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GATE EC 2022 Set 1 — Question 63

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NAT+2 / -0HardMAP & ML DetectionDigital Modulation & DetectionCommunicationsError Probability

Communications → Digital Modulation & Detection → Error Probability

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Question

Consider a channel over which either symbol xAx_A or symbol xBx_B is transmitted. Let the output of the channel YY be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for YY given xAx_A and xBx_B are:fY∣xA(y)=e−(y+1)u(y+1),f_{Y|x_A}(y) = e^{-(y+1)}u(y + 1),fY∣xB(y)=e(y−1)(1−u(y−1)),f_{Y|x_B}(y) = e^{(y-1)}(1 - u(y - 1)),where u(⋅)u(\cdot) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).
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