Secrecy Capacity Analysis of 4-WFRFT Based Physical Layer Security in MIMO System

The traditional information security based on cryptosystem is seriously threatened due to the exponential growth of computing capacity. In order to improve for the upper cryptosystem security, the secure transmission at the physical layer is introduced into the wireless communication system. However, considering the openness of wireless channel, the performance analysis of security wireless communication systems has become a hot issue in recent years. Due to the existence of the upper layer cryptosystem being cracked and the openness of wireless channel security problems, the Multiple-Input Multiple-Output (MIMO) technology increases the difference between channels, the development of its rich spatial degrees of freedom can greatly improve the channel capacity and achieve the purpose of enhancing the Physical layer security (PLS); On this basis, Weighted Type Fractional Fourier Transform (WFrFT) technology rotates and splits the constellation points of signals, it is equivalent to increasing the artificial noise to enhance the PLS. The Average security capacity is an important index to measure the PLS, Therefore, this paper deduces the Average security capacity in MIMO scenario and gives a specific closed expression when considering the channel correlation. By analyzing the expression, the increase of the number of MIMO antennas will improve the Average security capacity. When the estimated bias is 1 in 4-WFRFT, the Average security capacity will be significantly improved; the Average security capacity will reach the maximum value, thus enhancing the PLS.

Picture Fuzzy Interactional Aggregation Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making

The picture fuzzy set, characterized by three membership degrees, is a helpful tool for multi-criteria decision making (MCDM). This paper investigates the structure of the closed operational laws in the picture fuzzy numbers (PFNs) and proposes efficient picture fuzzy MCDM methods. We first introduce an admissible order for PFNs and prove that all PFNs form a complete lattice under this order. Then, we give some specific examples to show the non-closeness of some existing picture fuzzy aggregation operators. To ensure the closeness of the operational laws in PFNs, we construct a new class of picture fuzzy operators based on strict triangular norms, which consider the interaction between the positive degrees (negative degrees) and the neutral degrees. Based on these new operators, we obtain the picture fuzzy interactional weighted average (PFIWA) operator and the picture fuzzy interactional weighted geometric (PFIWG) operator. They are proved to be monotonous, idempotent, bounded, shift-invariant, and homogeneous. We also establish a novel MCDM method under the picture fuzzy environment applying PFIWA and PFIWG operators. Furthermore, we present an illustrative example for a clear understanding of our method. We also give the comparative analysis among the operators induced by six classes of famous triangular norms.