Carrier phase estimation in dispersion-unmanaged optical transmission systems

Abstract

Abstract-The study on carrier phase estimation (CPE) approaches, involving a one-tap normalized least-mean-square (NLMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm has been carried out in the long-haul high-capacity dispersion-unmanaged coherent optical systems. The close-form expressions and analytical predictions for biterror-rate behaviors in these CPE methods have been analyzed by considering both the laser phase noise and the equalization enhanced phase noise. It is found that the Viterbi-Viterbi algorithm outperforms the one-tap NLMS and the block-wise average algorithms for a small phase noise variance (or effective phase noise variance), while the three CPE methods converge to a similar performance for a large phase noise variance (or effective phase noise variance). In addition, the differences between the three CPE approaches become smaller for higher-level modulation formats.

Digital Signal Processing for Optical Communications and Networks

“…It has been demonstrated that the one-tap normalized LMS carrier phase estimation behaves similar to the differential phase estimation [28,53,55,76], of which the BER floor in the m-PSK coherent optical transmission systems can be approximately described by the following analytical expression, (15) where σ is the square root of the phase noise variance. The schematic of the onetap normalized LMS carrier phase estimation is illustrated in Figure 6.…”

“…The performance of the block-wise average carrier phase estimation method in the m-PSK coherent optical communication system can be derived based on the Taylor expansion of the estimated carrier phase error, and the BER floor in the block-wise average carrier phase estimation can be described using the following expression [52,53,55,79]:…”

“…It has been demonstrated that the one-tap normalized LMS carrier phase estimation behaves similar to the differential phase estimation [28,53,55,76], of which the BER floor in the m-PSK coherent optical transmission systems can be approximately described by the following analytical expression,…”

“…In the digital coherent transmission systems, the electrical signals output from the photodiodes are sampled and transformed into the discrete signals using highspeed analogue-to-digital convertors (ADCs), which can be further processed by the DSP algorithms. The phase locking and the polarization adjustment were the main obstacles in the traditional coherent lightwave systems, while they can be solved by the carrier phase estimation and the polarization equalization respectively in the digital coherent optical transmission systems [47][48][49][50][51][52][53][54][55]. Besides, the chromatic dispersion and the nonlinear effects can also be mitigated by using the digital signal processing techniques [56][57][58][59][60][61][62].…”

“…Schematic of Viterbi-Viterbi carrier phase estimation.The performance of the Viterbi-Viterbi carrier phase estimation in the m-PSK coherent optical communication system can also be derived employing the Taylor expansion of the estimated carrier phase. The BER floor in the Viterbi-Viterbi carrier phase estimation for the m-PSK transmission system can be expressed as follows[52,53,55]:…”