Association des Doctorants du campus STIC

´ Seminaires doctorants

6

18 octobre 2006

Actes ´edit´es par l’association des doctorants du campus STIC. Les travaux individuels publi´es restent l’unique propri´et´e de leurs auteurs. La copie et la distribution de ces actes dans leur int´egralit´e, cette notice comprise, sont toutes deux autoris´ees.

Table of Contents

Where Does UML Stand When It Comes to Real-Time Embedded Systems? Fr´ed´eric Mallet

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Tensor Approach for Blind Channel Identification . . . . . . . . . . . . . . . . . . . . . . Carlos Estˆev˜ ao R. Fernandes

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Where Does UML Stand When It Comes to Real-Time Embedded Systems? Fr´ed´eric Mallet Laboratoire I3S, Universit´e de Nice - Sophia Antipolis, France [email protected]

Abstract. Real-time embedded architectures consist of software and hardware parts. Meeting non-functional constraints (e.g. real-time constraints) greatly depends on the mappings from the system functionalities to software and hardware components. Thus, there is a strong demand for precise architecture and allocation modeling, amenable to performance analysis. This talk presents some issues raised when designing complex real-time embedded systems. We elaborate on the lack of a global solution from the system-level all the way down to code generation and synthesis. We advocate that UML2.1 could be used as a “unified” language for annotating high-level models and that model-based engineering should supplant the manual writing of domain-specific compilers. For this to happen, the UML semantics must be refined and a small subset of UML must be extracted to assure consistency amongst models. This action has begun, through the definition of the UML Profile for Modeling and Analysis of Real-Time and Embedded systems (MARTE) [1]. Starting from there, successive semi-automatic model transformations may transform a high-level UML specification, into specific formalisms amenable to performance analysis, code distribution and synthesis [2–4].

References 1. OMG: UML Profile for Modeling and Analysis of Real-Time and Embedded systems (MARTE). (2005) URL http://www.omg.org/docs/realtime/05-02-06.pdf. 2. Simone, R.D., Andr´e, C.: Towards a synchronous reactive UML subprofile? International Journal on Software Tools for Technology Transfer (STTT) 8 (2006) 146–155 3. Apvrille, L., Courtiat, J.P., Lohr, C., de Saqui-Sannes, P.: TURTLE: A real-time UML profile supported by a formal validation toolkit. IEEE Transactions on Software Engineering 30 (2004) 473–487 4. Mallet, F., Andr´e, C., Peraldi, M.A.: From UML to Petri nets for non functional property verification. In: IES’06, IEEE Symposium on Industrial Embedded Systems, IEEE Computer Society (2006)

Tensor Approach for Blind Channel Identification Carlos Estˆev˜ ao R. Fernandes

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Laboratoire I3S, Universit´e de Nice - Sophia Antipolis, France [email protected]

Abstract. In this talk we will introduce a blind channel identification method based on the Parallel Factor (Parafac) analysis of a 3rdorder tensor composed of the 4-th order output cumulants. Using a Parafac-based decomposition, we avoid any kind of pre-processing such as the prewhitening operation, which is mandatory in most methods using higher-order statistics (HOS). Moreover, our method retrieves the channel vector without any permutation or scaling ambiguities and it is extensible to a multiuser system involving multiple output instantaneous channels. An algorithm is proposed based on the decomposition of a 3rd-order tensor. Computer simulations illustrate performance gains with respect to other classical solutions. Initialization and convergence issues will also be addressed.

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Introduction to Blind Channel Identification

Blind channel identification and equalization consist in the retrieval of unknown information about the transmission channel and source signals from the knowledge of the received signal only. For several years, higher-order statistics (HOS) have been an important research topic in diverse fields including data communication, speech and image processing and geophysical data processing. The higherorder spectra have the ability to preserve both magnitude and (nonminimum-) phase information. Moreover, it is well-known that all cumulant spectra of order greater than 2 vanish for Gaussian signals, which makes HOS-based identification methods insensitive to an additive Gaussian noise. Relationships connecting different higher-order cumulant slices and the parameters of a finite impulse response (FIR) model exist and it is well known that larger sets of output cumulants have the ability to improve identification performance [1]. Existing approaches to exploit the sample output cumulants include the joint-diagonalization of cumulant matrices [2]. However, such techniques involve a prewhitening transformation over the cumulant matrices, which is often a source of increased complexity and estimation errors. The factorization of third-order tensors containing sample 4th-order cumulants has the advantage of avoiding the prewhitening operation by fully exploiting the three-dimensional nature of the cumulant tensor. ⋆

Joint work with G´erard Favier and Jo˜ ao Cesar M. Mota.

Tensor Approach for Blind Channel Identification

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Canonical Tensor Decomposition

The Parallel Factor analysis (Parafac) of an m-dimensional tensor with rank F consists in the decomposition of the tensor into a sum of F factors where each factor can be written as the outer product of m vectors [3]. The trilinear Parafac model (m = 3) has become very popular in the fields of Psychometrics and Chemometrics [4, 5] but it also has been widely used in Signal Processing applications [6, 7]. The key-point in the use of the Parafac is about its uniqueness property, which can be assured under simple conditions that are stated in the Kruskal Theorem [8].

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Conclusions and Perspectives

In this talk, we introduce a time-domain Parafac-based approach to recover the parameters of an FIR channel from a three-dimensional tensor of 4th-order cumulants. Our method fully exploits the three-dimensional nature of the cumulant tensor and has the advantage of avoiding any kind of pre-processing. Moreover, our tensor decomposition algorithm is based on a single-step LS procedure instead of the classical three-step alternating least squares (ALS) algorithm. Uniqueness and convergence issues will also be addressed. Computer simulations show that the Parafac-based approach provides better estimation performance than both the (closed-form) total least squares (TLS) solution and the joint-diagonalization based algorithm. Furthermore, the convergence of the PBCI algorithm can be accelerated when it is initialized with the TLS solution.

References 1. Comon, P.: MA identification using fourth order cumulants. Signal Processing 26 (1992) 381–388 2. Belouchrani, A., Derras, B.: An efficient fourth-order system identification FOSI algorithm utilizing the joint diagonalization procedure. In: Proc. of the 10-th IEEE Workshop on Statistical Signal and Array Processing, USA (2000) 621–625 3. Bro, R.: PARAFAC. tutorial and applications. Elsevier Chemometrics and Intelligent Laboratory Systems 38 (1997) 149–171 4. Harshman, R.A.: Foundations of the PARAFAC procedure: Model and conditions for an “explanatory” multi-mode factor analysis. UCLA Working papers in phonetics 16 (1970) 1–84 5. Sidiropoulos, N.D., Bro, R.: On the uniqueness of multilinear decomposition of N-way arrays. Journal of Chemometrics (2000) 229–239 6. Comon, P.: Blind identification and source separation in 2x3 under-determined mixtures. IEEE Trans. on Signal Processing 1 (2004) 11–22 7. Lathauwer, L.D.: Signal Processing Based on Multilinear Algebra. PhD thesis, Katholieke Universiteit Leuven, Belgium (1997) ESAT-SISTA/TR 1997-74. 8. Kruskal, J.B.: Three way arrays: rank and uniqueness of trilinear decompositions with applications to arithmetic complexity and statistics. Linear Algebra and Its Applications 18 (1977) 95–138

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C.E.R. Fernandes

Notes

Les s´ eminaires doctorants Les s´eminaires des doctorants STIC permettent aux futurs docteurs d’´echanger leurs exp´eriences dans leur travail de th`ese, tant sur le plan scientifique que sur le plan professionnel et ´educatif. Ces rencontres ont lieu mensuellement dans l’un des laboratoires STIC de Sophia Antipolis. Un s´eminaire est l’occasion de trois `a quatre interventions, dont une effectu´ee par un jeune permanent. Chaque intervention comporte un expos´e technique d’une vingtaine de minutes et une p´eriode d’´echanges et de retours d’exp´erience d’une dizaine de minutes. Ces actes compilent les r´esum´es en anglais des expos´es techniques du s´eminaire doctorant du 18 octobre 2006.

L’ADSTIC L’ADSTIC est l’association des doctorants du campus sciences et techniques de l’information et de la communication de l’universit´e de Nice Sophia Antipolis. Cr´e´ee en 2004, l’ADSTIC est une association loi 1901. Notre but essentiel est de faciliter les contacts entre les doctorants des diff´erentes disciplines pr´esentes sur le campus STIC, de les informer et de valoriser leur formation doctorale. L’ADSTIC se veut aussi un lien entre les doctorants pass´es, actuels et futurs... Pour plus de renseignements, visitez notre site Internet : http://adstic.free.fr.