Question

Suppose that a signal s that takes on values 1 and -1, with probability p and 1-p respectively, is sent from location A. The signal received at location B is Normally distributed with parameters (s, 2). Find the best estimate of the signal sent, in the Maximum Likelihood Estimate sense, if R, the value received at location B, is equal to r.

Answer 1

Answer:-

Given That,

Suppose that a signal s that takes on values 1 and -1, with probability p and 1-p respectively, is sent from location A. The signal received at location B is Normally distributed with parameters (s, 2). Find the best estimate of the signal sent, in the Maximum A Posteriori sense, if R, the value received at location B, is equal to r.

Given,

R : Signal received at location B

R ~ N(s, 2) with pdf f(r|s) and observed value r, and where s is a parameter with the prior distribution

p(s = 1) = p

p(s = -1) = 1 - p

The posterior distribution of the signal sent s is given by,  

Therefore,

Best estimate of s in the mse sense = posterior mean

= 1 *p(s = 1|r) + (-1) p(s = -1|r)

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