An approach is provided for compensating for non-linearity in an overlaid radio communication system, such as a satellite network, wherein a terminal and a hub station communicates bi-directionally using a composite signal that is transmitted from a relay station and includes an inbound signal overlaid with an outbound signal. A look-up table stores information used to determine an inverse of a function associated with a non-linear effect of a received composite signal. The inbound signal has a predetermined spectral configuration. The device also includes a multiplier configured to generate a product of the look-up table and the received composite signal. Also, the device includes an estimation module configured to output an estimate of the inbound signal based upon the product. Further, the device includes a filter configured to filter the estimate of the inbound signal according to the predetermined spectral configuration, wherein the filtered estimate is utilized to refine an estimate of the instantaneous operating point of an amplifier associated with the non-linearity (e.g., satellite transponder), wherein an output signal representing the inbound signal is generated based upon the refined estimate.