UCLA Extension

Orthogonal Frequency Division Multiplexing (Discrete Multitone)

In a standard QAM communication system, the bit stream is delivered sequentially by a series of translated and overlapping but mutually orthogonal Nyquist pulses. These Nyquist pulses occupy a common rectangular bandwidth but maintain mutual orthogonality by residing on each other’s time domain zeros crossings. An Orthogonal Frequency Division Multiplexed system simply reverses the roles of time and frequency. The bit stream is delivered in parallel by many simultaneous tone bursts occupying a common rectangular time interval, and these bursts, when observed in the frequency domain, are seen to be translated Nyquist shaped spectra residing on each other’s spectral zero crossings. Ultimately, the many QAM modulated sinusoids are presented to the channel as a parallel set of narrowband, long duration tone bursts which are less sensitive to channel dispersion.

Complete Details

Orthogonal Frequency Division Multiplexing (OFDM), also called Discrete Multitone (DMT), is a modulation process that delivers digital data to a channel as a parallel set of low rate, low bandwidth, and extended-duration time waveforms. By virtue of the extended time duration, the composite signal is insensitive to short time duration channel impairments as well as to channel dispersion. Consequently, OFDM has become a prime contender for delivery of high data rate signals through dispersive channels, such as mobile wireless and copper channels. Europe has embraced OFDM for Digital Audio Broadcast (DAD) and Digital Video Broadcasting (DVD-T). At the same time, DMT has become the choice of the Regional Bell Operating Systems for high-speed copper loop transmission, while OFDM is the modulation selected by a number of high data rate wireless LANs.

This course introduces participants to the essential elements of an OFDM communication system, where the OFDM signal is synthesized at the transmitter by an Inverse Discrete Fourier Transform (IDFT) and analyzed at the receiver by a Forward Discrete Fourier Transform (DFT). The OFDM modulation and demodulation processes, as well as standard timing and carrier acquisition processes, are examined and techniques to combat the effects of non-linear distortion due to amplifiers are addressed. Linear distortion, such as timing and carrier offsets, and implementation effects, such as I-Q gain and phase mismatches, also are discussed. The course presents a number of techniques to aid the receiver and combat the channel, including guard intervals, cyclic extensions, preambles, pilot probes, interleaving, channel coding, and frequency and time diversity.


Participants should have completed the foundational UCLA Extension short course, Communication Systems Using Digital Signal Processing, or have familiarity with Z-transforms, FIR filters, sampling theorem, and spectrum analysis techniques.

Course Materials

Lecture notes are distributed on the first day of the course. These notes are for participants only and are not for sale.

Coordinator and Lecturer

fredric j. harris, PhD, Cubic Signal Processing Chair Professor of Electrical and Computer Engineering, San Diego State University, California. Mr. harris is a recognized expert in the field of Digital Signal Processing (DSP), especially as applied to underwater acoustics, radio surveillance, satellite communications, radar, real-time acoustics, vibration monitoring equipment, and laboratory instrumentation. He is the author of the text, Multirate Signal Processing for Communication Systems. Since 1970, he has been a consultant to such organizations as the U.S. Navy Ocean Systems Center, Lockheed, ESL, Cubic, Hughes, BAE, Scientific Atlanta, Rockwell, Northrop Grumman, Boeing, and Inritsu. He also has presented courses on fast algorithms, adaptive algorithms, error-correcting codes, and control theory. Mr. harris has conducted seminars in DSP for Motorola, Northrop Grumman, BAE, Lockheed, Hewlett Packard, General Electric, Rockwell, Spectral Dynamics, and the U.S. Navy Research Laboratory.

Course Program

OFDM Signal Structure

  • Modulation by IDFT, demodulation by DFT

Channel Multi-Path Effects

  • Cyclic extension, equalizers

Amplifier Clipping

  • Spectral growth, inter-channel interference, suppression techniques

Transmitter and Receiver Imbalance

  • Gain and phase corrections, pre- and post-correction

Carrier Frequency Synchronization

  • Error effects, time domain, frequency domain

Symbol and Sample Timing

  • Error effects, frequency and phase errors and tracking

Channel Estimation

  • Pilots, preambles

OFDM Variants

  • Shaped OFDM and Carrier Interferometry CI-OFDM

Simulation and Implementation Considerations

Interpolators, Finite Arithmetic

Sample Systems and Standards

For more information contact the Short Course Program Office:
shortcourses@uclaextension.edu | (310) 825-3344 | fax (310) 206-2815