## 1 Introduction  
In the present era, the global navigation satellite system (GNSS) acts like an invisible net, providing us with high-precision positioning, navigation, and timing (PNT) services. Its significance is evident [1, 2]. However, much like a double-edged sword, while GNSS brings convenience, its vulnerability to various interferences and spoofing attacks poses a threat to applications in related fields [3, 4, 5, 6]. This vulnerability compels us to reevaluate the reliability of PNT services and information transmission, prompting us to actively explore reliable alternative or complementary technologies. In this context, the enhanced Loran (eLoran) ground backup system emerges. The eLoran system, with its strong anti-interference ability, wide coverage, stability, and excellent performance, serves as an important supplement and backup for the GNSS system [7, 8, 9, 10]. In recent years, many countries around the world have actively engaged in or resumed development of the eLoran system. This trend indicates that the establishment and advancement of the eLoran system are not only inevitable requirements for the construction of time-frequency systems in various countries but also indispensable and crucial parts of enhancing the national satellite-ground integrated PNT system [11, 12, 13]. In eLoran receivers, demodulation is a crucial signal processing module, directly affecting the accuracy of timing and information transmission. Globally, scholars have extensively researched eLoran demodulation technology. Currently, the commonly used eLoran demodulation technology is the envelope phase detection (EPD) method [14]. It extracts phase differences by sampling the envelopes of two orthogonal signal paths to achieve demodulation, but has limitations in anti-interference and noise resistance. In 2007, [PERSON] et al. proposed the signal matching correlation-pulse position detection (SMC-PPD) algorithm based on signal sliding correlation in the time domain [15]. However, as noise and interference increase, the error frequency of peak position detection significantly rises, leading to a higher bit error rate. In 2020, [PERSON] et al. proposed the envelope correlation-phase detection (EC-PD) algorithm, which combines two envelope correlation schemes for different scenarios [16]. It studies the impact of skywave on signal-to-noise ratio (SNR) gain and switches adaptively based on it, improving modulation performance to some extent. However, it remains in the time domain phase demodulation category. In 2022, [PERSON] et al. proposed an algorithm based on the log likelihood ratio (LLR) [17]. It calculates and compares the probability of each bit, skips the demodulation process, and improves the decoding success rate to a certain extent. However, it does not consider the impact of various interference environments on probability calculations and requires further derivation and verification. In 2024, our research achieved a remarkable breakthrough by successfully introducing machine learning into eLoran demodulation research. We deeply explored and proposed the application of machine learning algorithms like MSVM. The experimental results show their excellent performance and application potential. However, due to resource limitations, they could not be fully implemented, tested, and optimized, and thus were not used as comparison objects in this paper [18]. To enhance the performance of eLoran receivers in complex electromagnetic environments such as continuous wave interference (CWI) and high noise levels, and to ensure the functional realization of eLoran system, this study introduces an innovative phase spectrum smoothing demodulation (PSSD) algorithm from a new perspective. Based on the pulse form and spectral characteristics of eLoran signal, the PSSD algorithm employs advanced time-frequency domain signal processing techniques to minimize the impact of noise and interference. By leveraging phase difference discrimination in the frequency domain, it aims to enhance the accuracy and reliability of signal demodulation.