All-Analytic Statistical Modeling of Constellations in (Optical) Transmission Systems Driven by High-Speed Electronic Digital to Analog Converters Part I: DAC Mismatch Statistics, Metrics, Symmetries, Error Vector Magnitude

Abstract

This two-part work develops a comprehensive toolbox for the statistical characterization of nonlinear distortions of DAC-generated signal constellations to be transmitted over communication links, be they electronic (wireline, wireless) or photonic, Mach–Zehnder modulator (MZM)-based optical interconnects in particular. The all-analytic toolbox developed here delivers closed-form expressions for the second-order statistics (means, variances) of all relevant constellation metrics of the DACs’ building blocks and of DAC-driven MZM-based optical transmitters, all the way to the slicer in the optical receivers over a linear channel with coherent detection. The key impairment targeted by the model is the random current mismatch of the ASIC devices implementing the DAC drivers. In particular the (skew-)centrosymmetry of the DAC metrics is formally derived and explored. A key applicative insight is that the conventional INL/DNL (Integral NonLinearity/Differential NonLinearity) constellation metrics, widely adopted in the electronic devices and circuits community, are not quite useful in the context of communication systems, since these metrics are ill-suited to predict communication link statistical performance. To rectify this deficiency of existing electronic DAC metrics, we introduce modified variants of the INL|DNL, namely the integral error vector (IEV) and the differential error vector (DEV) constellation metrics. The new IEV|DEV represent straightforward predictors of relevant communication-minded metrics: error vector magnitude (EVM) treated here in Part I, and Symbol/Bit Error-Rates (SER, BER) treated in the upcoming Part II of this paper.