Ten lectures on wavelets
Essential wavelets for statistical applications and data analysis
Essential wavelets for statistical applications and data analysis
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
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In this paper we develop deterministic expressions for the channel path amplitudes and path phases using the wavelet transform of the received signal. We treat two cases. One case applies to pilot tone signaling and the other one is concerned with the detection of a sequence of symbols over the multipath channel. In the first case, intersymbol interference (ISI) is not a factor, while in the second, due to time dispersion of the transmitted symbols within the channel, ISI becomes a major contributor to the distortion to which the transmitted signal is subjected. We use a wideband model of the multipath channel based on which we derive a discrete representation of the received signal. The discrete samples are then used to compute the highest level wavelet coefficients, through convolution with the coefficients of the Haar wavelet. Using the computed wavelet coefficients, we apply simple algebra to resolve the individual path amplitudes and path phases.