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In this paper, we investigate a multiband-orthogonal frequency division multiplexing ultra-wideband (MB-OFDM UWB) system with very high data rates (VHDR) of several gigabits per second (Gbps). We propose a DSTTD-based VHDR MB-OFDM UWB system by incorporating a double space-time transmit diversity (DSTTD) scheme into the conventional MB-OFDM UWB system. At the receiver, an efficient soft-demapper that takes into consideration the noise enhancement due to a zero-forcing equalization is developed. Numerical simulations of the proposed system at a very high data rate of 2.Gbps over the IEEE 802.15.3a channel models are implemented. The simulation results show that this system could achieve a very good performance in a low signal-to-noise ratio (SNR) region.