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Understanding ultra-wide-band (UWB) propagation channels is a prerequisite for UWB system design as well as communication-theoretic and information-theoretic investigations. This paper surveys the fundamental properties of UWB channels, pointing out the differences to conventional channels. If the relative bandwidth is large, the propagation processes, and therefore path loss and shadowing, become frequency-dependent, and the well-known wide-sense stationary uncorrelated scattering model is not applicable anymore. If the absolute bandwidth is large, the shape of the impulse responses as well as the fading statistics change. This paper also describes methods for measuring UWB channels and extracing channel parameters. Throughout this paper, the relationship between channel properties and other areas of UWB research are pointed out.