Courses

Discrete-time Modem Design for Wireless Communications

Discrete-time Modem Design for Wireless Communications

This course covers a detailed design view of various physical-layer building blocks of a digital modem for wireless communications. The building blocks include modulation, demodulation, carrier frequency and phase offset compensation, timing synchronization, and equalization, with particular emphasis on discrete-time (digital) realizations. The theoretical coverage in the class is accompanied by rigorous computer assignments that progressively lead up to the students implementing their own software-defined baseband digital wireless modems. Using software-defined radios available in the lab, the students are also required to demonstrate the working of their implementations with real-world wireless links.

Error Correction Codes

This course provides a fundamental understanding of error correction coding, a necessary component of any digital communication system. The contents focus on both mathematical, as well as algorithmic foundations of error correction codes. Topics include classical block codes such as Hamming Codes, BCH Codes, and Reed Solomon Codes (used in Blu-Ray Discs, DSL), as well as trellis-based Convolution codes (used in GSM mobile communications and WiFi). The course also covers relatively modern codes such as Turbo codes (used in 3G mobile communications) and Low-density parity-check codes (used in DVB-S2 standard for satellite transmission of digital television). The concepts learnt in class are augmented with programming exercises that help students learn how to put coding to work.

Error Correction Codes
Stochastic Systems

Stochastic Systems

This is a first-year graduate level course in probability, random variables, and random processes. Besides fundamental concepts in random variables, density functions, and expectations, the course also includes coverage of random vectors and random signals/processes along with an emphasis on response of linear time-invariant systems to random inputs. The theoretical content is complemented with important applications of these concepts to diverse areas of electrical engineering including, but not limited to, communication systems, communication networks, control systems, and signal processing.

EE411: Digital Signal Processing (DSP):

Digital signal processing is a major field in the current era of engineering, with applications ranging from mobile and wireless communication, satellite communications, radar, sonar, acoustics, forensic sciences, biomedical, imaging, speech, earth observation, space-sciences and many more. This course covers the relevant background theory for processing any generic deterministic signals in digital domain. As an example, if a data stream is coming from a sensor, how to interpret this data as a discrete time signal and how can we use different domains along with mathematical tools to see and extract the amount of information contained in this "data" signal.

Digital Signal Processing

EE511: Advanced Digital Signal Processing (ADSP):

This is a second course in discrete-time signal processing where the focus is on comprehensive treatment of signal processing algorithms used for description/ representation of data and learning models from data. We deal with the mathematics to signal processing and data driven modelling. For learning the parameters and structures of data models, classical estimation theory is explored in the course. Algorithms such as least square filtering, maximum likelihood and maximum a posterior, sequential and adaptive algorithms to estimating the parameters/structures of a supposed model are covered under parametric estimation. While other techniques such as Kernel methods, Gaussian process regression and Neural networks are covered under non-parametric estimation.

Advanced Digital Signal Processing
Linear System Theory

EE560: Linear System Theory (LST):

This course aims to provide an applied introduction to linear dynamical systems theory. Dynamical system refers to a set of objects that evolve over time possibly under external excitation. The way the system evolves is called the dynamics of the system. A dynamical model of a system is a set of mathematical laws explaining in a compact form and in quantitative way how the system evolves over time. Linear dynamical system refers to the mathematical representation of a physical system whose dynamical model can be represented by a set of 1st order differential equations or first order difference equations for discrete time systems in the form called state-space representation. The course deals with how to derive these representations from physical description of dynamical systems and given this representation how can we control certain states or observe them along with answering theoretical questions dealing with the possibility of controlling or observing these states.

State and Parameter Estimation (SPE):

This course deals with advanced concepts related to statistical estimation theory. The foundation of the course is built on diverse concepts which are necessary to cover the subsequent part like linear and matrix algebra, matrix calculus, multi-variate random variables and random processes and some concepts about linear system theory. Main part focuses on the coverage of the classical estimation techniques like MVUE, BLUE, CRLB, least-square, ML estimation and their equivalence. Bayesian philosophy towards parameter estimation is covered along with general Bayesian estimator introduction, minimum mean square error estimation (MMSE), Linear MMSE and maximum a posterior (MAP) estimation. The course then deals with the techniques used in estimating the state of a dynamical system. In this part, more emphasis is given to Kalman Filtering along with some basic exposure to non-linear state estimation techniques e.g. Kalman filter variants for non-linear systems, particle filters, Markov Chain Monte Carlo (MCMC) techniques, re-sampling algorithms in MCMC and data-driven approaches towards dynamical system state estimation e.g. Gaussian Process regression and kernel methods.

State and Parameter Estimation
Feedback Control Systems

Feedback Control Systems

Design of linear feedback control systems for command-following, disturbance rejection, stability, and dynamic response specifications. Root-locus and frequency response design (Bode) techniques. Nyquist stability criterion. Design of dynamic compensators. Digitization and computer implementation issues.

Signals and Systems

This course introduces mathematical modeling techniques used in the study of signals and systems. Topics include sinusoids and periodic signals, spectrum of signals, sampling, frequency response, convolution and filtering, Fourier, Laplace and Z-transforms. Integrated computer based laboratory exercises.

Signals and Systems
Convex Optimization

Convex Optimization

This course focuses on theory, algorithms and applications of convex optimization. Convex optimization deals with the non-linear optimization problems where the objective function and the constraints of the problem are both convex. These problems appear in a variety of applications in diverse fields of science and engineering (e.g., statistics, signal/image processing, wireless communications, computational neuroanatomy, machine learning, and computational geometry, to name a few). Students will be given training to recognize, model and formulate the convex optimization problems. Topics include: review of least-squares, linear programming, convex sets and functions, convexity with reference to inequalities, linear optimization problems, quadratic optimization problems, geometric programming, duality (Lagrange dual function), norm approximation, regularized approximation, geometric problems, Algorithms (descend, Newton, interior-point). Implementation of optimization algorithms will be carried out in CVX (MATLAB based software for convex optimization).

Smart Data, Systems and Applications

Contact Details

School of Science & Engineering
Lahore University of Management Sciences

tahir@lums.edu.pk

(+92) 42 35608000 Ext. 8423, 8177, 8112