Accelerated optical MIMO equalization for SDM coherent optical communication systems

An integrated reconfigurable optical multiple-input multiple-output (MIMO) processor can effectively mitigate channel crosstalk in space-division multiplexing (SDM) systems in the optical domain, while significantly alleviating the power consumption, computational load, and processing latency compared with its digital signal processing (DSP) counterpart in the electrical domain. However, real-time reconfiguration of optical MIMO remains a significant challenge in transmission systems subject to time-varying channels under multiple impairments. This paper proposes a pilot-aided optical MIMO joint compensation scheme to address channel crosstalk, frequency offset (FO), and phase noise (PN) in SDM coherent optical communication systems. Frequency-domain pilot tones are embedded in digital subcarrier multiplexing (DSCM) signals to construct a composite transmission matrix that simultaneously characterizes channel crosstalk, FO, and PN. Phase shifters of Mach-Zehnder interferometers (MZIs) that compose an optical MIMO processor are dynamically controlled by an optimization algorithm to achieve optical mode decoupling, while the embedded pilot tones enable joint FO/PN compensation in the electrical domain. For an optical MIMO processor employing a cascaded structure, we introduce a staged optimization strategy and evaluate the convergence performance of various gradient algorithms, including gradient descent (GD), Nesterov's accelerated gradient (NAG), adaptive moment estimation (Adam), and Lookahead. Simulation results show that the staged strategy significantly accelerates convergence, with NAG converging in 20 iterations. For a simulated 800-Gb/s 2-mode 5-band DSCM dual-polarization (DP) 16-QAM signal transmission system, the proposed optical MIMO scheme incurs only a 0.2 dB OSNR sensitivity penalty relative to the theoretical 16-QAM limit at the 7% HD-FEC threshold.