Is theoretical physics the same thing as mathematics?

Xin Fan, Yan Huo

As Internet of Things (IoT) has boomed in recent years, many security issues have also been exposed. Focusing on physical layer security in wireless Internet of Things network communication, a series of security methods have been widely studied. Nevertheless, cooperative jamming methods in physical layer security to fight against collusive eavesdroppers have not been thoroughly studied yet. In this article, we study a cooperative-jamming-based physical layer secure transmission scheme for Internet of Things wireless networks in the presence of collusive eavesdroppers. We design a cooperative jamming strategy without knowing the channel state information of eavesdroppers. Considering the cooperation of multiple nodes with multiple antennas, this strategy can maximize the signal-to-interference-plus-noise ratio at an actuator (legitimate receiver). Meanwhile, the generated cooperative jamming signals can reduce the signal-to-interference-plus-noise ratio at eavesdroppers. To explore the theoretical security performance of our strategy, we perform a secrecy outage probability analysis and an asymptotic analysis. In the cases of cooperative jamming and without cooperative jamming, the closed-form expressions of the secrecy outage probability are deduced, and the influence of system parameters on the secrecy outage probability becomes more intuitive through a strict mathematical asymptotic behavior analysis. In addition, considering the energy limitation of Internet of Things devices, we propose a power allocation algorithm to minimize the total transmission power given the security requirements. The numerical results show the effectiveness of our schemes and are consistent with the theoretical analysis.

Gerard ’t Hooft

Karl K. Darrow

MORE than any other word of the language, the word atom is implicated with the history of human speculations concerning the nature uf things. It is introduced when people cease to content themselves with observing, and begin to philosophize. There are many of the fundamental and essential writings of the literature of physics in which it does not appear, or appears without warrant. These are the descriptions of things observed, the accounts of experiments, the records of measurements, on which the edifice of theoretical physics is founded. There are many articles of what is commonly called the “theoretical” sort in which it does not occur. Such are the papers on the motions of planets, on the vibrations of elastic solids, on the currents in electrical networks, on the courses of light-rays through optical systems-papers which are essentially descriptions, although they give the impression of being something greater and deeper because they relate to idealized cases, and are phrased in the laconic language of mathematics. When the word atom appears justifiably in a discourse, it means that the author has departed from the safe routine of describing observed and observable events, however selectively, however skilfully, however intelligently. It signifies that he has gone beyond the limits of observation, and has entered upon the audacious adventure of constructing by the side of the real universe an ideal one, which shall act as the real one does, and be intelligible through and through.

Charles Harding

Xin Fan, Yan Huo

With the great-leap-forward development of Internet of Things (IoT), it is extremely important to study secure wireless transmission for IoT systems. A cooperative jamming (CJ) strategy has been extensively studied to enhance physical layer security in IoT systems. However, CJ's secrecy performance has not been well studied in the scenario of collusive eavesdroppers. In this paper, we propose a CJ scheme for IoT systems to fight against multiple passive and collusive eavesdroppers of unknown channel state information. Considering nodes with multi-antenna in an IoT system, we design beamforming vectors to maximize signal-to- interference-plus-noise ratio (SINR) of the wireless link from a controller (transmitter) to an actuator (receiver). Under the worst-case assumption that eavesdroppers can aggregate all signals to enhance their eavesdropping abilities, we derive the closed- form expressions of the secrecy outage probability (SOP) with and without CJ. In addition, we employ a strict mathematical asymptotic analysis to provide insights into the effects of various system parameters on the SOP. Numerical results verify that the CJ scheme can effectively prevent eavesdropping and the effects of system parameters on SOP is consistent with theoretical analytical results.

Charles Harding