Segmented Compressed Sampling for Analog-to-Information Conversion: Method and Performance Analysis
Segmented Compressed Sampling for Analog-to-Information Conversion: Method and Performance Analysis
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DOI：
10.1109/tsp.2010.2091411
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发表时间：
2010-04
影响因子：
5.4
通讯作者：
O. Taheri;S. Vorobyov
中科院分区：
文献类型：
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作者：
O. Taheri;S. Vorobyov
提出了一种新的用于模拟信息转换（AIC）的分段压缩采样（CS）方法。由混频器和积分器 (BMI) 的多个并行分支测量的模拟信号（每个分支都具有特定的随机采样波形）首先按时间分段。然后，重复使用在不同细分和不同BMI上收集的子样本，以便收集比BMI数量更多的样本（最多）。该技术被证明相当于通过添加新行来扩展由 BMI 采样波形组成的测量矩阵，而无需实际增加 BMI 的数量。我们证明，如果 BMI 采样波形的原始测量矩阵满足限制等距性质，则扩展测量矩阵以压倒性概率满足它。我们还证明，如果使用我们的基于分段 CS 的 AIC 代替具有相同 BMI 数量的传统 AIC 进行采样，可以提高信号恢复性能。因此，可以通过稍微增加（成倍）每个BMI的采样率来提高重建质量。仿真结果验证了所提出的分段CS方法的有效性以及我们理论结果的有效性。特别是，我们的模拟结果表明，当使用分段的基于 CS 的 AIC 代替具有相同数量 BMI 的传统 AIC 时，信号恢复性能显着提高。
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 segments. Then the subsamples collected on different segments and different BMIs are reused so that a larger number of samples (at most ) 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 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.