Power and second order cyclic covertness of chip-wise Direct Sequence Spread Spectrum Faster-Than-Nyquist signaling

Covert wireless communications arouse great interest for both military and civilian wireless applications. The most commonly used technique to conceal wireless communications is the direct sequence spread spectrum (DSSS) technology, which spreads the transmit power into noise. However, this technology has two main limitations. The first one is a spectral efficiency loss, increasing as the number of users sharing the same spectral resource decreases. The second one is a second-order (SO) cyclic vulnerability, since a DSSS signal exhibits SO cyclostationarity, which can be detected by well-suited cyclic detectors. Over the years, several techniques have been proposed to reduce the cyclostationarity of DSSS signals to improve covertness. However these techniques only attenuate the cyclostationarity properties without improving the spectral efficiency. A promising solution to overcome these two limitations of DSSS signals is the chip-wise coupling of DSSS and faster-than-Nyquist (FTN) technologies, introduced very recently. It has been shown powerful performance of this technology for band-limited transmissions. However in practice, time-limited or truncated filters are used, which destroys the band-limited property of the communication. In this context, the purpose of this paper is to analyze the impact of the filter truncation on both the power and the cyclic covertness of chip-wise DSSS-FTN signaling, for arbitrary values of the squeezing factor, for both proper and improper constellations. This analysis is done through the introduction of a new cyclic vulnerability index, independent of both the signal and a potential eavesdropper bandwidth.