We investigate the use of a linear precoded orthogonal frequency division multiplexing (LP-OFDM) waveform for high-data-rate ultra-wideband (UWB) systems. This waveform applied for the first time to UWB applications is an evolution of the multiband OFDM (MB-OFDM) solution supported by WiMedia-MBOA (MultiBand OFDM Alliance). The aim of this paper is twofold. Firstly, an analytical study of the LP-OFDM waveform allows to find how to efficiently precode an OFDM signal in order to improve the robustness of the system. Secondly, a global system study is led to highlight the benefits of adding a precoding function to an OFDM signal in the UWB context. Different system choices and parameterization strategies are thus proposed. In both analytical and global system studies, the LP component is optimized without channel state information (CSI) at the transmitter side, as in the MBOA solution. To go further, the MBOA constraints are relaxed, and an additional optimization is performed, with a CSI at the transmitter. The analytical and simulation results show that the joint use of linear precoding and OFDM leads to a significant performance increase compared to the MBOA solution. This improvement is due to the precoding scheme that provides better exploitation of the channel diversity.