In order to mitigate the mutual interference between ultra-wideband (UWB) impulse radio and other existing wireless systems, a novel adaptive interference-avoiding UWB pulse, in the context of the appealing cognitive radio, is presented based on the radial basis function neural networks. Theoretical and implementation architecture for UWB pulse generator is addressed. Transmission performance in the presence of narrowband interference including tone interference is comprehensively analyzed. The presented generator can adaptively change the spectrum shape of UWB signals according to the authorized users' working states, and hence the mutual interference between UWB and other systems sharing the frequency bands can efficiently be avoided. The critical performance indication parameters, such as the SNR, SIR, and BER of UWB communication links, are also derived. Performance evaluations and comparisons between the proposed scheme and other pulse optimization methods have been provided based on the extensive numerical simulations. It is demonstrated that the presented pulse can indeed achieve much superior performance in terms of either single-link BER or anti-jamming capability.