Compensation of correlated autoregressive clock jitter in arrays of Analog-to-Digital Converters

In modern communication systems, the fidelity of analog-to-digital converters (ADCs) is limited by sampling clock jitter, i.e., small random timing deviations that undermine ideal sampling. Traditional scalar models often treat jitter as independent Gaussian noise, which makes it essentially untrackable, whereas real ADCs also exhibit temporally correlated (spectrally colored) imperfections. Moreover, spatial cross-correlations between channels in multiple-input multiple-output (MIMO) ADCs are commonly neglected. This paper addresses the joint tracking and compensation of random, cross-correlated timing errors in ADC arrays by modeling jitter as a coupled vector autoregressive process of order one (VAR(1)). We propose a pilot-tone-based Kalman smoother to track and compensate the jitter, and simulations demonstrate substantial reductions in jitter-induced distortion across diverse scenarios.