This document discusses OFDM (Orthogonal Frequency Division Multiplexing) and its advantages over conventional single-carrier communication systems. It explains that OFDM divides a high-rate data stream into multiple parallel sub-carriers to combat inter-symbol interference caused by multipath delays. Key points covered include: OFDM overcomes the bandwidth inefficiency of conventional FDM by using orthogonal sub-carriers; OFDM modulation and demodulation can be implemented efficiently using FFT; guard intervals and cyclic prefixes are used to prevent inter-symbol interference; and OFDMA extends OFDM to allow dynamic sub-carrier allocation between users. Carrier frequency offset is also discussed as a potential issue for OFDM that can cause inter-carrier interference
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
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.
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
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,
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.
14. 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
19. 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
20. 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.
21. 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.
23. 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
24. 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
25. 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
26. 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)
