This paper proposes a differentially-coded-quadrature-phase-shift-keying (DQPSK) coherent demodulator using a new simultaneous carrier and bit-timing recovery scheme (SCBR). The new DQPSK SCBR (DSCBR) scheme works with a frequently used preamble, whose baseband signal alternates between two diagonal decision points, for example, a repeated bit-series of "1001." With the DSCBR scheme, the proposed demodulator achieves a significantly agile carrier and bit-timing recovery using an open-loop approach with a one-part preamble. To illustrate this, a preamble of 8 symbols is applicable with the Eb/No degradation from the theory over AWGN of 0.2 dB. It is also shown that the proposed demodulator achieves an improvement in the required Eb/No of more than 2 dB over differential detection over Ricean fading communication channels. The channels are modeled for wireless broadband communication systems with directional antennas or line of sight (LOS) paths. This paper concludes that the proposed demodulator is a strong candidate for receivers in wireles broadband communication systems.