Question

Bit Error Probability: Consider the following model for a digital communication system: r =√Es + n where s {-1 1) with equal probability, and n is additive white Gaussian noise with zero mean and variance 1, and E is the signal to noise ratio. The receiver decides s = +1 if r > 0, and decides s = -1, if r <0. Estimate the error probability using Monte Carlo simulations by generating many samples and making as many decisions for s. Do this for different values of E, and plot the error probability versus 10 log10(E), where the y axis should be spaced logarithmically (semilog). The range of E should be chosen so that the error probability ranges from 1/2 to about 10

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Answer #1

Sdn andl_へ it.. Then 允> jtą re cee v.en- deL) ノ

Thein .호C.JE 9t or mei거 more NG

Graph For The Error Probabilities 30 20 -5 25 -15 -10 10log10(E)

İİİ) haN.Qー .ala-a p:/e_ Cle us au

R code for producing the graph:

prob=function(E,m)       #--- prob is the estimated error probabity for given values of signal to noise ratio E and sample size m
{
   stopifnot(E>=0 & m>0)       #--- this says that the function won't accept negative values of E and m shoulde be at least 1
   n=rnorm(m)               #--- this says that n is a random sample of size m from N(0,1) distribution
   m=mean(n< -sqrt(E))       #--- this says that m is the proportion of values in n which are less than the negative root of E
   return(m)               #--- this gives us the value of m, which is the estimated error probability
}

E=seq(0,2,by=0.001)
sam=1000
y=sapply(E,prob,m=sam)
p=10*log10(E)

plot(p,log(y),main="Graph For The Error Probabilities",xlab=expression(10*log[10](E)),ylab="log(Error Probability)",type="l")

Please rate my solution if you liked it.

Thank you

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Answer 1

Sdn andl_へ it.. Then 允> jtą re cee v.en- deL) ノ

Thein .호C.JE 9t or mei거 more NG

Graph For The Error Probabilities 30 20 -5 25 -15 -10 10log10(E)

İİİ) haN.Qー .ala-a p:/e_ Cle us au

R code for producing the graph:

prob=function(E,m)       #--- prob is the estimated error probabity for given values of signal to noise ratio E and sample size m
{
   stopifnot(E>=0 & m>0)       #--- this says that the function won't accept negative values of E and m shoulde be at least 1
   n=rnorm(m)               #--- this says that n is a random sample of size m from N(0,1) distribution
   m=mean(n< -sqrt(E))       #--- this says that m is the proportion of values in n which are less than the negative root of E
   return(m)               #--- this gives us the value of m, which is the estimated error probability
}

E=seq(0,2,by=0.001)
sam=1000
y=sapply(E,prob,m=sam)
p=10*log10(E)

plot(p,log(y),main="Graph For The Error Probabilities",xlab=expression(10*log[10](E)),ylab="log(Error Probability)",type="l")

Please rate my solution if you liked it.

Thank you