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Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel ? be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for ? given xA and xB are:
where ?(⋅) is the standard unit step function. The probability of symbol error for this system is _________(round off to two decimal places).
  • a)
    0.22
  • b)
    0.25
Correct answer is between '0.22,0.25'. Can you explain this answer?
Most Upvoted Answer
Consider a channel over which either symbol xA or symbol xB is transm...
Given that XA and XB are transmitted through a channel and given as input to a ML detector
Given conditional density functions are
The point of intersection of the above two conditional density functions gives optimum threshold.
Let, yth be the optimum threshold.
∴ Point of intersection can be found out as shown below.
Only yth = 0 satisfies the above equation.
∴ yth = 0 is the optimum threshold.
Diagrammatically, the optimum threshold can be represented as shown below.
∴ Probability of error will be,
Hence, the correct answer is 0.23.
Free Test
Community Answer
Consider a channel over which either symbol xA or symbol xB is transm...
Given that XA and XB are transmitted through a channel and given as input to a ML detector
Given conditional density functions are
The point of intersection of the above two conditional density functions gives optimum threshold.
Let, yth be the optimum threshold.
∴ Point of intersection can be found out as shown below.
Only yth = 0 satisfies the above equation.
∴ yth = 0 is the optimum threshold.
Diagrammatically, the optimum threshold can be represented as shown below.
∴ Probability of error will be,
Hence, the correct answer is 0.23.
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Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel ? be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for ? given xA and xB are:where ?(⋅) is the standard unit step function. The probability of symbol error for this system is _________(round off to two decimal places).a)0.22b)0.25Correct answer is between '0.22,0.25'. Can you explain this answer?
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