Binary communication system transmits bit 0 or 1 every bit interval. Probability of transmitting bit 1 and 0 are equally likely. Bit 1 is encoded as s(n)=1v and bit 0 is encoded as s(n)=-1v. The received waveform consists of signal plus noise r(n)=s(n)+w(n). Assume the white noise density function is zero mean Gaussian with variance =1.
(a) Generate 10,000 received waveforms and plot their histogram.
(a) The receiver assume the transmitted bit is 1 if r(n)>0, and transmitted bit is 0 if r(n)<0. Compute the bit error probability.
(b) Rater than make decision based on one sample at every bit interval, the decision is based on average value 10 samples over the bit interval. Compute the bit error probability.