Signal design for noncoherent PPM modulation with applications to UWB communications

By deriving the probability of error of a binary pulse-position modulated (PPM), ultra wide-band (UWB) impulse-radio system under noncoherent detection, it is shown that the optima! value for time shift parameter δ for PPM is fundamentally different from that for coherent reception. In particular, the optimal choice of δ is one that results in zero correlation between the two waveforms used in PPM modulation. By examining the performance sensitivity around possible optimal δ solutions for a commonly used UWB monopulse, we also show that it is still possible to employ δw, where T_w is the UWB monopulse width, yet achieve optimal and robust performance.