1. OFDM Transmission over Wideband Channel
Gwo-Ruey Lee

2. Outlines OFDM Transmission over Wideband Channel
The Time Dispersive Channel Model
Effects of Time Dispersive Channels on OFDM
Channel Estimation
Time Domain Channel Estimation
Frequency Domain Channel Estimation
Equalization
Comparisons of Time- and Frequency- Domain Equalization

3. The Time Dispersive Channel Model
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A time-dispersive channel can be characterized by its channel impulse response
where
is the number of multipath components
is the path gain of path i
is the path delay of path i

4. The Time Dispersive Channel Model
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Each path gain is a complex random variable with uniformly distributed phases and Rayleigh distributed magnitude.
The average power of each path decays exponentially.

5. The Time Dispersive Channel Model
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The mathematical model for the time dispersive channel is
where is the sampling period, and is
the root-mean-squared (RMS) delay spread.

6. Effects of Time Dispersive Channels on OFDM
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The phenomenon of multipath fading causes previous symbol to interfere with the latter symbol. This is known as the inter-symbol interference (ISI).
The received signal is the convolution of
the transmitted symbols and the discrete-time
channel impulse response.

7. Channel Estimation
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Channel estimation is the task of estimating the frequency response of the radio channel the transmitted signal travels before reaching the receiver antenna.
The channel estimation can be performed using the time domain approach and frequency domain approach.
Time domain channel estimation
Frequency domain channel estimation

8. Time Domain Channel Estimation
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This channel estimation is performed using the time domain approach, before FFT processing of the training symbols.
In this, the channel impulse response instead of the channel frequency response, is estimated.

9. Time Domain Channel Estimation
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The received time domain signals are
is the channel impulse response.
is the known symbol.
is noise.

10. Time Domain Channel Estimation
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The time domain convolution can be expressed as a matrix vector multiplication.
The parameter L is defined as the maximum length of the impulse response, L<64.

11. Time Domain Channel Estimation
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Then receive signal is expressed as

12. Time Domain Channel Estimation
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The least square (LS) estimate for is

13. Frequency Domain Channel Estimation
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This channel estimation is performed using the frequency domain approach.
In this, the channel frequency response is estimated by using two repeat training sequences.

14. Frequency Domain Channel Estimation
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We get (4.2) from (4.1) through FFT transform,
If we have two repeat sequences,

15. Frequency Domain Channel Estimation
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The least square (LS) estimate for each is

16. Comparisons of Time- and Frequency-Domain Equalization
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Time-domain Equalization
Frequency-domain Equalization
Convolution
One-tap multiplication
High complexity
when L is lager
Low complexity
when L is small
No FFT Required
FFT Required

17. References
[1] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude modulation – Principles and applications for personal communications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2000.
[2] Mark Engels, Wireless Ofdm Systems: How to Make Them Work? Kluwer Academic Publishers.
[3] John Terry, Juha Heiskala, OFDM Wireless LANs: A Theoretical and Practical Guide, Sams.