Resource allocation in DMT transmitters with per-tone pulse shaping

Per-tone pulse shaping has been proposed as an alternative to time domain spectral shaping for DMT transmitters, e.g. VDSL modems. It shapes the spectrum of individual tones such that the stop band energy of each tone can be minimized. This in particular enables transmitter to use more tones without violating the PSD mask constraint for data transmission. In per-tone pulse shaping based DMT transmitters a fixed length pulse shaping filter is typically used for every tone. The tones in the middle of the pass band however, contribute less to the overall stop band energy, so that using a high order pulse shaping filter for these tones does not result in a significant reduction of the stop band energy. As a result a significant number of pulse shaping filter taps are wasted on the tones in the middle of the pass band and do not bring any performance gain. Using a variable length pulse shaping filter which is designed such that the PSD mask constraint is not violated can then significantly reduce the total number of pulse shaping filter taps without compromising performance. In this paper, a resource allocation technique is presented for variable length pulse shaping filter design using a dual problem formulation. This optimally solves the problem of pulse shaping filter tap distribution over tones for given PSD mask constraints, with a relatively low complexity.