Sparse approximation based 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. It shapes the spectrum of individual tones such that their stop band energy contribution can be minimized. In per-tone pulse shaping based DMT transmitters a fixed order non-sparse pulse shaping filter is typically used for every tone. Furthermore, no specific power loading scheme is used. However, the contribution of a particular tone to the stop band energy depends on the amount of power transmitted on the tone and the distance of the tone from the band edges. Tones with sufficiently low power as well as tones sufficiently away from the band edges could be assigned a sparse pulse shaping filter, which could then help to reduce the overall number of filter taps. In general the combination of power loading and sparse pulse shaping filters can be used to achieve a high data rate under given resource constraints. In this paper we present an algorithm to optimally allocate the available resources, i.e., power and filter taps, under PSD mask constraints, which is based on a dual problem formulation. This algorithm achieves a high performance with relatively low complexity, which is also demonstrated by simulations.

► The use of fixed order non-sparse PTPS filter wastes computational resources.
► Sparse approximation techniques can be used to obtain sparse PTPS filters.
► The performance is not degraded using variably sparse PTPS filters.
► Power loading alongside the sparse filter computation improves performance.
► The number of non-zero filter taps can be significantly reduced by using this method.