Power efficiency remains a significant challenge in modern optical fiber communication systems, driving efforts to reduce the computational complexity of digital signal processing, particularly in chromatic dispersion compensation (CDC) algorithms. While various strategies for complexity reduction have been proposed, many lack the necessary hardware implementation to validate their benefits. This paper provides a theoretical analysis of the tap overlapping effect in CDC filters for coherent receivers, introduces a novel Time-Domain Clustered Equalizer (TDCE) technique based on this concept, and presents a Field-Programmable Gate Array (FPGA) implementation for validation. We developed an innovative parallelization method for TDCE, implementing it in hardware for fiber lengths up to 640 km. A fair comparison with the state-of-the-art frequency domain equalizer (FDE) under identical conditions is also conducted. Our findings highlight that implementation strategies, including parallelization and memory management, are as crucial as computational complexity in determining hardware complexity and energy efficiency. The proposed TDCE hardware implementation achieves up to 70.7\% energy savings and 71.4\% multiplier usage savings compared to FDE, despite its higher computational complexity.

We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion directly penalizes subband errors and includes a sparsity penalty term which is minimized using the damped regularized Newton's method. The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the system identification problem via computer simulations. Specifically, we study the effects of using different numbers of subbands and various sparsity penalty terms for quasi-sparse, sparse, and dispersive systems. The results show that the benefit of increasing the number of subbands is larger than promoting sparsity of the estimated filter coefficients when the target system is quasi-sparse or dispersive. On the other hand, for sparse target systems, promoting sparsity becomes more important. More importantly, the two aspects provide complementary and additive benefits to the GPtNSAF for speeding up convergence.

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise nonlinearity. Since the two first operations are well-defined only on regular-structured data such as audio or images, application of CNNs to contemporary datasets where the information is defined in irregular domains is challenging. This paper investigates CNNs architectures to operate on signals whose support can be modeled using a graph. Architectures that replace the regular convolution with a so-called linear shift-invariant graph filter have been recently proposed. This paper goes one step further and, under the framework of multiple-input multiple-output (MIMO) graph filters, imposes additional structure on the adopted graph filters, to obtain three new (more parsimonious) architectures. The proposed architectures result in a lower number of model parameters, reducing the computational complexity, facilitating the training, and mitigating the risk of overfitting. Simulations show that the proposed simpler architectures achieve similar performance as more complex models.