Extended Study on Equalization-Enhanced Phase Noise for High-Order Modulation Formats

Coherent optical receivers with electronic dispersion compensation (EDC) become ubiquitous for high-capacity and long-distance transmissions. However, their performance can be decimated by equalization-enhanced phase noise (EEPN). The existing reports have shown some unique features that deserve further studies, especially for high-order modulation formats. In this paper, we firstly show that the intra-symbol EEPN is dominated by the phase noise. Therefore, the probability density function (PDF) due to intra-symbol EEPN and inter-symbol EEPN are quite different. We derive the variances of EEPN-induced phase and amplitude noise for QPSK signals, and fully explain the elliptical PDF. Secondly, we show that the intra-symbol EEPN is scaled with the power of the different modulus, but the inter-symbol one, the average power of the constellation. Subsequently, we elucidate that for higher-order constellations with multiple moduli, the total EEPN, the EEPN-induced phase noise and amplitude noise, all distribute differently on the different moduli. Finally, we analyze the EEPN after the practical carrier phase recovery algorithms, also with a closed-form prediction. Our analysis of EEPN is readily extended to arbitrary modulation formats.