Wavelet packet based multicarrier modulation

A recent but already popular technique for broadband communications is multicarrier modulation, which divides the channel into several orthogonal, overlapping subchannels. Multicarrier modulation is normally implemented using a Fourier transform to create and detect the different subcarriers. This can be efficiently implemented using an (I)FFT. This transform however has the drawback that it uses a rectangular window, which creates rather high sidelobes. This leads to rather high interference when the channel impairments cannot be fully compensated. Looking at other transforms leads us to the wavelet transform, and more specifically the wavelet packet transform, which has more flexibility and due to the time-overlap can have much lower sidelobes. This article studies the implementation of these wavelet packets, and the effects this implementation has on the requirements imposed in the design of usable wavelets. It is shown that the restrictions imposed by the perfect reconstruction requirement necessitate the use of biorthogonal wavelets. This however influences the performance. Moreover, the frequency behaviour of the wavelet packet transform is not straightforward which limits the practical use of this transform in a multicarrier system.