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.Comment: 6 pages, 4 figures, presented in ICCC Kyoto 201

Noisy Channel-Output Feedback Capacity of the Linear Deterministic Interference Channel

In this paper, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which imple- menting channel-output feedback in only one of the transmitter- receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of the two pairs in terms of achievable individual rate improvements or simply, it turns out to be useless, i.e., the capacity regions with and without feedback turn out to be identical even in the full absence of noise in the feedback links.Comment: 5 pages, 9 figures, see proofs in V. Quintero, S. M. Perlaza, and J.-M. Gorce, "Noisy channel-output feedback capacity of the linear deterministic interference channel," INRIA, Tech. Rep. 456, Jan. 2015. This was submitted and accepted in IEEE ITW 201

Satisfaction Equilibrium: A General Framework for QoS Provisioning in Self-Configuring Networks

This paper is concerned with the concept of equilibrium and quality of service (QoS) provisioning in self-configuring wireless networks with non-cooperative radio devices (RD). In contrast with the Nash equilibrium (NE), where RDs are interested in selfishly maximizing its QoS, we present a concept of equilibrium, named satisfaction equilibrium (SE), where RDs are interested only in guaranteing a minimum QoS. We provide the conditions for the existence and the uniqueness of the SE. Later, in order to provide an equilibrium selection framework for the SE, we introduce the concept of effort or cost of satisfaction, for instance, in terms of transmit power levels, constellation sizes, etc. Using the idea of effort, the set of efficient SE (ESE) is defined. At the ESE, transmitters satisfy their minimum QoS incurring in the lowest effort. We prove that contrary to the (generalized) NE, at least one ESE always exists whenever the network is able to simultaneously support the individual QoS requests. Finally, we provide a fully decentralized algorithm to allow self-configuring networks to converge to one of the SE relying only on local information.Comment: Accepted for publication in Globecom 201

Modeling Noisy Feedback in Decentralized Self-Configuring Networks

This paper introduces a generalization of the notion of Nash equilibrium (NE), namely quantal response equilibrium (QRE). In the QRE, radio devices choose their transmit/receive configuration taking into account that the estimation of their own performance contains a noise component. Here, it is shown that the notion of QRE neatly models decentralized self-configuring networks (DCSN) where feedback messages are impaired by quantization noise or decoding errors. The main contribution of the paper is twofold. First, we show that under the presence of noise in the estimation expected utility, the notion of NE no longer holds, as players cannot be considered rational. Second, we introduce a learning technique that converges to a QRE in a fully decentralized fashion. We present numerical results in the context of a channel selection problem in a parallel multiple access channel in order to illustrate our theoretical results

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.Comment: Article accepted for publication in IEEE Journal on Selected Topics in Signal Processing, special issue in Game Theory in Signal Processing. 16 pages, 6 figure

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.Comment: 16 pages, 5 figures, 1 table. To appear in IEEE Communication Magazine, special Issue on Game Theor

Perfect Output Feedback in the Two-User Decentralized Interference Channel

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within $1$ bit/s/Hz and $\eta$ arbitrarily close to $1$ bit/s/Hz. The relevance of the $\eta$-NE region is that it provides the set of rate-pairs that are achievable and stable in the IC when both transmitter-receiver pairs autonomously tune their own transmit-receive configurations seeking an $\eta$-optimal individual transmission rate. Therefore, any rate tuple outside the $\eta$-NE region is not stable as there always exists one link able to increase by at least $\eta$ bits/s/Hz its own transmission rate by updating its own transmit-receive configuration. The main insights that arise from this work are: $(i)$ The $\eta$-NE region achieved with feedback is larger than or equal to the $\eta$-NE region without feedback. More importantly, for each rate pair achievable at an $\eta$-NE without feedback, there exists at least one rate pair achievable at an $\eta$-NE with feedback that is weakly Pareto superior. $(ii)$ There always exists an $\eta$-NE transmit-receive configuration that achieves a rate pair that is at most $1$ bit/s/Hz per user away from the outer bound of the capacity region.Comment: Revised version (Aug. 2015

Information-Theoretic Attacks in the Smart Grid

Gaussian random attacks that jointly minimize the amount of information obtained by the operator from the grid and the probability of attack detection are presented. The construction of the attack is posed as an optimization problem with a utility function that captures two effects: firstly, minimizing the mutual information between the measurements and the state variables; secondly, minimizing the probability of attack detection via the Kullback-Leibler divergence between the distribution of the measurements with an attack and the distribution of the measurements without an attack. Additionally, a lower bound on the utility function achieved by the attacks constructed with imperfect knowledge of the second order statistics of the state variables is obtained. The performance of the attack construction using the sample covariance matrix of the state variables is numerically evaluated. The above results are tested in the IEEE 30-Bus test system.Comment: 2017 IEEE International Conference on Smart Grid Communications (SmartGridComm