CentraleSupélec

About: CentraleSupélec is a based out in . It is known for research contribution in the topics: MIMO & Wireless network. The organization has 1330 authors who have published 2344 publications receiving 30533 citations. The organization is also known as: CentraleSupelec & CentraleSupelec of the Paris-Saclay University.

On Lazy Training in Differentiable Programming

Abstract: In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero training loss, with their parameters hardly varying. In this work, we show that this "lazy training" phenomenon is not specific to over-parameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding a model equivalent to learning with positive-definite kernels. Through a theoretical analysis, we exhibit various situations where this phenomenon arises in non-convex optimization and we provide bounds on the distance between the lazy and linearized optimization paths. Our numerical experiments bring a critical note, as we observe that the performance of commonly used non-linear deep convolutional neural networks in computer vision degrades when trained in the lazy regime. This makes it unlikely that "lazy training" is behind the many successes of neural networks in difficult high dimensional tasks.

Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design

Abstract: Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on co-located or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas $N$ . Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today's conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phase-drifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with $N$ while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as $\sqrt{N} $ , instead of linearly, by careful circuit-aware system design.

Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?

Abstract: Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas $M$ than scheduled users $K$ because the users’ channels are likely to be near-orthogonal when $M/K > 10$ . However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users $K^\star$ depends on $M$ and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of $K^\star$ in the large- $M$ regime is derived in closed form, while simulations are used to show what happens at finite $M$ , in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal $M/K$ is less than 10 in many cases of practical relevance. Interestingly, $K^\star$ depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same $K$ .

Asymptotic Max-Min SINR Analysis of Reconfigurable Intelligent Surface Assisted MISO Systems

Abstract: This work focuses on the downlink of a single-cell multi-user system in which a base station (BS) equipped with $M$ antennas communicates with $K$ single-antenna users through a reconfigurable intelligent surface (RIS) installed in the line-of-sight (LoS) of the BS. RIS is envisioned to offer unprecedented spectral efficiency gains by utilizing $N$ passive reflecting elements that induce phase shifts on the impinging electromagnetic waves to smartly reconfigure the signal propagation environment. We study the minimum signal-to-interference-plus-noise ratio (SINR) achieved by the optimal linear precoder (OLP), that maximizes the minimum SINR subject to a given power constraint for any given RIS phase matrix, for the cases where the LoS channel matrix between the BS and the RIS is of rank-one and of full-rank. In the former scenario, the minimum SINR achieved by the RIS-assisted link is bounded by a quantity that goes to zero with $K$ . For the high-rank scenario, we develop accurate deterministic approximations for the parameters of the asymptotically OLP, which are then utilized to optimize the RIS phase matrix. Simulation results show that RISs can outperform half-duplex relays with a small number of passive reflecting elements while large RISs are needed to outperform full-duplex relays.

Dynamics of Swirling Flames

Abstract: In many continuous combustion processes, such as those found in aeroengines or gas turbines, the flame is stabilized by a swirling flow formed by aerodynamic swirlers. The dynamics of such swirling flames is of technical and fundamental interest. This article reviews progress in this field and begins with a discussion of the swirl number, a parameter that plays a central role in the definition of the flow structure and its response to incoming disturbances. Interaction between the swirler response and incoming acoustic perturbations generates a vorticity wave convected by the flow, which is accompanied by azimuthal velocity fluctuations. Axial and azimuthal velocities in turn define the flame response in terms of heat--release rate fluctuations. The nonlinear response of swirling flames to incoming disturbances is conveniently represented with a flame describing function (FDF), in other words, with a family of transfer functions depending on frequency and incident axial velocity amplitudes. The FDF, howev...