Question

Binary data is to be transmitted over an AWGN channel with noise spect ral density N0​/2 using the rectangular pulses s0​(t)=ApT​(t) and s1​(t)=−ApT​(t). The receiver forms an output Z and decides "s sas sent" if Z>0 and " s1​ was sent" if Z≤0.

(a) (2 pts) Suppose that the output Z is given by Z =∫0T​ g(t)Y(t)dt where Y(t) is the transmitted signal plus noise and g(t) is the triangular waveform g(t)=
{ t, 0≤t{ T-t, T/2≤t{ 0 otherwise

Find the error probabilities Pe,0​ and Pe,1​.

Answer 1

The error probabilities Pe,0 and Pe,1 can be calculated using the formula for the probabilities of error for binary signaling over an AWGN channel.

Step-by-step explanation:

The error probabilities Pe,0 and Pe,1 can be calculated using the formula for the probabilities of error for binary signaling over an AWGN channel. The error probability Pe,0 is the probability of incorrectly deciding that s0 was sent when s1 was actually sent, and is given by Pe,0 = Q(sqrt(A^2/2N0)), where Q is the complementary error function. Similarly, the error probability Pe,1 is the probability of incorrectly deciding that s1 was sent when s0 was actually sent, and is given by Pe,1 = Q(sqrt(A^2/2N0)).

The probability of error can be further simplified by substituting values for A and N0/2. However, since the question does not provide these values, it is not possible to calculate the specific error probabilities without more information.