In this paper, a simple adaptive notch filter (ANF) scheme for reducing RFI over CAP/QAM-based VDSL systems is proposed. To alleviate the spectral null caused by notch filtering, a null reshaping scheme is introduced between the normal ANF and the decision feedback equalizer (DFE). The proposed filter scheme can control the width and depth of the null. The shallow and narrow null obtained by null reshaping reduces the loss of signal components and consequently improves the mean square error (MSE) at the output of the equalizer. The proposed null reshaping scheme also enables the infinite impulse response (IIR) type constrained ANF to have a smaller pole contraction factor α. This results in a fast convergence property in RFI frequency estimation with a recursive prediction error (RPE) algorithm. The performance variations of the proposed null reshaping are investigated with varying filter parameters. Compared to the conventional ANF, simulation results show that, at the expense of small system complexity, the proposed structure yields a 2-3 dB MSE gain and a fast convergence property for RFI estimation.

Irreducible components of canonical graphs for second order spectral null constraints at a rational submultiple of the symbol frequency fsk/n are studied where fs is the symbol frequency. We show that if n is prime then a canonical graph consists of disjoint irreducible components. We also show that the number of irreducible components of a canonical graphs is finite if n is prime. For the case n = 2 and p O mod n, all aperiodic irreducible components are identified explicitly where p is a parameter of a canonical graph.