Minimum-bandwidth optical intensity Nyquist pulses

The indoor diffuse wireless optical intensity channel is bandwidth-limited due to multipath distortion, and all transmitted signal amplitudes are constrained to be nonnegative. In order to control the impact of intersymbol interference (ISI) on this channel, pulse shaping is required. This paper derives the minimum bandwidth, ISI-free Nyquist pulse which satisfies the amplitude nonnegativity constraint. The minimum bandwidth required is twice that of conventional electrical channels. With the addition of excess bandwidth, the optimal bandlimited optical intensity pulse, in the sense of minimizing average optical power, is shown to be a squared double-jump pulse. Thus, a bandwidth versus optical power efficiency tradeoff in pulse design is quantified. The impact of timing jitter on the probability of symbol error for various excess bandwidths is quantified via simulation. Further, it is shown that there are no bandlimited root-Nyquist pulses satisfying the amplitude nonnegativity constraint. In fact, all practical optical intensity root-Nyquist pulses are shown to be necessarily time-limited to a single symbol interval.