Section: New Results

Multi-User Communications

Activities in axis 2 primarily focus on communicating multi-user systems. They represent the core of the research activity that will be pursued in Maracas team.

The first pillar of our research concerns the evaluation of fundamental limits of wireless systems (e.g. capacity) often express as a fundamental tradeoff : energy efficiency - spectral efficiency tradeoff, rate versus reliability, information versus energy transfert,... Our work relies mostly on information theory, signal processing, estimation theory and game theory.

The second pillar concerns the evaluation of real systems and their performance is confronted to the above mentioned fundamental limits. These activities rely on strong collaborations with industry (Nokia, Orange, SigFox, Sequans, SPIE-ICS,...) We also manage the FIT/CorteXlab testbed offering a remote access to a worldwide unique platform.

Beyond these two pillars, we also explore new research areas where our background is relevant. These prospective activities are performed with external collaborations and prepare the future activity of Maracas team. This year we explored molecular communications (supported by an Inria exploratory project), smart grids in collaboration with Sheffield, VLC in association with Agora team or Privacy preservation in collaboration with Privatics team.

Fundamental limits in communications

Variations on point to point capacity and related tools

In [31] discrete approximations of the capacity are introduced where the input distribution is constrained to be discrete in addition to any other constraints on the input. For point-to-point memoryless additive noise channels, rates of convergence to the capacity of the original channel are established for a wide range of channels for which the capacity is finite. These results are obtained by viewing discrete approximations as a capacity sensitivity problem, where capacity losses are studied when there are perturbations in any of the parameters describing the channel. In particular, it is shown that the discrete approximation converges arbitrarily close to the channel capacity at rate $O\left(\Delta \right)$, where $\Delta$ is the discretization level of the approximation. Examples of channels where this rate of convergence holds are also given, including additive Cauchy and inverse Gaussian noise channels.

In [30] the properties of finite frames are explored. Finite frames are sequences of vectors in finite dimensional Hilbert spaces that play a key role in signal processing and coding theory. We studied the class of tight unit-norm frames for ${ℂ}^d$ that also form regular schemes, called tight regular schemes (TRS). Many common frames that arise in applications such as equiangular tight frames and mutually unbiased bases fall in this class. We investigate characteristic properties of TRSs and prove that for many constructions, they are intimately connected to weighted 1-designs—arising from quadrature rules for integrals over spheres in ${ℂ}^d$ with weights dependent on the Voronoi regions of each frame element.

Interference channel with feedback

The interference channel is a well-known model used to represent simultaneous transmissions in a wireless environment. In the framework of Victor Quintero's PhD, we explored the performance of this model with noisy feedbacks.

In [35], an achievable $\eta$-Nash equilibrium ($\eta$-NE) region for the two-user Gaussian interference channel with noisy channel-output feedback is presented for all $\eta \ge 1$. This result is obtained in the scenario in which each transmitter-receiver pair chooses its own transmit-receive configuration in order to maximize its own individual information transmission rate. At an $\eta$-NE, any unilateral deviation by either of the pairs does not increase the corresponding individual rate by more than $\eta$ bits per channel use.

In [6], the capacity region of the linear deterministic interference channel with noisy channel-output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting; block-Markov superposition coding; and backward decoding. The proof of converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (GIC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within $4.4$ bits.

Wiretap channel

The Wiretap channel allows to address the secrecy constraint in an information theory framework. In [13], an analysis of an input distribution that achieves the secrecy capacity of a general degraded additive noise wiretap channel is presented. In particular, using convex optimization methods, an input distribution that achieves the secrecy capacity is characterized by conditions expressed in terms of integral equations. The new conditions are used to study the structure of the optimal input distribution for three different additive noise cases: vector Gaussian; scalar Cauchy; and scalar exponential.

Simultaneous Information and Energy Transmission

Simultaneous information and energy transmission (SIET) is an active research problem and aims at providing energy and information simultaneously from transmitters to receivers. We explore the optimal trade-offs in different settings.

In [34], a non-asymptotic analysis of the fundamental limits of simultaneous energy and information transmission (SEIT) is presented. The notion of information-capacity region, i.e., the largest set of simultaneously achievable information and energy rates, is revisited in a context in which transmissions occur within a finite number of channel uses and strictly positive error decoding probability and energy shortage probability are tolerated. The focus is on the case of one transmitter, one information receiver and one energy harvester communicating through binary symmetric memoryless channels. In this case, the information-capacity region is approximated and the trade-off between information rate and energy rate is thoroughly studied.

In [5], the fundamental limits of simultaneous information and energy transmission (SIET) in the two-user Gaussian interference channel (G-IC) with and without perfect channel-output feedback are approximated by two regions in each case, i.e., an achievable region and a converse region. When the energy transmission rate is normalized by the maximum energy rate  the approximation is within a constat gap. In the proof of achievability, the key idea is the use of power-splitting between two signal components: an information-carrying component and a no-information component. The construction of the former is based on random coding arguments, whereas the latter consists in a deterministic sequence known by all transmitters and receivers. The proof of the converse is obtained via cut-set bounds, genie-aided channel models, Fano's inequality and some concentration inequalities considering that channel inputs might have a positive mean. Finally, the energy transmission enhancement due to feedback is quantified and it is shown that feedback can at most double the energy transmission rate at high signal to noise ratios.

Modeling Interference in Large-Scale Uplink SCMA

Massive connectivity is a fundamental challenge for IoT, as discussed in the next section from a practical perspective. From a theoretical perspective, we propose to relax the assumption of Gaussian interference.

Fast varying active transmitter sets with very short length transmissions arise in communications for the Internet of Things. As a consequence, the interference is dynamic, leading to non-Gaussian statistics. At the same time, the very high density of devices is motivating non-orthogonal multiple access (NOMA) techniques, such as sparse code multiple access (SCMA). In [2], we study the statistics of the dynamic interference from devices using SCMA. In particular, we show that the interference is $\alpha -$stable with non-trivial dependence structure for large scale networks modeled via Poisson point processes. Moreover, the interference on each frequency band is shown to be sub-Gaussian $\alpha -$stable in the special case of disjoint SCMA codebooks. We investigate the impact of the $\alpha -$stable interference on achievable rates and on the optimal density of devices. Our analysis suggests that ultra dense networks are desirable even with $\alpha -$stable interference.

This contribution is a good introduction of the next section where the performance of IoT access techniques are evaluated.

General Massive Machine Type Communications Uplink

Non Orthogonal Multiple Access (NOMA) is expected to play an important role for IoT networks, allowing to reduce signaling overheads and to maximize the capacity of dense networks with multiple packets simultaneous transmission. In the uplink, NOMA can improve significantly the performance of an ALOHA random access if the receiver implements a multiuser detection algorithm. In [11], we compared the performance of a code domain NOMA with a classical ALOHA protocol, through simulations. The code domain NOMA uses random Gaussian codes at the transmitters and exploits compressive sensing at the receiver to maximize users detection and to minimize symbol error rates.

As the number of machine type communications increases at an exponential rate, new solutions have to be found in order to deal with the uplink traffic. At the same time, new types of Base Stations (BS) that use a high number of antennas are being designed, and their beamforming capabilities can help to separate signals that have different angles of arrivals. In [15], we consider a network where a BS serves a high number of nodes that lacks a receive chain, and we analyze the evolution of the outage probability as a function of the number of antennas at the BS. We then study the effect of an angle offset between the main beam and the desired node's direction in order to provide realistic results in a beam-switching scenario.

Multiple Base Stations Diversity for UNB Systems

In the framework of the long-term collaboration with Sigfox, the PhD of Yuqi Mo defended mast December, explored the performance of Ultra Narrow Band (UNB) with a focus on sophisticated signal processing techniques such as multi-BS processing or successive interference cancellation (SIC). UNB (Ultra Narrow Band) is one of the technologies dedicated to low-power wide-area communication for IoT, currently exploited by SigFox

In [33], [18], the specificity of UNB is the Aloha-type channel access scheme, asynchronous in both time and frequency domain. This randomness can cause partial spectral interference. In this paper, we take advantage of the spatial diversity of multiple base stations to improve the UNB performance, by using selection combining. In the presence of pathloss and spectral randomness of UNB, the channels are considered correlated. A theoretical analysis of outage probability is demonstrated by considering this correlation, for the case of 2 base stations. This methodology of probability computing can be extended to $K$ BSs. The diversity of multiple receivers is proved to be beneficial in enhancing the performance of UNB networks. This gain is shown to be related to the density of the base stations, as well as the distance between each of them. In [8], we propose to apply signal combining and interference cancellation technologies across multiple base stations in UNB networks, in order to take advantage of their spatial diversity. We evaluate and compare the performance enhancement of each technology, compared to single BS case. These technologies exploiting multi-BS diversity are proved to be significantly beneficial in improving UNB networks' scalability. We can gain until 28 times better performance with one iteration global SIC. We highlight that these results provide us a choice among the technologies according to the improvement needs and the implementation complexity.

Contributions in other application fields

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 [4], 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. In [29], we develop a general framework for the coexistence problem by drawing an analogy to the cognitive radio problem in wireless communication systems. For the particularly promising underlay strategy, we propose a formalization and outline key consequences.

Another key challenge in nanonetworking is to develop a means of coordinating a large number of nanoscale devices. Devices in molecular communication systems—once information molecules are released— are typically viewed as passive, not reacting chemically with the information molecules. While this is an accurate model in diffusion-limited links, it is not the only scenario. In particular, the dynamics of molecular communication systems are more generally governed by reaction-diffusion, where the reaction dynamics can also dominate. This leads to the notion of reaction-limited molecular communication systems, where the concentration profiles of information molecules and other chemical species depends largely on reaction kinetics. In this regime, the system can be approximated by a chemical reaction network. In [14], we exploit this observation to design new protocols for both point-to-point links with feedback and networks for event detection. In particular, using connections between consensus and advection theory and reaction networks lead to simple characterizations of equilibrium concentrations, which yield simple—but accurate— design rules even for networks with a large number of devices.

Smart Grids

Smart grids is another application field where information theory and signal processing can be useful. During 2018, we addressed security issues. In [41], random attacks that jointly minimize the amount of information acquired by the operator about the state of the grid and the probability of attack detection are presented. The attacks minimize the information acquired by the operator by minimizing the mutual information between the observations and the state variables describing the grid. Simultaneously, the attacker aims to minimize the probability of attack detection by minimizing the Kullback-Leibler (KL) divergence between the distribution when the attack is present and the distribution under normal operation. The resulting cost function is the weighted sum of the mutual information and the KL divergence mentioned above. The trade-off between the probability of attack detection and the reduction of mutual information is governed by the weighting parameter on the KL divergence term in the cost function. The probability of attack detection is evaluated as a function of the weighting parameter. A sufficient condition on the weighting parameter is given for achieving an arbitrarily small probability of attack detection. The attack performance is numerically assessed on the IEEE 30-Bus and 118-Bus test systems.

Privacy and tracking

In a joint work with Privatics team, we presented in [40] the analysis of an Ultrasound-based tracking application. By analyzing several mobile applications along with the network communication and sample of the original audio signal, we were able to reverse engineer the ultrasonic communications and some other elements of the system. Based on those finding we show how arbitrary ultrasonic signal can be generated and how to perform jamming. Finally we analyze a real world deployment and discuss privacy implications.

VLC

In a joint work with Agora, we present in [12] our efforts to design a communication system between an ordinary RGB light emitting diode and a smart-phone. This work in progress presents our preliminary findings obtained investigating this poorly known and unusual channel. We give engineering insights on driving an RGB light emitting diode for camera communication and discuss remaining challenges. Finally, we propose possible solutions to cope with these issues that are blockers for a user ready implementation.

Intelligent Transport

On-demand transport has been disrupted by Uber and other providers, which are challenging the traditional approach adopted by taxi services. Instead of using fixed passenger pricing and driver payments, there is now the possibility of adaptation to changes in demand and supply. Properly designed, this new approach can lead to desirable tradeoffs between passenger prices, individual driver profits and provider revenue. However, pricing and allocations - known as mechanisms - are challenging problems falling in the intersection of economics and computer science. In [3], we develop a general framework to classify mechanisms in on-demand transport. Moreover, we show that data is key to optimizing each mechanism and analyze a dataset provided by a real-world on-demand transport provider. This analysis provides valuable new insights into efficient pricing and allocation in on-demand transport.