100204-hw1 - (a) Find the Signal to Interference and Noise...

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EE522 - Communication Theory - Spring 2010 Homework #1 - Probability and Random Processes Date Assigned: Thursday, February 4, 2010 Date Due: Thursday, February 11 (1) A signal ( 29 t s having power spectral density ( 29 Π = Φ 000 , 10 8 f f s is passed through a channel in which additive white Gaussian noise ( 29 t n and interference ( 29 t i are present, resulting in a received signal of ( 29 ( 29 ( 29 t i t s t r + = . You may assume that the signal, noise and interference are all independent and that the noise has power spectral density ( 29 1 . 0 = Φ f n , and the interference has power spectral density ( 29 + Λ + - Λ = Φ 100 2000 50 100 2000 50 f f f i . The received signal is then filtered twice, first to bandlimit the signal and then to excise the interference, according to the following block diagram:
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Unformatted text preview: (a) Find the Signal to Interference and Noise Ratio (SINR) of r ( t ) (b) Find the SINR of y ( t ). (c) Find the SINR of z( t ). (2) Let ∑ = = 12 1 i i X Y , where each random variable i X is independent and identically distributed with pdf given by: ≤ ≤-= otherwise , 1 1 , 2 3 2 x x p i X Write an approximate expression for ( 29 y p Y the pdf of Y . (3) Proakis, Problem 2.37 (4) Proakis, Problem 2.45 ( 29 ( 29 ( 29 ( 29 t i t n t s t r + + = ( 29 Π = 000 , 10 1 f f H ( 29 t y ( 29 t z ( 29 + Π + -Π + Π = 2900 3550 2900 3550 3800 1 f f f f H...
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