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 A Posteriori 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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