Low-duty-cycle Ultra-wideband (UWB) radios have the potential to provide low-probability of detection (LPD) communications with low-power and low-complexity implementation. Pulse position modulation (PPM) is a prevalent scheme for UWB radios since it can further lower the transmitter complexity by avoiding pulse negation. However, the position shifts of impulse-like UWB waveforms, together with the severe frequency-selectivity of the propagation channels, aggravate the difficulty and complexity of timing synchronization and channel estimation. To circumvent both of these challenging tasks, we develop a differential encoder and its corresponding noncoherent demodulator for PPM-UWB signals. Relying on integrate-and-dump operations of "dirty" templates, our designs are operational when the timing offset and channel information both remain unknown.