Because of the small energy available aboard a satellite, the power amplifier must work with a restricted power supply which limits its maximum output power. To ensure a sufficient signal-to-noise power ratio (SNR) at the receiving side, the amplifier must work close to the saturation point. This is power efficient but, unfortunately, adds non-linear distortions in the communication channel. Several algorithms have been proposed to equalize this non-linear channel. The most widely used in the literature is the baseband Volterra filter. Recently, the Echo State Network (ESN), coming from the artificial neural network field, has been shown to perform equally well. To compensate for this channel, both equalizers adapt their coefficients with the help of a training sequence in order to recover the transmitted constellation points. We will show that, the usual detection, based on Euclidean distances, is no longer optimal. The aim of this paper is to first propose a new detection criterion which meets with the Maximum Likelihood (ML) criterion. Secondly, we will propose a modification of the training reference points to improve the performances of these equalizers and make the detection based on Euclidean distances optimal again. This last solution can offer a significant reduction of the Bit Error Rate (BER) without increasing the equalizers complexity. Only the new training reference points must be evaluated.