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.

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.