Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Inférence de cliques pour la résolution de Max-CSP

Peu de travaux sur les problèmes CSP, Max-CSP et CSP valués ont été réalisés dans le domaine de l'Optimisation Combinatoire alors que ce domaine ren- ferme de nombreux outils algorithmiques qui peuvent servir à la résolution de ces problèmes. Dans ce papier, nous décrivons une technique d'inférence d'ensembles de cliques à partir du Max-CSP que nous exploitons pour dénir une nouvelle modélisation en Programma- tion Linéaire (PL) du Max-CSP. Nous montrons que les estimations classiques du nombre minimum de con- traintes violées (bornes inférieures) basées sur la consis- tance d'arc telles que DAC[13], RDAC[8] et WAC[1] peu- vent être traduites par des relaxations duales Lagrangien- nes du PL. Nous tirons aussi prot de cette modélisation pour développer de nouvelles bornes inférieures. Dans un premier temps, an d'avoir une idée sur la qualité des bornes inférieures obtenues à partir du PL, nous avons évalué la valeur de la relaxation continue du PL à l'aide du solveur CPLEX, puis nous avons développé une méth- ode du type Branch and Bound intégrant une relaxation Lagrangienne du PL. Les résultats obtenus sont très en- courageants et ouvrent de nouvelles perspectives à ex- ploiter au mieux les outils de la programmation linéaire pour contribuer à la résolution de ces problèmes

A Decomposition Technique for Solving {Max-CSP}

International audienceThe objective of the Maximal Constraint Satisfaction Problem (Max-CSP) is to find an instantiation which minimizes the number of constraint violations in a constraint network. In this paper, inspired from the concept of inferred disjunctive constraints intro- duced by Freuder and Hubbe, we show that it is possible to exploit the arc-inconsistency counts, associated with each value of a net- work, in order to avoid exploring useless portions of the search space. The principle is to reason from the distance between the two best values in the domain of a variable, according to such counts. From this reasoning, we can build a decomposition technique which can be used throughout search in order to decompose the current prob- lem into easier sub-problems. Interestingly, this approach does not depend on the structure of the constraint graph, as it is usually pro- posed. Alternatively, we can dynamically post hard constraints that can be used locally to prune the search space. The practical interest of our approach is illustrated, using this alternative, with an experi- mentation based on a classical branch and bound algorithm, namely PFC-MRDAC

The complexity of general-valued CSPs seen from the other side

The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias, Bulatov, and Dalmau [ICALP'07] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithms (unconditionally) as bounded treewidth modulo homomorphic equivalence. The general-valued constraint satisfaction problem (VCSP) is a generalisation of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the $k$-th level of the Sherali-Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognising the tractable cases; the latter has an application in database theory.Comment: v2: Full version of a FOCS'18 paper; improved presentation and small correction

Opportunistic Angle of Arrival Estimation in Impaired Scenarios

This work if focused on the analysis and the development of Angle of Arrival (AoA) radio localization methods. The radio positioning system considered is constituted by a radio source and by a receiving array of antennas. The positioning algorithms treated in this work are designed to have a passive and opportunistic approach. The opportunistic attribute implies that the radio localization algorithms are designed to provide the AoA estimation with nearly-zero information on the transmitted signals. No training sequences or waveforms custom designed for localization are taken into account. The localization is termed passive since there is no collaboration between the transmitter and the receiver during the localization process. Then, the algorithms treated in this work are designed to eavesdrop already existing communication signals and to locate their radio source with nearly-zero knowledge of the signal and without the collaboration of the transmitting node. First of all, AoA radio localization algorithms can be classified in terms of involved signals (narrowband or broadband), antenna array pattern (L-shaped, circular, etc.), signal structure (sinusoidal, training sequences, etc.), Differential Time of Arrival (D-ToA) / Differential Phase of Arrival (D-PoA) and collaborative/non collaborative. Than, the most detrimental effects for radio communications are treated: the multipath (MP) channels and the impaired hardware. A geometric model for the MP is analysed and implemented to test the robustness of the proposed methods. The effects of MP on the received signals statistics from the AoA estimation point-of-view are discussed. The hardware impairments for the most common components are introduced and their effects in the AoA estimation process are analysed. Two novel algorithms that exploits the AoA from signal snapshots acquired sequentially with a time division approach are presented. The acquired signals are QAM waveforms eavesdropped from a pre-existing communication. The proposed methods, namely Constellation Statistical Pattern IDentification and Overlap (CSP-IDO) and Bidimensional CSP-IDO (BCID), exploit the probability density function (pdf) of the received signals to obtain the D-PoA. Both CSP-IDO and BCID use the statistical pattern of received signals exploiting the transmitter statistical signature. Since the presence of hardware impairments modify the statistical pattern of the received signals, CSP-IDO and BCID are able to exploit it to improve the performance with respect to (w.r.t.) the ideal case. Since the proposed methods can be used with a switched antenna architecture they are implementable with a reduced hardware contrariwise to synchronous methods like MUltiple SIgnal Classification (MUSIC) that are not applicable. Then, two iterative AoA estimation algorithms for the dynamic tracking of moving radio sources are implemented. Statistical methods, namely PF, are used to implement the iterative tracking of the AoA from D-PoA measures in two different scenarios: automotive and Unmanned Aerial Vehicle (UAV). The AoA tracking of an electric car signalling with a IEEE 802.11p-like standard is implemented using a test-bed and real measures elaborated with a the proposed Particle Swarm Adaptive Scattering (PSAS) algorithm. The tracking of a UAV moving in the 3D space is investigated emulating the UAV trajectory using the proposed Confined Area Random Aerial Trajectory Emulator (CARATE) algorithm

Partial lazy forward checking

Partial forward checking (PFC) may perform more consistency checks than really needed to detect dead-ends in MAX-CSP. After analyzing PFC, we have identified four causes of redundant check computation: (a) unnecessary lookahead when detecting an empty domain, (b) not always using the better bounds for future value pruning, (c) computing in advance inconsistency counts, and (d) lookahead is performed on the whole set of future variables. We present the partial lazy forward checking (PLFC) algorithm, which follows a lazy approach delaying as much as possible inconsistency count computation, keeping updated the contribution of future variables to the lower bound. This algorithm avoids the causes of redundant checks identified for PFC. It can be easily combined with DACs, producing the PLFC-DAC algorithm. Empirical results on random problems show that PLFC-DAC outperforms previous algorithms in both consistency checks and CPU time.Postprint (published version