[论文解读] Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio

Moslem Rashidi|arXiv (Cornell University)|Oct 11, 2010

Sparse and Compressive Sensing Techniques参考文献 37被引用 12

一句话总结

本文提出一种用于多带信号的周期性非均匀采样方法，结合压缩感知原理，可在低于奈奎斯特速率的情况下实现信号重建。通过优化采样参数以最小化条件数，并采用子空间方法与非线性最小二乘法进行谱估计，该方法在认知无线电中实现了高精度宽带谱感知，同时降低了采样率并提高了抗噪声能力。

ABSTRACT

Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of limitations encountered in current converters are due to a traditional assumption that the sampling state needs to acquire the data at the Nyquist rate, corresponding to twice the signal bandwidth. In this thesis a method of sampling far below the Nyquist rate for sparse spectrum multiband signals is investigated. The method is called periodic non-uniform sampling, and it is useful in a variety of applications such as data converters, sensor array imaging and image compression. Firstly, a model for the sampling system in the frequency domain is prepared. It relates the Fourier transform of observed compressed samples with the unknown spectrum of the signal. Next, the reconstruction process based on the topic of compressed sensing is provided. We show that the sampling parameters play an important role on the average sample ratio and the quality of the reconstructed signal. The concept of condition number and its effect on the reconstructed signal in the presence of noise is introduced, and a feasible approach for choosing a sample pattern with a low condition number is given. We distinguish between the cases of known spectrum and unknown spectrum signals respectively. One of the model parameters is determined by the signal band locations that in case of unknown spectrum signals should be estimated from sampled data. Therefore, we applied both subspace methods and non-linear least square methods for estimation of this parameter. We also used the information theoretic criteria (Akaike and MDL) and the exponential fitting test techniques for model order selection in this case.

研究动机与目标

• 解决传统奈奎斯特速率采样在高带宽认知无线电系统中的低效问题。
• 为稀疏多带信号开发一种低复杂度的采样策略，使其在低于奈奎斯特速率下运行。
• 通过优化采样模式选择，确保在噪声存在下仍能实现精确的信号重建。
• 在计算成本最小化和硬件需求降低的前提下，实现在认知无线电中的谱感知。
• 为从压缩采样中估计未知信号频带位置提供一个鲁棒框架。

提出的方法

• 建立一个频域模型，将压缩非均匀采样的傅里叶变换与未知信号谱联系起来。
• 应用压缩感知理论，从亚奈奎斯特采样中重建原始多带信号。
• 优化采样参数以最小化条件数，从而在噪声环境中提升重建稳定性。
• 采用子空间方法（如ESPRIT类方法）与非线性最小二乘法，估计未知信号频带位置。
• 应用信息论准则（AIC与MDL）及指数拟合检验，实现未知谱场景下的模型阶数选择。
• 整合条件数分析，以指导具有更好数值稳定性的采样模式设计。

实验结果

研究问题

• RQ1 如何从显著低于奈奎斯特速率的非均匀采样中重建多带信号？
• RQ2 何种采样模式参数可使条件数最小化，并在噪声存在下提升重建精度？
• RQ3 在宽带谱感知中，如何从压缩采样中可靠估计未知信号频带位置？
• RQ4 在谱未知的情况下，哪些模型阶数选择技术能有效识别活跃信号频带的数量？
• RQ5 非均匀采样在认知无线电应用中，能在多大程度上降低采样率，同时保持信号保真度？

主要发现

• 所提出的非均匀采样方法可在远低于奈奎斯特速率的采样率下，实现多带信号的精确重建。
• 条件数较低的采样模式显著提升了重建质量，尤其在噪声环境下表现更优。
• 基于子空间的方法与非线性最小二乘法能有效从压缩采样中估计未知信号频带位置。
• 信息论准则（AIC与MDL）在确定活跃频带数量方面提供了可靠的模型阶数选择。
• 指数拟合检验通过高精度检测谱分量，补充了模型阶数选择。
• 该框架实现了认知无线电中高效宽带谱感知，显著降低了硬件复杂度与计算负载。