Adaptive estimation and compensation of the time delay in a periodic non-uniform sampling scheme

Abstract

High sampling rate Analog-to-Digital Converters (ADCs) can be obtained by time-interleaving low rate (and thus low cost) ADCs into so-called Time-Interleaved ADCs (TI-ADCs). Nevertheless increasing the sampling frequency involves an increasing sensibility of the system to desynchronization between the different ADCs that leads to time-skew errors, impacting the system with non linear distortions. The estimation and compensation of these errors are considered as one of the main challenge to deal with in TI-ADCs. Some methods have been previously proposed, mainly in the field of circuits and systems, to estimate the time-skew error but they mainly involve hardware correction and they lack of flexibility, using an inflexible uniform sampling reference. In this paper, we propose to model the output of L interleaved and desynchronized ADCs with a sampling scheme called Periodic Non-uniform Sampling of order L (PNSL). This scheme has been initially proposed as an alternative to uniform sampling for aliasing cancellation, particularly in the case of bandpass signals. We use its properties here to develop a flexible on-line digital estimation and compensation method of the time delays between the desynchronized channels. The estimated delay is exploited in the PNSL reconstruction formula leading to an accurate reconstruction without hardware correction and without any need to adapt the sampling operation. Our method can be used in a simple Built-In Self-Test (BIST) strategy with the use of learning sequences and our model appears more flexible and less electronically expensive, following the principles of "Dirty Radio Frequency" paradigm: designing imperfect analog circuits with subsequently digital corrections of these imperfections.

Reconstruction from Periodic Nonstationary Sampling (PNS) without Resampling

“…It is possible to lower the price of devices by means of several samplers in parallel, and delayed alternately. Each sampler is modelled by a sequence like (7) and a set of samplers is equivalent to the PNSN (6) . To obtain a periodic sequence, the θ k have to verify the conditions θ k = θ + kT /N for some θ.…”

“…To obtain a periodic sequence, the θ k have to verify the conditions θ k = θ + kT /N for some θ. This last operation is commonly performed, it is expensive and can be avoided, staying in the PNS framework [7].…”

“…The generic name "Periodic Nonstationary Sampling" for the sequence ( 6) is unusual. We understand the part "periodic" which matchs subsequences (7) . The term "nonstationary" could be attributed either to the sequence t of ( 6) or to the samples (the Z (nT + θ k )).…”

On Stabilization of Non-Uniformly Sampled Control Systems - A Survey

“… Hardware An example of where non-uniform sampling occurs is A/D converters. In literature, for instance [64][65][66][67], it is presented structures of A/D converters. In [67] power consumption is taken into consideration and there is demonstrated that random-sampling decreases power consumption by 25%.…”

“…In literature, for instance [64][65][66][67], it is presented structures of A/D converters. In [67] power consumption is taken into consideration and there is demonstrated that random-sampling decreases power consumption by 25%. Other examples of hardware are introduced in [14], [33], and [68][69][70].…”