Interval Design for Signal Parameter Estimation From Quantized Data

We consider the problem of optimizing the quantization intervals (or thresholds) of low-resolution analog-to-digital converters (ADCs) via the minimization of a Cramér-Rao bound (CRB)-based metric. The interval design is formulated as a dynamic programming problem. A computationally efficient global algorithm, referred to as the
i
nterval
d
esign for
e
nhanced
a
ccuracy (IDEA) algorithm, is presented to solve this optimization problem. If the realization in hardware of a quantizer with optimized intervals is difficult, it can be approximated by a design whose practical implementation is feasible. Furthermore, the optimized quantizer can also be useful in signal compression applications, in which case no approximation should be necessary. As an additional contribution, we establish the equivalence between the Lloyd-Max type of quantizer and a low signal-to-noise ratio version of our IDEA quantizer, and show that it holds true if and only if the noise is Gaussian. Furthermore, IDEA quantizers for several typical signals, for instance normally distributed signals, are provided. Finally, a number of numerical examples are presented to demonstrate that the use of IDEA quantizers can enhance the parameter estimation performance.