OFDM Transmission over Wideband Channel

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 1/3 • 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 2/3 • 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 3/3 • 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 1/1 • 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 1/9 • 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 2/9 • 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 3/9 • The received time domain signals are is the channel impulse response. is the known symbol. is noise.

10. Time Domain Channel Estimation 4/9 • 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 5/9 • Then receive signal is expressed as

12. Time Domain Channel Estimation 6/9 • The least square (LS) estimate for is

13. Frequency Domain Channel Estimation 7/9 • 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 8/9 • We get (4.2) from (4.1) through FFT transform, • If we have two repeat sequences,

15. Frequency Domain Channel Estimation 9/9 • The least square (LS) estimate for each is

16. Comparisons of Time- and Frequency-Domain Equalization 1/1

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.