Comparative evaluation of the dual transform domain echo canceller for DMT-based systems

Dual domain echo cancellers for multirate discrete multitone systems

“…It can be easily verified that the polyphase matrices U k l are Toeplitz matrices, therefore, each one can be decomposed as in (2). In this case the decomposition U k l = G H N S k l G N is done at the lower data rate.…”

“…In existing echo cancellers, the dual transformation is partially used in the emulation part but avoided in the weight update part, in order to reduce the computational cost. As shown in [2], the adaptive weight update (5) in the transform domain is equivalent to…”

“…In this section, we present the expansion of the DTDC algorithm in [1], [2] for the multirate DSL systems. Two implementations are presented for the cancellers both at the RT and the CO transceivers: the direct approach and the polyphase decomposition approach.…”

“…This structure also provides a unifying representation of the previous algorithms for the echo cancellation. In [2], we showed that the DTDC algorithm can be implemented with a comparable complexity to the previous methods, while performing an exact adaptive update in the dual domain, which results in a faster convergence without requiring extra excitation on the unused tones.…”

“…For discrete multitone (DMT) modulated systems, the computational complexity of these cancellers can be reduced by using the structure present in the transmitted signal. In [1] and [2], we have proposed a novel dual domain echo canceller for symmetric rate DMT systems. In practical DSL systems, asymmetric bandwidths are used for the upstream and downstream transmissions, therefore, echo cancellers must be designed to work in multirate cases.…”