Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.

Spectral graph theory gives an algebraic approach to the analysis of the dynamics of a network by using the matrix that represents the network structure. However, it is not easy for social networks to apply the spectral graph theory because the matrix elements cannot be given exactly to represent the structure of a social network. The matrix element should be set on the basis of the relationship between persons, but the relationship cannot be quantified accurately from obtainable data (e.g., call history and chat history). To get around this problem, we utilize the universality of random matrices with the feature of social networks. As such a random matrix, we use the normalized Laplacian matrix for a network where link weights are randomly given. In this paper, we first clarify that the universality (i.e., the Wigner semicircle law) of the normalized Laplacian matrix appears in the eigenvalue frequency distribution regardless of the link weight distribution. Then, we analyze the information propagation speed by using the spectral graph theory and the universality of the normalized Laplacian matrix. As a result, we show that the worst-case speed of the information propagation changes up to twice if the structure (i.e., relationship among people) of a social network changes.

In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.

Random beamforming(RBF) is a simple and practical method that can realize multi-user multi-input multi-output (MU-MIMO) systems. In this letter, we analyze the average sum rate of RBF with minimum mean squared error (MMSE) receive beamforming. To this end, we exploit the empirical eigenvalue distribution [5] and extreme value theory. The numerical verification shows that the proposed analysis provides a good approximation of the average sum rate of RBF even for the small number of antennas.

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 letter focuses on the simplified capacity evaluation for the downlink of a distributed antenna system (DAS) with random antenna layout. Based on system scale-up, we derive a good approximation of the downlink capacity by developing the results from random matrix theory. We also propose an iterative method to calculate the unknown parameters in the approximated expression of the downlink capacity. The approximation is illustrated to be quite accurate and the iterative method is shown to be quite efficient by Monte Carlo simulations.

Owing to frequency diversity gain and simplicity, a chip interleaved multi-carrier code division multiple access (MC-CDMA) system has been considered in a multi-cell environment, and combining it with multiple input multiple output (MIMO) schemes offers high spectral efficiency. In spite of the advantages, the system is highly affected by inter code interferences. To control them, this letter analyzes the asymptotic performance of a MIMO MC-CDMA system with a symbol level MMSE receiver in a multi-cell environment and presents an appropriate multiplexed code ratio satisfying a required error rate.

In this letter, we investigate the sum-rate capacity of a power-controlled multi-user distributed antenna system (DAS) with antennas deployed symmetrically on a circle. The sum-rate capacity, when divided by user number, is proved to converge to an explicit expression as user number and antenna number go to infinity with a constant ratio. We further show how this theoretical result can be used to optimize antenna deployment. Simulation results are also provided to demonstrate the validity of our analysis and the applicability of the asymptotic results to a small-scale system.