MMSE decision feedback equalization of pulse position modulated signals

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 ISI, PPM is a candidate modulation scheme for ultra wideband (UWB), and may experience ISI in that application. First, we review the 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 stochastic gradient descent algorithms. Finally, we demonstrate the performance of the proposed equalizer with simulations.