Performance of several digital communication systems

S.S.B. a.s.k., o.q.a.s.k., q.a.s.k., m.s.k. and q.p.s.k. with rectangular shaping are modelled by a simple baseband system. It is assumed that the symbol shaping in the transmitter is either rectangular or sinusoidal, and that the detector filter is either matched or variously mismatched to the shaping signal. General formulas for the signal and noise variance at the detector output are presented, the assumption being made that the bandlimiting transmitter-receiver filter is causal, with a finite number of simple poles or of the Butterworth type from which the error probability can be computed. The error probability was actually computed assuming the transmitter filter is wideband and the receiver filter is of order 2 or 4 Butterworth. The conclusion is that for a small normalised bandwidth (0.5 ¿ B ¿ 1.1) the best system has a sinusoidal shaping filter and no detecting filter.