Decision-Aided Carrier Phase Estimation for Coherent Optical Communications

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We analytically studied the block length effect (BLE) of decision-aided maximum likelihood (DA ML) carrier phase estimation in coherent optical phase-modulated systems. The results agree well with the trends found using extensive Monte Carlo simulations. In order to eliminate the BLE and accurately recover the carrier phase, an adaptive decision-aided (DA) receiver is proposed that does not require knowledge of the statistical characteristics of the carrier phase, or any parameter to be preset. The simulation results show that using the adaptive DA receiver, the maximum tolerance ratio of the linewidth per laser to symbol rate <formula formulatype="inline"><tex Notation="TeX">$(\Delta \nu T)$</tex></formula> at a bit error rate <formula formulatype="inline"> <tex Notation="TeX">$({\rm BER}) = 10^{- 4}$</tex></formula> has been increased to <formula formulatype="inline"><tex Notation="TeX">$2.5 \times 10^{- 4}, 4.1 \times 10^{- 5}$</tex></formula>, and <formula formulatype="inline"><tex Notation="TeX">$9.5 \times 10^{- 6}$</tex></formula>, respectively, for quadrature-, 8- and 16-phase-shift keying formats. The ratio <formula formulatype="inline"> <tex Notation="TeX">$(\Delta \nu T)$</tex></formula> of the adaptive DA receiver in 16 quadrature amplitude modulation (QAM) is decreased to <formula formulatype="inline"> <tex Notation="TeX">$2 \times 10^{- 5}$</tex></formula> due to the constellation penalty from <formula formulatype="inline"><tex Notation="TeX">$2.5 \times 10^{- 5}$</tex></formula> by using DA ML with optimum memory length, though it consistently performs well without optimizing any parameters as in DA ML. The phase error variance of the adaptive DA receiver is also analytically investigated. In addition, an analog-to-digital converter with bit resolution higher than 4 bits is shown to be sufficient to implement our adaptive DA receiver. </para>