1.
ECNG 436/4312 Course
Project
Part I : OFDM basics
Mina Yonan
m.yonan@cu.edu.eg
m.yonan@aucegypt.edu

2.
Why OFDM ?
• In a single carrier communication system, the symbol period must be much
greater than the delay time in order to avoid inter-symbol interference (ISI).
• data rate is inversely proportional to symbol period, having long symbol
periods means low data rate and communication inefficiency

3.
Why OFDM ?

4.
Multicarrier Principle
• In Multicarrier, the high-rate stream of data symbols is first Serial-
to-Parallel (S/P) converted for modulation onto M parallel
subcarriers.
• This increases the symbol duration on each subcarrier by a factor
of approximately M, such that it becomes significantly longer than
the channel delay spread.

5.
Multi-carrier : Conventional FDM Multicarrier

6.
Multi-carrier : Conventional FDM Multicarrier
Conventional frequency division multiplexing : type of Multicarrier techniques A serial-
to-parallel (S-to-P) converter converts the high-rate stream into 𝒌 separate low-rate
substreams. As a result, each low-rate substream has a rate of 𝑹 𝒔/𝒌 sps.

7.
Multi-carrier : Conventional FDM Multicarrier
Advantages of Conventional FDM:
• It is effective at combating inter-symbol interference (ISI) and multipath fading.
• It can adjust modulation and coding for each subcarrier
• It has simple equalization.
Disadvantages of FDM:
• The transmitter needs to have K separate D-to-A converters and K separate radio
frequency (RF) modulators.
• FDM is not bandwidth efficient. The extra guard bands necessarily add to the total
bandwidth requirement

8.
OFDM Modulator basic

9.
Basics of OFDM
• The objective is still to transmit a high-rate stream using multiple subcarriers.
• OFDM overcomes the problem of the large bandwidth requirement imposed by guard
bands. Instead of using K local oscillators (LOs) and K multipliers in modulation,

10.
OFDM Modulator basic
න
m𝑇 𝑢
(m + 1) 𝑇𝑢
𝑥 𝑘1
∗(𝑡) . 𝑥 𝑘2(𝑡) 𝑑𝑡 = න
m𝑇𝑢
(m + 1) 𝑇𝑢
𝑒−𝑗2𝜋𝑘1∆𝑓 𝑡 𝑒 𝑗2𝜋𝑘2∆𝑓 𝑡 𝑑𝑡 = 0 when 𝑘1 ≠ 𝑘2

11.
OFDM Modulator basic
Subcarrier Orthogonality
• Orthogonality simplifies recovery of the N data streams
– Orthogonal subcarriers = No inter-carrier-interference (ICI)
• Time Domain Orthogonality:
– Every subcarrier has an integer number of cycles within symbol time
• Satisfies precise mathematical definition of orthogonality for complex
exponential (and sinusoidal) functions over the interval [0, 𝑇𝑢]

12.
OFDM Demodulator basic
• The basic principle of OFDM demodulation consisting of a bank of correlators,
one for each subcarrier.
𝑌 𝑘 = න
m𝑇 𝑢
(m + 1) 𝑇𝑢
𝑟(𝑡) 𝑒−𝑗2𝜋𝑘∆𝑓𝑡. 𝑑𝑡
= න
m𝑇𝑢
(m + 1) 𝑇𝑢
෍
𝑝=0
𝑁−1
𝑎 𝑝 𝑒 𝑗2𝜋𝑝∆𝑓𝑡
. 𝑒−𝑗2𝜋𝑘∆𝑓𝑡
. 𝑑𝑡
= ෍
𝑝=0
𝑁−1
𝑎 𝑝 න
m𝑇𝑢
(m + 1) 𝑇 𝑢
𝑒 𝑗2𝜋(𝑝−𝑘) ∆𝑓𝑡
. 𝑑𝑡
𝑌(𝑘) = ቊ
𝑎 𝑝 𝑘 = 𝑝
0 𝑘 ≠ 𝑝

13.
OFDM Implementation
• Bank of modulators/correlators to illustrate the basic principles of OFDM
modulation and demodulation, these are not the most appropriate
modulator/demodulator structures for actual implementation.
• OFDM allows for low-complexity implementation by means of
computationally efficient Fast Fourier Transform (FFT) processing

14.
OFDM Implementation
• 𝑁𝑐 : Number of sub-carriers spacing
• 𝑇𝑢 : Symbol-time duration
• 𝑇𝑆 : Sampling- time
- After reconstruction filter ( D/A)
𝑥 𝑂𝐹𝐷𝑀 𝑡 = ෍
𝑘=0
𝑁 𝑐−1
𝑎 𝑘 𝑒 𝑗2𝜋𝑘∆𝑓𝑡
𝑥 𝑛 = ෍
𝑘=0
𝑁 𝑐−1
𝑎 𝑘 𝑒
ൗ𝑗2𝜋𝑘𝑛
𝑁 𝑐
𝑁𝑐 =
𝑇𝑢
𝑇𝑠
, ∆𝑓 =
1
𝑇𝑢
𝑥 𝑛 = ෍
𝑘=0
𝑁 𝑐−1
𝑎 𝑘 𝑒 𝑗2𝜋𝑘∆𝑓𝑛 𝑇𝑠

15.
OFDM Implementation
• Time Domain: Guard Time

16.
OFDM Implementation
• Time Domain: Guard Time

17.
OFDMA Block

18.
Selection of OFDM Parameters
If OFDM is to be used as the transmission scheme in a mobile-communication
system, the following basic OFDM parameters need to be decided upon:
1. The subcarrier spacing Δf.
2. The number of subcarriers 𝑁𝑐 , which, together with the subcarrier spacing,
determines the overall transmission bandwidth of the OFDM signal
3. The cyclic-prefix length 𝑇𝑐𝑝. Together with the subcarrier spacing Δf = 1/ 𝑇𝑢.,
the cyclic-prefix length determines the overall OFDM symbol time
𝑇 = 𝑇𝑢 + 𝑇𝑐𝑝 Or, equivalently, the OFDM symbol rate

19.
Selection of OFDM Parameters
In summary, the following three design criteria can be identified:
𝑇𝐶𝑃 ≥ 𝑇𝑑 To prevent ISI,
𝑓 𝑑(𝑚𝑎𝑥)
∆𝑓
≪ 1 To keep ICI due to Doppler sufficiently low,
𝑇𝑐𝑝
𝑇𝑢 + 𝑇𝑐𝑝
≪ 1 For spectral efficiency.

20.
OFDMA: Multiple Access Extensions of OFDM
• LTE uses OFDMA which is a more advanced form of OFDM where subcarriers
can be allocated to different users over time. This provides much-needed
frequency diversity in cases where the data rate is low meaning a narrow
frequency allocation which is susceptible to narrow-band fading.

21.
OFDMA in LTE standard

22.
Carrier Frequency Offset (CFO)
This CFO in OFDM systems causes loss of orthogonality among subcarriers and
subsequently leads to significant performance degradation caused by :
• Misalignment between transmitter and receiver RF local oscillators
• Doppler spread caused by the relative motion of transmitter and receiver

23.
Carrier Frequency Offset (CFO)
- Doppler Frequency :
𝜹𝒇 =
𝒗
𝒄
. 𝒇 𝒄
In IEEE 802.11a standard :
Carrier frequency : 5 GHz
Velocity : 100 km/h,
The offset value is ∆f =1.6kHz, which is relatively insignificant compared to the carrier spacing of
312.5 kHz.
Misalignment between Tx and RX :
The other source of frequency offset is due to frequency errors in the oscillators. The IEEE
802.11a standard requires the oscillators to have frequency errors within 20 ppm
(or ± 𝟐𝟎 × 𝟏𝟎−𝟔 ). For a carrier of 5 GHz, this means a maximum frequency error of:
𝜹𝒇 𝒎𝒂𝒙 = 𝟐 × ±𝟐𝟎 × 𝟏𝟎−𝟔 × 𝟓 × 𝟏𝟎 𝟗 = ±𝟐𝟎𝟎 𝒌𝑯𝒛

24.
Effects of CFO in OFDM
• The orthogonality among the subcarriers is destroyed which leads to Inter Carrier Interference (ICI), resulting in a
significant degradation of the overall BER performance.
• The signal is attenuated and rotated.
ɛ =
𝜹𝒇
∆𝒇

25.
Effects of CFO in OFDM
The ICI between 𝑘 𝑡ℎ and (𝑘 + 𝑚) 𝑡ℎ subcarriers causes by frequency offset ɛ
can be found by their inner product
𝐼 𝑘 = න
0
𝑇𝑠
𝑠 𝑘 𝑡 𝑠 𝑘+𝑚
∗ 𝑡 =
𝑇𝑠(1 − 𝑒−𝑗2𝜋(𝑚+ɛ)
)
𝑗2𝜋(𝑚 + ɛ)