An equalization algorithm for wavelet packet based modulation schemes

A considerable amount of attention has been given in the literature to the use of wavelets for modulation and equalization. In this correspondence, we present an equalization algorithm for a wavelet packet-based modulation scheme. A nonideal channel can be divided into a set of bands, where each band can be approximated as a simple attenuation and delay channel. Wavelet packets, being narrowband and orthonormal, are a natural choice for realizing such bands. Thus, if the data sequence is used to modulate a set of wavelet packets, the equalization problem reduces to that of determining the delay introduced by the channel for each of the wavelet packets (if the wavelet packets do not overlap in the frequency domain) and possibly a change of sign in the decoded symbols. The attenuation affects the SNR at the output of the demodulator, which in turn affects the correct decoding of the transmitted symbols. A minimum square variance algorithm for adaptively choosing the delay has been proposed. The algorithm uses the statistics of the received sequence to pick the appropriate delay. Simulations have been conducted to study the performance of the equalization algorithm and compare it with that of DFT-based DMT scheme.