A new approach for designing orthogonal wavelets for multicarrier applications

The Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER, behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced. The Cramer–Rao lower bound is applied to access the BER performance of the proposed wavelet.