A Study on Sampling Penalties Reduction of Kramers-Kronig Receivers

Kramers-Kronig (KK) relation-based receiver can recover the field using a single-photodiode. However, the KK receiver requires a high carrier-to-signal power ratio (CSPR), and digital signal processing performed a few times faster than the Nyquist sampling rate. We propose a method to relax the requirements for sampling rate and CSPR by using digital upsampling with harmonic filtering. In the proposed method, log calculation of the KK algorithm is preceded by digital upsampling and followed by harmonics elimination and downsampling, respectively. Our results predict that the combination of digital upsampling and harmonic elimination can comply with the requirement of 2
^nd
generation FEC limit in 16-QAM 40-km transmission with the following signal parameters, CSPR 6.7 dB, ADC sampling rate 2.5 sps, digital upsampling 3 sps. We propose performing harmonic elimination in combination with Hilbert transform using a single finite impulse response (FIR) filter to increase computation efficiency. Compared with the frequency-domain implementation, similar performances were observed for FIR filters of length 33 or higher.