This document provides an introduction to orthogonal frequency division multiplexing (OFDM) modulation technology. It discusses how OFDM works by splitting a high-rate data stream into several lower data streams that are transmitted in parallel using orthogonal subcarriers. This allows for high spectral efficiency and better bandwidth utilization compared to traditional frequency division multiplexing. The document also outlines some key advantages of OFDM like high data rates and its use in various wireless technologies. It provides mathematical expressions to describe the orthogonality principle and modulation/demodulation processes. Challenges related to high peak-to-average power ratio and synchronization are also summarized.

1. Introduction of OFDM system
• Orthogonal frequency division multiplexing (OFDM) is a multi carrier
modulation technology.
• The carriers are mutually orthogonal to each other over a given time
interval.
• Split a high-rate data streams into a number of lower data streams.
• Transmit these streams in parallel using several orthogonal sub-carriers.
• Lower implementation complexity compared with the signal carrier, solution
with usage of Fast Fourier transform (FFT)/inverse (IFFT) blocks.
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2. Introduction (contd..)
Advantages of OFDM
• High spectral efficiency due to usage of closely spaced overlapping subcarriers.
• Better utilization of bandwidth.
• Higher capacity to handle inter symbol interference.
• Lower implementation complexity due to using IFFT/FFT in transmitter and
receiver respectively.
• High data rate communication system.
OFDM based Technologies
• Wi-Fi wireless standards (802.11a, 802.11g, 802.11n, 802.11ac, 802.11ax).
• Wi-Max (IEEE 802.16).
• DAB.
• DVB-T.
• 3GPP-LTE and LTE-A.
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3. OFDM Modulation
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𝑓1
𝑓0
𝑓𝑁−1
𝑋𝑁−1
𝑋1
𝑋𝑘
𝑋0
Input bit
stream
Serial to
Parallel
Convertor
QPSK/M-QAM
Mapper
𝑥 𝑡 =
1
𝑁 𝑘=0
𝑁−1
𝑋𝑘 𝑒𝑗2𝜋𝑓𝑘𝑡
Fig. 1: OFDM Modulation Process

4. OFDM Modulation (Contd..)
• Let 𝑋𝑘 be the complex symbols to be transmitted, then OFDM signal in
continuous time domain, can be expressed as
𝑥 𝑡 =
1
𝑁 𝑘=0
𝑁−1
𝑋𝑘 𝑒𝑗2𝜋𝑓𝑘𝑡
=
1
𝑁 𝑘=0
𝑁−1
𝑋𝑘 φ𝑘 𝑡 , 0 ≤ 𝑡 ≤ 𝑇𝑠 (1)
φ𝑘 𝑡 = 𝑒𝑗2𝜋𝑓𝑘𝑡
• Where, 𝑓𝑘 = 𝑓
0 + 𝑘∆𝑓, 𝑘 = 0, 1, … . 𝑁 − 1.
• 𝑇𝑠 and ∆𝑓: The symbol duration and subcarrier frequency spacing of OFDM.
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5. Orthogonality Principle
• If two signals are orthogonal, then the integral of their inner product over one
period should be zero.
• Mathematically, expression of two orthogonal signals φ𝑘 𝑡 and φ𝑚 𝑡 can be
written as
1
𝑇𝑠 0
𝑇𝑠
φ𝑘 𝑡 . φ𝑚 𝑡 ∗
𝑑𝑡 =
1
𝑇𝑠 0
𝑇𝑠
𝑒𝑗2𝜋𝑓𝑘𝑡
𝑒−𝑗2𝜋𝑓𝑚𝑡
𝑑𝑡
=
1
𝑇𝑠 0
𝑇𝑠
𝑒
𝑗2𝜋
𝑘
𝑇𝑠
𝑡
𝑒
−𝑗2𝜋
𝑚
𝑇𝑠
𝑡
𝑑𝑡
=
1
𝑇𝑠 0
𝑇𝑠
𝑒
𝑗2𝜋
(𝑘−𝑚)
𝑇𝑠
𝑡
𝑑𝑡
=
0, ∀ integer 𝑘 ≠ 𝑚
1 otherwise
(2)
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1. Cho, Yong Soo, et al. MIMO-OFDM wireless communications with MATLAB. John Wiley & Sons, 2010.

6. Comparison of FDM and OFDM
FDM
• Non orthogonal nature of carrier
frequencies of FDM.
• Large band gap is required to
avoid inter channel interference
which reduce the over all
spectral efficiency.
OFDM
• Sub carriers are orthogonal to
each other in OFDM .
• Due orthogonality of sub carrier
no band gap is required. thus
improve efficiency of spectral.

7. Comparison of FDM and OFDM..

8. Fig. 2: Block diagram Conventional OFDM System
𝑌𝑘[𝑁 − 1]
𝑌𝑘[0]
𝑥 𝑛 =
1
𝑁 𝑘=0
𝑁−1
𝑋𝑘 . 𝑒𝑗
2𝜋𝑘𝑛
𝑁 , 0 ≤ 𝑛 ≤ 𝑁 − 1
QPSK/QAM
De-mapper
𝑋𝑘[0]
𝑋𝑘[𝑁 − 1]
𝑦𝑛[0]
𝑦𝑛[𝑁 − 1]
Transmitted
signal
Received
signal
S/P
S/P
FFT
P/S
Cyclic Prefix
Removal
Cyclic Prefix
Addition
P/S
IFFT
Channel
QPSK/QAM
Mapper
Input
Output
IFFT/FFT based Implementation
Frequency Domain Time Domain
𝑋𝑘
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1. Cho, Yong Soo, et al. MIMO-OFDM wireless communications with MATLAB. John Wiley & Sons, 2010.

9. Cyclic prefix(CP)
• The OFDM guard interval can be inserted in
two different ways.
• One is the zero padding (ZP) that pads the
guard interval with zero.
• The other is cyclic extension of the OFDM
symbol with CP.
• CP is to extend the OFDM symbol by the
copying the last same of the OFDM symbol into
its front
• Extend OFDM symbols 𝑻𝒔𝒚𝒎= 𝑻𝒔𝒖𝒃+𝑻𝑮

10. Challenges in OFDM System
• In spite of several advantageous features, the OFDM systems have two
major concerns i.e.
1. High PAPR of transmitted signal
2. Synchronization at the receiver.
• The effects of all these issues are appearing in the form of degradation of
BER performance and inter-symbol interference(ISI) [1].
1. Cho, Yong Soo, et al. MIMO-OFDM wireless communications with MATLAB. John Wiley & Sons, 2010.
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11. Definition of PAPR
• PAPR=
Peak instantaneous power
Average power
.
• PAPR is calculated from the peak amplitude of the waveform divided by the
average value of the waveform.
• The value of the PAPR of conventional OFDM signal is directly
proportional to the number of subcarriers N and is given by
𝑃𝐴𝑃𝑅𝑚𝑎𝑥. 𝑑𝐵 = 10 log 𝑁 (3)
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12. • In IFFT operation, many sub carriers component are added in same phase and
cross correlation of symbols is non zero.
• Results in a high peak-to average power ratio of the system with large dynamic
range, which in turn effects on the efficiency of the high power amplifier (HPA) at
the transmitter.
• Therefore OFDM system are known to have a high PAPR compare with single
carrier system.
• High PAPR results in bringing the OFDM signal distortion in the non-linear region
of HPA and the signal distortion provides the degradation of Bit Error Rate (BER).
• The PAPR problem is more important since the efficiency of HPA is critical due
to the limited battery power in a mobile terminal.
Effect of high PAPR
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