Compressed spectrum sensing naturally pursues the use of fewer sampling resources to achieve spectrum support reconstruction and signal recovery. The theoretical lower boundary of averaging sampling rate to recover the multiband signal has been proved to be twice the Landau rate. However, it is still unreachable in practice. Based on the multicoset sampling architecture, this paper analyzes the influencing factors on perfect spectrum reconstruction from three aspects: data model, sampling pattern and greedy reconstruction algorithms, for which practical and feasible optimization schemes are proposed. To reduce redundant reconstruction for the multiple measurement vectors (MMV) signal model, a block MMV model is proposed to improve the accuracy in the spectrum support set reconstruction process. A sampling pattern selection algorithm is proposed to ensure a higher success rate of the spectrum support reconstruction to optimize the sensing matrix. We also deduced the representation of the signal and noise energy in the reconstructed spectrum based on the mathematical model of compressed sensing. We thus proposed a non-orthogonal double-threshold matching pursuit algorithm to avoid a high false-alarm rate due to the manually set converging conditions for matching pursuit algorithms. Numerical experiments on real-world wideband signals are carried out to demonstrate the feasibility and advantages of the proposed approaches. With integrated optimization, the required sampling density to ensure perfect reconstruction is approaching the sub-Nyquist sampling boundary.

中文翻译：

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逼近亚奈奎斯特边界：基于多陪集采样器的多波段信号优化压缩频谱感知

压缩频谱感知自然追求使用更少的采样资源来实现频谱支持重构和信号恢复。已证明平均采样率恢复多频带信号的理论下限是朗道率的两倍。但是，在实践中仍然无法实现。基于多集合采样架构，从数据模型、采样模式和贪心重构算法三个方面分析了完美谱重构的影响因素，提出了切实可行的优化方案。为了减少多测量向量（MMV）信号模型的冗余重构，提出了一种块MMV模型来提高频谱支持集重构过程的准确性。提出了一种采样模式选择算法，以确保频谱支持重构的成功率更高，以优化感知矩阵。我们还基于压缩感知的数学模型推导出了重建频谱中信号和噪声能量的表示。因此，我们提出了一种非正交双阈值匹配追踪算法，以避免由于手动设置匹配追踪算法的收敛条件而导致的高误报率。对现实世界的宽带信号进行了数值实验，以证明所提出方法的可行性和优势。通过集成优化，确保完美重建所需的采样密度正在接近亚奈奎斯特采样边界。