Estimation of Sparse MIMO Channels with Common Support

We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.Comment: 12 pages / 7 figures. Submitted to IEEE Transactions on Communicatio

Fast and Robust Parametric Estimation of Jointly Sparse Channels

We consider the joint estimation of multipath channels obtained with a set of receiving antennas and uniformly probed in the frequency domain. This scenario fits most of the modern outdoor communication protocols for mobile access or digital broadcasting among others. Such channels verify a Sparse Common Support property (SCS) which was used in a previous paper to propose a Finite Rate of Innovation (FRI) based sampling and estimation algorithm. In this contribution we improve the robustness and computational complexity aspects of this algorithm. The method is based on projection in Krylov subspaces to improve complexity and a new criterion called the Partial Effective Rank (PER) to estimate the level of sparsity to gain robustness. If P antennas measure a K-multipath channel with N uniformly sampled measurements per channel, the algorithm possesses an O(KPNlogN) complexity and an O(KPN) memory footprint instead of O(PN^3) and O(PN^2) for the direct implementation, making it suitable for K << N. The sparsity is estimated online based on the PER, and the algorithm therefore has a sense of introspection being able to relinquish sparsity if it is lacking. The estimation performances are tested on field measurements with synthetic AWGN, and the proposed algorithm outperforms non-sparse reconstruction in the medium to low SNR range (< 0dB), increasing the rate of successful symbol decodings by 1/10th in average, and 1/3rd in the best case. The experiments also show that the algorithm does not perform worse than a non-sparse estimation algorithm in non-sparse operating conditions, since it may fall-back to it if the PER criterion does not detect a sufficient level of sparsity. The algorithm is also tested against a method assuming a "discrete" sparsity model as in Compressed Sensing (CS). The conducted test indicates a trade-off between speed and accuracy.Comment: 11 pages, 9 figures, submitted to IEEE JETCAS special issue on Compressed Sensing, Sep. 201

EQUALIZATION BY THE PULSE SHAPE INVERSE OF THE INPUT TO THE FRI PROCESSING IN PULSE BASED COMMUNICATIONS

Certain aspects of the present disclosure relate to a method for equalizing a pulse signal corrupted by a noise and by various channel effects for obtaining a signal based on the periodic-sinc pulse, which is suitable for Finite Rate of Innovation (FRI) processing applied at a receiver of a pulse-based communication system (e.g., an Ultra-Wideband receiver)

Finite Rate of Innovation sampling techniques for embedded UWB devices.

This report studies the applicability of Finite Rate of Innovation (FRI) algorithms to UltraWide Band (UWB) communications, more precisely in the scope of Low Power Body Area Networks (LP-BAN ). Three main issues are studied and given proposed solutions. First, the classical FRI algorithm is modified to accomodate different symmetrical pulse shapes. Such a modification – necessary to get acceptable performances – is done by a simple equalization. Second, LP-BAN devices limitations such as drift, jitter and aggressive quantization are blended in the algorithm. It is done by adjusting the equalization template and development of a suited quantization algorithm. Third and last, the cost of FRI denoising procedure (Cadzow denoising) is greatly reduced to fit the requirements of a low power embedded device. It is centered on performing most of the computations in a low-dimension Krylov subspace of the matrix to be denoised. The particular structure of the projected matrix enables selective computation of the eigenpairs. The result is an algorithm able to resolve close paths within a reasonnable computational budget. Some issues remain on quantization

Couleur, matériau et lumière : la pensée chromatique dans l’Égypte ancienne

Afin d’étudier une civilisation qui attachait autant d’importance à la couleur que l’Égypte pharaonique, la compréhension de l’idée que les Anciens en avaient conçue apparaît déterminante. On s’aperçoit ainsi qu’ils prenaient non seulement en compte l’aspect visuel des couleurs, nous dirions leur longueur d’ondes dans le spectre visible, mais aussi la texture et surtout l’éclat des matériaux envisagés, sans distinction particulière entre apparence et nature desdits matériaux.Ils avaient, en outre, établi l’équivalence des couleurs et de la lumière solaire par le biais d’un cheminement intellectuel, non pas scientifique au sens moderne du terme mais hiéroglyphique, ce qui éclaire plusieurs choix iconographiques en décalage par rapport à la nature, et explique l’emploi précis de vernis brillants pour rehausser certains motifs.To study a civilization that attached as much importance to colour as Pharaonic Egypt, understanding the idea that the Ancients had conceived of it seems crucial. One thus realizes that they not only took into account the visual aspect of colours, i.e. their wavelength in the visible spectrum, but also the texture and, above all, the brilliance of the materials envisaged, without making any special distinction between the appearance and the nature of the said materials. They had also established the equivalence between colours and sunlight through a line of thought that was hieroglyphic rather than scientific in the modern sense of the term, which sheds light on several iconographic choices inconsistent with nature and explains the precise use of shiny varnishes to highlight certain motifs

FASTER CADZOW DENOISING BASED ON PARTIAL EIGENVALUE DECOMPOSITION

Certain aspects of the present disclosure relate to a method for speeding up the Cadzow iterative denoising algorithm as a part of the Finite Rate of Innovation (FRI) processing and for decreasing its computational complexity

Are Callirhytid erythrostoma (Dettmer, 1933) and C. erythrosoma (Dettmer, 1933) synonyms of Callirhytis erythrocephala (Giraud, 1859) or different species? (Hymenoptera: Cynipidae: Cynipini)

Un nou cicle heteroècic de cinípid ha estat tancat experimentalment: Callirhytis erythrocephala (Giraud, 1859) (Hymenoptera, Cynipidae: Cynipini). Callirhytis hartigi Förster, 1869 és una syn. nov. de C. erythrocephala. Es descriu per primera vegada la gala de la forma sexuada de C. erythrocephala. Es redescriuen les femelles sexuades i els mascles de C. erythrocephala, i es destaquen les característiques que permeten diferenciar aquesta forma sexuada d'altres ja conegudes en el gènere Callirhytis. Es discuteix la possibilitat de què Callirhytis erythrosoma i C. erythrocephala siguin espècies diferents en lloc d'espècies sinònimes.A new heteroecious life-cycle of an oak cynipid gallwasp Callirhytis erythrocephala (Giraud, 1859) (Hymenoptera, Cynipidae: Cynipini) has been closed experimentally. Callirhytis hartigi Förster, 1869 is a syn. nov. of C. erythrocephala. The sexual galls induced by C. erythrocephala are described for the first time. The sexual female and male of C. erythrocephala are re-described, and morphological characters of adults for the differentiation of the sexual form from other sexual forms of Callirhytis species are also given. It is questionable whether Callirhytis erythrosoma is synonymous with C. erythrocephala or represents a distinct species.Un nuevo ciclo heteroécico de cinípido ha sido cerrado experimentalmente: Callirhytis erythrocephala (Giraud, 1859) (Hymenoptera, Cynipidae: Cynipini). Callirhytis hartigi Förster, 1869 es una syn. nov. de C. erythrocephala. Se describe por primera vez la agalla de la forma sexuada de C. erythrocephala. Se redescriben las hembras sexuades y los machos de C. erythrocephala, y se destacan las características que permiten diferenciar esta forma sexuada de otras ya conocidas en el género Callirhytis. Se discute la posibilidad de que Callirhytis erythrosoma y C. erythrocephala sean especies diferentes en lugar de especies sinónimas

FINITE RATE OF INNOVATION (FRI) TECHNIQUES FOR LOW POWER BODY AREA NETWORK

Certain aspects of the present disclosure relate to a method for quantizing an analog received signal in a low-power body area network (LP-BAN) by using a limited number of quantization bits, while information of the received signal is preserved for accurate signal reconstruction. The quantized signal can be equalized in such a way to generate an output equalized signal based on the periodic-sine function, which is suitable for a subsequent Finite Rate of Innovation (FRI) processing. The noisy equalized signal can be further processed by applying improved (i.e., faster) Cadzow denoising algorithm as a part of the FRI processing