## 1 Introduction  
Research on long-wave radio science dates back to the late nineteenth century. Early telegraph operators occasionally heard sounds from telephone receivers, which they described as \"clicks\", \"grinders\", and \"sizzles\". These sounds were generated by rapid changes or pulsations in currents caused by sunspots, geomagnetic currents, and auroras, which coupled with the telephone lines [1]. By the 1950s, research on long-wave radio had become a relatively mature field. The experiences gained during World War II subsequently highlighted the value of radio research in communication and navigation, sparking renewed interest in electromagnetic waves in the long-wave band. The demand for submarine navigation and communication, as well as reliable global military communication, has indirectly driven the development of VLF and ELF wave propagation theories and experiments over the past fifty years [2, 3]. Before the advent of GPS, the United States established the first global navigation system, \"Omega\", which consisted of eight VLF transmitter beacons [4]. However, with the emergence of GPS, long-wave navigation systems have gradually become supplementary in environments where GPS signals are limited or unavailable, due to GPS's high precision and convenience. Subsequent research has shown that VLF signals are highly suitable for remote sensing of the lower ionosphere (60-90 km) [5; 6]. Measuring electron density in the lower ionosphere is difficult except through VLF techniques. High-frequency radio signals (e.g., those used in incoherent scatter radars) often suffer from insufficient reflection amplitudes, making them prone to being obscured by noise or interference. At these altitudes, the air density is too high for satellites, leading to excessive drag. Although rockets can provide satisfactory results, they are costly and can only offer instantaneous data, which are insufficient to address diurnal, seasonal, and latitudinal variations. In particular, the infrequent nighttime flights yield unreliable results [7]. Over the past thirty years, monitoring long-wave radio signals has primarily been used to study geophysical phenomena, such as lightning discharge signals [8; 9; 10; 11; 12; 13; 14], remote sensing and modeling of the ionospheric atmosphere [6; 15; 16; 17; 18], and observing relativistic runaway breakdown phenomena within thunderstorms [19]. As research into these phenomena progresses, the requirements for signal reception accuracy, sensitivity, signal-to-noise ratio, and bandwidth continue to rise. Increased sensitivity and bandwidth, along with more electromagnetic field components, enable the extraction of more information from long-wave signals, potentially revealing previously overlooked data. Furthermore, higher timing accuracy in multi-station cooperative direction finding and localization enhances both direction-finding and localization precision. Previous studies have proposed and an deployed various long-wave receivers with different performance characteristics, tailored to specific scenarios. For example, the Los Alamos Sferic Array (LASA) has a bandwidth of 200 Hz to 500 kHz, a timing precision of 2 us, and a sensitivity of 0.2 V/(m\(\sqrt{\mathrm{Hz}}\)). It can record lightning discharges over thousands of kilometers, making it suitable for detecting lightning activity, localization, and conducting thunderstorm research [20]. Palmer Station in Antarctica provides a bandwidth of 100 Hz to 50 kHz, a timing precision of 100 ns, and records lightning discharges over thousands of kilometers for studies on the correlation between lightning discharges and terrestrial gamma-ray flashes (TGFs) [21; 22]. A broadband digital low-frequency radio receiver with a bandwidth of 4 Hz to 400 kHz, a timing precision of 12 ns, and amplitude resolution of approximately 35 \(\mu\)V/(m\(\sqrt{\mathrm{Hz}}\)) was developed to observe radio signals from relativistic breakdown [19].