EE620-homework-01

EE620-homework-01 - Rayleigh fading channel with a...

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EE620: MIMO Wireless Communications Homework 1 (due on Feb. 18, before the class) A vehicle is moving at a constant speed of 60 miles per hour (96km/h). A user in the vehicle receives a 900MHz band signal from a base station. Assume that the fading channel between the user and base station experiences zero-mean complex Gaussian random variation (Rayleigh fading). The channel bandwidth is assumed to be 30 KHz. (1) (1 point) Determine the maximum Doppler frequency and the normalized maximum Doppler frequency. (2) (3 points) Use Jakes’ fading simulator (with M = 8 oscillators or N = 34) to generate the Rayleigh fading channel. Plot the first 200 channel samples (showing the channel amplitude | h ( t ) | , in dB). Plot the first 8000 channel samples in another figure. (Note: Normalize the channel samples such that the average power of each sample is 1.) (3) (3 points) Use Jakes’ fading simulator (with M = 8 oscillators or N = 34) to generate a
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Unformatted text preview: Rayleigh fading channel with a nomalized maximum Doppler frequency of f D,max T s = . 1. Plot the rst 200 channel samples (showing the channel amplitude | h ( t ) | , in dB). Compare this gure with the previous two gures. What do you observe? (4) (3 points) The theoretical pdf of the Rayleigh fading is (assuming the average channel power is 1) p | h ( t ) | ( x ) = 2 x e-x 2 , x . Plot this theoretical pdf. In the same gure, plot an experimental pdf by using the Rayleigh fading channel generated in (2) (you may need to generate 10 5 channel samples or more). Also plot another experimental pdf by using the Rayleigh fading channel generated in (3). Compare these two experimental pdfs with the theoretical pdf in one gure. Are they the same or not? Why? 1...
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