EE 6331, Spring, 2009 Advanced Telecommunication

1. EE 6331, Spring, 2009Advanced Telecommunication Zhu Han Department of Electrical and Computer Engineering Class 9 Feb. 17th, 2009

2. Outline • Review • Slow Fading • Fast Fading • Flat Fading • Frequency Selective Fading • Rayleigh and Ricean Distributions • Statistical Models ECE6331 Spring 2009

3. RMS Delay Spread ECE6331 Spring 2009

4. Coherence Bandwidth Frequency correlation between two sinusoids: 0 <= Cr1, r2 <= 1. Coherence bandwidth is the range of frequencies over which two frequency components have a strong potential for amplitude correlation.  is rms delay spread If correlation is above 0.9, then If correlation is above 0.5, then This is called 50% coherence bandwidth Example 5.5 ECE6331 Spring 2009

5. Doppler Spread Measure of spectral broadening caused by motion, the time rate of change of the mobile radio channel, and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. We know how to compute Doppler shift: fd Doppler spread, BD, is defined as the maximum Doppler shift: fm = v/l If the baseband signal bandwidth is much less than BD then effect of Doppler spread is negligible at the receiver. ECE6331 Spring 2009

6. Coherence Time Coherence time is the time duration over which the channel impulse response is essentially invariant. If the symbol period of the baseband signal (reciprocal of the baseband signal bandwidth) is greater the coherence time, than the signal will distort, since channel will change during the transmission of the signal . TS Coherence time (TC) is defined as: TC f2 f1 Dt=t2 - t1 t1 t2 ECE6331 Spring 2009

7. Different Types of Fading With Respect To SYMBOL PERIOD TS Flat Fast Fading Flat Slow Fading Symbol Period of Transmitting Signal st Frequency Selective Fast Fading Frequency Selective Slow Fading TC TS Transmitted Symbol Period ECE6331 Spring 2009

8. Different Types of Fading With Respect To BASEBAND SIGNAL BANDWIDTH BS Frequency Selective Fast Fading Frequency Selective Slow Fading Transmitted Baseband Signal Bandwidth BC Flat Fast Fading Flat Slow Fading BD BS Transmitted Baseband Signal Bandwidth ECE6331 Spring 2009

9. Fading Distributions Describes how the received signal amplitude changes with time. Remember that the received signal is combination of multiple signals arriving from different directions, phases and amplitudes. With the received signal we mean the baseband signal, namely the envelope of the received signal (i.e. r(t)). It is a statistical characterization of the multipath fading. Two distributions Rayleigh Fading Ricean Fading ECE6331 Spring 2009

10. Rayleigh Distributions Describes the received signal envelope distribution for channels, where all the components are non-LOS: i.e. there is no line-of–sight (LOS) component. ECE6331 Spring 2009

11. Ricean Distributions Describes the received signal envelope distribution for channels where one of the multipath components is LOS component. i.e. there is one LOS component. ECE6331 Spring 2009

12. Rayleigh Fading ECE6331 Spring 2009

13. Rayleigh Fading ECE6331 Spring 2009

14. Rayleigh Fading Distribution The Rayleigh distribution is commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. The envelope of the sum of two quadrature Gaussian noise signals obeys a Rayleigh distribution.  is the rms value of the received voltage before envelope detection, and 2 is the time-average power of the received signal before envelope detection. ECE6331 Spring 2009

15. Rayleigh Fading Distribution The probability that the envelope of the received signal does not exceed a specified value of R is given by the CDF: rpeak= and p()=0.6065/ ECE6331 Spring 2009

16. Rayleigh PDF 0.6065/s mean = 1.2533s median = 1.177s variance = 0.4292s2 5s s 2s 3s 4s ECE6331 Spring 2009

17. A typical Rayleigh fading envelope at 900MHz. ECE6331 Spring 2009

18. Ricean Distribution When there is a stationary (non-fading) LOS signal present, then the envelope distribution is Ricean. The Ricean distribution degenerates to Rayleigh when the dominant component fades away. ECE6331 Spring 2009

19. Ricean Fading Distribution When there is a dominant stationary signal component present, the small-scale fading envelope distribution is Ricean. The effect of a dominant signal arriving with many weaker multipath signals gives rise to the Ricean distribution. The Ricean distribution degenerates to a Rayleigh distribution when the dominant component fades away. The Ricean distribution is often described in terms of a parameter K which is defined as the ratio between the deterministic signal power and the variance of the multipath. K is known as the Ricean factor As A0, K  - dB, Ricean distribution degenerates to Rayleigh distribution. ECE6331 Spring 2009

20. CDF Cumulative distribution for three small-scale fading measurements and their fit to Rayleigh, Ricean, and log-normal distributions. ECE6331 Spring 2009

21. PDF Probability density function of Ricean distributions: K=-∞dB (Rayleigh) and K=6dB. For K>>1, the Ricean pdf is approximately Gaussian about the mean. ECE6331 Spring 2009

22. Rice time series ECE6331 Spring 2009

23. Nakagami Model Nakagami Model r: envelope amplitude Ω=<r2>: time-averaged power of received signal m: the inverse of normalized variance of r2 Get Rayleigh when m=1 ECE6331 Spring 2009

24. Small-scale fading mechanism Assume signals arrive from all angles in the horizontal plane 0<α<360 Signal amplitudes are equal, independent of α Assume further that there is no multipath delay: (flat fading assumption) Doppler shifts ECE6331 Spring 2009

25. Small-scale fading: effect of Doppler in a multipath environment fm, the largest Doppler shift ECE6331 Spring 2009

26. Carrier Doppler spectrum Spectrum Empirical investigations show results that deviate from this model Power Model Power goes to infinity at fc+/-fm ECE6331 Spring 2009

27. Baseband Spectrum Doppler Faded Signal Cause baseband spectrum has a maximum frequency of 2fm ECE6331 Spring 2009

28. Simulating Doppler/Small-scale fading ECE6331 Spring 2009

29. Simulating Doppler fading Procedure in page 222 ECE6331 Spring 2009

30. Level Crossing Rate (LCR) Threshold (R) LCR is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified threshold level R in a positive going direction. It is given by: ECE6331 Spring 2009

31. Average Fade Duration Defined as the average period of time for which the received signal is below a specified level R. For Rayleigh distributed fading signal, it is given by: Example 5.7, 5.8, 5.9 ECE6331 Spring 2009

32. Fading Model: Gilbert-Elliot Model Fade Period Signal Amplitude Threshold Time t Bad (Fade) Good (Non-fade) ECE6331 Spring 2009

33. Gilbert-Elliot Model 1/AFD Bad (Fade) Good (Non-fade) 1/ANFD The channel is modeled as a Two-State Markov Chain. Each state duration is memory-less and exponentially distributed. The rate going from Good to Bad state is: 1/AFD (AFD: Avg Fade Duration) The rate going from Bad to Good state is: 1/ANFD (ANFD: Avg Non-Fade Duration) ECE6331 Spring 2009

34. Simulating 2-ray multipath a1 and a2 are independent Rayleigh fading 1 and 2 are uniformly distributed over [0,2) ECE6331 Spring 2009

35. Simulating multipath with Doppler-induced Rayleigh fading ECE6331 Spring 2009

36. Review ECE6331 Spring 2009

37. Review ECE6331 Spring 2009

38. Review ECE6331 Spring 2009

39. Review ECE6331 Spring 2009

40. Homework and Exam 4.9, 4.15, 4.16, 4.19, 4.25, 4.34, 5.2, 5.6, 5.7 a,b,c,d, 5.15, 5.28, 5.29, 5.30 Due 2/26/09 ECE6331 Spring 2009