State estimation, which computes the best possible approximation for the system state based on the perceived information transmitted from sensors to the estimators, is vital for control system performance in industrial cyber-physical systems (ICPSs) with the integrated techniques of control, communication and computing. Thus the performance of state estimation relies on the communication reliability. In order to improve the reliability, redundant channels/slots are reserved for the data transmission in industrial wireless techniques, such as WirelessHART. However, the redundancy scheme burdens the increasingly over-crowded ISM spectrum band due to the envisioned emerging ubiquitous industrial wireless monitoring in the architecture of ICPS in the near future. The cognitive radio (CR) technology can intelligently explore the available spectrum opportunities on licensed channels, and it motivates this paper to consider the redundant transmission through the opportunistically available licensed channels to guarantee the transmission reliability for state estimation. Unfortunately, spectrum sensing takes extra energy consumption, thus it is necessary to take into account the energy efficiency for the battery-powered IWSN. Then a CR enabled energy-efficiency maximization problem is formulated by regarding the convergence of state estimation as a constraint of the resource allocation problem. In order to solve the non-convex and mixed integer programming, the Dinkelbach and Lagrangian relaxation techniques are adopted to transform the problem into a convex programming and furthermore reduce the computational complexity. Numerical results demonstrate that the CR technology can significantly release the spectrum for the redundancy design from the ISM band while guarantee the reliability for the effective state estimation.
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