Decision-Feedback Equalization for Pulse-Position Modulation

In this paper, we propose a minimum mean squared error (MMSE) decision feedback equalizer (DFE) for pulse position modulated (PPM) signals in the presence of intersymbol interference (ISI). While traditional uses of PPM may not have had ISI, PPM is increasingly being considered for use in situations where ISI is an issue, such as high-performance optical communication systems and ultrawideband communications. First, we review previous work on the subject which used the zero-forcing criterion under strict assumptions about the channel and equalizer lengths. Then, we derive a computationally efficient MMSE equalizer which removes these restrictions, and is suitable for use with training-based stochastic gradient-descent algorithms. Finally, we demonstrate the performance of the proposed equalizer with simulations.