Thesis Supervisor: Gregory W. Wornell
Title: Professor of Electrical Engineering and Computer ScienceTraditionally, the sampling of a signal is performed using a single component such as an
analog-to-digital converter. However, many new technologies are motivating the use of
multiple sampling components to capture a signal. In some cases such as sensor networks,
multiple components are naturally found in the physical layout; while in other cases like
time-interleaved analog-to-digital converters, additional components are added to increase
the sampling rate. Although distributing the sampling load across multiple channels can
provide large benefits in terms of speed, power, and resolution, a variety mismatch errors
arise that require calibration in order to prevent a degradation in system performance.
In this thesis, we develop low-complexity, blind algorithms for the calibration of distributed
sampling systems. In particular, we focus on recovery from timing skews that
cause deviations from uniform timing. Methods for bandlimited input reconstruction from
nonuniform recurrent samples are presented for both the small-mismatch and the low-SNR
domains. Alternate iterative reconstruction methods are developed to give insight into the
geometry of the problem.
From these reconstruction methods, we develop time-skew estimation algorithms that
have high performance and low complexity even for large numbers of components. We also
extend these algorithms to compensate for gain mismatch between sampling components.
To understand the feasibility of implementation, analysis is also presented for a sequential
implementation of the estimation algorithm.
In distributed sampling systems, the minimum input reconstruction error is dependent
upon the number of sampling components as well as the sample times of the components. We
develop bounds on the expected reconstruction error when the time-skews are distributed
uniformly. Performance is compared to systems where input measurements are made via
projections onto random bases, an alternative to the sinc basis of time-domain sampling.
From these results, we provide a framework on which to compare the effectiveness of any
calibration algorithm.
Finally, we address the topic of extreme oversampling, which pertains to systems with
large amounts of oversampling due to redundant sampling components. Calibration algorithms
are developed for ordering the components and for estimating the input from ordered
components. The algorithms exploit the extra samples in the system to increase estimation
performance and decrease computational complexity
