A Min-Max Optimization Framework for Designing Sigma Delta Learners: Theory and Hardware

作者：Gore Amit^*; Chakrabartty Shantanu

来源：IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2010, 57(3): 604-617.

DOI：10.1109/TCSI.2009.2025002

• Manifold learning
• high-dimensional signal processing
• Sigma Delta conversion
• signal decorrelation
• analog-to-digital conversion (ADC)
• multichannel ADC

In this paper, we present a framework for constructing Sigma Delta learning algorithms and hardware that can identify and track low-dimensional manifolds embedded in a high-dimensional analog signal space. At the core of the proposed approach is a min-max stochastic optimization of a regularized cost function that combines machine learning with Sigma Delta modulation. As a result, the algorithm not only produces a quantized sequence of the transformed analog signals but also a quantized representation of the transform itself. The framework is generic and can be extended to higher order Sigma Delta modulators and for different signal transformations. In this paper, the Sigma Delta learning is demonstrated for identifying linear compression manifolds, which can eliminate redundant AD conversion (ADC) paths. This improves the energy efficiency of the proposed architecture compared to a conventional multichannel data acquisition system. Measured results from a four channel prototype fabricated in a 0.5 mu m CMOS process has been used to verify the energy efficiency of the Sigma Delta learner and to demonstrate its real-time adaptation capabilities that are consistent with the theoretical and simulated results. One of the salient features of Sigma Delta learning is its self-calibration property, whereby the performance remains unchanged even in the presence of computational artifacts (mismatch and nonlinearities). This property makes the proposed architecture ideal for implementing practical high-dimensional AD converters.

• 出版日期2010-3