In a binary PAM system, the input to the detector is y m = a m + n m + i m where a m = ±1 is the…

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In a binary PAM system, the input to the detector is

ym = am + nm + im

where am = ±1 is the desired signal, nm is a zero-mean Gaussian random variable with variance σ2n , and im represents the ISI due to channel distortion. The ISI term is a random variable that takes the values −1 2 , 0, and ½ with probabilities ¼ , ½ , and ¼ , respectively. Determine the average probability of error as a function of σ2n .