A Linear System Approach to Wave Propagation - Non-Credit

Linear System Approach

Date: February 4, 2021 - May 15, 2021

This section of the course has been modified from its original format of a Masters Level for credit class, to provide working professionals the opportunity to learn this material without the associated assignments and exams. The video recordings are from the live online sessions of the class and will be made available for viewing every Friday.

There will be a live session each month (four in total) specifically designed for the working professional and will provide opportunities for learners to ask questions, network, and share their own experiences and feedback with the instructor.

Cost: $2,000.00

Apply Now 

Course Description

This course treats systems governed by the wave equation via the tools of linear system theory: convolutions and space/time Fourier transforms. In contrast, the traditional physicist's approach to teaching the subject entails scalar and vector potentials, the method of separation of variables, spherical coordinates, and the use of special functions – all of which we circumvent. The course will benefit both wireless communication researchers and signal processing researchers. It will equip them to pursue advanced research topics, such as super-directive antenna arrays, large intelligent surfaces, holographic MIMO, wireless power transfer, wavefield extrapolation, and video motion detection. The course also serves as a physical introduction to multidimensional signal processing. The concepts learned in this course are readily applicable to geophysics, acoustics, and ultrasonics. 


Key Take-aways

- Maxwell's equations describe a linear time/shift-invariant system

- All your linear system insight is applicable: space/time convolutions; Fourier transforms

- Any distribution of transmitters creates, externally, a spectrum of plane-waves: no approximation

- Any system of antennas, whether close together or far apart, is completely described by an impedance matrix and classical circuit theory

Who Should Take This Course

- Wireless researchers

- Signal processing engineers

- Geophysicists

- Acousticians

- Applied mathematicians

Prerequisites: undergraduate linear systems, electromagnetics, and complex variables.


Start Date: February 4, 2021

Recorded lectures will be released at 10 AM on Friday of each week the course is in session. Please note live sessions in bold.

Live Session: Feb 4, 2021 - 6:30 - 8:00EST

Week 01 (Feb 5): Classical network theory

  • N-port networks
  • impedance matrix and properties
  • real and reactive power
  • application: wireless power transmission

Live Session: Feb 8, 2021 -  6:30 - 8:00PM EST

Week 02 (Feb 12): Scalar (acoustic) wave equation

  • physical derivation with distributed source
  • Helmholtz equation
  • review of space/time Fourier transforms
  • solution in frequency/wavenumber domain
  • 1D system (wave-guide)

Week 03 (Feb 19): Plane-wave expansion of the radiated field

  • review of Cauchy residue theorem
  • plane-wave expansion of the spherical wave
  • Green's function (impulse response) solution
  • plane-wave solution for arbitrary distributed source

Week 04 (Feb 24): Methods of computing real power 

  • integration over far-field
  • integration over a source distribution
  • integration over plane waves

Week 05 (March 5): Reactive power; self/mutual impedance

  • computation in space-domain
  • computation in the wavenumber domain
  • physically meaningful sources

Live Session - March 8, 2021 - 6:30 - 8:00PM EST

Week 06 (March 12): Degrees of freedom for 1D, 2D, 3D arrays

  • non-line-of-sight propagation: plane-wave scattering
  • application: MIMO communications

Week 07 (March 19): Week Off (Exams)

Week 08 (March 26): Maxwell's equations; distributed sources

  • review of Maxwell's equations
  • direct solution in frequency/wavenumber domain

Live Session - April 1, 6:30 - 8:00 EST

Week 09 (April 2): Plane-wave expansion of the radiated field

  • Polarization
  • vertical and horizontal plane-wave amplitudes

Live Session - April 5, 6:30 - 8:00PM EST

Week 10 (April 9): MIMO communications

  • degrees-of-freedom for 1D, 2D, 3D polarimetric arrays
  • non-line-of-sight propagation: plane-wave scattering

Week 11 (April 16): Power: real/reactive; self/mutual impedance

  • methods of computation
  • idealized antennas

Week 12 (April 23): Application: super-directive antenna arrays

  • wireless communication
  • wireless power transfer

Week 13 (April 30): Multi-dimensional digital signal processing

  • video motion detection using space/time fan filters
  • inference of far-field antenna pattern from near-field measurements

Week 14: (May 7) Additional applications

  • random field models for small-scale fading
  • electromagnetic imaging

Live Session (May 10, 2021) 6:30 - 8:00PM EST