The present invention relates to design and implementation of low complexity adaptive echo and NEXT cancellers in multi-channel data transmission systems. In this invention, a highly efficient weight update scheme is proposed to reduce the computational cost of the weight update part in adaptive echo and NEXT cancellers. Based on the proposed scheme, the hardware complexity of the weight update part can be further reduced by applying the word-length reduction technique. The proposed scheme is general and suitable for real applications such as design of a low complexity transceiver in 10GBase-T. Different with prior work, this invention considers the complexity reduction in weight update part of the adaptive filters such that the overall complexity of these adaptive cancellers can be significantly reduced.