Cramér-Rao Bound for Signal Parameter Estimation From Modulo ADC Generated Data

Abstract

To mitigate the dynamic range problems that low-bit quantization of conventional analog-to-digital converters (ADCs) suffer from, we shift our attention to the novel modulo ADCs (Mod-ADCs). We consider the Cramér-Rao bound (CRB) analysis for signal parameter estimation from Mod-ADC generated data. Four CRB formulas are derived assuming known or unknown folding-counts, for both quantized and unquantized cases. We analyze many of their characteristics, such as monotonicity, boundedness and convergence; and perform detailed comparisons of the CRBs among the conventional ADCs and the two different types of Mod-ADCs. Numerical examples are presented to demonstrate these characteristics, and that the low-bit Mod-ADCs can provide satisfactory signal parameter estimation performances even in high dynamic range situations.