Performance of linear minimum-output energy receiver for self and alien crosstalk mitigation in upstream vectored very high-speed digital subscriber line

Linear zero-forcing (ZF) canceller does not perform well in the presence of alien crosstalk (AXT) while the receivers based on minimum-mean-square-error (MMSE) criterion require perfect knowledge of the noise covariance matrices. In this study, the authors consider the use of a constrained linear minimum-output energy (MOE) receiver in the presence of self-crosstalk and AXT in upstream vectored very high-speed digital subscriber line systems, that does not require knowledge of the noise correlation matrices and can be trained using the received signals without the use of training sequences. They derive bounds on the performance of the MOE receiver in the digital subscriber line environment and show that it reaches the MMSE performance for self-crosstalk cancellation. They also show that the performance of the proposed receiver lies in between that of the ZF receiver and the non-linear ZF generalised decision feedback equaliser receiver. An adaptation of the canceller coefficients using MOE algorithm shows comparable performance to that of the least mean squares algorithm. The effect of noise correlation on the capacity has also been highlighted via the Cramer-Rao lower bound. Computer simulations are presented to verify the analytical results and demonstrate the performance of the proposed receiver.