Related papers: Spectra of large block matrices
A Wishart matrix is said to be spiked when the underlying covariance matrix has a single eigenvalue $b$ different from unity. As $b$ increases through $b=2$, a gap forms from the largest eigenvalue to the rest of the spectrum, and with…
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance…
This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input…
We present a novel block reduction method for the study of a general class of random band matrices (RBM) defined on the $d$-dimensional lattice $\mathbb{Z}_{L}^d:=\{1,2,\ldots,L\}^{d}$ for $d\in \{1,2\}$, with band width $W$ and an almost…
This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…
We derive novel bounds for the performance of algorithms that estimate the downlink covariance matrix from the uplink covariance matrix in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. The focus is…
A block Markov chain is a Markov chain whose state space can be partitioned into a finite number of clusters such that the transition probabilities only depend on the clusters. Block Markov chains thus serve as a model for Markov chains…
This paper addresses channel estimation and data equalization on frequency-selective 1-bit quantized Multiple Input-Multiple Output (MIMO) systems. No joint processing or Channel State Information is assumed at the transmitter, and…
A positive semidefinite Toeplitz matrix, which often arises as the finite covariance matrix of a stationary random process, can be decomposed as the sum of a nonnegative multiple of the identity corresponding to a white noise, and a…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
This paper investigates the capacity scaling of multicell massive MIMO systems in the presence of spatially correlated fading. In particular, we focus on the strong spatial correlation regimes where the covariance matrix of each user…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…
We consider the channel acquisition problem for a wideband terahertz (THz) communication system, where an extremely large-scale array is deployed to mitigate severe path attenuation. In channel modeling, we account for both the near-field…
We derive the limiting distribution for the largest eigenvalues of the adjacency matrix for a stochastic blockmodel graph when the number of vertices tends to infinity. We show that, in the limit, these eigenvalues are jointly multivariate…
This letter proposes an energy efficient distributed worst case robust power allocation in massive multiple input multiple output (MIMO) system. We assume a bounded channel state information (CSI) error and all channels lie in some bounded…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes…
Let $f=(f_1,\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda\in\mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\mathbb{C}^n\backslash\{0\}$ with $f(v)=\lambda v$,…
We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of $C$ are independent and…