{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw3_2010

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

This preview shows pages 1–2. Sign up to view the full content.

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 g i ( t ) are complex Gaus- sian (i.e., Rayleigh fading) and are independent, with powers given by:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online