Related papers: Bounds on Eigenvalues of a Spatial Correlation Mat…
We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
The extreme eigenvalues of adjacency matrices are important indicators on the influences of topological structures to collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme…
Movable antenna (MA) systems have emerged as a promising technology for future wireless communication systems. The movement of antennas gives rise to mutual coupling (MC) effects, which have been previously ignored and can be exploited to…
Massive spatial modulation aided multiple-input multiple-output (SM-MIMO) systems have recently been proposed as a novel combination of spatial modulation (SM) and of conventional massive MIMO, where the base station (BS) is equipped with a…
The proliferation of large multi-antenna configurations operating in high frequency bands has recently challenged the conventional far-field, rich-scattering paradigm of wireless channels. Extra large antenna arrays must usually work in the…
In this paper, we analyze the large n-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three distinct eigenvalues are $-a,0,a$. For the case $a^2>3$, we…
This study investigates the mean capacity of multiple-input multiple-output (MIMO) systems for spatially semi-correlated flat fading channels. In reality, the capacity degrades dramatic due to the channel covariance (CC) when correlations…
This work considers an uplink wireless communication system where multiple users with multiple antennas transmit data frames over dynamic channels. Previous studies have shown that multiple transmit and receive antennas can substantially…
To explore the full potential of ultra-massive multiple-input multiple-output (MIMO) communication systems, it is fundamental to understand new ultra-massive MIMO channel characteristics and establish pervasive channel models. On this…
The analytic expression of CRLB and the maximum likelihood estimator for spatial correlation matrices in time-varying multipath fading channels for MIMO OFDM systems are reported in this paper. The analytical and numerical results reveal…
In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization…
This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matrix sum is dominated by the maximum eigenvalue of a Gaussian…
We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random…
We study the maximal number of pairwise distinct columns in a $\Delta$-modular integer matrix with $m$ rows. Recent results by Lee et al. provide an asymptotically tight upper bound of $O(m^2)$ for fixed $\Delta$. We complement this and…
This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…
The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms,…