A promising coherent Impulse-Radio Ultra-Wideband (IR-UWB) communication system with one relay. IR-UWB communications attracted significant attention as a strong candidate solution for short-range high data-rate applications. UWB is a modulation and data transmission method which has potential to change the wireless picture entirely in future. The non-orthogonal cooperation in narrow-band wireless networks often requires deploying distributed space-time codes with joint encoding of several symbols at the source and relays; in addition, it requires joint decoding of these symbols at the destination. But the proposed non-orthogonal cooperation scheme realized within one symbol duration. This means the proposed strategy is adapted to the structure of the Pulse Position Modulation (PPM) that constitutes the most popular modulation scheme associated with UWB transmissions. This strategy also proposes a simple and efficient power allocation strategy that further boosts the performance of the proposed cooperation strategy. This paper illustrates various pulses using Gaussian monocycle and doublet.