ENEE 620: Random Processes in Communication and Control

Course Goals:

Establish an adequate theoretical basis for modern communication, control and signal processing systems and make selected applications. Review the basic ideas of probability spaces (sample spaces, events, probability functions), and random variables and vectors (distribution functions, expectation). Introduce random sequences and processes and their classification into major types. Discuss in detail two types of major importance in this application area: second-order stationary and Markov sequences and processes. Discuss selected applications: e.g., optimal (Wiener, Kalman) filtering, queueing chains, spectral estimation.

Course Prerequisite:

ENEE 324 or equivalent, an undergraduate course in probability, random variables,and second-order stationary random processes.

Topic Prerequisite:

Probability functions, conditional probability, independence; random variables, probability distributions, conditional distributions, transformations, expectation and moments, conditional expectation; bi- and multi-variate distributions, transformations, random processes, covariance and spectral density, Gaussian, Brownian, and Poisson types.

References:

  1. Gray Davisson, Random Processes, Prentice-Hall, 1986.
  2. Larson Shubert, Prob. Models in Engr. Sci., 1979.
  3. Hoel, Port Stone, Introd. to Stoch. Proc., 1972.
  4. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd ed., McGraw-Hill, 1991.
  5. Picinbono, Random Signals and Systems, Prentice-Hall, 1993.
  6. Karlin Taylor, A First Course in Stochastic Processes, Academic Press, 1975.
  7. Ross, Stochastic Processes, Wiley (1983).

Core Topics:

  • Probability Spaces: sample spaces, families of events, probability measure, expectation, denumerable and nondenumerable spaces.
  • Random variables and Random Vectors: distribution function and decomposition, conditional expectation, least mean-square estimation, orthogonality principle.
  • Random Sequences and Processes: classification, modes of convergence (distribution, probability, mean-square, almost sure).
  • Second Order: (wide-sense) Stationary Random sequences and processes, covariance, spectral distribution and decomposition, linear, invariant operations (filtering), linear least-mean-square estimation, normal equations, rational spectral density and autoregressive-moving average models.
  • Markov Sequences and Processes: Markov chain sequences, stationary and steady-state distributions, ergodicity, Markov chain processes, Kolmogoroff and Fokker-Planck equations, Poisson processes, queueing models (M/M/1).
  • Independent and Orthogonal Increment Processes: Brownian motion; Wiener and Poisson processes; spectral representation of random sequences and processes.
  • Applications: linear least-mean-square (Wiener and Kalman) filtering, queueing networks.

Optional Topics:

  • Stochastic approximation
  • Representations: Karhunen-Loeve, spectral