# 
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

sigma_n = 1
sigma_b = 2
m_1 = 5

erfc = function(x) { return( 1 - pnorm(x) ) } 

gamma = seq( from=0, to=20, length.out=200 )

P_F = 2 * erfc( gamma/sigma_n )
P_D = 2 * erfc( gamma/sqrt( (m_1*sigma_b)^2 + sigma_n^2 ) )

#postscript("../../WriteUp/Graphics/Chapter2/prob_2.2.6.eps", onefile=FALSE, horizontal=FALSE)

plot( P_F, P_D, col="black", type="l", xlim=c(0,1), ylim=c(0,1) )
lines( gamma, gamma, col="gray", type="l" )

# Evaluate the minimum probability of error operating point:
#
tot_var = m_1^2 * sigma_b^2 + sigma_n^2 
gamma_mpe = ( ( 2 * tot_var * sigma_n^2 )/( m_1^2 * sigma_b^2 ) ) * log( sqrt( tot_var/sigma_n^2 ) )
print( gamma_mpe)

P_F_mpe = 2 * erfc( gamma_mpe/sigma_n )
P_D_mpe = 2 * erfc( gamma_mpe/sqrt( (m_1*sigma_b)^2 + sigma_n^2 ) )
lines( P_F_mpe, P_D_mpe, col="red", type='o', pch=10, cex=1.5 )

Pr_error = 0.5 + 0.5 * ( P_F_mpe - P_D_mpe )
print(Pr_error)

#dev.off()