Geometric Clustering for Hardware-Efficient Implementation of Chromatic Dispersion Compensation

TL;DR

The paper tackles the high energy cost of chromatic dispersion compensation (CDC) in coherent optical links and proposes a hardware-aware Time-Domain Clustered Equalizer (TDCE) that leverages tap overlapping to reduce time-domain FIR complexity. It develops two TDCE variants, TDCE KNN and TDCE GD, and validates them against a standard FFT-based frequency-domain equalizer (FDE) on FPGA for fiber spans up to 640 km, demonstrating substantial energy efficiency gains. Key findings show up to about 70% energy savings and over 70% multiplier reductions with TDCE, while memory organization and parallelization are crucial to hardware performance, sometimes enabling higher-complexity algorithms to use fewer resources. The work provides a practical route to hardware-efficient CDC, showing that system-level design choices can dominate raw algorithmic complexity in determining power and area in FPGA/ASIC implementations.

Abstract

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.

Figures (11)

• Figure 1: Tap redundancy illustration. On the left, each gray circle represents a filter tap in the complex plane, showing clearly the tap accumulation. On the right, a heat map shows spots in areas of high concentration of filter taps. Filter taps calculated for 80km, 32Gbaud, 2 samples/symbol, dispersion coeff. $D$ = 16.8 ps/(nm$\cdot$km) and $\lambda$ = 1550nm
• Figure 2: Circular histograms showing how many filter taps are present in each bin (30 bins in total, 12°/bin). On the left, a clear clustered distribution of the filter taps is shown for the 80km equalizer filter, whilst on the right, a uniform-like distribution is shown for a higher dispersion scenario (8000km). Both equalizer filters are calculated for 32Gbaud, 2 samples/symbol, $D$ = 16.8 ps/(nm$\cdot$km) and $\lambda$ = 1550nm
• Figure 3: Uniformity analysis, showing that as the dispersion increases (in this case fixed 32Gbaud and increasing distance) the difference between the number of taps in the most populated and least populated bins becomes less significant ($\rho \leq 1$) in comparison to the average value ($\mu$). This means that there are still clusters, but for high dispersion scenarios, they are not highly localized, depicting a more uniform distribution.
• Figure 4: Methodology used to find the clusters quantities and FFT sizes (top row) and comparison of different clustering approaches (bottom row). a)Truncated filter response for different filter sizes with thresholds utilized for FFT filter and for clustered filter before KNN b) Clustered filter performance for different cluster quantities with pre-FEC threshold c) FDE complexity for different sizes and architectures to find the optimum FFT size d) Cluster location found by KNN in complex plane matching the cluster location visually inferred in the circular histogram (9 complex clusters - circular distribution) e) Cluster location found by KNN applied in the complex plane and optimized by GD algorithm f) Complexity comparison plot between FDE and different clustering approaches for different distances.
• Figure 5: Proposed approach to find the clusters in the transfer function known a priori and how to use this information to achieve a low complexity hardware implementation. On the left side, the real and imaginary parts of the complex transfer function, given by Eq. (\ref{['taps-equation']}), are analyzed in the complex plane using the KNN algorithm to generate the clustered filter taps $g_C$ (centroids), and the sample mapping sets $Q$. On the right, sample mappings are used to direct the input samples to the right group of samples that will be summed together to create the pre-summed $x_S$ array before the multiplication by the clustered filter taps (centroids) in the FPGA implementation.