Related papers: Spectra of large block matrices

In this work, a new energy-efficiency performance metric is proposed for MIMO (multiple input multiple output) point-to-point systems. In contrast with related works on energy-efficiency, this metric translates the effects of using finite…

The reflection matrix R=S^{\dagger}S, with S being the scattering matrix, differs from the unit one, when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the…

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…

Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable…

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…

This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from…

Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We…

Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…

The block maximum method, which is widely used in extreme value analysis, uses a generalized extreme value distribution to approximate that of the maximum of m observations. The quality of this approximation depends on the value of m and…

This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.

We study the determination problem of the channel capacity for the discrete memoryless channels in the finite blocklength regime. We derive explicit lower and upper bounds of the capacity. We shall demonstrate that the information spectrum…

We investigate the problem of multi-hop scheduling in self-backhauled millimeter wave (mmWave) networks. Owing to the high path loss and blockage of mmWave links, multi-hop paths between the macro base station and the intended users via…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused at the distribution close to its…

Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in…

Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…

This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions…

The possibility of flexibly assigning spectrum resources with channels of different sizes greatly improves the spectral efficiency of optical networks, but can also lead to unwanted spectrum fragmentation.We study this problem in a scenario…

We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a…

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…