Segmented Compressed Sampling for Analog-to-Information Conversion: Method and Performance Analysis

摘要

A new segmented compressed sampling (CS) method for analog-to-information conversion (AIC) is proposed. An analog signal measured by a number of parallel branches of mixers and integrators (BMIs), each characterized by a specific random sampling waveform, is first segmented in time into $M$ segments. Then the subsamples collected on $M$ different segments and $K$ different BMIs are reused so that a larger number of samples (at most $K^2$) than the number of BMIs is collected. This technique is shown to be equivalent to extending the measurement matrix, which consists of the BMI sampling waveforms, by adding new rows without actually increasing the number of BMIs. We prove that the extended measurement matrix satisfies the restricted isometry property with overwhelming probability if the original measurement matrix of BMI sampling waveforms satisfies it. We also prove that the signal recovery performance can be improved if our segmented CS-based AIC is used for sampling instead of the conventional AIC with the same number of BMIs. Therefore, the reconstruction quality can be improved by slightly increasing (by $M leq K$ times) the sampling rate per each BMI. Simulation results verify the effectiveness of the proposed segmented CS method and the validity of our theoretical results. Particularly, our simulation results show significant signal recovery performance improvement when the segmented CS-based AIC is used instead of the conventional AIC with the same number of BMIs.