Equalization for multipulse modulation

Equalization for inter-symbol interference (ISI) channels for single-pulse modulation schemes such as pulse- and quadrature amplitude modulation (PAM, QAM) is a mature branch of communication theory. However, multipulse modulation, a simple example of which is FSK, is seen as a nonlinear modulation technique, so that equalization of ISI channels for such modulation is described as being difficult (Lee and Messerschmitt, 1994). It is demonstrated here that that is not the case. In particular, we obtain linear and decision feedback zero-forcing equalizers for multipulse modulation. These equalizers are multi-input, multi-output (MIMO) filters and they are the natural counterparts of the single-input, single-output (SISO) linear and decision feedback zero-forcing equalizers for single-pulse modulation.