In a system, known digital representations are generated, and test analog signals are generated using the known digital representations. The test analog signals are transmitted using a transmitter of a transmission system. The test analog signals are received using a receiver of the transmission system and used to generate test received digital representations. The test received digital representations are cross-correlated with the known digital representations to generate a mixing matrix. The mixing matrix is inverted to generate a de-mixing matrix, which is applied to subsequent digital data to be encoded onto a signal and transmitted by the transmitter to generate pre-compensated digital data.