This article tackles the topic of performance analysis for Spectrum Sensing based on Compressive Sampling (CS). More precisely, the lower bound on the variance of any unbiased estimator, the Cramér-Rao Bound (CRB), is investigated in the context of spectral parametric estimation. Compressed samples are obtained from a multiband architecture like the Modulated Wideband Converter, the Quadrature-Analog-to-Information Converter or the Periodic Non Uniform Sampler. An expression of the Fisher information matrix, which allows to compute the CRB, is established for a compressive multiband architecture assuming a disjoint spectral subband model. The relationships between Fisher matrices in a generic framework are exposed: first between compressive multiband and subsampling architectures, then between subsampling and Nyquist sampling architectures. Based on these new considerations, the issue of interferer detection, a canonical case and also a huge thorn in the side of wideband radiofrequency receivers is tackled. A benchmark between Nyquist, Subsampling and Compressive Multiband Sampling approaches is provided for frequency and amplitude estimation of dual-tone signals. This analysis illustrates the way in which interferences between parameters occur in estimation with Compressive Sampling. It is then shown how properties of the sensing matrix for popular compressive architectures enable to control the precision of spectral parametric estimation in specific subbands. This control opportunity opens the door to adaptive methods.

本文解决基于压缩采样（CS）的频谱感知性能分析的主题。更准确地说，在频谱参数估计的背景下研究了任何无偏估计量Cramér-RaoBound（CRB）的方差下限。压缩样本是从多频带体系结构中获得的，例如调制宽带转换器，正交模拟-信息转换器或周期性非均匀采样器。对于假设不相交的频谱子带模型的压缩多带体系结构，建立了允许计算CRB的Fisher信息矩阵的表达式。公开了通用框架中Fisher矩阵之间的关系：首先在压缩多频带与子采样体系结构之间，然后在子采样与Nyquist采样体系结构之间。基于这些新的考虑，解决了干扰源检测，规范案例以及宽带射频接收器方面的巨大难题。提供了Nyquist，二次采样和压缩多频带采样方法之间的基准，用于双音信号的频率和幅度估计。该分析说明了使用压缩采样进行估计时参数之间发生干扰的方式。然后示出了用于流行的压缩架构的感测矩阵的属性如何使得能够控制特定子带中的频谱参数估计的精度。这种控制机会为适应性方法打开了大门。提供了Nyquist，二次采样和压缩多频带采样方法之间的基准，用于双音信号的频率和幅度估计。该分析说明了使用压缩采样进行估计时参数之间发生干扰的方式。然后示出了用于流行的压缩架构的感测矩阵的属性如何使得能够控制特定子带中的频谱参数估计的精度。这种控制机会为适应性方法打开了大门。提供了Nyquist，二次采样和压缩多频带采样方法之间的基准，用于双音信号的频率和幅度估计。该分析说明了使用压缩采样进行估计时参数之间发生干扰的方式。然后示出了用于流行的压缩架构的感测矩阵的属性如何使得能够控制特定子带中的频谱参数估计的精度。这种控制机会为适应性方法打开了大门。然后示出了用于流行的压缩架构的感测矩阵的属性如何使得能够控制特定子带中的频谱参数估计的精度。这种控制机会为适应性方法打开了大门。然后示出了用于流行的压缩架构的感测矩阵的属性如何使得能够控制特定子带中的频谱参数估计的精度。这种控制机会为适应性方法打开了大门。