Performance analysis of multi-pulse PPM with imperfect slot synchronization in optical direct-detection channel

The performance of multi-pulse pulse position modulation (MPPM) consisting of m slots and 2 pulses, denoted as (m, 2) MPPM, with imperfect slot synchronization is analyzed. The word error probability of (m, 2) MPPM in the presence of timing offset is analyzed, and the optimum symbol sets of (m, 2) MPPM minimizing the symbol error probability are assigned. When an unassigned symbol is detected, the receiver decodes the unassigned symbol as one of the assigned symbols having the highest probability of transition from the assigned symbol to the unassigned symbol. The bit error probability of (m, 2) MPPM in the presence of the timing offset is analyzed, and the bit error probability of (m, 2) MPPM is compared with that of PPM for the same transmission bandwidth and the same transmission rate. Moreover, the bit error probability of (m, 2) MPPM synchronized by a phase-locked loop (PLL) is also analyzed. It is shown that a word with two continuous pulses has better performance than a word with two separate pulses. It is also shown that when the timing offset occurs, and when the slot clock is synchronized by a PLL, (m, 2) MPPM performs better than PPM because (m, 2) MPPM has the optimum assigned symbols, and can decode detected words more correctly than PPM.