On the power spectral density of time-hopping impulse radio

The power spectral density (PSD) of time-hopping (TH) ultra wide band (UWB) signals plays a major role in key aspects like coexistence with conventional radio systems. In the past, several papers have been published, presenting on the one hand the effects of modulation and timing jitter on the PSD assuming random TH codes. On the other hand, papers have been presented dealing with the PSD of specific TH codes without modulation. This paper presents a mathematical framework that enables the evaluation of the PSD of a modulated impulse radio signal using a deterministic TH code. Besides being of theoretical interest, our results can be the starting point for the development of TH code design criteria aimed at the spectral shaping of the UWB signal.