Accurate BER evaluation for lumped DPSK and OOK systems with PMD and PDL

New forms using Dirac bra-ket notations and their transformations to express electrically filtered currents are presented for optical systems using either binary differential phase-shift keying (2-DPSK) or ON-OFF keying (OOK) with lumped first-order PMD and PDL, arbitrary optical and electrical filtering and pulse shaping. Based on these forms, the moment generating functions (MGFs) and bit-error-ratios (BERs) for different systems are obtained. Our results show that, for a given BER, 2-DPSK requires ~ 5dB lower input signal-to-noise ratio than OOK. By comparing BERs for different polarization systems, we also show that the PDL-induced partially polarized noise can significantly improve system performance and reduce BER variation caused by the random couplings between signal polarization, PDL and PMD vectors.