USF Spectral Estimation: Prevalence of Gaussian Cram'er-Rao Bounds Despite Modulo Folding
🤖 AI Summary
解决信号处理中动态范围与分辨率无法同时优化的问题，采用模数非线性硬件方法，推导出噪声模数折叠样本的Cramér-Rao界，验证其与高斯Cramér-Rao界的关系。
Application Category
📝 Abstract
Spectral Estimation (SpecEst) is a core area of signal processing with a history spanning two centuries and applications across various fields. With the advent of digital acquisition, SpecEst algorithms have been widely applied to tasks like frequency super-resolution. However, conventional digital acquisition imposes a trade-off: for a fixed bit budget, one can optimize either signal dynamic range or digital resolution (noise floor), but not both simultaneously. The Unlimited Sensing Framework (USF) overcomes this limitation using modulo non-linearity in analog hardware, enabling a novel approach to SpecEst (USF-SpecEst). However, USF-SpecEst requires new theoretical and algorithmic developments to handle folded samples effectively. In this paper, we derive the Cram'er-Rao Bounds (CRBs) for SpecEst with noisy modulo-folded samples and reveal a surprising result: the CRBs for USF-SpecEst are scaled versions of the Gaussian CRBs for conventional samples. Numerical experiments validate these bounds, providing a benchmark for USF-SpecEst and facilitating its practical deployment.
Problem
Research questions and friction points this paper is trying to address.
Overcoming dynamic range vs resolution trade-off in spectral estimation
Developing theory for spectral estimation with modulo-folded samples
Deriving Cramér-Rao bounds for noisy modulo-based spectral estimation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Modulo non-linearity enables dynamic range and resolution
Derived Cramér-Rao Bounds for noisy modulo-folded samples
Scaled Gaussian CRBs benchmark USF-SpecEst performance
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