Residual LSTM Equalization versus Classical Equalizers in Linear, Polynomial, and Long-State Nonlinear Channels

This work investigates the performance of classical and neural equalization schemes under different channel memory and nonlinearity regimes. Four equalizers are compared: Zero Forcing (ZF), Least Mean Squares (LMS), diagonal Volterra equalization, and a residual Long Short-Term Memory (LSTM) equalizer. Three representative communication channel scenarios are considered: (i) linear-memory-dominant channels, (ii) polynomial nonlinear channels, and (iii) long nonlinear state-memory channels. These regimes emulate practical impairments observed in optical wireless links, RF front-ends, photonic systems, visible light communication (VLC), nonlinear power amplification systems, and coherent optical receivers. Simulation results show that classical linear equalizers are highly effective in predominantly linear channels, Volterra equalization is advantageous in polynomial nonlinear regimes, and LSTM equalization becomes preferable when the channel exhibits long nonlinear temporal dependencies and state dynamics.