A Novel Iterative Structure for Online Calibration of $M$-channel Time-Interleaved ADCs

This paper proposes a computationally efficient calibration structure for online estimation and compensation of offset, gain and frequency response mismatches in M-channel time-interleaved (TI) analog-to-digital converters (ADCs). The basic idea of the proposed approach is to reserve some sampling instants for estimating and tracking the mismatch parameters of sub-ADCs with reference to a known input. Since the estimation problem is analogous to a standard system identification problem, we propose two simple variable digital filter (VDF) based adaptive filter structures which are derived from the least mean squares (LMS) and normalized LMS algorithms. On the other hand, the reservation of some sampling instants in the normal operation of TI ADC implies that part of samples have to be sacrificed. Based on a general time-varying linear system model for the mismatch and the spectral property of a slightly oversampled input signal, we also propose a novel iterative framework to solve the resulting underdetermined problem. It not only embraces a number of iterative algorithms for the tradeoff between convergence rate and arithmetic complexity but also admits efficient update structure based again on VDFs. Therefore, thanks to the well-known efficient implementation of VDFs, the adaptability of both estimation and compensation algorithms allows us to combine them seamlessly to form an online calibration structure, which is able to track and compensate for the channel mismatches with low complexity and high reconstruction accuracy. Finally, we demonstrate the usefulness of the proposed approach by means of computer simulations.