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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 ﬁrst 200 channel samples (showing the channel amplitude | h ( t ) | , in dB). Compare this ﬁgure with the previous two ﬁgures. 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 ﬁgure, 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 pdf’s with the theoretical pdf in one ﬁgure. Are they the same or not? Why? 1...
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