Aiming to reduce the power/mass requirements in satellite transponders and to reduce mission costs, joint amplification of multiple carriers using a single high-power amplifier (HPA) is being considered. In this scenario, a careful investigation of the resulting power efficiency is essential as amplification is nonlinear, and multicarrier signals exhibit enlarged peak-to-average power ratio. Thus, operating the amplifier close to saturation vastly increases signal distortion resulting in a severe degradation of performance, especially for higher order modulations. This paper proposes a reduced-complexity digital predistortion (DPD) scheme at the transmitter and a corresponding equalizer (EQ) at the receiver to mitigate these nonlinear effects. Scenarios include both the forward as well as the return links. In particular, the paper exploits the MIMO Volterra representation and builds on a basis pursuit approach using a LASSO (least absolute shrinkage and selection operator) algorithm to achieve an efficient basis representation, avoiding large computational complexity, to describe the selection of predistorter/equalizer model. The work further compares and contrasts the two mitigation techniques taking various system aspects into consideration. The gains in performance and amplification efficiency demonstrated by the use of DPD/ EQ motivate their inclusion in next-generation satellite systems.