Transmitter and receiver impairment monitoring using adaptive multi-layer linear and widely linear filter coefficients controlled by stochastic gradient descent.

We propose a monitoring method for individual impairments in a transmitter (Tx) and receiver (Rx) by using filter coefficients of multi-layer strictly linear (SL) and widely linear (WL) filters to compensate for relevant impairments where the filter coefficients are adaptively controlled by stochastic gradient descent with back propagation from the last layer outputs. Considering the order of impairments occurring in a Tx or Rx of coherent optical transmission systems and their non-commutativity, we derive a model relating in-phase (I) and quadrature (Q) skew, IQ gain imbalance, and IQ phase deviation in a Tx or Rx to the WL filter responses in our multi-layer filter architecture. We evaluated the proposed method through simulations using polarization-division multiplexed (PDM)-quadrature phase shift keying and a transmission experiment of 32-Gbaud PDM 64-quadrature amplitude modulation over a 100-km single-mode fiber span. The results indicate that both Tx and Rx impairments could be individually monitored by using the filter coefficients of adaptively controlled multi-layer SL and WL filters precisely and simultaneously, decoupled by chromatic dispersion and frequency offset, even when multiple impairments existed.