Linearly Constrained Adaptive Echo Cancellation for Discrete Multitone Systems

Achieving the full duplex transmission in digital subscriber lines (DSL) is possible by using echo cancellation methods. Most of the methods available for echo cancellation, in DSL systems based on the discrete multitone (DMT) modulation, deploy partial echo cancellation in the time and frequency domain. In these systems, the weights of the FIR filter emulating the echo in the time domain are mapped from the frequency-domain adaptive echo weights. This mapping can be regarded as a linear constraint on an extended weight vector containing weights in the time and frequency domain, and echo cancellation can then be regarded as a linearly constrained optimization on this extended linear space. In this paper, linearly constrained adaptive echo cancellation for DMT-based DSL systems is proposed. Two approaches are introduced based on the adaptive algorithms by Frost and by Griffiths. The proposed structure provides a unifying and flexible framework for echo cancellation in different DSL systems. Furthermore, in the proposed method the proper choice of the constraint can address the drifting problem in the presence of the narrow band noise in the DSL systems.