Orthogonal Frequency Division Multiplexing (OFDM)

By:

Loren Karl Robinson Schwappach

Senior Electrical Engineering & Computer Engineering Student

At Colorado Technical University (CTU) Colorado Springs

Prepared for:

Dr. John Santiago

EE463 Communications 1

Novemeber 2010

What is Orthogonal Frequency-Division Multiplexing?:In OFDM a single data stream is divided into several parallel data streams (Using a Serial to Parallel Converter). Each of these parallel data streams is then sampled (multiplied in the Time Domain) at intervals of Ts where Ts=T/N (T=Period, N = Number of Subcarriers). Thus, each subcarrier frequency is spaced at intervals fn=n/T. This ensures each carriers spectrum lands at the center of all other carriers for Zero Inter-Carrier Interference and Signals with high “orthogonality” and thus high resistance to interference!

Now.. Why use OFDM?:Consider a transmission medium such as a telephone line (Cat 3) cable that has the arbitrary squared frequency response shown by figure 7.25a. It is clear that this medium will alter the transmitted spectrum of Fig. 7.25b (Single-carrier spectrum) and cause significant intersymbol interference. However, consider the Multi-carrier spectrum shown by Fig. 7.25c. Where a single transmitter employs multiple carriers, each being responsible for a piece of the overall data rate. The medium will have the same effect on the overall spectrum, but the spectrum of the individual carriers is relatively undistorted except for possible gain change and phase rotation as shown by fig. 7.25d.

Advantages of OFDM:•Subcarrier frequencies are continuous from one symbol interval to the next, meaning there is no distortion of spectral properties and thus OFDM is robust against crosstalk between channels that are close together and can adapt easily to bad channels (noisy, etc)

•Since subcarriers are multiples of the symbol period they are orthogonal over the symbol period and thus OFDM is robust against Intersymbol interference (ISI) and fading caused by multipath propagation.

•Adjacent channels are spaced at intervals of 1/Ts; High spectral efficiency due to spectral overlap and thus minimum Bandwidth.

•Symbols may be continuously extended by a simple repetition referred to as cyclic prefix or postfix; beneficial in channels that tend to lengthen the pulse interval.

•Resistant to Fading and more..

Applications of OFDM:•ADSL and VDSL

•Power line communication

•Wireless LAN, namely 802.11a,g, and n, and HiperLAN/2 (802.11b uses Direct-sequence spread spectrum)

•Some Digital radio systems

•Some Digital TV systems, most notably DVB-T•For broadcasting (TV and Radio)•Wi-Fi LAN, Wireless local loop (WLL)•Fourth generation Cellular transmission.•WiMax•And many others…

Block Diagram of OFDM:

Why this Works:Equation 7.56 in book (Sampled Multi-Carrier Signal) is simply the inverse discrete Fourier transform.

Questions:

References:

Haykin, S., “Analog and Digital Communications 2nd Edition” John Wiley & Sons, Haboken, NJ, 2007.