Graduate School and Research Center in Digital Sciences

Digital communications

T Technical Teaching


  • This course covers the fundamentals for the analysis and design of physical layer digital communication systems.
  • It serves as the basic building block for understanding modern mathematical procedures that enable communication via different physical media (e.g. radio, twisted-pair wireline, coaxial cable, fiber-optical).
  • Both the deterministic and random characterizations of common transmit signal and noise processes are covered as well as optimal receivers and their performance using different digital signalling methods.




  •  Deterministic Signals : Continuous and discrete-time signals, signal spaces, orthonormal expansions, non-linear characterizations, bandpass and complex baseband equivalent signals, sampling and reconstruction, Nyquist's criterion for zero intersymbol-interference.
  • Digital Modulation : Linear modulation, finite-state machines and trellis representations, constellations, OFDM, spread-spectrum, constant-envelope modulation.
  • Probability and Random Processes : Review of basic probability and random variables, complex random variables and circular symmetry, Gaussian random variables and the Qfunction, moment generating functions, quadratic forms and the Karhunen- Loève expansion, random processes, ergodicity, power-spectral density, linear transformation of random processes, KL-expansion of random processes, system aspects of noise processes, statistical characterization of digitally-modulated signals.
  • Detection theory and Receiver Design : Bayesian detection theory, detection of known signals in Gaussian noise, matched filters, error probabilities, non-coherent detection.
  • Sequence Detection and Equalization Maximum-likelihood detection of linear modulation over channels with finite-length impulse response, the Viterbi algorithm, linear equalizers, decision-feedback equalizers.
  • Selected topics : Modern digital receiver design, carrier, phase and timing synchronization, channel estimation.
Nb hours: 42.00
Nb hours per week: 3.00
Control form: examen écrit