# Gaussian-Distributed Spread-Spectrum for Covert Communications
###### Abstract  
Covert communication techniques play a crucial role in military and commercial applications to maintain the privacy and security of wireless transmissions from prying eyes. These techniques ensure that adversaries cannot detect or exploit the existence of such transmissions. Covert communications, also known as low probability of detection (LPD) communication, are instrumental in preventing attacks such as eavesdropping, jamming, or interference that could compromise the confidentiality, integrity, and availability of wireless communication. Direct-sequence spread-spectrum (DSSS) is a widely used covert communication scheme that expands the bandwidth to mitigate interference and hostile detection effects, reducing the signal power spectral density (PSD) to a low level. However, DSSS signals possess cyclostationary random properties that an adversary can exploit using cyclic spectral analysis to extract useful features from the transmitted signal. These features can then be used to detect and analyse the signal, making it more susceptible to electronic attacks such as jamming. To overcome this problem, a method to randomise the transmitted signal and reduce its cyclic features is proposed in this paper. This method produces a signal with a probability density function (PDF) similar to thermal noise, which masks the signal constellation to appear as thermal white noise to unintended receivers. This proposed scheme, called Gaussian distributed spread-spectrum (CDSS), is designed such that the receiver does not need to know any information about the thermal white noise used to mask the transmit signal to recover the message. The paper presents the details of the proposed scheme and investigates its performance in comparison to the standard DSSS system. This study used three detectors, namely, a high-order moments based detector, a modulation stripping detector, and a spectral correlation detector, to evaluate the detectability of the proposed scheme. The detectors were applied to noisy signals, and the results revealed that the moment-based detector failed to detect the GDSS signal with a spreading factor, \(N=256\) at all signal-to-noise ratios (SNRs), whereas it could detect the DSSS signals up to an SNR of \(-12\) dB. The results obtained using the modulation stripping detector showed no significant phase distribution convergence for the GDSS signals, similar to the noise-only case, whereas the DSSS signals generated a phase distribution with a distinct shape, indicating the presence of a valid signal. Additionally, the spectral correlation detector applied to the GDSS signal at an SNR of \(-12\) dB showed no identifiable peaks on the spectrum, providing further evidence of the effectiveness of the GDSS scheme and making it a favourable choice for covert communication applications. A semi-analytical calculation of the bit error rate is also presented for the uncoded system. The investigation results show that the GDSS scheme can generate a noise-like signal with reduced identifiable features, making it a superior solution for covert communication. However, achieving this comes at a cost of approximately \(2\) dB on the signal-to-noise ratio.  
covert communications; spread-spectrum schemes; communications signal processing; low probability of detection; secure communications; signal constellations +
Footnote †: journal: _Sensors_**2023**, 23, 4081. [[https://doi.org/10.3390/s23084081](https://doi.org/10.3390/s23084081)]([https://doi.org/10.3390/s23084081](https://doi.org/10.3390/s23084081))