Optimal Wavelet Design for Multicarrier Modulation with Time Synchronization Error

Wavelet packet based multi-carrier modulation (WPMCM) is an efficient transmission technique which has the advantage of being a generic scheme whose characteristics can be customized to fulfill a design specification. However, WPMCM is sensitive and vulnerable to time synchronization errors because its symbols overlap. In this paper, we design new wavelets to alleviate WPMCM´s vulnerability to timing errors. First, a filter design framework that facilitates the development of new wavelet bases is built. Then the expressions for errors due to time offset in WPMCM transmission are derived and stated as a convex optimization problem. Finally, an optimal filter that best handles these deleterious effects is designed by means of semi definite programming (SDP). Through computer simulations the performance advantages of the newly designed filter over standard wavelet filters are proven.