Theoretical sensitivity of direct-detection multilevel modulation formats for high spectral efficiency optical communications

Sensitivities of several direct-detection multilevel modulation formats, including M-ary differential phase-shift keying (M-DPSK), M-ary differential amplitude-phase-shift keying (M-DAPSK), and M-ary differential polarization-phase-shift keying (M-DPoIPSK) are systematically calculated. The theory is based on a unified mathematical framework for direct-detection receivers using optical delay interferometers and balanced detectors. Results quantitatively elucidate the tradeoffs between these direct-detection multilevel modulation formats as well as the classic multilevel modulation format, M-ary amplitude-shift keying (MASK). Although the conventional bit error rate estimation method based on the eye Q-factor with Gaussian approximation is not accurate enough for DPSK and DQPSK, it is found to be reasonably accurate for M-DPSK with M \u3e 8 and in M-DPoIPSK