The problem of wideband spectrum sensing/sampling in the sub-Nyquist domain is solved in this paper using sparse (low-density) binary-valued measurement matrices. Key objectives are (i) to achieve an efficient compression ratio, and (ii) improve the signal reconstruction performance. We propose a novel RF front-end with parallel branches that we have called Low-Density Wideband Converter (LDWC). We show that the LDWC implements a binary Low-Density Parity Check (LDPC) matrix as the compressive sensing (CS) measurement matrix. We evaluate, using an Information-Theoretic approach, the asymptotic bound on the required number of LDWC parallel branches for sparsity detection. We develop two new belief propagation (BP) algorithms that operate on the Tanner graph of the CS measurements. We have derived the first algorithm by assuming independence among the variable nodes (VNs) of the Tanner graph. For the second method, we have accounted for the joint probability distribution of the VNs. Analytical and simulated performance results prove the concepts of the LDWC and the proposed BP algorithms and quantify the attainment of objectives (i) and (ii) stated above.

中文翻译：

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使用低密度测量矩阵对稀疏宽带信号进行亚奈奎斯特频谱感测

本文使用稀疏（低密度）二进制值测量矩阵解决了亚奈奎斯特域中的宽带频谱感测/采样问题。关键目标是 (i) 实现有效的压缩比，以及 (ii) 提高信号重建性能。我们提出了一种具有并行分支的新型 RF 前端，我们将其称为低密度宽带转换器 (LDWC)。我们展示了 LDWC 实现了二进制低密度奇偶校验 (LDPC) 矩阵作为压缩感知 (CS) 测量矩阵。我们使用信息理论方法评估了稀疏检测所需的 LDWC 并行分支数量的渐近边界。我们开发了两种新的置信传播 (BP) 算法，它们在 CS 测量的 Tanner 图上运行。我们通过假设 Tanner 图的变量节点 (VN) 之间的独立性来推导出第一个算法。对于第二种方法，我们已经考虑了 VN 的联合概率分布。分析和模拟的性能结果证明了 LDWC 和提议的 BP 算法的概念，并量化了上述目标 (i) 和 (ii) 的实现。