Abstract
In order to protect the distributed network from complex-valued attack, a secure diffusion augmented complex-valued normalized subband adaptive filter algorithm is proposed in this article, which is derived from a novel complex-valued detection method. This complex-value detection method can be considered to consist of two parts. First, a non-cooperative augmented complex-valued normalized subband adaptive filter algorithm is used to provide reliable reference estimations under complex-valued attacks, and then the threshold test is constructed by using the reliable reference estimations to detect the trustworthy neighbors of each node. The second part is to reassemble the information from the trustworthy neighbors by using the diffusion augmented complex-valued normalized subband adaptive filter algorithm. Then, the theoretical analyses of the mean and mean-square performance of the proposed algorithm are derived based on the energy conservation framework. Finally, some experiments are performed to show the effectiveness of the proposed algorithm under non-time-varying and time-varying complex-valued attacks, respectively.
Highlights
R ECENT advancements in wireless sensor networks (WSNs) have shown that it is an attractive and challenging research area
The distributed strategies for data processing over networks can be divided into incremental strategy, consensus strategy and diffusion strategy [4]
Since the incremental strategy requires a cyclic path that runs across the nodes to obtain the parameter estimation, it is sensitive to the link failures
Summary
R ECENT advancements in wireless sensor networks (WSNs) have shown that it is an attractive and challenging research area. To give a good estimation performance over WSNs in the presence of circular or noncircular complexvalued attacks, a novel detection method is proposed, and a secure diffusion augmented complex-valued normalized subband adaptive filter (SD-ACNSAF) algorithm is derived. 1) By using a novel threshold test, the SD-ACNSAF algorithm is proposed for protecting distributed network from complex-valued attacks. To make full use of the available second-order information, a novel detection method suitable for complex-valued signals is proposed to detect the circular and noncircular attacks in the following part. The reference vectors can be considered as reliable value for detecting whether the network is attacked or not (The detailed explanation is given in Appendix). In order to reduce the probability of occurrence of the above situation, the thresholds γk(n) and εk(n) are all initialized to 0
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