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.

This paper provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of available observations is comparable in magnitude to the observation dimension. An exact expression as well as an empirical, asymptotically accurate, approximation of the limiting variance is derived. Simulations are performed that corroborate the theoretical claims.

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.

This article provides a central limit theorem for a consistent estimator of the population eigenvalues of a class of sample covariance matrices. An exact expression as well as an empirical and asymptotically accurate approximation of the limiting variance is also derived. These results are applied in a cognitive radio context featuring an orthogonal-CDMA primary network and a secondary network whose objective is to maximise the coverage of secondary transmissions under low probability of interference with primary users.

This paper introduces a unified framework for the detection of a single source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum Likelihood Test is studied and yields the analysis of the ratio between the maximum eigenvalue of the sampled covariance matrix and its normalized trace. Using recent results from random matrix theory, a practical way to evaluate the threshold and thep-value of the test is provided in the asymptotic regime where the numberKof sensors and the numberNof observations per sensor are large but have the same order of magnitude. The theoretical performance of the test is then analyzed in terms of Receiver Operating Characteristic (ROC) curve. It is, in particular, proved that both Type I and Type II error probabilities converge to zero exponentially as the dimensions increase at the same rate, and closed-form expressions are provided for the error exponents. These theoretical results rely on a precise description of the large deviations of the largest eigenvalue of spiked random matrix models, and establish that the presented test asymptotically outperforms the popular test based on the condition number of the sampled covariance matrix.

In this paper, the capacity-achieving input covariance matrices for coherent block-fading correlated multiple input multiple output (MIMO) Rician channels are determined. In contrast with the Rayleigh and uncorrelated Rician cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In the asymptotic regime where the number of transmit and receive antennas converge to infinity at the same rate, new results related to the accuracy of the approximation of the average mutual information are provided. Based on the accuracy of this approximation, an attractive optimization algorithm is proposed and analyzed. This algorithm is shown to yield an effective way to compute the capacity achieving matrix for the average mutual information and numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information.

This paper deals with the detection of a continuous random process described by an Ornstein-Uhlenbeck (O-U) stochastic differential equation. Randomly spaced sensors or equivalently a random time sampler which deliver noisy samples of the process are used for this detection. Two types of tests are considered: either H0 refers to the presence of the noisy O-U process or H0 refers to the sole presence of noise. For any fixed false alarm probability, it is shown that the type II error probability decreases to zero exponentially in the number of samples. The exponents, which do not depend on the false alarm probability, are characterized. This work completes former contributions that consider noiseless O-U process with a random sampling or noisy O-U processes with a regular sampling.

In this talk, we will discuss some problems related to cooperative spectrum sensing, and show how random matrix theory can help to address them. We will propose a simple test for frequency band sensing in wireless networks. The test is based on the analysis of the ratio of the extreme eigenvalues related to the gain matrix of the channel. The novelty relies in the fact that the test does not require the knowledge of the noise statistics. Large random matrix results allow us to build the threshold for the test, and also to study its type II error. This in particular enables us to compare this test with a different although popular test already proposed in the literature. We will show that our test is uniformly more powerful.

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 article, large random matrix theory is used to study Shannonpsilas mutual information of a general class of multiple input multiple output radio channels with random correlated gains. In the literature, there exists an approximation of this mutual information in the asymptotic regime where the number of transmitting antennas and the number of receiving antennas grow toward infinity at the same pace. This contribution is devoted to the study of the mutual informationpsilas fluctuations around this deterministic approximation under the form of a central limit theorem (CLT). In particular, this CLT provides an approximation of the outage probability, which represents a fundamental performance index for communications on slow fading channels. The proof of this CLT relies on martingale theory.

This paper adresses the behavior of the mutual information of correlated multiple-input multiple-output (MIMO) Rayleigh channels when the numbers of transmit and receive antennas converge to$+\infty $at the same rate. Using a new and simple approach based on PoincarÉ–Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information when properly centered and rescaled converges to a standard Gaussian random variable. Simple expressions for the centering and scaling parameters are provided. These results confirm previous evaluations based on the powerful but nonrigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.

This paper studies high SNR approximations of the ergodic mutual information of block fading MIMO correlated Rician channels. The exact expression of the mutual information of such channels is quite complicated, and difficult to use to obtain convenient high SNR approximations. In this paper, it is replaced by an accurate large system approximant obtained in the case where the number of transmit and receive antennas t and r converge to +infin at the same rate. The large system approximant is studied at high SNR, and it is shown that 3 different behaviours are possible depending on r/t, the rank of the line of sight component and the Rician factor. The accuracy of the high SNR approximant is shown to be connected to the support of the deterministic large system approximant of the eigenvalue distribution of the Gram matrix of the channel. This allows to infer that the approximant is accurate for realistic values of r and t if r and t or if r npar t, the line of sight component is invertible and the Rician factor is greater than a certain threshold.