This paper investigates the downlink (DL) transmission in millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) systems especially focusing on a high speed mobile scenario. To complete the DL transmission within an extremely short channel coherence time, we propose a novel DL transmission framework that eliminates the need for channel state information at the transmitter (CSIT), of which acquisition process requires a substantial overhead, instead fully exploiting the given channel coherence time. Harnessing the characteristic of mmWave channel and uniquely designed CSIT-free unitary precoding, we propose a symbol detection method along with the simultaneous CSI at the receiver (CSIR) and Doppler shift estimation method to completely cancel the interferences while achieving a full combining gain. Via simulations, we demonstrate the effectiveness of the proposed method comparing with the existing baselines.