Digital twins are becoming an important tool for designing, developing, testing, and optimizing next-generation wireless communication systems. Over the past decade, system softwarization has become a reality, and wireless communication systems are no exception. Software-Defined Radios (SDRs), in general, and Universal Software Radio Peripherals (USRPs), in particular, are often used for prototyping and testing advanced wireless systems. Unfortunately, there is currently no end-to-end, software-based, general-purpose testing environment for SDR-based systems: developers often rely on benchtop setups or even small testbeds, but those are costly and cumbersome to build. At the other end of the spectrum, simulations often rely on simplified channel/radio models and typically do not execute full-stack production code, which can increase development effort and reduce fidelity. In this paper, we propose ACHEM (A Channel Emulator), the first software-based, end-to-end wireless channel emulation environment and toolset for communication systems based on SDRs, specifically USRPs. With the proposed emulator and toolkit, any USRP-based system can be fully emulated at the I/Q level in a pure digital environment without requiring specialized hardware (e.g., vehicles, USRPs, FPGAs, or GPUs). The proposed emulator supports multiple transmitters and receivers, MIMO communications, multiple frequencies, heterogeneous sampling rates, real-time node mobility through vehicle emulation, antenna radiation patterns, and various channel models. ACHEM facilitates wireless digital twin development and deployment. ACHEM is validated with several popular open-source USRP-based wireless communication applications, including GNU Radio, srsRAN 4G/5G, and OpenAirInterface.