TABLE OF CONTENTS If the channel filtering, including the receive filter, satisfies the Nyquist criteria, as presented in Section 3.4, then the sampling and threshold comparison receiver is defined as a Nyquist receiver. The differences between the Nyquist receiver and the matched filter receiver, or their equivalence, must now be established and clearly defined. We tackle this problem by asking very specific questions and by presenting detailed answers.
Is the probability of error performance of the matched filter, P e (MF) , as derived in the preceding section, identical to the probability of error performance of the Nyquist channel model, P e (NYQ), derived in Section 3.6?
Is the Nyquist channel model (receiver) identical with the matched filter receiver?
Is the matched filter receiver (correlation receiver) suitable for the reception of synchronous bandlimited data?
These questions have been asked by many design engineers who are required to apply their theoretical knowledge to the design of operational systems.
A detailed analysis of these three questions now follows:
1. Is the Probability of Error P e (MF)= P e (NYQ)? The probability of error of the matched filter receiver P e(MF), derived in the preceding section, is
where
E av=average received signal energy at the input of the matched filter (correlation) receiver; in binary systems, E av= E b , where E b is the bit energy
N o
