Résumé :
Using Double Contractions to Derive the Tensor Structure of Slice-wise Multiplications of Tensors with Applications to PARAFAC2 and MIMO OFDM
The slice-wise multiplication of two tensors is required in a variety of tensor decompositions(including PARAFAC2   and   PARATUCK2)   and is   encountered   in   many   applications, including the analysis of multidimensional biomedical data (EEG, MEG, etc.) or multi-carrier MIMO  systems.  In  this  talk,  we  propose  a  new  tensor  representation  that  is  not  based  on  a  slice-wise (matrix) description, but can be represented by a double contraction of two tensors. Such  a  double  contraction  of  two  tensors  can  be  efficiently  calculated  via  generalized  unfoldings. It leads to new tensor models of the investigated system that do not depend on the chosen  unfolding  and reveal  the  tensor  structure  of  the  data  model  (such  that  all  possible  unfoldings  can  be  seen  at  the  same  time).  As  an  example,  we  express  the  PARAFAC2  decomposition  in  terms  of  this  new  explicit tensor description (constrained  CP  model)  utilizing  the  double contraction  operator.  Moreover,  we  show  that  this  explicit  tensor description opens several efficient ways to compute the PARAFAC2 decomposition.Furthermore,  we  apply  this  new  concept  to the  design  of  new  receivers  for  multi-carrier MIMO  systems  in  wireless  communications.  In  particular,  we  consider  MIMO  OFDM  systems  with  and  without  Khatri-Rao  coding.  The  proposed  receivers  exploit  the  channel  correlation  between  adjacent  subcarriers,  require  the  same  amount  of  training  symbols  as traditional OFDM techniques, but have an improved performance in terms of the symbol error rate.  The  tensor  structure  can  also  be  exploited  via  more  iterations  to  decrease  the  symbol  error rate even further.

Biographie :

Martin  Haardt  has  been  a  Full  Professor  in  the  Department  of  Electrical  Engineering  and  Information  Technology  and  Head  of  the  Communications  Research  Laboratory  at  Ilmenau  University  of  Technology,  Germany,  since  2001.  From  2012 to  2017,  he  also  served  as  an  Honorary Visiting Professor in the Department of Electronics at the University of York, UK.After studying electrical engineering at the Ruhr-University Bochum, Germany, and at Purdue University,  USA,  he  received  his  Diplom-Ingenieur  (M.S.)  degree  from  the  Ruhr-University Bochum  in  1991  and  his  Doktor-Ingenieur  (Ph.D.)  degree  from  Munich  University  of  Technology in 1996. In  1997  he  joint  Siemens  Mobile  Networks  in  Munich,  Germany,  where  he  was  responsible  for  strategic  research  for  third  generation  mobile  radio  systems.  From  1998  to  2001  he  was  the   Director   for   International   Projects   and   University   Cooperations   in   the   mobile   infrastructure   business   of   Siemens   in   Munich,   where   his   work   focused   on   mobile   communications  beyond  the  third  generation.  During  his  time  at  Siemens,  he  also  taught  in  the  international  Master  of  Science  in  Communications  Engineering  program  at  Munich  University of Technology. In  2018,  Martin  Haardt  has been  named  an  IEEE  Fellow  “for  contributions  to  multi-user MIMO  communications  and  tensor-based  signal  processing.” He has received  the  2009  Best  Paper Award from the IEEE Signal Processing Society, the Vodafone (formerly Mannesmann Mobilfunk)  Innovations-Award  for  outstanding  research  in  mobile  communications,  the  ITG  best paper award from the Association of Electrical Engineering, Electronics, and Information Technology (VDE), and the Rohde & Schwarz Outstanding Dissertation Award. In the fall of 2006  and  the  fall  of  2007  he  was  a  visiting  professor  at  the  University  of  Nice  in  Sophia-Antipolis,  France,  and  at  the  University  of  York,  UK,  respectively.  His  research  interests  include   wireless   communications,   array   signal   processing,   high-resolution   parameter   estimation, as well as numerical linear and multi-linear algebra. Prof.  Haardt  has  served  as  an  Associate  Editor  for  the  IEEE  Transactions  on  Signal  Processing (2002-2006 and 2011-2015), the IEEE Signal Processing Letters (2006-2010), the Research  Letters  in  Signal  Processing  (2007-2009),  the  Hindawi  Journal  of  Electrical  and  Computer Engineering (since 2009), the EURASIP Signal Processing Journal (2011-2014), as a  senior  editor  of  the  IEEE  Journal  of  Selected  Topics  in  Signal  Processing  (JSTSP,  since  2019), and  as  a  guest  editor  for  the  EURASIP  Journal  on  Wireless  Communications  and  Networking as well as the IEEE JSTSP. Since  2011  he  has  been  an  elected  member  of  the  Sensor  Array  and  Multichannel  (SAM)  technical  committee  of  the  IEEE  Signal  Processing  Society,  where  he  served  as  the  Vice Chair (2015 – 2016), Chair (2017 – 2018), and Past Chair (2019).
Moreover, he has served as the  technical  co-chair  of  PIMRC  2005  in  Berlin,  Germany,  ISWCS  2010  in  York,  UK,  the  European Wireless 2014 in Barcelona, Spain, as well as the Asilomar Conference on Signals, Systems,  and  Computers  2018,  USA,  and  as  the  general  co-chair  of  WSA  2013 in  Stuttgart,  Germany,  ISWCS  2013  in  Ilmenau,  Germany,  CAMSAP  2013  in  Saint  Martin,  French  Antilles,  WSA  2015  in  Ilmenau,  SAM  2016  in  Rio  de  Janeiro,  Brazil,  CAMSAP  2017  in  Curacao, Dutch Antilles, and SAM 2020 in Hangzhou, China.