Pulse shaping for linear time varying channels

Abstract

Pulse shaping is the one of the important an critical area for wireless communication. In this article we show the relation between pulse shaping for wide sense stationary uncorrelated scattering (WSSUS) channels and the notion of approximate eigenstructure for time-varying channels. Optimal link adaption to the scattering function of WSSUS channel is still an unsolved problem. In ulticarrier transmission such link adaption is performed by pulse shaping by properly adjusting transmitter and receiver filters. We consider pulse shaping for general signaling scheme called Weyl-Heisenberg signaling which includes Orthogonal Frequency Division Multiplexing (OFDM) and Offset Quadrature amplitude modulation (OQAM). We establish a general mathematical framework for joint transmitter and receiver pulse shape. Pulse design problem in the view of optimal averaged SINR is an interplay between localization and optimization strategies. The Localization problem can be expressed in terms of eigenvalues of approximate eigenstructure of Linear Time Varying (LTV) channel operators. In this thesis, we will show approximate eigenstructure and its relation with pulse design and several iterative algorithms for optimization.