On Space–Time Coding With Pulse Position and Amplitude Modulations for Time-Hopping Ultra-Wideband Systems

In this work, we propose novel families of space-time (ST) block codes that can be associated with impulse radio ultra-wideband (IR-UWB) communication systems. The carrier-less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes. In fact, the last generation of complex-valued ST codes (namely, the perfect codes) cannot be associated with IR-UWB systems where the phase reconstitution at the receiver side is practically infeasible. On the other hand, while the perfect codes were considered mainly with quadrature amplitude modulation (QAM) and hexagonal (HEX) constellations, IR-UWB systems are often associated with pulse-position modulation (PPM) and hybrid PPM-PAM (pulse-amplitude modulation) constellations. In this paper, instead of adopting the classical approach of constructing ST codes over infinite fields or for the perfect codes), we study the possibility of constructing modulation-specific codes that are exclusive to PPM and PPM-PAM. The proposed full-rate codes are totally real, information lossless, and have a uniform average energy per transmit antenna. They permit to achieve a full diversity order with any number of transmit antennas. In some situations, the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real. Simulations performed over realistic indoor UWB channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras.