# Initial Results from SQUID Sensor: Analysis and Modeling for the ELF/VLF Atmospheric Noise
## 4 Statistical Analysis and Modeling for the Atmospheric Noise  
Spectral analysis can only provide the global characteristics of the data without any time information. The data measured at 8:10 UT on 2 nd March with a length of 8 s is shown in spectrogram form calculated by the function \"spectrogram\" in MATLAB in Figure 6. The data are divided into overlapping time bins, followed with a short-time Fourier transform performed on each time bin, between 0 and 50 kHz. The data bin size is 50 ms (i.e., \(\Delta\)F = 20 Hz) with 50% overlapping. Longer bins have less bandwidth within each bin and thus higher resolution in spectra, but the time resolution is reduced, correspondingly. The amplitude of received signals in each frequency bin, and for each time bin, is indicated with the colorbar in Figure 6.  
The thin vertical lines correspond to impulsive radio atmospherics, originated by lightning strikes, which can be observed at global distances from the receiver and are guided by the Earth-ionosphere waveguide. It can be observed that the magnetic field decreases as the frequency increases. This phenomenon is mainly due to the different attenuation of the electromagnetic wave propagated in the earth-ionosphere waveguide [25]. In order to get more details about the low-frequency noise characteristics, the spectrogram of the atmospheric noise lower than 10 kHz is given in Figure 7. It can  
Figure 5: Processed data by the proposed method: (**a**) waveform after processing, and (**b**) comparison of Spectra.  
Figure 6: Spectrogram of the atmospheric noise.  
be seen that the components of impulsive noise located in 1\(\sim\)5 kHz are not significant and that may be the reason why 1.51 kHz and only its third harmonic are adopted in ELF/VLF communication using heating ionosphere in [7]. Moreover, there are many man-made interference mainly radiated by band limited VLF transmitter in Figure 6. The horizontal lines between 16 and 30 kHz correspond to constant minimum shift keying (MSK)-modulated VLF transmitters operated by various national navies for long-distance communication with naval vessels and submarines. The pulsed signals with a duration of 0.4 s between 10 and 15 kHz correspond to the so-called Alpha navigation system, a set of three VLF transmitters operated by Russia [13].  
Limited by the bandwidth of the transmitter, existing works are mainly focused on the analysis and modeling for the narrowband ELF/VLF atmospheric noise. In [26], the atmospheric noise is regarded as symmetric \(\alpha\)-stable (S\(\alpha\)S) distribution and the bit error rate (BER) of Gaussian detectors for different digital modulation schemes are analyzed. Relevant analysis for the wideband ELF/VLF atmospheric noise is rarely reported, which limit the application of ELF/VLF communication by ionosphere heating. Mixed Gaussian distribution and Hall model are adopted to describe the pdf of the wideband ELF and VLF noise, respectively in [7]. However, comparisons with other widely used models are absent. Consequently, we perform statistical analysis and modeling for the wideband atmospheric noise to provide theoretical basis for the design of wideband communication system. According to the distribution of the carrier frequency, we choose 1.51 kHz and its third harmonic 4.53 kHz as the center frequency in ELF and VLF band, respectively. The collected data were filtered by a 16 th-order Butterworth lowpass filter with a cutoff frequency of 5 kHz, followed by a factor of 10 downsampling. After this, the processed data were further filtered by narrowband channel filters with different bandwidths, i.e., 50 Hz, 200 Hz and 400 Hz, respectively.