1. Introduction
The phase-diversity homodyne receiver can restore the in-phase and quadrature components of the complex amplitude of the optical electric field. However, the complex amplitude thus obtained includes the phase noise, which stems from semiconductor lasers used for the transmitter and the local oscillator. Therefore, the phase reference needs to be extracted for symbol decision. The M-ary PSK format usually employs feed-forward carrier-phase estimation [1], which takes the M-th power of the complex amplitude with digital signal processing (DSP). Although such a feed-forward scheme is also applicable to the 16-QAM format, rather complicated amplitude discrimination must be introduced before carrier-phase estimation [2] [3]. On the other hand, we have proposed the much simpler decision-directed phase-locked loop (PLL) for carrier-phase estimation, which is based on the least-mean square (LMS) algorithm. Transmission of 10-Gsymbol/s 16-QAM signals has been demonstrated by using this method [4].