Received signal strength (RSS)-based localization techniques rely on the transmit power of nodes, with many existing approaches assuming full knowledge of this parameter. However, transmit power depends on various factors like battery levels, antenna orientation, and component aging. To address this issue, existing techniques typically employ semidefinite programming (SDP), which exhibits significantly high computational complexity. In this paper, we present a cooperative RSS-based localization technique named CR-CA (Convex Relaxation with Centralized Armijo optimization), which jointly estimates nodes’ locations and transmit power. CR-CA transforms the unconstrained maximum likelihood (ML) of the RSS-based localization problem into a constrained optimization problem using a convex approximation of the non-convex and discontinuous objective function. We demonstrate that the relaxed ML objective function possesses a Lipschitz continuous gradient. We solve the relaxed ML problem using the augmented Lagrange multiplier method and provide the theoretical proof of its convergence. Additionally, we derive the Cramer-Rao Lower Bound (CRLB) for RSS-based cooperative localization under scenarios where transmit power is unknown. We conduct extensive simulations and real-world experiments to verify the effectiveness of CR-CA, showcasing its superior accuracy in estimating nodes’ locations and transmit power. Simulations and experiments further validate that CR-CA exhibits linear computational complexity with the number of wireless links, thus making it suitable for large-scale networks.

This paper proposes a novel non-terrestrial networks (NTNs) system that integrates optical intelligent reflecting surfaces (OIRS) and simultaneous transmitting and reflecting Intelligent reflecting surfaces (STAR-IRS) to address critical challenges in next-generation communication networks. The proposed system model features a signal transmitted from the optical ground station (OGS) to the earth station (ES) via an OIRS mounted horizontally on a high altitude platform (HAP). The ES uses an amplify-and-forward (AF) relay with fixed gain for signal relaying, which is then transmitted through a STAR-IRS vertically installed on a building to facilitate communication with both indoor and outdoor users. The FSO link incorporates (multiple-input multiple-output) MIMO technology, and this paper develops a channel model specifically designed for scenarios where the number of OIRS units exceeds one. For the radio-frequency (RF) link, a novel and highly precise approximation method is introduced, offering superior accuracy compared to traditional approaches based on the central limit theorem (CLT). Closed-form analytical expressions for key performance metrics, including outage probability (OP), ergodic capacity and average bit error rate (BER) are derived in terms of the bivariate Fox-H function for this novel five hops system. Asymptotic expressions at high SNR are also presented, providing insights into system diversity order.

In this work, we propose an innovative system that combines high-altitude platforms (HAPs) and optical intelligent reflecting surfaces (OIRS) to address line-of-sight (LOS) challenges in urban environments. Our three-hops system setup includes an optical ground station (OGS), a HAP, an OIRS, and a user. Signals are transmitted from the OGS to the HAP via a free space optical (FSO) link, with the HAP functioning as an amplify-and-forward (AF) relay that redirects signals through an OIRS, effectively bypassing obstacles such as buildings and trees to improve connectivity for non-line-of-sight (NLOS) User. For the OIRS link, we address key channel impairments, including atmospheric turbulence, pointing errors, attenuation, and geometric and misalignment losses (GML). An accurate approximation for the Hoyt-distributed GML model is derived, enabling us to obtain closed-form expressions for outage probability (OP) and various performance metrics, such as average bit error rate (BER) and channel capacity of the OIRS-assisted FSO link. Furthermore, we analyze the end-to-end signal-to-noise ratio (SNR) and derive closed-form expressions for OP and performance metrics. Asymptotic expressions are provided for high-SNR regimes, allowing the system’s diversity order to be calculated.

In this work, we study the design of receivers for uplink multi-user systems, aiming to estimate both the channel and the transmitted symbols. We consider two estimation strategies: 1) a joint estimation approach, where the channel and symbols are estimated simultaneously; and 2) a sequential estimation approach, where the channel is first estimated and then used for symbol detection. For both strategies, we derive the Cramér-Rao Bound (CRB) for symbol estimation to characterize fundamental performance limits. When efficient receivers achieving the CRB exist, these bounds provide accurate lower bounds on the mutual information. In general, however, such receivers may not be available, and we instead use these same CRB-based metrics as practical proxies for achievable throughput. Leveraging tools from random matrix theory (RMT), we analyze the asymptotic behavior of these lower bounds under various asymptotic regimes for both estimation strategies. This analysis enables the derivation of generic power allocation guidelines that asymptotically maximize the proxy metrics. Simulation results confirm the accuracy of the asymptotic expressions and their effectiveness in guiding resource allocation decisions.

This work provides a precise performance analysis of a joint antenna selection and precoding technique for massive multiple-input-single-output (MISO) multi-user systems with limited dynamic range power amplifiers. The proposed precoder is formulated as an optimization problem that aims to minimize distortion error power while incorporating an ℓ1-regularization term to promote sparsity and enable antenna selection. It also includes constraints to ensure that the maximum power at each antenna remains within the permissible range for low-dynamic range power amplifiers. Utilizing the convex-Gaussian min-max theorem framework, we offer a precise characterization of the proposed solution’s performance as the number of users and antennas at the base station simultaneously increases. Through extensive numerical experiments, we evaluate the accuracy of our results and derive valuable insights into the effectiveness of the proposed joint antenna selection and precoding approach.

This paper presents a performance analysis of two distinct techniques for antenna selection and precoding in downlink multi-user massive multiple-input single-output systems with limited dynamic range power amplifiers. Both techniques are derived from the original formulation of the regularized-zero forcing precoder, designed as the solution to minimizing a regularized distortion. Based on this, the first technique, called the ℓ1-norm precoder, adopts an ℓ1-norm regularization term to encourage sparse solutions, thereby enabling antenna selection. The second technique, termed the thresholded ℓ1-norm precoder, involves post-processing the precoder solution obtained from the first method by applying an entry-wise thresholding operation. This work conducts a precise performance analysis to compare these two techniques. The analysis leverages the Gaussian min-max theorem which is effective for examining the asymptotic behavior of optimization problems without explicit solutions. While the analysis of the ℓ1-norm precoder follows from the conventional convex Gaussian min-max theorem framework, understanding the thresholded ℓ1-norm precoder is more complex due to the non-linear behavior introduced by the thresholding operation. To address this complexity, we develop a novel Gaussian min-max theorem tailored to these scenarios. We provide precise asymptotic behavior analysis of the precoders, focusing on metrics such as received signal-to-noise and distortion ratio and bit error rate. Our analysis demonstrates that the thresholded ℓ1-norm precoder can offer superior performance when the threshold parameter is carefully selected. Simulations confirm that the asymptotic results are accurate for systems equipped with hundreds of antennas at the base station, serving dozens of user terminals.

Modern technology has contributed to the rise of high-dimensional data in various domains such as bio-informatics, chemometrics, and face recognition. In the recent literature, random projections and, in particular, randomly-projected ensembles based on the classical Linear Discriminant Analysis (LDA), have been proposed for classification problems involving such high-dimensional data. In this work, we study the two main classes of randomly-projected LDA ensemble classifiers, namely discriminant averaging and vote averaging. Through asymptotic analysis in a growth regime where the problem dimensions are assumed to grow at constant rates to each other for a fixed ensemble size, we determine the exact mechanism through which the ensemble size affects the classification performance. Furthermore, we investigate whether projection selection truly matters in an ensemble setting, and, ultimately, derive the optimal form of the randomly-projected LDA ensemble. Motivated by these findings, we propose a framework for efficient tuning of the optimal classifier's ensemble size and projection dimension based on an estimator of the classifier probability of misclassification which is consistent under the assumed growth regime. The proposed framework is shown to outperform the existing rule-of-thumb, as well as other methods for parameter tuning, on both real and synthetic data.

Reconfigurable intelligent surfaces (RIS) have been advocated as a promising technology to overcome blockage issues in mmWave communications caused by severe propagation absorption and high directivity. This paper investigates the design of finite resolution phase shifters at the RIS to maximize the signal-to-noise ratio of a point-to-point multiple-input single output mmWave communication system. Both the transmitting antennas at the base station and the reflecting elements on the RIS are modeled as uniform planar arrays. The optimization of the discrete RIS design remains a computationally expensive procedure, especially for large reflecting surfaces and high resolution phase shifts. As a solution, we propose in this work a low-complexity suboptimal approach that exploits the structure of mmWave propagation channels. Specifically, the developed algorithms rely on decomposing the reflecting beamforming vectors and the channel path vectors into Kronecker products of factors of uni-modulus vectors. In addition to the computational complexity advantage, the proposed solutions also promise to require only partial information of the cascaded channel rather than the full one, the estimation of which is more practically convenient due to the passive nature of the RIS. To enable the proposed reflecting beamforming designs, we propose a channel estimation technique that invokes the atomic norm minimization framework to estimate the parameters of the channel, namely, the path’s magnitudes and their associated departure and arrival angles. Simulation results confirm the superiority of the proposed reflecting design and channel estimation scheme as compared to other existing techniques.

Reconfigurable intelligent surfaces (RIS) can be crucial in next-generation communication systems. However, designing the RIS phases according to the instantaneous channel state information (CSI) can be challenging in practice due to the short coherent time of the channel. In this regard, we propose a novel algorithm based on the channel statistics of massive multiple input multiple output systems rather than the instantaneous CSI. The beamforming at the base station (BS), power allocation of the users, and phase shifts at the RIS elements are optimized to maximize the minimum signal-to-interference and noise ratio (SINR), guaranteeing fair operation among various users. In particular, we design the RIS phases by leveraging the asymptotic deterministic equivalent of the minimum SINR that depends only on the channel statistics. This significantly reduces the computational complexity and the amount of controlling data between the BS and RIS for updating the phases. This setup is also useful for electromagnetic fields (EMF)-aware systems with constraints on the maximum user’s exposure to EMF. The numerical results show that the proposed algorithms achieve more than 100 % gain in terms of minimum SINR, compared to a system with random RIS phase shifts, when 40 RIS elements, 20 antennas at the BS and 10 users, are considered.

Fluid antenna systems (FAS) are an emerging technology that promises a significant diversity gain even in the smallest spaces. It consists of a freely moving antenna in a small linear space to pick up the strongest received signal. Previous works in the literature provide a simple yet insightful parameterization of the FAS channel that leads to single-integral expressions of the probability of outage and various insights on the achievable performance. Nevertheless, this channel model may not accurately capture the correlation between the FAS ports, given by Jake’s model. This work builds on the state-of-the-art by incorporating more parameters into the channel model to accurately approximate the FAS channel distribution while maintaining analytical tractability. The approximation is performed in two stages. The first stage approximation considerably reduces the number of multi-fold integrals in the probability of outage expression, while the second stage approximation represents it in a single integral form. Numerical results validate our approximations of the FAS channel model and demonstrate a limited performance gain under a more accurate correlation model. Further, our work opens the door for future research to investigate scenarios in which the FAS provides a performance gain compared to the current multiple antenna solutions.

Nonterrestrial 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 article, we present a comprehensive literature review on the RIS-assisted nonterrestrial networks (RANTNs). First, the framework of the RANTNs is introduced with detailed discussion about distinct properties of RIS in NTNs and the two deployment 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.

This paper aims to derive expressions of the downlink ergodic user rates in a multi-cell large-scale multi-user multiple-input single-output (MISO) system under the assumption that each base station (BS) employs maximum ratio transmission (MRT) precoding and that single-antenna users in each cell are divided into groups, where channels of users in the same group share common covariance matrices and follow the double scattering channel model. Moreover, both channel estimation errors and pilot contamination effects caused by re-use of pilot sequences in neighboring cells are taken into consideration in this work. The analysis is carried out using statistical tools under the exact and asymptotic regimes in which the number of antennas at BS$N$, the number of users in each cell$K$, and the number of scatterers$S$grow large at the same pace. Furthermore, the obtained exact expressions and deterministic approximations of the ergodic rates are expressed in simplified closed-forms under the special case of multi-keyhole channels to yield useful insights. They reveal that signal-to-noise plus interference ratio (SINR) without user grouping in a multi-keyhole channel is similar to that under standard Rayleigh channel in the asymptotic regime. However, under user grouping, we show that the massive multiple-input multiple-output (MIMO) gains promised by deploying large-scale antenna arrays in multi-cell settings are limited by the number of scatterers even if the number of antennas grows large. Simulation results illustrate the close match provided by the asymptotic analysis for moderate system dimensions and confirm the insights drawn from the theoretical findings.

Reconfigurable intelligent surface (RIS) has emerged as a promising mean to enhance wireless transmission. The effective reflected paths provided by RIS are able to alleviate the susceptibility to blockage effects, especially in high-frequency band communications, where signals experience severe path loss and high directivity. This paper is concerned with an RIS-assisted system over the millimeter wave (mmWave) channel characterized by sparse propagation paths. A base station tries to connect with the desired user through an RIS, while the undesired user can also receive the signal transmitted from BS unavoidably, which is treated as the interference signal. All terminals are assumed to be equipped with a single antenna for the sake of simplicity. The paper aims to propose an appropriate design of the phase shifts of each element at the RIS so as to maximize the received signal power transmitted from the base station (BS) at the desired user, while nulling the received interference signal power at the undesired user. The proposed reflecting design relies on the decomposition of the reflecting beamforming vectors and all channel path vectors into Kronecker product of factors being uni-modulus vectors. By exploiting characteristics of Kronecker mixed products, different factors of the reflecting are designed for either nulling the interference signal at the undesired user, or coherently combining data paths at the desired user. Furthermore, a channel estimation strategy is proposed to enable the proposed reflecting beamforming design. The magnitude, azimuth, and elevation arrival and departure angles of desired and undesired paths are estimated by an efficient 2-dimension (2-D) line spectrum optimization technique based on the atomic norm minimization (ANM) framework. The performance of the reflecting designs and channel estimation scheme is analyzed and demonstrated by simulation results.

In this paper, we study the hard and soft support vector regression techniques applied to a set of $n$ linear measurements of the form $y_i=\boldsymbol{\beta}_\star^{T}{\bf x}_i +n_i$ where $\boldsymbol{\beta}_\star$ is an unknown vector, $\left\{{\bf x}_i\right\}_{i=1}^n$ are the feature vectors and $\left\{{n}_i\right\}_{i=1}^n$ model the noise. Particularly, under some plausible assumptions on the statistical distribution of the data, we characterize the feasibility condition for the hard support vector regression in the regime of high dimensions and, when feasible, derive an asymptotic approximation for its risk. Similarly, we study the test risk for the soft support vector regression as a function of its parameters. Our results are then used to optimally tune the parameters intervening in the design of hard and soft support vector regression algorithms. Based on our analysis, we illustrate that adding more samples may be harmful to the test performance of support vector regression, while it is always beneficial when the parameters are optimally selected. Such a result reminds a similar phenomenon observed in modern learning architectures according to which optimally tuned architectures present a decreasing test performance curve with respect to the number of samples.

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 the 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 convergence properties of the 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*, and that of the max-margin (SVM) solution when κ > κ*. Next, using the convex Gaussian min-max theorem (CGMT), we sharply characterize the performance of both the ML and SVM solutions. Combining these results, we obtain curves that explicitly characterize the test error of GD for varying values of κ. The numerical results validate the theoretical predictions and unveil “double-descent” phenomena that complement similar recent observations in linear regression settings.

This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call centered kernel ridge regression (CKRR), also known in the literature as kernel ridge regression with offset. This modified technique is obtained by accounting for the bias in the regression problem resulting in the old kernel ridge regression but with centered kernels. The analysis is carried out under the assumption that the data is drawn from a Gaussian distribution and heavily relies on tools from random matrix theory (RMT). Under the regime in which the data dimension and the training size grow infinitely large with fixed ratio and under some mild assumptions controlling the data statistics, we show that both the empirical and the prediction risks converge to a deterministic quantities that describe in closed form fashion the performance of CKRR in terms of the data statistics and dimensions. A key insight of the proposed analysis is the fact that asymptotically a large class of kernels achieve the same minimum prediction risk. This insight is validated with synthetic data.

In this paper, we consider the problem of recovering a binary phase shift keying (BPSK) modulated signal in a massive multiple-input-multiple-output (MIMU) system. The recovery process is done using the box-relaxation method, in which the discrete set {±I}nis relaxed to the convex set [-I,+I]nand solved by a convex optimization program followed by hard thresholding. We assume that the system has a Gaussian channel matrix with one sided left correlation. The entries of the noise vector are assumed to be independent and identically distributed (iid) zero-mean Gaussian. In this work, we precisely characterize the mean squared error (MSE) and the bit error rate (BER) of the box-relaxation decoder in the asymptotic regime where both dimensions grow simultaneously large at a fixed ratio. Numerical simulations validate the theoretical expressions derived in this paper.

Linear discriminant analysis (LDA) is a popular classifier that is built on the assumption of common population covariance matrix across classes. The performance of LDA depends heavily on the quality of estimating the mean vectors and the population covariance matrix. This issue becomes more challenging in high-dimensional settings where the number of features is of the same order as the number of training samples. Several techniques for estimating the covariance matrix can be found in the literature. One of the most popular approaches are estimators based on using a regularized sample covariance matrix, giving the name regularized LDA (R-LDA) to the corresponding classifier. These estimators are known to be more resilient to the sample noise than the traditional sample covariance matrix estimator. However, the main challenge of the regularization approach is the choice of the optimal regularization parameter, as an arbitrary choice could lead to severe degradation of the classifier performance. In this work, we propose an improved LDA classifier based on the assumption that the covariance matrix follows a spiked covariance model. The main principle of our proposed technique is the design of a parametrized inverse covariance matrix estimator, the parameters of which are shown to be easily optimized. Numerical simulations, using both real and synthetic data, show that the proposed classifier yields better classification performance than the classical R-LDA while requiring lower computational complexity.

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.

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.

This paper studies the ergodic rate performance of maximum ratio transmission (MRT) precoding in the downlink of a multi-user multiple-input single-output (MISO) system, where the channel between the base station (BS) and each user is modeled using the double scattering model. We utilize the minimum-mean-square-error (MMSE) channel estimate for this model, which is used in the design of the MRT precoding. Within this setting, we are interested in deriving tight approximations of the ergodic rate under the assumption that the number of BS antennas (N), the number of users (K) and that of scatterers (S) grow large with the same pace. These approximations are expressed in simplified closed-form expressions for the special case of multi-keyhole channels. They reveal that unlike the standard Rayleigh channel in which the SINR grows as O(N), K the SINR associated with a multi-keyhole channel scales as O(S). This particularly shows that the reaped gains of the K large-scale MIMO over double scattering channels do not linearly increase with the number of antennas and are limited by the number of scatterers. We further provide simulation results that confirm the close match provided by the asymptotic analysis for moderate system dimensions and provide some useful insights into the interplay between N, K and S.

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.

We investigate random projections in the context of randomly projected linear discriminant analysis (LDA). We consider the case in which the data of dimension p is randomly projected onto a lower dimensional space before being fed to the classifier. Using fundamental results from random matrix theory and relying on some mild assumptions, we show that the asymptotic performance in terms of probability of misclassification approaches a deterministic quantity that only depends on the data statistics and the dimensions involved. Such results permits to reliably predict the performance of projected LDA as a function of the reduced dimension d <; p and thus helps to determine the minimum d to achieve a certain desired performance. Finally, we validate our results with finite-sample settings drawn from both synthetic data and the popular MNIST dataset.

In this paper, we investigate the impact of the wavelength and the water turbidity on the performance of non-line-of-sight underwater communication links. Using the chlorophyll-based model proposed in [1], we demonstrate the variability of the scattering and absorption properties for a given wavelength with respect to the water turbidity level. To facilitate the use of this model in Monte Carlo simulations, we approximate the phase function by a two-term Henyey Greenstein function. The obtained phase function as well as the absorption and scattering coefficients of this model are then injected to Monte Carlo simulations to assess the path loss performance. Interestingly, we show by simulations that water turbidity, often regarded as a limiting performance factor, can lead to better received power in non-line of sight environments.

We carry out a theoretical analysis of the uplink (UL) of a massive MIMO system with per-user channel correlation and Rician fading, using two processing approaches. First, we examine the linear-minimum-mean-square-error receiver under training-based imperfect channel estimates. Second, we propose a statistical combining technique that is more suitable in environments with strong line-of-sight (LoS) components. We derive closed-form asymptotic approximations of the UL spectral efficiency (SE) attained by each combining scheme in single and multi-cell settings, as a function of the system parameters. These expressions are insightful in how different factors such as LoS propagation conditions and pilot contamination impact the overall system performance. Furthermore, they are exploited to determine the optimal number of training symbols, which is shown to be of significant interest at low Rician factors. The study and numerical results substantiate that stronger LoS signals lead to better performances, and under such conditions, the statistical combining entails higher SE gains than the conventional receiver.

This paper considers a Massive MIMO network with L cells, each comprising a base stations (BS) with M antennas and K single-antenna user equipments. Within this setting, we are interested in deriving approximations of the achievable rates in the uplink and downlink under the assumption that single-cell linear processing is used at each BS and that each intracell link forms an uncorrelated MIMO Rician fading channel matrix; that is, with a deterministic line-of-sight (LoS) path and a stochastic non-LoS component describing a spatial uncorrelated multipath environment. The analysis is conducted assuming that N and K grow large with a given ratio N/K under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, an arbitrary large scale attenuation and LoS components. Numerical results are used to prove that the approximations are asymptotically tight, but accurate for systems with finite dimensions. The asymptotic results are also used to evaluate the impact of LoS components. In particular, we exemplify how the number of antennas for achieving a target rate can be substantially reduced with LoS links of only a few dBs of strength.

A unified statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical communication (UWOC) channels in the presence of air bubbles and temperature gradient for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture exponential-generalized gamma (EGG) distribution. We use the expectation-maximization algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, we show that the application of the EGG model leads to closed-form and analytically tractable expressions for key UWOC system performance metrics such as the outage probability, the average bit-error rate, and the ergodic capacity. To the best of our knowledge, this is the first-ever comprehensive channel model addressing the statistics of optical beam irradiance fluctuations in underwater wireless optical channels due to both air bubbles and temperature gradient.

In this paper, we focus on the downlink ergodic sum rate of a single-cell large-scale multiuser MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments (TIEs). A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each TIE uses a specific power and each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming that N and K grow large with a given ratio and perfect channel state information is available at the base station. New results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of system parameters, spatial correlation matrix, and Rician factor. Numerical results are used to validate the accuracy of asymptotic approximations in the finite system regime and to evaluate the performance under different operating conditions. It turns out that the asymptotic expressions provide accurate approximations even for relatively small values of N and K.

This paper studies the ergodic rate performance of regularized zero-forcing (RZF) precoding in the downlink of a multi-user multiple-input single-output (MISO) system, where the channel between the base station (BS) and each user is modeled by the double scattering model. This non-Gaussian channel model is a function of both the antenna correlation and the structure of scattering in the propagation environment. This paper makes the preliminary contribution of deriving the minimum-mean-square-error (MMSE) channel estimate for this model. Then under the assumption that the users are divided into groups of common correlation matrices, this paper derives deterministic approximations of the signal-to-interference-plus-noise ratio (SINR) and the ergodic rate, which are almost surely tight in the limit that the number of BS antennas, the number of users, and the number of scatterers in each group grow infinitely large. The derived results are expressed in a closed-form for the special case of multi-keyhole channels. The simulation results confirm the close match provided by the asymptotic analysis for moderate system dimensions. We show that the maximum number of users that can be supported simultaneously, while realizing large-scale MIMO gains, is equal to the number of scatterers.

This work considers the uplink (UL) of a multicell massive MIMO system with L cells, having each K monoantenna users communicating with an N-antennas base station (BS). The channel model involves Rician fading with distinct per-user Rician factors and channel correlation matrices and takes into account pilot contamination and imperfect CSI. The objective is to evaluate the performances of such systems with different single-cell and multi-cell detection methods. In the former, we investigate MRC and single-cell MMSE (S-MMSE); as to the latter, we are interested in multi-cell MMSE (MMMSE) that was recently shown to provide unbounded rates in Rayleigh fading. The analysis is led assuming the infinite N limit and yields informative closed-form approximations that are substantiated by a selection of numerical results for finite system dimensions. Accordingly, these expressions are accurate and provide relevant insights into the effects of the different system parameters on the overall performances.

This paper studies the sum-rate performance of regularized zero-forcing (RZF) precoding in a multi-user multiple-input single-output (MISO) system, where the channel between the base station (BS) and each user is modeled by the double scattering channel model. This non-Gaussian channel accounts for both the spatial correlation in the antenna arrays and the structure of scattering in the propagation environment. The user population is divided into G groups, where the users in the same group experience similar propagation conditions and are characterized by common correlation matrices. Under this setting, we derive deterministic approximations of the signal-to-interference-plus-noise ratio (SINR) and the sum-rate with RZF precoding, which are almost surely tight in the large system limit. Simulation results confirm the close match provided by the asymptotic analysis for moderate system dimensions.

We consider the evaluation of the outage probability (OP) for L-branch equal gain combining diversity receivers operating over fading channels, i.e. equivalently the cumulative distribution function (CDF) of the sum of the L channel envelopes. Generally, closed-form expressions of the OP values are out of reach. Moreover, the use of naive Monte Carlo (MC) simulations is not a good alternative since it is expensive in terms of number of samples when small values of OP are considered. In this paper, we use the concept of importance sampling (IS), being known to yield accurate estimates using few number of simulations runs. The proposed IS scheme is essentially based on sample rejection where the IS probability density function (PDF) is the truncation of the underlying PDF over the L dimensional sphere. It assumes the knowledge of the CDF of the sum of the L channel gains in a closed-form expression. Such an assumption is not restrictive since it holds for various challenging fading models. As an illustration, we apply the proposed estimator to the cases of independent Rayleigh, correlated Rayleigh, and independent and identically distributed Rice fading channels and prove that it achieves the well-desired bounded relative error property. Finally, we validate these theoretical results through some selected experiments.

We study in this article the asymptotic performance of spectral clustering with inner product kernel for Gaussian mixture models of high dimension with numerous samples. As is now classical in large dimensional spectral analysis, we establish a phase transition phenomenon by which a minimum distance between the class means and covariances is required for clustering to be possible from the dominant eigenvectors. Beyond this phase transition, we evaluate the asymptotic content of the dominant eigenvectors thus allowing for a full characterization of clustering performance. However, a surprising finding is that in some particular scenarios, the phase transition does not occur and clustering can be achieved irrespective of the class means and covariances. This is evidenced here in the case of the mixture of two Gaussian datasets having the same means and arbitrary difference between covariances.

We consider the problem of evaluating outage probability (OP) values of generalized selection combining diversity receivers over fading channels. This is equivalent to computing the cumulative distribution function (CDF) of the sum of order statistics. Generally, closed-form expressions of the CDF of order statistics are unavailable for many practical distributions. Moreover, the naive Monte Carlo method requires a substantial computational effort when the probability of interest is sufficiently small. In the region of small OP values, we propose instead an efficient, yet universal, importance sampling (IS) estimator that yields a reliable estimate of the CDF with small computing cost. The main feature of the proposed IS estimator is that it has bounded relative error under a certain assumption that is shown to hold for most of the challenging distributions. Moreover, an improvement of this estimator is proposed for the Pareto and the Weibull cases. Finally, the efficiency of the proposed estimators are investigated through various numerical experiments.

In this work, we focus on the uplink (UL) of a single-cell large-scale multi-user MIMO system where mono-antenna users communicate with a BS equipped with antennas. This latter estimates the Ricean correlated channels based on training symbols and uses maximum-ratio-combining or linear-minimum-mean-square-error receivers for signal processing. Assuming a fixed number of users with an asymptotic antenna regime, we derive closed-form approximations of the achievable UL rates as a function of the system's parameters, the Ricean factors and the training sequence's length. Accordingly, these expressions are instructive in how the aforementioned parameters impact the performances. Plus, a different processing approach using only the statistics of the channels is investigated and found to be a judicious choice when the Ricean factor is high enough. Although our analytical results are based on a large antenna-limit, we show by simulations that they provide very accurate approximations even for finite system dimensions.

This paper focuses on studying the performance of general regularized discriminant analysis (RDA) classifiers based on the Gaussian mixture model with different means and covariances. RDA offers a rich class of regularization options, covering as special cases the regularized linear discriminant analysis (RLDA) and the regularized quadratic discriminant analysis (RQDA) classifiers. Based on fundamental results from random matrix theory, we analyze RDA under the double asymptotic regime where the data dimension and the training size both increase in a proportional way. Under the double asymptotic regime and some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that only depends on the data statistical parameters and dimensions. This result can be leveraged to select the optimal parameters that minimize the classification error, thus yielding the optimal classifier. Numerical results are provided to validate our theoretical findings on synthetic data showing high accuracy of our derivations.

The 3GPP Release-13 has recently introduced full-dimension multiple-input multiple-output (FD-MIMO) technology as a practical way to deploy massive MIMO arrays within feasible base station (BS) form factors through the use of active antenna systems with two-dimensional (2D) planar array structures. The 2D arrangement of antenna elements, where the elements in each antenna port are fed with downtilt weights, allows for adaptive electronic beamforming in the elevation as well as the conventional azimuth dimensions. This work focuses on the previously unaddressed problem of determining the optimal downtilt weight vectors for the antenna ports in each cell of a multi-cell multi-user system. The optimization criterion is to maximize the minimum signal to intra-cell interference ratio within a cell while constraining the inter-cell interference leakage. The quasi-optimal weight vectors are obtained through the application of semi-definite relaxation and Dinkelbach's method. The proposed algorithm performs better than the existing approximate schemes even under the effects of pilot contamination.

Visible light communication (VLC) is recognized as a promising technology to complement existing wireless communication systems due to its main advantages such as ease of deployment, low cost and large unlicensed bandwidth. This paper considers the precoding design for a multi-user multiple-input-single-output VLC system. Two major concerns need to be considered while solving such a problem. The first one is related to the inter-user interference, basically inherent to our consideration of a multi-user system, while the second results from the users' mobility, causing imperfect channel estimates. To address both concerns, we propose robust precoding designs that solve both max-min SINR and minimal illumination level problems. The first problem allows users' rates maximization while ensuring fairness and the second problem decides the feasibility of a certain set of target SINRs. The proposed robust designs are studied under different conditions, and are shown to achieve a high gain over their nonrobust counterparts.

This paper discusses full-dimension multiple-input-multiple-output (FD-MIMO) technology, which is currently an active area of research and standardization in wireless communications for evolution toward Fifth Generation (5G) cellular systems. FD-MIMO utilizes an active antenna system (AAS) with a 2-D planar array structure that not only allows a large number of antenna elements to be packed within feasible base station form factors, but also provides the ability of adaptive electronic beamforming in the 3-D space. However, the compact structure of large-scale planar arrays drastically increases the spatial correlation in FD-MIMO systems. In order to account for its effects, the generalized spatial correlation functions for channels constituted by individual elements and overall antenna ports in the AAS are derived. Exploiting the quasi-static channel covariance matrices of users, the problem of determining the optimal downtilt weight vector for antenna ports, which maximizes the minimum signal-to-interference ratio of a multi-user multiple-input-single-output system, is formulated as a fractional optimization problem. A quasi-optimal solution is obtained through the application of semi-definite relaxation and Dinkelbach's method. Finally, the user-group specific elevation beamforming scenario is devised, which offers significant performance gains as confirmed through simulations. These results have direct application in the analysis of 5G FD-MIMO systems.

This paper considers the problem of selecting a set of k measurements from n available sensor observations. The selected measurements should minimize a certain error function assessing the error in estimating a certain m dimensional parameter vector. The exhaustive search inspecting each of the (n) possible choices would require very high computational k complexity and as such is not practical for large n and k. Alternative methods with low complexity have recently been investigated but their main drawbacks are that they require perfect knowledge of the measurement matrix and they need to be applied at the pace of change of the measurement matrix. To overcome these issues, we consider the asymptotic regime in which k, n, and m grow large at the same pace. Tools from random matrix theory are then used to approximate in closed-form the most important error measures that are commonly used. The asymptotic approximations are then leveraged to properly select k measurements exhibiting low values for the asymptotic error measures. Two heuristic algorithms are proposed. The first one merely consists in applying the convex optimization artifice to the asymptotic error measure. The second algorithm is a low-complexity greedy algorithm that attempts to look for a sufficiently good solution for the original minimization problem. The greedy algorithm can be applied to both the exact and the asymptotic error measures and can be thus implemented in blind and channel-aware fashions. We present two potential applications where the proposed algorithms can be used, namely, antenna selection for uplink transmissions in large scale multiuser systems and sensor selection for wireless sensor networks. Numerical results are also presented and sustain the efficiency of the proposed blind methods in reaching the performances of channel-aware algorithms.

We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally, closed-form expressions of the CDF of the sum of order statistics are unavailable for many practical distributions. Moreover, the naive Monte Carlo (MC) method requires a substantial computational effort when the probability of interest is sufficiently small. In the region of small OP values, we instead propose two effective variance reduction techniques that yield a reliable estimate of the CDF with small computing cost. The first estimator, which can be viewed as an importance sampling estimator, has bounded relative error under a certain assumption that is shown to hold for most of the challenging distributions. A possible improvement of this estimator is then proposed for the Pareto and the Weibull cases. The second is a conditional MC estimator that achieves the bounded relative error property for the generalized Gamma case and the logarithmic efficiency for the Log-normal case. Finally, the efficiency of these estimators is compared via various numerical simulations.

A novel statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical channels in the presence of air bubbles for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture Exponential-Gamma distribution. We use the expectation maximization (EM) algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all the channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, the application of the Exponential-Gamma model leads to closed-form and analytically tractable expressions for key system performance metrics such as the outage probability and the average bit-error rate.

This paper investigates the problem of recovering an n-dimensional BPSK signal x0∈ {−1, 1}nfrom m-dimensional measurement vector y = Ax+z, where A and z are assumed to be Gaussian with iid entries. We consider two variants of decoders based on the regularized least squares followed by hard-thresholding: the case where the convex relaxation is from {−1, 1}nto ℝnand the box constrained case where the relaxation is to [−1, 1]n. For both cases, we derive an exact expression of the bit error probability when n and m grow simultaneously large at a fixed ratio. For the box constrained case, we show that there exists a critical value of the SNR, above which the optimal regularizer is zero. On the other side, the regularization can further improve the performance of the box relaxation at low to moderate SNR regimes. We also prove that the optimal regularizer in the bit error rate sense for the unboxed case is nothing but the MMSE detector.

This work considers the downlink of a multicell massive MIMO system in which L base stations (BSs) of N antennas each communicate with K single-antenna user equipments randomly positioned in the coverage area. Within this setting, we are interested in evaluating the sum rate of the system when MRT and RZF are employed under the assumption that each intracell link forms a MIMO Rician uncorrelated fading channel. The analysis is conducted assuming that N and K grow large with a non-trivial ratio N/K under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, and an arbitrary large scale attenuation. Numerical results are used to validate the asymptotic analysis in the finite system regime and to evaluate the network performance under different settings. The asymptotic results are also instrumental to get insights into the interplay among system parameters.

Visible light communication (VLC) is an emerging technique that uses light-emitting diodes (LED) to combine communication and illumination. It is considered as a promising scheme for indoor wireless communication that can be deployed at reduced costs while offering high data rate performance. In this paper, we focus on the design of the downlink of a multi-user VLC system. Inherent to multi-user systems is the interference caused by the broadcast nature of the medium. Linear precoding based schemes are among the most popular solutions that have recently been proposed to mitigate inter-user interference. This paper focuses on the design of the optimal linear precoding scheme that solves the max-min signal-to-interference-plus-noise ratio (SINR) problem. The performance of the proposed precoding scheme is studied under different working conditions and compared with the classical zero-forcing precoding. Simulations have been provided to illustrate the high gain of the proposed scheme.

The BOX-LASSO is a variant of the popular LASSO that includes an additional box-constraint. We propose its use as a decoder in modern Multiple Input Multiple Output (MIMO) communication systems with modulation methods such as the Generalized Space Shift Keying (GSSK) modulation, which produces constellation vectors that are inherently sparse and with bounded elements. In that direction, we prove novel explicit asymptotic characterizations of the squared-error and of the per-element error rate of the BOX-LASSO, under iid Gaussian measurements. In particular, the theoretical predictions can be used to quantify the improved performance of the BOX-LASSO, when compared to the previously used standard LASSO. We include simulation results that validate both these premises and our theoretical predictions.

This letter focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment-based approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

The Gamma-Gamma distribution has recently emerged in a number of applications ranging from modeling scattering and reverberation in sonar and radar systems to modeling atmospheric turbulence in wireless optical channels. In this respect, assessing the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance. In many circumstances, this is related to the difficult question of analyzing the statistics of a sum of Gamma-Gamma random variables. Answering this question is not a simple matter. This is essentially because outage probabilities encountered in practice are often very small, and hence, the use of classical Monte Carlo methods is not a reasonable choice. This lies behind the main motivation of this paper. In particular, this paper proposes a new approach to estimate the left tail of the sum of Gamma-Gamma variates. More specifically, we propose robust importance sampling schemes that efficiently evaluates the outage probability of diversity receivers over Gamma-Gamma fading channels. The proposed estimators satisfy the well-known bounded relative error criterion for both maximum ratio combining and equal gain combining cases. We show the accuracy and the efficiency of our approach compared with naive Monte Carlo via some selected numerical simulations.

The outage probability (OP) of the signal-to-interference-plus-noise ratio (SINR) is an important metric that is used to evaluate the performance of wireless systems. One difficulty toward assessing the OP is that, in realistic scenarios, closed-form expressions cannot be derived. This is, for instance, the case of the Log-normal environment, in which evaluating the OP of the SINR amounts to computing the probability that a sum of correlated Log-normal variates exceeds a given threshold. Since such a probability does not admit a closed-form expression, it has thus far been evaluated by several approximation techniques, the accuracies of which are not guaranteed in the region of small OPs. For these regions, simulation techniques based on variance reduction algorithms are a good alternative, being quick and highly accurate for estimating rare event probabilities. This constitutes the major motivation behind this paper. More specifically, we propose a generalized hybrid importance sampling scheme, based on a combination of a mean shifting and a covariance matrix scaling, to evaluate the OP of the SINR in a Log-normal environment. We further our analysis by providing a detailed study of two particular cases. Finally, the performance of these techniques is performed both theoretically and through various simulation results.

In this paper, we develop a novel moment-based approach for the evaluation of the outage probability (OP) in a generalized fading environment with interference and noise. Our method is based on the derivation of a power series expansion of OP of the signal-to-interference-plus-noise ratio. It does not necessitate stringent requirements, the only major ones being the existence of a power series expansion of the cumulative distribution function of the desired user power and the knowledge of the cross moments of the interferers' powers. The newly derived formula is shown to be applicable for most of the well-practical fading models of the desired user under some assumptions on the parameters of the powers' distributions. A further advantage of our method is that it is applicable irrespective of the nature of the fading models of the interfering powers, the only requirement being the perfect knowledge of their cross moments. In order to illustrate the wide scope of applicability of our technique, we present a convergence study of the provided formula for the Generalized Gamma and the Rice fading models. Moreover, we show that our analysis has direct bearing on recent multi-channel applications using selection diversity techniques. Finally, we assess by simulations the accuracy of the proposed formula for various fading environments.

Elevation beamforming and Full Dimension MIMO (FD-MIMO) are currently active areas of research and standardization in 3GPP LTE-Advanced. FD-MIMO utilizes an active antenna array system (AAS), that provides the ability of adaptive electronic beam control over the elevation dimension, resulting in a better system performance as compared to the conventional 2D MIMO systems. FD-MIMO is more advantageous when amalgamated with massive MIMO systems, in that it exploits the additional degrees of freedom offered by a large number of antennas in the elevation. To facilitate the evaluation of these systems, a large effort in 3D channel modeling is needed. This paper aims at providing a summary of the recent 3GPP activity around 3D channel modeling. The 3GPP proposed approach to model antenna radiation pattern is compared with the ITU approach. A closed-form expression is then worked out for the spatial correlation function (SCF) for channels constituted by individual antenna elements in the array by exploiting results on spherical harmonics and Legendre polynomials. The proposed expression can be used to obtain correlation coefficients for any arbitrary 3D propagation environment. Simulation results corroborate and study the derived spatial correlation expression. The results are directly applicable to the analysis of future 5G 3D massive MIMO systems.

In this work, we focus on the ergodic sum rate in the downlink of a single-cell large-scale multi-user MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments. A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming N and K grow large with a non trivial ratio and perfect channel state information is available at the base station. Recent results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of the system parameters, the spatial correlation matrix and the Rician factor. Numerical results are used to evaluate the performance gap in the finite system regime under different operating conditions.

This work focuses on the downlink of a single-cell large-scale MIMO system in which the base station equipped with M antennas serves K single-antenna users. In particular, we are interested in reducing the implementation complexity of the optimal linear precoder (OLP) that minimizes the total power consumption while ensuring target user rates. As most precoding schemes, a major difficulty towards the implementation of OLP is that it requires fast inversions of large matrices at every new channel realizations. To overcome this issue, we aim at designing a linear precoding scheme providing the same performance of OLP but with lower complexity. This is achieved by applying the truncated polynomial expansion (TPE) concept on a per-user basis. To get a further leap in complexity reduction and allow for closed-form expressions of the per-user weighting coefficients, we resort to the asymptotic regime in which M and K grow large with a bounded ratio. Numerical results are used to show that the proposed TPE precoding scheme achieves the same performance of OLP with a significantly lower implementation complexity.

In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.

In this paper, we develop a generalized moment-based approach for the evaluation of the outage probability (OP) in the presence of co-channel interference and additive white Gaussian noise. The proposed method allows the evaluation of the OP of the signal-to-interference-plus-noise ratio by a power series expansion in the threshold value. Its main advantage is that it does not require a particular distribution for the interference channels. The only necessary ingredients are a power series expansion for the cumulative distribution function of the desired user power and the cross-moments of the interferers' powers. These requirements are easily met in many practical fading models, for which the OP might not be obtained in closed-form expression. For a sake of illustration, we consider the application of our method to the Rician fading environment. Under this setting, we carry out a convergence study of the proposed power series and corroborate the validity of our method for different values of fading parameters and various numbers of co-channel interferers.

In this work, we propose a new regularization approach for linear least-squares problems with random matrices. In the proposed constrained perturbation regularization approach, an artificial perturbation matrix with a bounded norm is forced into the system model matrix. This perturbation is introduced to improve the singular-value structure of the model matrix and, hence, the solution of the estimation problem. Relying on the randomness of the model matrix, a number of deterministic equivalents from random matrix theory are applied to derive the near-optimum regularizer that minimizes the mean-squared error of the estimator. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods for various estimated signal characteristics. In addition, simulations show that our approach is robust in the presence of model uncertainty.

This paper presents a comprehensive performance analysis of full-duplex multiuser relay networks employing opportunistic scheduling with noisy and compressive feedback. Specifically, two feedback techniques based on compressive sensing (CS) theory are introduced and their effect on the system performance is analyzed. The problem of joint user identity and signal-to-noise ratio (SNR) estimation at the base-station is casted as a block sparse signal recovery problem in CS. Using existing CS block recovery algorithms, the identity of the strong users is obtained and their corresponding SNRs are estimated using the best linear unbiased estimator (BLUE). To minimize the effect of feedback noise on the estimated SNRs, a backoff strategy that optimally backsoff on the noisy estimated SNRs is introduced, and the error covariance matrix of the noise after CS recovery is derived. Finally, closed-form expressions for the end-to-end SNRs of the system are derived. Numerical results show that the proposed techniques drastically reduce the feedback air-time and achieve a rate close to that obtained by scheduling techniques that require dedicated error-free feedback from all network users. Key findings of this paper suggest that the choice of half-duplex or full-duplex SNR feedback is dependent on the channel coherence interval, and on low coherence intervals, full-duplex feedback is superior to the interference-free half-duplex feedback.

This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. Following the approach proposed by Vallet et al., we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication, in which this kind of matrices naturally arise.

The outage probability (OP) of the signal-to-interference-plus-noise ratio (SINR) is an important metric used to evaluate the performance of wireless communication systems operating over fading channels. One major difficulty toward assessing the OP is that, in most of the realistic scenarios, closed-form expressions cannot be derived. This is for instance the case of Log-normal fading environments, in which evaluating the OP of the SINR amounts to computing the probability that a sum of correlated Log-normal variates exceeds a given threshold. Since such a probability is not known to admit a closed-form expression, it has thus far been evaluated by several approximation techniques, the accuracies of which are unfortunately not guaranteed in the interesting region of small outage probabilities. For these regions, simulation techniques based on variance reduction algorithms can represent a good alternative, being well-recognized to be quick and highly accurate for estimating rare event probabilities. This constitutes the major motivation behind our work. More specifically, we propose an efficient importance sampling approach which is based on a covariance matrix scaling technique and illustrate its computational gain over naive Monte Carlo simulations through some selected simulation results.

This paper lies in the lineage of recent works studying the asymptotic behaviour of robust-scatter estimators in the case where the number of observations and the dimension of the population covariance matrix grow at infinity with the same pace. In particular, we analyze the fluctuations of bilinear forms of the robust shrinkage estimator of covariance matrix. We show that this result can be leveraged in order to improve the design of robust detection methods. As an example, we provide an improved generalized likelihood ratio based detector which combines robustness to impulsive observations and optimality across the shrinkage parameter, the optimality being considered for the false alarm regulation.

Motivated by the recent interest in 3D beamforming to enhance system performance, we present an information-theoretic channel model for multiple-input multiple-output (MIMO) systems, that can support the elevation dimension. The principle of maximum entropy is used to determine the distribution of the channel matrix consistent with the prior angular information. We provide an explicit expression for the cumulative density function (CDF) of the mutual information in the large number of transmit antennas and paths regime. The derived Gaussian approximation is quite accurate even for realistic system dimensions. The simulation results study the achievable performance through the meticulous selection of the transmit antenna downtilt angles. The results are directly applicable to the analysis of 5G 3D massive MIMO systems.

The outage capacity (OC) is among the most important performance metrics of communication systems over fading channels. The evaluation of the OC, when Equal Gain Combining (EGC) or Maximum Ratio Combining (MRC) diversity techniques are employed, boils down to computing the Cumulative Distribution Function (CDF) of the sum of channel envelopes (equivalently amplitudes) for EGC or channel gain (equivalently squared enveloped/amplitudes) for MRC. Closed-form expressions of the CDF of the sum of many generalized fading variates are generally unknown and constitute open problems. In this paper, we develop a unified hazard rate twisting Importance Sampling (IS) based approach to efficiently estimate the CDF of the sum of independent arbitrary variates. The proposed IS estimator is shown to achieve an asymptotic optimality criterion, which clearly guarantees its efficiency. Some selected simulation results are also shown to illustrate the substantial computational gain achieved by the proposed IS scheme over crude Monte-Carlo simulations.

In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for the standardized three-dimensional (3D) multiple-input multiple-output (MIMO) channel. This novel SCF is developed for a uniform linear array of antennas with non-isotropic antenna patterns. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials to obtain a closed-form expression for the SCF for arbitrary angular distributions and antenna patterns. The resulting expression depends on the underlying angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. Numerical results validate the proposed analytical expression and study the impact of angular spreads on the correlation. The derived SCF will help evaluate the performance of correlated 3D MIMO channels in the future.

Multiple-input-multiple-output (MIMO) systems of current LTE releases are capable of adaptation in the azimuth only. Recently, the trend is to enhance system performance by exploiting the channel's degrees of freedom in the elevation, which necessitates the characterization of 3D channels. We present an information-theoretic channel model for MIMO systems that supports the elevation dimension. The model is based on the principle of maximum entropy, which enables us to determine the distribution of the channel matrix consistent with the prior information on the angles. Based on this model, we provide analytical expression for the cumulative density function (CDF) of the mutual information (MI) for systems with a single receive and finite number of transmit antennas in the general signal-to-interference-plus-noise-ratio (SINR) regime. The result is extended to systems with finite receive antennas in the low SINR regime. A Gaussian approximation to the asymptotic behavior of MI distribution is derived for the large number of transmit antennas and paths regime. We corroborate our analysis with simulations that study the performance gains realizable through meticulous selection of the transmit antenna downtilt angles, confirming the potential of elevation beamforming to enhance system performance. The results are directly applicable to the analysis of 5G 3D-Massive MIMO-systems.

Three dimensional (3D) beamforming (also elevation beamforming) is now gaining interest among researchers in wireless communication. The reason can be attributed to its potential for enabling a variety of strategies such as sector or user specific elevation beamforming and cell-splitting. Since these techniques cannot be directly supported by current LTE releases, the 3GPP is now working on defining the required technical specifications. In particular, a large effort is currently being made to get accurate 3D channel models that support the elevation dimension. This step is necessary as it will evaluate the potential of 3D and full dimensional (FD) beamforming techniques to benefit from the richness of real channels. This work aims at presenting the on-going 3GPP study item “study on 3D-channel model for elevation beamforming and FD-MIMO studies for LTE” and positioning it with respect to previous standardization works.

This paper presents a new synthesis method for Hybrid Filter Banks A/D converters (HFB-ADC). As most of the classical methods minimizes a SDR criterion, which is too restrictive, this method minimizes the SNR criterion. Unlike the few methods minimizing also the SNR, this one does not involve any optimization process.

In this paper, the problem of fast point-to-point multiple-input-multiple-output channel mutual information estimation is addressed, in the situation where the receiver undergoes unknown colored interference, whereas the channel with the transmitter is perfectly known. The considered scenario assumes that the estimation is based on a few channel use observations during a short sensing period. Using large dimensional random matrix theory, an estimator referred to as G-estimator is derived. This estimator is proved to be consistent as the number of antennas and observations grow large and its asymptotic performance is analyzed. In particular, the G-estimator satisfies a central limit theorem with asymptotic Gaussian fluctuations. Simulations are provided which strongly support the theoretical results, even for small system dimensions.

In the context of multidimensional signals, the linear Wiener receiver is frequently encountered in wireless communication and in array processing; it is in fact the linear receiver that achieves the lowest level of interference. In this contribution, we focus on the study of the associated Signal-to-interference plus noise ratio (SINR) at its output in the context of Ricean multiple-input multiple-output (MIMO) channels. The case of Ricean channels, which induces non-centered random variables, can be encountered in several practical environments and has not been studied so far, as it raises substantial technical issues. With the help of large random matrix theory, which has shown to be fruitful to successfully address several problems in wireless communications, we study the behaviour of the SINR, together with its fluctuations via a central limit theorem. As realistic models also involve non-Gaussian random variables, we relax the Gaussian assumption. This results in an extra term involving the fourth cumulant in the expression of the variance.

In this paper, we address the problem of fast point-to-point channel capacity estimation in the case where the receiver undergoes unknown interference from multiple sources, whereas the channel with the transmitter is perfectly known. For this particular context, we propose a fast estimator for the capacity estimation, and compare its performance with that of the traditional methods. More precisely, we analyse the fluctuations of the traditional and proposed techniques and prove that their behaviors can be approximated by Gaussian random variables for which we derive the variances.

In this paper, the quasi-convexity of a sum of quadratic fractions in the form Σi=1n[(1+ci x2)/((1+dix)2)] is demonstrated wherecianddiare strictly positive scalars, when defined on the positive real axis R+. It will be shown that this quasi-convexity guarantees it has a unique local (and hence global) minimum. Indeed, this problem arises when considering the optimization of the weighting coefficient in regularized semi-blind channel identification problem, and more generally, is of interest in other contexts where we combine two different estimation criteria. Note that V. Buchoux have noticed by simulations that the considered function has no local minima except its unique global minimum but this is the first time this result, as well as the quasi-convexity of the function is proved theoretically.

This paper addresses the issue of the optimization of the regularization constant in semi-blind channel estimation techniques, in which the training sequence-based criterion is combined linearly with the blind subspace criterion. In such semi-blind estimation techniques, the optimization of the regularizing constant with respect to the channel estimation error is mandatory, otherwise, the expected improvement in performance could not be achieved. In this context, recent works proposed numerical methods for the setting of the regularization constant. However, these methods are often sub-optimum and involve high computational complexities. In this paper, we propose to optimize with respect to a regularizing matrix instead of a regularizing scalar. We prove that interestingly in this case, a closed-form expression for the optimum regularizing matrix exists, thereby avoiding iterative algorithms as for the conventional techniques. We also prove that the obtained scheme has slightly better performance in terms of mean square error and bit error rate while ensuring lower complexity.

This paper is devoted to the study of the performance of the linear minimum mean-square error (LMMSE) receiver for (receive) correlated multiple-input multiple-output (MIMO) systems. By the random matrix theory, it is well known that the signal-to-noise ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to+infin at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate (BER) and the outage probability, especially for small system dimensions, Li proposed convincingly to assume that the SNR follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this paper, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.

This paper is devoted to the performance study of the linear minimum mean squared error (LMMSE) estimator for multidimensional signals in the large-dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the signal-to-interference-plus-noise ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiple-antenna as well as spread-spectrum transmission models. The expression of the deterministic approximation of the SINR in the large-dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large-dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.

In this paper, we propose a novel frequency scheduling strategy for an OFDM switched-beam system. We deal with dynamic frequency allocation based on the distance of the user from the serving base station (BS) or on the power of the channel response received by the user. The key idea is to reduce the interference among the neighboring cells. To do so, we consider a time-space-frequency allocation scheme where users are assigned with the appropriate set of subcarriers according to their serving beam at any given time. We evaluate the performance of the proposed frequency allocation scheme when Kalman filtering is used for joint channel estimation and beam selection. A system-level simulator is developed which computes the signal to interference ratio (SIR) for a reference mobile user with different resource allocation strategies. Previously obtained link-level throughput vs. signal to noise ratio (SNR) results are then translated into a system-level cumulative distribution function (cdf) of the user throughput. Link-level frame error rate (FER) results suggest that the proposed Kalman-based OFDM switched-beam system offers high performance over slow fading channels. System-level SIR results show that the proposed frequency scheduling scheme reduces significantly the interference. Our scheme enhances the system throughput compared to other allocation schemes.

In this paper, a generalized technique for the design automation of fs/4 bandpass SigmaDelta modulators using feedback FIRDACs is proposed. The FIRDACs are used to increase the degrees of freedom in order to perform an exact equivalence with high order discrete-time SigmaDelta modulators and also to allow a more efficient circuit implementation of the LC filter. The design technique is based on discrete time-continuous time equivalence simplified by using the method of partial fractions expansion. The excess loop delay is taken into account without making more difficult the calculations since we define how to get the orders of the FIRDACs. Several examples of design are simulated with different values of excess loop delay

A general technique for the design of undersampled LC bandpass modulators using feedback FIRDACs is proposed. The coefficients of the FIRDACs are used to increase the degrees of freedom in order to perform an exact equivalence between undersampled LC bandpass Sigma-Delta and high order discrete-time sigma-delta modulators. Using FIRDACs coefficients, it is also possible to simplify the circuit implementation by removing internal summing nodes and by decreasing coefficients spread. An undersampled 4th order LC sigma-delta is given as a design example. The effect of the undersampling ratio on the performance of finite quality factor LC sigma-delta modulators is also studied