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Complex field network coding (CFNC) enables signal transmission and information fusion to be operated over nonorthogonal channels, which essentially improves both the bandwidth efficiency and transmission reliability of the wireless sensor networks (WSNs). This paper investigates the power allocation for the CFNC assisted WSNs. By improving the accuracy of the approximation for Q function, the closed-form expression of the pairwise error probability bound for the considered network is derived, so as to improve the optimization efficiency of the power allocation. On the basis of the expression, the relay power coefficient is optimized under the fixed power constraint. Besides, the impacts of the topology parameters on the power allocation are also analyzed accordingly. Simulations demonstrate that the proposed power allocation outperforms the benchmark in terms of the detection performance. The obtained expression of the power coefficient and insights can provide useful suggestions for the power allocation design of the CFNC assisted WSNs

Optimal Distributed Detection for Complex Field Network Coding Assisted Wireless Sensor Networks with Nonorthogonal Communications