A ground station system for use with a satellite communication system, wherein the ground station system is in a footprint of a satellite transponder having a satellite transponder power amplifier, the ground station system comprising: a transmitter receiving an input hub signal, said transmitter having a pre-distorter that pre-distorts the input hub signal to provide a pre-distorted hub signal, and a filter that receives the pre-distorted hub signal and limits spectral regrowth of the pre-distorted hub signal to provide a filtered pre-distorted hub signal, wherein the filtered pre-distorted hub signal is to be transmitted by the transmitter to the satellite transponder; a receiver configured to receive a downlink signal transmitted by the satellite transponder, wherein the downlink signal includes a distorted hub signal that is an amplification and distortion of the filtered pre-distorted hub signal by the satellite transponder PA; and a self-interference canceller with distortion estimator (SICDE) configured to estimate a nonlinear characteristic of the satellite transponder PA based on the filtered pre-distorted hub signal and the downlink signal, characterized in that said pre-distorter receives the estimated nonlinear characteristic and pre-distorts the input hub signal by: mapping an average value of a symbol constellation comprising a plurality of symbols to a 0dB back-off point of the estimated nonlinear characteristic, using a relative power level of each symbol to lookup the estimated nonlinear characteristic, and modify each symbol by an inverse, in amplitude, and negative, in phase, of the respective value of the estimated nonlinear characteristic to generate a pre-distorted symbol constellation. a transmitter receiving an input hub signal, said transmitter having a pre-distorter that pre-distorts the input hub signal to provide a pre-distorted hub signal, and a filter that receives the pre-distorted hub signal and limits spectral regrowth of the pre-distorted hub signal to provide a filtered pre-distorted hub signal, wherein the filtered pre-distorted hub signal is to be transmitted by the transmitter to the satellite transponder; a receiver configured to receive a downlink signal transmitted by the satellite transponder, wherein the downlink signal includes a distorted hub signal that is an amplification and distortion of the filtered pre-distorted hub signal by the satellite transponder PA; and a self-interference canceller with distortion estimator (SICDE) configured to estimate a nonlinear characteristic of the satellite transponder PA based on the filtered pre-distorted hub signal and the downlink signal, characterized in that said pre-distorter receives the estimated nonlinear characteristic and pre-distorts the input hub signal by: mapping an average value of a symbol constellation comprising a plurality of symbols to a 0dB back-off point of the estimated nonlinear characteristic, using a relative power level of each symbol to lookup the estimated nonlinear characteristic, and modify each symbol by an inverse, in amplitude, and negative, in phase, of the respective value of the estimated nonlinear characteristic to generate a pre-distorted symbol constellation. mapping an average value of a symbol constellation comprising a plurality of symbols to a 0dB back-off point of the estimated nonlinear characteristic, using a relative power level of each symbol to lookup the estimated nonlinear characteristic, and modify each symbol by an inverse, in amplitude, and negative, in phase, of the respective value of the estimated nonlinear characteristic to generate a pre-distorted symbol constellation.