1. IV. Orthogonal Frequency Division Multiplexing (OFDM)

2. Evolution of Wireless Communication Standards
Introduction
Evolution of Wireless Communication Standards
OFDM

3. Wireless Communication Channels
From “Wireless Communications” Edfors, Molisch, Tufvesson
Communications over wireless channels suffer from multi-path propagation
Multi-path channels are usually frequency selective
OFDM supports high data rate communications over frequency selective channels

4. Multi-Path Propagation Modeling
Power
Multi-Path Components τ0 τ1 τ2
Time
Multi-path results from reflection, diffraction, and scattering off environment surroundings
Note: The figure above demonstrates the roles of reflection and scattering only on multi-path

5. Multi-Path Propagation Modeling
Power
Multi-Path Components τ0 τ1 τ2
Time
As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies

6. Multi-Path Propagation Modeling
Power
Multi-Path Components τ0 τ1 τ2
Time
As the mobile receiver (i.e. car) moves in the environment, the strength of each multi-path component varies

7. Multi-Path = Frequency-Selective!
0.5
0.5 1 1
0.5
1 μs
1 μs
f=1 MHz 1
0.5
0.5 1
0.5
-0.5 -1 -1
1 μs
1 μs
f=500 KHz 1 1
0.5
0.5
0.5
-0.5 -1 -1
1 μs
1 μs

8. Multi-Path = Frequency-Selective!
h(t)
|H(f)|
0.5
0.5 1
f (MHz)
0.5 1
1.5 2
1 μs
A multi-path channel treats signals with different frequencies differently
A signal composed of multiple frequencies would be distorted by passing through such channel

9. Frequency Division & Coherence Bandwidth
Power
Frequency
Subdivide wideband bandwidth into multiple narrowband sub-carriers
Bandwidth of each channel is selected such that each sub-carrier approximately displays Flat Fading characteristics
The bandwidth over which the wireless channel is assumed to display flat fading characteristics is called the coherence bandwidth

10. Example Frequency Response for 3G Channel
Power Delay Profile (Vehicular A Channel Model)
Snapshot for Frequency Response
Resolvable Path
Relative Delay (nsec)
Average Power (dB) 1
0.0 2
310
-1.0 3
710
-9.0 4
1090
-10.0 5
1730
-15.0 6
2510
-20.0
Simulation Assumptions
Rayleigh Fading for each resolvable path
System Bandwidth = 5 MHz
Coherence Bandwidth = 540 KHz
Number of Sub-Carriers = 64
Sub-Carrier Bandwidth = KHz

11. Example Frequency Response for 3G Channel
Power Delay Profile (Vehicular A Channel Model)
Snapshot for Frequency Response
Resolvable Path
Relative Delay (nsec)
Average Power (dB) 1
0.0 2
310
-1.0 3
710
-9.0 4
1090
-10.0 5
1730
-15.0 6
2510
-20.0
Simulation Assumptions
Rayleigh Fading for each resolvable path
System Bandwidth = 5 MHz
Coherence Bandwidth = 540 KHz
Number of Sub-Carriers = 64
Sub-Carrier Bandwidth = KHz

12. Frequency Division Multiplexing (FDM)+
Binary
Encoder
Transmitting
Filter (f1)
Modulation
Filter (f2)
Filter (fN)
Wireless
Channel
Bandpass
Demod.

13. Orthogonal FDM
Is it possible to find carrier frequencies f1, f2 … fN such that

14. Orthogonal FDM
Is it possible to find carrier frequencies f1, f2 … fN such that

15. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

16. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

17. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

18. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

19. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

20. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

21. Orthogonality of Sub-CarriersTs
The sinusoid signals with frequencies f1, f2, f3, f4 are all mutually orthogonal over the symbol period Ts

22. Orthogonal FDM + Wireless Channel Binary Encoder Transmitting
Filter (f1)
Modulation
Filter (f2)
Filter (fN)
Wireless
Channel
Correlate
with (f1)
Demod.
with (f2)
with (fN)
f2=f1+1/2TS
fN=f1+1/2(N-1)TS

23. Number of Subcarriers in OFDM
For band-limited FDM if the system bandwidth is B, number of sub-carriers is given by:
For OFDM if the system bandwidth is B, Number of sub-carriers is given by:
OFDM has the potential to at least double the number of sub-carriers (i.e., double the total transmission rate over the system bandwidth)

24. OFDM a New Idea? The idea of OFDM has been out there since the 1950s
OFDM was first used in military HF radios in late 1950s and early 1960s
Early use of OFDM has been limited in commercial communication systems due to the high costs associated with the requirements for hundreds/thousands of oscillators
The use of OFDM has experienced a breakthrough in the 1990s with advancements in DSP hardware
Currently, OFDM has been adopted in numerous wire-line and wireless communications systems, such as:
Digital audio and video broadcasting
Digital subscriber lines (DSL)
Wireless LAN
WiMAX
LTE (Long term Evolution), 4G Cellular Networks

25. OFDM & DFT (Discrete Fourier Transform)
OFDM Signal over 4 Sub-carriers Ts
-f1 f1
-f2 f2
-f3 f3
-f4 f4
OFDM Signal:
Time Domain
OFDM Signal:
Freq. Domain

26. OFDM & DFT (Discrete Fourier Transform)
OFDM Signal over 4 Sub-carriers
OFDM Signal:
Time Domain
OFDM Signal:
Freq. Domain
DFT is means to generate samples of the OFDM signal in the frequency and time domain without the use of oscillators
At the transmitter OFDM uses IDFT to convert samples of the spectrum of the OFDM signal into a corresponding equal number of samples from the OFDM signal at the time domain
At the receiver OFDM uses DFT to restore the signal representation in the frequency domain and proceed with symbols detection

27. OFDM & DFT (Discrete Fourier Transform)
OFDM Signal over 4 Sub-carriers
(Separated by 1/2Ts)
We need to compute the composite spectrum in the frequency domain to be able to compute the 4 samples used by the IDFT

28. OFDM & DFT (Discrete Fourier Transform)
OFDM Signal over 4 Sub-carriers
(Separated by 1/Ts)
The separation between carriers guarantee that samples from individual spectrum of sub-carriers correspond to samples from the composite spectrum

29. Number of Subcarriers in OFDM with DFT
For band-limited FDM if the system bandwidth is B, number of sub-carriers is given by:
For OFDM if the system bandwidth is B, Number of sub-carriers is given by:
OFDM with DFT has the potential to at increase the number of sub-carriers compared to FDM for α>0 (remember that α=0 filter is not physically realizable )
DFT implementation of OFDM avoids the needs for oscillators to generate the OFDM signal