Related papers: Quickest Eigenvalue-Based Spectrum Sensing using R…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form…
We study community detection in the \emph{symmetric $k$-stochastic block model}, where $n$ nodes are evenly partitioned into $k$ clusters with intra- and inter-cluster connection probabilities $p$ and $q$, respectively. Our main result is a…
This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M xK MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated…
Spectrum Sensing (SS) is one of the most challenging issues in Cognitive Radio (CR) systems. Cooperative Spectrum Sensing (CSS) is proposed to enhance the detection reliability of a Primary User (PU) in fading environments. In this paper,…
Quantum two-mode squeezing (QTMS) radars and noise radars detect targets by correlating the received signal with an internally stored recording. A covariance matrix can be calculated between the two which, in theory, is a function of a…
We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM…
Accurate detection of signal components is a frequently-encountered challenge in statistical applications with low signal-to-noise ratio. This problem is particularly challenging in settings with heteroscedastic noise. In certain…
Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the…
Spectrum sensing (SS) in cognitive radio (CR) systems is of paramount importance to approach the capacity limits for the Secondary Users (SU), while ensuring the undisturbed transmission of Primary Users (PU). In this paper, we formulate a…
We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $(…
Spectral clustering is one of the most popular algorithms for community detection in network analysis. Based on this rationale, in this paper we give the convergence rate of eigenvectors for the adjacency matrix in the $l_\infty$ norm,…
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…
Recently there has been many works on adaptive subspace filtering in the signal processing literature. Most of them are concerned with tracking the signal subspace spanned by the eigenvectors corresponding to the eigenvalues of the…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…
In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…
We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…
The subspace-based techniques are widely utilized in various scientific fields, and they need accurate estimation of the signal subspace dimension. The classic RMT estimator for model order estimation based on random matrix theory assumes…
We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A noise-uncertainty-free detector that is optimal in the low signal to noise ratio regime is analyzed in such a…