An Optimal 2 × 2 Space-Time Code for Time-Hopping Ultra-Wideband Systems with binary Pulse Position Modulation

The golden code (Belfiore, 2005) is a 2 x 2 space-time (ST) code that achieves the best known performance with all constellations carved from Zopf[i]. On the other hand, impulse radio (IR) time-hopping (TH) ultra wideband (UWB) is a carrier-less baseband transmission technique. Therefore, being complex-valued, the golden code can not be associated with IR-UWB systems. In this paper, we propose a new ST code that satisfies all of the construction constraints of the golden code and that has the additional advantage of being totally real making it suitable for low cost carrier-less UWB terminals. Unlike the golden code that can be associated with all constellations carved from Zopf[i], the proposed code is optimal with binary pulse position modulation (PPM) which is a popular modulation scheme for TH-UWB. Moreover, the proposed scheme permits to achieve full transmit diversity with hybrid pulse position and amplitude modulations (PPAM) having two modulation positions.