# Gaussian-Distributed Spread-Spectrum for Covert Communications
## 4 Detectability of GDSS Signals
### Cyclostationary Analysis  
Signal detectors based on cyclostationary analysis offer superior detection performance compared to energy detectors in low SNR environments. However, they may require more computational resources and expertise in signal properties. Cyclostationary analysis is a powerful technique used for detecting and analysing communication signals by leveraging their cyclostationary properties. These properties refer to repetitive characteristics of the signal, such as a constant modulation and coding scheme or a fixed synchronisation sequence embedded in the communication waveform. By exploiting these properties, cyclostationary analysis can provide more reliable detection and analysis of signals in challenging environments with low SNR.  
Cyclostationary analysis normally involves estimating the spectral correlation function (SCF) of a signal. The SCF is a measure of the correlation between different frequency components of the signal, as a function of frequency offset and time lag. In a cyclostationary signal, the SCF exhibits peaks at certain frequency offsets and time lags, known as cyclic frequencies and cycle periods, respectively. These peaks correspond to the cyclostationary properties of the signal and can be used to detect the presence of the signal operating under the noise floor. By exploiting these peaks, cyclostationary analysis can offer a more robust and reliable detection of weak signals.  
This section aims to validate the effectiveness of GDSS signals in hiding under the noise floor using the fast spectral correlation method proposed in [41]. We present a comparison of the results obtained with the DSSS signal, as shown in Figure 10.  
The DSSS signal is generated using a repetitive spreading sequence, and the Gaussian masking process is applied to develop the GDSS signal. To ensure a fair comparison, we keep the observation period and spreading factor constant for both the DSSS and GDSS signals. By analysing the spectral correlation of the two signals, we demonstrate that the GDSS signal provides superior hiding capabilities compared to the DSSS signal under similar conditions. Our findings highlight the potential of GDSS signals for use in low  
Figure 10: Spectral correlation spectrum for various signals, \(N=256\).  
power and covert communication systems where signal detection and interception are critical concerns.  
The spectral correlation density plots shown in Figure 10 illustrate the significant difference between the DSSS and GDSS signals. The DSSS signal exhibits prominent peaks in its spectrum, indicating the presence of repetitive spreading sequences and modulation. In contrast, the application of the Gaussian masking process to the DSSS signal has almost entirely eliminated these peaks. As a result, the GDSS spectrum closely resembles the spectral correlation spectrum generated for the noise-only case (i.e., without any signal). GDSS signal exhibits a much flatter spectrum, with no noticeable peaks. These findings provide strong evidence supporting the superiority of the GDSS method over the DSSS. By eliminating the characteristic peaks of the DSSS signal, the GDSS signal is much harder to detect and intercept, making it a better choice for covert communication systems.