Signal shapes for multi-carrier communication systems

Abstract

Signals transmitted over the wireless channels are affected by dispersion. In order to combat the dispersion, the signal shapes employed must decay very rapidly both in time and frequency. In this work, we introduce a novel method for orthonormalizing any given function by employing a two dimensional Fourier transform for any given integer lattice density. Then, by using this method, we propose pulse shapes that increase the capacity of multi-carrier pulse shapes significantly. In the literature, it is assumed that the best localized orthogonal signal, isotropic orthogonal transfer algorithm (IOTA) can be achieved by orthogonalizing the best localized nonorthogonal signal, namely the Gaussian signal. We show that by combining Hermite functions and orthogonalizing them, an orthogonal signal with better localization than the IOTA signal can be achieved. Multi-carrier schemes employing offset-quadrature-amplitude modulation employ lattice densities of 0.5 due to the Wilson expansions that are employed. In this dissertation, we extend the analysis to other density levels providing a trade-off between localization and capacity. We also provide a localized pulse shape for unit density lattices. By employing more than one Weyl-Heisenberg frames that are orthonormal both within the frame and in between the frames, the capacity of multi-carrier systems are increased. Different lattice diversity scenarios are investigated for capacity enhancement. It is shown that by employing this methodology, the capacity of a multi-carrier system can be doubled. Additionally, a system level comparison as well as the inter-operability of the novel pulse shapes are presented.