Construction of optimal bases for wavelet packet modulation under phase offset errors

Wavelet Packet Modulation (WPM) is a new multi carrier communication technique where orthogonal wavelet packet (WP) bases modulated by information bearing symbols are superimposed and transmitted. The orthogonal WP bases are obtained from fundamental two-channel half-band high and low pass filter pairs. The advantage is that by altering the properties of these filters the transmission characteristics of the WPM system can be customized to a given design specification. In this article we evaluate the impact of phase offset on the WPM system performance analytically and derive WP bases that better tackle phase offset errors. The mathematical expressions for the disturbances in WPM transmission caused by phase errors are derived and the design objective is posed as an optimization problem. Numerical solvers are used to solve the problem and the performances evaluated through simulation studies.