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In order to achieve higher data throughput on fixed-bandwidth satellite non-linear channels, using higher-order modulations, we propose the use of a Volterra-model based nonlinear channel equalizer. Typically, a travelling wave tube (TWT) amplifier or a solid-state power amplifier (SSPA) is used in the satellite nonlinear channels. For higher than 4-QAM schemes, the nonlinear characteristics of the power amplifier stage in the transmitter typically introduce significant amplitude and phase distortions to the transmitted signal. We also propose the use of lower-order Volterra-series based adaptive filters for this application especially if rectangular-pulse shaping is used. This enables us to speed up the convergence time of the algorithm. Simulations results using 16-QAM and 32-QAM are presented to support the claims.