The radio technique of cosmogenic neutrino detection, which relies on the Cherenkov signals coherently emitted from the particle showers in dense medium, has now become a mature field. We present an alternative approach to calculate such Cherenkov pulse by a numerical code based on the finite difference time-domain (FDTD) method that does not rely on the far-field approximation. We show that for a shower elongated by the LPM (Landau-Pomeranchuk-Migdal) effect and thus with a multi-peak structure, the generated Cherenkov signal will always be a bipolar and asymmetric waveform in the near-field regime regardless of the specific variations of the multi-peak structure, which makes it a generic and distinctive feature. This should provide an important characteristic signature for the identification of ultra-high energy cosmogenic neutrinos.