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*  # Introduction In order to meet the blooming demand for the transmission capacity of the modern optical communication systems, complex modulation format comprising high order phase and amplitude modulations, such as binary and quadrature phase-shift keying (BPSK and QPSK), quadrature amplitude modulation (QAM), have become drastically interesting and been widely deployed in recent optical communication systems. As a consequence, apart from the conventional/life-long requirement of the low noise optical amplifiers for optical transmission links for optical communication and microwave photonics links, phase noise mitigation and quadrature decomposition are extensively desired.   To meet the ever-growing traffic requirement driven by the explosive emergence of various Internet based applications, advanced complex high-order modulation formats, exploiting both phase quadratures and amplitude of optical signals, significantly benefit from their high spectrally efficient, thus have been extensively employed for the sake of scaling up the transmission capacity of the modern optical communication system and networks.