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Comparison between wavelet-based and Fourier-based multicarrier UWB systems

The use of wavelet transform in multicarrier ultra wideband (UWB) systems is analysed and the results are compared with Fourier-based multicarrier UWB systems. It is well known that convolution in time domain is equivalent to multiplication in frequency domain; however, there is no closed-form expression in the literature for convolution's counterpart in the wavelet domain. A formula is derived to represent convolution's counterpart in the wavelet domain. Furthermore, the effects of choice and type of wavelet filters and different decomposition levels are investigated. Finally, a performance comparison of both techniques for IEEE 802.15.3a channel models using IEEE802.15.3a multiband-orthogonal frequency division multiplexing UWB specifications is provided.