The PDSM pulse for binary 0 can be represented mathematically as
We have chosen VPPM, one of the modulation schemes adopted in IEEE 802.15.7 , as a benchmark for comparison with various features of PDSM. The pulse shapes for VPPM are shown in Fig.
To compare the spectral efficiencies of PDSM and VPPM, the spectra of both pulse types can be represented as Fourier transforms.
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.
A low-pass filter (LPF) is used as a receive filter to suppress noise, and to show the effect of an LPF on a PDSM pulse, the LPF outputs of a pulse with light intensity index [beta] = 0.75, A = 1, and T = 1 ms are drawn in Fig.
In PDSM, the values of v([t.sub.s1]) and v([t.sub.s2]) can be determined from (1) once the light intensity is known.
9 shows graphs of both the simulated and analytical BERs of a PDSM signal with A = 1, T = 1 ms, [p.sub.i] = 0.1, S = 0.1 V, [N.sub.0] = [10.sup.-6] J, and B = 3 x [10.sup.3] Hz.
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, using the correlation detection relation, the BER of the PDSM signal becomes
To determine the BER of a PDSM signal using dual sampling, (12), with [p.sub.i] = 0, is used in conjunction with (13).
Because two given correlator output differences will not be independent when three pulse shapes overlap, it is not easy to formulate the BER mathematically in closed form when [p.sub.i] > 0; therefore, we used a Monte Carlo simulation to determine the BER of correlation detection for PDSM and VPPM signals that include the idle state, and we used (12) to determine the BER of PDSM using dual sampling.