Coherent optical transmitter IQ imbalance mitigation with embedded carrier phase and frequency offset estimation

We present a 4×4 real-valued channel equalizer with embedded phase estimator, designed for carrier phase and frequency offset estimation and compensation in coherent optical communications with in-phase/quadrature (IQ) impairments. These impairments include IQ timing skew, gain imbalance, and quadrature phase errors at the transmitter side. To achieve adaptive control of the equalizer's filter coefficients, we employ the decision-directed least mean square (DD-LMS) algorithm. This algorithm minimizes the error between the filter outputs and the desired signals in a symbol-by-symbol manner, resulting in faster channel coefficients adaptation speed. Simulation results for a 60 GBaud polarization-multiplexing 16 quadrature amplitude modulation (PM-16QAM) signal demonstrate that our proposed equalizer outperforms a 2×2 cascaded multi modulus algorithm-based (CMMA-based) equalizer, a 2×2 complex-valued method based on the DD-LMS algorithm, and the 4×4 real-valued equalizer without embedded frequency offset estimation (FOE), when the transmitter IQ impairments exist. Experimental validation is also conducted for the 60 GBaud PM-16QAM and 45 GBaud PM-64QAM signals. Similar to the simulation results, our experiments show that the proposed 4×4 real-valued equalizer with embedded FOE can achieve effective SNR penalties of less than 0.41 dB at 7 ps skew, 1.33 dB at 3.5 dB gain imbalance, and 1.64 dB at the bias voltage shift of 0.5 V for the 60 GBaud PM-16QAM signal. Finally, our experimental results confirm the effectiveness of our proposed method in carrier phase estimation as well as the frequency offset compensation, when compared with 4×4 real-valued equalizer without embedded FOE.