## Section: New Results

### Multi-User Communications

#### Fundamental Limits

##### Approximate Capacity Region of the Gaussian Interference Channel with Feedback

An achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (G-IC-NOF) are presented [42], [30], [43], [47]. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits per channel use.

##### Full Characterization of the Capacity Region of the Linear Deterministic Interference Channel with Feedback

The capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) has been fully characterized [29]. This result allows the identification of several asymmetric scenarios in which implementing 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.

##### Full Characterization of the Information Equilibrium Region of the Multiple Access Channel

The fundamental limits of decentralized information transmission in the $K$-user Gaussian multiple access channel (G-MAC), with $K\u2a7e2$, are fully characterized [38]. Two scenarios are considered. First, a game in which only the transmitters are players is studied. In this game, the transmitters autonomously and independently tune their own transmit configurations seeking to maximize their own information transmission rates, ${R}_{1}$, ${R}_{2}$, $\cdots $ , ${R}_{K}$, respectively. On the other hand, the receiver adopts a fixed receive configuration that is known a priori to the transmitters. The main result consists of the full characterization of the set of rate tuples $({R}_{1},{R}_{2},...,{R}_{K})$ that are achievable and stable in the G-MAC when stability is considered in the sense of the $\eta $-Nash equilibrium (NE), with $\eta >0$ arbitrarily small. Second, a sequential game in which the two categories of players (the transmitters and the receiver) play in a given order is presented. For this sequential game, the main result consists of the full characterization of the set of rate tuples $({R}_{1},{R}_{2},...,{R}_{K})$ that are stable in the sense of an $\eta $-sequential equilibrium, with $\eta >0$.

##### Full Characterization of the Information-Energy Capacity Region of the Multiple Access Channel with Energy Harvester with and without Feedback

The fundamental limits of simultaneous information and energy transmission in the two-user Gaussian multiple access channel (G-MAC) with and without feedback have been fully characterized [10], [15]. More specifically, all the achievable information and energy transmission rates (in bits per channel use and energy-units per channel use, respectively) are identified. In the case without feedback, an achievability scheme based on power-splitting and successive interference cancelation is shown to be optimal. Alternatively, in the case with feedback (G-MAC-F), a simple yet optimal achievability scheme based on power-splitting and Ozarow's capacity achieving scheme is presented. Two of the most important observations in this work are: (a) The information-energy capacity region of the G-MAC without feedback can be a proper subset of the information-energy capacity region of the G-MAC-F and (b) Feedback can at most double the energy rate when the information transmission rate is kept fixed at the sum-capacity of the G-MAC.

##### Full Characterization of the Information-Energy Equilibrium Region of the Multiple Access Channel with Energy Harvester

The fundamental limits of decentralized simultaneous information and energy transmission in the two-user Gaussian multiple access channel (G-MAC) have been fully characterized for the case in which a minimum energy transmission rate b is required for successful decoding [14], [39]. All the achievable and stable information-energy transmission rate triplets $({R}_{1},{R}_{2},B)$ are identified. ${R}_{1}$ and ${R}_{2}$ are in bits per channel use measured at the receiver and $B$ is in energy units per channel use measured at an energy-harvester (EH). Stability is considered in the sense of an $\eta $-Nash equilibrium (NE), with $\eta >0$ arbitrarily small. The main result consists of the full characterization of the $\eta $-NE information-energy region, i.e., the set of information-energy rate triplets $({R}_{1},{R}_{2},B)$ that are achievable and stable in the G-MAC when: $\left(a\right)$ both transmitters autonomously and independently tune their own transmit configurations seeking to maximize their own information transmission rates, ${R}_{1}$ and ${R}_{2}$ respectively; $\left(b\right)$ both transmitters jointly guarantee an energy transmission rate $B$ at the EH, such that $B>b$. Therefore, any rate triplet outside the $\eta $-NE region is not stable as there always exists one transmitter able to increase by at least $\eta $ bits per channel use its own information transmission rate by updating its own transmit configuration.

##### Duality Between State-Dependent Channels and Wiretap Channels

A duality between wiretap and state-dependent channels with non-causal channel state information at the transmitter has been established [13]. First, a common achievable scheme is described for a certain class of state-dependent and wiretap channels. Further, state-dependent and wiretap channels for which this scheme is capacity (resp. secrecy capacity) achieving are identified. These channels are said to be dual. This duality is used to establish the secrecy capacity of certain state-dependent wiretap channels with non-causal channel state information at the transmitter. Interestingly, combatting the eavesdropper or combatting the lack of state information at the receiver turn out to be two non-concurrent tasks.

##### Energy efficiency - Spectral Efficiency (EE-SE) Tradeoffs in Wireless RANs

Even for a point-to-point communication, the Shannon capacity can be interpreted for a Gaussian channel as a fundamental spectral and energy efficiency (SE-EE) trade-off. Extending this fundamental trade-off in the context of multi-user communications is not straightforward as it may depend on many parameters. We proposed in [8] a simple and effective method to study this trade-off in cellular networks, an issue that has attracted significant recent interest in the wireless community. The proposed theoretical framework is based on an optimal radio resource allocation of transmit power and bandwidth for the downlink direction, applicable for an orthogonal cellular network. The analysis is initially focused on a single cell scenario, for which in addition to the solution of the main SE-EE optimization problem, it is proved that a traffic repartition scheme can also be adopted as a way to simplify this approach. By exploiting this interesting result along with properties of stochastic geometry, this work is extended to a more challenging multi-cell environment, where interference is shown to play an essential role and for this reason several interference reduction techniques are investigated. Special attention is also given to the case of low signal to noise ratio (SNR) and a way to evaluate the upper bound of EE in this regime is provided. This methodology leads to tractable analytical results under certain common channel properties, and thus allows the study of various models without the need for demanding system level simulations.

##### Spatial Continuum Channel Models

In the context of the deployment of Internet of Things (see next section for more details about our protocol developments), it is expected that a unique cell could serve millions of radio nodes transmitting sporadic short packets. In [18] and [41], our objective is to study this problem from an information theory point of view to derive the fundamental limit in terms of maximal information rates that can be transmitted in such a dense cell. This work proposes a new model called spatial continuum asymmetric channels to study the channel capacity region of asymmetric scenarios in which either one source transmits to a spatial density of receivers or a density of transmitters transmit to a unique receiver. This approach is built upon the classical broadcast channel (BC) and multiple access channel (MAC). For the sake of consistency, the study is limited to Gaussian channels with power constraints and is restricted to the asymptotic regime (zero-error capacity). The reference scenario comprises one base station in Tx or Rx mode, a spatial random distribution of nodes (resp. in Rx or Tx mode) characterized by a probability spatial density of users $u\left(x\right)$ where each of them requests a quantity of information with no delay constraint, thus leading to a requested rate spatial density $\rho \left(x\right)$. This system is modeled as an ‚àû‚àíuser asymmetric channel (BC or MAC). To derive the fundamental limits of this model, a spatial discretization is first proposed to obtain an equivalent BC or MAC. Then, a specific sequence of discretized spaces is defined to refine infinitely the approximation. Achievability and capacity results are obtained in the limit of this sequence while the access capacity region $\mathcal{C}\left(Pm\right)$ is defined as the set of requested rates spatial densities $\rho \left(x\right)$ that are achievable with a transmission power $Pm$. The uniform capacity defined as the maximal symmetric achievable rate is also computed.

##### Finite Block-Length Coding in Wireless Networks

In the context of IoT, the information to be transmitted will be divided in very small packets especially when control and commands will be transmitted over the network. The classical asymptotic information theory relies on the statistic properties of channels and information sources, when the coding block-length tends to infinity. Therefore this framework is not appropriate to study the fundamental limits of short packets transmission over wireless networks. Fortunately, information theory is not only about the asymptotic regime. Shannon himself derived the preliminary foundations of a theory for finite block-length. Later, Gallager extended this framework. Recently this question gained interest after the work of Y. Polyanskiy which extended former results on finite block length to Gaussian channels. This fundamental contribution opens a way for studying wireless networks under finite block-length regime. But this relatively new paradigm suffers from strong problems relative to the compexity of the underlying estimation problem. Starting to work on this topic in the framework of the associated team with Princeton, we exploited in [35] the recent results on the non-asymptotic coding rate for fading channels with no channel state information at the transmitter and we analyzed the goodput in additive white Gaussian noise (AWGN) and the energy-efficiency spectral-efficiency (EE-SE) tradeoff where the fundamental relationship between the codeword length and the EE is given. Finally, the true outage probability in Ricean and Nakagami-m block fading channels is investigated and it is proved that the asymptotic outage capacity is the Laplace approximation of the average error probability in finite blocklength regime. This preliminary work constitutes one of the starting point for our future works in the framework of the ANR project ARBURST.

#### Algorithm and Protocol Design for Multi-User Communication Scenarios

##### Interference Management in OFDM/MIMO Wireless Networks

Modern cellular networks in traditional frequency bands are notoriously interference-limited especially in urban areas, where base stations are deployed in close proximity to one another. The latest releases of Long Term Evolution (LTE) incorporate features for coordinating downlink transmissions as an efficient means of managing interference. In [4], we review recent field trial results and theoretical studies of the performance of joint transmission (JT) coordinated multi-point (CoMP) schemes. These schemes revealed, however, that their gains are not as high as initially expected, despite the large coordination overhead. These schemes are known to be very sensitive to defects in synchronization or information exchange between coordinating bases stations as well as uncoordinated interference. In this article, we review recent advanced coordinated beamforming (CB) schemes as alternatives, requiring less overhead than JT CoMP while achieving good performance in realistic conditions. By stipulating that, in certain LTE scenarios of increasing interest, uncoordinated interference constitutes a major factor in the performance of CoMP techniques at large, we hereby assess the resilience of the state-of-the-art CB to uncoordinated interference. We also describe how these techniques can leverage the latest specifications of current cellular networks, and how they may perform when we consider standardized feedback and coordination. This allows us to identify some key roadblocks and research directions to address as LTE evolves towards the future of mobile communications.

Among the different techniques described above, we studied in [32] an interference Alignment (IA) technique that, in a large sense, makes use of the increasing signal dimensions available in the system through MIMO and OFDM technologies in order to globally reduce the interference suffered by users in a network. In this paper, we addressed the problem of downlink cellular networks, the so-called interfering broadcast channels, where mobile users at cell edges may suffer from high interference and thus, poor performance. Starting from the downlink IA scheme proposed by Suh et al., a new approach is proposed where each user feeds back multiple selected received signal directions with high signal-to-interference gain. A exhaustive search based scheduler selects a subset of users to be served simultaneously, balancing between sum-rate performance and fairness, but becomes untractable in dense network scenarios where many users send simultaneous requests. Therefore, we develop a sub-optimal scheduler that greatly decreases the complexity while preserving a near-optimal data rate gain. More interestingly, our simulations show that the IA scheme becomes valuable only in correlated channels, whereas the matched filtering based scheme performs the best in the uncorrelated scenarios.

##### Performance of Ultra-NarrowBand Techniques for Internet of Things

This section makes echo to the section entitled Spatial Continuum Channel Models where fundamental limits are studied for a similar scenario. In this section, we investigate the scenario for an existing PHY layer technology, Ultra Narrow Band (UNB) technique, proposer by Sigfox. The ALOHA protocol is regaining interest in the context of the Internet of Things (IoT), especially for UNB signals (dedicated to long range and low power transmission in IoT networks). In this case, the classical assumption of channelization is not verified anymore, modifying the ALOHA performances. Indeed, UNB signals suffer from a lack of precision on the actual transmission carrier frequency, leading to a behavior similar to a frequency unslotted random access. More precisely, the channel access is Random-FTMA, where nodes select their time and frequency in a random and continuous way. The frequency randomness prevents from allocating orthogonal resources for transmission, and induces uncontrolled interference.

In [19], the success probability and throughput of ALOHA is generalized to further describe frequency-unslotted systems such as UNB. The main contribution of this work is the derivation of a generalized expression of the throughput for the random time-frequency ALOHA systems, when neglecting channel attenuation. Besides, this study permits to highlight the duality of ALOHA in time and frequency domain.

Besides, in [26] and [27], to introduce diversity, we propose the use of replication mechanism to enhance the reliability of UNB wireless network. Considering the outage probability, we theoretically evaluate the system performance and show that there exists an optimal number of transmissions. Finally, we highlight that this number of repetitions can be easily optimized by considering a unique global parameter.

Finally, in [28], we also take into consideration the channel effect for such specific network. Indeed, the UNB randomness leads to a new behavior of the interference which has not been theoretically analyzed yet, when considering the pathloss of nodes located randomly in an area. In this work, in order to quantify the system performance, we derive and exploit a theoretical expression of the packet error rate in a UNB based IoT network, when taking into account both interference due to the spectral randomness and path loss due to the propagation.

##### Algorithms and Protocols for BANs

Body Area Networks (BANs) represent a challenging area of research for networking design. Indeed, the topology of these networks differe significantly from classical networks. BANs are dynamic, multi-scale, energy limited and require real time protocols for many applications related to localization. Our work is related to the design of dynamic protocols to gather and exploit localization information in dynamic BANs. Our first contribution is related to the context of group navigation and was developed in the framework of the FUI SMACS project dealing with the localisation of runners during bike races. The problem is to develop fast and reliable protocols to dynamically gather mobility information from moving nodes toward moving sinks.

Our second contribution is relative to the mobility of a single BAN and with the objective of improving localization algorithms based on ranging measures between nodes spread on the body. This work was done in the framework of the ANR CORMORAN project with the PhD of Arturo Gimenez-Guizar who defended his PhD in October 2016 [1].

##### Information Gathering in a Group of Mobile Users

In [16], we propose an efficient approach to collect data in mobile wireless sensor networks, with the specific application of sensing in bike races. Recent sensor technology permits to track GPS position of each bike. Because of the inherent correlation between bike positions in a bike race, a simple GPS log is inefficient. The idea presented in this work is to aggregate GPS data at sensors using compressive sensing techniques. We enforce, in addition to signal sparsity, a spatial prior on biker motion because of the group behaviour (peloton) in bike races. The spatial prior is modeled by a graphical model and the data aggregation problem is solved, with both the sparsity and the spatial prior, by belief propagation. We validate our approach on a bike race simulator using trajectories of motorbikes in a real bike race.

##### MAC Protocols and Algorithms for Localization at the Body Scale

In this work [20], we have considered the positioning success rate for localization applications deployed in Wireless Body Area Networks (WBAN). Localization is performed with Ultra Wide Band (UWB) pulses, which permits to estimate distances as defined by 3 Way Ranging protocol (3WR). Two channels are considered : the empirical channel CM3, and with our model obtained from our measurement campaign. We first evaluate the positioning loss when considering an aggregation and broadcast scheduling strategy (A&B) upon TDMA MAC. We highlight the channel effects depending on the targeted receiver sensitivity. We then improve the performances by proposing a cooperative algorithm based on conditional permutation of anchors.

#### Cyber-Physical Systems

##### Attacks in the Electricity Grids

Multiple attacker data injection attack construction in electricity grids with minimum-mean-square-error state estimation has been studied for centralized and decentralized scenarios [6], [11]. A performance analysis of the trade-off between the maximum distortion that an attack can introduce and the probability of the attack being detected by the network operator is considered. In this setting, optimal centralized attack construction strategies are studied. The decentralized case is examined in a game-theoretic setting. A novel utility function is proposed to model this trade-off and it is shown that the resulting game is a potential game. The existence and cardinality of the corresponding set of Nash Equilibria (NEs) of the game is analyzed. Interestingly, the attackers can exploit the correlation among the state variables to facilitate the attack construction. It is shown that attackers can agree on a data injection vector construction that achieves the best trade-off between distortion and detection probability by sharing only a limited number of bits offlline. For the particular case of two attackers, numerical results based on IEEE test systems are presented.

##### Recovering Missing Data in Electricity Grids

The performance of matrix completion based recovery of missing data in electricity distribution systems has been analyzed [17]. Under the assumption that the state variables follow a multivariate Gaussian distribution the matrix completion recovery is compared to estimation and information theoretic limits. The assumption about the distribution of the state variables is validated by the data shared by Electricity North West Limited. That being the case, the achievable distortion using minimum mean square error (MMSE) estimation is assessed for both random sampling and optimal linear encoding acquisition schemes. Within this setting, the impact of imperfect second order source statistics is numerically evaluated. The fundamental limit of the recovery process is characterized using Rate-Distortion theory to obtain the optimal performance theoretically attainable. Interestingly, numerical results show that matrix completion based recovery outperforms MMSE estimator when the number of available observations is low and access to perfect source statistics is not available.