Photo

Mohamed Kadhem Karray's Homepage

Doctor in mathematical modelisation at Orange Labs
44 avenue de la République
92320 Châtillon, France

Email: mohamed.karray (at) orange (dot) com
Tél: 33 6 85549735

Further websites

Youtube channel, LinkedIn

Data science: Video lectures

Video lectures on mathematical foundations of machine and deep learning available on my Youtube channel:

    Multivariate statistics

    -    Lecture I : Basic statistics (pdf)

    Machine and deep learning

    -    Lecture 0 : Python softwares (pdf and code examples)
    -    Lecture I : Machine learning frameworks (pdf)
    -    Lecture II: Vapnik-Chervonenkis theory (pdf)
    -    Lecture III: Results from empirical processes theory (pdf)
    -    Lecture IV: Learnability characterization (pdf)
    -    Lecture V: Examples of learning problems (pdf)
    -    Lecture VI: Neural networks (pdf)
    -    Lecture VII: Approximation theory in neural networks (pdf)

Books 

  1. F. Baccelli, B. Błaszczyszyn, M.K. Karray (2020). Random measures, point processes and stochastic geometry. [ HAL ]
  2. B. Błaszczyszyn, M.K. Karray (2023). Data science : From multivariate statistics to machine, deep learning. Book in preparation.
  3. B. Błaszczyszyn, M.K. Karray (2023). Information theory. Book in preparation.

Journal Papers 

  1. B. Błaszczyszyn, M.K. Karray (2019). Performance analysis of cellular networks with opportunistic scheduling using queueing theory, stochastic geometry. IEEE Transactions on Wireless Communications, December 2019,  vol. 18, no. 12. [ HAL | IEEE Xplore ]
  2. B. Blaszczyszyn,  R. Ibrahim, M.K. Karray (2016). Spatial disparity of QoS metrics between base stations in wireless cellular networks. IEEE Transactions on Communications, August 2016, vol. 64, no. 10. [ HAL | IEEE Xplore ]
  3. B. Blaszczyszyn, M.K. Karray (2016). Spatial distribution of the SINR in Poisson cellular networks with sector antennas. IEEE Transactions on Wireless Communications, January 2016, vol. 15, no. 1. [ HAL | IEEE Xplore ]
  4. M.K. Karray, M. Jovanovic, B. Blaszczyszyn (2015) Theoretical expression of link performance in OFDM cellular networks with MIMO compared to simulation, measurements, in Annals of telecommunications (Springer), December 2015, vol. 70, no. 11, pp 479-490. [ Springer ]
  5. B. Blaszczyszyn, M.K. Karray, H.P. Keeler (2015) Wireless networks appear Poissonian due to strong shadowing, in IEEE Transactions on Wireless Communications, April 2015, vol. 14, no. 8, pp 4379-4390. [ IEEE Xplore ] 
  6. B. Blaszczyszyn, M. Jovanovic, M.K. Karray (2014) Quality of real-time streaming in wireless cellular networks: Stochastic modeling, analysis, in IEEE Transactions on Wireless Communications, June 2014, vol. 13, no. 6. [ pdf | bib ]
  7. S. El Ayoubi, S. Jeux, M.K. Karray, Y. Khan (2013)  A novel hybrid simulation methodology for capacity estimation in mobile networks, in Physical Communication, Elsevier. [ pdf | bib ]
  8. M. Jovanovic, M.K. Karray (2013)  A queueing theoretic approach to the dimensioning of wireless cellular networks serving variable bit-rate calls, in IEEE Transactions on Vehicular Technology, July 2013, vol. 62, no. 6. [ pdf | bib ]
  9. B. Blaszczyszyn, M.K. Karray (2013)  Quality of service in wireless cellular networks subject to log-Normal shadowing, IEEE Transactions on Communications, February 2013, vol. 61, no. 2. [ pdf | bib ]
  10. B. Blaszczyszyn, M.K. Karray (2012) Effect of opportunistic scheduling on the quality of service perceived by the users in OFDMA cellular networks, in Annals of telecommunications (Springer), April 2012, vol. 67, no. 3. [ pdf | bib ]
  11. M.K. Karray (2010) User's mobility effect on the performance of wireless cellular networks serving elastic traffic, in Wireless Networks (Springer). [ pdf | bib ]
  12. M.K. Karray (2010) Analytical expressions for blocking, dropping probabilities for mobile streaming users in wireless cellular networks, in Wireless Networks (Springer), November 2010, vol. 16, no. 8. [ pdf | bib ]
  13. M.K. Karray (2010) Analytical evaluation of QoS in the downlink of OFDMA wireless cellular networks serving streaming, elastic traffic, in IEEE Transactions on Wireless Communications, May 2010, vol. 9, no. 5. [ pdf | bib ] 
  14. F. Baccelli, B. Blaszczyszyn, M.K. Karray (2004) Up, downlink admission/congestion control, maximal load in large homogeneous CDMA networks, in Mobiles Networks, Applications (MONET), vol. 9, no. 6. [ pdf | bib ]

Conference papers 

  1. B. Blaszczyszyn, M.K. Karray (2015) What frequency bandwidth to run cellular network in a given country? - a downlink dimensioning problem, in Proc. of WiOpt/SpaSWiN 2015. [ HAL | IEEE Xplore ]
  2. B. Blaszczyszyn, M. Jovanovic, M.K. Karray (2015) Performance laws of large heterogeneous cellular networks, in Proc. of WiOpt/SpaSWiN 2015. [ HAL | IEEE Xplore ]
  3. M. Jovanovic, M.K. Karray, B. Blaszczyszyn (2014) QoS, network performance estimation in heterogeneous cellular networks validated by real-field measurements, in Proc. of PM2HW2N, Montreal, Canada. [ pdf | bib | Slides ]
  4. B. Blaszczyszyn, M. Jovanovic, M.K. Karray (2014) How user throughput depends on the traffic demand in large cellular networks. in Proc. of WiOpt/SpaSWiN, Hammamet, Tunisia. [ pdf | bib | Slides ]
  5. H. P. Keeler, B. Blaszczyszyn, M.K. Karray (2013) SINR-based k-coverage probability in cellular networks with arbitrary shadowing. in Proc. of IEEE ISIT, Istanbul, Turkey.  [ pdf | bib ]
  6. B. Blaszczyszyn, M.K. Karray, H.P. Keeler (2013) Using Poisson processes to model lattice cellular networks, in Proc. of IEEE Infocom, Turin, Italy. [ pdf | bib ]
  7. M.K. Karray , M. Jovanovic (2012) Theoretically feasible QoS in a MIMO cellular network compared to the practical LTE performance, in Proc. of International Conference on Wireless, Mobile Communications (ICWMC), Venice, Italy.  [ pdf | bib | Slides ]
  8. B. Blaszczyszyn, M.K. Karray (2012) Linear-regression estimation of the propagation-loss parameters using mobiles' measurements in wireless cellular networks, in Proc. of WiOpt, Germany. [ pdf | bib ]
  9. M.K. Karray, Y. Khan (2012) Evaluation, comparison of resource allocation strategies for new streaming services in wireless cellular networks, in Proc. of International Conference on Communications, Networking (ComNet), Hammamet, Tunisia. [ pdf | bib ]
  10. M.K. Karray (2010) Spectral, energy efficiencies of OFDMA wireless cellular networks, in Proc. of IFIP Wireless Days, Venice, Italy. Best paper award. [ pdf | bib | Slides ]
  11. M.K. Karray (2010) Evaluation of the blocking probability, the throughput in the uplink of wireless cellular networks, in Proc. of International Conference on Communications, Networking (ComNet), Tozeur, Tunisia. [ pdf | bib | Slides ]
  12. B. Blaszczyszyn, M.K. Karray, F-X. Klepper (2010) Impact of the geometry, path-loss exponent, random shadowing on the mean interference factor in wireless cellular networks, in Proc. of IFIP Wireless, Mobile Networking Conference (WMNC), Budapest, Hungary. Best paper award. [ pdf | bib ]
  13. M.K. Karray (2010) Electromagnetic exposure, quality of service in the downlink of wireless cellular networks, in Proc. of International Conference on Wireless, Mobile Communications (ICWMC), Valence, Spain. [ pdf | bib | Slides ]
  14. M.K. Karray (2009) Study of a key factor for performance evaluation of wireless cellular networks: The f-factor, in Proc. of IFIP Wireless Days, Paris, France. [ pdf | bib ]
  15. B. Blaszczyszyn, M.K. Karray (2009) Fading effect on the dynamic performance evaluation of OFDMA cellular networks, in Proc. of International Conference on Communications, Networking (ComNet), Hammamet, Tunisia. Best paper award. [ pdf | bib ]
  16. B. Blaszczyszyn, M.K. Karray (2009) Dimensioning of the downlink in OFDMA cellular networks via an Erlang's loss model, in Proc. of European Wireless Conference, Aalborg, Denmark. [ pdf | bib ]
  17. B. Blaszczyszyn, M.K. Karray (2008) An efficient analytical method for dimensioning of CDMA cellular networks serving streaming calls, in Proc. of ValueTools Conference, Athens, Greece. [ pdf | bib ]
  18. B. Blaszczyszyn, M.K. Karray (2008) Impact of mean user speed on blocking, cuts of streaming traffic in cellular networks, in Proc. of European Wireless Conference, Praha, Czech Republic. [ pdf | bib ]
  19. B. Blaszczyszyn, M.K. Karray (2007) Performance evaluation of scalable congestion control schemes for elastic traffic in cellular networks with power control, in Proc. of IEEE Infocom, Anchorage, Alaska, USA. [ pdf | bib  ]
  20. F. Baccelli, B. Blaszczyszyn, M.K. Karray (2005) Blocking rates in large CDMA networks via a spatial Erlang formula, in Proc. of IEEE Infocom, Miami, USA. [ pdf | bib ]

Thesis

Analytic evaluation of wireless cellular networks performance by a spatial Markov process accounting for their geometry, dynamics, control schemes, 10 Septembre 2007, ENST, Paris under the guidance of Eric Moulines, Bartek Blaszczyszyn. [ pdf | bib ]

Teaching

Teaching assistant at Math Spé M' (Louis Le Grand) (1990-1992).
Teaching assistant at Ecole Centrale Paris for the courses by Claude Lamoureux : 'Applied Mathematics' (1992-1996).
Teaching assistant at Ecole Normale Supérieure  (ULM, Paris) for the courses by Pierre Brémaud,  François Baccelli and Bartłomiej Blaszczyszyn :
  1. 'Information, coding theories: Source, channel coding, Shannon theorems' (2016-2023)
  2. 'Random algorithms, structures: Random graphs, Monte Carlo simulation' (2008-2009)
  3. 'Mathematical principles of signal processing' (2007-2008)
  4. 'Markov processes, Queueing theory' (2006-2007)
  5.  'Probability, stochastic processes' (2005-2006)
Teaching at Ecole Polyetechnique, Telecom ParisTech with Bartłomiej Blaszczyszyn and Laurent Decreusefond:

Patents

  1. F. Baccelli, B. Blaszczyszyn, M.K. Karray (2003) Contrôle de charge dans le sens montant pour les systèmes de communication sans fil avec contrôle de puissance, April 2003, FR03 05355. 
  2. F. Baccelli, B. Blaszczyszyn, M.K. Karray (2003) Dispositif et procédé de contrôle de charge avec contrôle de puissance, April 2003, FR03 05354. 

Invited presentations

  1. B. Blaszczyszyn, R.Ibrahim, M.K. Karray, (2016) Predicting explicitly the QoS in mobile cellular networks by leveraging stochastic geomety, queueing theory, European Conference on Queueing Theory, Toulouse, France.
  2. B. Blaszczyszyn, M.K. Karray, (2015) How performance metrics depend on the traffic demand in large cellular networks, Simons Conference on Networks, Stochastic Geometry, University of Texas at Austin. [ Slides ]
  3. B. Blaszczyszyn, M. Jovanovic, M.K. Karray, (2014) Quality of real-time streaming in wireless cellular networks: Stochastic modeling, analysis, Keynote Speaker at WiOpt/WiVid conference, Hammamet, Tunisia. [ Slides ] 
  4. M.K Karray (2014) Stochastic modeling, analysis of wireless cellular networks, Keynote Speaker at WiOpt/SpaSWiN conference, Hammamet, Tunisia. [ Slides ] 
  5. B. Blaszczyszyn, M.K. Karray (2011) Wireless cellular networks with shadowing, GDR ISIS, Paris, France.
  6. M.K Karray (2010) Global performance evaluation of wireless cellular networks : user's QoS, dimensioning, optimisation, Keynote Speaker at ComNet conference, Tozeur, Tunisia. [ bib | Slides ] 
  7. B. Blaszczyszyn, M.K. Karray (2010) Fading effect on the dynamic performance evaluation of OFDMA cellular networks, INRIA/TREC, radio flexible chair (Supélec), Paris, France.

Thesis direction

  1. L. Darlavoix, (2023-2026) Machine learning for QoS evaluation and dimensioning of wireless cellular networks. Co-directed with B. Blaszczyszyn.
  2. M. Jovanovic, (2012-2015) Evaluation, optimization of the quality perceived by mobile users for new services in cellular networks. Here is the thesis report. Co-directed with B. Blaszczyszyn.

Short Biography

I received my diploma in engineering from Ecole Polytechnique (Paris, France), Ecole Nationale Supérieure des Télécommunications (Paris, France) in 1991, 1993, respectively.
In 1993 I joined France Telecom R&D (Orange Labs) in Issy-les-Moulineaux, France.
My research activities aim to evaluate the performance of communication networks. My principle tools are probability, stochastic processes, more specifically information, queueing theories, stochastic geometry, as well as machine and deep learning. In my research work I show how to articulate the tools of these theories to build global analytical performance evaluation methods for wireless cellular networks which are validated by measurements in real networks. These methods are used by Orange Operator for dimensionning its networks, for several practical studies of performance evaluation of these networks.
I also teached at Ecole Normale Supérieure,  Ecole Polyetechnique, Ecole Centrale Paris, and prepared several mathematical books (see corresponding section above). Recently, I prepared video lectures on mathematical foundations of machine and deep learning available on my Youtube channel.