OFDM explanation, Introduction to OFDM basics

1. 1WILCO 2017
OFDM

2. 2WILCO 2017
Introduction to OFDM
• Basic idea
 Using a large number of parallel narrow-band
subcarriers instead of a single wide-band
carrier to transport information.
• Advantages
 Very easy and efficient in dealing with
multi-path.
 Robust again narrow-band interference.
• Disadvantages
 Sensitive to frequency offset and phase
noise.
 Peak-to-average problem reduces the
power efficiency of RF amplifier at the
transmitter.
• Adopted for various standards
 DSL, 802.11a, DAB, DVB

3. 3WILCO 2017
Why OFDM is better?
• Multiple sub-channels (sub-carriers) carry samples sent at a lower
rate
 Almost same bandwidth with wide-band channel.
• Only some of the sub-channels are affected by interferers or
multi-path effect

4. 4WILCO 2017
Multipath can be described in two domains:
time and frequency

5. 5WILCO 2017
Importance of Orthogonality
• Why not just use FDM (frequency division multiplexing)
 Not orthogonal
• Need guard bands between adjacent frequency bands

6. 6WILCO 2017
Difference between FDM and OFDM

7. 7WILCO 2017
Multicarrier vs. Single Carrier
Drawbacks
• Weak in multipath fading.
• Very short pulses
• ISI is comparatively long.
• Complicated equalizer
• Poor spectral efficiency
because of band guards
Advantages
• Strong in multipath fading
• N long pulses
• ISI is comparatively short.
• Simple equalizer.
• Poor spectral efficiency
because of band guards
To improve the spectral efficiency:
Eliminate band guards between carriers
To use orthogonal carriers (allowing overlapping)

8. 8WILCO 2017
Orthogonal Frequency Division Modulation
Features
• No inter carrier
guard bands.
• Controlled overlapping
of bands.
• Maximum spectral
efficiency.
• Easy implementation
using IFFTs.
• Very sensitive to freq.
synchronization

9. 9WILCO 2017
OFDM Modulation and Demodulation
using FFTs

10. 10WILCO 2017
Orthogonality of Sub-carriers

11. 11WILCO 2017
Inter Symbol Interference (ISI)

12. 12WILCO 2017
Cyclic Prefix (CP)

13. 13WILCO 2017
Cyclic Prefix (CP)

14. 14WILCO 2017
Side Benefit of CP
• Allow the signal to be decoded even if the packet is
detected after some delay.

15. 15WILCO 2017
OFDM Architecture

16. 16WILCO 2017
BPSK BER with OFDM modulation

17. 17WILCO 2017
IEEE 802.11a specifications

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Cyclic prefix
The signal energy is spread over time 𝑇𝑑 + 𝑇𝐶𝑃 whereas the bit energy is spread
over the time 𝑇𝑑
𝐸𝑠. 𝑇𝑑 + 𝑇𝐶𝑃 = 𝐸 𝑏. 𝑇𝑑
Simplifying,
𝐸𝑠 =
𝑇𝑑
𝑇𝑑 + 𝑇𝐶𝑃
𝐸 𝑏

19. 19WILCO 2017
Frequency spread
• In OFDM transmission, all the available subcarriers from the DFT is not used for
data transmission. Typically some subcarriers at the edge are left unused to
ensure spectrum roll off.
• For the example scenario, out of the available bandwidth from -10MHz to
+10MHz, only subcarriers from -8.1250MHz (-26/64*20MHz) to +8.1250MHz
(+26/64*20MHz) are used.
• This means that the signal energy is spread over a bandwidth of 16.250MHz,
whereas noise is spread over bandwidth of 20MHz (-10MHz to +10MHz).
• 20𝑀𝐻𝑧. 𝐸𝑠 = 16𝑀𝐻𝑧. 𝐸 𝑏
• Simplifying,
• 𝐸𝑠 =
𝑛𝐷𝑆𝐶
𝑛𝐹𝐹𝑇
𝐸 𝑏

20. 20WILCO 2017
Relation between Eb/No and Es/No in OFDM
The relation between symbol energy and the bit energy is as follows:
𝐸𝑠
𝑁0
=
𝐸 𝑏
𝑁0
𝑛𝐷𝑆𝐶
𝑛𝐹𝐹𝑇
𝑇𝑑
𝑇𝑑 + 𝑇𝐶𝑃
Expressing in decibels,
𝐸𝑠
𝑁0
𝑑𝐵 =
𝐸 𝑏
𝑁0
𝑑𝐵 + 10𝑙𝑜𝑔10
𝑛𝐷𝑆𝐶
𝑛𝐹𝐹𝑇
+ 10𝑙𝑜𝑔10
𝑇𝑑
𝑇𝑑 + 𝑇𝐶𝑃

21. 21WILCO 2017
Theoretical bit error rate for BPSK modulation
𝑃𝑏 =
1
2
𝑒𝑟𝑓𝑐
𝐸 𝑏
𝑁0
In the simulation model, assumed that the
(a) Number of data subcarriers is 52
(b) Modulation is BPSK
(c) There is no coding
(d) fft size is 64
(e) Cyclic prefix size is 16 samples
(f) Symbol duration is 80 samples

22. 22WILCO 2017
Simulation model
The simulation script performs the following:
a) Generation of random binary sequence
b) BPSK modulation : bit 0 represented as -1 and bit 1 represented as +1
c) Assigning to multiple OFDM symbols where data subcarriers from -26 to -1 and
+1 to +26 are used, adding cyclic prefix, concatenation of multiple symbols to
form a long transmit sequence.
d) Adding White Gaussian Noise.
e) Grouping the received vector into multiple symbols, removing cyclic prefix,
taking the desired subcarriers.
f) Demodulation and conversion to bits.
g) Counting the number of bit errors.

23. 23WILCO 2017
Bit Error Rate plot for BPSK using OFDM modulation