A General Framework for Mixed-Domain Echo Cancellation in Discrete Multitone Systems

In full-duplex communication systems with discrete multi-tone (DMT) modulation, echo cancellers are employed to cancel echo by means of adaptive filters. Generally, the structure present in the DMT signals is used to decrease the computational complexity of these cancellers by splitting the operations between the time and frequency domains. In this work, we introduce a general framework for designing echo cancellers for such systems in an arbitrary mixed domain. This is achieved by introducing a generic decomposition of the Toeplitz data matrix at the transmitter in terms of arbitrary unitary matrices. Then, based on this decomposition, a new mixed-domain echo cancellation structure is derived, which performs an exact instantaneous gradient-type adaptation. This mixed-domain configuration is also extended for realizing constrained adaptation whereby linear constraints are used to ensure the proper mapping of the weight vectors in different domains. The proposed structures offer a unified framework to study existing cancellers and to design new ones with better performance measures. This framework is employed to propose a new canceller based on discrete trigonometric transformations. The analytical and numerical results presented show that this canceller has a faster convergence rate than the existing ones with similar complexity and is more robust.