Short 30 minute lecture on Orthogonal Frequency Division Multiplexing (OFDM) given during a faculty position visit.

1. John W. Thomas
PhD Candidate - University of Texas at Dallas

2. OFDM Presentation Contents
Speaker Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM

3. Academic
Speaker Biography Professional
• Morehouse College
o Atlanta, GA
o B.S - Mathematics and Physics, 2000
o Minor - Economics
• Columbia University
o New York City, NY
o M.S. - Electrical Engineering, 2002
o Concentration - Wireless Communications
• University of Texas at Dallas
o Richardson, TX
o PhD - Electrical Engineering, 2013
o Dissertation - Element Management System for a Telemedicine
Sensor Environment

4. Academic
Speaker Biography Professional
• Motorola - R&D Lab - Communications Research Lab
o Schaumburg, IL - 2002-2008
o Medium Access - standards work (3GPP HSPA+, IEEE WiMax, 3GPP
LTE)
o PHY/MAC development of proprietary OFDM-based Antenna
Array Platform
o Multiple published articles
• Texas Instruments, Inc. - R&D Lab intern
o Dallas, TX - Summer 2009 and 2010
o Simulation work for 3GPP LTE SON ICI compression standar
o Simulation work for WiFi Alliance WiFi Direct standard
o Multiple patents filed
• TCT Mobile - Alcatel One Touch - Validation Engineering Consultant
o Irvine, CA - 2010-present
o Device RF lab manager/tester

5. OFDM Presentation Contents
Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM

6. Definitions
FDM - Frequency Division Multiplexing
Introduction to OFDM Orthogonality
• a method of encoding digital data on multiple carrier frequencies
o Wikipedia
• an FDM modulation technique for transmitting large amounts of
digital data over a radio wave
o Webopedia
• a method of digital modulation in which a signal is split into
several narrowband channels at different frequencies.
o SearchNetworking
• A digital transmission technique that uses a large number of
carriers spaced apart at slightly different frequencies
o PC Magazine Encyclopedia

7. Definitions
Introduction to OFDM FDM - Frequency Division Multiplexing
Orthogonality
• Definition
o Total bandwidth available within a communications system is divided into
smaller non-overlapping frequency sub-bands
o Usually a separate data signal is associated to each frequency sub-band
o Passband filter at receiver extracts requested frequency sub-band / data signal
• Concerns
o Sub-band spacing – guard bands
o Interference
o Tuned filters at receiver
o Spectral Efficiency – Max Baud/Data rate
• Usage Examples
o Cable television (channel, video, color, audio multiplexing) - NTSC
o Satellite Communications

8. Definitions
FDM - Frequency Division Multiplexing
Introduction to OFDM Orthogonality
• Definition
o In terms of real functions, the integral of the product of any two different functions is zero.
‫ݏ‬௫ ‫ ݐ‬ൌ ‫ܣ‬௫ ‫ ݐ‬cos 2ߨ݂ ‫ ݐ‬൅ ߶௫ ‫ݐ‬
௫ , ‫ ∈ ݔ‬Ժା , 0 ൑ ‫ ݐ‬൑ ܶ
‫ݏ‬௬ ‫ ݐ‬ൌ ‫ܣ‬௬ ‫ ݐ‬cos 2ߨ݂ ‫ ݐ‬൅ ߶௬ ‫ݐ‬
௬ , ‫ ∈ ݕ‬Ժା , 0 ൑ ‫ ݐ‬൑ ܶ
Az(t) – Amplitude of z signal at time t
Φz(t) – Phase of z signal at time t
fz – Frequency of z signal
T – symbol duration – useful duration
If and only if,
݊
݂௫ െ ݂௬ ൌ , ݊ ∈ Ժା
ܶ
Then,
் Cross-correlation coefficient = 0
‫ݏ‬௫ ‫ݏ , ݐ‬௬ ‫ݐ‬ ൌ න ‫ݏ‬௫ ሺ‫ݐ‬ሻ ‫ݏ‬௬ ‫ ݐ݀ ݐ‬ൌ 0 Linearly Independent
଴
• Concerns
• How do you ensure signals are orthogonal? How complex is the process?

9. OFDM Presentation Contents
Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM

10. Transmitter
OFDM System Model Receiver
Serial to parellel conversion
• Series of bits divided into N parallel frames of size F
• N - # of subchannels, F - # bits per symbol = 4
ி
෍ ܾ௜ ൌ ‫ܤ‬௙
௜ୀଵ
QPSK modulation
• Differ signal by phase to transfer information
• Xn - Modulated symbol
ߨ
sሾ݊ሿ ൌ cos 2ߨ݂݊ ൅ 2݉ െ 1 , ݉ ൌ ሾ1 4ሿ
4

11. Transmitter
OFDM System Model Receiver
Inverse Fast Fouier Transform
• Creates N carriers that are all orthogonal
DAC
• Integrated circuit that converts the digital signal to analog signal

12. Transmitter
OFDM System Model Receiver
Low Pass Filter
• Eliminate unwanted signals
ADC
• Integrated circuit that converts the analog signal to digital signal
Fast Fourier Transform

13. OFDM Presentation Contents
Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM

14. IFFT - IDFT
OFDM Mathematical Model
Euler Formula
• Connects exponential functions to trigonometry
Previously defined data signal can also be expressed differently using the above formula
‫ ݐ ݏ‬ൌ ‫ ܣ‬cos 2ߨ݂‫ ݐ‬൅ ߶ ൌ ܴ݁ሼ‫ ܣ‬exp ݆ሺ2ߨ݂‫ ݐ‬൅ ߶ሻ ሽ
Summation of all OFDM carriers
ேିଵ
‫ݏ‬ே ‫ ݐ‬ൌ 1⁄ܰ ෍ ‫ܣ‬௡ exp ݆ሺ2ߨ݊Δ݂‫ ݐ‬൅ ߶௡ ሻ
௡ୀ଴
If the continuous data signal is sampled at multiples of the symbol duration
t = kT
ேିଵ ேିଵ
‫ݏ‬ே ݇ܶ ൌ 1⁄ܰ ෍ ‫ܣ‬௡ exp ݆ሺ2ߨ݊Δ݂݇ܶ ൅ ߶௡ ሽ ൌ 1⁄ܰ ෍ ‫ܣ‬௡ exp ݆2ߨ݊Δ݂݇ܶ expሺ݆߶௡ ሻ
௡ୀ଴ ௡ୀ଴
If difference in frequency between carriers is a multiple of inverse of sample duration, then sN is
equal to generalized IFFT equation
∆f = 1/NT

15. OFDM Presentation Contents
Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM

16. Advantages
Characteristics of OFDM Disadvantages
• Can easily adapt to severe channel conditions without complex time-domain
equalization.
• Robust against narrow-band co-channel interference.
• Robust against intersymbol interference (ISI) and fading caused by multipath
propagation.
• High spectral efficiency as compared to conventional modulation schemes, spread
spectrum, etc.
• Efficient implementation using Fast Fourier Transform (FFT).
• Low sensitivity to time synchronization errors.
• Tuned sub-channel receiver filters are not required (unlike conventional FDM).
• Facilitates single frequency networks (SFNs); i.e., transmitter macrodiversity.

17. Advantages
Characteristics of OFDM Disadvantages
• Sensitive to Doppler shift.
• Sensitive to frequency synchronization problems.
• High peak-to-average-power ratio (PAPR), requiring linear transmitter
circuitry, which suffers from poor power efficiency.
• Loss of efficiency caused by cyclic prefix/guard interval.

18. OFDM Presentation Contents
Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM

19. Wired
Usage of OFDM Wireless
OFDMA - Variation of OFDM
• Wired
o Power Line Communications
o Modern DSL modems
• Wireless
o Modern WiFi access points – IEEE 802.11g
o HD Radio broadcasts

20. Wired
Wireless
Usage of OFDM OFDMA - Variation of OFDM
• Orthogonal Frequency Division Multiple Access protocol
• Variation of OFDM into a protocol for multiple users accessing multiple data
channels
• Multiple users are provided access to bandwidth via a subset of available
frequency sub-bands
WiMax – IEEE 802.16e
- Clearwire, Clear, Sprint
- Comcast/Time Warner Mobile
LTE – Long Term Evolution – 4G Cellular
- Verizon Wireless
- AT&T Wireless
- T-Mobile

21. OFDM Presentation Contents
Biography
Introduction to OFDM
OFDM System Model
OFDM Mathematical Model
Characteristics of OFDM
Advantages
Disadvantages
Usage of OFDM
Thank You!!!