1. Orthogonal Frequency Division Multiplexing - OFDM

2. Impact of fading S(f) High bit rate H(f) f r(t) s(t) f h(t) t t S(f)
Low bit rate f t
r(t)
s(t) t t

3. Frequency Selective fading flat fading
s(t)
H(f) t
r(t) f
p1(t)
h(t) t
p2(t) t
p3(t)
p3(t) t
p4(t)
p4(t) t

4. FDM  OFDM Frequency Division Multiplexing OFDM
GAIN IN SPECTRAL EFFICIENCY

5. OFDM DEFINITION OFDM = Orthogonal FDM
Carrier centers are put on orthogonal frequencies
ORTHOGONALITY - The peak of each signal coincides with zero crossing of other signals
Subcarriers are spaced by 1/ Ts

6. A simplified view S-P + s(t) S-P P-S r(t) Cos 2f1t Input bits
Output
bits
Cos 2f8t

7. OFDM THEORY s s s s s s The baseband OFDM signals can be written as
where is the central frequency of the mth sub-channel and
is the corresponding transmitted symbol.
The signals are orthogonal over [0, T ] as
illustrated below: s s s s s s s

8. Continuous Time: Orthogonal Time Signal Set

9. Discrete Time: Orthogonal Time Signal Set
Ts = N T

10. k (t)
OFDM Modulator

11. OFDM Demodulator

12. OFDM is a Block Process

13. Discrete Time Equivalent
Inverse Discrete Fourier Transform 
s(n) =  dk exp( j 2 k n/N)
N-point IDFT  N2 complex multiplications
Inverse Fast Fourier Transform
Radix 2 N-point IFFT  (N/2). log2 N
Radix 4 N-point IFFT  (3/8). N. ( log 2 N - 2)
N -1
k=0

14. Generic OFDM Transmitter
OFDM symbol
bits
Serial to
Parallel
Pulse shaper
FEC
IFFT
Linear PA
&
DAC
add cyclic extension fc
view this as a time to
frequency mapper
Complexity (cost) is transferred back from the digital to the analog domain!

15. (of all tones sent in one OFDM symbol)
Generic OFDM Receiver
Slot &
Timing
AGC
Sync.
P/S and
Detection
Error
Sampler
FFT
Recovery fc
gross offset
VCO
Freq. Offset
fine offset
Estimation
(of all tones sent in one OFDM symbol)

16. Complexity of OFDM versus Single Carrier
Key difference between OFDM and single carrier transmission is FFT versus equalizer
Complexity of 64 point radix-4 FFT in IEE a OFDM=96 million multiplications per second
16 taps OQPSK or GMSK Equalizer for same data rates above needs 768 million multiplications per second
OFDM order of magnitude less complex

17. Salient features
BASIC IDEA : Channel bandwidth is divided into multiple
subchannels to reduce ISI and frequency-selective fading.
Multicarrier transmission : Subcarriers are orthogonal each other
in frequency domain.
Time-domain spreading:
Spreading is achieved in the time-domain by repeating the same information in an OFDM symbol on two different sub-bands => Frequency Diversity.
Frequency-domain spreading:
Spreading is achieved by choosing conjugate symmetric inputs for the input to the IFFT (real output)
Exploits frequency diversity and helps reduce the transmitter complexity/power consumption.

18. OFDM ADVANTAGES OFDM is spectrally efficient
IFFT/FFT operation ensures that sub-carriers do not interfere with each other.
OFDM has an inherent robustness against narrowband interference.
Narrowband interference will affect at most a couple
of subchannels.
Information from the affected subchannels can be
erased and recovered via the forward error
correction (FEC) codes.
Equalization is very simple compared to Single-Carrier systems

19. OFDM ADVANTAGES
OFDM has excellent robustness in multi-path environments.
Cyclic prefix preserves orthogonality between sub-
carriers.
Cyclic prefix allows the receiver to capture multi-
path energy more efficiently.
Ability to comply with world-wide regulations:
Bands and tones can be dynamically turned on/off
to comply with changing regulations.
Coexistence with current and future systems:
for enhanced coexistence with the other devices.

20. OFDM DRAWBACKS High sensitivity inter-channel interference, ICI
OFDM is sensitive to frequency, clock and phase offset
The OFDM time-domain signal has a relatively large peak-to-average power ratio
tends to reduce the power efficiency of the RF amplifier
non-linear amplification destroys the orthogonality of the OFDM signal and introduced out-of-band radiation

21. Adjacent Symbol Interference (ASI) Symbol Smearing Due to Channel

22. Guard Interval Inserted Between Adjacent Symbols to Suppress ASI

23. Cyclic Prefix Inserted in Guard Interval to Suppress Adjacent Channel Interference (ACI) and retain orthogonality

24. Data Length Defines Sinc Width: Spectral Spacing Matches Width

25. Extended Data Length Reduces Sinc Width: Spectral Spacing Preserved

26. DFT (FFT) as Signal Generator for Complex Sinusoids

27. DFT (FFT) As Signal Analyzer for Complex Sinusoids

28. Radix-2 FFT Flow Diagrams

29. Input Vector FFT Mapped to Output Time Series, Up-Sampled, Converted Via DAC to Waveform, and I-Q Up-Converted

30. The FFT as Signal Generator and Interpolator

31. OFDM Modulation With IFFT and Interpolator

32. OFDM Demodulation With FFT

33. OFDM Transceiver