认知网络中分布式信号检测的分散特征值算法
Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Cognitive Networks
摘要：
在本文中，我们推导和分析两种算法-被称为分散功率法（DLA）和分散Lanczos算法（DLA）-分布式计算的一个（最大的）或多个特征值的样本协方差矩阵在无线网络上。所提出的算法，基于顺序平均共识步骤的矩阵向量产品和内部向量产品的计算，首先被证明是等同于他们的集中式同行的情况下，确切的分布式共识。然后，非理想的共识所引入的误差的封闭形式的表达式推导出这两种算法。在给定的条件下，一致性误差序列的误差渐近消失。最后，我们考虑在认知无线电网络中的频谱感知的应用程序，我们表明，几乎所有的文献中提出的基于特征值的测试可以实现在分布式设置中使用的DLA或DLA。仿真结果验证了所提出的算法的有效性，在实际感兴趣的条件下（大规模网络，小样本数，有限的迭代次数）。
英文摘要：
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).
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