Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for applying non-linearity to digital subcarriers. A receiver includes a detector circuit operable to receive a first optical signal over an optical link, the first optical signal carrying first data. The receiver includes a carrier recovery estimation circuit operable to generate compensated data by correcting errors in the first data. The receiver includes a non-linear coefficient estimation circuit operable to (i) receive the compensated data, and (ii) estimate one or more non-linear coefficients, wherein information indicative of the estimated non-linear coefficients is transmitted over an optical network, such that a second optical signal is transmitted based, at least in part, on the estimated non-linear coefficients, the second optical signal being received by the receiver.