In modern optical communications, pulse amplitude modulation 4 (PAM4) is employed to achieve higher data rates than that achieved by conventional non-return-to-zero format. Meanwhile, there is an increasing interest to convert wired connections to wireless in data centers using high-speed millimeter-wave and terahertz (THz) links. Here, we introduced the PAM4 modulation for THz wireless communications using a resonant tunneling diode (RTD) receiver. Compared with a Schottky-barrier diode receiver, the RTD receiver has higher sensitivity, and a stronger nonlinearity at low input power when it is operated with an amplified detection scheme. We achieved 24-Gbaud (48-Gbit/s) transmission in the 300-GHz band with a quasi-real-time digital signal processing (DSP), which is the fastest PAM4 wireless communication without an offline DSP to the best of our knowledge.