In any conditions where DC and RF power are at a prime, such as in satellite systems, transmit amplifiers are operated close to the saturation region to maximize both output power and DC-to-RF efficiency, at the price of introducing non-negligible spectral regrowth and in-band distortion. In order to mitigate these effects, predistortion techniques can be applied at the transmitter; however, mass-produced terminal equipment have operating characteristics that exhibit large dispersion, and for cost reasons calibration procedures are ruled out. Therefore, feedback from the power amplifier output is required to apply predistortion, but the presence of phase noise over the feedback signal impairs the correct recovery of the amplifier phase characteristics, and attention must be focused on amplitude only. This paper proposes two adaptive predistortion schemes which are able to track and compensate the amplitude distortion in the power amplifier, based on neural networks and on look-up-tables, respectively. The two techniques are compared both in terms of performance and complexity, giving insights on the available design trade-offs. Thanks to the reduced spectral regrowth, the techniques are shown to enable the adoption of high order modulations also in those cases where it would have been prevented by out-of-band spectral masks.