An information-theoretic look at MIMO energy-efficient communications

International audienceOne of the main objectives of this paper is to provide an information-theoretic answer on how to maximize energy- effciency in MIMO (multiple input multiple output) systems. In static and fast fading channels, for which arbitrarily reliable communications are possible, it is shown that the best precoding scheme (which includes power allocation) is to transmit at very low power (Q ->0). Whereas energy-effciency is maximized in this regime, the latter also corresponds to communicating at very small transmission rates (R ->0). In slow fading or quasi-static MIMO systems (where reliability cannot be ensured), based on the proposed information-theoretic performance measure, it is proven that energy-effciency is maximized for a non-trivial precoding scheme; in particular, transmitting at zero power or saturating the transmit power constraint is suboptimal. The determination of the best precoding scheme is shown to be a new open problem. Based on this statement, the best precoding scheme is determined in several special but useful cases. As a second step, we show how to use the proposed energy-effciency measure to analyze the important case of distributed power allocation in MIMO multiple access channels. Simulations show the benefits brought by multiple antennas for saving energy while guaranteeing the system to reach a given transmission rate target

Energy-Efficient Precoding for Multiple-Antenna Terminals

International audienceThe problem of energy-efficient precoding is investigated when the terminals in the system are equipped with multiple antennas. Considering static and fast-fading multiple-input multiple-output (MIMO) channels, the energy-efficiency is defined as the transmission rate to power ratio and shown to be maximized at low transmit power. The most interesting case is the one of slow fading MIMO channels. For this type of channels, the optimal precoding scheme is generally not trivial. Furthermore, using all the available transmit power is not always optimal in the sense of energy-efficiency (which, in this case, corresponds to the communication-theoretic definition of the goodput-to-power (GPR) ratio). Finding the optimal precoding matrices is shown to be a new open problem and is solved in several special cases: 1. when there is only one receive antenna; 2. in the low or high signal-to-noise ratio regime; 3. when uniform power allocation and the regime of large numbers of antennas are assumed. A complete numerical analysis is provided to illustrate the derived results and stated conjectures. In particular, the impact of the number of antennas on the energy-efficiency is assessed and shown to be significant

Performance Analysis for the AF-based Frequency Division Cooperative Channel

International audienceThis paper considers a system where one transmitter broadcasts a single common message to two receivers. These receivers can cooperate through a bidirectional channel that is assumed to be orthogonal to the downlink channel. For the case where the assumed cooperation protocol is amplify-and-forward we calculated the final equivalent SNR in the MRC output at each receiver for an arbitrary number of cooperation exchanges. The corresponding analytical expressions can then be used for evaluating different performance criteria in order to discuss issues such as: Which receiver should start cooperating first' Is there an optimum number of cooperation exchanges' What is the difference between asymmetric and symmetric cooperations

Gaussian Broadcast Channels with an Orthogonal and Bidirectional Cooperation Link

International audienceThis paper considers a system where one transmitter broadcasts a single common message to two receivers linked by a bidirectional cooperation channel, which is assumed to be orthogonal to the downlink channel. Assuming a simplified setup where, in particular, scalar relaying protocols are used and channel coding is not exploited, we want to provide elements of response to several questions of practical interest. Here are the main underlying issues: (1) the way of recombining the signals at the receivers; (2) the optimal number of cooperation rounds; (3) the way of cooperating (symmetrically or asymmetrically, which receiver should start cooperating in the latter case); and (4) the influence of spectral resources. These issues are considered by studying the performance of the assumed system through analytical results when they are derivable and through simulation results. For the particular choices we made, the results sometimes do not coincide with those available for the discrete counterpart of the studied channel

A Survey on Energy-Efficient Communications

International audienceIn this paper, we review the literature on physical layer energy-efficient communications. The most relevant and recent works are mainly centered around two frameworks: the pragmatic and the information theoretical approaches. Both of them aim at finding the best transmit and/or receive policies which maximize the number of bits that can be reliably conveyed over the channel per unit of energy consumed. Taking into account both approaches, the analysis starts with the single user SISO (single-input single-output) channel, and is then extended to the MIMO (multiple-input multiple-output) and multi-user scenarios

Recombinaison de signaux décodés et transférés pour le canal à relais à division fréquentielle

International audienceCe papier traite le canal à relais. Il est une extension de [6] où on s'intéresse aux méthodes de recombinaison des signaux à la destination lorsque tous les relais utilisent la stratégie decode-and-forward. Contrairement à [6], la source et les relais ne sont plus contraints d'utiliser une modulation à deux états. On s'intéresse plus particulièrement au cas où le relais a de moins bonnes conditions de réception que la destination et la puissance de coopération est suffisamment grande. Dans ce cas, l'utilisation du Maximum Ratio Combining (MRC) conventionel dégrade sévèrement les performances à la destination. Pour cette raison nous présenterons ici le combineur optimal au sens de l'erreur quadratique moyenne (MMSE) et celui au sens du maximum de vraisemblance (ML) a¯n de tirer pro¯t de la coopération quelque soit le scénario des rapports signal-à-bruit (SNR)

Jeux d'allocation de puissance pour les canaux à interférence à relais

International audienceDans cet article nous étudions l'interaction entre deux terminaux cognitifs qui communiquent avec leurs récepteurs respectifs sur Q>=2 bandes de fréquence orthogonales. Nous supposons que sur chaque bande il y a un nœud relais disponible pour améliorer les performances des transmissions. Ce système peut être modélisé par plusieur canaux à interférence à relais (CIR) en parallèle. Le problème de l'allocation de puissance des deux utilisateurs entre les bandes disponibles est modélisé en utilisant la théorie des jeux non-coopératifs. Pour différents protocoles de relayage (amplifier-et-transférer, décoder-et-transférer et estimer-et-transférer) nous montrons l'existence d'un état stable du système tel qu'aucun utilisateur ne peut pas améliorer son débit de transmission en déviant unilatéralement de cet état (équilibre de Nash). L'efficacité du système à l'équilibre, la position optimale du relais qui maximise le débit somme du système et aussi la gestion de l'interférence multi-utilisateurs sont évalués par simulation

Resource allocation games in interference relay channels

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Learning Distributed Power Allocation Policies in MIMO Channels

International audienceIn this paper, we study the discrete power allocation game for the fast fading multiple-input multiple-output multiple access channel. Each player or transmitter chooses its own transmit power policy from a certain finite set to optimize its individual transmission rate. First, we prove the existence of at least one pure strategy Nash equilibrium. Then, we investigate two learning algorithms that allow the players to converge to either one of the NE states or to the set of correlated equilibria. At last, we compare the performance of the considered discrete game with the continuous game in [7]