New Insights into the PAPR Computation and Analysis of Chip-Wise DSSS-FTN Signaling

The Faster-Than-Nyquist (FTN) technology has attracted a great deal of interest in recent decades to increase the spectral efficiency (SE) of communications without increasing the bandwidth and the transmitted power. Recently, FTN signaling has also been considered for Physical Layer Security and to increase the covertness of communications through the chip-wise coupling of FTN with the Direct Sequence Spread Spectrum (DSSS) technology, giving rise to the chip-wise DSSS-FTN signaling. However, an objective comparison of DSSS-FTN and DSSS-Nyquist signaling requires a multi-criteria approach involving SE, reliability, potential covertness, receiver complexity and Peak to Average Power Ratio (PAPR). For this purpose, the PAPR must be computed, which may be cumbersome due to a high combinatorics, increasing with the filter length, the message duration and the number of states of the chip constellation and which can even make the PAPR incalculable for high order constellations. In this context, the first purpose of this paper is to show that, at least for ASK, PSK and QAM chip constellations, the PAPR of DSSS-FTN signaling is the product of the chip PAPR, analytically computable, and the PAPR of a filter function, over a chip period, which dramatically reduces the combinatorics. Then, a complete parametrical analysis of the PAPR of DSSS-FTN signaling is presented. Finally, DSSS-FTN and DSSS-Nyquist signaling are compared through a multi-criteria approach, showing the great interest of DSSS-FTN signaling.