Secure Full-Duplex Small-Cell Networks in a Spectrum Sharing Environment

In this paper, we propose three relay selection schemes for full-duplex heterogeneous networks in the presence of multiple cognitive radio eavesdroppers. In this setup, the cognitive small-cell nodes (secondary network) can share the spectrum licensed to the macro-cell system (primary network) on the condition that the quality-of-service of the primary network is always satisfied subjected to its outage probability constraint. The messages are delivered from one small-cell base station to the destination with the help of full-duplex small-cell base stations, which act as relay nodes. Based on the availability of the network’s channel state information at the secondary information source, three different selection criteria for full-duplex relays, namely: 1) partial relay selection; 2) optimal relay selection; and 3) minimal self-interference relay selection, are proposed. We derive the exact closed-form and asymptotic expressions of the secrecy outage probability for the three criteria under the attack of non-colluding/colluding eavesdroppers. We demonstrate that the optimal relay selection scheme outperforms the partial relay selection and minimal self-interference relay selection schemes at the expense of acquiring full channel state information knowledge. In addition, increasing the number of the full-duplex small-cell base stations can improve the security performance. At the illegitimate side, deploying colluding eavesdroppers and increasing the number of eavesdroppers put the confidential information at a greater risk. Besides, the transmit power and the desire outage probability of the primary network have great influences on the secrecy outage probability of the secondary network. 

Reversibility Iteration Method to Understand Reaction Networks and to Solve Micro-Kinetics in Heterogeneous Catalysis

Solving microkinetics of catalytic systems, which bridges microscopic processes and macroscopic reaction rates, is currently vital for understanding catalysis in silico. However, traditional microkinetic solvers possess several drawbacks that make the process slow and unreliable for complicated catalytic systems. In this paper, a new approach, the so-called reversibility iteration method (RIM), is developed to solve microkinetics for catalytic systems. Using the chemical potential notation we previously proposed to simplify the kinetic framework, the catalytic systems can be analytically illustrated to be logically equivalent to the electric circuit, and the reaction rate and coverage can be calculated by updating the values of reversibilities. Compared to the traditional modified Newton iteration method (NIM), our method is not sensitive to the initial guess of the solution and typically requires fewer iteration steps. Moreover, the method does not require arbitrary-precision arithmetic and has a higher probability of successfully solving the system. These features make it ∼1000 times faster than the modified Newton iteration method for the systems we tested. Moreover, the derived concept and the mathematical framework presented in this work may provide new insight into catalytic reaction networks.