Free probability theory, which has become a main branch of random matrix theory, is a valuable tool for describing the asymptotic behavior of multiple systems, especially for large matrices. In this paper, using asymptotic free probability theory, a new cooperative scheme for spectrum sensing is proposed, which shows how the asymptotic free behavior of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for cognitive radio. Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance than the energy detection techniques and the Maximum-minimum eigenvalue (MME) scheme even for the case of a small sample of observations.

Based on Free Probability Theory (FPT), which has become an important branch of Random Matrix Theory (RMT), a new scheme of frequency band sensing for Cognitive Radio (CR) in Direct-Sequence Code-Division Multiple-Access (DS-CDMA) multiuser network is proposed. Unlike previous studies in the field, the new scheme does not require the knowledge of the spreading sequences of users and is related to the behavior of the asymptotic free behavior of random matrices. Simulation results show that the asymptotic claims hold true even for a small number of observations (which makes it convenient for time-varying topologies) outperforming classical energy detection scheme and another scheme based on random matrix theory.

This paper addresses the issue of transmission scheduling in wireless ad hoc networks. We propose a Time Division Multiple Access (TDMA) scheduling scheme based on edge coloring and probabilistic assignment, called CP-TDMA. We categorize the conflicts suffered by wireless links into two types: explicit conflicts and implicit conflicts, and utilize two different strategies to deal with them. Explicit conflicts are avoided completely by a simple distributed edge-coloring algorithm µ-M, and implicit conflicts are minimized by applying probabilistic time slot assignments to links. We evaluate CP-TDMA analytically and numerically, and find that CP-TDMA, which requires only local information exhibits a better performance than previous work.

The statistical properties of insertion losses and return losses for optical connectors are investigated theoretically using the probability theory and the Monte Carlo simulation. Our investigation is focused on an orientation method for reducing insertion loss by which a fiber-core center is adjusted in a region of within a certain angle to the positioning key direction. It is demonstrated that the method can significantly improve insertion losses, and that an adjusting operation angle of 90 degrees is sufficient to realize an insertion loss of less than 0.5 dB with 99% cumulative probability. Good agreement was obtained between the theoretical distribution and the experimental results for single-mode fiber connection. Consequently, it is indicated that the statistical distributions of insertion losses and return losses of optical connectors in the field can be predicted theoretically from the values measured in the factory by connection to a master connector.