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F4B101A / TP2 / Détection quadratique





In [5]:



    


using DataFrames
using Distributions
using Gadfly



    











In [6]:



    


q(x) = (1/2) * erfc(x / sqrt(2));
p_e(x) = q(sqrt(x+1).*sqrt(log(1+x)./x)) + (1/2) - q(sqrt(log(x+1)./x));

X = linspace(1,100,1000);
PE = p_e(X);

df_pe_theoretical = DataFrame(x=X, y=PE, f="Theoretical error probability");



    


















    






WARNING: Method definition q(Any) in module Main at In[2]:1 overwritten at In[6]:1.
WARNING: Method definition p_e(Any) in module Main at In[2]:2 overwritten at In[6]:2.

















In [ ]:



    






    











In [7]:



    


# On fixe sigma_b et on fait varier sigma_s (et donc le SNR)
sigma2_b = 1;
sigma2_s = X;

SNR = sigma2_s / sigma2_b;
lambda2 = sigma2_b * ((SNR+1)/SNR) * log(SNR+1);

# Pour chaque valeur de SNR on fait n_tirages et on compare a lambda
n_tirages = 100;
ratios = zeros(length(SNR));

for i = 1:length(SNR)
    detected = 0;
    for j = 1:n_tirages
        # Tirage aléatoire
        y = rand(Normal(0, sigma2_s[i])) + rand(Normal(0, sigma2_b));
        # Détection
        if (y^2 > lambda2[i])
           detected += 1 
        end
    end
    ratios[i] = 1 - (detected/n_tirages);
end

df_pe_simulated = DataFrame(x=X, y=ratios, f="Simulated error probability");



    











In [8]:



    


plot(vcat(df_pe_theoretical, df_pe_simulated), x=:x, y=:y, color=:f, Geom.line, Scale.x_log10)



    


















    
Out[8]:









  
    x
  
  
    10-2.5
    10-2.0
    10-1.5
    10-1.0
    10-0.5
    100.0
    100.5
    101.0
    101.5
    102.0
    102.5
    103.0
    103.5
    104.0
    104.5
    10-2.0
    10-1.9
    10-1.8
    10-1.7
    10-1.6
    10-1.5
    10-1.4
    10-1.3
    10-1.2
    10-1.1
    10-1.0
    10-0.9
    10-0.8
    10-0.7
    10-0.6
    10-0.5
    10-0.4
    10-0.3
    10-0.2
    10-0.1
    100.0
    100.1
    100.2
    100.3
    100.4
    100.5
    100.6
    100.7
    100.8
    100.9
    101.0
    101.1
    101.2
    101.3
    101.4
    101.5
    101.6
    101.7
    101.8
    101.9
    102.0
    102.1
    102.2
    102.3
    102.4
    102.5
    102.6
    102.7
    102.8
    102.9
    103.0
    103.1
    103.2
    103.3
    103.4
    103.5
    103.6
    103.7
    103.8
    103.9
    104.0
    10-2
    100
    102
    104
    10-2.0
    10-1.8
    10-1.6
    10-1.4
    10-1.2
    10-1.0
    10-0.8
    10-0.6
    10-0.4
    10-0.2
    100.0
    100.2
    100.4
    100.6
    100.8
    101.0
    101.2
    101.4
    101.6
    101.8
    102.0
    102.2
    102.4
    102.6
    102.8
    103.0
    103.2
    103.4
    103.6
    103.8
    104.0
  
  
    
      Theoretical error probability
      Simulated error probability
    
    
      
      
    
    
      f
    
  

  
    
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
        
        
      
    
    
      
        
        
      
      
        
      
      
        
      
      
        
        
      
    
  

  
    -0.6
    -0.5
    -0.4
    -0.3
    -0.2
    -0.1
    0.0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    1.1
    -0.50
    -0.48
    -0.46
    -0.44
    -0.42
    -0.40
    -0.38
    -0.36
    -0.34
    -0.32
    -0.30
    -0.28
    -0.26
    -0.24
    -0.22
    -0.20
    -0.18
    -0.16
    -0.14
    -0.12
    -0.10
    -0.08
    -0.06
    -0.04
    -0.02
    0.00
    0.02
    0.04
    0.06
    0.08
    0.10
    0.12
    0.14
    0.16
    0.18
    0.20
    0.22
    0.24
    0.26
    0.28
    0.30
    0.32
    0.34
    0.36
    0.38
    0.40
    0.42
    0.44
    0.46
    0.48
    0.50
    0.52
    0.54
    0.56
    0.58
    0.60
    0.62
    0.64
    0.66
    0.68
    0.70
    0.72
    0.74
    0.76
    0.78
    0.80
    0.82
    0.84
    0.86
    0.88
    0.90
    0.92
    0.94
    0.96
    0.98
    1.00
    -0.5
    0.0
    0.5
    1.0
    -0.50
    -0.45
    -0.40
    -0.35
    -0.30
    -0.25
    -0.20
    -0.15
    -0.10
    -0.05
    0.00
    0.05
    0.10
    0.15
    0.20
    0.25
    0.30
    0.35
    0.40
    0.45
    0.50
    0.55
    0.60
    0.65
    0.70
    0.75
    0.80
    0.85
    0.90
    0.95
    1.00
  
  
    y
  


  
  






















In [ ]:

Content source: maxmouchet/tb

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