Impact of sampling frequency and the number of quantization bit of analog-to-digital conversion (ADC) in a direct detection lightwave system using Kramers-Kronig (KK) relation, which has been attracting attention in recent years, are numerically investigated. We studied the effect of spectral broadening caused by nonlinear operations (logarithm, square root) of the KK algorithm when the frequency gap (shift frequency) between the modulated signal and the optical tone is varied. We found that reception performances depend on both the ADC bandwidth and the relative positions of the optical tone and the spectrum. Spectral broadening caused by the logarithm operation of the KK algorithm is found to be the dominant factor of signal distortion in an ADC bandwidth limited system. We studied the effect of the number of quantization bit on the error vector magnitude (EVM) of KK relation based reception in a carrier-to-signal power ratio (CSPR) adjustable transmission system. We found that performances of KK relation based receiver can be improved by increasing the number of quantization bits. For minimum-phase-condition satisfied KK receiver, the required number of quantization bit was found to be 5 bits or more for detection of QPSK, 16-QAM and 64-QAM-modulated signal after 20-km transmission.

In this paper, N-CSK (N parallel Codes Shift Keying) using modified pseudo orthogonal M-sequence sets (MPOMSs) to realize the parallel combinatory spread spectrum (PC/SS) communication system for the optical communications is proposed. Moreover, the upper bound of data transmission rate and the bit error rate (BER) performance of this N-CSK system using the chip-level detection are evaluated through theoretical analysis by taking into account the scintillation, background-noise, avalanche photo-diode (APD) noise, thermal noise, and signal dependence noise. It is shown that the upper bound of data transmission rate of the proposed system is better than those of OOK/CDM and SIK/CDM. Moreover, the upper bound of data transmission rate of the proposed system can achieve about 1.5 [bit/chip] when the code length of MPOMS is 64 [chip].