Problem .
Suppose the bit detection sample at the receiver is V + noise volts when the sample corresponds to a transmitted '1', and 0.0 + noise volts when the sample corresponds to a transmitted '0', where noise is a zero-mean Normal(Gaussian) random variable with standard deviation σ_{NOISE}.
so the bit-error rate is given by 0.5*erfc(V/(sqrt(8)*sigma)). Note that sigma = sqrt(N0/2) using the definition of N0. This formula is related to the 0.5*sqrt(E_s/N0) from Chapter 5 and the lecture; E_s in our case is V*V/4.
Problem .
Messages are transmitted along a noisy channel using the following protocol: a "0" bit is transmitted as -0.5 Volt and a "1" bit as 0.5 Volt. The PDF of the total noise added by the channel, H, is shown below. It is not a Gaussian.
def digitize(r): if r < -2A: s = sminus3 elif r < 0: s = sminus1 elif r < 2A: s = splus1 else: s = splus3 return s
Ben wants to calculate the symbol error rate for BASS, i.e., the probability that the symbol chosen by the receiver was different from the symbol transmitted. Note: we are not interested in the bit error rate here. Help Ben calculate the symbol error rate by answering the following questions below from 2 through 8