Question

Find the approximate probability of error for an ASK signal with equi-probable binary symbols, if the average signal SNR is 10 dB, the signal detection uses an envelope detection technique at passband for two threshold detection cases, with a threshold detector having a thresholds of ~1.2 volts (case 1),~2.2 volts (case 2). The standard deviation of the corrupting Gaussian noise is 1. Use Marcum's Q function to create your solution and label a binary transition probability channel model to illustrate your solution results. Draw a bifurcated pdf representation showing the 2.2 volt threshold and the integrated probability areas for your calculations.

Answer 1

Using equation

Px|y(i|v) = py|x(v|i) · px(i)

py(v)

Pc = 1 − Pe = 1 − P{mˆ 6= m} = P{mˆ = m}

the above will become

Pe,ML =

M

X−1

i=0

px(i) · Pe,ML/i

= Pe,ML/i

Pr will be 0.8945