Simulation and Data Processing of Beamforming Experiments with Four 21CMA Stations

We present an end-to-end simulation and data-processing framework for digital beamforming experiments conducted with four stations of the 21 Centimeter Array (21CMA). Motivated by the need to characterize instrumental systematics, such as those arising from station-level digital beam synthesis and two-stage channelization, and to validate the data-processing pipeline framework for a future upgraded 21CMA with beamforming capability across all stations, we simulate interferometric visibilities using realistic four-station layouts with radio interferometer simulation software OSKAR. Two representative pointings are considered: a bright, complex Cassiopeia A field and a near-north celestial pole (NCP) calibration field. The sky model combines cataloged point sources with a diffuse Galactic component from the Global Sky Model (GSM), and frequency-dependent thermal noise is injected. We further quantify the imprint of two-stage channelization by comparing an ideal beamformer with a coarse-channel phase approximation, demonstrating that off-axis sources exhibit a characteristic piecewise-linear spectral modulation across coarse-channel boundaries. A data-processing pipeline, including Radio Frequency Interference (RFI) mitigation, calibration, imaging, and mosaicking steps consistent with current low-frequency radio astronomy practice, is constructed. The resulting synthetic images and background root-mean-square (RMS) noise measurements demonstrate the feasibility of adapting established 21CMA calibration and imaging strategies to digital beamforming modes, and provide a framework that can be further developed for beam-aware processing in future full-scale 21CMA beamforming observations.