Carrier Phase Recovery for Set-Partitioning QAM Formats

The set-partitioning quadrature amplitude modulation (SP-QAM) formats are highly preferred for the next generation fiber optical transmission system, due to the Euclidean distance increment of constellation and its power efficiency. However, the existing carrier phase recovery (CPR) scheme of SP-QAM is independently implemented between two polarization signals, and the laser linewidth tolerance of SP-QAM is restricted the same as that of conventional QAM signals. Here, we propose a novel four-dimensional (4-D) CPR scheme for the SP-QAM formats. After the phase offset estimation and precompensation between two polarizations, we implement blind phase search (BPS) algorithm in the 4-D space. Meanwhile, traditional decision circuit is replaced by 4-D detection of SP-QAM and 4-D distance is calculated as the cost function for identifying the desired test phase angle. We carry out numerical simulations under conditions of 28 Gbaud SP-128-QAM, SP-512-QAM, and SP-2048-QAM coherent transmissions. The CPR performance of our proposed 4-D BPS scheme is much better than that of conventional BPS. Given the 1 dB required optical signal-to-noise ratio penalty at <inline-formula><tex-math notation="LaTeX">${\rm{BER}} = 1 \times {10^{-3}}$</tex-math></inline-formula>, the linewidth times symbol duration products of <inline-formula><tex-math notation="LaTeX">$5.2 \times {10^{-4}}$ </tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$2 \times {10^{-4}}$</tex-math> </inline-formula>, and <inline-formula><tex-math notation="LaTeX">$7 \times {10^{-5}}$</tex-math></inline-formula> are tolerable for SP-128-QAM, SP-512-QAM, and SP-2048-QAM, respectively. We further experimentally verify the performance of the proposed 4-D BPS under the scenarios of 28 Gbaud SP-128-QAM back-to-back and standard single-mode fiber transmission from 750 to 1500 km, indicating of the robustness to the amplified spontaneous emission noise and transmission impairments.