hw3_2010 - EE 5505 Wireless Communication Homework 3 Due:...

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EE 5505 Prof. Jindal Wireless Communication February 13, 2010 Homework 3 Due: Friday, February 19, 4:00 PM Please turn in your MATLAB scripts in addition to your solutions and plots. 1. Consider the general tap-delay model h ( τ ; t ) = L i =1 g i ( t ) δ ( τ - τ i ) , (1) where the coefficients g 1 ( t ) , . . . , g L ( t ) are independent and each is complex Gaussian with zero mean and E [ | g i ( t ) | 2 ] = α i for i = 1 , . . . , L . The frequency response with respect to τ is given by (we derived this in lecture): C ( f ; t ) = -∞ c ( τ, t ) e - j 2 πfτ (2) = L i =1 g i ( t ) e - j 2 πfτ i (3) (a) Show that C ( f ; t ) is complex Gaussian. (b) Compute the mean and variance of C ( f ; t ) Hint: Multiplying a complex Gaussian random variable (with iid real and imaginary parts, as we consider in this model) by a phase term (e.g., e ) does not change the distribution of the complex Gaussian. 2. In this problem we will simulate a wideband channel according to a 3 tap model: c ( τ, t ) = 3 i =1 g i ( t ) δ ( τ - τ i ) . (4) Let us assume the typical model, as discussed in class (Rayleigh tap coefficients, with temporal correlation given by the Jakes model): Delays: τ 1 = 0, τ 1 = 1 μ sec, τ 2 = 3 μ sec Stationary distribution: Each of the tap coefficients
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This note was uploaded on 11/21/2011 for the course EE 5505 taught by Professor Jindal,n during the Spring '08 term at Minnesota.

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hw3_2010 - EE 5505 Wireless Communication Homework 3 Due:...

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