On the optimum linear receiver for impulse radio systems in the presence of pulse overlapping

In impulse radio ultra-wideband systems, multipath delay may cause received pulses to overlap with each other. Pulse overlapping causes inter-pulse interference (IPI) which may, especially in dense multipath environments, severely limit the system performance. In this letter, we build a mathematical model with pulse overlapping considered and derive an optimum minimum mean-square error (MMSE) receiver. A simpler RAKE receiver is to take samples for each received pulse and perform maximal ratio combining (MRC) by ignoring the IPI. We then show, by an analytical approach, that the optimum linear MMSE receiver performs exactly the same as the simpler MRC receiver.