An approach is provided estimating non-linear characteristics of an amplifier (such as a Travelling Wave Tube Amplifier) used to amplify a composite signal in a radio communication system. The composite signal, which includes a plurality of inbound signals overlay on an outbound signal, is sampled. The outbound signal is utilized as a training signal. Coarse estimates of the response of the amplifier is generated based on the samples of the composite signal and the training signal. Further, the interference associated with the inbound signals are removed from the estimation of the response of the amplifier by curve-fitting and estimating interference characteristics of the composite signal. An estimated response of the amplifier is thus output, and can be utilized to provide accurate non-linearity compensation and cancellation.