Mérouane Debbah

Green Small-Cell Networks

The exponentially increasing demand for wireless data services requires a massive network densification that is neither economically nor ecologically viable with the current cellular system architectures. A promising solution to this problem is the concept of small-cell networks (SCNs), which is founded by the idea of a very dense deployment of self-organizing, low-cost, low-power, base stations (BSs). Although SCNs have the potential to significantly increase the capacity of cellular networks while reducing their energy consumption, they pose many new challenges to the optimal system design. We show in this article how a large system analysis based on random matrix theory (RMT) can provide tight and tractable approximations of key performance measures of SCNs.

Methodologies for analyzing equilibria in wireless games

Non exhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection, and efficiency are provided. The paper will focus on technical problems arising at the physical and medium access layers of a wireless network, and not on economic aspects related to it, like the auction problem for spectrum, even though it is also an important scenario where game theory is used.

On the necessity of binning for the distributed hypothesis testing problem

A distributed hypothesis testing (HT) problem is considered, comprising two nodes and a unidirectional communication link. The receiving node is required to make a decision as to the probability distribution in effect. A binning process is used in order to minimize the probability of error, resulting in a new achievable error-exponent. A sub-class of HT problems with general hypotheses is defined, which contains many interesting and relevant problems. The advantage of the binning strategy in comparison to the non-binning approach is demonstrated by means of a binary symmetric example.

Base Station Cooperation for Power Minimization in the Downlink: Large System Analysis

This work focuses on the downlink of a large-scale multi-cell multi-user MIMO system in which L base stations (BSs) of N antennas each communicate with KL single-antenna user equipments. We consider the design of the linear precoder that minimizes the total power consumption while ensuring target user rates. Two configurations with different degrees of cooperation among BSs are considered: the coordinated beamforming scheme (only channel state information is shared between BSs) and the coordinated multipoint MIMO technology (channel state and data cooperation). The analysis is conducted assuming that N and K grow large with a non trivial ratio K/N and imperfect channel state information is available at the BSs. In both configurations, tools of random matrix theory are used to compute, often in closed form, deterministic approximations for: i) the parameters of the optimal precoder; ii) the powers needed to ensure target rates; and iii) the total transmit power. These results are instrumental to get further insights into the structure of the optimal precoder and also to reduce the complexity of its implementation in large-scale networks. Numerical results are used to validate the asymptotic analysis in the finite system regime and to make comparisons among the two different configurations.

Collaborative distributed hypothesis testing with general hypotheses

The problem of collaborative distributed hypothesis testing is investigated. In this setting, a binary decision is required about the joint distribution of two arbitrary dependent memoryless processes that are sampled at different physical locations (nodes) in the system. Interactive rate-limited communication is allowed between these nodes. Defining two types of error events, the error exponent for an error of the second type is investigated, under a prescribed probability of error of the first type. A general achievable error exponent, as a function of the total available communication resources, is proposed, for the case of two general hypotheses. The special case of testing against independence is revisited for which it is shown that optimality can be attained, as a special case of the general achievable exponent, provided the constraint over the error probability of the first type goes to zero.

Random Matrix Methods for Wireless Communications: Acronyms

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents, and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanations of the key results and all fundamental lemmas required for the readers to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO, and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.

Random Matrix Methods for Wireless Communications: Applications to wireless communications

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents, and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanations of the key results and all fundamental lemmas required for the readers to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO, and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.

Random Matrix Methods for Wireless Communications: Acknowledgments

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents, and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanations of the key results and all fundamental lemmas required for the readers to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO, and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.

Rate region of correlated MIMO multiple access channels and broadcast channels

In this paper, the rate region of large multi-antenna multiple access channels and broadcast channels are investigated. The propagation channels between transmitters and receivers are modelled as independent Gaussian with separable variance profiles. It is shown in particular that the large antenna rate regions do not depend on the specific channel realization, but only on the channel transmit and receive covariance matrices. The theoretical results are corroborated by simulations.