A Multistage CPE Scheme Based on Crossed Constellation Transformation for M-QAM

A multistage carrier phase estimation (CPE) scheme for any
$m$
-ary quadrature amplitude modulation (QAM) formats is proposed and analyzed in coherent optical communication systems. The scheme is based on the crossed constellation transformation algorithm that is transparent to all modulation formats whose constellations are on the square grid. Simulation results show that the hardware complexity of the proposed CPE scheme can be significantly reduced by the group factors of 6.1/8.6, 4.7/6, and 2.6/3.3 (in the form of multipliers/adders) for 32-QAM, 64-QAM, and 128-QAM compared with the single-stage blind phase search algorithm. In 32-QAM, 64-QAM, and 128-QAM, coherent optical communication systems with 1-dB SNR penalty at bit error rate is
$1\times 10^{-2}$
, the comparable linewidth symbol duration can be reached with the values of
$6\times 10^{-5}$
,
$4\times 10^{-5}$
, and
$8\times 10^{-6}$
, respectively.