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Wireless Compressive Sensing Over Fading Channels With Distributed Sparse Random Projections

机译:分布稀疏随机投影的衰落信道上的无线压缩感测

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We address the problem of recovering a sparse signal observed by a resource constrained wireless sensor network with fading channels. Sparse random matrices are exploited to reduce the communication cost in forwarding information to a fusion center. The presence of channel fading leads to inhomogeneity and non-Gaussian statistics in the effective measurement matrix that relates the measurements collected at the fusion center and the sparse signal being observed. We analyze the impact of channel fading on recovery of a given sparse signal by leveraging the properties of heavy-tailed random matrices. We quantify the additional number of measurements required to ensure reliable signal recovery in the presence of nonidentical fading channels compared to that is required with identical Gaussian channels. Our analysis provides insights into how to control the probability of sensor transmissions at each node based on the channel fading statistics to minimize the number of measurements collected at the fusion center for reliable sparse signal recovery. We further discuss recovery guarantees of a given sparse signal with any random projection matrix where the elements are subexponential with a given subexponential norm. Numerical results are provided to corroborate the theoretical findings.
机译:我们解决了恢复具有衰落信道的资源受限无线传感器网络观察到的稀疏信号的问题。利用稀疏随机矩阵来减少将信息转发到融合中心时的通信成本。信道衰落的存在导致有效测量矩阵中的不均匀性和非高斯统计,该矩阵将在融合中心收集的测量结果与所观察到的稀疏信号相关联。我们通过利用重尾随机矩阵的属性来分析信道衰落对给定稀疏信号恢复的影响。与相同的高斯信道相比,我们量化了在不相同的衰落信道下确保可靠信号恢复所需的额外测量数量。我们的分析提供了有关如何基于信道衰落统计信息来控制每个节点处传感器传输概率的见解,以最小化在融合中心收集的测量数量,从而实现可靠的稀疏信号恢复。我们进一步讨论具有任意随机投影矩阵的给定稀疏信号的恢复保证,其中元素是给定次指数范数的次指数。提供数值结果以证实理论发现。

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