Analysis of a Multicarrier Communication System Based on Overcomplete Gabor Frames

A multicarrier signal can be seen as a Gabor family whose coefficients are the symbols to be transmitted and whose generators are the time-frequency shifted pulse shapes to be used. In this article, we consider the case where the signaling density is increased such that inter-pulse interference is unavoidable. Such an interference is minimized when the Gabor family used is a tight frame. We show that, in this case, interference can be approximated as an additive Gaussian noise. This allows us to compute theoretical and simulated bit-error-probability for a non-coded system using a quadrature phase-shift keying constellation. Such a characterization is then used in order to predict the convergence of a coded system using low-density parity check codes. We also study the robustness of such a system to errors on the received bits in an interference cancellation context