In this work, the frequency response of gate-all-around (GAA) Ge/GaAs heterojunction tunneling field-effect transistor (TFET) with hetero-gate-dielectric (HGD) and pnpn channel doping profile has been analysed by technology computer-aided design (TCAD) device-circuit mixed-mode simulations, with comparison studies among ppn, pnpn, and HGD pnpn TFET devices. By recursive tracing of voltage transfer curves (VTCs) of a common-source (CS) amplifier based on the HGD pnpn TFET, the operation point (Q-point) was obtained at $V_{DS}=1V$, where the maximum available output swing was acquired without waveform distortion. The slope of VTC of the amplifier was 9.21 V/V (19.4 dB), which mainly resulted from the ponderable direct-current (DC) characteristics of HGD pnpn TFET. Along with the DC performances, frequency response with a small-signal voltage of 10 mV has been closely investigated in terms of voltage gain ($A_v$), unit-gain frequency ($f_{unity}$), and cut-off frequency ($f_T$). The Ge/GaAs HGD pnpn TFET demonstrated $A_v=19.4dB$, $f_{unity}=10THz$, $f_T=0.487$ THz and $f_{max}=18THz$.