Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Cognitive Networks
Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Cognitive Networks
复制标题
认知网络中分布式信号检测的分散特征值算法
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
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-称为分散功率方法（DPM）和分散Lanczos算法(DLA) -用于无线网络上样本协方差矩阵的一个（最大）或多个特征值的分布式计算。本文提出的算法基于矩阵-向量积和内向量积计算的顺序平均共识步骤，首先证明了在精确分布式共识的情况下，算法与集中式算法等效。然后，导出了两种算法的非理想一致性误差的封闭表达式。在一定条件下，DPM的误差在一致性误差序列上渐近消失。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，几乎所有在文献中提出的基于特征值的测试都可以在使用DPM或DLA的分布式设置中实现。仿真结果验证了所提算法在实际情况下（大规模网络、少量样本和有限迭代次数）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 non-ideal 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).