MLSE Output Visualization and Transmitter Compliance Metric

Intensity-modulation and direct-detection (IMDD) systems using two- or four-level pulse amplitude modulation (PAM) are widely used in data centers (DC) optical links, passive optical networks (PON), short metro links, and many other applications. The transmitted optical signal is distorted by noise, intersymbol interference (ISI), and nonlinearities caused by optical/electrical components and fiber. Therefore, the received signal must be recovered by an equalization technique that is realized either in the analog or digital domain or a combination thereof. Continuous-time linear equalizers (CTLE) and few-tap linear feed-forward equalizers (FFE) are often used in IMDD receivers. Besides bit error rate (BER) and symbol error rate (SER), the reconstructed one-dimensional modulation format signals are frequently characterized by eye diagrams and histograms. Complex modulation formats can be analyzed similarly by e.g., plotting eye diagrams and histograms per dimension. Equalized signal visualization tools are beneficial in assessing signal performance, sensitivity to clock jitter variations, amount of noise that can be added to the received signal to meet the forward error correction (FEC) threshold, etc. It is straightforward to generate an eye diagram after the FFE or after the decision feedback equalizer (DFE). However, the next generation of optical transceivers will likely be based on a computationally complex Volterra equalizer followed by a noise decorrelator and a maximum likelihood sequence estimation (MLSE) or a maximum a posteriori probability (MAP) algorithm. In this paper, we introduce a novel method for histogram reconstruction after the MLSE/MAP. The histogram reconstruction is extended to the plotting of the MLSE/MAP eye diagram. As some standardization bodies already consider an MLSE reference receiver to estimate transmitter dispersion eye closure quaternary (TDECQ), we use our MLSE-based histogram reconstruction method and upgrade the conventional FFE-based TDECQ technique to develop a very accurate technique for TDECQ calculation in FFE-MLSE receivers.