# Gaussian-Distributed Spread-Spectrum for Covert Communications
## 6 Conclusions  
In this paper, we propose a novel signalling scheme called GDSS for covert (LPD) communications, which aims to conceal the existence of wireless transmissions for enhanced security compared to cryptography and steganography-based schemes. We evaluate the performance of GDSS and compare it with the commonly used DSSS technique, which, despite its popularity, is susceptible to exploitation by adversaries due to various weaknesses. These vulnerabilities stem from the use of fixed modulation and repeatable spreading sequences. In contrast, the proposed GDSS scheme takes advantage of naturally occurring thermal noise at the transmitter to create non-repetitive, featureless signals for communication, which eliminates many of the shortcomings associated with DSSS. In this paper, the proposed GDSS scheme is compared with the DSSS system. The findings indicated that the signals produced by the GDSS approach have fewer distinctive characteristics compared to the DSSS signals, resulting in a reduced likelihood of detection for anyone attempting to intercept the transmission. The Gaussianity test demonstrated that the distribution of the noise-free GDSS signals closely resembled that of the naturally occurring noise in the receiver. To assess the detectability of the signals generated by the proposed scheme by an adversary, this study utilised three detectors: a high-order moments based detector, a modulation stripping detector, and a detector based on cyclostationary analysis. These detectors are applied to signals corrupted with noise. The results showed that the moment-based detector failed to detect the GDSS signal with \(N=256\) at all SNRs, whereas it could easily detect the DSSS signals as low as -12 dB. We applied the modulation stripping detector to both the GDSS and DSSS signals at an SNR of 0 dB and -5 dB, respectively. Our analysis revealed that the GDSS signals exhibited no significant phase distribution convergence, similar to the noise-only case (i.e., without any signal). In contrast, the DSSS signals generated a phase distribution with a distinct shape, indicating the presence of a valid signal. Moreover, we applied the spectral correlation detector to the GDSS signal at an SNR of -12 dB. Our analysis showed no identifiable peaks on the spectral correlation spectrum, providing additional evidence of the effectiveness of the GDSS scheme and the lack of distinguishable peaks in the spectrum suggests that the GDSS signal is difficult to detect and intercept, making it an ideal choice for covert communication applications. A quasi-analytical expression is also used to derive the BER for the uncoded GDSS, and the results were consistent with the simulation. The comparison of BER between the uncoded GDSS and DSSS systems showed a penalty of 2 to 3 dB for GDSS. However, LDPC coding helped recover this loss and significantly improved the overall BER performance. As expected, the LDPC-coded GDSS performed about 2 dB worse than the corresponding LDPC-coded DSSS system. This paper did not investigate the effects of high power amplifiers on the generated GDSS signals. The GDSS scheme is capable of generating signals with a high peak-to-average power ratio (PAPR), which is a measure of the dynamic range of a signal. Consequently, amplifying GDSS signals can cause distortion or clipping, as the amplifier may not be able to handle the high instantaneous power levels (albeit rarely happen), which can result in reduced signal quality and performance degradation. In future work, we plan to analyse the information-theoretic optimality of the proposed GDSS scheme and its variants. We would also like to investigate the impact of real-world factors such as radio impairments, channel effects, and receiver synchronisation on the performance of the GDSS system. These factors can significantly affect the quality and reliability of the communication channel, and thus it is crucial to study their effects on the proposed scheme.