Preprint Article Version 1 This version is not peer-reviewed

# Analytical Investigations on Carrier Phase Recovery in Dispersion-Unmanaged n-PSK Coherent Optical Communication Systems

Version 1 : Received: 22 August 2016 / Approved: 23 August 2016 / Online: 23 August 2016 (10:40:19 CEST)

How to cite: Xu, T.; Jacobsen, G.; Popov, S.; Li, J.; Liu, T.; Zhang, Y.; Bayvel, P. Analytical Investigations on Carrier Phase Recovery in Dispersion-Unmanaged n-PSK Coherent Optical Communication Systems. Preprints 2016, 2016080194 (doi: 10.20944/preprints201608.0194.v1). Xu, T.; Jacobsen, G.; Popov, S.; Li, J.; Liu, T.; Zhang, Y.; Bayvel, P. Analytical Investigations on Carrier Phase Recovery in Dispersion-Unmanaged n-PSK Coherent Optical Communication Systems. Preprints 2016, 2016080194 (doi: 10.20944/preprints201608.0194.v1).

## Abstract

Using coherent optical detection and digital signal processing, laser phase noise and equalization enhanced phase noise can be effectively mitigated using the feed-forward and feed-back carrier phase recovery approaches. In this paper, theoretical analyses of feed-back and feed-forward carrier phase recovery methods have been carried out in the long-haul high-speed n-level phase shift keying (n-PSK) optical fiber communication systems, involving a one-tap normalized least-mean-square (LMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm. The analytical expressions for evaluating the estimated carrier phase and for predicting the bit-error-rate (BER) performance (such as the BER floors) have been presented and discussed in the n-PSK coherent optical transmission systems by considering both the laser phase noise and the equalization enhanced phase noise. The results indicate that the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms for small phase noise variance (or effective phase noise variance), while the one-tap normalized LMS algorithm shows a better performance than the other two algorithms for large phase noise variance (or effective phase noise variance). In addition, the one-tap normalized LMS algorithm is more sensitive to the level of modulation formats.

## Subject Areas

coherent optical detection; optical fiber communication; carrier phase recovery; feed-back and feed-forward; laser phase noise; equalization enhanced phase noise; n-level phase shift keying