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Merouane Debbah

Publications and source records attributed to Merouane Debbah.

At least 361 records · Page 20Linked to original sources
arXiv2009

Asynchronous CDMA Systems with Random Spreading-Part I: Fundamental Limits

Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency-flat fading. Signal to interference and noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean square error (MMSE) detectors, are derived. The approach is general and optionally allows even for statistics obtained by under-sampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit. It turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the Nyquist bandwidth, e.g., positive roll-off factors. For example, with the pulse shaping demanded in the UMTS standard, user synchronization reduces spectral efficiency up to 12% at 10 dB normalized signal-to-noise ratio. The benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space, if the users are de-synchronized on the chip-level. The analysis of linear MMSE detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of the effective interference spectral density arises. This generalizes and refines Tse and Hanly's concept of effective interference. In Part II, the analysis is extended to any linear detector that admits a representation as multistage detector and guidelines for the design of low complexity multistage detectors with universal weights are provided.

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arXiv2009

Asynchronous CDMA Systems with Random Spreading-Part II: Design Criteria

Totally asynchronous code-division multiple-access (CDMA) systems are addressed. In Part I, the fundamental limits of asynchronous CDMA systems are analyzed in terms of spectral efficiency and SINR at the output of the optimum linear detector. The focus of Part II is the design of low-complexity implementations of linear multiuser detectors in systems with many users that admit a multistage representation, e.g. reduced rank multistage Wiener filters, polynomial expansion detectors, weighted linear parallel interference cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay distribution on CDMA with suboptimum linear receiver structures are investigated. Recursive expressions for universal weight design are given. The performance in terms of SINR is derived in the large-system limit and the performance improvement over synchronous systems is quantified. The considerations distinguish between two ways of forming discrete-time statistics: chip-matched filtering and oversampling.

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arXiv2009

Distributed Coalition Formation Games for Secure Wireless Transmission

Cooperation among wireless nodes has been recently proposed for improving the physical layer (PHY) security of wireless transmission in the presence of multiple eavesdroppers. While existing PHY security literature answered the question ``what are the link-level secrecy rate gains from cooperation?'', this paper attempts to answer the question of ``how to achieve those gains in a practical decentralized wireless network and in the presence of a cost for information exchange?''. For this purpose, we model the PHY security cooperation problem as a coalitional game with non-transferable utility and propose a distributed algorithm for coalition formation. Through the proposed algorithm, the wireless users can cooperate and self-organize into disjoint independent coalitions, while maximizing their secrecy rate taking into account the security costs during information exchange. We analyze the resulting coalitional structures for both decode-and-forward and amplify-and-forward cooperation and study how the users can adapt the network topology to environmental changes such as mobility. Through simulations, we assess the performance of the proposed algorithm and show that, by coalition formation using decode-and-forward, the average secrecy rate per user is increased of up to 25.3 % and 24.4 % (for a network with 45 users) relative to the non-cooperative and amplify-and-forward cases, respectively.

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arXiv2009

Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem.

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arXiv2009

Magnetworks: how mobility impacts the design of Mobile Networks

In this paper we study the optimal placement and optimal number of active relay nodes through the traffic density in mobile sensor ad-hoc networks. We consider a setting in which a set of mobile sensor sources is creating data and a set of mobile sensor destinations receiving that data. We make the assumption that the network is massively dense, i.e., there are so many sources, destinations, and relay nodes, that it is best to describe the network in terms of macroscopic parameters, such as their spatial density, rather than in terms of microscopic parameters, such as their individual placements. We focus on a particular physical layer model that is characterized by the following assumptions: i) the nodes must only transport the data from the sources to the destinations, and do not need to sense the data at the sources, or deliver them at the destinations once the data arrive at their physical locations, and ii) the nodes have limited bandwidth available to them, but they use it optimally to locally achieve the network capacity. In this setting, the optimal distribution of nodes induces a traffic density that resembles the electric displacement that will be created if we substitute the sources and destinations with positive and negative charges respectively. The analogy between the two settings is very tight and have a direct interpretation in wireless sensor networks.

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arXiv2009

A Bayesian Framework for Collaborative Multi-Source Signal Detection

This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization procedure based on recent tools of finite random matrix theory, in conjunction with the maximum entropy principle, is used to compute the hypothesis selection criterion. Quite remarkably, explicit expressions for the Bayesian detector are derived which enable to decide on the presence of signal sources in a noisy wireless environment. The proposed Bayesian detector is shown to outperform the classical power detector when the noise power is known and provides very good performance for limited knowledge on the noise power. Simulations corroborate the theoretical results and quantify the gain achieved using the proposed Bayesian framework.

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arXiv2009

Physical Layer Security: Coalitional Games for Distributed Cooperation

Cooperation between wireless network nodes is a promising technique for improving the physical layer security of wireless transmission, in terms of secrecy capacity, in the presence of multiple eavesdroppers. While existing physical layer security literature answered the question "what are the link-level secrecy capacity gains from cooperation?", this paper attempts to answer the question of "how to achieve those gains in a practical decentralized wireless network and in the presence of a secrecy capacity cost for information exchange?". For this purpose, we model the physical layer security cooperation problem as a coalitional game with non-transferable utility and propose a distributed algorithm for coalition formation. Through the proposed algorithm, the wireless users can autonomously cooperate and self-organize into disjoint independent coalitions, while maximizing their secrecy capacity taking into account the security costs during information exchange. We analyze the resulting coalitional structures, discuss their properties, and study how the users can self-adapt the network topology to environmental changes such as mobility. Simulation results show that the proposed algorithm allows the users to cooperate and self-organize while improving the average secrecy capacity per user up to 25.32% relative to the non-cooperative case.

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arXiv2009

Secured Communication over Frequency-Selective Fading Channels: a practical Vandermonde precoding

In this paper, we study the frequency-selective broadcast channel with confidential messages (BCC) in which the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of N symbols followed by a guard interval of L symbols, the frequency-selective channel can be modeled as a N * (N+L) Toeplitz matrix. For this special type of multiple-input multiple-output (MIMO) channels, we propose a practical Vandermonde precoding that consists of projecting the confidential messages in the null space of the channel seen by receiver 2 while superposing the common message. For this scheme, we provide the achievable rate region, i.e. the rate-tuple of the common and confidential messages, and characterize the optimal covariance inputs for some special cases of interest. It is proved that the proposed scheme achieves the optimal degree of freedom (d.o.f) region. More specifically, it enables to send l <= L confidential messages and N-l common messages simultaneously over a block of N+L symbols. Interestingly, the proposed scheme can be applied to secured multiuser scenarios such as the K+1-user frequency-selective BCC with K confidential messages and the two-user frequency-selective BCC with two confidential messages. For each scenario, we provide the achievable secrecy degree of freedom (s.d.o.f.) region of the corresponding frequency-selective BCC and prove the optimality of the Vandermonde precoding. One of the appealing features of the proposed scheme is that it does not require any specific secrecy encoding technique but can be applied on top of any existing powerful encoding schemes.

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arXiv2009

On the Compound MIMO Broadcast Channels with Confidential Messages

We study the compound multi-input multi-output (MIMO) broadcast channel with confidential messages (BCC), where one transmitter sends a common message to two receivers and two confidential messages respectively to each receiver. The channel state may take one of a finite set of states, and the transmitter knows the state set but does not know the realization of the state. We study achievable rates with perfect secrecy in the high SNR regime by characterizing an achievable secrecy degree of freedom (s.d.o.f.) region for two models, the Gaussian MIMO-BCC and the ergodic fading multi-input single-output (MISO)-BCC without a common message. We show that by exploiting an additional temporal dimension due to state variation in the ergodic fading model, the achievable s.d.o.f. region can be significantly improved compared to the Gaussian model with a constant state, although at the price of a larger delay.

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arXiv2009

Asymptotic Capacity and Optimal Precoding in MIMO Multi-Hop Relay Networks

A multi-hop relaying system is analyzed where data sent by a multi-antenna source is relayed by successive multi-antenna relays until it reaches a multi-antenna destination. Assuming correlated fading at each hop, each relay receives a faded version of the signal from the previous level, performs linear precoding and retransmits it to the next level. Using free probability theory and assuming that the noise power at relaying levels-- but not at destination-- is negligible, the closed-form expression of the asymptotic instantaneous end-to-end mutual information is derived as the number of antennas at all levels grows large. The so-obtained deterministic expression is independent from the channel realizations while depending only on channel statistics. Moreover, it also serves as the asymptotic value of the average end-to-end mutual information. The optimal singular vectors of the precoding matrices that maximize the average mutual information with finite number of antennas at all levels are also provided. It turns out that the optimal precoding singular vectors are aligned to the eigenvectors of the channel correlation matrices. Thus they can be determined using only the known channel statistics. As the optimal precoding singular vectors are independent from the system size, they are also optimal in the asymptotic regime.

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arXiv2009

Coalitional Game Theory for Communication Networks: A Tutorial

Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and autonomic networks, it has become imperative to seek suitable game theoretical tools that allow to analyze and study the behavior and interactions of the nodes in future communication networks. In this context, this tutorial introduces the concepts of cooperative game theory, namely coalitional games, and their potential applications in communication and wireless networks. For this purpose, we classify coalitional games into three categories: Canonical coalitional games, coalition formation games, and coalitional graph games. This new classification represents an application-oriented approach for understanding and analyzing coalitional games. For each class of coalitional games, we present the fundamental components, introduce the key properties, mathematical techniques, and solution concepts, and describe the methodologies for applying these games in several applications drawn from the state-of-the-art research in communications. In a nutshell, this article constitutes a unified treatment of coalitional game theory tailored to the demands of communications and network engineers.

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arXiv2009

On the Benefits of Bandwidth Limiting in Decentralized Vector Multiple Access Channels

We study the network spectral efficiency of decentralized vector multiple access channels (MACs) when the number of accessible dimensions per transmitter is strategically limited. Considering each dimension as a frequency band, we call this limiting process bandwidth limiting (BL). Assuming that each transmitter maximizes its own data rate by water-filling over the available frequency bands, we consider two scenarios. In the first scenario, transmitters use non-intersecting sets of bands (spectral resource partition), and in the second one, they freely exploit all the available frequency bands (spectral resource sharing). In the latter case, successive interference cancelation (SIC) is used. We show the existence of an optimal number of dimensions that a transmitter must use in order to maximize the network performance measured in terms of spectral efficiency. We provide a closed form expression for the optimal number of accessible bands in the first scenario. Such an optimum point, depends on the number of active transmitters, the number of available frequency bands and the different signal-to-noise ratios. In the second scenario, we show that BL does not bring a significant improvement on the network spectral efficiency, when all transmitters use the same BL policy. For both scenarios, we provide simulation results to validate our conclusions.

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arXiv2009

Coalitional Games for Distributed Collaborative Spectrum Sensing in Cognitive Radio Networks

Collaborative spectrum sensing among secondary users (SUs) in cognitive networks is shown to yield a significant performance improvement. However, there exists an inherent trade off between the gains in terms of probability of detection of the primary user (PU) and the costs in terms of false alarm probability. In this paper, we study the impact of this trade off on the topology and the dynamics of a network of SUs seeking to reduce the interference on the PU through collaborative sensing. Moreover, while existing literature mainly focused on centralized solutions for collaborative sensing, we propose distributed collaboration strategies through game theory. We model the problem as a non-transferable coalitional game, and propose a distributed algorithm for coalition formation through simple merge and split rules. Through the proposed algorithm, SUs can autonomously collaborate and self-organize into disjoint independent coalitions, while maximizing their detection probability taking into account the cooperation costs (in terms of false alarm). We study the stability of the resulting network structure, and show that a maximum number of SUs per formed coalition exists for the proposed utility model. Simulation results show that the proposed algorithm allows a reduction of up to 86.6% of the average missing probability per SU (probability of missing the detection of the PU) relative to the non-cooperative case, while maintaining a certain false alarm level. In addition, through simulations, we compare the performance of the proposed distributed solution with respect to an optimal centralized solution that minimizes the average missing probability per SU. Finally, the results also show how the proposed algorithm autonomously adapts the network topology to environmental changes such as mobility.

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arXiv2009

Asymptotic Behaviour of Random Vandermonde Matrices with Entries on the Unit Circle

Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent, identically distributed (i.i.d.) entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided, and deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications.

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arXiv2009

Power Allocation Games for MIMO Multiple Access Channels with Coordination

A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their individual transmission rates (in particular they can ignore some specified centralized policies). A simple coordination mechanism between users is introduced. The nature and influence of this mechanism is studied in detail. The coordination signal indicates to the users the order in which the receiver applies successive interference cancellation and the frequency at which this order is used. Two different games are investigated: the users can either adapt their temporal PA to their decoding rank at the receiver or optimize their spatial PA between their transmit antennas. For both games a thorough analysis of the existence, uniqueness and sum-rate efficiency of the network Nash equilibrium is conducted. Analytical and simulation results are provided to assess the gap between the decentralized network performance and its equivalent virtual multiple input multiple output system, which is shown to be zero in some cases and relatively small in general.

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arXiv2008

Cognitive OFDM network sensing: a free probability approach

In this paper, a practical power detection scheme for OFDM terminals, based on recent free probability tools, is proposed. The objective is for the receiving terminal to determine the transmission power and the number of the surrounding base stations in the network. However, thesystem dimensions of the network model turn energy detection into an under-determined problem. The focus of this paper is then twofold: (i) discuss the maximum amount of information that an OFDM terminal can gather from the surrounding base stations in the network, (ii) propose a practical solution for blind cell detection using the free deconvolution tool. The efficiency of this solution is measured through simulations, which show better performance than the classical power detection methods.

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arXiv2008

A maximum entropy approach to OFDM channel estimation

In this work, a new Bayesian framework for OFDM channel estimation is proposed. Using Jaynes' maximum entropy principle to derive prior information, we successively tackle the situations when only the channel delay spread is a priori known, then when it is not known. Exploitation of the time-frequency dimensions are also considered in this framework, to derive the optimal channel estimation associated to some performance measure under any state of knowledge. Simulations corroborate the optimality claim and always prove as good or better in performance than classical estimators.

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