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EE 131A project

# EE 131A project - Table of Matlab gaussian S=1 0 dB M 1 10...

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Table of Matlab: 1. Analytical calculations for Case A and Case B: 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 - -∞ -∞ - = = - = For s = 1, P(e) = Q(1) = 0.1587 For s = 2.009093, P(e) = Q(2.009093) = 0.0223 1 gaussian S=1 2.009093 0 dB 6.06dB M mean std(SS) std(N) mean std(SS) std(N) 1 0 0.2063 0 0 0 0.2154 0 0 10 0 0.4752 0.8433 0.9226 0 1.0806 0.8433 0.9226 100 0.1042 0.0787 1.0042 0.9764 0.0208 0.0384 1.0042 0.9764 1000 0.142 0.0441 1.0004 1.003 0.0256 0.0583 1.0004 1.003 10000 0.1617 -0.004 1 1.0089 0.026 -0.0022 1 1.0089 100000 0.1627 -0.0101 1 1.0002 0.0237 -0.0117 1 1.0002 1000000 0.1597 -0.0015 1 1.0004 0.0228 -0.0013 1 1.0004 10000000 0.1586 -1.09E-04 1 1 0.0222 -3.00E-04 1 1 expected 0.1586 0 1 1 0.0222 0 1 1 laplacian S=1 2.009093 0 dB 6.06dB M mean std(SS) std(N) mean std(SS) std(N) 1 0 2.3865 0 0 0 3.3956 0 0 10 0.125 0.3694 0.8433 0.6967 0 0.9748 0.8433 0.6967 100 0.0833 0.0412 1.0042 0.7311 0 8.56E-04 1.0042 0.7311 1000 0.1164 0.0157 1.0004 0.982 0.0178 0.0298 1.0004 0.982 10000 0.1288 -0.0026 1 1.0049 0.0291 -7.48E-04 1 1.0049 100000 0.1213 -0.006 1 0.9956 0.029 -0.0076 1 0.9956 1000000 0.1215 -7.25E-04 1 0.9978 0.0288 -5.84E-04 1 0.9978 10000000 0.1216 5.11E-05 1 1 0.029 -1.39E-04 1 1 expected 0.121558 0 1 1 0.0291 0.00E+00 1 1

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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 a 1xM Gaussian noise vector by using random function in Matlab. Store the vector to N. Step 2. Generating a 1xM random binary data vector of ±S values with equal probability.
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EE 131A project - Table of Matlab gaussian S=1 0 dB M 1 10...

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