Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Wireless Networks
Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Wireless Networks
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DOI：
10.1109/tsp.2014.2373334
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发表时间：
2015
影响因子：
5.4
通讯作者：
F. Penna;S. Stańczak
中科院分区：
文献类型：
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作者：
F. Penna;S. Stańczak
在本文中，我们推导并分析了两种算法 - 称为分散功率法（DPM）和分散 Lanczos 算法（DLA） - 用于在无线网络上分布式计算样本协方差矩阵的一个（最大）或多个特征值。所提出的算法基于用于计算矩阵向量乘积和内部向量乘积的顺序平均共识步骤，首先表明在精确分布式共识的情况下与集中式算法等效。然后，为两种算法导出由非理想共识引入的误差的封闭式表达式。在共识错误序列上的给定条件下，DPM 的错误被证明渐近消失。最后，我们考虑了认知无线电网络中频谱感知的应用，并且我们表明，实际上文献中提出的所有基于特征值的测试都可以使用 DPM 或 DLA 在分布式环境中实现。仿真结果验证了所提出的算法在实际感兴趣的条件（大规模网络、少量样本和有限迭代次数）下的有效性。
In this paper, we derive and analyze two algorithms - referred to as decentralized power method (DPM) and decentralized Lanczos algorithm (DLA) - for distributed computation of one (the largest) or multiple eigenvalues of a sample covariance matrix over a wireless network. The proposed algorithms, based on sequential average consensus steps for computations of matrix-vector products and inner vector products, are first shown to be equivalent to their centralized counterparts in the case of exact distributed consensus. Then, closed-form expressions of the error introduced by nonideal consensus are derived for both algorithms. The error of the DPM is shown to vanish asymptotically under given conditions on the sequence of consensus errors. Finally, we consider applications to spectrum sensing in cognitive radio networks, and we show that virtually all eigenvalue-based tests proposed in the literature can be implemented in a distributed setting using either the DPM or the DLA. Simulation results are presented that validate the effectiveness of the proposed algorithms in conditions of practical interest (large-scale networks, small number of samples, and limited number of iterations).