arXiv subjects

Xavier Mestre

Publications and source records attributed to Xavier Mestre.

34 records · Page 2Linked to original sources

arXiv2021

On the detection of low-rank signal in the presence of spatially uncorrelated noise: a frequency domain approach

This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M xK MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statistics based on the eigenvalues of an estimate of the spectral coherence matrix (SCM), obtained as a renormalization of the frequency-smoothed periodogram of the observed signal. If N denotes the sample size and B the smoothing span, it is proved that in the high-dimensional regime where M, B, N converge to infinity while K remains fixed, the SCM behaves as a certain correlated Wishart matrix. Exploiting well-known results on the behaviour of the eigenvalues of such matrices, it is deduced that the standard tests based on linear spectral statistics of the SCM fail to detect the presence of the useful signal in the high-dimensional regime. A new test based on the SCM, which is proved to be consistent, is also proposed, and its statistical performance is evaluated through numerical simulations.

cs.IT↗

arXiv2021

On the asymptotic behaviour of the eigenvalue distribution of block correlation matrices of high-dimensional time series

We consider linear spectral statistics built from the block-normalized correlation matrix of a set of $M$ mutually independent scalar time series. This matrix is composed of $M \times M$ blocks that contain the sample cross correlation between pairs of time series. In particular, each block has size $L \times L$ and contains the sample cross-correlation measured at $L$ consecutive time lags between each pair of time series. Let $N$ denote the total number of consecutively observed windows that are used to estimate these correlation matrices. We analyze the asymptotic regime where $M,L,N \rightarrow +\infty$ while $ML/N \rightarrow c_\star$, $0<c_\star<\infty$. We study the behavior of linear statistics of the eigenvalues of this block correlation matrix under these asymptotic conditions and show that the empirical eigenvalue distribution converges to a Marcenko-Pastur distribution. Our results are potentially useful in order to address the problem of testing whether a large number of time series are uncorrelated or not.

math.PR↗

arXiv2020

On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima.

eess.SP↗

arXiv2017

Spectral Convergence of Large Block-Hankel Gaussian Random Matrices

This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from complex Gaussian correlated stationary random sequences. In the asymptotic regime where M \rightarrow \infty, N \rightarrow +\infty and ML/N \rightarrow c > 0, it is shown using the Stieltjes transform approach that the empirical eigenvalue distribution of W_N W_N* has a deterministic behaviour which is characterized.

math.PR↗

arXiv2016

Uplink FBMC/OQAM-based Multiple Access Channel: Distortion Analysis under Strong Frequency Selectivity

This paper computes the distortion power at the receiver side of an FBMC/OQAM-based OFDMA uplink channel under strong frequency selectivity and/or user timing errors. More precisely, it provides a distortion expression that is valid for a wide class of prototype pulses (not necessarily perfect-reconstruction ones) when the number of subcarriers is sufficiently large. This result is a valuable instrument for analyzing how users interfere to one another and to justify, formally, the common choice of placing an empty guard band between adjacent users. Interestingly, the number of out-band subcarriers contaminated by each user only depends on the prototype pulses and not on the channel nor on the equalizer. To conclude, the distortion analysis presented in this paper, together with some simulation results for a realistic scenario, also provide convincing evidence that FBMC/OQAM-based OFDMA is superior to classic circular-prefix OFDMA in the case of asynchronous users.

cs.IT↗

arXiv2016

Single-Tap Precoders and Decoders for Multi-User MIMO FBMC-OQAM under Strong Channel Frequency Selectivity

The design of linear precoders or decoders for multiuser (MU) multiple-input multiple-output (MIMO) filterbank multicarrier (FBMC) modulations in the case of strong channel frequency selectivity is presented. The users and the base station (BS) communicate using space division multiple access (SDMA). The low complexity proposed solution is based on a single tap per-subcarrier precoding/decoding matrix at the base station (BS) in the downlink/uplink. As opposed to classical approaches that assume flat channel frequency selectivity at the subcarrier level, the BS does not make this assumption and takes into account the distortion caused by channel frequency selectivity. The expression of the FBMC asymptotic mean squared error (MSE) in the case of strong channel selectivity derived in earlier works is developed and extended. The linear precoders and decoders are found by optimizing the MSE formula under two design criteria, namely zero forcing (ZF) or minimum mean squared error (MMSE). Finally, simulation results demonstrate the performance of the optimized design. As long as the number of BS antennas is larger than the number of users, it is shown that those extra degrees of freedom can be used to compensate for the channel frequency selectivity.

cs.IT↗

arXiv2016

Parallelized Structures for MIMO FBMC under Strong Channel Frequency Selectivity

A novel architecture for MIMO transmission and reception of filterbank multicarrier (FBMC) modulated signals under strong frequency selectivity is presented. The proposed system seeks to approximate an ideal frequency-selective precoder and linear receiver by Taylor expansion, exploiting the structure of the analysis and synthesis filterbanks. The resulting architecture is implemented by linearly combining conventional MIMO linear transceivers, which are applied to sequential derivatives of the original filterbank. The classical per-subcarrier precoding/linear receiver configuration is obtained as a special case of this architecture, when only one stage is fixed at both transmitter and receiver. An asymptotic expression for the resulting intersymbol/intercarrier (ISI/ICI) distortion is derived assuming that the number of subcarriers grows large. This expression can in practice be used in order to determine the number of parallel stages that need to be implemented in the proposed architecture. Performance evaluation studies confirm the substantial advantage of the proposed scheme in practical frequency-selective MIMO scenarios.

cs.IT↗

arXiv2015

A CLT for an improved subspace estimator with observations of increasing dimensions

This paper deals with subspace estimation in the small sample size regime, where the number of samples is comparable in magnitude with the observation dimension. The traditional estimators, mostly based on the sample correlation matrix, are known to perform well as long as the number of available samples is much larger than the observation dimension. However, in the small sample size regime, the performance degrades. Recently, based on random matrix theory results, a new subspace estimator was introduced, which was shown to be consistent in the asymptotic regime where the number of samples and the observation dimension converge to infinity at the same rate. In practice, this estimator outperforms the traditional ones even for certain scenarios where the observation dimension is small and of the same order of magnitude as the number of samples. In this paper, we address a performance analysis of this recent estimator, by proving a central limit theorem in the above asymptotic regime. We propose an accurate approximation of the mean square error, which can be evaluated numerically.

stat.ME↗

arXiv2015

Performance analysis of an improved MUSIC DoA estimator

This paper adresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while it is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.

stat.AP↗

arXiv2015

White Paper: Radio y Redes Cognitivas

Traditionally, two different policies to access the radio spectrum have coexisted: licensed regulation, whereby the rights to use specific spectral bands are granted in exclusivity to an individual operator; or unlicensed regulation, according to which certain spectral bands are declared open for free use by any operator or individual following specific rules. While these paradigms have allowed the wireless communications sector to blossom in the past, in recent years they have evidenced shortcomings and given signs of exhaustion. For instance, it is quite usual to encounter fully overloaded mobile communication systems coexisting with unused contiguous spectral bands. This clearly advocates for a more flexible and dynamic allocation of the spectrum resources which can only be achieved with the advent of the so-called cognitive radios and networks. This whitepaper provides an accurate description of priority research activities and open challenges related to the different functionalities of cognitive radios and networks. First, we outline the main open problems related to the theoretical characterization of cognitive radios, spectrum sensing techniques as well as the optimization of physical layer functionalities in these networks. Second, we provide a description of the main research challenges that arise from a system point of view: MAC protocol optimization, traffic modelling, RRM strategies, routing paradigms or security issues. Next, we point out other problems related to the practical hardware implementation of cognitive radios, giving especial emphasis to sensing capabilities, reconfigurability and cognitive control and management. Finally, we succinctly report on a number of current activities related to the standardization of cognitive radio systems.

cs.NI↗

arXiv2013

The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation

Consider the matrix $Σ_n = n^{-1/2} X_n D_n^{1/2} + P_n$ where the matrix $X_n \in \C^{N\times n}$ has Gaussian standard independent elements, $D_n$ is a deterministic diagonal nonnegative matrix, and $P_n$ is a deterministic matrix with fixed rank. Under some known conditions, the spectral measures of $Σ_n Σ_n^*$ and $n^{-1} X_n D_n X_n^*$ both converge towards a compactly supported probability measure $μ$ as $N,n\to\infty$ with $N/n\to c>0$. In this paper, it is proved that finitely many eigenvalues of $Σ_nΣ_n^*$ may stay away from the support of $μ$ in the large dimensional regime. The existence and locations of these outliers in any connected component of $\R - \support(μ)$ are studied. The fluctuations of the largest outliers of $Σ_nΣ_n^*$ are also analyzed. The results find applications in the fields of signal processing and radio communications.

math.PR↗

arXiv2012

A CLT on the SNR of Diagonally Loaded MVDR Filters

This paper studies the fluctuations of the signal-to-noise ratio (SNR) of minimum variance distorsionless response (MVDR) filters implementing diagonal loading in the estimation of the covariance matrix. Previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples. Specifically, a central limit theorem (CLT) is established for the fluctuations of the SNR of the diagonally loaded MVDR filter, under both supervised and unsupervised training settings in adaptive filtering applications. Our second-order analysis is based on the Nash-Poincaré inequality and the integration by parts formula for Gaussian functionals, as well as classical tools from statistical asymptotic theory. Numerical evaluations validating the accuracy of the CLT confirm the asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.

cs.IT↗

arXiv2011

Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings.

q-fin.PM↗

arXiv2011

Improved subspace estimation for multivariate observations of high dimension: the deterministic signals case

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones. It has recently been suggested that this situation (where the sample size is small compared to the observation dimension) can be very accurately modeled by considering the asymptotic regime where the observation dimension $M$ and the number of snapshots $N$ converge to $+\infty$ at the same rate. Using large random matrix theory results, it can be shown that traditional subspace estimates are not consistent in this asymptotic regime. Furthermore, new consistent subspace estimate can be proposed, which outperform the standard subspace methods for realistic values of $M$ and $N$. The work carried out so far in this area has always been based on the assumption that the observations are random, independent and identically distributed in the time domain. The goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals. In practice, this allows to use the proposed approach regardless of the statistical properties of the source signals. In order to construct the proposed estimators, new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of Information plus Noise complex Gaussian models are established. These results are believed to be of independent interest.

cs.IT↗

arXiv2011

Large information plus noise random matrix models and consistent subspace estimation in large sensor networks

In array processing, a common problem is to estimate the angles of arrival of $K$ deterministic sources impinging on an array of $M$ antennas, from $N$ observations of the source signal, corrupted by gaussian noise. The problem reduces to estimate a quadratic form (called "localization function") of a certain projection matrix related to the source signal empirical covariance matrix. Recently, a new subspace estimation method (called "G-MUSIC") has been proposed, in the context where the number of available samples $N$ is of the same order of magnitude than the number of sensors $M$. In this context, the traditional subspace methods tend to fail because the empirical covariance matrix of the observations is a poor estimate of the source signal covariance matrix. The G-MUSIC method is based on a new consistent estimator of the localization function in the regime where $M$ and $N$ tend to $+\infty$ at the same rate. However, the consistency of the angles estimator was not adressed. The purpose of this paper is to prove the consistency of the angles of arrival estimator in the previous asymptotic regime. To prove this result, we show the property that the singular values of M x N Gaussian information plus noise matrix escape from certain intervals is an event of probability decreasing at rate O(1/N^p) for all p. A regularization trick is also introduced, which allows to confine these singular values into certain intervals and to use standard tools as Poincaré inequality to characterize any moments of the estimator. These results are believed to be of independent interest.

math.PR↗

arXiv2008

Impact of CSI on Distributed Space-Time Coding in Wireless Relay Networks

We consider a two-hop wireless network where a transmitter communicates with a receiver via $M$ relays with an amplify-and-forward (AF) protocol. Recent works have shown that sophisticated linear processing such as beamforming and distributed space-time coding (DSTC) at relays enables to improve the AF performance. However, the relative utility of these strategies depend on the available channel state information at transmitter (CSIT), which in turn depends on system parameters such as the speed of the underlying fading channel and that of training and feedback procedures. Moreover, it is of practical interest to have a single transmit scheme that handles different CSIT scenarios. This motivates us to consider a unified approach based on DSTC that potentially provides diversity gain with statistical CSIT and exploits some additional side information if available. Under individual power constraints at the relays, we optimize the amplifier power allocation such that pairwise error probability conditioned on the available CSIT is minimized. Under perfect CSIT we propose an on-off gradient algorithm that efficiently finds a set of relays to switch on. Under partial and statistical CSIT, we propose a simple waterfilling algorithm that yields a non-trivial solution between maximum power allocation and a generalized STC that equalizes the averaged amplified noise for all relays. Moreover, we derive closed-form solutions for M=2 and in certain asymptotic regimes that enable an easy interpretation of the proposed algorithms. It is found that an appropriate amplifier power allocation is mandatory for DSTC to offer sufficient diversity and power gain in a general network topology.

cs.IT↗