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EE 131A Class Project

# EE 131A Class Project - EE 131A Class Project Liting Huang...

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EE 131A Class Project Liting Huang

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ID#: 403-532-150 Date: June 10, 2008 1. Analytical calculations for Case A and Case B: SNR(dB) = 0 dB 0 20 10 1 dB s σ = = 1 s σ = = SNR(dB) = 6.06 dB 6.06 20 10 2.00909 dB s σ = = 2.00909 s = Case A: S N x S N + = - + 1 0 , "1" , "0" H H = = (0,1) N N : P(e) = P(e|H 1 )= 0 ( ) ( ) ( ) ( ) s N N f x s dx f x F s Q s - -∞ -∞ - = = - = 2
For s = 1, P(e) = Q(1) = 0.1587 For s = 2.00909, P(e) = Q(2.00909) = 0.0223 Case B: N = Laplacian Noise with σ = 1 2 n N f e α α - = n -∞ < < ∞ 2 2 2 σ α = 1 σ = 2 α = | | ( ) 0 0 0 0 ( ) ( | ) ( ) 2 2 x s x s N P e P e H f x s dx e dx e dx α α α α - + - + = = + = = ( ) 2 0 1 1 1 2 2 2 x s s s e e e α α α α - + - - - = = = For s = 1, P(e) = 2(1) 1 0.121558 2 e - = For s = 2.00909, P(e) = 2(2.00909) 1 0.029175 2 e - = 2. Monte Carlo Simulation Case A: Step 1. Generating an 1xM iid Gaussian noise vector by using randn function in Matlab. Store the vector to N. Step 2. Generating an 1xM random binary data vector of ±S values with equal probability. a. Generate uniformly distributed pseudo-random numbers by using rand function in Matlab. b. Set the numbers greater or equal to 0.5 to 1, and the others to 0. c. Scale the binary vector to values of S ± by using the function SS = S*(2*S2-1) 3

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SS is the transmitted data.
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