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The achievable rate of training-based UWB systems is investigated. Assuming a block-fading model and the IEEE 802.15.3a channel model it is found that training-based UWB systems, that restrict the transmitted signals in their power- spectral density, are able to utilize the available bandwidth efficiently. This is in contrast to recent results for power limited systems which predict a diminishing mutual information with increasing bandwidth if white-like signals are used. The bounds developed are independent of the particular channel estimator used. An optimization of the training sequence length shows that a training sequence length of about 2% of the coherence interval is optimal independent of the signal bandwidth.