arXiv subjects

Mérouane Debbah

Publications and source records attributed to Mérouane Debbah.

At least 217 records · Page 12Linked to original sources

arXiv2014

Designing Multi-User MIMO for Energy Efficiency: When is Massive MIMO the Answer?

Assume that a multi-user multiple-input multiple-output (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bit/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closed-form expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signal-to-noise ratio (SNR) regimes in which the use of interference-suppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interference-suppressing regularized zero-forcing precoding.

cs.IT↗

arXiv2014

Massive MIMO Systems with Hardware-Constrained Base Stations

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas. Such large antenna arrays offer huge spatial degrees-of-freedom for transmission optimization; in particular, great signal gains, resilience to imperfect channel knowledge, and small inter-user interference are all achievable without extensive inter-cell coordination. The key to cost-efficient deployment of large arrays is the use of hardware-constrained base stations with low-cost antenna elements, as compared to today's expensive and power-hungry BSs. Low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the excessive degrees-of-freedom of massive MIMO would bring robustness to such imperfections. We herein prove this claim for an uplink channel with multiplicative phase-drift, additive distortion noise, and noise amplification. Specifically, we derive a closed-form scaling law that shows how fast the imperfections increase with the number of antennas.

cs.IT↗

arXiv2014

Circuit-Aware Design of Energy-Efficient Massive MIMO Systems

Densification is a key to greater throughput in cellular networks. The full potential of coordinated multipoint (CoMP) can be realized by massive multiple-input multiple-output (MIMO) systems, where each base station (BS) has very many antennas. However, the improved throughput comes at the price of more infrastructure; hardware cost and circuit power consumption scale linearly/affinely with the number of antennas. In this paper, we show that one can make the circuit power increase with only the square root of the number of antennas by circuit-aware system design. To this end, we derive achievable user rates for a system model with hardware imperfections and show how the level of imperfections can be gradually increased while maintaining high throughput. The connection between this scaling law and the circuit power consumption is established for different circuits at the BS.

cs.IT↗

arXiv2013

Massive MIMO and Small Cells: Improving Energy Efficiency by Optimal Soft-Cell Coordination

To improve the cellular energy efficiency, without sacrificing quality-of-service (QoS) at the users, the network topology must be densified to enable higher spatial reuse. We analyze a combination of two densification approaches, namely "massive" multiple-input multiple-output (MIMO) base stations and small-cell access points. If the latter are operator-deployed, a spatial soft-cell approach can be taken where the multiple transmitters serve the users by joint non-coherent multiflow beamforming. We minimize the total power consumption (both dynamic emitted power and static hardware power) while satisfying QoS constraints. This problem is proved to have a hidden convexity that enables efficient solution algorithms. Interestingly, the optimal solution promotes exclusive assignment of users to transmitters. Furthermore, we provide promising simulation results showing how the total power consumption can be greatly improved by combining massive MIMO and small cells; this is possible with both optimal and low-complexity beamforming.

cs.IT↗

arXiv2013

Low-Complexity Channel Estimation in Large-Scale MIMO using Polynomial Expansion

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as "massive MIMO". Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

cs.IT↗

arXiv2013

Matching with Externalities for Context-Aware User-Cell Association in Small Cell Networks

In this paper, we propose a novel user-cell association approach for wireless small cell networks that exploits previously unexplored context information extracted from users' devices, i.e., user equipments (UEs). Beyond characterizing precise quality of service (QoS) requirements that accurately reflect the UEs' application usage, our proposed cell association approach accounts for the devices' hardware type (e.g., smartphone, tablet, laptop). This approach has the practical benefit of enabling the small cells to make better informed cell association decisions that handle practical device-specific QoS characteristics. We formulate the problem as a matching game between small cell base stations (SBSs) and UEs. In this game, the SBSs and UEs rank one another based on well-designed utility functions that capture composite QoS requirements, extracted from the context features (i.e., application in use, hardware type). We show that the preferences used by the nodes to rank one another are interdependent and influenced by the existing network-wide matching. Due to this unique feature of the preferences, we show that the proposed game can be classified as a many-to-one matching game with externalities. To solve this game, we propose a distributed algorithm that enables the players (i.e., UEs and SBSs) to self-organize into a stable matching that guarantees the required applications' QoS. Simulation results show that the proposed context-aware cell association scheme yields significant gains, reaching up to 52% improvement compared to baseline context-unaware approaches.

cs.GT↗

arXiv2013

Hardware Impairments in Large-scale MISO Systems: Energy Efficiency, Estimation, and Capacity Limits

The use of large-scale antenna arrays has the potential to bring substantial improvements in energy efficiency and/or spectral efficiency to future wireless systems, due to the greatly improved spatial beamforming resolution. Recent asymptotic results show that by increasing the number of antennas one can achieve a large array gain and at the same time naturally decorrelate the user channels; thus, the available energy can be focused very accurately at the intended destinations without causing much inter-user interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are still reasonable in the asymptotic regimes. This paper analyzes the fundamental limits of large-scale multiple-input single-output (MISO) communication systems using a generalized system model that accounts for transceiver hardware impairments. As opposed to the case of ideal hardware, we show that these practical impairments create finite ceilings on the estimation accuracy and capacity of large-scale MISO systems. Surprisingly, the performance is only limited by the hardware at the single-antenna user terminal, while the impact of impairments at the large-scale array vanishes asymptotically. Furthermore, we show that an arbitrarily high energy efficiency can be achieved by reducing the power while increasing the number of antennas.

cs.IT↗

arXiv2013

Vandermonde-subspace Frequency Division Multiplexing for Two-Tiered Cognitive Radio Networks

Vandermonde-subspace frequency division multiplexing (VFDM) is an overlay spectrum sharing technique for cognitive radio. VFDM makes use of a precoder based on a Vandermonde structure to transmit information over a secondary system, while keeping an orthogonal frequency division multiplexing (OFDM)-based primary system interference-free. To do so, VFDM exploits frequency selectivity and the use of cyclic prefixes by the primary system. Herein, a global view of VFDM is presented, including also practical aspects such as linear receivers and the impact of channel estimation. We show that VFDM provides a spectral efficiency increase of up to 1 bps/Hz over cognitive radio systems based on unused band detection. We also present some key design parameters for its future implementation and a feasible channel estimation protocol. Finally we show that, even when some of the theoretical assumptions are relaxed, VFDM provides non-negligible rates while protecting the primary system.

cs.IT↗

arXiv2013

On the Fly Self-Organized Base Station Placement

In this paper, we address the deployment of base stations (BSs) in a one-dimensional network in which the users are randomly distributed.In order to take into account the users' distribution to optimally place the BSs we optimize the uplink MMSE sum rate. Moreover, given a massive number of antennas at the BSs we propose a novel random matrix theory-based technique so as to obtain tight approximations for the MMSE sum rate in the uplink. We investigate a cooperative (CP) scenario where the BSs jointly decode the messages and a non-cooperative (NCP) scheme in which the BS can only decode its own users. Our results show that the CP strategy considerably outperforms the NCP case. Moreover, we show that there exists a trade off in the BS deployment regarding the position of each BS. Thus, through location games we can optimize the position of each BS in order to maximize the system performance.

cs.NI↗

arXiv2012

"To sense" or "not to sense" in energy-efficient power control games

A network of cognitive transmitters is considered. Each transmitter has to decide his power control policy in order to maximize energy-efficiency of his transmission. For this, a transmitter has two actions to take. He has to decide whether to sense the power levels of the others or not (which corresponds to a finite sensing game), and to choose his transmit power level for each block (which corresponds to a compact power control game). The sensing game is shown to be a weighted potential game and its set of correlated equilibria is studied. Interestingly, it is shown that the general hybrid game where each transmitter can jointly choose the hybrid pair of actions (to sense or not to sense, transmit power level) leads to an outcome which is worse than the one obtained by playing the sensing game first, and then playing the power control game. This is an interesting Braess-type paradox to be aware of for energy-efficient power control in cognitive networks.

cs.GT↗

arXiv2012

Implicit cooperation in distributed energy-efficient networks

We consider the problem of cooperation in distributed wireless networks of selfish and free transmitters aiming at maximizing their energy-efficiency. The strategy of each transmitter consists in choosing his power control (PC) policy. Two scenarios are considered: the case where transmitters can update their power levels within time intervals less than the channel coherence time (fast PC) and the case where it is updated only once per time interval (slow PC). One of our objectives is to show how cooperation can be stimulated without assuming cooperation links between the transmitters but only by repeating the corresponding PC game and by signals from the receiver. In order to design efficient PC policies, standard and stochastic repeated games are respectively exploited to analyze the fast and slow PC problems. In the first case a cooperation plan between transmitters, that is both efficient and relies on mild information assumptions, is proposed. In the second case, the region of equilibrium utilities is derived from very recent and powerful results in game theory.

cs.GT↗

arXiv2012

Distributed Power Allocation with SINR Constraints Using Trial and Error Learning

In this paper, we address the problem of global transmit power minimization in a self-congiguring network where radio devices are subject to operate at a minimum signal to interference plus noise ratio (SINR) level. We model the network as a parallel Gaussian interference channel and we introduce a fully decentralized algorithm (based on trial and error) able to statistically achieve a congiguration where the performance demands are met. Contrary to existing solutions, our algorithm requires only local information and can learn stable and efficient working points by using only one bit feedback. We model the network under two different game theoretical frameworks: normal form and satisfaction form. We show that the converging points correspond to equilibrium points, namely Nash and satisfaction equilibrium. Similarly, we provide sufficient conditions for the algorithm to converge in both formulations. Moreover, we provide analytical results to estimate the algorithm's performance, as a function of the network parameters. Finally, numerical results are provided to validate our theoretical conclusions. Keywords: Learning, power control, trial and error, Nash equilibrium, spectrum sharing.

cs.GT↗

arXiv2012

Network Formation Games Among Relay Stations in Next Generation Wireless Networks

The introduction of relay station (RS) nodes is a key feature in next generation wireless networks such as 3GPP's long term evolution advanced (LTE-Advanced), or the forthcoming IEEE 802.16j WiMAX standard. This paper presents, using game theory, a novel approach for the formation of the tree architecture that connects the RSs and their serving base station in the \emph{uplink} of the next generation wireless multi-hop systems. Unlike existing literature which mainly focused on performance analysis, we propose a distributed algorithm for studying the \emph{structure} and \emph{dynamics} of the network. We formulate a network formation game among the RSs whereby each RS aims to maximize a cross-layer utility function that takes into account the benefit from cooperative transmission, in terms of reduced bit error rate, and the costs in terms of the delay due to multi-hop transmission. For forming the tree structure, a distributed myopic algorithm is devised. Using the proposed algorithm, each RS can individually select the path that connects it to the BS through other RSs while optimizing its utility. We show the convergence of the algorithm into a Nash tree network, and we study how the RSs can adapt the network's topology to environmental changes such as mobility or the deployment of new mobile stations. Simulation results show that the proposed algorithm presents significant gains in terms of average utility per mobile station which is at least 17.1% better relatively to the case with no RSs and reaches up to 40.3% improvement compared to a nearest neighbor algorithm (for a network with 10 RSs). The results also show that the average number of hops does not exceed 3 even for a network with up to 25 RSs.

cs.IT↗

arXiv2011

Equilibria of Channel Selection Games in Parallel Multiple Access Channel

In this paper, we study the decentralized parallel multiple access channel (MAC) when transmitters selfishly maximize their individual spectral efficiency by selecting a single channel to transmit. More specifically, we investigate the set of Nash equilibria (NE) of decentralized networks comprising several transmitters communicating with a single receiver that implements single user decoding. This scenario is modeled as a one-shot game where the players (the transmitters) have discrete action sets (the channels). We show that the corresponding game has always at least one NE in pure strategies, but, depending on certain parameters, the game might possess several NE. We provide an upper bound for the maximum number of NE as a function of the number of transmitters and available channels. The main contribution of this paper is a mathematical proof of the existence of a Braess-type paradox. In particular, it is shown that under the assumption of a fully loaded network, when transmitters are allowed to use all the available channels, the corresponding sum spectral efficiency achieved at the NE is lower or equal than the sum spectral efficiency achieved when transmitters can use only one channel. A formal proof of this observation is provided in the case of small networks. For general scenarios, we provide numerical examples that show that the same effect holds as long as the network is kept fully loaded. We conclude the paper by considering the case of successive interference cancellation at the receiver. In this context, we show that the power allocation vectors at the NE are capacity maximizers. Finally, simulations are presented to verify our theoretical results.

cs.GT↗

arXiv2011

Quality-Of-Service Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach

This paper introduces a particular game formulation and its corresponding notion of equilibrium, namely the satisfaction form (SF) and the satisfaction equilibrium (SE). A game in SF models the case where players are uniquely interested in the satisfaction of some individual performance constraints, instead of individual performance optimization. Under this formulation, the notion of equilibrium corresponds to the situation where all players can simultaneously satisfy their individual constraints. The notion of SE, models the problem of QoS provisioning in decentralized self-configuring networks. Here, radio devices are satisfied if they are able to provide the requested QoS. Within this framework, the concept of SE is formalized for both pure and mixed strategies considering finite sets of players and actions. In both cases, sufficient conditions for the existence and uniqueness of the SE are presented. When multiple SE exist, we introduce the idea of effort or cost of satisfaction and we propose a refinement of the SE, namely the efficient SE (ESE). At the ESE, all players adopt the action which requires the lowest effort for satisfaction. A learning method that allows radio devices to achieve a SE in pure strategies in finite time and requiring only one-bit feedback is also presented. Finally, a power control game in the interference channel is used to highlight the advantages of modeling QoS problems following the notion of SE rather than other equilibrium concepts, e.g., generalized Nash equilibrium.

cs.IT↗

arXiv2011

Spectrum Leasing as an Incentive towards Uplink Macrocell and Femtocell Cooperation

The concept of femtocell access points underlaying existing communication infrastructure has recently emerged as a key technology that can significantly improve the coverage and performance of next-generation wireless networks. In this paper, we propose a framework for macrocell-femtocell cooperation under a closed access policy, in which a femtocell user may act as a relay for macrocell users. In return, each cooperative macrocell user grants the femtocell user a fraction of its superframe. We formulate a coalitional game with macrocell and femtocell users being the players, which can take individual and distributed decisions on whether to cooperate or not, while maximizing a utility function that captures the cooperative gains, in terms of throughput and delay.We show that the network can selforganize into a partition composed of disjoint coalitions which constitutes the recursive core of the game representing a key solution concept for coalition formation games in partition form. Simulation results show that the proposed coalition formation algorithm yields significant gains in terms of average rate per macrocell user, reaching up to 239%, relative to the non-cooperative case. Moreover, the proposed approach shows an improvement in terms of femtocell users' rate of up to 21% when compared to the traditional closed access policy.

cs.GT↗

arXiv2011

On the Nash Equilibria in Decentralized Parallel Interference Channels

In this paper, the 2-dimensional decentralized parallel interference channel (IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static game. Each transmitter is assumed to be a fully rational entity with complete information on the game, aiming to maximize its own individual spectral efficiency by tuning its own power allocation (PA) vector. Two scenarios are analysed. First, we consider that transmitters can split their transmit power between both dimensions (PA game). Second, we consider that each transmitter is limited to use only one dimension (channel selection CS game). In the first scenario, the game might have either one or three NE in pure strategies (PS). However, two or infinitely many NE in PS might also be observed with zero probability. In the second scenario, there always exists either one or two NE in PS. We show that in both games there always exists a non-zero probability of observing more than one NE. More interestingly, using Monte-Carlo simulations, we show that the highest and lowest network spectral efficiency at any of the NE in the CS game are always higher than the ones in the PA.

cs.GT↗

arXiv2011

Learning Equilibria with Partial Information in Decentralized Wireless Networks

In this article, a survey of several important equilibrium concepts for decentralized networks is presented. The term decentralized is used here to refer to scenarios where decisions (e.g., choosing a power allocation policy) are taken autonomously by devices interacting with each other (e.g., through mutual interference). The iterative long-term interaction is characterized by stable points of the wireless network called equilibria. The interest in these equilibria stems from the relevance of network stability and the fact that they can be achieved by letting radio devices to repeatedly interact over time. To achieve these equilibria, several learning techniques, namely, the best response dynamics, fictitious play, smoothed fictitious play, reinforcement learning algorithms, and regret matching, are discussed in terms of information requirements and convergence properties. Most of the notions introduced here, for both equilibria and learning schemes, are illustrated by a simple case study, namely, an interference channel with two transmitter-receiver pairs.

cs.LG↗