This paper provides a novel performance analysis for ultra-wideband (UWB) systems that successfully captures the unique multipath-rich property and multipath-clustering phenomenon of UWB channels. Using the Saleh-Valenzuela model, we characterize pairwise error probability and outage probability for UWB systems employing multiband OFDM based on the cluster arrival rate, the ray arrival rate within a cluster, and the cluster and ray decay factors. Furthermore, an approximation technique is established, which allows us to obtain closed-form performance formulations that provide insightful understanding of the effect of channel characteristics on the performances of UWB systems. Finally, we characterize the effect of random-clustering phenomenon on the performance of UWB-multiple-input-multiple-output systems. The theoretical results reveal that regardless of the clustering behavior of UWB channels, the diversity gain can be improved by increasing the number of jointly encoded subcarriers, the number of jointly encoded orthogonal frequency-division multiplexing symbols, or the number of antennas. The coding gain on the other hand, depends heavily on the cluster-arriving channels. Extensive simulation results are provided to support the theoretical analysis.