OFDM system

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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