Adaptive digital back propagation exploiting adjoint-based optimization for fiber-optic communications.

This work proposes a novel and powerful adaptive digital back propagation (A-DBP) method with a fast adaption process. Given that the total transmission distance is known, the proposed A-DBP algorithm blindly compensates for the linear and nonlinear distortions of optical fiber transmission systems and networks, without knowing the launch power and channel parameters. An adjoint-based optimization (ABO) technique is proposed to significantly accelerate the parameters estimation of the A-DBP. The ABO algorithm utilizes a sequential quadratic programming (SQP) method coupled with an adjoint sensitivity analysis (ASA) approach to rapidly solve the A-DBP training problem. The design parameters are optimized using the minimum overhead of only one extra system simulation. Regardless of the number of A-DBP design parameters, the derivatives of the training objective function with respect to all parameters are estimated using only one extra adjoint system simulation per optimization iterate. This is contrasted with the traditional finite-difference (FD)-based optimization methods whose sensitivity analysis calculations cost per iterate scales linearly with the number of parameters. The robustness, performance, and efficiency of the proposed A-DBP algorithm are demonstrated through applying it to mitigate the distortions of 4-span and 20-span optical fiber communication systems. Coarse-mesh A-DBPs with less number of virtual spans are also used to significantly reduce the computational complexity of the equalizer, achieving compensation performance higher than that obtained using the coarse-mesh DBP with the exact channel parameters and full number of virtual spans.