Étude et génération de formes d'ondes ad hoc pour les communications. Une approche algébrique pour l'étude de l'efficacité spectrale et la réduction du PAPR dans TDCS

For about ten years, spectrum scarcity and the growing need of bandwidth have pushed the studies on cognitive-radio technologies to counter this waste. Among them: the Transform Domain Communication System (TDCS), on which this thesis focuses. Until now, TDCS' performance in terms of spectral and power efficiency was largely unknown. After introducing the thesis' industrial and scientific context, the TDCS is introduced and compared with popular technologies such as OFDM and MC-CDMA. The system is then studied by means of the linear modulations' algebraic framework. This has led to the TDCS' spectral efficiency determination and to new design rules to jointly achieve a better spectral efficiency and a lower BER. Several methods are then proposed to further increase the spectral efficiency by means of a dense multidimensional modulation. Since a TDCS signal is made of several sines, it suffers from a strong Peak-to-Average Power Ratio (PAPR). Set theoretic estimation is then introduced in a third part and new PAPR-reduction algorithms such as Douglas-Rachford and Reflection Onto Convex Sets are brought to light and achieve better performance than the usual POCS algorithm regarding to the convergence rate, as well as the achieved PAPR.