FTN multicarrier transmission based on tight Gabor frames

Alexandre Marquet,Pierre Siohan,Cyrille Siclet,Damien Roque

doi:10.1186/s13638-017-0878-3

Abstract

A multicarrier signal can be synthesized thanks to a symbol sequence and a Gabor family (i.e., a regularly time–frequency shifted version of a generator pulse). In this article, we consider the case where the signaling density is increased such that inter-pulse interference is unavoidable.Over an additive white Gaussian noise channel, we show that the signal-to-interference-plus-noise ratio is maximized when the transmitter and the receiver use the same tight Gabor frame. What is more, we give practical efficient realization schemes and show how to build tight frames based on usual generators. Theoretical and simulated bit-error probability are given for a non-coded system using quadrature amplitude modulations. Such a characterization is then used 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.

Highlights

In most of current communication systems, information symbols can be transmitted and reconstructed thanks to linear operations
With an increasing need of spectral efficiency driven by overcrowded frequency bands, the main strategy relies on an increase of constellation size while keeping a constant transmission power, bandwidth, and symbol rate
We study a linear multicarrier system operating with overcomplete Gabor frames, as it plays a fundamental role in more complex systems

Summary

Introduction

In most of current communication systems, information symbols can be transmitted and reconstructed thanks to linear operations. FTN transmission techniques can be extended to multicarrier modulations [4] In this case, denoting F0 the inter-carrier spacing and T0 the multicarrier symbol duration, it can be shown that if ρ = 1/(F0T0) > 1, the synthesis and analysis families, respectively used for transmission and reception, can no longer be biorthogonal but can still form overcomplete frames [5,6,7]. This leads to IPI both in time and/or frequency. The 2-inner product and its induced norm is defined in the case of discrete-time signals

System model

Theoretical error probability with a linear M-ary system

Discrete-time implementation of the linear system

Discrete-time equivalent linear system

Simulations

Conclusions