Compressive Sensing ADC Calibration for Frequency Offset Mismatch
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Solution Overview
Problem
Conventional analog-to-digital converters (ADCs) face inefficiencies due to energy wastage from compressing data after conversion, and sparsifying basis mismatch during compressive sensing, which limits reconstruction performance.
Innovation Solution
An ADC system that samples at a frequency below the Nyquist rate using a controller with a CLEAN dictionary that compensates for sparsifying basis mismatch by iteratively isolating spectral terms and determining their offsets, constructed using a least square algorithm, to generate a digital signal equivalent to Nyquist frequency conversion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If compressive sensing is used to sample below Nyquist rate, then energy consumption is reduced and productivity is improved, but reconstruction accuracy deteriorates due to sparsifying basis mismatch
Solution Approach 1:
The patent changes the parameters of the sparsifying basis by estimating frequency offsets and adjusting the basis vectors to match the actual signal frequencies. This parameter adjustment resolves the basis mismatch problem while maintaining sub-Nyquist sampling, thereby improving reconstruction accuracy without sacrificing sampling efficiency.
Solution Approach 2:
The patent implements a feedback mechanism where the system estimates frequency offsets from the compressed measurements, uses these estimates to adjust the sparsifying basis, and then performs reconstruction. This iterative feedback loop continuously improves reconstruction accuracy by adapting the basis to the actual signal characteristics.
2Measurement precision
If conventional ADC sampling at Nyquist rate is used, then reconstruction accuracy is maintained, but energy consumption increases due to sampling and compressing data after conversion
Solution Approach 1:
The patent performs compression during the sampling process itself rather than after conversion. By integrating the compression operation into the sampling stage through compressed sensing, the system eliminates the need for separate compression steps, reducing energy consumption while maintaining reconstruction accuracy through basis mismatch compensation.
3Productivity
If sub-Nyquist sampling is used to reduce energy consumption, then productivity is improved, but sparsifying basis mismatch occurs causing spectral leakage
Solution Approach 1:
The patent estimates frequency offsets caused by basis mismatch and adjusts the sparsifying basis parameters accordingly. By changing the basis parameters to match actual signal frequencies, the system eliminates spectral leakage while maintaining the benefits of sub-Nyquist sampling.
Solution Approach 2:
The patent takes the frequency offset information, which initially causes spectral leakage and basis mismatch, and converts it into a useful parameter for improving reconstruction. By estimating and utilizing these offsets to adjust the basis, the system transforms the harmful effect into a benefit that enhances reconstruction accuracy.
Data Source
AI summary
A calibration method to compensate for a sparsifying basis mismatch is provided. 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 to generate a first digital signal. Each of a plurality of spectral terms is iteratively isolated from the first digital signal, and the offset for each of the plurality of spectral terms is iteratively determined. A dictionary is then constructed using the offset for each of the plurality of spectral terms, where the dictionary compensates for mismatch from a sparsifying basis.