arXiv subjects

Andrea Giorgetti

Publications and source records attributed to Andrea Giorgetti.

21 records · Page 2Linked to original sources

arXiv2019

Model Order Selection Based on Information Theoretic Criteria: Design of the Penalty

Information theoretic criteria (ITC) have been widely adopted in engineering and statistics for selecting, among an ordered set of candidate models, the one that better fits the observed sample data. The selected model minimizes a penalized likelihood metric, where the penalty is determined by the criterion adopted. While rules for choosing a penalty that guarantees a consistent estimate of the model order are known, theoretical tools for its design with finite samples have never been provided in a general setting. In this paper, we study model order selection for finite samples under a design perspective, focusing on the generalized information criterion (GIC), which embraces the most common ITC. The theory is general, and as case studies we consider: a) the problem of estimating the number of signals embedded in additive white Gaussian noise (AWGN) by using multiple sensors; b) model selection for the general linear model (GLM), which includes e.g. the problem of estimating the number of sinusoids in AWGN. The analysis reveals a trade-off between the probabilities of overestimating and underestimating the order of the model. We then propose to design the GIC penalty to minimize underestimation while keeping the overestimation probability below a specified level. For the considered problems, this method leads to analytical derivation of the optimal penalty for a given sample size. A performance comparison between the penalty optimized GIC and common AIC and BIC is provided, demonstrating the effectiveness of the proposed design strategy.

stat.ML↗

arXiv2019

On Oversampling-Based Signal Detection

The availability of inexpensive devices allows nowadays to implement cognitive radio functionalities in large-scale networks such as the internet-of-things and future mobile cellular systems. In this paper, we focus on wideband spectrum sensing in the presence of oversampling, i.e., the sampling frequency of a digital receiver is larger than the signal bandwidth, where signal detection must take into account the front-end impairments of low-cost devices. Based on the noise model of a software-defined radio dongle, we address the problem of robust signal detection in the presence of noise power uncertainty and non-flat noise power spectral density (PSD). In particular, we analyze the receiver operating characteristic of several detectors in the presence of such front-end impairments, to assess the performance attainable in a real-world scenario. We propose new frequency-domain detectors, some of which are proven to outperform previously proposed spectrum sensing techniques such as, e.g., eigenvalue-based tests. The study shows that the best performance is provided by a noise-uncertainty immune energy detector (ED) and, for the colored noise case, by tests that match the PSD of the receiver noise.

eess.SP↗

arXiv2018

Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices

One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution.

cs.IT↗