Signal design for non-coherent 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 non-coherent detection, it is shown that the optimal value for time shift parameter delta for PPM is fundamentally different from that for coherent reception. In particular, the optimal choice of delta is one that results in zero correlation between the two waveforms used in PPM modulation. By examining the performance sensitivity around possible optimal delta solutions for a commonly used UWB monopulse, we also show that it is still possible to employ delta < T-w, where T-w is the UWB mono-pulse width, yet achieve optimal and robust performance.