Performance evaluation of hybrid DPSK-MPPM techniques in long-haul optical transmission

In this paper, we evaluate the performance of hybrid differential phase shift keying-multipulse pulse position modulation (DPSK-MPPM) techniques in long-haul nonlinear-dispersive optical fiber transmission. An expression for the nonlinear interference variance is obtained analytically using the Gaussian noise (GN) model. We derive upper-bound expressions that take into account the fiber nonlinearity impact on the DPSK-MPPM system's performance for both bit- and symbol-error rates (BER and SER). The tightness of the BER's upper bound is verified using Monte Carlo simulation. The numerical analysis is carried out based on the proposed setup supplemented by a realistic simulation scenario for the DPSK-MPPM long-haul optical transmission system. Our results reveal that while the hybrid DPSK-MPPM technique outperforms both traditional DPSK and MPPM techniques under amplified spontaneous emission (ASE) noise (linear limit), it is less robust when fiber nonlinearity is considered. However, under the impact of low nonlinearity, the performance of a hybrid technique still surpasses the traditional ones. We also discuss the effect of some wavelength-division multiplexing (WDM) parameters on optimal system performance. The nonlinear interference penalties on the maximum reachable distances by both hybrid and traditional modulation systems are then investigated at a forward-error correction (FEC) requirement (BER=10^-3). In particular, at an average launch power of -8  dBm, the hybrid DQPSK-MPPM system with a total frame length of eight time slots including two signal time slots outreaches a traditional DQPSK system by 950 km.