Abstract
Throughout recent years, the discrete wavelet transform (DWT) was used in communications for wavelet modulation (WM). One of its features is the mother wavelets (MW) used. An important number of MW were already proposed in the literature. We investigate in this paper the selection of the MW for the WM, on the basis of its time-frequency localization. We prove, with the aid of Balian-Low theorem, that wavelets have better time-frequency localization than the elements of the bases which are used for signal decomposition in other orthogonal modulation techniques, as, for example, in orthogonal frequency division multiplexing (OFDM). A procedure for the evaluation of the time-frequency localization of MW belonging to Daubechies family is proposed. This procedure is next compared against the WM transmission on different channel types, which reveal the best MW to be used. This advantage of the WM versus OFDM is highlighted by simulation results in fading channels.
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