Hierarchical blind phase search for correcting imperfect phase rotation in QAM signals synthesized via optical coherent superposition

Abstract

Coherent superposition has been proposed to synthesize high-order quadrature amplitude modulation (QAM) by coherently superposing low-order QAMs in the optical domain. These approaches could effectively relax the digital-to-analog converter resolution and reduce the complexity of the driving electronics. However, in the superposition process, imperfect phase rotations (IPRs) in low-order QAMs will be transferred to the resultant high-order QAM. Importantly, the induced IPR cannot be compensated for by conventional linear equalizers and carrier recovery methods. To combat the induced IPR, herein, we propose a hierarchical blind phase search (HBPS) algorithm to compensate for the IPRs in synthesized high-order QAMs. The proposed HBPS can match the generation mechanism of the IPRs in coherent superposition, by tracing back and estimating the IPR in the QPSK-like constellation of each hierarchy and finally correcting the induced IPRs. Simulation and experimental results verify that this algorithm could effectively compensate for the IPR in the resultant 16-QAMs synthesized using coherent superposition approaches. The proposed HBPS shows significant optical signal-to-noise ratio (OSNR) gains compared to the conventional blind phase search (BPS) method for high-order QAMs coherently superposed using optical signal processing (OSP) and tandem modulators (TMs). Specifically, at the BER of 2.4e-2, the HBPS achieves a 1.5-dB OSNR sensitivity enhancement over the BPS in either OSP or TMs-based schemes, even with an imperfection rotation of up to 20∘.