Signal design for non-coherent UWB with PPM modulation in fading channels

We address the problem of signal design for non-coherent, binary pulse-position modulated (PPM) UWB communications in the presence of fading. By deriving the probability of error in closed form, it is shown that the optimal value for the time shift parameter, δ, used in pulse position modulation is fundamentally different from that of coherent reception. In particular, we show that the optimal choice of δ is one that results in zero correlation between the two waveforms used for binary pulse position modulation. By examining the performance sensitivity around several possible optimal δ solutions for a commonly used UWB mono-pulse, we also show that it is still possible to employ δw, where T_w is the UWB mono-pulse width, yet achieve optimal and robust performance with non-coherent reception.