申論題

3.(Total=15%) Consider a communication system in which the received signal y(t) is given by
  
where w(t) is white Gaussian noise with (zero mean) power spectral density N₀/2 and s(t) is shown below

 At the receiver, the received signal y(t) is passed through a filter with impulse response h(t) = s(T-t). The output of the filter is sampled at time to that - provides a decision statistic Y with
 where are the filtered/sampled outputs of s(t) and w(t), respectively. The maximum likelihood (ML) decision rule is then used based on Y to decide whether "I" or "0" is sent. Assume the noise process is independent of which signal is sent.