The state-of-the-art time domain synchronous OFDM (TDS-OFDM) transmit diversity schemes are only suitable either for fast time-varying but weakly frequency-selective channels, or deeply frequency-selective but slowly time-varying channels. In this paper, a novel TDS-OFDM transmit diversity scheme based on the space-time shifted constant amplitude zero autocorrelation (CAZAC) sequence is proposed over doubly selective broadcasting channels. The space-shifted CAZAC sequence is used for the unbiased maximum likelihood (ML) channel estimation. The time-shifted sequence is utilized for the low-complexity cyclicity reconstruction of the received inverse discrete Fourier trans form (IDFT) block. Compared with the existing solutions, the signal-to-noise ratio (SNR) gain of about 2.5 dB can be achieved by the proposed scheme at the uncoded bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> over the deeply frequency-selective single frequency network (SFN) broadcasting channel when the receiver velocity is 140 km/h, at the cost of the spectral efficiency penalty of about 2.88%.