arXiv subjects

Abla Kammoun

Publications and source records attributed to Abla Kammoun.

At least 37 records · Page 2Linked to original sources

arXiv2021

Non-terrestrial Communications Assisted by Reconfigurable Intelligent Surfaces

Non-terrestrial communications have emerged as a key enabler for seamless connectivity in the upcoming generation networks. This kind of network can support high data rate communications among aerial platforms (i.e., unmanned aerial vehicles (UAVs), high-altitude platforms (HAPs), and satellites) and cellular networks, achieving anywhere and anytime connections. However, there are many practical implementation limitations, especially overload power consumption, high probability of blockage, and dynamic propagation environment. Fortunately, the recent technology reconfigurable intelligent surface (RIS) is expected to be one of the most cost-efficient solutions to address such issues. RIS with low-cost elements can bypass blockages and create multiple line-of-sight (LoS) links, and provide controllable communication channels. In this paper, we present a comprehensive literature review on the RIS-assisted non-terrestrial networks (RANTNs). Firstly, the framework of the RANTNs is introduced with detailed discussion about distinct properties of RIS in NTNs and the two types of RIS, that is, terrestrial RISs (TRISs), and aerial RISs (ARISs), and the classification of RANTNs including RIS-assisted air-to-ground (A2G)/ground-to-air (G2A), ARIS-assisted ground-to-ground (G2G), and RIS-assisted air-to-air (A2A) communications. In combination with next-generation communication technologies, the advanced technologies in RANTNs are discussed. Then we overview the literature related to RANTNs from the perspectives of performance analysis and optimization, followed by the widely used methodologies. Finally, open challenges and future research direction in the context of the RANTNs are highlighted.

cs.IT↗

arXiv2020

Precise Error Analysis of the LASSO under Correlated Designs

In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the high dimensional asymptotic performance of the LASSO under correlated design matrices using the Convex Gaussian Min-max Theorem (CGMT). We define appropriate performance measures such as the mean-square error (MSE), probability of support recovery, element error rate (EER) and cosine similarity. Numerical simulations are presented to validate the derived theoretical results.

math.ST↗

arXiv2020

Improved Design of Quadratic Discriminant Analysis Classifier in Unbalanced Settings

The use of quadratic discriminant analysis (QDA) or its regularized version (R-QDA) for classification is often not recommended, due to its well-acknowledged high sensitivity to the estimation noise of the covariance matrix. This becomes all the more the case in unbalanced data settings for which it has been found that R-QDA becomes equivalent to the classifier that assigns all observations to the same class. In this paper, we propose an improved R-QDA that is based on the use of two regularization parameters and a modified bias, properly chosen to avoid inappropriate behaviors of R-QDA in unbalanced settings and to ensure the best possible classification performance. The design of the proposed classifier builds on a refined asymptotic analysis of its performance when the number of samples and that of features grow large simultaneously, which allows to cope efficiently with the high-dimensionality frequently met within the big data paradigm. The performance of the proposed classifier is assessed on both real and synthetic data sets and was shown to be much better than what one would expect from a traditional R-QDA.

stat.ML↗

arXiv2020

Data-Driven False Data Injection Attacks Against Power Grids: A Random Matrix Approach

We address the problem of constructing false data injection (FDI) attacks that can bypass the bad data detector (BDD) of a power grid. The attacker is assumed to have access to only power flow measurement data traces (collected over a limited period of time) and no other prior knowledge about the grid. Existing related algorithms are formulated under the assumption that the attacker has access to measurements collected over a long (asymptotically infinite) time period, which may not be realistic. We show that these approaches do not perform well when the attacker has a limited number of data samples only. We design an enhanced algorithm to construct FDI attack vectors in the face of limited measurements that can nevertheless bypass the BDD with high probability. The algorithm design is guided by results from random matrix theory. Furthermore, we characterize an important trade-off between the attack's BDD-bypass probability and its sparsity, which affects the spatial extent of the attack that must be achieved. Extensive simulations using data traces collected from the MATPOWER simulator and benchmark IEEE bus systems validate our findings.

cs.CR↗

arXiv2020

Performance Analysis of Dual-Hop Underwater Wireless Optical Communication Systems over Mixture Exponential-Generalized Gamma Turbulence Channels

In this work, we present a unified framework for the performance analysis of dual-hop underwater wireless optical communication (UWOC) systems with amplify-and-forward fixed gain relays in the presence of air bubbles and temperature gradients. Operating under either heterodyne detection or intensity modulation with direct detection, the UWOC is modeled by the unified mixture Exponential-Generalized Gamma distribution that we have proposed based on an experiment conducted in an indoor laboratory setup and has been shown to provide an excellent fit with the measured data under the considered lab channel scenarios. More specifically, we derive the cumulative distribution function (CDF) and the probability density function of the end-to-end signal-to-noise ratio (SNR) in exact closed-form in terms of the bivariate Fox's H function. Based on this CDF expression, we present novel results for the fundamental performance metrics such as the outage probability, the average bit-error rate (BER) for various modulation schemes, and the ergodic capacity. Additionally, very tight asymptotic results for the outage probability and the average BER at high SNR are obtained in terms of simple functions. Furthermore, we demonstrate that the dual-hop UWOC system can effectively mitigate the short range and both temperature gradients and air bubbles induced turbulences, as compared to the single UWOC link. All the results are verified via computer-based Monte-Carlo simulations.

cs.IT↗

arXiv2020

High-Dimensional Quadratic Discriminant Analysis under Spiked Covariance Model

Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield high classification performance, an accurate estimation of the covariance matrices is required. Such a task becomes all the more challenging in high dimensional settings, wherein the number of observations is comparable with the feature dimension. A popular way to enhance the performance of QDA classifier under these circumstances is to regularize the covariance matrix, giving the name regularized QDA (R-QDA) to the corresponding classifier. In this work, we consider the case in which the population covariance matrix has a spiked covariance structure, a model that is often assumed in several applications. Building on the classical QDA, we propose a novel quadratic classification technique, the parameters of which are chosen such that the fisher-discriminant ratio is maximized. Numerical simulations show that the proposed classifier not only outperforms the classical R-QDA for both synthetic and real data but also requires lower computational complexity, making it suitable to high dimensional settings.

cs.LG↗

arXiv2020

Performance of Multibeam Very High Throughput Satellite Systems Based on FSO Feeder Links with HPA Nonlinearity

Due to recent advances in laser satellite communications technology, free-space optical (FSO) links are presented as an ideal alternative to the conventional radio frequency (RF) feeder links of the geostationary satellite for next generation very high throughput satellite (VHTS) systems. In this paper, we investigate the performance of multibeam VHTS systems that account for nonlinear high power amplifiers at the transparent fixed gain satellite transponder. Specifically, we consider the forward link of such systems, where the RF user link is assumed to follow the shadowed Rician model and the FSO feeder link is modeled by the Gamma-Gamma distribution in the presence of beam wander and pointing errors where it operates under either the intensity modulation with direct detection or the heterodyne detection. Moreover, zero-forcing precoder is employed to mitigate the effect of inter-beam interference caused by the aggressive frequency reuse in the user link. The performance of the system under study is evaluated in terms of the outage probability, the average bit-error rate (BER), and the ergodic capacity that are derived in exact closed-forms in terms of the bivariate Meijer's G function. Simple asymptotic results for the outage probability and the average BER are also obtained at high signal-to-noise ratio.

cs.IT↗

arXiv2020

Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise

We consider a fading channel in which a multi-antenna transmitter communicates with a multi-antenna receiver through a reconfigurable intelligent surface (RIS) that is made of $N$ reconfigurable passive scatterers impaired by phase noise. The beamforming vector at the transmitter, the combining vector at the receiver, and the phase shifts of the $N$ scatterers are optimized in order to maximize the signal-to-noise-ratio (SNR) at the receiver. By assuming Rayleigh fading (or line-of-sight propagation) on the transmitter-RIS link and Rayleigh fading on the RIS-receiver link, we prove that the SNR is a random variable that is equivalent in distribution to the product of three (or two) independent random variables whose distributions are approximated by two (or one) gamma random variables and the sum of two scaled non-central chi-square random variables. The proposed analytical framework allows us to quantify the robustness of RIS-aided transmission to fading channels. For example, we prove that the amount of fading experienced on the transmitter-RIS-receiver channel linearly decreases with $N$. This proves that RISs of large size can be effectively employed to make fading less severe and wireless channels more reliable.

cs.IT↗

arXiv2020

A Model of Double Descent for High-dimensional Binary Linear Classification

We consider a model for logistic regression where only a subset of features of size $p$ is used for training a linear classifier over $n$ training samples. The classifier is obtained by running gradient descent (GD) on logistic loss. For this model, we investigate the dependence of the classification error on the overparameterization ratio $κ=p/n$. First, building on known deterministic results on the implicit bias of GD, we uncover a phase-transition phenomenon for the case of Gaussian features: the classification error of GD is the same as that of the maximum-likelihood (ML) solution when $κ<κ_\star$, and that of the max-margin (SVM) solution when $κ>κ_\star$. Next, using the convex Gaussian min-max theorem (CGMT), we sharply characterize the performance of both the ML and the SVM solutions. Combining these results, we obtain curves that explicitly characterize the classification error for varying values of $κ$. The numerical results validate the theoretical predictions and unveil double-descent phenomena that complement similar recent findings in linear regression settings as well as empirical observations in more complex learning scenarios.

stat.ML↗

arXiv2020

Intelligent Reflecting Surface Assisted Multi-User MISO Communication: Channel Estimation and Beamforming Design

The concept of reconfiguring wireless propagation environments using intelligent reflecting surfaces (IRS)s has recently emerged, where an IRS comprises of a large number of passive reflecting elements that can smartly reflect the impinging electromagnetic waves for performance enhancement. Previous works have shown promising gains assuming the availability of perfect channel state information (CSI) at the base station (BS) and the IRS, which is impractical due to the passive nature of the reflecting elements. This paper makes one of the preliminary contributions of studying an IRS-assisted multi-user multiple-input single-output (MISO) communication system under imperfect CSI. Different from the few recent works that develop least-squares (LS) estimates of the IRS-assisted channel vectors, we exploit the prior knowledge of the large-scale fading statistics at the BS to derive the Bayesian minimum mean squared error (MMSE) channel estimates under a protocol in which the IRS applies a set of optimal phase shifts vectors over multiple channel estimation sub-phases. The resulting mean squared error (MSE) is both analytically and numerically shown to be lower than that achieved by the LS estimates. Joint designs for the precoding and power allocation at the BS and reflect beamforming at the IRS are proposed to maximize the minimum user signal-to-interference-plus-noise ratio (SINR) subject to a transmit power constraint. Performance evaluation results illustrate the efficiency of the proposed system and study its susceptibility to channel estimation errors.

cs.IT↗

arXiv2020

Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants

Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order to rectify the issues associated with classification in such a setting, the classifier in [1], composed of an ensemble of randomly projected linear discriminants, seems especially promising; it is computationally efficient and, with the optimal projection dimension parameter setting, is competitive with the state-of-the-art. In this work, we seek to further understand the behavior of this classifier through asymptotic analysis. Under the assumption of a growth regime in which the dataset and projection dimensions grow at constant rates to each other, we use random matrix theory to derive asymptotic misclassification probabilities showing the effect of the ensemble as a regularization of the data sample covariance matrix. The asymptotic errors further help to identify situations in which the ensemble offers a performance advantage. We also develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator, which is conventionally used for parameter tuning. Finally, we demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.

stat.ML↗

arXiv2020

On the Precise Error Analysis of Support Vector Machines

This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\toδ$) drawn from a Gaussian mixture distribution. Sharp predictions of the classification error rate of the hard-margin and soft-margin SVM are provided, as well as asymptotic limits of as such important parameters as the margin and the bias. As a further outcome, the analysis allow for the identification of the maximum number of training samples that the hard-margin SVM is able to separate. The precise nature of our results allow for an accurate performance comparison of the hard-margin and soft-margin SVM as well as a better understanding of the involved parameters (such as the number of measurements and the margin parameter) on the classification performance. Our analysis, confirmed by a set of numerical experiments, builds upon the convex Gaussian min-max Theorem, and extends its scope to new problems never studied before by this framework.

cs.IT↗

arXiv2019

Intelligent Reflecting Surface Assisted Wireless Communication: Modeling and Channel Estimation

The recently completed 5G new radio standard is a result of several cutting-edge technologies, including massive multiple-input multiple-output (MIMO), millimeter (mm)-Wave communication and network densification. However, these technologies face two main practical limitations 1) the lack of control over the wireless channel, and 2) the high power consumption of the wireless interface. To address the need for green and sustainable future cellular networks, the concept of reconfiguring wireless propagation environments using Intelligent Reflecting Surfaces (IRS)s has emerged. An IRS comprises of a large number of low-cost passive antennas that can smartly reflect the impinging electromagnetic waves for performance enhancement. This paper looks at the evolution of the reflective radio concept towards IRSs, outlines the IRS-assisted multi-user multiple-input single-output (MISO) communication model and discusses how it differentiates from the conventional multi-antenna communication models. We propose a minimum mean squared error (MMSE) based channel estimation protocol for the design and analysis of IRS-assisted systems. Performance evaluation results at 2.5 GHz operating frequency are provided to illustrate the efficiency of the proposed system.

eess.SP↗

arXiv2019

Asymptotic Max-Min SINR Analysis of Reconfigurable Intelligent Surface Assisted MISO Systems

This work focuses on the downlink of a single-cell multi-user system in which a base station (BS) equipped with $M$ antennas communicates with $K$ single-antenna users through a reconfigurable intelligent surface (RIS) installed in the line-of-sight (LoS) of the BS. RIS is envisioned to offer unprecedented spectral efficiency gains by utilizing $N$ passive reflecting elements that induce phase shifts on the impinging electromagnetic waves to smartly reconfigure the signal propagation environment. We study the minimum signal-to-interference-plus-noise ratio (SINR) achieved by the optimal linear precoder (OLP), that maximizes the minimum SINR subject to a given power constraint for any given RIS phase matrix, for the cases where the LoS channel matrix between the BS and the RIS is of rank-one and of full-rank. In the former scenario, the minimum SINR achieved by the RIS-assisted link is bounded by a quantity that goes to zero with $K$. For the high-rank scenario, we develop accurate deterministic approximations for the parameters of the asymptotically OLP, which are then utilized to optimize the RIS phase matrix. Simulation results show that RISs can outperform half-duplex relays with a small number of passive reflecting elements while large RISs are needed to outperform full-duplex relays.

cs.IT↗

arXiv2019

On Robust Spectrum Sensing Using M-estimators of Covariance Matrix

In this paper, we consider the spectrum sensing in cognitive radio networks when the impulsive noise appears. We propose a class of blind and robust detectors using M-estimators in eigenvalue based spectrum sensing method. The conventional eigenvalue based method uses statistics derived from the eigenvalues of sample covariance matrix(SCM) as testing statistics, which are inefficient and unstable in the impulsive noise environment. Instead of SCM, we can use M-estimators, which have good performance under both impulsive and non-impulsive noise. Among those M-estimators, We recommend the Tyler's M-estimator instead, which requires no knowledge of noise distribution and have the same probability of false alarm under different complex elliptically symmetric distributions. In addition, it performs better than the detector using sample covariance matrix when the noise is highly impulsive. It should be emphasized that this detector does not require knowledge of noise power which is required by the energy detection based methods. Simulations show that it performs better than conventional detector using sample covariance matrix in a highly impulsive noise environment.

eess.SP↗

arXiv2019

Large-System Analysis of Massive MIMO with Optimal M-MMSE Processing

We consider the uplink of a Massive MIMO network with $L$ cells, each comprising a BS with $M$ antennas and $K$ single-antenna user equipments. Recently, [1] studied the asymptotic spectral efficiency of such networks with optimal multicell minimum mean-squared error (M-MMSE) processing when $M\to \infty$ and $K$ is kept fixed. Remarkably, [1] proved that, for practical channels with spatial correlation, the spectral efficiency grows unboundedly, even with pilot contamination. In this paper, we extend the analysis from [1] to the alternative regime in which $M,K\to \infty$ with a given ratio. Tools from random matrix theory are used to compute low-complexity approximations which are proved to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations.

cs.IT↗

arXiv2019

A Large Dimensional Study of Regularized Discriminant Analysis Classifiers

This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under mild assumptions, we show that the asymptotic classification error approaches a deterministic quantity that depends only on the means and covariances associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized discriminant analsysis, in practical large but finite dimensions, and can be used to determine and pre-estimate the optimal regularization parameter that minimizes the misclassification error probability. Despite being theoretically valid only for Gaussian data, our findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from the popular USPS data base, thereby making an interesting connection between theory and practice.

stat.ML↗

arXiv2019

Elevation Beamforming with Full Dimension MIMO Architectures in 5G Systems: A Tutorial

Full dimension (FD) multiple-input multiple-output (MIMO) technology has attracted substantial research attention from both wireless industry and academia in the last few years as a promising technique for next-generation wireless communication networks. FD-MIMO scenarios utilize a planar two-dimensional active antenna system (AAS) that not only allows a large number of antenna elements to be placed within feasible base station (BS) form factors, but also provides the ability of adaptive electronic beam control over both the elevation and the traditional azimuth dimensions. This paper presents a tutorial on elevation beamforming analysis for cellular networks utilizing FD Massive MIMO antenna arrays. In contrast to existing works that focus on the standardization of FD-MIMO in the 3rd Generation Partnership Project (3GPP), this tutorial is distinguished by its depth with respect to the theoretical aspects of antenna array and 3D channel modeling. In an attempt to bridge the gap between industry and academia, this preliminary tutorial introduces the relevant array and transceiver architecture designs proposed in the 3GPP Release 13 that enable elevation beamforming. Then it presents and compares two different 3D channel modeling approaches that can be utilized for the performance analysis of elevation beamforming techniques. The spatial correlation in FD-MIMO arrays is characterized and compared based on both channel modeling approaches and some insights into the impact of different channel and array parameters on the correlation are drawn. All these aspects are put together to provide a mathematical framework for the design of elevation beamforming schemes in single-cell and multi-cell scenarios. Simulation examples associated with comparisons and discussions are also presented. To this end, this paper highlights the state-of-the-art research and points out future research directions.

cs.IT↗