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We propose a time-division multiple-access (TDMA) scheme for the binary phase-shift keying (BPSK) modulated single carrier block transmission with frequency domain equalization (SC-FDE) over ultra-wideband (UWB) channels. The transmitter and receiver matrices for the proposed TDMA SC-FDE system are derived to achieve the multiple-access interference (MAI) free and interblock-interference (IBI) free transmission without the insertion of cyclic prefix (CP) between blocks, avoiding long CP and large fast Fourier transform (FFT) size in high-speed UWB communications. The performance of the proposed TDMA SC-FDE system over UWB channels is investigated and compared with that of the block spread code-division multiple-access (CDMA) scheme. The impact of oversampling diversity and imperfect channel estimation on the performance of the proposed system are also investigated. Results show that the proposed TDMA scheme can effectively eliminate the error floor in CDMA due to insufficient CP, and it is more efficient to accommodate larger number of users than CDMA in high data rate transmission.