On the estimation of improper noise in multicarrier DSL systems

In this paper we consider the estimation of improper noise in multicarrier DSL systems. We show that the improperness of baseband noise relates to the mirrored frequency components in the positive and negative frequency halves. Spectral leakage in the receiver requires in general widely linear estimation (WLE) techniques of the noise instead of less complex linear estimation (LE) techniques. We describe how to take into account for the improperness in the estimation and how it is possible to neglect it by using smooth receiver windowing. This is demonstrated by using two similar but conceptually different noise estimators, which are based on deterministic and stochastic noise models, combined with LE or WLE. We also describe some practical properties of improper noise estimation in multicarrier DSL systems by showing intuition pleasing connections to spectral leakage, receiver windowing, dimensionality and model parameters, residual noise interference, and complexity.