Malika Kharouf

A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large-Dimensional Signals

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.

BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels

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.

On the fluctuations of the mutual information for non centered MIMO channels: The non Gaussian case

The use of Multiple Input Multiple Output (MIMO) systems has been widely recognized as an efficient solution to increase the data rate of wireless communications. In this regard, several contributions investigate the performance improvement of MIMO systems in terms of Shannons mutual information. In most of these contributions, elements of the MIMO channel matrix are assumed to belong to a multivariate Gaussian distribution. The non Gaussian case, which is realistic in many practical environments, has been much less studied. This contribution is devoted to the study of the mutual information of MIMO channels when the channel matrix elements are Ricean with the non-Ricean component being iid but non-Gaussian. In this context, the mutual information behavior is studied in the large dimensional regime where both channel matrix dimensions converge to infinity at the same pace. In this regime, a Central Limit Theorem on the mutual information is provided. In particular, the mutual information variance is determined in terms of the parameters of the channel statistical model. Since non Gaussian entries are allowed, a new term proportional to the fourth cumulant of their distribution arises in the expression of the asymptotic variance. In addition, a bias term proportional to this fourth order cumulant appears.

Fluctuations of the SNR at the wiener filter output for large dimensional signals

Consider the linear Wiener receiver for multidimensional signals. Such a receiver is frequently encountered in wireless communications and in array processing, and the Signal to noise ratio (SNR) at its output is a popular performance index. The SNR can be modeled as a random quadratic form and in order to study this quadratic form, one can rely on well-know results in Random Matrix Theory, if one assumes that the dimension of the received and transmitted signals go to infinity, their ratio remaining constant. In this paper, we study the asymptotic behavior of the SNR for a large class of multidimensional signals (MIMO, CDMA, MC-CDMA transmissions). More precisely, we provide a deterministic approximation of the SNR, that depends on the system parameters; furthermore, the fluctuations of the SNR around this deterministic approximation are shown to be Gaussian, with variance decreasing as 1/K, where K is the dimension of the transmitted signal.

Outage probability approximation for the wiener filter SINR in MIMO systems

This paper studies the fluctuations of the post-processing SNR at the output of the linear MMSE receiver in (receive) correlated multiple input multiple output (MIMO) systems. Although it is known that asymptotically, the SNR behaves like a Gaussian random variable, this approximation may yield to inaccurate estimates for small dimension. In order to circumvent this, we use gamma and generalized gamma distributions to approximate the probability distribution of the SINR. The first three asymptotic moments of the SNR are computed and are used to adjust gamma and generalized gamma distributions and to accurately approximate the bit error rate (BER) and its outage probability. We provide simulations which strongly support the gamma approximation, even for a small number of emitting/receive antennas.

On the fluctuations of the SINR at the output of the Wiener filter for non centered channels: The non Gaussian case

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.