To compare the spectral efficiencies of PDSM and VPPM, the spectra of both pulse types can be represented as Fourier transforms.
The Fourier transform of the VPPM pulse waveform for binary 1 shown in Fig.
4 compares the spectra of PDSM and VPPM pulse waveforms at light intensity indices of 0.25 and 0.75.
For example, when the light intensity index is 0.25, the PDSM pulse covers 90% of the pulse energy below 1334 Hz, whereas the VPPM pulse covers 90% of the pulse energy below 2619 Hz, which means that PDSM uses approximately one half of the required frequency bandwidth required to deliver the VPPM pulse at the same light intensity.
To develop a correlation detector for PDSM and VPPM, we start with a case in which there is no idle pulse, i.e., the source sends only binary 0 or 1, before expanding this analysis to investigate a case including binary 0, 1, and idle.
and the BER of the VPPM signal can be calculated using the correlation detection relation above as
Three BER graphs of PDSM and VPPM at various values of are shown in Fig.
To model a VPPM signal with idle pulses, we create an idle pulse located in the center of a pulse with a duration corresponding to a constant area for binary 0 or 1, as shown in Fig.