scenarios. First, we investigate four-dimensional (4D) constellations for the forward link. Second, we focus on the mobile scenario and introduce an adaptive algorithm which selects the optimal tuple of modulation order, coding rate, and MIMO scheme that maximizes the throughput constraint to a maximum packet error rate. Finally, we describe the operation of radio transceivers which cancel actively the self-interference posed by the transmit signal when operating in full-duplex mode.