Abla Kammoun

Preliminary Results on 3D Channel Modeling: From Theory to Standardization

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.

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.

A Generalized Spatial Correlation Model for 3D MIMO Channels Based on the Fourier Coefficients of Power Spectrums

Previous studies have confirmed the adverse impact of fading correlation on the mutual information (MI) of two-dimensional (2D) multiple-input multiple-output (MIMO) systems. More recently, the trend is to enhance the system performance by exploiting the channels degrees of freedom in the elevation, which necessitates the derivation and characterization of three-dimensional (3D) channels in the presence of spatial correlation. In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for 3D MIMO channels. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials. The resulting expression depends on the underlying arbitrary 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. The developed SCF determines the covariance matrices at the transmitter and the receiver that form the Kronecker channel model. In order to quantify the effects of correlation on system performance, the information-theoretic deterministic equivalents of the MI for the Kronecker model are utilized in both mono-user and multi-user cases. Numerical results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns. Some useful insights into the behavior of MI as a function of downtilt angles are provided. The derived model will help evaluate the performance of correlated 3D MIMO channels in the future.

Outage performance of cooperative small-cell systems under Rician fading channels

We consider a general class of Rician fading multiple-input multiple-output (MIMO) channels, modeled by a random, non-centered channel matrix with a variance profile, i.e., the independent elements of the matrix are allowed to have each a different mean and variance. This channel model is motivated by the recent interest in cooperative small-cell systems where several densely deployed base stations (BSs) cooperatively serve multiple user terminals (UTs). We study the fluctuations of the mutual information of this channel under the form of a central limit theorem (CLT) and provide an explicit expression of the asymptotic variance. The result can be used to compute an approximation of the outage probability of such channels. Although the derived expressions are only tight in the large system limit, we show by simulations that they provide very accurate approximations for realistic system dimensions.

Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals

A central limit theorem for bilinear forms of the type a ? C ? N ( ? ) - 1 b , where a , b ? C N are unit norm deterministic vectors and C ? N ( ? ) a robust-shrinkage estimator of scatter parametrized by ? and built upon n independent elliptical vector observations, is presented. The fluctuations of a ? C ? N ( ? ) - 1 b are found to be of order N - 1 2 and to be the same as those of a ? S ? N ( ? ) - 1 b for S ? N ( ? ) a matrix of a theoretical tractable form. This result is exploited in a classical signal detection problem to provide an improved detector which is both robust to elliptical data observations (e.g., impulsive noise) and optimized across the shrinkage parameter ? .

3D Massive MIMO Systems: Modeling and Performance Analysis

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 channels 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.

Efficient Linear Precoding for Massive MIMO Systems using Truncated Polynomial Expansion

Massive multiple-input multiple-output (MIMO) techniques have been proposed as a solution to satisfy many requirements of next generation cellular systems. One downside of massive MIMO is the increased complexity of computing the precoding, especially since the relatively “antenna-efficient” regularized zero-forcing (RZF) is preferred to simple maximum ratio transmission. We develop in this paper a new class of precoders for single-cell massive MIMO systems. It is based on truncated polynomial expansion (TPE) and mimics the advantages of RZF, while offering reduced and scalable computational complexity that can be implemented in a convenient parallel fashion. Using random matrix theory we provide a closed-form expression of the signal-to-interference-and-noise ratio under TPE precoding and compare it to previous works on RZF. Furthermore, the sum rate maximizing polynomial coefficients in TPE precoding are calculated. By simulation, we find that to maintain a fixed peruser rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and signal-to-noise ratio.

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.

Eigenvalue Estimation of Parameterized Covariance Matrices of Large Dimensional Data

This article deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although such a regime is of interest for many current statistical signal processing and wireless communication issues, traditional methods fail to produce consistent estimators and only recently results relying on large random matrix theory have been unveiled. In this paper, we develop the parametric framework proposed by Mestre, and consider a model where the covariance matrix to be estimated has a (known) finite number of eigenvalues, each of it with an unknown multiplicity. The main contributions of this work are essentially threefold with respect to existing results, and in particular to Mestres work: To relax the (restrictive) separability assumption, to provide joint consistent estimates for the eigenvalues and their multiplicities, and to study the variance error by means of a Central Limit Theorem.

Asymptotic analysis of downlink MISO systems over Rician fading channels

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.