Elena Veronica Belmega

Energy-Efficient Precoding for Multiple-Antenna Terminals

The 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.

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.

Distributed Learning Policies for Power Allocation in Multiple Access Channels

We analyze the power allocation problem for orthogonal multiple access channels by means of a non-cooperative potential game in which each user distributes his power over the channels available to him. When the channels are static, we show that this game possesses a unique equilibrium; moreover, if the networks users follow a distributed learning scheme based on the replicator dynamics of evolutionary game theory, then they converge to equilibrium exponentially fast. On the other hand, if the channels fluctuate stochastically over time, the associated game still admits a unique equilibrium, but the learning process is not deterministic; just the same, by employing the theory of stochastic approximation, we find that users still converge to equilibrium. Our theoretical analysis hinges on a novel result which is of independent interest: in finite-player games which admit a (possibly nonlinear) convex potential, the replicator dynamics converge to an e-neighborhood of an equilibrium in time O(\log(1/e)).

On the base station selection and base station sharing in self-configuring networks

We model the interaction of several radio devices aiming to obtain wireless connectivity by using a set of base stations (BS) as a non-cooperative game. Each radio device aims to maximize its own spectral efficiency (SE) in two different scenarios: First, we let each player to use a unique BS (BS selection) and second, we let them to simultaneously use several BSs (BS Sharing). In both cases, we show that the resulting game is an exact potential game. We found that the BS selection game posses multiple Nash equilibria (NE) while the BS sharing game posses a unique one. We provide fully decentralized algorithms which always converge to a NE in both games. We analyze the price of anarchy and the price of stability for the case of BS selection. Finally, we observed that depending on the number of transmitters, the BS selection technique might provide a better global performance (network spectral efficiency) than BS sharing, which suggests the existence of a Braess type paradox.

A survey on energy-efficient communications

In 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.

An information-theoretic look at MIMO energy-efficient communications

One of the main objectives of this paper is to provide an information-theoretic answer on how to maximize energy-efficiency 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-efficiency 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-efficiency 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-efficiency 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.

Power allocation games in wireless networks of multi-antenna terminals

We consider wireless networks that can be modeled by multiple access channels in which all the terminals are equipped with multiple antennas. The propagation model used to account for the effects of transmit and receive antenna correlations is the unitary-invariant-unitary model, which is one of the most general models available in the literature. In this context, we introduce and analyze two resource allocation games. In both games, the mobile stations selfishly choose their power allocation policies in order to maximize their individual uplink transmission rates; in particular they can ignore some specified centralized policies. In the first game considered, the base station implements successive interference cancellation (SIC) and each mobile station chooses his best space-time power allocation scheme; here, a coordination mechanism is used to indicate to the users the order in which the receiver applies SIC. In the second framework, the base station is assumed to implement single-user decoding. For these two games a thorough analysis of the Nash equilibrium is provided: the existence and uniqueness issues are addressed; the corresponding power allocation policies are determined by exploiting random matrix theory; the sum-rate efficiency of the equilibrium is studied analytically in the low and high signal-to-noise ratio regimes and by simulations in more typical scenarios. Simulations show that, in particular, the sum-rate efficiency is high for the type of systems investigated and the performance loss due to the use of the proposed suboptimum coordination mechanism is very small.

Distributed energy-efficient power optimization in cellular relay networks with minimum rate constraints

In this work, we derive a distributed power control algorithm for energy-efficientuplink transmissions in interference-limited cellular networks, equipped with either multiple or shared relays. The proposed solution is derived by modeling the mobile terminals as utility-driven rational agents that engage in a noncooperative game, under minimum-rate constraints. The theoretical analysis of the game equilibrium is used to compare the performance of the two different cellular architectures. Extensive simulations show that the shared relay concept outperforms the distributed one in terms of energy efficiency in most network configurations.

Resource allocation games in interference relay channels

In this paper we study a distributed network comprising an interference channel in parallel with an interference relay channel. Therefore each source node can use two frequency bands and has to implement a certain power allocation policy. An example of application of such a model is the case where the performance of terminals operating in unlicensed bands would be enhanced by being allowed to exploit an additional frequency band in which a relay is available. In this network model, each user is selfish and wants to maximize its Shannon transmission rate. We analyze two cases. In the first case, the relaying node is assumed to implement an amplify-and-forward (AF) protocol while in the second case it implements the decode-and-forward (DF) protocol introduced by Cover and El Gamal. For both cases we analyze the existence and uniqueness issues of the equilibrium of the aforementioned power allocation games. Several interesting and new results are provided. In particular: 1. The existence of a Nash equilibrium is shown to be always guaranteed in the case of the AF protocol; 2. The performance of a user or the network does not necessarily increase with the transmit power available at the relay; 3. We show that there is naturally a game in interference relay channels (even if the power allocation policy is fixed) when the DF protocol is used; this game is induced by the decentralized choice of the cooperation degree between each source node and the relay node.

Decentralized handovers in cellular networks with cognitive terminals

We consider a network that comprises a group of K users, equipped with single-antenna terminals, who want to selfishly maximize their individual transmission rates and S single-antenna base stations. The information rates and the transmit power levels of the users are not dictated by the base stations. In this context we introduce the problem of decentralized handovers: each terminal is equipped with a cognitive radio used to sense the quality of its links with the different base stations and share, in a smart way, its transmit power among them. In the hard handover case, for which there is a unique stable Nash equilibrium, we determine the selfish repartition of the users between the base stations and then we assess its social efficiency, which is measured in terms of sum-rate. In the soft handover case, the problem consists in determining the optimum selfish power allocation for each user and analyzing its sum-rate efficiency with respect to the equivalent virtual K x S multiple input multiple output (MIMO) network. We also show how to extend the provided results to the case of multi-antenna terminals and base stations and provide simulations to illustrate the presented results.