This document discusses OFDM (Orthogonal Frequency Division Multiplexing), including its basic idea of using multiple narrowband subcarriers instead of a single wideband carrier. OFDM has advantages like being robust to multipath interference and narrowband interference. It is sensitive to issues like frequency offset and phase noise. OFDM uses orthogonal subcarriers to maximize spectral efficiency and allows overlapping bands. Guard intervals and cyclic prefixes help mitigate inter-symbol interference. OFDM is used in standards like DSL, 802.11a, DAB and DVB. Simulation results show the theoretical and simulated bit error rates for OFDM with BPSK modulation.

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OFDM

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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

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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

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Multipath can be described in two domains:
time and frequency

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

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Difference between FDM and OFDM

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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)

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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

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OFDM Modulation and Demodulation
using FFTs

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Orthogonality of Sub-carriers

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Inter Symbol Interference (ISI)

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Cyclic Prefix (CP)

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Cyclic Prefix (CP)

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

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OFDM Architecture

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BPSK BER with OFDM modulation

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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

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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

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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

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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

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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.

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Bit Error Rate plot for BPSK using OFDM modulation