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The log-normal probability distribution has been commonly used in wireless communications to model the shadowing and, recently, the small-scale fading for indoor ultrawideband (UWB) communications. In this paper, a tight closed-form approximation of the ergodic capacity over log-normal fading channels is derived. This expression can be easily used to evaluate and compare the ergodic capacities of communication systems operating over log-normal fading channels. We also utilize this expression to show that the capacity of a multi-antennas UWB system operating over the IEEE 802.15.3a channel can be improved mainly through receive diversity.