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Introduction To Wireless Fading Channels
- 1. An Introduction to Wireless Fading Channels Name of the author: Nitin Jain Date Created : 8 th Jan 2010
- 9. Free Space Path Loss log (distance) Rx signal power(dBm)
- 11. With Shadow Fading log (distance) Rx signal power(dBm) Shadow Fading Path loss
- 20. Rayleigh Fading waveform envelope
- 21. Time Dispersion phenomenon time h(t) Freq Freq transform Different frequencies suffer different attenuation
- 22. Delay Spread –Time Domain interpretation
- 24. Delay Spread- Freq. Domain Interpretation
- 27. Bit Rate Limitations by Delay Spread
- 33. Basic Doppler effect t) Propagation time is a function of time due to mobile car. c is the light velocity and v m is the car speed
- 34. Doppler spread in Multipath freq |X(f)| f c f c + f d1 f c + f d2 f c + f d |Y(f)| freq Due to multipaths, a single sinusoid by base station is perceived as summation of 3 sinusioids f c +f d1 , f c +f d2 and f c +f d , where f d is maximum doppler frequency = f c *(v m /d). Due to different arrivals of angle due to multipaths, perceived velocity is different for multipaths. After passing through multipath channel v m v m cos ( θ 1 ) v m cos ( θ 2 ) θ 1 θ 2
- 35. Doppler Spectrum This is called classical Doppler spectrum & shows how a single sinusoid ends up having a broad spectrum due to multipath & relative motion between Tx and Rx. A popular model assumes that distribution of angle of arrival is distributed uniformly between 0 & 2 π which leads to following spectrum Imagine now multiple paths with different angles of arrival causing amagamalation of various frequencies between f c +f d & f c -f d .
- 37. Frequency Dual Fourier Transform T 0 Function denotes space time correlation for the channel response to a sinusoid . So this indicates the amount of correlation between two sinusoids sent at different times t 1 & t 2 .
- 38. Waveform of Rayleigh Fading Signal
- 41. Summary of Overall Fading
- 42. Summary of Multipath Fading characterization
Editor's Notes
- Think wireless channel as a FIR filter with a practically finite impulse response. The response of the filter keeps on changing due to time varying coefficients. The taps of the filter are corresponding to multipaths’s amplitude.
- Coherence bandwidth f0 is a statistical measure of the range of frequencies over which all the signal spectral components are affected in a similar way by the channel i.e. exhibiting fading or no fading. Coherence bandwidth is inversely proportional to excess delay spread. Same channel can show flat fading behaviour depending upon
- This just illustrates how delay spread puts a limit on maximum achievable data rate without needing an eqaulizer. Of course, various communication standards use various techniques to overcome this limits.
- Doppler shift will be positive or negative depending upon whether mobile is moving to or going away from base station.
- Here the effect of time dispersion & time variant behaviour of the model can be seen easily. When Doppler spread is larger, time between two consecutive fades is shortened accordingly.