## Section: New Results

### Multi-User Communications

#### Fundamental limits : contributions in Multi-User Information Theory (MU-IT)

##### Interference channel with feedback

In this work [29], [44], [43], the $\eta -$Nash equilibrium ($\eta -$NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $\eta >0$. The $\eta -$NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta -$NE. More specifically, given an $\eta -$NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than η bits per channel use. Existing results such as the η-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result. We also characterized in [15] the price of anarchy (PoA) and the price of stability (PoS) of this $\eta -$NE. The price of anarchy is the ratio between the sum-rate capacity and the smallest sum-rate at an $\eta -$NE. The price of stability is the ratio between the sum-rate capacity and the biggest sum-rate at an $\eta -$NE. Some of the main conclusions of this work are the following: (a) When both transmitter-receiver pairs are in low interference regime, the PoA can be made arbitrarily close to one as $\eta $ approaches zero, subject to a particular condition. More specifically, there are scenarios in which even the worst $\eta -$NE (in terms of sum-rate) is arbitrarily close to the Pareto boundary of the capacity region. (b) The use of feedback plays a fundamental role on increasing the PoA, in some interference regimes. This is basically because in these regimes, the use of feedback increases the sum-capacity, whereas the smallest sum-rate at an $\eta -$NE remains the same. (c) The PoS is equal to one in all interference regimes. This implies that there always exists an $\eta -$NE in the Pareto boundary of the capacity region. The ensemble of conclusions of this work reveal the relevance of jointly using equilibrium selection methods and channel-output feedback for reducing the effect of anarchical behavior of the network components in the $\eta -$NE sum-rate of the interference channel.

##### Simultaneous information and energy transmission

In this work [42], [25], [48], the fundamental limits of simultaneous information and energy transmission in the two-user Gaussian interference channel (G-IC) with and without feedback are fully characterized. More specifically, an achievable and converse region in terms of information and energy transmission rates (in bits per channel use and energy-units per channel use, respectively) are identified. In both cases, with and without feedback, an achievability scheme based on power-splitting, common randomness, rate splitting, block-Markov superposition coding, and backward decoding is presented. Finally, converse regions for both cases are obtained using some of the existing outer bounds for information transmission rates, as well as a new outer bound for the energy transmission rate.

##### Ultra-dense wireless networks

Ultra-dense networks represent an interesting model for future IoT networks. The analysis of these metworks relies on the association of stochastic geometry models with information theory in the finite blocklength regime. Considering an isolated wireless cell containing a high density of nodes, the fundamental limit can be defined as the maximal number of nodes the associate base station can serve under some system level constraints including maximal rate, reliability, latency and transmission power. This limit can be investigated in the downlink, modeled as a spatial continuum broadast channel (SCBC) as well as in the uplink modeled as a spatial continuum multiple access channel (SCMAC). In this work, we define the different steps towards the characterization of this fundamental limit, considering four figures of merit: energy efficiency, spectral efficiency, latency, reliabilty [13]. To address this question in the uplink scenario [10], we uses a large scale Multiple Access Channel (MAC) to model IoT nodes randomly distributed over the coverage area of a unique base station. The traffic is represented by an information rate spatial density $\rho \left(x\right)$. This model, referred to as the Spatial Continuum Multiple Access Channel, is defined as the asymptotic limit of a sequence of discrete MACs. The access capacity region of this channel is defined as the set of achievable information rate spatial densities achievable with vanishing transmission errors and under a sum-power constraint. Simulation results validate the model and show that this fundamental limit theoretically achievable when all nodes transmit simultaneously over an infinite time, may be reached even with a relatively small number of simultaneous transmitters (typically around 20 nodes) which gives credibility to the model. The results also highlight the potential interest of non-orthogonal transmissions for IoT uplink transmissions when compared to an ideal time sharing strategy. We then developed a powerful analytical model of wireless network with Superposition Coding (SC), also referred to as Non Orthogonal Multiple Access (NOMA), taking into consideration a multi cell interference limited network. This model allows to establish a closed form expression of the minimum power a base station (BS) needs to transmit to its users and to achieve a given SINR (signal to interference plus noise ratio) whatever its location in the area covered by the base station. It moreover allows to establish a closed form expression of the minimum total transmit power of a base station. These closed form expressions allow to establish performance of wireless networks, by minimizing the base stations transmit powers. As an application, we show that these closed form expressions allow to quantify the energetic performance, spectral efficiency, total throughput and the coverage of a BS, in a simple and quick way.

##### Broadcast channel in the Finite Blocklength regime

In order to analyse wireless networks with short packets, theoretical results in information theory for the finite blocklength regime in multi-user scenarios were missin. In [34], [33], we analyzed the performance of superposition coding for Gaussian broadcast channels with finite blocklength. To this end, we adapted two different achievability bounds, the dependence testing and the $\kappa -\beta -$bounds introduced by Polyanskiy et al. in 2010 to the broadcast setting. The distinction between these bounds lies in fixing either the input or the output distributions of the channel. For the first case of the dependence testing bound, an upper bound on the average error probability of the system is derived whereas for the latter, lower bounds on the maximal code sizes of each user are presented.

##### Capacity sensitivity

In this work [22], [40], a new framework based on the notion of *capacity sensitivity* is introduced to study the capacity of continuous memoryless point-to-point channels. The capacity sensitivity reflects how the capacity changes with small perturbations in any of the parameters describing the channel, even when the capacity is not available in closed-form. This includes perturbations of the cost constraints on the input distribution as well as on the channel distribution. The framework is based on continuity of the capacity, which is shown for a class of perturbations in the cost constraint and the channel distribution. The continuity then forms the foundation for obtaining bounds on the capacity sensitivity. As an illustration, the capacity sensitivity bound is applied to obtain scaling laws when the support of additive $\alpha -$stable noise is truncated.

#### Performance evaluation of large scale systems

##### UNB networks performance evaluation

UNB (Ultra Narrow Band) stands out as one promising PHY solution for low-power, low-throughput and long-range IoT. The dedicated MAC scheme is RFTMA (Random Frequency and Time Multiple Access), where nodes access the channel randomly both in frequency and in time domain, without prior channel sensing. This blind randomness sometimes introduces interference and packet losses. In order to quantify the system performance, we have derived and exploited a theoretical expression of the outage probability in a UNB based IoT network, when taking into account both interference due to the spectral randomness and path loss due to the propagation [14], [5]. Besides, we also proposed to use the well-known SIC (Successive Interference Cancellation) to cancel the interference in a recursive way. We provided a theoretical analysis of network performance, when considering jointly SIC and the specific spectral randomness of UNB. We analytically and numerically highlighted the SIC efficiency in enhancing UNB system performance [26].

##### Wireless networks on FIT/CorteXlab

In this work we study the FIT/CorteXlab platform where all radio nodes are confined to an electromagnetically (EM) shielded environment and have flexible radio-frequency (RF) front-end for experimenting on software defined radio (SDR) and cognitive radio (CR). A unique feature of this testbed is that it offers roughly 40 SDR nodes that can be accessed from anywhere in the world in a reproducible manner: the electromagnetic shield prevents from external interference and channel variability. In this work [16] we show why it is important to have such a reproducible radio experiment testbed and we highlight the reproducibility by the channel characteristics between the nodes of the platform. We back our claims with a large set of measurements done in the testbed, that also refines our knowledge on the propagation characteristics of the testbed.

One of the major goals of the 5G technology roadmap is to create disruptive innovation for the efficient use of the radio spectrum to enable rapid access to bandwidth-intensive multimedia services over wireless networks. The biggest challenge toward this goal lies in the difficulty in exploiting the multicast nature of the wireless channel in the presence of wireless users that rarely access the same content at the same time. Recently, the combined use of wireless edge caching and coded multicasting has been shown to be a promising approach to simultaneously serve multiple unicast demands via coded multicast transmissions, leading to order-of-magnitude bandwidth efficiency gains. However, a crucial open question is how these theoretically proven throughput gains translate in the context of a practical implementation that accounts for all the required coding and protocol overheads. In [3], in collaboration with Nokia Bell Labs, New Jersey, we first provide an overview of the emerging caching- aided coded multicast technique, including state-of-the-art schemes and their theoretical performance. We then focus on the most competitive scheme proposed to date and describe a fully working prototype implementation in CorteXlab, one of the few experimental facilities where wireless multiuser communication scenarios can be evaluated in a reproducible environment. We use our prototype implementation to evaluate the experimental performance of state-of-the-art caching-aided coded multicast schemes compared to state-of-the-art uncoded schemes, with special focus on the impact of coding computation and communication overhead on the overall bandwidth efficiency performance. Our experimental results show that coding overhead does not significantly affect the promising performance gains of coded multicasting in small-scale realworld scenarios, practically validating its potential to become a key next generation 5G technology.

#### Cognitive networks

##### Game theory based approaches

In [4], a generalization of the satisfaction equilibrium (SE) for games in satisfaction form (SF) is presented. This new solution concept is referred to as the generalized satisfaction equilibrium (GSE). In games in SF, players choose their actions to satisfy an individual constraint that depends on the actions of all the others. At a GSE, players that are unsatisfied are unable to unilaterally deviate to be satisfied. The concept of GSE generalizes the SE in the sense that it allows mixed-strategy equilibria in which there exist players who are unable to satisfy their individual constraints. The pure-strategy GSE problem is closely related to the constraint satisfaction problem and finding a pure-strategy GSE is proven to be NP-hard. The existence of at least one GSE in mixed strategies is proven for the class of games in which the constraints are defined by a lower limit on the expected utility. A dynamics referred to as the satisfaction response is shown to converge to a GSE in certain classes of games. Finally, Bayesian games in SF and the corresponding Bayesian GSE are introduced. These results provide a theoretical framework for studying service-level provisioning problems in communications networks as shown by several examples.

Device-to-device (D2D) communications can enhance spectrum and energy efficiency due to direct proximity communication and frequency reuse. However, such performance enhancement is limited by mutual interference and energy availability, especially when the deployment of D2D links is ultra-dense. In this contribution [9], we present a distributed power control method for ultra-dense D2D communications underlaying cellular communications. In this power control method, in addition to the remaining battery energy of the D2D transmitter, we consider the effects of both the interference caused by the generic D2D transmitter to others and interference from all others' caused to the generic D2D receiver. We formulate a mean-field game (MFG) theoretic framework with the interference mean-field approximation. We design the cost function combining both the performance of the D2D communication and cost for transmit power at the D2D transmitter. Within the MFG framework, we derive the related Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations. Then, a novel energy and interference aware power control policy is proposed, which is based on the Lax-Friedrichs scheme and the Lagrange relaxation. The numerical results are presented to demonstrate the spectrum and energy efficiency performances of our proposed approach. Index Terms—Device-to-device communication, mean field game, spectrum efficiency, energy efficiency.

##### Learning approaches

Fast initialization of cognitive radio systems is a key problem in a variety of wireless communication systems, particularly for public safety organizations in emergency crises. In the initialization problem, the goal is to rapidly identify an unoccupied frequency band. In this contribution [21], we formalize the initialization problem within the framework of active hypothesis testing. We characterize the optimal scanning policy in the case of at most one free band and show that the policy is computationally challenging. Motivated by this challenge for the implementation of the optimal policy and the need to cope with an unknown number of interferers larger than one, we propose the constrained DGF algorithm. We show that for strict constraints on the maximum number of observations, the constrained DGF algorithm can outperform the error probability of the state-of-the-art C-SPRT algorithm by an order of magnitude, for comparable average delays.

##### Asynchronous transmissions in VLC

In a visible light communications system (VLC), light sources are responsible for both illumination, communications and positioning. These light sources inevitably interfere each others at the receiver. To retain the appealing advantage that VLC systems can reuse existing lighting infrastructure, using an extra network to control or synchronize the light sources should be avoided. This work [31] proposes an uncoordinated multiple access scheme for VLC systems with positioning capability. The proposed scheme does not require a central unit to coordinate the transmission of the transmitters. Transmitters can be asynchronous with one another and with the receiver. Each transmitter is allocated a unique codeword with L chips for a system with up to $(L-1)/2$ transmitters where $L$ is prime. Due to the linear growth in complexity with respect to number of transmitters, our proposed scheme is feasible for systems with large numbers of transmitters. Our novel decoder can minimize the effect of additive Gaussian noise at the receiver side. Simulation results show that the proposed decoder outperforms zero-forcing decoder.

#### Contributions in other application fields

##### Smart Grids

The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore, paramount. In this context, an algorithm for recovering missing state variable observations in electricity distribution systems is presented in [47]. The proposed method exploits the low rank structure of the state variables via a matrix completion approach while incorporating prior knowledge in the form of second order statistics. Specifically , the recovery method combines nuclear norm minimization with Bayesian estimation. The performance of the new algorithm is compared to the information-theoretic limits and tested trough simulations using real data of an urban low voltage distribution system. The impact of the prior knowledge is analyzed when a mismatched covariance is used and for a Markovian sampling that introduces structure in the observation pattern. Numerical results demonstrate that the proposed algorithm is robust and outperforms existing state of the art algorithms.

In addition, 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 in [38]. 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 (KL) 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.

##### Molecular Communications

Molecular communications is emerging as a technique to support coordination in nanonetworking, particularly in biochemical systems. In complex biochemical systems such as in the human body, it is not always possible to view the molecular communication link in isolation as chemicals in the system may react with chemicals used for the purpose of communication. There are two consequences: either the performance of the molecular communication link is reduced; or the molecular link disrupts the function of the biochemical system. As such, it is important to establish conditions when the molecular communication link can coexist with a biochemical system. In this work [45], we develop a framework to establish coexistence conditions based on the theory of chemical reaction networks. We then specialize our framework in two settings: an enzyme-aided molecular communication system; and a low-rate molecular communication system near a general biochemical system. In each case, we prove sufficient conditions to ensure coexistence.