FDM, OFDM & OFDMA
Following is an interactive overview of OFDMA, which is used many wireless standards, including 5G NR, to enable efficient use of bandwidth for multiple users.
Sinc pulse §
The rectangular function rect(t), when passed through a Fourier transform, becomes the sinc function sinc(f). This is sometimes called a “sinc pulse”.
In otherwords, a rectangular wave in the time domain becomes a “sinc pulse” in the frequency domain1:
+ - - + - - + - - + - - + - - + - - + - - + - - + - - + - - +
+-----------+
| |
| |
| |
| |
| |
| |
| |
| |
+ + .-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
.---. / \ | | / \ .---.
/ \ / \ / \ / \ / \
\___/ \ / \ / \___/
\_/ \_/FDM §
FDM (Frequency-Division Multiplexing) operates in the frequency domain, so we use “sinc pulses” to represent each signal being transmitted. In FDM, a series of non-overlapping frequency bands are used for transmission, typically with guard bands separating each signal to avoid interfrequency interference.
For example, if we are sending three signals using FDM, each signals is modulated with a different carrier frequency (fc1, fc2 & fc3) and a guard band inbetween. We refer to each respective signal as a subcarrier (sc1, sc2, sc3):
+-------+ +-------+
| | | |
| | | |
| | | |
| | | |
| Guard | | Guard |
| Band | | Band |
| | | |
| | | |
+ - - + - - + - - + - - + - - + - - + - - + - - + - - + - - + + - - + - - + - - + - - + - - + - - + - - + - - + - - + - - + + - - + - - + - - + - - + - - + - - + - - + - - + - - + - - +
| | | |
+-------+ +-------+
sc1
|
|
v
.-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
.---. / \ | | / \ .---.
/ \ / \ / \ / \ /
\___/ \ / \ / \___/
\_/ ^ \_/
|
fc1 sc2
|
|
v
.-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
.---. / \ | | / \ .---.
\ / \ / \ / \ /
\___/ \ / \ / \___/
\_/ ^ \_/
|
fc2 sc3
|
|
v
.-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
.---. / \ | | / \ .---.
\ / \ / \ / \ / \
\___/ \ / \ / \___/
\_/ ^ \_/
|
fc3
+-------+ +-------+
| | | |
| | | |
| | | |
| | | |
| Guard | | Guard |
| Band | | Band |
| | | |
| | | |
+ + + +
| | | |
+-------+ +-------+
OFDM §
In OFDM (Orthogonal Frequency-Division Multiplexing), the carrier frequencies overlap, but are arranged such that when one is at its peak, all the others are at zero. In other words, the subcarriers are orthogonal to one another. This allows for much more efficient use of available bandwidth compared to FDM:
<---Δf----> <---Δf---->
+ - - + - - + - - + - - + - - + - - + - - + - - + - - + - - +
sc1
|
|
v
.-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
/ \ | | / \ .---.
/ \ / \ / \ / \
\ / \ / \___/
\_/ ^ \_/
|
fc1
sc2
|
|
v
.-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
.---. / \ | | / \ .---.
/ \ / \ / \ / \ / \
\___/ \ / \ / \___/
\_/ ^ \_/
|
fc2
sc3
|
|
v
.-.
/ \
/ \
| |
/ \
/ \
| |
.-. / \ .-.
.---. / \ | | / \
/ \ / \ / \ / \
\___/ \ / \ /
\_/ ^ \_/
|
fc3The gap between each subcarrier is Δf. This is the subcarrier spacing:
- In 4G,
Δfis 15KHz. - In 5G,
Δfis variable.
OFDMA §
Finally, this brings us to OFDMA (Orthogonal Frequency Division Multiple Access). Instead of “M” for Multiplexing, it is now “MA” for Multiple Access.
What is the difference between OFDM and OFDMA? In short, the subcarriers may be assigned to different users, hence Multiple Access.
Specifically, the wave
rect(t)in the time domain transforms tosin(f)/forsinc(f)in the frequency domain. ↩︎