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A binary differential impulse radio-ultra wide band (IR-UWB) communication scheme over a single-mode optical fibre is examined. For a receiver structure, the conventional electrical receiver as well as an optical receiver structure, which is similar to the optical receiver used for digital, optically phase-modulated differential phase shift keying, are considered. The optical receiver can alleviate the IR-UWB receiver implementation challenges and it is studied for the first time in the context of IR-UWB. Considering various important noises, for example, phase noise, laser intensity noise, thermal noise and shot noise, analytical expressions for the error probability of the aforementioned receivers are derived. The mathematical models for optical components including laser diode and single-mode fibre, along with the analytical expressions for the receiver's error probability, are used to evaluate the overall performance of an UWB communication system over a fibre transmission medium. Furthermore, the electrical receiver is compared with the optical receiver and it is shown that the performance of the optical receiver can be as good as that of the electrical receiver and even better. The impact of wireless channel fading, bias current of laser diode and the coherence time of laser diode on the UWB over fibre system performance is also examined.