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We investigate the inter-carrier interference (ICI) caused by relative motion between transmitter and receiver in orthogonal frequency division multiplexing (OFDM) based ultra wide-band (UWB) communications. Since the Doppler shift is proportional to the subcarrier frequency, the time-selective fading is subcarrier dependent. An exact expression as well as bounds are derived for the degradation in performance, as measured by signal-to-interference ratio (SIR). A design example is given to illustrate the concepts developed In the work.