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.