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Timing offset and quantization error trade-off in interleaved multi-channel measurements

Time-interleaved analog-to-digital converters (ADCs)
are traditionally designed with equal quantization granularity in
each channel and uniform sampling offsets. Recent work suggests
that it is often possible to achieve a better
signal-to-quantization noise ratio (SQNR) with different
quantization granularity in each channel, non-uniform sampling, and
appropriate reconstruction filtering. This thesis develops a
framework for optimal design of non-uniform sampling constellations
to maximize SQNR in time-interleaved ADCs. The first portion of
this thesis investigates discrepancies between the additive noise
model and uniform quantizers. A simulation is implemented for the
multi-channel measurement and reconstruction system. The simulation
reveals a key inconsistency in the environment of time-interleaved
ADCs: cross-channel quantization error correlation. Statistical
analysis is presented to characterize error correlation between
quantizers with different granularities. A novel ADC architecture
is developed based on weighted least squares (WLS) to exploit this
correlation, with particular application for time-interleaved ADCs.
A "correlated noise model" is proposed that incorporates error
correlation between channels. The proposed model is shown to
perform significantly better than the traditional additive noise
model for channels in close proximity. The second portion of this
thesis focuses on optimizing channel configurations in
time-interleaved ADCs. Analytical and numerical optimization
techniques are presented that rely on the additive noise model for
determining non-uniform sampling constellations that maximize SQNR.
Optimal constellations for critically sampled systems are always
uniform, while solution sets for oversampled systems are larger.
Systems with diverse bit allocations often exhibit "clusters" of
low-precision channels in close proximity. Genetic optimization is
shown to be effective for quickly and accurately determining
optimal timing constellations in systems with many channels.
Finally, a framework for efficient design of optimal channel
configurations is formulated that incorporates statistical analysis
of cross-channel quantization error correlation and solutions based
on the additive noise model. For homogeneous bit allocations, the
framework proposes timing offset corrections to avoid performance
degradation from the optimal scenario predicted by the additive
noise model. For diverse bit allocations, the framework proposes
timing corrections and a "unification" of low-precision quantizers
in close proximity. This technique results in significant
improvements in performance above the previously known optimal
additive noise model solution.