  We present the results of the comparative analysis of the performance versus
complexity for several types of artificial neural networks (NNs) used for
nonlinear channel equalization in coherent optical communication systems. The
comparison has been carried out using an experimental set-up with transmission
dominated by the Kerr nonlinearity and component imperfections. For the first
time, we investigate the application to the channel equalization of the
convolution layer (CNN) in combination with a bidirectional long short-term
memory (biLSTM) layer and the design combining CNN with a multi-layer
perceptron. Their performance is compared with the one delivered by the
previously proposed NN equalizer models: one biLSTM layer, three-dense-layer
perceptron, and the echo state network. Importantly, all architectures have
been initially optimized by a Bayesian optimizer. We present the derivation of
the computational complexity associated with each NN type -- in terms of real
multiplications per symbol so that these results can be applied to a large
number of communication systems. We demonstrated that in the specific
considered experimental system the convolutional layer coupled with the biLSTM
(CNN+biLSTM) provides the highest Q-factor improvement compared to the
reference linear chromatic dispersion compensation (2.9 dB improvement). We
examine the trade-off between the computational complexity and performance of
all equalizers and demonstrate that the CNN+biLSTM is the best option when the
computational complexity is not constrained, while when we restrict the
complexity to lower levels, the three-layer perceptron provides the best
performance. Our complexity analysis for different NNs is generic and can be
applied in a wide range of physical and engineering systems.
