SAR ADC Reconstruction Using Box-Constrained Compressive Sensing
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional analog-to-digital converters (ADCs) require sampling at the Shannon-Nyquist rate, leading to energy wastage and inefficiency, as they compress data after conversion, whereas compressive sensing aims to compress data before capture by adjusting the ADC's sampling theory, necessitating a more accurate reconstruction methodology.
Innovation Solution
An ADC system using a successive approximation register (SAR) architecture with a box constrained linear optimization process that samples at a frequency below the Nyquist rate, employing a sample-and-hold circuit, comparator, and capacitive digital-to-analog converter, and a controller that generates a second digital signal through a box constrained optimization process to minimize errors, achieving accurate reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional ADCs sample at the Shannon-Nyquist rate, then measurement precision is maintained, but energy consumption increases and efficiency decreases
Solution Approach 1:
The patent changes the sampling rate parameter from the conventional Nyquist rate to a sub-Nyquist rate, enabling compressive sensing operation. This parameter change allows the system to sample at lower rates while maintaining reconstruction accuracy through the box constrained optimization algorithm, thereby reducing energy consumption without sacrificing measurement precision
Solution Approach 2:
The patent replaces the conventional uniform sampling mechanism with a compressive sensing approach that uses random sampling followed by optimization-based reconstruction. This substitution transforms the sampling paradigm from time-domain uniform sampling to a compressed domain representation, achieving energy efficiency while maintaining signal fidelity
2Loss of substance
If data compression is performed after ADC conversion, then storage space is reduced, but energy is wasted during conversion
Solution Approach 1:
The patent performs compression action during the sampling process itself rather than after conversion. By integrating compressive sensing into the ADC operation, the system compresses the signal representation at the acquisition stage, preventing energy waste from converting full-resolution signals that will later be compressed anyway
3Use of energy by moving object
If sampling rate is reduced below Nyquist frequency, then energy efficiency improves, but reconstruction accuracy deteriorates
Solution Approach 1:
The patent employs a feedback mechanism through the box constrained optimization algorithm that iteratively refines the signal reconstruction. The algorithm uses the sub-Nyquist samples as input and continuously adjusts the reconstructed signal to satisfy the measurement constraints, providing feedback-driven correction that maintains accuracy despite reduced sampling rates
Solution Approach 2:
The patent combines sub-Nyquist sampling with a sophisticated optimization algorithm (box constrained linear optimization) to create a composite approach. The combination of reduced-rate sampling and advanced reconstruction methodology achieves both energy efficiency and high reconstruction accuracy, neither of which could be achieved alone
4Measurement precision
If box constrained optimization is used for reconstruction, then accuracy improves by nearly one bit ENOB, but computational complexity increases by 30%
Solution Approach 1:
The patent changes the optimization constraints from conventional approaches to box constraints, which bound the solution space in a way that improves accuracy. This parameter change in the constraint formulation enables the algorithm to achieve nearly one additional bit of effective resolution while managing computational complexity through efficient implementation
Data Source
AI summary
Compressive sensing is an emerging field that attempts to prevent the losses associated with data compression and improve efficiency overall, and compressive sensing looks to perform the compression before or during capture, before energy is wasted. Here, a reconstruction algorithm is proposed for a compressive sensing successive approximation register (SAR) analog-to-digital converter (ADC). Accordingly, an analog signal is converted to a first digital signal at a sampling frequency that is less than a Nyquist frequency for the analog signal, and a second digital signal is constructed from the first digital signal with a box constrained linear optimization process such that the second digital signal is approximately equal to an analog-to-digital conversion of the analog signal at the Nyquist frequency for the analog signal.