Analytical evaluation of bit error rates for hard detection of optical differential phase amplitude shift keying (DPASK)

Recently introduced extensions of differential phase-shift keying (DPSK), referred to here as optical differential phase amplitude shift keying (DPASK), explore an increase in the data throughput for a given bandwidth by effectively multiplexing differential phase encoding and amplitude modulation onto the same fiber link. The DPASK systems proposed and demonstrated so far apply phase and amplitude modulation in tandem, jumping between either two or four equispaced phase values as well as independently selecting between two amplitude levels. In this paper, closed-form expressions for the quantum limits of bit error rate (BER) for such DPASK optical transmission systems are derived for the first time, verifying the analytic expressions by numerical multicanonical Monte Carlo simulations. The resulting quantum-limit sensitivities indicate that the two-level binary phase DPASK incurs a considerable photonic sensitivity penalty in return for its improved spectral efficiency. On the positive side, the more complex quaternary phase DPASK format exceeds the performance of its 8-ary DPSK scheme counterpart.