## 3 Method Description
### SNR Gain  
In eLoran systems and other radio systems, noise significantly impacts signal demodulation performance. SNR gain, which enhances the signal strength relative to noise during demodulation through specific algorithms or techniques, is crucial for improving the system's demodulation accuracy and reliability. The EPD algorithm, although improving the SNR to some extent through BFF, is evidently insufficient in handling in-band noise. Particularly in high-intensity noise environments, the residual noise energy can cause signal distortion and adversely affect demodulation accuracy. In sharp contrast, the newly proposed PSSD algorithm showcases significant advantages in handling in-band noise, especially under low SNR conditions. The PSSD method leverages phase difference information from the in-band phase spectrum for demodulation. Firstly, a truncation acquisition technology is employed to collect the useful segment of the signal by means of windowing and perform FFT, effectively reducing noise and interference energy. Subsequently, a Gaussian window is used to smooth the effective part of the spectrum, further enhancing the in-band SNR. This  
Figure 5: Flowchart of PSSD algorithm. processing method cleverly combines the unique pulse characteristics of eLoran signal waveform and the shape characteristics of the broadband amplitude spectrum. In order to quantify the improvement in demodulation performance brought by this gain, we introduce a new metric, \"Effective Signal-to-Noise Ratio\" (ESNR), defined as the ratio of eLoran signal power \(P_{signal\_inband}\) to noise power \(P_{noise\_inband}\) within the effective bandwidth \(L_{freq}\) (92-108 kHz), as shown in Equation (1). This metric is specifically designed to assess the performance of eLoran signals in the key frequency range and can provide an intuitive reflection of the power dynamics within the effective bandwidth. \[\text{ESNR}=\frac{P_{signal\_inband}}{P_{noise\_inband}} \tag{13}\]  
To illustrate the advantages of the truncation window and spectral smoothing in PSSD algorithm, an example under SNR = \(-\)10 dB white noise environment is presented. Figure 6 depict the phase difference vector curves for three different modulations. It is evident that these curves, post-truncation window sampling and spectral smoothing filtering, exhibit remarkable smoothness, closely resembling noise-free conditions, effectively reducing the risk of phase jumps. In contrast, without truncation and smoothing, the phase fluctuates dramatically. In Figure 6b,c, the weighted phase differences are calculated as 0.0485\(\pi\) and 0.2871\(\pi\), respectively, which are within the wrong threshold range, leading to incorrect modulation decisions of \"0\" and \"+\". Furthermore, we modulated the eLoran pulse group with time codes and added white noise with different SNRs. Conducting multiple sets of experiments according to the algorithm steps. Meanwhile, using Formula (13), we can accurately estimate the ESNR in frequency domain before and after filtering, thereby deriving the statistical mean value of ESNR gain, \(\Delta\)ESNR, and combining it with demodulation accuracy rate (DAR) for in-depth discussion. The above types of data are comprehensive organized in Table 1.  
Figure 6: Phase difference vector of: (**a**) “0” modulation; (**b**) “+” modulation; (**c**) “\(-\)” modulation. As indicated by Table 1, under different SNRs, there is a significant gain in ESNR, which is further converted into an improvement in demodulation performance. For instance, at SNR = \(-10\) dB, AESNR is 9.14 dB. Compared with the case without truncation window and smoothing, the DAR of PSSD algorithm remarkably increases from 52.94% to 84.61%, while that of the EPD algorithm is only 68.40%. In addition, in other SNR environments, a similar conclusion can be drawn, and the lower the SNR, the more significant the improvement in demodulation performance.