Error Probability Performance of Equi-Energy Combined Transmission of Differential Phase, Amplitude, and Polarization

A unified framework was recently developed for optimizing the bit error rate (BER) incurred in the simultaneous differential modulation of the optical resources of polarization, phase, and/or amplitude, extending the conventional Stokes´ parameters of polarization optics to a set of D² generalized Stokes´ parameters (GSPs). Novel optimal receiver structures were identified for multienergy polarization shift keying (POLSK), the optimality of differential phase amplitude shift keying (DPASK) and multichip differential phase shift keying (MC-DPSK) modulation formats was assessed, and optimal receivers for combinations of POLSK and DPSK were formulated. In this paper, the probability of error performance was evaluated for the newly introduced family of advanced modulation formats combining differential phase, polarization, and/or amplitude modulation, generically described as multichip differential state of POLSK. The symbol error rate and the BER for such systems are derived here in terms of the geometry of Stokes´ signal space (the space of GSPs). The resulting formalism is applied to assess the performance of recently introduced MC-DPSK and MUB-coded systems (differential phase constellations based on maximally unbiased bases), as well as DPASK formats, establishing improved tradeoffs between sensitivity and spectral efficiency relative to conventional optical DPSK systems